Cosmology, Mathematics and Philosophy

Particles are nothing more than cognitive syntheses...

2011-12-29T05:43:00.000-08:00

http://www.interactions.org/cms/

http://economictimes.indiatimes.com/opinion/cosmic-uplink/heads-tails/articleshow/11287047.cms

Particles are nothing more than cognitive syntheses/structures of the fields’ sustainability rhythmic dynamics.

To speak of a measurement/quantification of particles is a gross nonsense, one can speak of perception/interpretation in the sense that the quanta express an enactive nature of the fields’ strategic dynamics of sustainability.

As to the particle and field proposed by Higgs, it may at most correspond to dynamics that may have taken place at a certain temporal rhythm of this reality we call cosmos, signalized at a beginning. To think that it is possible to reconstitute that beginning is a scientific nonsense, it is to ignore or overlook the role of the spontaneity dynamics in the sustainability of the systemic integrity as permanence, which depend upon the game occurred in a simultaneity dynamics of a temporal flux from the future to the present now, let us call it future now. The game of existence/life is, thus, strongly linked to the systemic spontaneity.

If it is true that there is a dependence from the past as memory, as experience, the present does not come from the past, the present comes from the future. Each moment now came from the future and never from the past.

That which is signalized as mass has to do with the gravitic dynamics that intervene in any cognitive synthesis: mass is enacted in that synthesis.

More mass or less mass depends upon the nature of the relations: links/connections, rhythms of the links/connections, autopoietic self-sustained strategies, dynamics in the retension/protension...

What can we know? What can we do? How can we know how to survive? How can we survive?

In the end, we are going around in circles, forgetting the fundamental, which are the questions: what is existence? What is life? In fundamental terms, what is the relation between existence and life? Can one reduce being to existence and existence to being? What is that thing that we call being (noun) and being (verb) and that is common to all things there (?): I am, you are, we are: the being (noun) is being (verb)...,

"chemical scum"...,

2011-12-05T03:41:00.000-08:00

http://www.jpl.nasa.gov/news/news.cfm?release=2010-087

«The human race is just a chemical scum on a moderate-sized planet, orbiting around a very average star in the outer suburb of one among hundreds of billion of galaxies. We are so insignificant that I can't believe the whole universe exists for our benefit. That would be like saying that you would disappear if I closed my eyes.»

Hawking interviewed by Ken Campbell (1995).

One of the best dixit from Stephen Hawking! (Perhaps, however, the term "race" is not a good term, the term "species" is a better term.)

It is not only the human organisms that are self-sustained "chemical scum", it may be pertinent to state that: all life is "chemical scum".

Biochemics is enacted by a electrochemical gravitic mix, the "scum"/humus is the enacted substance.

Planck gap? Planck energy? Gappiness in Planck?

2011-11-29T07:58:00.000-08:00

http://en.wikipedia.org/wiki/File:KleinBottle-02.png

Planck gap? Planck energy? Gappiness in Planck?

It is not the case that Planck’s energy is some thing that can be actualized. It does not have that dispositional nature, it cannot be approached as a dispositional nature.

Planck energy? Is energy a good term? Is it some thing like energy or is it a neutral thing which is towards energy, but not energy itself?

Is it a gift? A medium? A gap? A “Manna” for the thing that is being/making, as its fundamental possibility(?)...

...simultaneously a presence/absence, presence because it is computed by the cells, absence because it does not exist as a concrete thing.

Perhaps..., in the “Planck’s gap” is projectively compressed all the information of the originating dynamics present in the formation of our cosmic system and that accompanies us, because we depend upon it evolutionarily, it has to do with that which we were in the beginning and that which we are in the end as things that are born, die, and are.

The information, in this case, is not some thing that is measured, weighed, packaged and launched in the market of knowledge as object of consumption, by information, in this case, one must understand some thing like an "Apeiron", very close (but not the same) to the sense that Plotinus gave it: as an alterity-there (Aoristos).

Things, sometimes, are far more simple than they appear. Although, it may be a bit complicated to understand how our cells enact the reflexibility that makes emerge the projection of that gap that can be called “umbilical cord”/“umbilical string(?, perhaps...)”.

Our cells process-to-enact themselves and through the gap.

Through enactive reflexivity the gap provides for the “aion nexus” between the thing’s reflexivity and its reflexibility to itself: “to einai”.

Loops of Vibrating Strings,...and Systemic Sustainability

2011-11-26T04:13:00.000-08:00

http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold

“String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string.” By Edward Witten (on http://www.pbs.org/wgbh/nova/elegant/view-witten.html)

Physics’ large theories are, all of them, built from conjectural assumptions/postulates, because of that, criteria of correction must accompany the growth of the theory in proportion to the empirical evidence that allows the growth of theory itself, in terms of rigor of approximation between the abstract “planes/territories” and that which is the concrete reality of the things in survival interface.

String theory is a theory in adaptive growth and development, we all know that. The statement of Edward Witten, quoted above, has, certainly, a mathematical/physical interpretation, but..., we do not know if Edward Witten has noticed..., it is also much more: what we call “localities” are sustained by: little loops of vibrating strings.

In systemic terms, the looping of vibrating strings is tremendously compatible with the dynamics of sustainability of the topoi, working from the original sense of the term topos: irreducible place of the body, of each body. Not a place for the body, but the place of the body.

Eternity: Life: Endless Devourers...

2011-08-25T04:28:00.000-07:00

http://blogs.discovermagazine.com/80beats/2011/08/12/exoplanet-reflects-practically-no-light-and-why-its-so-dark-is-a-mystery/

This is not a pipe, this is not a planet..., this is PerhapsPerhaps an autopoietic example of eternity. Of course, for some thing to be eternal it has to consume all available vital energy, like a “Wraith” (Stargate Atlantis).

Anyway, any gravitic structure that achieves a density such as the one that seems to be exhibited by the structure in question is potentially a “candidate” to eternity.

Such structures are not of God nor of the Devil, such structures even feed off the vital energy of God and the Devil, if there is such a thing as a God and a Devil. Endless devourers... this is why we urgently need another definition of life.

As for conventional Time, it only exists as a cognitive phenotype...

2011-07-04T11:28:00.000-07:00

“Integral challenges physics beyond Einstein”

http://www.esa.int/esaCP/SEM5B34TBPG_index_0.html

“Einstein’s General Theory of Relativity describes the properties of gravity and assumes that space is a smooth, continuous fabric. Yet quantum theory suggests that space should be grainy at the smallest scales, like sand on a beach.”

To substantialize space as an existent to the things is a scientific error that cannot be hidden under the rug. Of course one cannot find what is not there. The space is enacted inter-relationally by the existents/structures/entities/res and gravity is not a matter of space and time, gravity is a matter of things/res and relations between the things/res.

As for conventional Time, it only exists as a cognitive phenotype. The time has come to work with rhythmic time(s), to work with the rhythms as the rhythms of the things and with the times as the times of the rhythms, and, why not, with the “passus” of the things?!

On Information

2011-04-02T11:06:00.000-07:00

Sic transit mundi cum mundus...

...The becoming of each thing is in relation. Each thing (“res”) that is being, is being as thing in the world with the others (“mitsein”), and, as such, the becoming of each thing partakes of the thing’s living web in the game of life.

The act and the fact actualize the presence in the world in one of its modes of existence but that is not information to the others or to itself.

Information is a “towards-be(ing)” in the relations among the things, taking part in what is, in the systems, a “making” of the “come to existence” of that which is a (co)existence towards interfaces of (co)existing survival (“mitsein”).

In this sense, there is no information outside the existence, but there is also not information in the act and the fact. The fact that is/becomes, takes place in an actualization in the process of (inter)systemic becoming, linked to the systems’ arbitria.

In a game situation, there is the fact and there is the act of the existence and of the (co)existents, as players with their positions and dispositions in their topoi.

Each player/agent assumes, in the game, a “dispositional role” as a strategically intended position towards the others: one chooses one’s position in the game (arbitria towards position). The player’s chosen position assumes a strategic value enacting a certain disposition of the systemic situation itself. In ontological terms, from a position, the system makes emerge a disposition towards adaptivity in the game.

And it is the enacted disposition that carries information over to the players, about the potential figures/scenes that can be enacted in the game itself. One states “carries information” because information does not have a proper topos, information is always (co)enacted by a dispositional situational dynamics. The information is not a figure but a “towards the place”, thus, the information is between the action and the result of the action.

In a game, the information does not have as reference the players, but that which the players are capable of doing, may do, or will do. That is, the value of the information is not in those that enact it, but in the enacted result.

The information is not an act, it is not a potency, it is the result of a (co)judgment that enacts a connection between the strategically intended figure that is to be(come) and the figure that is now.

…,truth…,…truths…, presence/absence…, and existence.

2011-03-29T09:38:00.000-07:00

It is pertinent to consider that the truth of an organism enactively participates from the truth of the cosmos, as the reflexivity of the structure’s proper (“proprius”) reflexibility.

This is not a matter of exemplification of a property but of an enacting of a “proprius” of the systemic individuation as cosmic entity, which explains the sense of “enactively participates”.

In this sense, the truth of the systemic structure is not what is shown by reflexibility in the systemic structure’s own light, it is what is or can be seen about that which is shown. What is shown is the structure’s “proprius”, the truth is the to-itself of that “proprius”, which means that the truth is not the “ontos”, but an expression of that “ontos”.

What is in-itself/“ontos” cannot be constituted as truth to the others, since it is about an absolute, in the sense of permanence and of being of the “proprius” of the system, hence not subject to change, therefore, it is not perspectivically approachable, because it is a non-formalizable completeness, since it is without measure and written logos (how does one “figure out” an “ontos” and places it into writing?), one is talking about an endless in terms of permanence and permanent that remains, subsists and persists in a strange loop as absence and presence.

Thus, in this way, the truth of a systemic structure is the truth of a permanent making of itself as positions of a same structure in a same topos. And here one can think in dynamics of alterity.

A being or entity can be a to-itself as father, son, worker etc…, still maintaining his own truth as being/“to be”, and the truth is what can be seen in that permanent making itself of an in itself to itself as alterity of itself.

Because of that we can speak of the becoming of ourselves, of the becoming of the things, without dissolution. Difference and alterity are not lies, they are just aspects or positions of a same structure in becoming.

In this sense, there is no quantum truth, or quantum degrees of truth. What fails in the logics (classical, quantum, etc.) is that the logical truth(s) presupposes a falsehood and an ontological structure towards an epistemological statement of truthness.

But any statement of truth and/or falsehood fails, in that sense, to be a statement about the ontology of the system’s truth, because, unlike the logical truths, the system’s truth is about the integrity and about what remains despite the change. In this way, it becomes ineffective to speak of neguentropy, since there is to entropy towards the truth of the system as an in-itself and to-itself, because a system’s truth as an ontological fact cannot be reduced to information.

Following this line of reasoning, there cannot be a bit in the it. The bit arises only in terms of relations with and to the others (“mitsein”), the bit is “mitseined” from the it. Following this line of reasoning, one is never a bit to oneself (which frees us from looking for a chicken and egg problem in the systems’ ontologies).

The truth of a system is in the accordance of the parts to the whole of the system. In this sense, the system’s to-in-itself is the according of the nature of truth as its relation to the essence.

It is a mistake to state that a system has an essence, in the sense of permanence, the system (re)enacts its own essence through the enactive process that is linked to the “noumenon” and the “noumenic”.

The “noumenic” is to the “noumenon” the necessity of the truth in the essence. The essence is, to the “noumenon”, the link between the noumenic and the noumenon in accordance with the living structure.

And, in the end, this is all about life and existence: to be born, to die, and to persist in the existence as being that is, as presence and as absence. Socrates, the Greek one, was a presence and now is an absence. But Socrates remains as being, that was PresencePresent and now is PresenceAbsent, and that is Socrates’ freedom and autonomy and, thus, Socrates remains being with the others and that is about Socrates’ dignity (“mitsein”).

..., existence (re)memoring and the things umbilical cords...,

2011-03-28T09:26:00.000-07:00

Considering the systems, in their ontological existence, it is pertinent to address the process of “(re)memoring” (as a bring-to-presence of the before-to-after) of any systemic structure as a (re)projective process that computes the “noumenic” in the “noumenon”, from the initial conditions up to the present moment and that thus brings to presence the present moment in the initial conditions (in this sense it is (re)projective), in the retension towards the protension.

This allows one to address the configuration of a permanent “umbilical cord” as a systemic “no-presence”/“opening gap”, permanently enacted by the systemic structure from its root in its being (noun) that is being (verb), as existent-there among other existents (“mitsein”).

Taking the matter further, one is led to an “accord” between the things’ “umbilical cords”, such that this “in-according” is that they are part of the same past, they share a similar memory, which is the echo of the cosmos, as universe that began and begot.

In this sense, all that exists-there is a child of the same womb, and, thus, sibling among siblings, that equally share from a same sense of existence, from a same dignity, from a same responsibility.

...laws/rules of form and cosmic bricolage...

2011-03-26T04:38:00.000-07:00

Event horizon? No, not at all! There is no such thing! All singularities have to be naked!

All happens in the intervals between things: the things emerge emerging, the forms make themselves forming themselves.

The rules emerge with the things that make themselves in the making of the things.

It is in the intervals between things that the things are born and that the things die.

Cosmic interplay/bricolage: the dance is made dancing. There is no dance without the dancing.

There is no form, there is no structure without the structuring. It is the structuring that makes the form emerge and the “laws/rules” of form come to be (enacted). There is no rule without a forming topos.

The game (of life) itself and its respective rules are enacted in the formative dancing of the living cosmic bricolage.

http://www.youtube.com/watch?v=qt0RxTT37cc

Laws of physics? Or laws of structure?

2010-09-14T03:01:00.000-07:00

Laws of physics? Or laws of structure? Can we speak of laws of physics, or should we speak of laws of structure? There are ontological differences that are escaping the “computo” of the physicists. Systems and subsystems that are not being considered, rhythms that are ignored. The laws of physics can change? And how could they not change?

http://www.newscientist.com/article/dn19429-laws-of-physics-may-change-across-the-universe.html

http://arxiv.org/abs/1008.3907

What thing is that... the time?

2010-07-23T04:35:00.000-07:00

What is time? What thing is that… the time, if not the cosmic rhythms, that express themselves in the marking of the resonating rotating logos of the cosmos of which they are rhythms, rhythms of the cosmos, rhythm of the things of the cosmos that make the cosmos as the cosmos. Tocata and fugue...,

Things, Good, Perfection...,

2010-07-20T11:05:00.000-07:00

In philosophical terms, the Good (Bene) is postulated as a coincidence between the being and the “to must be” (obligation, imperative) and, thus, the good (bene) of a thing is the coincidence between what that thing is and what it must be (necessity), as synchronized resonating rotative coincidence of itself, or, in other words, individuated identity.

Linked to the notion of Good (Bene) is the notion of perfection, from the Latin perfectio, with origin in per+facere and whose prefix indicates a finished action. The notion of perfection synthesizes, thus, an idea of completion.

Any living structure, because of the fact that it is and, as such, exists, it also, necessarily, “must be” (obligation, imperative) and, thus, it is good (bene).

Any living sucture is necessarily complete, and, thus, perfect.

Any living structure: cell, virus, stone, ant, plant, rat, human, star, black hole, etc… is good (bene) and, thus, it is perfect.

,...holography; hologram...,

2010-07-17T11:53:00.000-07:00

It is reasonably legitimate to postulate the holography as a “systemic property”, but it is not legitimate to reduce the system to its holographic record. The holography is systemic, but it is not the system.

The hologram, like the holography, is systemic but it is not the system. The hologram is the output of the system’s identity, computed in a strange loop and that includes the whole information of the system, including its initial conditions.

…neutrinos… what are they?

2010-07-12T02:41:00.001-07:00

…neutrinos… what are they? Gravitic phenomenon evoked, in the systems, by the presence of the gap, of the zero…, neutrinos... pieces of the form of the worlds that attach themselves to the “aion gaps”…

fundament: ratio/reason...

2010-01-06T06:23:00.001-08:00

By: Maria Odete Madeira

In a statement, the fundament is the ratio/reason prior and interior to the statement of which it is the fundament.

If the fundament of an event is unknown, then, the nature of the event in what regards its fundamental causality remains unknown.

...the there-of-the-being…

2009-12-20T05:34:00.000-08:00

By: Maria Odete Madeira

The anticipation of the future, the recovering of the past and the opening of the present constitute, in Heidegger’s thinking, experiences of the human discovery of the sense of the being of the Dasein, that is: its temporality, the there-of-the-being, the topos of the discovery of the being, placed in the existence as being-the-there, that is: being ente, being that one, or that thing that refers itself and addresses the being, itself, as ontological difference of the same being projected towards the anticipated future... losing itself in the decadence of the present that lives the anguish of having been.

Between the paradox and the antinomy...

2009-12-09T07:41:00.000-08:00

By: Maria Odete Madeira

Veritas acquist exegesis aliqua res...

Between the paradox and the antinomy there is a fundamental ontological and epistemological difference, marked by the resonating rotative interval of the rhythmic meaning (significado) of the genetic interval of separation between the topologies of the “in itself” (em si) and of the “to itself” (para si), approachable from the systemic notions: ontology-in-web and ethos-in-web.

Perhaps more interesting than the meanings of each of the terms (paradox and antinomy), may be the perception, reflection and the respective cognitive processing of the ontological difference that individuates them.

...,ambiguitas...

2009-12-07T06:51:00.000-08:00

By: Maria Odete Madeira

In an amphibology (amphibolia,…, ambiguitas, atis) of the Being and of the ens/ente (the one that is, quod est), the human ear is seduced by the resonance of the Verb: the dictum, as Verb, displaces the essence of the Essence as constituent difference between the Being in the Being and the Nothing in the “Same Being”, in a simultaneity of the Being, itself, as rotative metabolized processing of “Itself”: Being and Nothing…, …

…Paradox? Are there Paradoxes? How could there not be Paradoxes?

Will we ever be able to schematize a plenitude?

2009-11-02T06:20:00.000-08:00

By: Maria Odete Madeira

…The radical evil is out there…, for that "the bell tolls for us"…

Will we ever be able to schematize a plenitude?

Plenitude (Plenitudo) signalizes totality (totum).

The Good (Bem, Bene) signalizes plenitude and perfection.

The harmony between the concrete being and its eidos is plenitude and perfection.

The Good is the coincidence between the being and the must be.

The Good is the coincidence between that which some thing is and that which that same thing must be.

Will we ever be able to schematize: good, plenitude and perfection?

Will we ever, us humans, be able to make coincide the being with the must be?

And what about death and suffering? In the light of the eidos of Justice, are death and suffering just? Can death and suffering be called examples of Good?

Particular extreme situations, depending upon the person, can make emerge feelings and extreme practices of altruism, accompanied by feelings of elevation that can give access to planes of Good that help people become better persons, in the sense of acting in conformity with the eidos of Good (Bene).

However, the perception of the eidos of Good does not have to pass by particular extreme situations, it can happen when one is still very young and in a spontaneous way, in a simple looking at the world, in a simple looking at the suffering of the others.

One can approach the perception of the planes of Good, in relation with the reflexibility of which the Cosmos, itself, and all the things in it, are gifted.

Percontor, aris, ari, atus sum..., percontari aliquem...

2009-11-01T03:13:00.000-08:00

By: Maria Odete Madeira

Percontor, aris, ari, atus sum: to probe, to question, to inquire. Percontari aliquem: to question someone about some thing.

The primitive sense of the term incorporates an impulse of formative reason, of vital metaphysical root, marked by the imperative of survival of each existent, as presence and opening to the world, opening to itself, to the life, to its life, to the life of the things, as existing things that show themselves, that appear (aparecem), that seem (parecem), remain and (dis)appear.

The experience (exp-perior) of the question signalizes an existential sense of proof, a sense of necessity, a sense of unity, a sense of truth, and is situated in the opening of the being to the being (itself), as being of the things, of all the things.

Each question, any question, synthesizes a systemic point of possibility, constituted by an asymmetry of constitutive authenticity, displaced in the being of all the things by the dynamics of a question to an answer.

Reflection, Reflexivity, Reflexibility

2009-10-05T05:50:00.000-07:00

By: Maria Odete Madeira

Reflection, from the Latin reflectere, has the meaning of turning back, and it regards the projective rotative systemic activity of the agents, of any agents, be these agents: particle, field, atom, molecule, cell, animal, person, or thing, ens or entitas. This activity being connected to the respective strategies and effectivenesses, entangled in the computation and exchanges with the environment, included in the computation/production of deliberative judicative valorative syntheses.

Reflexivity, from the Latin reflexu, means folded on itself, and it is a dispositional systemic rotative capability that allows the agents and/or the systems the direct valorative cognitive processing of themselves, from the causes, or originating formative reasons to which each system directs itself intentionally with the objective of producing (re)evaluative deliberative judicative valorative syntheses.

