Wednesday, June 11, 2008

Charles Bennett, Definition of Organization and Complexity

Bennett: there is a difference between dissipation (irreversible net increase in entropy) and reversible transfers of entropy.
: "it is usually more practical to stop a moving car with breaks than by saving its kinetic energy in a flywheel."
: Neurons have poor efficiency, dissipating about 10^11 kT per discharge, explained by macroscopic size.
: On the other hand, the molecular apparatus of DNA replication, transcription and protein synthesis, whose components are truly microscopic, has a realatively high energy efficiency, dissipating 20-100 kT per nucleotide or amino acid inserted under physiological conditions.


: In the modern world view, thermodynamic driving forces, such as the temperature difference between the hot sun and the cold night sky, have taken over one of the functions of God: they make matter transcend its clod-like nature and behave instead in dramatic and unforseen ways, for example molding itself into thunderstorms, people, and umbrellas.
: Organization defined as "logical depth", a notion based on algorithmic information and computational time complexity.
: Logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin.
: Candidates for definitions of "organization" and "complexity" can be divided into those based on function and those based on structure.


: In spite of the well-known ability of dissipative systems to lower their entropy at the expense of their surroundings, flouting the spirit of the second law while they obey its letter, organization cannot be directly identified with thermodynamic potentials such as entropy or free energy: the human body is intermediate in entropy between a crystal and a gas...
: Subjective organization seems to obey a "slow growth law" which states that, except by a lucky accident, organization cannot increase quickly in any deterministic or probabilistic process, but it can increase slowly...This in turn, means that subjective organization is not additive: 1 bacterium contains much more organization than 0 bacteria, but 2 sibling bacteria contain about the same as 1.
: an object's information content is the number of bits required to specify it uniquely -- as distinction, as a "self-contained unity" (Rosenzweig, pg. 11)
FN (on "The new world Nietzsche unlocked to reason, beyond the orbit described by ethics."): "Now a self-contained unity rebelled against this totality which encloses the All as a unity, and extorted its withdrawal as a singularity, as the singular life of the singular person. The All can thus no longer claim to be all: it has forfeited its uniqueness." Pg. 11
FN (Lebensanschauung vs. Weltanschauung): "One must acknowledge the otherworldliness of the new inquiry as against everything which the concept of ethics hitherto solely meant and solely was meant to mean, the more so if one wants the spiritual achievement of the past to count for everything which it accomplishd rather than to destroy it in a