Reflexibility is an intrinsic dispositional systemic property, common to all things, as existing things and, because of that, rotatively present in their own light, in themselves, to themselves and by themselves.

The reflexibility is in the things themselves: ens or entitas, and has to do with the visibility or perception of these same things, ens or entitas, as a proper mode of being, a character, while things that show themselves, make their apparition (aparecem) and seem (parecem), in their visibility. All the things have the power, as a capability, of showing, of reflecting their own light, their own truth, that which they are, that which they do, and in those, ens or entitas, that are gifted of thought, speech and will, that which they think, want, desire.

Ontologies: On the Concepts of: Possibility, Possible, 'Acaso', Aleatorial and Chaos

2009-09-09T07:59:00.000-07:00

Maria Odete Madeira

Massacritica, Lda.

Carlos Pedro Dos Santos Gonçalves

UNIDE - ISCTE Business School - Lisbon University Institute

September 7, 2009

Abstract:
In addressing the interdisciplinary field that is growing at the intersection between chaos theory and risk science it becomes necessary to reconsider the notion of chaos in its linkages with the notions of possible, possibility, “acaso” and aleatorial.

Aiming at such an interdisciplinary effectiveness, the present article addresses the notions of possible, possibility, “acaso”, aleatorial and chaos in terms of their respective constituent and constitutive systemic topoi, from the formative ontological systemic dynamics, structurally dependent upon the initial conditions of the respective systems and cognitively computed/processed by these same systems, from the perception and recognition of themselves, as individuated resonating rotative positions, in the inter-systemic web of survival.

The (inter)systemic risk is, then, addressed in connection with the chaos in the deterministic systems. An example of Malcolm effects and synchronized risk being researched upon for a two-dimensional nonlinear map that produces multifractal chaos. This allows for the signaling of conceptual linkages that occur at the intersection of chaos theory and risk science, between homeostatic mechanisms, synchronization and chaos.

Keywords: Possibility, possible, “acaso”, aleatorial, stochastic, clinamen, chaos, Malcolm effect, multifractal chaos, synchronization, risk, risk science, multifractal self-organized criticality

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1469613

Can an amoeba be a genius?

2009-08-19T08:59:00.000-07:00

By Maria Odete Madeira

What does the notion of genius synthesize? What values? What cultural, social and, above all, political values, are involved here?

Any organism is dispositionally gifted to perform tasks that concern its survival, some organisms exhibit greater ease in the performance of some tasks while others exhibit greater ease in the performance of other tasks. Genius is just a name for those that can maximize these abilities in order to transcend patterns considered normal, but this depends on training, willpower, and also of available means. All of us can be geniuses in different ways. For instance, a "simple" domestic worker, especially gifted to that kind of work, can be a genius, even if society would not classify such a worker as a genius, because it is a type of work without sufficiently relevant social value (no Nobel prize for domestic workers).

In certain societies the genius would be the one who found good solutions to the community's problems, and, not necessarily, for instance, the individual capable of feats of abstract reasoning but otherwise socially awkward and capable of having contra-adaptive responses when put before basic survival problems. Thus, for instance, the pattern of genius, in the first case, might depend upon an ability for common sense thinking and/or for finding good responses to adaptive problems. In such a sense, even an amoeba or any organism that reveals robust adaptive effectiveness can be considered a genius.

All the neurobiological cognitive work is supported by an image space and a dispositional space, supported, in turn, by distinct neural bases activated in the limbic cortices and in subcortical nuclei, whose work depends upon and is inseparable of an integrated organismic work, in permanent interface with the environment. And when we speak of organism we speak of bones, flesh, blood, homeostatic mechanisms, emotions, feelings, etc…

Anaximander - "apeiron"

2009-08-19T08:55:00.000-07:00

By: Maria Odete Madeira

Maybe the most important notion of Anaximander' s thinking is the notion of apeiron. The apeiron was described and interpreted by the community of the Greek thinkers, and among them Aristotle (Metaph), as a kind of undifferentiated mixture, without defined limits and rigorously uncharacterizable.

But, in the physical system of Anaximander, every process is conceived as a motion of separation. The apeiron corresponds to an initial chaos, which birthed a vortex that initiated a separation process. In the apeiron exists a principle of latent separation.

The mixture must be interpreted as a state of mutual neutralization of potentially separable opposites, a latent state of indifference.

What is a thing?

2009-08-18T15:23:00.001-07:00

By: Maria Odete Madeira

What is a thing (Latin causa)? What do we think, or can think about, when we state and refer ourselves to the word thing? An event is a thing? A feeling is a thing? A thought is a thing? A process is a thing? A system is a thing? Plans, strategies and convictions are things? The beautiful, the good, the bad and the ugly are things? We, the humans, are things? Is God a thing?What makes a thing a thing?

The Latin word causa also means res. From res formed the terms reality and realism. In general terms, the notion of causa applies to all reality and means everything that exists, or can exist.

In scholastic philosophy, res was an attribute of the being, in Thomas Aquinas it was a synonym of quiddity. In modern and contemporaneous philosophy the being of a thing is being an existent, any existent, that, as such, can be thought on and known.

Afairesis, Abstractio or Abstraction

2009-08-01T03:48:00.000-07:00

By: Maria Odete Madeira

Abstractio was the term chosen by Boetius for the translation of the Greek term afairesis. Abstractio or abstraction is a systemic operative cognitive dynamics, through which a part, a characteristic or an element of an integrated systemic whole is separated from that same whole upon which it constitutively depends, as concrete existent, particular and contingent, to be constituted (that part) as an object of thought, conceptually existent and available to be approached and cognitively synthesized as a universal entity with an objective value.

The Problem of Time in Quantum Cosmology and Non-Chronometric Temporality

2009-07-25T11:30:00.000-07:00

Carlos Pedro dos Santos Gonçalves

UNIDE - ISCTE Business School - Lisbon University Institute

Maria Odete Madeira

Massacritica, Lda.July 23, 2009

Abstract:

We review two lines of argument regarding the problem of time in quantum cosmology and in quantum gravity, one that invokes the path integral formalism for quantum gravity to state the absence of time between two three-geometries, and another that defends the absence of time, as a fundamental notion in physics, in terms of: (a) the configuration space argument, put forward by Barbour, Smolin and Kauffman, and (b) the Wheeler-DeWitt equation. We argue that although being correct with respect to a space-time dependent physical chronometrizable clock-time frame, both of these lines of argument fail with respect to a general sense of temporality, expressed in terms of the more elementary notions of a before and an after of a quantum computation. With respect to the first line of argument, it is shown that the early works on the subject address two kinds of temporalities, one that is the space-time geometric dependent temporality, which coincides with the usual definition of a space-time dependent physical chronometrizable clock-time frame, the other is a temporality associated to the notions of input and output of a general quantum gravity computation, that is expressed, in the theoretical discourse of quantum gravity, through the usage of the concepts of: (1) propagation of a wave functional in superspace, as addressed by Wheeler; (2) transition amplitudes of three-geometries and (3) the pathintegral formalism, used to calculate such amplitudes, as addressed by Hartle and Hawking. While the first temporality (space-time dependent temporality) disappears from the theory, the second plays a fundamental role, not only in the several aspects of the theory’s construction, but in the clock-time independence as well, as Wheeler showed. Given this notion of time, different from a chronometrizable, space-time geometry internal notion, we search for a general mathematical and logical structure that is capable of addressing it from a formal point of view. This is done through a family of mathematical structures that is more general than the mathematical category. These structures not only will allow us to address the nature of the temporality present in the transition amplitudes between two three-geometries, but they will also allow us to refute the configuration space argument and to show how a static clock-time-independent quantum state, can be put into a non-clock-time processual expression in terms of fine-grained computational histories, obtained from the relations between different observable’s bases.

Keywords: quantum cosmology, time, relational structures, relational nexus

Working Paper Series

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1438013

http://www.scribd.com/doc/14810246/Time-in-Quantum-Cosmology

A Systems Theoretical Formal Logic for Category Theory

2009-04-29T13:07:00.000-07:00

Carlos Pedro Gonçalves

Mathematics researcher at UNIDE-ISCTE

cpdsg.research@gmail.com (primary); cpdsg@iscte.pt

Maria Odete Madeira

Interdisciplinary researcher in philosophy of science and systems science

mosmg.research@gmail.com (primary), mariaodete.sm@gmail.com

Abstract

A systems theoretical thinking on the categorial object and morphism is developed, leading to areflection on the philosophical and mathematical foundations of category theory, which allowsfor the introduction of a formal language for category theory and of a categorial calculus as amorphic web-based logical calculus. A formal system, built from such calculus, is proposed and the logical semantics is addressed. Both syntax and semantics are independent from set theory.

Keywords: System, object, morphism, morphic web, individuation, entity, identity, categories,n-categories

1. Introduction

"In the present work, we propose a systems theoretical approach to category theory, introducing a formal language (LCat) and a formal system (FCat′ ), that incorporate the main system theoretic foundations of the categorial object and morphism. The formal system is based upon a morphic web calculus that we call categorial calculus. Both the logical syntax and semantics of such calculus are addressed and shown to be independent from set theory, which makes the theory itself independent from set theory.

In section 2., we address the categorial object as a system, providing for the philosophical ground of the main work. In section 3., we introduce the formal language LCat and a formal system FCat1−6 that is able to address the simpler structures of category theory.

In section 4., we address the morphic wholes as systems, through the so-called border marker. This leads to a development of the identity laws into a more ontologically and systemically complete logic, that addresses both systemic individuation and identity. The formal system, developed in section 4., is called FCat′ and it is capable of dealing with category theory, n-category theory and a different class of structures that cross systemic levels, which are more complex hierarchical structures than the ones worked upon in n-category theory.

In section 5., we address the logical semantics. In section 6. we conclude with a few final remarks.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1396841

The Problem of Time in Quantum Cosmology

2009-04-29T13:04:00.000-07:00

The Problem of Time in Quantum Cosmology
and Non-chronometric Temporality
by
Carlos Pedro Gonçalves
Mathematics researcher at UNIDE-ISCTE

cpdsg.research@gmail.com (primary); cpdsg@iscte.pt

Maria Odete Madeira
Interdisciplinary researcher in philosophy of science and systems science
mosmg.research@gmail.com (primary), mariaodete.sm@gmail.com

Abstract

"We review two lines of argument regarding the problem of time in quantum cosmology and in
quantum gravity, one that invokes the path integral formalism for quantum gravity to state the
absence of time between two three-geometries, and another that defends the absence of time, as
a fundamental notion in physics, in terms of: (a) the configuration space argument , put forward
by Barbour, Smolin and Kauffman, and (b) the Wheeler-DeWitt equation.

We argue that although being correct with respect to a space-time dependent physical
chronometrizable clock-time frame, both of these lines of argument fail with respect to a general
sense of temporality, expressed in terms of the more elementary notions of a before and an after
of a quantum computation.

With respect to the first line of argument, it is shown that the early works on the subject
address two kinds of temporalities, one that is the space-time geometric dependent temporality,
which coincides with the usual definition of a space-time dependent physical chronometrizable
clock-time frame, the other is a temporality associated to the notions of input and output of a
general quantum gravity computation, that is expressed, in the theoretical discourse of quantum
gravity, through the usage of the concepts of: (1) propagation of a wave functional in superspace,
as addressed by Wheeler; (2) transition amplitudes of three-geometries and (3) the pathintegral
formalism, used to calculate such amplitudes, as addressed by Hartle and Hawking.
While the first temporality (space-time dependent temporality) disappears from the theory, the
second plays a fundamental role, not only in the several aspects of the theory’s construction, but
in the clock-time independence as well, as Wheeler showed.

Given this notion of time, different from a chronometrizable, space-time geometry internal
notion, we search for a general mathematical and logical structure that is capable of addressing
it from a formal point of view. This is done through a family of mathematical structures that is
more general than the mathematical category. These structures not only will allow us to address
the nature of the temporality present in the transition amplitudes between two three-geometries, but they will also allow us to refute the configuration space argument and to show how a static clock-time-independent quantum state, can be put into a non-clock-time processual expression in terms of fine-grained computational histories, obtained from the relations between different observable’s bases."

http://www.scribd.com/doc/14810246/Time-in-Quantum-Cosmology

Nietzsche: excesso de real

2009-04-09T15:41:00.000-07:00

Por: Maria Odete Madeira

“Eu, que sou filho da terra, sinto as doenças do Sol como se fossem eclipses meus e como dilúvios que submergem a alma”. Nem espírito, nem razão, nem pensamento, nem consciência, nem alma, nem querer, nem verdade, para Nietzsche, o Eu é uma certa espécie animal, uma individuação constituída por cadeias de forças múltiplas e articuladas entre si. Forças torrenciais jorrantes, cujo movimento de rotação se desloca incessantemente na direcção de outras forças, sobre as quais exercem a sua pressão, crescendo ou diminuindo, rizomando, conforme os trajectos e as trajectividades.

“O homem, grupo de átomos, absolutamente dependente, nos seus movimentos, de todas as forças cósmicas – da sua repartição, das suas modificações – é, não obstante, imprevisível e, como qualquer átomo, é um ser em si”, um território de fluxos de forças individuadas, cujas fronteiras estão criticamente situadas entre dois limites: o infinitamente grande e o infinitamente pequeno.

Como fluxo integrante do carácter do universo, simultaneamente uno e múltiplo, mutante e permanente, o homem conhece o universo, na medida em que se espanta consigo mesmo e com a sua complexidade. Nem substância, nem essência, para Nietzsche, o homem é, apenas, uma individuação de fluxos de forças em devir cósmico, “(…) Que nome darei à angústia das almas mais livres? A nostalgia sem fim, a questão mais dolorosa, a que mais me despedaça o coração, que a si mesmo pergunta: “Onde poderei eu sentir-me em casa?” ”.

Formado pela rotação aleatória de fragmentos, os restos e os resíduos do mundo orgânico em devir, Nietzsche procura, no devir de todas as coisas, o padrão trajectivo e perspectivo que sinaliza e localiza, em cada momento presente, a sua individuação, o seu território de forças individuadas, o qual pode ser interpretado como uma perspectiva combinatória e topológica do devir, na sua relação com o (co)devir de todas as individuações em permanente trânsito cósmico. “Eis o Outono e a farta colheita, o entardecer dos mares distantes! Mas é agora que necessito de transformar-me em pássaro e voar para longe de vós, para as regiões meridionais. É do seio do vosso Outono que eu vos anuncio o Inverno e uma pobreza gelada.”.

Cada combinatória é formada por fluxos de momentos de pontos vibratórios e efémeros, trajectivamente marcados por graus de forças em luta, constituindo a própria combinatória uma interpretação do território de forças em relação, em movimento, sinalizadora de um presente rotativo, permanentemente fragmentado em passado e futuro e em permanente retorno a si como fluxo renovado. Fluxo que deveio e é interpretado como outro presente, porque no devir, cada momento é uma individuação perspectivada do tempo, e assim uma singularidade. No devir, todas as coisas são aspectos, perspectivas e interpretações, em permanente deslocação rotativa.

A aparência é a forma como a realidade se constitui e pode ser percebida. Aquilo a que chamamos mundo verdadeiro, diz Nietzsche, não existe, o chamado mundo verdadeiro apenas pode ser concebido como uma réplica do mundo aparente. A aparência é o modo de ser das coisas, como coisas que existem, um modo adequado aos nossos instintos práticos. “O mundo é essencialmente um mundo de relações; visto de pontos diversos, apresenta outros tantos rostos diferentes; o seu ser é essencialmente diferente em cada ponto (…).”.

O perspectivismo é o carácter da aparência, os padrões que observamos e comparamos são configurados trajectivamente pelo deslocamento interactivo das forças. Cada padrão é uma interpretação do nosso movimento de rotação, segundo a perspectiva topológica passante e errante do nosso organismo. Não há neutralidade de lugares, todos os pontos de observação são perspectivas. “Não existe ser que seja outro ou verdadeiro, ou essencial – o que exprimiria um mundo sem acção ou reacção. A antinomia do mundo aparente e do mundo verdadeiro reduz-se à antinomia do mundo e do nada.”.

A unidade é uma perspectiva vibratória e fluida da multiplicidade, interpretada a partir de padrões marcados por forças tensionais interrelacionadas. “Se há alguma unidade em mim, ela não consiste certamente no meu eu consciente, no sentir, no querer, no pensar, ela está algures no saber global do meu organismo, ocupado em conservar-se, em assimilar, em eliminar, em vigiar o perigo, o meu eu consciente outra coisa não é do que o instrumento disso (…).”.

Os padrões, os ritmos, as harmonias são um exercício de prazer biológico das forças de acção/reacção que recusam, escolhem, modelam e adaptam os trajectos aos seus próprios instintos nutritivos. A assimilação de ordem, ou padrões, satisfaz aquilo que Nietzsche interpreta como a vontade orgânica de poder. A ordem, os padrões ou formas criadas e perspectivamente interpretadas são metabolizadas por fluxos de forças actuantes que alargam, assim, o seu espaço de dominação.

Cada padrão criado é um território, configurado por fluxos de forças individuadas. Qualquer corpo é perspectivamente uma forma, um padrão. As forças nutrem-se de outras forças. Para um instinto arquétipo como a vontade de poder, criar territórios é, também, criar nutrientes, importantes para o seu desejo de expansão e de domínio, “(…) qualquer corpo específico tende a tornar-se dominador de todo o espaço e a desdobrar a sua força (a sua vontade de poder) e a rechaçar tudo o que resiste à sua expansão. Mas ele embate incessantemente nos esforços análogos dos outros corpos e acaba por chegar a um compromisso (por se unir) com os que lhe são suficientemente análogos. Segue-se uma concertação de poderes, e o processo continua…”.

Instinto criador, nutritivo, dotado de apetite insaciável e rizomaticamente invasivo, assim é a vontade de poder Nietzscheana, presente no pensar, no sentir, no querer e no desejar. Todas as funções orgânicas podem ser conduzidas àquilo que Nietzsche considera como vontade fundamental, ou seja, a vontade de poder. "A vida não é a adaptação de condições internas às condições exteriores; ela é a vontade de poder que, partindo de dentro, submete e assimila uma parte crescente da realidade exterior.".

Geneticamente replicada pelo fluxo topológico, metabolizado diferencialmente pelo jogo territorial de pulsões e repulsões, a vontade de poder é, ela mesma, a diferença aleatoriamente criada, deslocada e individuada no território, actuando estimulada por um princípio genético de prazer. “Sendo verdade que a essência mais íntima do ser é a vontade de poder – e que todo o aumento de poder é prazer, como todo o sentimento de não poder resistir, de não poder dominar, é dor – não poderemos nós colocar o prazer e a dor como marcos cardinais? Será o querer possível sem essa dupla oscilação, do sim e do não”.

A realidade está, deste modo, associada ao prazer, mais real significa mais prazer. Assim, na raiz da vontade de poder, está presente o prazer como operador fundamental que compromete perspectivamente o prazer com a criação de real, sendo o prazer expresso pela excitação da sensação de poder, perante a oposição à mesma criação. A criação de real, dá-se, pois, a partir da acção/reacção trajectiva, efectiva e positiva da combinação do diferencial de forças que jogam em cada território individuado. “Mas quem sente então o prazer? E quem quer então o poder? Questão absurda, sendo o ser por si vontade de poder – portanto, sensação de prazer e de dor. Contudo ele necessita de contradições, de resistências – portanto de unidades que contendem com ele.”.

A vontade de poder interpreta, fixa e delimita perspectivamente os marcadores vibratórios e diferenciais (acção/reacção) de poder, correspondendo este movimento ao trajecto de assimilação, necessário ao crescimento genético do real perspectivo, ou seja, das formas, dos padrões, das linhas, cores, ritmos, esperanças, imaginações, orações e maldições que satisfarão a vontade de poder. “A vontade de poder só pode exprimir-se contra resistências; por isso ela procura aquilo que lhe resiste. É a tendência primitiva do protoplasma, quando estende os pseudópodes para tactear em redor. A apropriação e a assimilação consistem numa vontade de dominar o que fica no exterior, de dar-lhe forma, modelá-lo e transformá-lo – até que a substância vencida fique inteiramente sob o domínio do atacante e venha aumentá-lo.”.

Nietzsche territorializa a vontade de poder, dá-lhe mundo e chão, interpretando-a como a matéria viva primordial, aquela que constitui o corpo celular de todos os organismos vivos e que é dotada de uma propensão de mobilidade mecânica vital de acção/reacção, na raiz da qual está o prazer que se quer exceder e a dor que se quer libertar (um outro modo de se exceder), como catalisadores daquilo que se pretende como excesso transbordante de eclipses e dilúvios, ou de explosões contínuas de poder que subsistem devêm e decorrem. “Havia um imperador que pensava constantemente na instabilidade de todas as coisas, para que desse modo não pudesse atribuir-lhes demasiada importância e assim ficar em paz. Comigo a instabilidade produz um efeito bem diferente: tudo me parece infinitamente mais precioso exactamente porque tudo é fugidio. É como se os vinhos mais preciosos, os manjares mais apetecidos desde sempre fossem lançados ao mar…”.

Se os eclipses, dilúvios, vinhos preciosos e manjares podem ser interpretados, numa perspectiva de excesso de real, o movimento pelo qual tudo devém opera como um mecanismo de inflação desse excesso. Aquilo que é fugidio, que corre e flui, também diverge e transforma. Tudo parece infinitamente mais precioso porque tudo dá mais prazer e tudo dá mais prazer, quando tudo muda permanentemente de aspecto. No devir essa mudança é permanente. O devir faz com que o excesso transborde em mais excesso. Acrescenta mais valor nutritivo ao real e, assim, também, mais prazer e mais poder.

O retorno é a topologia do devir, o eterno retornar de todas as coisas, na, também, eterna transformação das suas formas, posições e rotações. “Nem num só momento o oxigénio é o que fora no momento precedente; é um corpo novo (…)”.

A permanente repetição da transformação do mundo em novas formas e ritmos aparece como uma necessidade nutritiva da vontade de poder. O devir de todas as coisas, em cada momento presente, constitui o excesso de real que alimenta a vida, considerada esta, por Nietzsche, como um instinto criador ou uma vontade de poder. “Qualquer instinto é uma espécie de ambição de dominar; segundo a nossa perspectiva (…)”.

Importa relevar a dinâmica criativa que o modelo interpretativo de Nietzsche propõe. Aquilo que é permanentemente recriado não é as próprias coisas ou a sua diferença relativa e irredutível, mas sim o diferencial rotativo, reconfigurado diferencialmente, em cada presente, pelo deslocamento trajectivo e divergente dos fluxos de forças que as constituem, o qual é interpretado, por Nietzsche, como um jogo aleatório, (acção/reacção), de perspectivas ramificadas que agem a partir do desejo (de prazer ou dor, vida ou morte, a vida, o protoplasma também se alimenta de morte). “A coexistência de duas coisas perfeitamente idênticas é impossível: isso pressuporia uma génese, absolutamente idêntica, de toda a eternidade (…) É possível demonstrar com uma só diversidade a absoluta diversidade e desigualdade de tudo o que coexiste, excluindo seja o que for. Quando uma coisa muda, a reacção fá-la diversificar de tudo.”
Quando as forças agem, ou se deslocam, fazem-no em redes entrelaçadas. Qualquer movimento de acção/reacção de uma força altera não apenas a sua própria trajectividade gravitacional, mas, também, em termos relativos e perspectivos, a de todas as outras forças que se deslocam em cada território.

O movimento de uma força condiciona diferencialmente o de todas as outras, o que significa que de momento a momento, num território de forças, são combinatoriamente criadas e deslocadas novas figuras, formas, ou padrões. “Num mundo em devir, em que está tudo condicionado, a hipótese do incondicionado, da substância do ser da coisa… só pode ser um erro.”.

A única constante num território de forças é, conforme Nietzsche, o devir, o qual aparece perspectivamente interpretado como o ser de todas as coisas, sendo o ser uma generalização do conceito de viver. Deste modo, o devir é o viver da vontade de poder, considerada, esta, como a matéria viva primordial ou o instinto criador, que cria aleatoriamente, porque cria no fluxo, no qual em cada momento tudo se mistura aleatoriamente.

Não importa que topologia de formas, ou padrões, ou, ainda, que perspectivas são criadas, porque aquilo que é importante é o próprio movimento de criar e a intensidade em graus de forças investidas no movimento de criação e assimiladas nutricionalmente pela vontade de poder como formas, ou padrões e, a partir das ou dos quais, podemos falar num aumento de poder, o qual será conforme aos graus de intensidade investidos pelas forças envolvidas, na criação dos respectivos padrões ou formas que configuram aquilo que nos aparece, parece e interpretamos e, por isso, chamamos, de acordo com o autor, realidade.

Nietzsche não parece preocupar-se com o rigor científico do modelo cosmológico no qual localiza e interpreta o devir. A sua grande questão é a de trabalhar o diferencial aleatório produzido pela repetição ramificada e divergente de todas as coisas, em cada momento presente, pois é precisamente esse diferencial que lhe permite combinar de novo os instintos e acrescentar real ao real e, deste modo, poder à vontade de poder.

Neste sentido, a eternidade, ela própria, aparece e parece um instinto desejante que investe no excesso nutritivo divergente de si mesma, por isso, a importância do devir permanente de todas as coisas. Apenas o permanente devir de tudo pode satisfazer um instinto desejante que existe eternamente. Com efeito, é o movimento de devir que faz emergir, por deslocação, o diferencial topológico e perspectivo, permanentemente recriado em cada recorrência, em que todas as coisas mudam de posições relativas. No limite, trata-se de dar uma volta estranha e criar o seu próprio limite topológico, ou seja, tornar-se no devir crítico, diferencial e auto-organizado de si.

A estrela de Sírius, uma aranha que passa, um pensamento, um momento presente e outro momento presente são tudo coisas que permanecem porque devêm, decorrem e retornam. “ Homem! Toda a tua vida é uma ampulheta, que circula e volta, e cujo conteúdo se escoará vezes sem fim, separado pelo intervalo de um longo minuto de tempo (…).”.

O mundo é o retorno do mundo, um monstro de força, uma soma fixa de força, em permanente devir, sem começo nem fim, “ um mar de forças tempestuosas e em perpétuo fluxo, eternamente pronto para mudar, eternamente pronto para refluir, com gigantescos períodos de regular retorno; com fluxo e refluxo nas formas”.

É no fluxo aleatório, turbulento e inseguro das forças que Nietzsche procura embriagar-se de excesso de real. A embriaguez é o excesso inflacionado que permite criar, acrescentar real ao real, satisfazendo, assim, a vontade de poder. É no movimento de criação que o desejo cresce, acelera, dilata e transborda, e a vontade de poder mais e melhor se alimenta. “Eis o meu universo dionisíaco, que eternamente se recria e se destrói a si mesmo; mundo este misterioso, de redobradas volúpias: o meu “para lá do bem e do mal”, sem fim, sem querer (…)”.

Dionísio é Nietzsche inflacionado, se ele mesmo pode ser interpretado, como excesso, a figura dionisíaca é o estímulo desejante que o põe em delírio exponenciado e que o arrasta para o núcleo do protoplasma que ele dá como exemplo interpretativo da vontade de poder. No protoplasma, Nietzsche é o protoplasma. “Onde está o raio que vos irá lamber com a sua chama? Onde está o delírio contra o qual será necessário inocular-vos? Vede, eu anuncio-vos o Super-humano. É ele esse raio, é ele esse delírio!”.

Nietzsche, a estrela dançante, é Dionísio, a imediatez e a espontaneidade a pulsão e o instinto que desafia Apolo. O criador precisa de outro criador. As forças actuam aos pares (acção/reacção). Nietzsche precisa de Apolo, juntos podem criar um emaranhamento crítico, genético e nutritivo, de topologia criadora.

Dois personagens e dois instintos, dois impulsos criativos carregados de desejo. Dionísio e Apolo desafiam-se e combinam-se como forças artísticas que brotam do seio da natureza sem a mediação da individuação humana, e em relação às quais todo o “artista” humano é um imitador que entra em delírio com o frémito dionisíaco, renunciando a si mesmo, para com o poder da força do sonho de Apolo entrar numa experiência de unidade e identificação com as forças primordiais e essenciais da vida. “Quero unir-me aos criadores, aos ceifeiros, aos que descansam só depois de cumprido o trabalho; mostrar-lhes-ei o arco-íris e todas as escadas que levam ao Super-humano”.

Unindo-se a Dionísio, Nietzsche metaboliza a força criativa primordial que lhe permite a experiência de dissolução no desejo da vontade de poder, e é precisamente essa dissolução que lhe permite, igualmente, no sonho apolíneo, unir-se à vontade de poder e inflacionar a sua individuação, o seu território, ele é Zaratustra, o excesso alucinatório metabolicamente sintetizado e sublimado.

Zaratustra é Nietzsche criado por Nietzsche, a obra de arte que irrompeu um dia, de súbito, como fluxo individuado. Um território de forças em permanente devir, oferecido à humanidade como o mais belo e trágico presente alguma vez concedido. “Venerais-me: mas, que acontecerá se um dia a vossa veneração esmorecer? Tende cuidado, não vos mate uma estátua! Agora, intimo-vos a perder-me e a encontrar-vos; e só quando todos me tiverdes renegado, é que retornarei para o meio de vós…”.

Nietzsche metaboliza Nietzsche, a sua obra metafisicamente criada, como o objecto de prazer embriagante que diviniza a sua existência que sabemos ser sofredora. A embriaguez estimula os seus instintos estéticos. Nietzsche metabolizado é Dionísio, e é Zaratustra divinizado e imortalizado. A força do prazer e a força da dor, combinadas, sintetizam o excesso inquietante que o configura e que alimenta a sua devoradora vontade de poder. “«Devo ser mais sábio! Devo ser pura sabedoria. Como a minha serpente (…) Peço, porém, o impossível; pedirei, pois, que a minha altivez caminhe sempre a par da minha Sabedoria (…) E se um dia a minha Sabedoria me abandonar – ai agrada-lhe tanto fugir! – possa então a minha Altivez voar com a minha Loucura!»”.

Nietzsche introduziu, no seu território de forças individuadas, a sua diferença metafísica e arquetípica, rotativamente contrária à espécie dos homens. O fluxo do seu próprio devir tornou-se poderoso e excessivo, desterritorializando quaisquer mecanismos de controlo homeostático. A percepção de si mesmo, como diferença individuada, estimulou a sua vontade de poder para além do seu limite crítico suportável. “O que hoje sou, o lugar em que hoje me encontro – numa altura em que já não falo com palavras mas com relâmpagos (…)”.

As trocas de energia passaram a ser feitas, através dos reenvios entre duas topologias rotativas num mesmo território individuado, os de Nietzsche e os da sua diferença metafísica. Outras trocas de energia tornaram-se meramente residuais. O território, inicialmente aberto, do autor, fechou-se a outros territórios. As duas rotações, física e metafísica, começaram a tecer um emaranhado de forças cada vez mais denso que as localizou e interpretou como uma nova singularidade, uma nova identidade sistémica que reivindicou para si a imortalidade do artista, aquele que no presente fecunda o passado e gera o futuro. “Na previsão de que em breve terei de surgir perante a humanidade com a mais difícil exigência que se lhe fez, parece-me indispensável dizer quem sou. No fundo, todos o deviam saber: com efeito, não deixei de dar testemunho de mim.”.

Dionísio ou a rotação genética do arquétipo, replicada em Zaratustra e em Nietzsche sofredor na multidão, alimentando-se das suas próprias chamas. Nietzsche, o amor fati, mas o amor de um destino metafisicamente projectado pelos ritos dos fluxos e refluxos das forças de vida, de loucura e de morte que actuavam no seu território individuado e que repetiam o movimento rotativo de uma vontade de poder, cujos marcadores topológicos formavam um emaranhamento de reenvios rizomáticos, uma coreografia ritualizante que arrastava Nietzsche para lá de uma topologia, apenas, humana.

O humano era a disformidade, a náusea, a pedra monstruosa que precisava do escultor sobre-humano, ou seja, ele próprio, o super-homem anunciado por Zaratustra, o instinto arquetípico, o desejo de desejar, a fome devoradora na saciedade liberta de deus e de deuses, criada pela sua natureza dionisíaca e deslocada no fluxo como a sua diferença metafísica, tensionalmente fragmentada e reconfigurada no fluxo do devir.

O delírio rítmico e protoplásmico, ritualizado no território Nietzscheano, projectou um vórtice de emaranhamentos topológicos disjuntivos e perspectivos. Fragmentos físicos e metafísicos são permanentemente deslocados como nutrientes alucinatoriamente desejados. “Destroços de astros: Destes destroços construí um mundo”.

Nietzsche investiu toda a sua cota libidinal disponível na sua aparência territorial metafísica, com a qual se emaranhou devindo paradoxo rizomatizado e embriagado de potência de criar, embriagado de excesso de perspectiva, aquele que havia de ensinar aos homens o sentido da sua existência, o relâmpago que devia jorrar da sombria nuvem humana.

A sua loucura é uma interpretação do seu campo potencial de forças, externalizado numa topologia de intervalo entre duas fronteiras, a de Nietzsche humano e a de Nietzsche sobre-humano. “Com efeito, trago sobre os ombros o destino da humanidade.”. Uma zona de excesso de fluxo intenso, território de paradoxo, individuação sem rosto que vive na sua própria luz e que reabsorve em si as chamas que de si brotam. Nietzsche, o louco vivo, combinatoriamente quantizado pela metabolização das forças de Dionísio, de Apolo, de Zaratustra e de si mesmo, devém fogo cósmico criador. Aquele fogo grego primordial que sempre existiu e sempre há-de existir.

Finalmente, Nietzsche, a natureza contrária à espécie dos homens, podia sentir-se em casa. “Que se passa? É o mar que cai? Não, é a minha terra que cresce! Um fogo novo a Levanta!”. Amor fati, singularidade e fatalidade projectada. Esquecido da compaixão de si. Só Louco! Só Poeta!

Bibliografia:

Nietzsche, A Origem da Tragédia.
Nietzsche, A Vontade de Poder, vol. I, II, III.
Nietzsche, Assim Falava Zaratustra.
Nietzsche, Ecce Homo.
Nietzsche, Para Além de Bem e Mal.
Nietzsche, Poemas.

on gravity

2009-03-29T05:36:00.000-07:00

By: Maria Odete Madeira

Gravity may be thought of as more than just a mechanics of attraction and repulsion. One should not also make a simplistic reduction to a curvature phenomenon.

A point of synchronization can be thought of as a gravity point with Newtonian-like properties. On the other hand, the matter of the synchronization horizon of a system resends towards a gravity with Einsteinian-like properties. The synchronization horizons are linked to dynamic limits of affection/perception.

Gravity is fundamental when dynamic systemic mechanisms of religare/synchronization are present.

Some memes and memeplexes can be considered to produce more meme-gravity than others, for instance, the memeplexes that are produced by religions, capable of attracting a great number of followers, and repelling a great number as well, generate large gravitic volumes.

Memes and memeplexes' gravitic volumes, in this line of thinking, are related to their replicative value, interconectable with the self-sustained co-evolving spirals, referred by Dawkins in Unweaving the Rainbow.

School shootings can be considered to produce social, historical gravity, and meme-gravity, their gravitic volume being related to their replicative value.

Viral videos make-web (fazem-teia) and, by making-web (fazendo-teia), they make-gravity (fazem-gravidade).

In this line of thinking, one can also state that stand alone complexes can produce a lot of gravity.

When one works with horizons of discourse, one should take into account that they are very gravitic, in this more general sense of gravity. Without gravity, for instance, we would not have a doubly articulated human language. The esphenoid needs a lot of "gravitic help". Without gravity there would be no such things as thoughts and feelings, without gravity there would be no organisms, there would be no life, without gravity there would be no structures.

on subjectivity/objectivity

2009-03-29T02:47:00.000-07:00

By: Maria Odete Madeira

The problem of subjectivity/objectivity has been exhaustively addressed, since the Greeks. More recently, it was addressed by Popper, in the problem of the demarcation between the empirical statements and the metaphysical statements.

The problem of objectivity is topologically (topos: the place of the body) connected with an intersubjective communicational interface.One can, consistently, speak of objectivity, from planes of communicational reciprocity between cognitive structures, compatibilized in an external active relational space of synchronized systemic simultaneity.

Lucretius: "declination"

2009-03-27T06:11:00.000-07:00

Se pela sua declinação os átomos não tomam a iniciativa de um movimento que rompa as leis do destino, para impedir a sucessão indefinida das causas, de onde vem a liberdade concedida a tudo o que respira sobre a terra, de onde vem o poder arrancado aos destinos, que nos faz caminhar por qualquer sítio aonde a nossa vontade nos conduz e, tal como os átomos, nos permite mudar de direcção sem sermos determinados pelo tempo ou o lugar, mas, pelo contrário, nos permite mudar de acordo com o desejo do nosso espírito?

In Lucretius De rerum natura

If by its declination the atoms do not take the initiative of a motion that is able to break with the laws of the fate, to impede the undefined succession of the causes, from where comes the freedom conceded to all that breathes upon the earth, from where comes the power plucked out from the fates, that makes us walk by any place to where our will drives us and, such as the atoms, that allows us to change direction without us being determined by the time or the place, but, on the contrary, allows us to change in accordance with the desire of our spirit?

In Lucretius De rerum natura

To be in a body is to be in the world

2009-03-10T03:17:00.000-07:00

By: Maria Odete Madeira

To be in a body is to be in the world, to Feuerbach. Each body exists as a totality submersed and rooted in the world. Each human being lives in an intra-mundane existence and in a daily reality that is inhabited and experienced in permanent situation. The consciousness of each existence is inseparable from an intra-mundane human space localized in a daily reality.

To Feuerbach, each present moment is a point of reference of differentiation, situated between the before and the after. The here and now of each existence occurs in a space that can be approached as a concrete place, a determined place in a time that must be understood as lived duration, that precedes any dynamics of projective consciousness.

Of himself/herself, as body rooted in the world, the human being knows and understands only the present, of the past he/she retains solely that past that left vestiges, whose active causality survived, and prolonged itself until the present.

Digitizing the Continuum

2009-03-08T05:54:00.000-07:00

by Carlos Pedro Gonçalves

The reign of the digital imposes itself with the digitocracy over the continuum. The mathematical continuum, irreducible to the countable, is negated as interdict, as dangerous illegality.

Of mathematics, it is demanded a logocentered logicity, a reifying and imprisoning reduction that strives to reduce the semantic to the syntactic and, thus, extends the formal incompleteness to a semantics that does not possess it.

The mathematical intuition is substituted by the cold deduction that, incapable of scaling new horizons because it lacks imaginative capability, does not explore the mathematical idea and its apprehension by the mathematician that intuits it in a sensual immediateness produced by an imaginative synthesis, idea, itself, by nature, irreducible to a logical logocentrism, as Gödel proved it.

To scale new horizons… to think beyond the barriers of the code… dangerous activities… incompatible with a digitocracy extended to the mathematical activity itself. The formal language ceases being just an instrument of discursive organization and of formalization auxiliary to the proof, to become an instrument of thought control.

From abstractive auxiliars, the language and the formal system become instruments of alienation of the mathematical thinking itself, that, to think the formal, empty of semantics, loses its object of intentionality – the mathematical object, in itself, as abstract object of thought, which, as Gödel proved it, is irreducible to the purely syntactic, to the purely logical.

To digitize the mathematical continuum in the mathematical discrete means to abolish, from the thought, a universe of thinkable forms, to impose the limit of the digital, useful to an effort of computative mechanocracy in which the instrument of the number abolishes the analogical and, thus, the interval itself and the continuum. Without interval, without continuum, without shades, without infinitesimal differences, without empty spaces, thought as empty spaces because continua of nothing. End of the différance towards the end of the différence.

Even if different, digitized, we come to occupy the same houses in the bar codes in which we become, clones in our condition of slaves to the digit.

Badly interpreted Gödel’s theorem, to justify that the notion itself of mathematical truth is reducible to a logical validity, in a first step towards the algorithmization of truth, of geometry, of the continuum, of the interval, of the grey, of the individual as individual, separated from the rest, and non-slaved to the number… and non-slaved to a machine incapable of imagining, incapable of innovating, incapable of jumping outside the tyranny of the formal system, itself limited in itself and right from the point in which it deals with the numbers themselves and with simple arithmetic.

The end of the mathematician (second target), as well as the end of the philosopher (first target) are the two first steps to abdicate from our thought and from those natural systems of systemic homeostasis, thinkable as antibodies that protect us from the dictatorships of the formal and of the machines as ends in themselves.

Digitalização do Contínuo

2009-03-07T03:14:00.000-08:00

Carlos Pedro Gonçalves

O reino do digital impõe-se com a digitocracia sobre o contínuo. O contínuo matemático, irredutível ao contável, é negado como interdito, como ilegalidade perigosa.

Da matemática, é exigida uma logicidade logocentrada, uma redução reificante e aprisionadora que tenta reduzir o semântico ao sintáctico e, assim, estende a incompletude formal a uma semântica que não a possui.

A intuição matemática é substituída pela dedução fria, incapaz de escalar novos horizontes, porque não possui capacidade imaginativa, não explora a ideia matemática e a sua apreensão pelo matemático que a intui numa imediatez sensual produzida por uma síntese imaginativa, ideia, esta, por natureza, irredutível a um logocentrismo lógico, como o demonstrou Gödel.

Escalar novos horizontes… pensar para além das barreiras do código… actividades perigosas… incompatíveis com uma digitocracia alargada à própria actividade matemática. A linguagem formal deixa de ser somente um instrumento de organização discursiva e de formalização auxiliar à demonstração, para passar a ser um instrumento de controlo de pensamento.

De auxiliares abstractivos, a linguagem e o sistema formal passam a ser instrumentos de alienação do próprio pensamento matemático, que, para pensar o formal, vazio de semântica, perde o seu objecto de intencionalidade – o objecto matemático, em si mesmo, enquanto objecto abstracto de pensamento, o qual, como Gödel demonstrou, é irredutível ao puramente sintáctico, ao puramente lógico.

Digitalizar o contínuo matemático no discreto matemático significa abolir do pensamento um universo de formas pensáveis, para impor o limite do digital, útil a um esforço de mecanocracia computativa em que o instrumento do número abole o analógico e, assim, o próprio intervalo e o contínuo. Sem intervalo, sem contínuo, sem matizes, sem diferenças infinitesimais, sem espaços vazios pensados como espaços vazios porque contínuos de nada. Fim da différance para o fim da différence.

Ainda que diferentes, digitalizados, passamos a ocupar as mesmas casas nos códigos de barra em que nos tornamos, clones na nossa condição de escravos do dígito.

Teorema de Gödel mal interpretado para justificar que a própria noção de verdade matemática seja redutível a uma validade lógica, num primeiro passo para algoritmização da verdade, da geometria, do contínuo, do intervalo, do cinzento, do indivíduo enquanto indivíduo separado dos restantes, e não escravizado ao número… e não escravizado a uma máquina incapaz de imaginar, incapaz de inovar, incapaz de saltar para fora da tirania do sistema formal, ele próprio limitado em si mesmo, e desde logo, quando lidando com os próprios números e aritmética simples.

O fim do matemático (segundo alvo), assim como o fim do filósofo (primeiro alvo) são os dois primeiros passos para abdicarmos do nosso pensamento e daqueles sistemas naturais de homeostasia sistémica, pensáveis como anticorpos que nos protegem das ditaduras do formal e das máquinas enquanto fins em si mesmos.

humanity

2009-03-05T03:38:00.000-08:00

By: Maria Odete Madeira

The intersubjective recognition of the humanity, in us, as a supreme constitutive telos that life has gifted us with, commits us responsibly with the right and the duty to defend our humanity as a good that is ours, that is unconditional and that is inalienable.

humanidade

2009-03-05T00:41:00.000-08:00

Por Maria Odete Madeira

O reconhecimento intersubjectivo da humanidade, em nós, como um telos constitutivo supremo que a vida nos doou, compromete-nos responsavelmente com o direito e o dever de defender a nossa humanidade como um bem que é nosso, que é incondicional e que é inalienável.

Sovereign Good

2009-02-15T03:27:00.000-08:00

by Maria Odete Madeira

It is the words... it is the discourse of the others... that address us… it is the face of the others… the gaze of the others… it is the existence of the others… that searches, in us, the imperative that unites our voice… our discourse… our existence… to the voice… to the discourse… to the existence… of the others that gaze upon us and that address us, invoking and evoking the good… the wisdom… the justice… in us.

Philosophy

2009-01-25T04:15:00.000-08:00

by Maria Odete Madeira

Philosophical arguments are not developed from answers but from questions. One thing is the authors of philosophy and the thinking and models of these authors, another thing is the philosophical thinking, itself.

To have philosophical thinking implies a very hard work and a development of capabilities to be able to unfold monadologically a locality in a non-locality, and for that it is necessary training, because it is not about the thinking of each one, but about the capability that each one has to access an eidos/logos, and to learn from that eidos/logos, to learn how to question about the things.

Each answer brings already, in the mechanism of unfolding of that answer, a new question. A philosopher is not whoever wants to be one, because it is not about the thinking of each one, it is about a capability to ascend to a non-local universal that is independent of each one, and in order to do that it is not enough to want to do so, it is necessary to learn, and to learn, and to learn, and… above all, it is necessary to learn how to question the things, themselves. It is not a matter of what we know, it is a matter of what we know not.

It is not about making algorithmic reductions, or logical deductions, or to affirm oneself as philosopher, it is not about dogmatic revelations.

As an exercise of questioning the things, one cannot be afraid or annoyed with the questions, it is necessary some humility.

Unfortunately, the fast-food teaching and the pragmatic application-oriented science, where it only matters the immediate answers that solve immediate problems, algorithmized for an easier consumption, does not allow nor favor an exercise of a fundamental thinking based on questioning; questions, beyond a certain point, become a nuisance.

One cannot give, in philosophy, a ready to consume answer. To address, philosophically, an issue is to address it with questions. A philosophical discussion starts with questions and does not end, but go on, indefinitely with more questions. Question to question, to question, to question,… (verb and process).

Within such an exercise of questioning, one cannot abruptly end the debate with a quick and superficial exit, and must follow the questions where they lead.

The questions cannot be placed in the most general form and only skim very lightly the real subject. In a philosophical debate all the cards have to be laid out on the table, since the questions have to be about the things themselves and not about the (often manipulated) shadows of the things.

Beyond the essences: the pathos

2009-01-10T03:37:00.000-08:00

by Maria Odete Madeira

The term pathos can mean: event, experience, suffering, emotion, attribute.

In general terms it means: something that happens, that can have by reference that which is the cause, or that which is the effect of that which happens.

In Aristotle, the pathos is the logos of the contingence, it is the logos of the event, it is the logos of the attributes acquired by the subjects, it is the logos beyond the essences.

Pathos is the place of the difference subtracted to the identity, the mark of the asymmetry that prevails in the proposition and that determines it, as such.

Destined to be surpassed in the identity and by the identity of the subject, the pathos is, simultaneously, all that the subject is not, and all that the subject sees.

Rotatively displaced by a fundamental ambiguity, the pathos trajects and projects a (co)condition of constitutive irreducibility that, simultaneously, imposes that a subject cannot be its attribute and that its attribute cannot be a substance.

In Aristotle, the identity of the logical subject supports itself in the pathos, resending towards the origin of a propositional order whose contradictory character allows the unveiling of a presence of an identity inscribed in an order of permanent reason that has in itself an active principle of becoming, as an active principle of the being, itself, as potency, that makes it come to the presence, from itself, as eksistente dasein (Heidegger), or act.

Quantum Game of Life II

2008-12-01T04:06:00.000-08:00

by Carlos Pedro Gonçalves

Below is a video of a simulation of the quantum game of life, implemented in Netlogo.

Following the previous blog post on this game, each cell (patch) can be in a vacuum state, or it can become punctured by a qubit state.In the video the grey cells correspond to the vacuum states that may potentially become occupied by a qubit state Q> = a0>+b1>, while the black and white cells have become occupied (in act) by a qubit state. Each color corresponding to one of the two basis states of the qubit, that is, white corresponds to 0> and black corresponds to 1>.

The actualization of each of the two qubit computational basis states occurs through a probabilistic process since there is decoherence in the qubit histories. The model works with two gate rules, a simple Haddamard rule, and a chaotic rule that exemplifies path dependent quantum computation. The video above uses path dependent quantum computation, in the dynamics of creation and anihilation as well as in the qubit information dynamics.

The video is also available at:

http://www.youtube.com/watch?v=14jdqWEe0wE

Quantum Game of Life

2008-11-29T07:40:00.000-08:00

by Carlos Pedro Gonçalves

The following are pictures of a simulation of a quantum game of life, implemented in Netlogo:

Initial Configuration

After a Few Steps

Each cell (patch) can be in a vacuum state, or it can become punctured by a qubit state. In the pictures the black cells correspond to the vacuum states that may potentially become occupied by a qubit state, while the white cells have become occupied (in act) by a qubit state.

Quantum information is, thus, created and annihilated out of an information vacuum. A clustered patchworked dynamic geometry emerges, in the current simulation, from local connectivity rules that make it more probable for clustering to occur.

Defining Complexity

2008-11-28T14:20:00.000-08:00

by Maria Odete Madeira

Diversity and complexity are contextually (co)implicated , depending, the nature of each, from the nature of the context, in which they are rooted and upon which they systemically depend. This means that to refer the term complexity to a single definition would be not only impoverishing but also difficult in terms of a desirable explicative rigor.

To speak of complexity one must comprehend complexity, itself. To comprehend comes from the Latin cum+prehender that means to apprehend conjointly, thus, the term “comprehend” folds, it its own definition, the diversity that allows one to design it also as complex, in the sense in which it folds in the same act of comprehension, successive resendings between different individuals, or subjects, which implies an explicare and, thus, an unfolding of the subjectivity in intersubjectivity.

Any attempt to define complexity will have to consider, in the act itself of defining complexity, the complexity implicated in the act of comprehension, necessary to that definition.

Comprehending complexity systemically depends upon individuals, groups, species, cultures, societies and civilizations, in their differences, multiplicities and diversities.

Being and Existence

2008-11-18T02:34:00.000-08:00

by Maria Odete Madeira

In Plato, as in Parmenides, the Being is not addressed, from the plane of the Existence, but from the plane of the Truth.

The Being is the very act of Being, immediately realized within the Being, itself.
To Be the Being is the realization of the Unity in its irreducible absolute act of Being.

When, within a Platonic position, one states that the Beauty, the Good or the Truth ARE, one is stating that the Beauty, the Good, or the Truth are in themselves as such: Beauty, Good and Truth.

This in itself means a pure functionality of the Being, as condition of itself, depurated of any constitutive relational element, but that, because of that, it can, itself, constitute itself necessarily as condition of possibility of the existence of the entities in the relative rotative relational positions of the multiple and divergent modes of the being there (dasein).

Nietzsche - Man... a chain of forces...

2008-11-05T02:23:00.000-08:00

by Maria Odete Madeira

“Eu que sou filho da terra, sinto as doenças do sol como se fossem eclipses meus (…)” (Nietzsche, The Will to Power)

“I, that am son of the earth, feel the diseases of the sun as if they were my eclipses (…)”

For Nietzsche, the “I” is a sort of animal, an individuation constituted by chains of multiple forces articulated between each other and whose motion of rotation displaces itself incessantly in the direction of other forces upon which it exerts its pressure, growing or diminishing, rizhomating in accordance with the trajects and trajectivities.

Man… a chain of forces dependent upon all the cosmic forcers, man… a territory of fluxes of individuated forces, whose frontiers are critically situated between two limits: the infinitely large and the infinitely small, and…, yet, unpredictable, and…, as any small particle, man is a being in itself, simultaneously potential/virtual and actual, simultaneously wave and particle.

The Nothing

2008-11-02T10:49:00.000-08:00

by Maria Odete Madeira

Nihilum or Nothing is a referential expression that signals the non-existence of all the things.

The Nothing is understood in its relation with the Being: the Being is and the Nothing is-not; the Being is the Being, because the Being is, and the Nothing is the Not-Being because the Nothing is-not.

However, the Nothing is also Being, because the Nothing is the Nothing, that is, the Nothing is the Being of the Not-Being.

Every referential expression resends towards a referent. The referential expression Nothing resends towards a referent: the Being of all the things.

In any language the referent can be defined as an object of perception. In the referential expression Nothing, the referent is the Being itself that, as such, has the power of generating its own negation: the Not-Being of the Being, understood as a non-presence and, in this way, as a non-existence.

Parmenides introduced, in the Western thinking, the concept of eternity as total presence of the Being. In accordance with Parmenides, the Being exists as total presence, the Being is not born nor dies, the Being is and exists as an eternal present.

However, the Not of the negation imposed itself on the human thinking and language as a power of the Being, as capability of displacing oneself, in a strange loop, from the Being to the Not-Being, in the same flow of Being, as total presence, and, thus, simultaneous, coincident and permanent rotativity of oneself, in oneself and for oneself.

Heidegger experienced, through a feeling of anguish, the interval of thinking between the Being and the Entity. It is dived in a profound anguish that the author conjectures that the entities are not the Being and that the truth of the entities is in that which they are not: the Being itself.

For Heidegger, in front of the Being, the man is helpless, lost in the Nothing. Because the Being, itself, is neither this nor that: the Being, itself, is Nothing.

Cognition, Truth, Essence and Substance

2008-10-24T04:02:00.000-07:00

by Maria Odete Madeira

Every cognitive act is about one or more relations. This about is never neutral, it is committed with an intentionality that points towards a signaled relation. To point is also to orient oneself towards the existing things as presences in the world (ousia, dasein), in relation with one another (Heidegger, 1969).

In Plato’s Fedon and Phaedrus, the problem of the knowledge is placed in what regards its object, being concluded that the response to the problem would have to be found through knowledge itself, but for that, and in accordance with the platonic procedures, it was necessary that one first defined what knowledge is in itself.

In the Menon an exercise of fundamental reflexibility is developed towards defining knowledge, in regards to its origin and nature, but it is in the Book VII of the Republic that a theory of knowledge is developed, whose archetypal operationality still remains in all the Western scientific thinking. This theory of knowledge proposes a cognitive model, in which the knowledge acquired through the senses is linked to the change, which is a configurator of ephemeral appearances, and, because of that, this knowledge is considered an uncertain knowledge, particular and subjective, a knowing of opinion or doxa (Note 1). The true knowledge or episteme, is sought for in an immutable reality, intelligible and supra-sensitive, only accessible to the human intellect.

The Greek terms episteme and logos that mean, respectively, science (true discourse) and discourse, compose the term epistemology. This term still remains, in all the Western thinking, reflexively committed with the Greek matrix in what regards the conditions of truth, consistency, legitimacy and legality of knowledge, that refers it and relates it with the existence and reality of the things.

The Greeks understood and considered reality to simply be that which things were. However, this principle of definition would become more complex and controversial, by the need for the development of the concept itself, from the first causes and first principles of the things themselves, that is, from that which explained the nature of these things, in what regarded their origin, which led to the need to work upon two fundamental notions: the notion of matter (Note 2) and the notion of form (Note 3).

These two notions appeared and were developed in the Greek thinking as two primary epistemological oppositions. The first Greek philosophers and, later on, the atomists, considered the first causes and the first principles, according to matter, while Socrates, Plato and Aristotle considered these same causes and principles, according to form. This division has configured, along the whole Western thinking, the interpretative trajectivity of notions fundamental to the exercise of the reflexive thinking in its relation with the conditions of truth, synthesized in the scientific statements.

Heraclitus conjectured an idea of truth persisting and governing through the permanent change of all the things, that is, an order and proportion that the logos expressed and that constituted a universal explicative pattern accessible to all and that, because of that, should be consensually interpreted.

Parmenides, on the contrary, argued for the existence of a truth inaccessible to the common of mortals, being beyond every aspects and perspectives of the daily experiences, that are linked to change or to opinion (doxa). This truth was only accessible to the pure thought or noema.

One can state that with Heraclitus and Parmenides it was trajected, in the Western thinking, a perspectivic genetics that replicated, in the scientific statements, a fundamental opposition between the senses and the intellect or reason, the first, linked to the change and the experience of this change, as well as to the visibility of this change, and, the latter, linked to what is considered to be invisible, permanent and immutable.

However, and even though the methodological criteria diverged, in each of the two thinkers, Heraclitus and Parmenides wished to access the same permanent order and proportion responsible for the existence of all the things and from which any discourses could be stated as true.

The character of permanence, immutability and indestructibility constituted, thus, the fabric of the notion of truth and of the true discourse which, in turn, were linked to the notion of necessity (agakh, necessitas). Some thing could be considered true only when that same thing was necessarily true. The necessity was defined by Aristotle as that which has to be in that way and cannot be in any other way (Meta., V, 5, 1015a; 1015b).

The notion of necessity signals an idea of permanence that, in turn, places it in relation with the notion of essence, from the Latin essentia, term derived from esse which can mean, as verb, to be or to exist and, as name, the being.

Essence has its Greek correspondent in ousia, noun formed from "to einai" which, in turn, also means to be. In its origin, essence meant, just, being, later on, and through the usage, it came to mean that which is. The accent in the verb displaced itself to the subject (ypokeímenon, subjectum) to which the being is attributed.

Later on, the notion of essence came to coincide with the notion of substance, from the Latin substare (to underlie), interpreted (the notion of substance) as subject and substratum of accidents. In simple and general terms, one can speak of the essence of the substance and of the accidents.

With Plato, the term eidos (Note 4) (eidos or idea) came also to designate that which was understood by essence (or essences) of the things.

For Plato, in the line of Parmenides, the ideas or essences existed separate from the concrete things. According to the author, the corruptible nature of all the things that constituted the world of sensitive experience, made it impossible the access to a true explanation about the things. The true knowledge or episteme should, thus, be sought in a supra-sensitive reality, only accessible to the intellect, that is, in the ideas or intelligible essences.

The theoretical or intuitive nature of the platonic knowledge is associated with an intelligence or cosmic reason, nous, also designated by spirit, related with the ideas or essences, which were considered to be the cause of the nous in the soul, by participation. The operativity of the nous was that of facilitating the access of the human intellect to the true knowledge.

Aristotle, dissolved the nous in a dynamis (potency) and in an energeia (act), criticizing Plato about the theory of the eidos. For this author, the essences did not constitute a subsistent separate from the things, being just their formal cause.

By knowing the things we could also know their eidos. The true knowledge or episteme could be found in them as an energeia or principle of being (esse, enai), by opposition to dynamis, which Aristotle considered as a principle of determinable indetermination, that is, the dynamis could only be determined by the energeia that, in itself, was the determination.

The scholastics interpreted the energeia as a synonym of force (vis), that is, a causal principle of action, belonging to the category of quality. The medieval philosophers called it impetus, Descartes called it quantity of motion, Leibniz and Newton called it living force (vis viva).

While disagreeing between each other as to the locality of the universal essences, both Plato and Aristotle agreed, however, that the scientific discourse could only be considered to be true, when it satisfied criteria of universality and of necessity. Thus, it was imposed as a demand of any scientific inquiry, to find the fundament of any statement of truth or of falsehood, in that which were the first causes and the first principles of the things.

In this way, for there to be discursive rigor, the matter and its forms or essences should be analyzed separately as things that are different from each other, both in terms of their identity as well as of the value attributed to them. The epistemic analysis of one should not interpretatively contaminate the analysis of the others.

The object of the knowledge, its form or essence, meaning and definition obeyed, for Plato as well as for Aristotle, rigorous criteria of adequability and agreement that allowed a general semantics of deductive nature (Note 5) that prolonged itself in Euclides geometry and in Arquimedes’ statics, both based upon a system of axioms that constituted self-evident truths, and upon a system of theorems derived from those same axioms.

The semantic determinism of the Greek scientific discourse generalized itself as an epistemic model until Epicurus, distancing himself from the primitive and deterministic atomism of Democritus (Note 6) introduced the notion of clinamen (declination) as a capability that the atoms have of spontaneously deviating themselves from their trajectories. Thus, Epicurus introduced, in the scientific discourse, an element of irreducible unpredictability, absent until then, with epistemological consequences about that which was considered as criterion of truth.

Note 1 – The distinction between true knowledge or episteme and knowledge of opinion or doxa, the latter considered as inferior knowledge, dates back to Xenophanes. In the poem of Parmenides the sensation or aisthesis regards the appearance or opinion (doxa). The sensation has to do with the perception of the senses (aistheta) that Parmenides excluded from that which he considered as truthful knowledge, which belongs only to the domain of the being (on).

Note 2 – Matter, with origin in the Latin materia, corresponds to the Greek terms: arché (principle); stoichein (element); chora (receptacle); and hyle (materia prima). To explain the nature (physis) and the change of the things, the first Greek physicists or cosmologists conjectured that all things came from one single or several principles (archai), these being considered as substantial beings that existed in themselves and by themselves, such as: the water, the air, the energy or the atoms. Aristotle was the first Greek philosopher to use the term hyle (materia prima) (Meta Z 3, 1029a) as subject of substantial or accidental change, that is, hyle as the first substratum of each thing, or immanent principle, from which some thing comes to the being (Physics, I, 7. 129a; 190b – 192b). Hyle is the indeterminate and the potential principle of the being, opposed to the form, this last considered as actual principle of the being. The term materia prima or hyle was introduced by the scholastics, who added the term materia secunda or deutera hyle. The concept materia prima corresponded to the concept of potential matter (in fieri), and, the concept of materia secunda, to the concept of actual matter (in actu).

Note 3 – The form can be designated by the Greek terms eidos (conceptual form, species) and morphe (real material form).

Note 4 – The notion of eidos, translated by idea, became one of the fundamental concepts of all the Western thinking. Originally, the eidos was that which was seen, the aspect, the appearance or the form, normally designated the form of the bodies. In the time of Herodotus, the eidos and its cognate the idea, that meanwhile started to become common use in the Greek society, assumed the meaning of characteristic property or type. Frequently, the eidos/idea appeared as technical term, linked to the notion of potency (dynamis). The eidos/idea can be considered as a linguistic sign, whose semantic richness guarantees its applicability to a certain variety of contexts without that constituting a loss in its original connotative or denotative value, that is, the identity of its primitive nature as linguistic sign is not lost, despite its adaptive growth. Plato recognized its richness and plurality of senses and vastly applied it in different contexts. Being, however, more important that sense which is projected by its metaphysically substantivated application as subsistent essence in an incorporeal intelligible and incorruptible world. This notion, that constituted the core of the theory of the ideas, has its roots in the Socratic eidos, as subsistent essence of certain modes of ethical behavior. In its set, according to Plato, the ideas constituted the archetypes or models in imitation of which all the things had been done, being, because of that, only them (the ideas), the guarantee of all the scientific knowledge (Sophist, 246b; Fedon, 99e; Parmenides, 132d; Timaeus, 52a). The terms eidos and idea were used by Aristotle with the same meaning that Plato attributed to them (Meta., I, 6, 9).

Note 5 – Aristotle created a theory of demonstrative judgments which he called syllogism, from the Greek sullogizomai which means to bring together. In the formal logic, syllogism means the external signal of the deductive reasoning. In its traditional (Aristotelic) form, it is an inference in which a conclusion is inferred from two premises with a common term and through the elimination of that same term. The inference is always made by means of deductive reasonings, from the Latin deducere which means to extract or to diminish. The deduction is a reasoning through which, from one or more considered propositions (antecedents), one concludes necessarily an unknown proposition (consequent). The notion of deduction is in conformity and agrees with the Theory of the Syllogism of Aristotle. The syllogism is, in terms of its structure, considered the most complete and robust expression of the deductive reasoning.

Note 6 – The primitive atomism was attributed to Leucippus and Democritus. Leucippus has remained as a vague and obscure figure, more being known about Democritus and of his writings. Of the little information that has been gathered, it is conjectured that Democritus must have developed the fundaments of the primitive atomism from Leucippus, these fundaments agreed with the Parmenidean principle that all things had their explicative principle in an immutable and imperishable order, but, these same fundaments, were not in agreement with Parmenides, when these stated that that same order had a material nature that was constituted by solid corpuscles that alternately and eternally collided and repelled each other, in accordance with a regular and determined mechanics, in an unlimited space. These small particles or atmoi were considered the smallest particles of matter, solid, hard and indestructible, different from each other in size and shape and in its relative topological positions, in terms of motion and distance.

On Risk and Responsibility

2008-09-29T07:47:00.000-07:00

By Maria Odete Madeira

Responsibility, from the Latin, respondere, is a name for a systemic capability that any autonomous human agent has of being able to account for his/her actions and respective effects, accepting the consequences of these actions (to be accountable).

Because of this capability, the human agents have the right and the duty to account (respondere) for their actions.

“(…) Today the guiding hand of natural selection is unmistakably human with potentially Earth-shaking consequences.

The fossil record and contemporary field studies suggest that the average rate of extinction over the past hundred million years has hovered at several species per year. Today the extinction rate surpasses 3,000 species per year and is accelerating rapidly; it may soon reach the tens of thousands. In contrast, new species are appearing at a rate of less than one per year (…) The broad path for biological evolution is now set for the next several million years. And in this sense the extinction crisis – the race to save the composition, structure, and organization of biodiversity as it exists today – is over, and we have lost.”

Stephen M. Meyer, 2006, The end of the wild, pp.3-5.

The question about the responsibility of the human agents is now stretched to the limit point from which we must ask: what fundamental value do we assign to the planet?

In a risk assessment, where the agents involved have an interest in a support to a certain action, there is the inevitable contamination of that assessment with an undervaluation of the scenarios considered to be unfavorable to the intended course of action. This includes, not only, biases in the assumptions and in the processes of risk quantification, but, also, biases in the interpretations of the results.

Many of the technologies that we are now beginning to produce may open up the risk of situations with catastrophic consequences to the planet.

Some of the risk scenarios associated with these situations are known, and worked upon by the sciences involved and by risk science.

It is necessary, within a scientific approach to risk, to consider risk as a fundamental ontological operator linked to the mechanism of life and death. Generally, the risk assessment is made from the perspective of superstructures that transcend the ontological planes of immanence.

Any systemic cognitive synthesis includes an evaluation of risk and it may be more, or less, accurate in accordance with the functioning of the systemic homeostatic mechanisms.

The question that is placed about the human assessment of risk is that the type of evaluation of risk is being done in planes that ontologically transcend the systems and problems themselves, call these planes of transcendence, for instance.

In these planes of transcendence, we have what we call the political, economic, military and scientific games, that introduce an ontologic systemic bias in what regards the life and death of the systems. The evaluations of the risks are not being done about what may constitute a threat or an opportunity to the systems, what are being done are evaluations of the discourses and strategies of power, compromised with the economy, politics, military and science.

The risk has become, in today's economies, a product aimed at the satisfaction of pleasure, which raises a question: what are the phenotypic effects synthesized and metabolized by a neurocognition of the risk? To what point are the homeostatic mechanisms, that include, for instance, background feelings, being organismically blocked?

What are the risk assessments that the human agents, as consumers of risk products, may produce? In what way are they being affected by the effects of a risk culture and a risk economy?

Furthermore, the economy itself is feeding upon the risk for its own development. Besides a risk consumption culture and economy, there are the technological and scientific risks, as well as the power dynamics of wars and of natural disaster aftermaths.

No less important is to consider the role, in the perception of risk, of the religions as power institutions supported by dogmatically organized discourses of faith, built from conventioned truths and that are supported by active ideological mechanisms of convincing and vanquishing. To what point is it not the case that religions constitute a mechanism of alienation, effective and with structural effects, that blocks the cognitive processes linked to the risk perception?

Intelligence and Reason

2008-09-14T10:28:00.000-07:00

by Maria Odete Madeira

Intelligence has its etymological root in the Latin intelligentia, term composed of intus,which means within, and legere, which means to choose, to elect.

Intelligence is a dispositional systemic capability to capture, select and process data and knowledge, from cognitive dynamics, linked to mechanisms of interpretation and comprehension, genetically incorporated in all the living systems.

Reason has its etymological origin in the Latin Ratio, meaning Calculation. Rationem ducere means computare, to calculate.

All the living systems actively depend upon the cognitive processes.

All the living systems are producers and consumers of knowledge.

In any cognitive processing intervene mechanisms of Intelligence and mechanisms of Reason. Intelligence and Reason are not mechanisms exclusive of a given living system, but of all the living systems.

on homogeneization and heterogeneization

2008-08-27T08:41:00.000-07:00

by Maria Odete Madeira

While the homogeneization, understood as a dynamic process, is intentionally directed towards capturing, in the systems, patterns that exhibit similarities between each other, towards a systemic identity, the heterogeneization, on the other hand, positions itself, with respect to the homogeneization, as an energetic antagonism, intentionally directed towards capturing, in the systems, patterns that are different and divergent between each other.

The energetic antagonism implies an undefined enchaining of contradictories, that, in the systems, can potentiate mechanisms of autopoiesis capable of producing the so-called systemic fracturing evolutionary jumps, from which lines of fugue can be traced as a threat or opportunity to the systems in what regards their growth and development.

Hegel - to think

2008-08-25T02:41:00.000-07:00

by Maria Odete Madeira

To Hegel, the territory of science is the thinking, to think is to integrate the existence in a plane of non-reductionist universality, that is, the universality must be considered in a perspective of a systemic totality in relation with the respective parts that constitute it.

Hegel designates by element or ether the constitutive horizon of science, characterizing that element or ether from its translucid and simple character, that allows one to signal it as a standpoint (standpunkt), that is, as a taking of position that preoccupies itself with the reality from its fundament.

The ether constitutes, for Hegel, a universal principle of possibility of all the experience.

Color - light and gravity

2008-08-10T10:51:00.000-07:00

by Maria Odete Madeira

The human brain reconstructs the color, from the luminous energies, reflected by the diverse colored surfaces. To that end, neural areas, specialized in the perception of the colors, are mobilized, as well as areas of the cerebral cortex specialized in the analysis of the forms, of the disposition in the space and of the motion (Changeux, 1994).

In the presence of the objects, the eyes capture the luminous radiations that these emit, converting them in electrical impulses that propagate themselves to the cerebral cortex, the place where an internal representation of the color is built.

The human eyes are sensitive to the electromagnetic radiations, in a band called the visible spectrum, in which are localized seven visible colors that distinguish themselves by their respective wave lengths.

The perception of the light takes place through the incidence of the luminous rays that penetrate to the retina that converts them in electrical signals, posteriorly transmitted, through the optic nerve, to the brain that interprets them, configuring an internal image that corresponds to the external image responsible for the emission of light.

The world, such as we see it, is filled with colored forms. Our physical perception of the objects involves the perception of the color. This perception is a dynamic act, that passes through the apprehension of external variables that implicate the spatialization of the color, as actualization of this same color, in a real and communicational time that relates the observed color with the observer.

We can, therefore, speak of an overcoding, associated with the color. If, on the one hand, in the spatial unfolding, the color unfolds, reflexively, the senses implicated in it, on the other hand, it folds the memories and experiences, subjectively triggered in the observer, as observer that is affected by the interpellation of the color.

In this sense, the color affects and is affected, in a reflexive nanodynamics expanded to proto-conscious levels that mobilize sets of neurons that enter in resonance with the overcoded senses, in the act of subject/observer and color/observed, intercrossing short or medium term memories, with those of long term, all of them interpellating coded and codifier living experiences.

The experience of the color is, also, and experience of light and gravity. Affections that fold and unfold, explicate and implicate, intercrossing perceptions and projections of light and gravity.

In a primordial dialogue of convincing and vanquishing, shaded and alchemical blacks are dramatically crossed by solid, material, measurable and quantifiable lights. Tensional spaces, geometrized by light and shadow are, thus, configured.

Black and crepuscular inquietudes alternate with swift, intense and extenuated whites, reflecting hybrid and undecided harmonies, chiseled of night and day, light and gravity.

White theories, objective and explicative, twist and turn through dissymmetric, bifurcating, faithful to Plato’s cave, molecular black flows, in the eternal and eternized struggle between white and black, light and gravity.

Between the cave and the sun, intersections of straight lines, planes, volumes, intervals, regions, translucid and empty white intuitions, shadows, secrets and senses triangulate themselves.

Limits that intercross, agitate, hesitate and ramify, in dissipating, metallurgic, prosthetic and projective webs.

Between the white and the black, between the light and the gravity, are the intersection, the shadow, the remain, the trace, the debris, the sense as pre-figurative energies.

We have disconnected ourselves, little by little, from the space of the land in which we live. Little by little, under our eyes, disappeared the space of the sunlight, of the agriculture, of the sacred, of the war, of the states, of the written page that geometry expressed in its intimidating purity (borrowing Serres, 1993).

Since then, a bundle of bodies, messages, knowings and light circulate. In a global land, a new communicational space installed itself in multiple and interlinked networks. A space of mixture, a shaded space.

Referent and Reference

2008-08-04T12:04:00.000-07:00

by Maria Odete Madeira

Any existent can, in any language, be considered a referent, whose existence can be linguistically built in a statement external to it.

Any referential expression is directed towards one or more referents, with which the respective sense(s) and meaning(s) are related.

We are before an act of reference, whenever one states an expression that identifies or names an existent.

In a semiotic language, any sign can be approached as a referent or as a reference, depending upon the position and systemic dynamics of each entity/sign in the statement.

In a situation or process of self-reference, a rotative coincidence is realized, in which the system folds upon itself, in itself. Whenever this occurs, we are before a dynamics of autopoiesis.

On Phenomenology - Discipline and Method

2008-07-26T16:20:00.000-07:00

by Maria Odete Madeira

Phenomenology is a branch of philosophy, applied to the study of the phenomena.

Phenomenon (phainomenon) is that which reveals itself, by itself and in itself. Thus, all existing things can be considered to be phenomena.

Phenomenology is not a method, it is a disciplinary area constituted by a theoretical body, available as fundament for the construction of methods and methodologies aimed at the study of any existing reality that, genetically, by itself and in itself, reveals itself as position rooted in the world.

Criticizing the positivism as a mere construction of facts, Husserl (1907) held that the so-called crisis of the sciences had to do with a reduction of humans to constructed facts. In the positivistic model, humans, as such, were alienated in the human facticity, derooted from that which constituted them as beings that are intentionally inscribed in the world, from which they received the sense of themselves and of the things with which they related.

For Husserl, the world was the originary datum, that was turned towards humans and towards which they, themselves, turned self-reflexively, in order to determine and distinguish the sense of the things.

Protesting against the reduction of human reason to mere exercises of calculation, Husserl defended phenomenology as the science of the phenomena. In Husserl, the phenomenon is an eidos that reveals itself in an intuition that is defined by an intentionality that assigns a plenitude of presence to the eidos (phenomenon) that is aimed at. Each eidos is accessible, only, to a certain type of intuition: the intuition that refers and identifies it in an immediate way and that, because of that, captures it in all its totality.

Intuition has its origin in the Latin terms tueri (to see) and in (in, within) that conjointly mean the action of seeing directly within the things, thus, signaling a mode of immediate knowledge of an existing object that, because it exists, shows itself, as such, to the consciousness that aims at it, and, because it shows itself, it also demonstrates itself in its modes of existence, so that it can be described from its fundament (eidos).

The experience, in Husserl, assumes the sense of lived world (Lebenswelt), as that which is in the origin of the knowledge and that is before any reflexive activities. That is, the objects present themselves to the consciousness, giving themselves in their completeness (eidos) in order to be, only after, and through a conscious act of radical reflexibility, on the part of the subject, actively apprehended by the consciousness that intentionally signaled them as existents in themselves, and by themselves, and, in this way, as autonomies.

The noumenon, that was impossible to be categorized in Kant, appears, in Husserl, as that which is immediately intuited. Thus, Husserl turned away from the criteria that transcended the experience, to be able to, in the same experience (Lebenswelt), and in a direct way, capture that which in the phenomena was their noumenic sense.

In Heidegger, the notion of experience lost the theoretical sense present in Husserl, to mix itself with the notion of existence. The author considered that, originarily, the things do not “make their apparition” and do not “appear to be” to the humans as phenomena or objects of thought, but, instead, as entities that (co)exist in a complex system of references that constitutes the world where each human exists, understands and interprets himself as being-the-there (dasein), projectively launched to a future that he existentially anticipates.

This perspective, of a gnoseology, as activity rooted in the worldly experience, was, also, developed by Merleau-Ponty (1945), who considered that all the universe of science is constituted upon the lived world. The notions of subjectivity and objectivity are synthesized in the notion of the world, lived and understood by subjects incarnated in it. The phenomenological perception is, thus, considered as an originary pre-reflexive experience of each subject with an own body (corps propre), that body, understood, as a node of living significations that is incorporated by an operating intentionality that links it to the world of life.

In this way, the phenomenological perception constitutes itself as the ground that is previous to all reflexive activity. Assuming that knowledge is, always, the apprehension of an ontologically constituted structure, an ontologically constituted structure that, as such, is given to any originary human consciousness, (a consciousness) which is fully rooted in a world that is previous to it, exterior to it and autonomous.

On Individuation

2008-07-21T09:15:00.000-07:00

by Maria Odete Madeira

Individuation is a philosophical term that designates the intrinsic, constitutive, genetic and autopoietic event of separation of each individual within a same species.

It is a systemic principle of separation that operates from the first causes and the first principles that were involved in the genesis of each individual, be these principles entities, situations, processes or events.

In methodological terms, it constitutes an ontological principle used as a classificative criterion of identity.

On Penrose's Argument Against Density Operators

2008-07-21T03:57:00.000-07:00

by Carlos Pedro Gonçalves

What is a quantum state?

Should we speak of a quantum state at all?

Should we speak of quantum states or of quantum processes?

These questions can be raised from the work of Baugh, Finkelstein and Galiautdinov (http://arxiv.org/abs/hep-th/0206036) and from the results obtained by Gonçalves and Madeira (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1438013), about the connection between a stationary quantum state and the consistent histories formalism, these results being obtained from the relational structure of the different bases in which a stationary quantum state can be expanded.

A different, but related, problem arises from Penrose’s Road to Reality (Penrose, 2004), where the author questions the mathematical structure that should be used to formalize what is usually called a quantum state.

Thinking about these two threads, one is lead to the following question:

What is the most fundamental mathematical structure that should be used to describe the quantum system, and, what is the nature of the physical semantics that this structure formalizes?

This is the main question to which we shall return, recurrently, during this article.

Looking at Penrose's (2004) work, and regarding the first part of the question, we find that Penrose (2004) raised the problem of formalizing the quantum state by:

A) The density operator, whose entropy zero space (using von Neumann’s notion of entropy) is comprised of the density operators for the so-called "pure states".

B) The normalized kets (for the "pure states")

It is clear that the density operator is more general, since it can be used for statistical mixtures, but is it more fundamental than the ket for pure states? And, should we call these states at all?

The notion of a zero entropy density operator is effectively equivalent to a projective notion of a (pure) quantum state, as Penrose noticed. Therefore, one might take the position that such density operators appropriately describe a “physical quantum state”, taking the perspective that only that which has an impact in measurement problems can be considered to be physical.

About this, however, Penrose (2004, p.796) argues that:

“(…) I feel uncomfortable about regarding such a ‘pure-state density matrix’ as the appropriate mathematical representation of a ‘physical state’. The phase factor (…) is only ‘unobservable’ if the state under consideration represents the entire object of interest. When considering some state as part of a larger system, it is important to keep track of these phases (…)”

Penrose’s main issue is related to the superposition principle. As Penrose puts it, the basic quantum linearity is obscured in the density operator description. Indeed, an objection of Penrose against the density operator is that the density operator makes complex the simpler linearity of the ket formalism.

So far, Penrose’s arguments equally apply to the density operator and to the density matrix. In pages 797 to 800 of Road to Reality, however, Penrose proceeds discussing what he considers to be the “confused ontological status of the density matrix”, in this case, the argument centers itself in the matrix and not in the operator. Indeed, some of the statements, used as counter-argumens apply correctly to the density matrix but not to the operator.

The major argument refers to the inability of the density matrix to distinguish between different kinds of entangled pairs. For instance, consider the following scheme/example:

Even though we have two different kinds of entangled pairs, the density matrix is the same, that is, the density matrix does not seem to distinguish the bases.

However, this is not the case if we take into account the density operator. The density operators are, not only, different, but if we determine the projection, for instance, of the second density operator with respect to the basis in which the first is represented, we obtain:

Indeed, the second operator is a statistical mixture between two pure states of superposition of 0> and 1> (+> and ->).

What the above results show is that the projections of the second density operator to the basis {0>, 1>} and to the basis {+>,->}, differ, with respect to the probabilities assigned to the quantum events formalized by these projections.

We can use a density matrix for reading probabilities, however, one must never confuse the matrix with the operator, and one must always use the operator, for the fundamental description.

The problems of ontological confusion, raised by Penrose, can be raised with respect to the density matrix but not with respect to the density operator.

This stresses the importance of precision of language, and the issue of the generalized practice of calling the density operator a density matrix (a practice followed by Penrose, and called into attention by Feynman in his Lectures on Physics, as a practical but mathematically imprecise simplification). This must be considered as a simplification of language, as Feynman stressed, but, nonetheless, it is a mathematical imprecision in the usage of the terminology, and, when dealing with fundamental arguments, one must take into account the distinction between the density matrix and the density operator.

However, Penrose’s argument about the phase seems to stand for both operator and matrix, quoting Penrose (2004, p.803):

“Under normal circumstances, moreover, one must regard the density matrix as some kind of approximation to the whole quantum truth. For there is no general principle providing an absolute bar to extracting detailed information from the environment. Maybe a future technology could provide means whereby quantum phase relations can be monitored in detail, under circumstances where present-day technology would simply ‘give up’. It would seem that the resort to a density-matrix description is a technology-dependent prescription! With better technology, the state-vector could be maintained for longer, and the resort to a density matrix put off until things get really hopelessly messy! It would seem to be a strange view of physical reality to regard it to be ‘really’ described by a density matrix (…)”

Although these arguments may seem compelling, one may place a question regarding the statement on the approximation to the whole quantum truth, the question is: what about the so-called 'impure states'?

As Penrose notices, one cannot discard that, at the quantum level, detailed phase relations may get “lost”, because of some deep overriding basic principle. It is still too soon to discard such a hypothesis, and this, indeed, may be likely, if one considers a foamy Planck scale space-time (quantum foam) (Penrose, 2004).

Furthermore, there is still a division in the community in what regards the information loss in black holes. Even if many believe, including, more recently, Hawking (http://arxiv.org/abs/hep-th/0507171), that information may not be lost, we cannot yet reject this possibility.

It seems that, accepting Penrose's argument, leads to the position that if we wish to use a fundamental mathematical description of physical reality, we must use two different formalisms, a ket for the pure states and a density operator for all the other cases, and we cannot discard the need for the usage of the density operator.

Thus, to the first part of our main question (what is the most fundamental mathematical structure that should be used to describe the quantum system?)The arguments seem to point towards using the density operator only when necessary, as a technological tool.

But is this sustainable? Do the phases matter?

The answers to these questions cannot be entirely solved by appealing to mathematics alone.

Indeed, a mathematician might be divided between: (a) a choice where one would work with what can be argued to be a more fundamental structure with respect to the information conserved in the description (the phase information), but two formalisms would be used for two different situations (pure vs impure states); (b) a choice where one works with a single formalism but part of the information (the phase) is lost.

Since we are dealing with physics, all that matters is whether or not the phase is physically relevant, or, even, whether or not the density operator expresses, formally, the most fundamental physical nature, the normalized ket just being a useful representation, that can be shown to be equivalent to the density operator up to a global phase factor.

In effect, so far, all that we can get from the system is the information contained in the density operator. The question of whether or not there might be some technology to recover the phase from a measurement, is still open to discussion.

One may argue that, physically, the phase is irrelevant, one may alternatively argue that the phase is not physically irrelevant. However, to do the latter would demand the mathematical formulation of what might constitute a measurement procedure for the phase, leading inevitably to the problem of the physical meaning and measurability of a complex number.

If one chooses to spend some time with this issue, one is led to this bifurcation of perspectives, where the choice depends less on mathematics and more on physics, in particular, our main question «what is the most fundamental mathematical structure that should be used to describe the quantum system, and what is the nature of the physical semantics that this structure formalizes?» should be considered as a whole, since one cannot really consider the formalism, independently from the object of intentionality of the formalization (that which the formalization is about and that justifies the development of the formalization itself). What is fundamental for the mathematical structures of the formalism, may not be so for the object of formalization.

In the end, the interpretation of quantum mechanics that one follows may decide the choice between the two paths, if one wishes to make such a choice at all, or if, and until, a fundamental thinking about physics demands such a choice.

An interpretation of quantum mechanics that thinks about the nature of quantum processes, inevitably restricts our choices about what is fundamental due to the ontological and epistemological commitments that we assume, along the way of the construction of a scientifically grounded interpretation.

In the interpretations that assign a physical nature to the wave function as corresponding to a pilot wave, the phases are relevant, even if they cannot be measured, since the fundamental object of formalization is that pilot wave.

For a follower of Bohr, on the other hand, the whole discussion would be pointless, since the quantum formalism is just a useful tool used to predict results of experiments, whether we use a ket, a wave function or a density operator is irrelevant.

Furthermore, Bohr was “suspicious” of complex numbers, these could be useful tools, but, in the end, all that mattered were the predictions, and if a phase is unobservable by current technology it is a waste of time to think about it or to assign it a physical significance.

In the Aristotle-based realist interpretation, followed by Heisenberg, the density operator should be taken as the formalization of the fundamental physical structure, since what the formalism “formalizes” is the tendency of a potential alternative to be actualized, this intensity of the dynamis corresponds is quantifiable in terms of a degree, a degree with which probabilities coincide numerically, when these probabilities are interpreted as being proportional to the physical propensity of the potential alternative to be actualized, which is nothing but the intensity of the dynamis associated with that alternative.

Taking this into account, the diagonal terms of the density operator are the fundamental structure, since they are in the direct correspondence with the object of formalization of the theory, i.e., they formalize the most fundamental physical structure, and their interpretation is naturally processual, a processual nature that is obscured by the ket representation.

A closely related mathematical argument can be found in Bohm, Davies and Hiley's paper Algebraic Quantum Mechanics and Pregeometry (http://arxiv.org/abs/quant-ph/0612002), where the authors built quantum theory from the primitive idempotents that are directly related to the different entries of the density operator. Bohm et al. show that the ket notation hides the fact that each ket represents an object with two labels.

Thus, in the end, one’s solution to the phase problem and the answer to the central question placed here, depends on one’s choice of interpretation of quantum mechanics.

On Situation

2008-07-19T10:35:00.000-07:00

By Maria Odete Madeira

The term situation comes from the Latin situs that means relational position or relational disposition of some thing.

The notion of situation has been largely worked upon by philosophy. Besides the scholastic authors, other authors such as Jaspers, Sartre, Merleau-Ponty, Kierkegaard and Heidegger were some of the philosophers that developed philosophical criteria called situationists, in which the situation is thought upon as a concrete and objective reality that underlies all existing things.

Any existent is considered an existent-in-situation, because any existent is one among other contingent existents, situationally launched in the world.

The term world is genetically related to the term nature, that comes from the Latin natura (gnatura, natus, gnatus, nasci), which means to be born. This term has its Greek equivalent in ousia, which means to produce, to give origin to (fazer nascer, faire naître).

Both terms (natura and ousia) are equivalent to the Greek term gignomai, which means to come to be.

Natura and ousia are both related to the Greek term genesiz (birth). All that exists, exists as presence and existence (natura, ousia, dasein).

The Production of Judgments in Kant

2008-07-18T08:24:00.000-07:00

by Maria Odete Madeira

For Kant, the production of judgments consists in thinking the diverse of the empirical experience as if it was contained in a universal.

If the universal is previously given, as a rule, principle or law, indicating, a priori, the conditions in which the empirical diverse can be subsumed, then the judgment is said to be determinant and it is objective. However, if only the empirical diverse is given, the faculty of judgment (existent in all subjects capable of thought and reason) has to find the universal to that empirical diverse, then, the judgment is said to be reflexive, indeterminate and subjective.

For Kant, to judge is, always, an exercise of subsuming the empirical diverse in unifying rules. Be it a subjective or an objective judgment, that judgment has, always, its foundation and its condition of possibility in general rules of unity of synthesis of the diverse of the experience. These rules are considered, by Kant, rules a priori, without which no possible experience could be thought or known.

Thus, in Kant, every general unity of synthesis has its condition of possibility in a reflexive capability, dispositionally existent in all the subjects capable of thought and reason.

On Transdisciplinarity

2008-07-16T02:50:00.000-07:00

by Maria Odete Madeira

No researcher can rigorously identify the border that separates the interdisciplinary from the transdisciplinary work. In question are matters such as individual and collective experiences, processual and methodological convergences and integration of the disciplinary knowledge.

The plurality of the senses and meanings, synthesized by each concept, trigger self-referent systemic lines of fugue that can oscillate between the interdisciplinarity and the transdisciplinarity.

Thus, any transdisciplinary exercise is conditioned by a structuring systemic uncertainty, in regards to the interpretation, comprehension and verbalization of the signs and respective meanings that emerge from the borders of each system involved in the processes.

The great challenge that is placed to the transdisciplinary work is, precisely, the development of techniques and technologies that allow the researchers to capture, in the systems, all the available information about the identity of each of these systems, as well as to capture the respective autopoietic processes involved in the systems’ development, evolution and growth.

on observation and experience

2008-07-09T07:47:00.000-07:00

During the Renaissance, the impulse towards observation trajected and projected new criteria based upon the notion of experience, from the Latin experientia, that signals a sense of proof through which some thing is acquired or learned.

The observation and experience, during this same period, became the basic elements of a new and compulsive rationality, that tried to apprehend quickly the laws of nature, in order to apply them to fundamental methodologies.

The notion of experience became a fundamental notion that oriented itself by criteria of true/objective knowledge, conditioned by two proposals: a notion of experience linked to the empirism, and a notion of experience linked to the critical rationalism.

Linked to the empirism, the experience is defined as individual living experience/action, accumulation of information and evidence of the immediate/qualitative observation.

Linked to the critical rationalism, experience is approached from criteria of quantitative/repeated qualitative, compared, transmissible with fundamentation and pluripersonal observation. The accumulation of information does not constitute evidence/certainty and the individual experience is considered only in terms of specific information.

On Transcendental - Aristotle, Aquinas, Kant and Husserl

2008-07-01T01:00:00.000-07:00

By: Maria Odete Madeira

The notion of transcendental assumed, in Aristotle, a metaphysical sense of characterization of attributes, such as, the unity, the true and the bene.

Thomas Aquinas assumed Aristotle’s transcendental attributes and added other two: res and aliquid.

Kant introduced a new sense to the notion of transcendental, relating it to the Copernican Revolution, thus, this notion that, until Kant, was taken in a "formal-logical" sense that fundamented the things in themselves, after Kant, came to constitute the condition a priori of the possibility of something to constitute itself as a phenomenon and object for any subject capable of thought and knowledge, in this way, concepts or categories assumed the value of transcendentals and, because of that, existed, according to Kant, a priori (dispositionally) in each human subject.

The transcendental no longer operated at the fundament of the things in themselves, but, only, at the fundament of the phenomena and respective objects of knowledge for any subject capable of knowing.

Husserl maintained the Kantian sense of the term, but radicalized it by making the reduction to subjectivity (epoché) as the ultimate fundament of the sense and validity of the experience.

Why something and not nothing? Why the entity and not nothing?

2008-06-27T08:41:00.000-07:00

by Maria Odete Madeira

"Why something and not nothing?” (Leibniz) Nihil est sine ratione; “Why the entity and not nothing?” (Heidegger).

The matter of the foundation of the Being is a good, endless and disturbing metaphysical question that started with Parmenides and was lengthily developed by Heidegger.

Schelling placed the question of the foundation as a self-position of the Being unfolded in two positions: one as Absolute in itself and another as the other of itself, this last, reciprocally presupposed in a circular topology.

By placing itself as the foundation of itself, the Being placed itself in existence, as a difference from which all things come.

For Heidegger, each entity is one of the modes of the Being, and, each entity, is also its difference, each entity is the being-there (dasein) referring to itself (ek-sistence).

The truth of the Being (aletheia) belongs to the Being itself, Being physis is aletheia. The Being gives itself (es gibt) as Being and Time and, thus, as something that has given itself, the being is event (Ereignis), the logos that wants to be heard.

Love (Hegel, Höderling, Unitrinity, Schelling...)

2008-06-26T08:35:00.001-07:00

by Maria Odete Madeira

Hegel and Höderling introduced a new thinking about sensitivity, in opposition to the anguish and insecurity before alterity (natural, personal and social), that were at the origin of Aufklärung.

This new thinking tried to capture and recuperate the pulsional dynamism and the affective dimension that constitute the human being.

The issue of love was developed as a reply to intrinsic problems and to an internal determinant dialectics, that operated as function of synthesis in the system, that is, a middle-term between the theoretical order and the practical domain.

Love was incorporated, in Hegel’s logical system, as fundament of the harmony of the “Spirit”, in its function of unification of reflexive and effective synthesis of the thought and the feeling.

Love configurated, in Hegel, the dialectical motion of reason, as exposition, negation and return of reason to itself, surpassed. The loving dynamics adequately described the character of the “Absolute” as a fundament of itself, that is, the reconciled return to itself, from its other (Vorlesungen über die Ästhetik, Theorie Werkausgabe).

A different thinking about the feeling of love, seems to come from the notion of Unitrinity, that inscribes itself in the kenosis of the Son (Christ) that reveals God’s mystery as love, a gift that inscribes in space-time an ineffable exchange within the divinity itself. That is, the love as a feeling towards the other, because God as unity does not exclude the other (Son), the Son is already within divinity itself as object of intentionality, for the realization of the love, realizing what can be considered a Superunity (Pseudo-Dionysius the Areopagite).

In the unity, the feeling of love is already a communion with the other without negation, unlike Hegel, and closer to Schelling.

One cannot find, however, in any philosopher, a feeling without an intentionality, without an underlying reason for its being, in the case of Hegel this reason is to be negated and surpassed.

In a neurobiological framework and in a philosophical framework, both feelings and emotions possess an unsurpassable intentionality, they are always about something (their object of intentionality) that relates the individual/agent/subject with his/her environment (culture, civilization, people, recollections, artifacts, etc), possessing a fundamental adaptive value.

Love (Hegel, Höderling, Unitrinity, Schelling...)

2008-06-26T08:35:00.000-07:00

Epicurus - Clinamen

2008-06-23T07:44:00.000-07:00

by Maria Odete Madeira

While disagreeing, with regards to the topos of the universal essences, Plato and Aristotle were in agreement with regards to a fundamental point: the scientific discourse (episteme) could only be considered as true when that same discourse satisfied criteria of universality and of necessity. Thus, it was demanded of the inquiry to find the foundation of any statement of truth or of falsehood, in what were the first causes and the first principles of the things, themselves.

In this way, in order to have discursive rigor, the matter and its forms or essences (eidos) should be analyzed separately as different things, both in terms of their identity as well as of the value that was assigned to them. The epistemic analysis of one should not contaminate, interpretatively, the epistemic analysis of the others.

The object of knowledge, that object's matter and its form or essence, as well as its meaning and definition, obeyed, for Plato and for Aristotle, rigorous criteria of appropriateness and agreement, that would allow a general deductive semantics. These criteria prolonged themselves in Euclid’s geometry and in the statics of Archimedes, both based upon a system of axioms that constituted self-evident truths, and upon a system of theorems derived from those same axioms.

The semantic determinism of the Greek scientific discourse was generalized as an epistemic model until Epicurus, distancing himself from the primitive atomism of Democritus, introduced the notion of clinamen (declination) as a capability, an arbitriu that the atoms have to deviate themselves spontaneously from their trajectories. Thus, Epicurus incorporated, in the philosophical and scientific discourse, an irreducible element of unpredictability at the epistemic level, absent up until then, with ontological and epistemological consequences about that which was considered as criterion of truth.

Without putting into question the “general laws of nature”, known at the time, the author localized a present and permanent dispositional element of constitutive arbitrariness (arbitriu), in any process of formation of emergent structures, as an element incorporated in the dispositional genetics of these same structures with consequences at the level of the systemic perception and cognitive processing/computation, and at the ontological level of the threat of destructuration and the opportunity of structuration, present in any physical existent, and that function as mechanisms of potential risk (linked to the mechanisms of life and death) and, thus, undetermined, permanently displaced, within the structure itself.

About the Life of Knowledge and the Knowledge of Life

2008-06-07T11:30:00.000-07:00

by Maria Odete Madeira

Any production of knowledge is supported by an organizing activity that acts in accordance to rules that have, as their objective, the resolution of problems that promote the organism’s survival and adaptive fitness.

The discovery of the double-helix, by Watson and Crick, allowed the application, to the notion of living organization, of the cybernetic scheme of a machine governed by an informational program, inscribed in the structure of the DNA molecules, that organizes and directs all the activities of the cellules (Morin, 1986).

In this way, a living organization can be signaled and referred as a self-cognitive, self-organizing and self-replicating agent that is capable, through exchanges with the environment, of concentrating, in itself, the flows of order that feed it and sustain it as a spatio-temporally localized individuated structure.

The knowledge of the life of the systems introduces us to the life of the knowledge, itself. Being, doing and knowing are, thus, inseparable.

The development of communication networks, between the different agents, allowed the transformation, of the natural flows and turbulences, in the subjugated motricity that was at the origin of the human space of millions of years ago, and that can be signaled as a bio-anthropological space aimed at the satisfaction of the biological needs of survival and of the immediate and practical interests, full of feelings and emotions, fantastic visions and terrors, but also full of techniques and precise calculations, synchretically linked to the objects.

In that historical time, the time of the myth, the interface with the environment was profoundly biological, accompanied by that which Damásio (1999) designates by core consciousness, characterized by a weak grasping ability and a weak reflexive operativity that did not allow the exercise of abstract thinking.

The type of thinking produced was profoundly linked to the aleatority of the motion of the natural forces, whose nature revealed itself as powerful, threatening and dramatic.

In this way, the production of judgments exhibited a perceptual and conceptual pattern that allowed the hominidian networks to signal, identify an classify the ecosystemic space, as a fluid and fluctuating nature, determined by local dynamic, unstable, coevolutionary and organic rules, foundationally conditioned by locally emergent mechanisms of territorialization and deterritorialization, rhizomatically aleatorial, producer of myths (meudh, mudh, myo, mytheo, mythos) and of rites, linked to the vital emotions and feelings of immediate survival and creators of visual, tactile, acoustic, and olphactive action spaces, conceptually non-schematizable, but that interacted with the strategic calculus that allowed the development of techniques of working the stone, then the bone and, also, the metal, as well as the development of cognitive memories, associated with the knowledge of the plants, of the animals and of the environment.

From the passage of the mythological thinking towards the so-called rational thinking, the knowledge came to be explicitly referred to as kosmos, or order, and as logos, term of Greek origin, derived from the verb legein that, originally meant to gather, to enumerate or to choose.

In turn, the noun logos, that initially meant collection and (re-)collection of the multiple, came to mean the discourse or language.

The kosmos and the logos, that substituted the myth as an attempt of interpretation and explanation of the reality, in its complexity, corresponded to the development of the capability of the organismic human grasp, accompanied by the expansion of consciousness.

The core consciousness, thus, lost operative protagonism to the extended consciousness, which came, since then, to operate in the interface with the environment. In accordance with Damásio (1999), if core consciousness is the indispensable foundation of consciousness, extended consciousness is its glory.

Unlike core consciousness, extended consciousness allows to work on temporally more expanded interaction surfaces, connectable to mechanisms of retension and protension.

Unity and System

2008-05-05T06:57:00.000-07:00

by Maria Odete

The unity (unitas, atis) is a syntax that can be operationalized to capture, in the systems, that which, in them, is about their internal cohesion, consistency and coherence.

These internal systemic properties (cohesion, consistency and coherence), enactively produced by the system (Varela), signal, refer and identify the system as a being or entity, and, therefore, also an identity.

The system, considered in terms of its individuation, bearer of an identity, is, thus, signaled as a concrete spatio-temporally localized existent in permanent rotative coincidence with itself.

In this way, from an ontological approach, the unity can be thought of as a concrete relational existence, coexistent with that which, in the system, is multiplicity, division and dispersion.

If it is the case that, to form itself, the system needs the existence of a principle of unity enactively present in the system itself, it is also the case that the existence of that same principle of unity depends, constitutively, upon the capability of the relational dynamics of the system to produce and operationalize that principle of unity as a permanent organizing principle, dispositionally available in the system, and that can be thought of as an ontological, logical and epistemological attribute that makes any judicative syntheses about the nature of the unity of the system dependent upon the relations that are coexistent and actively present in the system, since the unity itself of the system is grounded (urgrund) upon those relations.

In this way, the unity can be consistently considered, in the statements, as an organizing principle, systemically synthesized, monadologically complex, relational and in network.

Without relations there can be no systemic unity.

On Mathematics

2008-04-27T12:02:00.000-07:00

by Carlos Pedro Gonçalves

In formulating the question “what is mathematics?” it is important to notice that the intellectual matrix and structure that underlies our concept of mathematics is Greek. This should not be confused with a statement that mathematical activity started in Greece, it does mean, however, that our usage of the term mathematics and our conception of what it means to “do mathematics” has a Greek root.

Thus, in trying to answer the question “what is mathematics?” we should, perhaps, first look at the Greek root of the word mathematics, which is mathematike which comes from manthein (to learn, to study), meaning learning, study, science. It is also important to look at the expression mathematike tekhne, which places mathematical activity as science techne, in Latin being translated to ars mathematica.

As a science techne, the mathematical activity tries to find the quantities, structures and patterns exemplified by the things, and builds an abstraction of these quantities, structures and patterns that allows the study of these quantities, structures and patterns in themselves, in their nature and generative mechanisms.

Fundamental Asymmetries

2008-04-16T09:29:00.000-07:00

by Carlos Pedro Gonçalves

“Again we have to ask whether, in particle physics, fundamental structures of nature have been found. I think one can say that the fundamental symmetries have been revealed. The term fundamental symmetry means that the natural law which determines the spectrum of particles and their interactions is invariant under certain groups of transformations. These groups define the total space in which the real world occurs (…) Such a radical change in the conceptual framework of science – from the fundamental particles to the fundamental symmetries – is not easily accepted (…)”

Heisenberg. 1974. The Role of Elementary Particle Physics in the Present Development of Science.

Fundamental Asymmetries

Should physics focus on fundamental symmetries and consider the symmetry breaking an anomaly, or are there fundamental asymmetries that play a foundational part in the cosmogenesis? Are symmetry breakings of fundamental symmetries physical anomalies with respect to what would otherwise be a mathematically and aesthetically elegant symmetrical world? Or are symmetry breakings themselves fundamental? Should we search for physical laws expressed in terms of fundamental asymmetries?

Quinn and Nir (2008) addressed this issue with respect to the fundamental cosmological puzzle of the asymmetry between the number of particles and antiparticles, on an article in New Scientist No. 2651, 12 April, 2008. Their review of the problematic and their reflections upon the subject resends us to the problematic of the origins, and the first causes and first principles of the universe. For context, it is important to consider the following quote from said article:

“The stars and galaxies that light up the heavens would not exist today if matter had not won over antimatter at some very early time in the evolution of the universe. How and when did this happen? Why is there something rather than nothing? These questions are at the root of our very existence, but as yet science has no clear answers.”

For our universe to be the way it is, a matter dominated universe, an imbalance had to take place, in the very early universe, between matter and antimatter. As stressed by Quinn and Nir, it only needed to be a minute imbalance, with as few as one extra particle of matter surviving for every thirty million antimatter particles.

As also stressed by Quinn and Nir, this couldn’t occur by chance, even such a small excess is too large to occur as a random fluctuation in the hot, early universe.

So the question can be raised about the nature and the role of fundamental asymmetries in the birth or the universe and in process of formation and organization of the cosmos.

Looking at the evidence, a first pertinent question, on this regard, is the one posed by Quinn and Nir: “was the cosmos born lopsided?”

If the asymmetry between matter and antimatter had been an initial condition, it would be, as noticed by Quinn and Nir, a very peculiar one. By studying the amount of initial light elements from the early universe, one can advance with the conjecture of the proportion of asymmetry being one surviving particle of matter per thirty million antimatter particles.

Such a proportion is unlikely to be the result of a pure chance, an aleatorial intruder on what is a fundamentally and foundationally symmetric universe. However, if there was such a lopsided beginning, the evidence regarding inflation, seems to point towards a physical memory loss of any eventual structures that might be present in the initial conditions of the universe, including an asymmetry, due to the rapid expansion of the universe. This seems to point towards the conjecture that the excess of matter was generated after inflation.

Ultimately, however, we are led to question ourselves about the nature of inflation and what it does to the laws of physics, in particular: “should a fundamental process lying at the origin of the lopsidedness be changed by inflation, or is that origin conserved with inflation continuing to act in the cosmos after the inflationary process ended?”

If the universe did indeed begin lopsided, and if the physical foundations of that lopsidedness had their origin in some fundamental physical laws, that explained the asymmetry, then, one may be led to question whether those laws could or not be changed by inflation. If they were not changed in the post-inflation cosmos, then, it is reasonable to consider that the post-inflationary origin of matter/antimatter asymmetry finds its explanation in the same fundamental reason underlying the hypothetical lopsided initial condition. The questions in this case are: how much memory loss does inflation entail? What were the physical laws before inflation and how did they change after inflation?

In terms of physical theory, this leads to the problematic of the systemic nature of the laws of physics. Which is a still open problem.

Quinn and Nir offer a critical reflection upon the different attempts to explain the asymmetries. The first attempt, by Sakharov focuses upon a conjecture about a possible “legal void” in the laws of physics, more specifically, Sakharov argued that there is no physical symmetry principle governing a conservation law that can forbid reactions that effectively change the balance between particles and antiparticles.

It would then appear to exist a legal loophole that allowed particles and antiparticles to differ in numbers. From a logical and ontological point of view we must necessarily state that since there seems to be indeed an observed asymmetry then that asymmetry must be physically possible, which, using the notion of physical possibility from modal logic and from metaphysics, means that we are led to the conclusion that there is no law or laws of physics that imply the negation of an asymmetry between matter and antimatter.

But from a physical possibility of asymmetry to a physical necessity of asymmetry, there is a great difference. To speak of a physical necessity of asymmetry, we would have to find a physical explanation for it that would establish that asymmetry with a character of physical necessity, and, in that case, we would have a physical law not based upon a symmetry principle but, instead, based upon an asymmetry principle.

As Quinn and Nir stress, Sakharov did provide for what can be considered to be a statement that points towards an acceptance of an asymmetry principle, this principle being at the basis of a statement of necessity about the physical possibility of a matter/antimatter asymmetry. In order for such a physical possibility to be physically necessary Sakharov defended the existence an asymmetry in the laws of physics themselves, more specifically, the laws of physics would have to be different for matter and antimatter.

This fundamental asymmetry in the laws of physics was confirmed experimentally with particles called long-lived kaons. These showed that the weak force does not act equally on quarks and antiquarks.

Finally, Sakharov defended that a third condition had to occur in the early universe, in order for the imbalance between matter and antimatter to take place. According to Sakharov there would have to have been a period, early in the universe’s history, when the various reactions occurring between the different particles, antiparticles and radiation in the primordial plasma, started to take place at different rates, which can only occur through a deviation from thermal equilibrium (another asymmetry – a thermal asymmetry).

This could explain how a universe with initial equal amounts of matter and antimatter could evolve, from that initial state, to an asymmetric state.

The Sakharov’s proposal remains theoretically relevant today, acting as an important guide for our theories of the early universe, and providing for an important conjectural framework in regards to the matter/antimatter asymmetry.

Nonetheless, this is still an open problem, and it provides for one of the most clear examples that may support the theoretical discussion about the fundamental role that asymmetries may play in physics.

In the same way that Heisenberg found problematic the acceptance of a change in the theoretical focus from fundamental particles to fundamental symmetries, the acceptance and search for fundamental asymmetries, and the formulation of physical laws of asymmetries, may also be problematic. Especially since, from the moment in which we accept asymmetry principles within physics, and discuss their role as a fundamental part of nature, then, we are led to the uncomfortable problem of not being able to ignore as mere noise the non-realization of some exact symmetry in nature, when that symmetry plays a foundational role in the theory itself.

The Death of John Wheeler

2008-04-14T13:56:00.000-07:00

by Carlos Pedro Gonçalves

“I like to say, when asked why I pursue science, that it is to satisfy my curiosity, that I am by nature a searcher, trying to understand. Now, in my eighties, I am still searching. Yet I know that the pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before. Somewhere in the child that urge is born.”

John Wheeler, Geons, Black Holes and Quantum Foam, p.84.

The passing away of John Wheeler:

http://jayryablon.wordpress.com/2008/04/14/john-archibald-wheeler-rip/

The “it from bit”

The “it from bit” is a fundamental perspective about the foundations of quantum theory, and about the nature of the universe.

Given the choice, by Wheeler, of the Aristotelic realistic framework, the philosophically consistent interpretation of the “it from bit” means that an actualized reality (the it) comes from a question that nature asks itself, as a result of a particular kind of physical interaction where a quantum system is “asked a question” about the pattern of exemplification of a physical property, such a question is of such a nature that it begs a yes/no answer on the part of the system, hence, the term the it (actualized reality) comes from the bit.

A physicist would state, using the terminology proper of quantum theory, that a decoherence inducing interaction would produce a local diagonal density operator with respect to an expansion of some observable’s eigenbasis, an eigenbasis to which the “observing system” is physically sensitive. The “observing system” does not need, according to Wheeler, an elaborate level of reflexibility, something as simple as a piece of mica, for instance, does the job!

The term decoherence refers to the process that produces a local loss of interference terms of the system’s state. Through the decoherence process, the system’s environment interacts with the system in such a way that an entanglement is produced with respect to a certain observable’s eigenbasis.

Thus, for instance, if there is a system of particles that effectively acts as an obstacle that is able of localize the particle, the potential regions of localization correspond to a correlated potential state of the particle’s position and a potential state of the system of particles. The positioning pattern of interaction introduces a decoherence with respect to the position observable. Informationally, this can be considered to correspond to a yes/no question placed by the system of particles to the particle. Prosaically, the system of particles asks the particle, with respect to each potential region of localization: “Are you here?”.

A typical physical experiment of this is the double slit experiment.

Now, what Wheeler states is that when the particle is asked this question, and when decoherence occurs, the branching of potential alternatives forces a “choice” of a potential branch to be actualized. This actualization depends on the degree to which each branch tends to be actualized, which is nothing but the measure of the intensity of the dynamis or potentia. As it is the nature of the dynamis to tend towards the act.

In terms of quantum cosmology, this is a perspective with fundamental consequences:

- Before the actualized universe we have to consider a myriad of potential universes, each tending to be actualized with different propensities;

- A quantum computation inducing entanglement had to take place that led to the actualization of a given universe, or, at least of some characteristics of the universe.

The second point makes us question the nature of the first event. Either there was a single actualized event that originated the universe, which would mean an initial maximal entanglement with respect to the relevant cosmological observables, or, there were a series of actualizations that processually produced the final result of the big bang. Wheeler admits the theoretical possibility that some parts of what could be considered to be in the universe’s past may only be actualized some time in the future. This is visually expressed by the Wheeler’s eye (see beginning of the article), which pictorically represents the question placed by Wheeler: Does looking back “now” give actual reality to what happened “then”?

About this question Wheeler defends that the point is that the universe can be thought of as a grand synthesis, putting itself together all the time as a whole. Its history is, in this sense, not a history as we usually conceive history. It is not one thing happening after another after another. It is a totality in which what happens “now” actualizes what happened “then”, determining what happened then.

The Conceptual Confusion between Potentia and Possibility in Physics

2008-04-13T05:24:00.000-07:00

by Maria Odete Madeira

Some errors of interpretation of philosophical concepts used in science lead to fundamental problems at the root of the theories, when these concepts play a foundational role in the edifice of that theory. An example of this is the statement, by Heisenberg, of an equivalence between dynamis (potentia) and possibility.

Heisenberg established, incorrectly, an equivalence between the Aristotelic notion of dynamis and possibility.

The dynamis and the possibility are two distinct notions, both logically as well as ontologically. All existing things, situations, events, beings or entities, are contingent things, and, because of that, are, as such, subjects of change, in this way, all physical existents are a composite of dynamis (potentia) and energeia (actus), the dynamis being as real as the energeia.

The dynamis that composes each physical existent is, logically and ontologically, a principle and, also, a temporal moment of determinable indetermination, its determination being done by the energeia that corresponds to it, logically and ontologically, as its principle of determination. Every situation, event, being, entity is constituted by these two principles: dynamis and energeia.

The possibility is an abstract term of any language, be that language logical, epistemological or ontological. The possibility designates the intelligible structure of the possible: possible is all that can be or not be, without logical contradiction.

Any physical existent has in itself, as such, its own possibility, as a neutral element that precedes and accompanies it along its existence. All that is, or exists, must be possible to be or exist, because it, effectively, is, or exists, and, equally, all that is not, or does not exist, must be possible not to be, or not to exist, because it, effectively, is not.

The category of possibility is, in the motion energeia/dynamis/energeia, logically and ontologically, a neutral element. One can talk about a determination of the dynamis by the energeia, and, thus, of an actualization, but one cannot talk about an actualization of the possibility, nor establish an equivalence between the notion of possibility with the notion of dynamis.

On Metaphysics

2008-03-31T08:40:00.001-07:00

by Maria Odete Madeira

The term metaphysics (ta meta ta physika) was introduced by Andronicus of Rhodes to classify a collection of texts of the Corpus Aristotelicum that concerned those matters that did not have place in the books of physics.

Metaphysics refers to the branch of philosophy that studies the first causes and the first principles of all things.

As a science of the first principles and the first causes of all existing things, metaphysics is an archeology (arche). As science of the being as being it is an ontology.Metaphysics is irreducibly a philosophical concept about the first causes and the first principles of all existing things. One must stress that we are not addressing anything that is outside the universe (kosmos). Indeed, every physical object is also a metaphysical object, in its connection with its first cause and first principle, as its foundation.

In this way, as a methodological criterion, metaphysics concerns the foundation of all the existing things as such. It is, thus, about researching in the things themselves, that which in them is present as their originary and originating condition, which means that a metaphysical research demands that one questions the foundation itself, that, as such, is present in the things, themselves, as that which maintains them and sustains them as entities, identities and integrities existent and subsistent, in themselves and by themselves.

The foundation is a principle of reason and, thus, of proportion or number. As Leibniz stated “nihil est sine ratione”. The foundation is incorporated in the nature of the things themselves, as their possibility as existent things, in themselves and by themselves (autonomy).

That which the metaphysics strives for is to find not only that proportion but that which preceded it. It is no longer, in this last case, about researching the being, entity or identity, but about questioning the foundation itself, and, thus, searching for the originating principle of the foundation itself, as its existing potential (Aristotle) anteriority, that is, what ordering principle (number, pattern, order) underlies the foundation itself as an existent foundation of each individuated existent.

Whenever a cosmologist is talking about the first causes and the first principles of the universe, inquiring about the nature of the laws of physics, or upon the foundations of physics he/she is in a metaphysical inquiry, having to make an effort to interpret that which exists in the world and in the cosmos outside his/her logocentrically conventioned closed mental models, which, in many cases, and in an abusive way, are called metaphysical models, putting into evidence a total lack of knowledge of the notion of metaphysics itself.

Music and Eternity

2008-03-14T03:31:00.000-07:00

By Maria Odete Madeira

The myth assigned music a divine origin. The Pythagoreans, in turn, referred it (music) to a metaphysical acoustic, in which the intervals and the numerical relations, underlying the relations of consonance, were considered to the formulation of a doctrine of the ethos of the tonality, of the rhythms and of the instruments, all of this correlated with the effects produced in the listeners.

The order of the world and of everything was configured by the harmony and union of the diverse (Philolaus), and this harmony was determined by numerical relations. The soul of each man, as sound, could enter in tune with the order of things and with the music of the spheres.

As Mathesis Universalis, music can be considered as a combinatorial topology of signs that expresses in a hieroglyphic resonance that which the logos hides, Leibniz called it the hidden exercise of an arithmetic of the soul.

This is about questioning the organic and trans-organic feeling (the nostalgy in Mähler/Adorno) about the temporality and trans-temporality to attain an outside of the chronological time an urgrund (Schelling), and hence concurrent with the first creation.

Musicality is not necessarily restricted to musical pieces. Letters and phrases evoke sounds, and it is possible to convey an additional sense through the topological motion of the verb. The written text has a musical semantics and syntax naturally embedded through the resendings between the written text itself and the verbal articulation (even interior to the reader) of that same text.

Each written text resends towards a metaphysical sense as its first cause. The text is not surrounded, but crossed through by its limit, marked in its interior by the multiple tracks of its margin. Proposing simultaneously the monument and the mirage of the trace (différance, Derrida, Marges de la Philosophie), the trace, simultaneously marked and erased, simultaneously alive and dead, lives, as always, from simulating the life in its kept inscription.

Schopenhauer considered the existence of an infinite will, independent of all the individuation, existing in any living being as an infinite principle, unique and indivisible (or noumenon), without any connection to space/time/causality that, for Schopenhauer, constituted the principium individuationis. This will objectivates itself as an eidos, accessible through art, revealing itself in music as direct and immediate presence of a transcendence (a perspective that Wagner’s music exemplifies).

As Schrödinger (What is life?) stated, in the work of art, the aesthetical experience of direct and immediate apprehension of something, of some sense that escapes the sayable record of "spacetime", is only possible through music. Steiner (Grammars of Creation) states that music signals and puts in resonant motion that which, in humans, exists as noumenon.

Spinoza's conatus

2008-03-11T06:41:00.000-07:00

by Maria Odete

Spinoza considered the exercise of human reason as an intense desiderative activity in which the desire could obtain the plenitude of satisfaction. The reason, as ratio cognoscendi, positions itself as a terminal phase of the desire and as the complete satisfaction of that desire.

Spinoza's conatus, that influenced Nietzsche so much, was thought of as a primordial energy or potentia that exceeded the human reason and in which the desire had its origin. Man was first defined by Spinoza, in the book III of ethics, as a conatus, and, only after, considered as a rational being. The conatus is active and in act and explicates itself by the power of being affected and, because of that, possesses a tendency to maintain at the maximum the capability of being affected.

The thought is an attribute in a permanent circuit of resendings to the conatus or potentia and, it is, by itself, all the objective condition that the absolute potentia of thinking possesses a priori as unconditioned totality.

Damásio (2003) interpreted the conatus as an impetus of self-preservation in permanent actualization, locating it in the cerebral circuits as an aggregate of dispositions that, once activated by the internal or external environment, represent themselves by chemical and neural signals and lead to a search for overlife and well being.

Nietzsche - the übermensch

2008-03-11T02:20:00.000-07:00

by Maria Odete Madeira

The übermensch announced by Zaratustra, was a protoplasmic figure synthesized by the dionisiac universe created by Nietzsche, who, affected by the profound suffering caused by his illness, invested all his creative potential in an individuation, which he called the übermensch and that dragged him to a metaphysical rotation. The human was, for Nietzsche, the deformity and the nausea. The übermensch was, himself, Nietzsche, considered by Nietzsche as an archetype self-creating instinct freed from god and gods, tensionally fragmented and permanently reconfigured in a territory of forces in permanent becoming.

The übermensch, configured from flows and reflows of forces of life, of madness and of death and, despite the suffering, and because of the suffering, amor fati, but the love of a fate metaphysically projected. Nietzsche was, himself, and in himself, amor fati.

http://en.wikipedia.org/wiki/Ubermensch

http://joe-jitsu.spaces.live.com/blog/cns!D25B2ECC7C29CB05!341.entry

Time and relativity

2008-03-09T15:41:00.000-07:00

by Maria Odete Madeira

Relativity theory applies to our universe, but beyond our universe, we can only conjecture, and inside a field of scientific reasonableness and plausibility any conjectures can be considered pertinent.

The question of the physical existence and nature of the time proposes irrecusably the conjectural problem of its origin, and, in this way, it is pertinent the construction of possible scenarios open to whatever cosmological models.

It seems to be irrecusable that the cosmic fabric that constitutes the time, as being or physical entity, from which we may perceive general patterns and laws, would have to be potentially available.

The potentia or dynamis is an ability of something without form, and, because of that, undetermined, to be capable of gaining form or determination. The potentia is nothing more than a principle of change and movement to an act. Some thing that is potential has the ability to of enduring indefinitely as potentia, or of being concretely determinated (act, energeia).

The model of Einstein functions for the time coupled to the space, but does not explain anything about the time in itself, about its intrinsic nature and origin, and we do not have any physical evidence of the validity of Einstein’s theory of relativity at the beginning of the universe.

Besides that, to approach the matter of the origin and nature of the time, we have to uncouple it from its relation with space, in the sense that time, not space-time, is our object of discursive intentionality. And a question that becomes unsurpassable is that of the physical integrity of the time, as, for instance, the coincident and permanent ontological rotation that time has with itself in each present moment, and that in no way can be considered relative, this rotation has to be considered absolute, in any other way, the time would lose its integrity and we would not be here talking about it.

And it is precisely here that it becomes important to work out the question of the eternity, disambiguated from the various religious senses.

The notion of eternity (aeviternitas, aeternitas) has an original and originating meaning of absolute permanence with oneself that all things, considered as existents and totally present in each moment, have.

time and motion

2008-02-25T08:13:00.000-08:00

The concept of motion belongs to the categories of property and relation, and can be defined in a restricted sense, in which motion is mechanic and local, and can be exemplified by the variation of position of a physical body, in relation to another physical body, both situated in the same space-time, which is the fundamental condition to the possibility of the physical displacement itself of each position, that is considered and relationally quantizable as available information.

In a general sense, the motion means any change occurred in space-time, informationally available: substantial or accidental, quantitative or qualitative.

In a mathematical definition: the motion is the function or variable relation between space and time.

The space and the time are scalar quantities or numbers of motion that give us the quantitative dimensions (points and instants); the velocity is a vector quantity that gives us the qualitative dimension (variation).

The mathematical function can be represented, in analytical geometry, by the vector or kinematic line, in the plane O(x,y): e = v.f(t). And also in the complex plane (of Gauss): O(e,ti), where e is a real number, ti is an imaginary number and v is a vector.

The properties of motion: it is continuous, relative and irreversible. The continuity can be proven by the notions of cut or of limit: v = {P – I}<->C. The relativity of motion can be real and metric.

The motion is a fieri of space-time, produced by the displacement in space-time of the individuated informational patterns, available for measurement and accessible, unconditionally, from that same space-time.

If we want, with legitimacy, to assume the existence of motion, then we cannot make statements such as: the time does not exist.

If there exists motion, then the time must exist in some way. The fact that we cannot provide a good, realistic and consistent definition of time that is consensual, in terms of evidence and clarity to all, does not allow us to make a categorical and definitive scientific statement that time does not have a physical existence. We still do not have a unified physics and we still know very little about the fundamental nature of the universe.

We cannot go on applying, with legitimacy, the easy rule: the problems that we cannot solve, simply, do not exist. If science is today in a critical stand-off, it is greatly because we consider that reality is just that reality which is considered by our measurement instruments.

If we want to exclude time, then we must change the main physical categories and quantities with which we work, this includes the concept of motion. If we negate the existence of time, then we must also negate the existence of motion.

What is the time?

2008-02-24T03:38:00.000-08:00

by Maria Odete Madeira

The statement: the time is! Makes irrecusable the tautology that, as such, the time is the time, which legitimates the statement that the time is an entity and an identity and, thus, the time is a physical existent, an individuated nature, or a singularity.

But what is the time? Any attempts to answer this kind of questioning demand some exercise of reflexibility that relates the questioning itself with a general notion of origin. What is the time? That is a fundamental question that, as such, demands an, also fundamental, scientific approach. And this because the origin of the time, according to the general notion of origin, does not coincide with the time itself. The origin of any physical existent (being or entity) is topologically and processually before its absence.

The origin of the time, or the origin of whatever thing that is, situates itself, in a rotative potential (dynamis) ontological interval, as a tendency for its respective actualization (energeia).

Metaphysics...

2008-02-14T08:04:00.000-08:00

by Maria Odete Madeira

The term metaphysics (ta meta ta physika) refers to the branch of philosophy that studies the first causes and the first principles of all things.

As a science of the first principles and the first causes of all existing things, metaphysics is an archeology (arche). As science of the being as being it is ontology

Metaphysics is irreducibly a philosophical concept about the first causes and the first principles of all existing things, one must stress that we are not addressing anything that is outside the universe (kosmos). Indeed, every physical object is also a metaphysical object, in its connection with its first cause and first principle, as its foundation.

Whenever a cosmologist is talking about the first causes and the first principles of the universe, inquiring about the nature of the laws of physics, or upon the foundations of physics he/she is in a metaphysical inquiry, metaphysics plays an important part in today's cosmology, a fact that is undeniable and widely known throughout the scientific community. When one does research about the foundations of science one is also within a metaphysical context of discourse.

Defining Knowledge - About Intentionality

2008-02-09T15:08:00.000-08:00

by Maria Odete Madeira

Aristotle introduced the concept of intentionality, when he worked in the problem "relation/knowing", having concluded that the mode of reference of a particular individual's idea to the object constituted the intentionality of the individual's idea.

The medieval scholastics returned to the concept proposing, for it, the expression "intendere arcum in" (the act of pointing an arrow towards something). Intentionality, in the philosophical sense of the term, simply means an aboutness, that should be interpreted as a directedness towards something.

The mechanism of intentionality applies to any entity that may be considered as an agent dispositionally gifted of a strategically operative internal structure. The origins of life can be traced to the origins of agency, the biological activity possesses, foundationally, in its adaptive nature an intentional drive, as the organism actively addresses (is directed towards) the environment and its own survival.

The self-replicating macromolecules, the thermostats, the amoebas, the mice, the bats, people and, even, chess playing computers are intentional systems (Dennett). In a more general sense any complex adaptive system is an intentional system (Holland; Gell-Mann; Damásio).

All living organisms, both those that are made up of a single cell, as well as those that are made up of billions of cells are systematically formed by spatialized intentional structures, temporally permanent, strategically committed to their survival, limited by borders, in permanent interface with the environment, depending, the individuality of each organism, upon the existence of that border.

A living organism such as an amoeba, being alive, it is strongly committed to keep on living. Being a creature with no brain, certainly it is not aware of the intentions of its organism in the same way that an organism with a brain may know its organism's intentions, nonetheless, the tiny creature exhibits in a very dynamic and effective form of intentionality in the way it is able to maintain the chemical profile of its internal milieu, while, around it, in the external environment, everything changes quickly. As Lewontin stressed, all living organisms have the ability to act in function of time and of regulating biological rates which, in mathematical discourse, is equivalent to stating that they also make integral and differential calculations.

Defining Knowledge II

2008-02-04T10:05:00.001-08:00

by Maria Odete Madeira

We can talk about the knowledge as an existent, in itself and by itself, trying to define it, as such, or we can talk about the knowledge, from its production or its creation.Any production of knowledge is supported by an organizing activity that acts intentionally according to rules and whose objective is the resolution of problems and its own replication. The discovery of the double helix, by Watson and Crick, allowed one to apply, to the notion of living organization, the cybernetic scheme of a machine governed by an informational program, inscribed in the structure of the molecules of DNA, that organizes and runs all the cellular activity. In this way, a living organization can be signaled and referred to as a self-cognitive, self-organizing and self-replicating agent that is capable, through exchanges with the environment, of concentrating in itself the flows of order that prevent its disaggregation. "Being, doing and knowing are inseparable" (Morin).The access to knowledge, as well as any attempt of definition, can only be made, through the activity of the organizations, of the agents, of the beings or entities, or of the subjects, this, if we wish to have definitions of knowledge disambiguated, plausible and empirically verifiable.

Defining Knowledge

2008-02-02T09:27:00.000-08:00

by Maria Odete Madeira

If one makes the assumption that all living systems are cognitive systems, then all the living processes, as such, are cognitive processes (Maturana and Varela), with empirical evidence in the cellular organization (Morin).The value attributed to cognition imposes that one should know something about the term cognition, itself, whose Latin root is cognitio (cognoscere), and whose Greek root is gignwskw and gnwsiz, and in Sanskrit is jnana with the (co)meaning of conjoint caption and understanding. The Indo-European common trunk allows the relation between the term gnwsiz and the term genesiz, which allows, equally, the signaling and codification, in the definition of the term cognition, of a constitutive genetic sense that attributes to it a replicative value. In this way, each cognitive act envisions its own replication.In this sense, it is pertinent and consistent the statement that the knowledge is a presence or existence (ousia, dasein) that proposes and exposes something or some thing (Heidegger), thus understood, the knowledge is aletheia (entbergung, to come to presence).

Nature, Diversity and Relation

2007-11-24T03:58:00.000-08:00

The irreducibility of the diversity may be a fundamental point in common among different branches of science when they look at nature. The complexity sciences, the life sciences, cosmology and relational quantum mechanics are a few examples.

There is a common thread in how various scientists from various fields are thinking about nature: diversity. The irreducible necessity of the relation for the cosmic organization and for every living organization, presupposes the presence of at least two.
If the process of entanglement does play a role in the actualization process, then, one can state with propriety that the universe would still be in a cloud of potentiality with no hope of ever being actualized if an individuation of at least two systems had not formed. The reduction of diversity to a single unity would perhaps transform the universe and everything in it into a cloud of potentiality. Decoherence seems to tell us that nothing can exist in act without something else.

The importance of diversity seems to be constitutional, a quite pervasive sine qua non. On this regard it is interesting to listen to John D. Barrow (The Artful Universe Expanded, pp.282, 286):

“Over thousands of years, the scientific perspective upon the world has focused attention upon the simplicities and regularities of Nature. Those regularities have been found to reside in the rules governing the events that we see around us, rather than in the structure of the events themselves. The world is full of complex structures and erratic events that are the outcome of a small number of simple and symmetrical laws. As we have learned, this is possible because the outcomes of the laws of Nature need not possess the symmetrical properties of the laws themselves. Laws can be the same everywhere and at all times; their outcomes need not be. This is how the Universe spawns complexity from simplicity. It is why we can talk about finding a Theory of Everything, yet fail to understand a snowflake (…) Science, quick to see uniformity, has at last begun to appreciate diversity (…)”

C. Pedro

RE: Quantum Life and Quantum Cognition

2007-11-08T03:12:00.000-08:00

Reply by Maria Odete Madeira on Quantum Life and Quantum Cognition subject, given in the discussion groups:

cosmology-mathematics-and-philosophy@yahoogroups.com,
cosmology-mathematics-and-philosophy@googlegroups.com
stephenhawking@yahoogroups.com,
qm2@yahoogroups.com,
quantum-gravity@yahoogroups.com,
quantumcosmology@yahoogroups.com,
NuclearStructure@yahoogroups.com,
time-space2@yahoogroups.com

During the development and growth of the scientific and technological work in general, we can identify sequences of coexistent conceptual systems that organize, articulate, distribute and circulate themselves around the problems that are specific of each historical times, and that configure enuntiative theoretical/empirical networks, that constitute the domains of discourse and of memory, in which it is related that which was learnt, that which was seen, that which is deduced or induced, that which is admitted as probable, true or valid and that which is postulated.

The technologies with which we, currently, work and coexist, are a natural consequence of the human work applied to the science and the technology. With the help of fragmentary and mechanical technologies, our bodies were interactively projected in space-time. Presently, in accordance with Lévy (2000), we participate in a silent explosion of the infinitely reticulate hypercortex of the World Wide Web, trajectively configured as a new workspace. This new workspace can be interpreted starting from the two fundamental notions: the notion of knowledge and the notion of information. The term information has its root in the Latin informatio, which means the action of forming, representation, sketch, plan, idea or conception.

This term appeared, in the 13th Century, designating the set of the susceptible acts of establishing the proof of an infraction and of revealing its authors, in the course of the preliminary instruction of a process, later on having come to be defined as a designator of events or facts that can be known. Since the 20th Century, it acquired new semantic contents, through its usage, by some disciplinary areas. Thus, in biology, it designates the set of the elements that a living being permanently exchanges, forming part of the energy exchange that allows the maintenance of this being’s structure and that impedes its disaggregation. Later on, and from this usage, systems’ theory introduced, in terms of an epistemological framework, an equivalence between the information and the mathematical notion of probability measure of the occurrence of an event i, in the set of possible events. The quantity of information of an event i is a logarithmic function, inversely proportional to that event’s probability. In accordance with Shannon and Weaver’s (1948) formula:

Meanwhile, a polysemy was developed, associated to the usage of the term, and vehiculated by information theory, as a scientific discipline that studies the communicational matters as well as the formal regulation of the problems raised by the communication media. Currently, and ever more, by way of the technological developments, connected to the expansion of the Internet, information is becoming a self-referential and complex web of devices that extends itself reticularly throughout the whole planet.

At the root of information theory, lie the concerns, of post-industrial (Bell) society, to find a medium of message transmission that would be, simultaneously, more economic and safer. Thus, aiming at a theoretical construction of a communications system, towards a practical application in which a transmitter could transmit, through a certain channel, a message to a receiver.

The flexibility linked to the development of the concept of information, in its theoretical/practical use, agilized its application to all disciplinary areas, making its usage indispensable, as a fundamental scientific criterion of any statement.

In an ontological approach, the information can be defined as a signalized pattern (logos, order, proportion, or number) situated in space-time and, in itself, dependent of the environment or context in which it was or is localized, in the form of data flows, and that is divisible in apprehended regularities that are synthesizable in schemata or rules that can be conjectured in sequences of images that can be worked over in an abstract way or in practical concrete applications, such as the description of a system, the prediction of an event or the solution to a problem.

The locality of information, as signalized pattern, allows one to assign it a physical existence of systemic nature. For instance, a gene can be defined in terms of units of organized and systematized informational communication that are capable of attaining an almost potential immortality. Theoretically, each DNA molecule can exist, if it is successful, in the form of copies of itself, during 100 million years (Dawkins, 1989). We may state that the molecules of DNA constitute the fundamental elements of an information technology with a biological effectiveness, in the sense that they are capable of packaging and preserving an immense quantity of precise digital information, using a diminute space and occurring, in all this process, an occasional margin of error, just enough to introduce variations.

Starting from the DNA molecule, considered as the replicating entity more common in our planet, Dawkins proposes the existence of new replicating units of informational communication or cultural memes that have a propagation similar to that of genes, the genes propagating by jumping from body to body in the genetic pool, and the memes propagating by jumping from brain to brain in the memetic pool, through a process of repetitive mimetic interactions that, to be effective in terms of informative replication, involves a work of adhesion and learning, when it is about, for instance, traditions, values, mores, criteria or scientific theories, or about adaptive agility, as is the case of the interface with the new information technologies.

In this approach, the brains are configured as data manipulation units, capable of processing complex patterns of information and of registering them in memory, being able to exhibit them, through a system of languages’ networks that are supported by the new communication technologies and that allow an interface that, in turn, allows the agilization of information itself, in terms of its development, growth and expansion, which contributes to its diversity and complexity.

Each organism remains, since its origin, in permanent interface with the environment, exchanging information with that environment, in accordance to its own parameters and internal design. This information, that was captured and maintained in the form of record, is dispersed throughout various regions and cerebral circuits that are coordinated with effectiveness by neural connections, in order for the organism to be able to quickly remember their contents in the form of patterns (Damásio, 1999).

This dynamics depends and results from a physical, chemical and electric process, reflexively worked out by each organism in its relation with the environment, depending, the circulation of information, upon a permanent and vulnerable construction of operations that are integrated in circuits, in which the border of the organism intervenes selectively, considering, evaluating and signaling, in accordance with adaptive criteria, that which is favorable and that which is harmful to that same organism, in terms of the homeostasis necessary to its integrity, growth, development and survival.

Considered as an open and dynamic system, each organism, or system, is reflexively and functionally connected to the other organisms, or systems, or, even, subsystems, with which it exchanges information.

Any physical existent is fundamentally constituted by patterns of spatio-temporal information, call it being, entity, thing, phenomenon, object, subject, animal, vegetable, mineral, particles, waves, forces or fields, whatever it is that exists can be, theoretically, reduced to dynamically reflexive patterns of spatio-temporal information. Understanding, by reflexibility, the capability that every physical existent has to relate to itself, in order to maintain its homeostasis and integrity. Both the identity of each physical existent, as well as the systemic relations that each physical existent maintains with the environment have, as condition, the natural disposition of each existent towards a fundamental exercise of reflexibility.

Quantum Life and Quantum Cognition

2007-11-03T05:10:00.000-07:00

With the development of quantum computation, quantum game theory and decoherence we are confronted with some fundamental problems that are at the heart of quantum theory and biology, specifically, our views on the following two questions must be considered in a new light:

What is life?
What is consciousness?

This is the first part of a two-part paper being published at this blog. In this part we deal with the first question, and will address some of the consequences of quantum computation and decoherence, leading to the argument that the border between the living and the non-living must be revised, and that quantum computation implies that a quantum system can already be considered as a living, individuated structure. This implication may seem, at first sight, and in a superficial perspective, as surprising, but the argument is straightforward enough, being the consequence of a standard conception of what a living organism is and of the basic results from decoherence and quantum information theory.

Quantum life?

The question - what is life? - is far from trivial. A very rough rule of thumb for defining a living organism can be introduced in terms of the following criteria:

It must be an individuated structure;
It must possess a metabolism;
Its activity is directed towards its homeostasis, perpetuating of the life of the organism for a sustainable period of time.

The research developed in quantum computation has shown us that a quantum information processing system can give rise to individuated structures that become computing subsystems with stable degrees of freedom.

Furthermore, decoherence tells us that, given a sufficiently complex isolated quantum system (with a Hilbert space with a dimensionality greater than three), there are quantum logical gates that produce a separation of the system in different subsystems, that correspond to degrees of freedom that are measured by other subsystems. Each subsystem becomes completely described by the local degrees of freedom selected by the quantum logical gate, its local state becoming diagonal with respect to all local observables, so that the subsystem gains a border in its potential reality and acquires an actuality due to the measurement, an actuality which is described by a probabilistic actualization of the values for the local degrees of freedom that characterize the system.

Since relative decoherence, as proposed by Gonçalves and Golçalves (2007) holds in this case, it follows that classical expectations can be formed for all the local observables, so that the system is completely individuated in its physicality, both actual and potential.

Furthermore, it possesses a metabolism. The word metabolism comes from the Greek metaballein, which means change, or exchange. As Schrödinger argued in his book (What is life?) the metabolism of the living organism can be considered as an exchange of entropy, and, furthermore, given the relation between entropy and information, it can be considered as an exchange of quantities of information. The organism is maintaining its integrity through actively processing the environment and feeding upon negative entropy and exporting positive entropy.

Let us pick up this last idea, and, for purely expository purposes, consider a simple example of an isolated system of three qubits. We can subdivide this system into three subsystems: S0, S1 and S2. Let us assume that S0 is our system of interest and that initially we have the state:

Now, let us introduce the following state transition:

Since the state transition was unitary, information was conserved, which means that the von Neumann entropy (measured in qubits) is left unchanged at zero.

Now, we know that the joint von Neumann entropy of two quantum systems can be divided as follows:

The last term in the sum is the conditional entropy. As addressed by Horodecki et al. (2005), the conditional entropy of a quantum system A on a second quantum system B, can be measured as the amount of information that A had to send B, in order for B to have a complete information about A, that is, it measures the "amount of ignorance" that B has about A. For the present case we have:

Taking the variation, and knowing that the initial entropy of S0 and the initial conditional entropy are both zero, we obtain the result:

Now, since the state transition is unitary, it follows that the joint entropy is zero, which means that the increase in entropy on the system S0 is exactly matched by the information that the system gains on the environment. Indeed, because the conditional entropy is the amount of ignorance that the system has about its environment, the fact that it is negative and that it exactly matches the increase in entropy of the system, means that the entropy increase in the system is compensated by an increase in negative entropy that is associated with an increase in the information that the system has on its environment. We should stress that the exact same result would be obtained if we had considered S1+S2 as the system of interest and S0 as the environment!

This last statement should not surprise us, basically what is being stated is that if you consider the system Y to be the environment of a system X, then, we see the entropy of X increasing, and being compensated by a simultaneous increase in conditional entropy due to entanglement.

There is a clear exchange of information taking place here, due to the formation of correlations. This type of metabolism will be addressed again in the second part of the present work.

Taking, now, into account Kribs' work on noiseless subsystems (see bibliography for references), if there is a set of degrees of freedom, which leads to a set of subsystems, that are resilient to decoherence with respect to an environment of other subsystems, then, even if there are parts of this resilient set that become entangled with each other, on the whole set, the information is conserved. Considering this, we have a self-sustained information conserving system, in which the information inside the system may be locally exchanged, but, on the whole, it is conserved. The system's whole is self-sustained in its computation, and can be considered in its activity as maintaining its internal millieu in the form of local information exchanges. That is, the system's computing activity is simultaneously metabolic (in the form of the internal exchanges of information) and it conserves information, which means that it is a self-sustained computing system, that actively maintains a state of homeostasis.

Furthermore, even if we consider interactions between subsystems, as long as a subsystem remains individuated in its degrees of freedom, and interacts with other systems as such, then, we have a network of metabolic exchanges and computations in which the subystem, even if open, remains individuated as a system, during an indefinite amount of time (depending on the case).

This research on noiseless subsystems and the interactions between them is a key research problem for the Bilson-Thompson et al. (2006) proposal.

This completes the three conditions that were reviewed above, as making up a rule of thumb to define a living organism.

Bibliography

Beny, C.; Kempf, A.; Kribs, S. W., 2007, Quantum error correction of observables. arXiv:0705.1574

Bilson-Thompson, S.O.; Markopoulou, F.; Smolin, L., 2006, Quantum gravity and the standard model. hep-th/0603022

Gonçalves, C.P., and Gonçalves, C., 2007, An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=982086, http://mpej.unige.ch/mp_arc/c/07/07-89.pdf

Horodecki, Michael; Oppenheim, Jonathan; Winter, Andreas, 2005, Quantum information can be negative. quant-ph/0505062

Kribs, D.W., and Spekkens, R.W., 2006, Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems. quant-ph/0608045

Kribs, D.W., and Markopoulou, F., 2005, Geometry from quantum particles. gr-qc/0510052

What is the meaning of Gödel's theorem?

2007-10-09T11:29:00.000-07:00

Hofstadter's most recent book "I am a strange loop" deals with cognitive science, mathematics and the problem of consciousness and self-consciousness.

By their very nature, these works can only be critically considered in terms of the intersection of disciplines that they involve. I would like to consider a dimension of Hofstadter's work that is sometimes overlooked and that is of fundamental intrinsic value for both science and mathematics.

Hofstadter understood something about the fundamental nature of mathematics that is sometimes overlooked by his readers, who focus on the cognitivistic dimension of his work, an example of this is Deutsch's most recent review of the above cited book (http://physicsworld.com/cws/article/print/30347).

Deutsch believed (as stated in the review) that Hofstadter’s point was that the brain worked like acomputer and that consciousness was an attribute of certain programs, when, in fact, this is not the case, in Hofstadter’s proposal.

Indeed, Hofstadter’s work is actually a deep insight into Gödel’s work, and the significance of Gödel’s work for mathematics.

In order to make this point clearer, and the reason why Hofstadter’s strange loop is fundamentally an insight into the nature of mathematical objects, it is important to understand the argumentative position of Gödel with respect to Hilbert’s project for mathematics. Hilbert believed that all mathematics could be expressed in terms of formal languages, and that any proof could be conducted through a series of mechanical steps, within a formal system, which included that formal language and the rules of deduction of well formed formulas.

If Hilbert was right, then, mathematics could be reduced to a purely syntactical game, more properly, each mathematical object would be, upon formalization, essentially dispossessed of its meaning beyond the pure meaningless syntax. Mathematics could be reduced to logic. Gödel put this into question by showing that mathematical truth and mathematics cannot be reduced to logic. A formal system, simple enough to include only the rules of arithmetic, would, either, be inconsistent, or, incomplete. This had a twofold consequence, mathematics may possess an irreducible semantics and not all mathematical knowledge is accessible to the mathematician.

Not all could be proven using deduction rules within a formal system, this was the common understanding of the meaning Gödel’s work. However, Hofstadter uncovered a second layer of meaning, deeply present within Gödel’s work – the paradox is the necessary point of fracture that triggers a mathematical evolutionary expansion from a formal system to another.

In order to transcend the paradox, one needs to move beyond the formal system, a motion that is made by the mathematician, but that is fundamentally inscribed in the very nature of the formal system itself. It is mathematics that demands the motion, in that sense the motion can be identified as present within mathematics itself, and independent of the mathematician, the mathematician must follow the nature and motion of the mathematical object.

The fundamental limitations of the formal system are simultaneously the threat to that formal system and the opportunity for mathematics to grow. Turning in on itself, the self-referential statement logically precedes the mathematical leap.

Carlos Pedro Gonçalves

Mathematics researcher at UNIDE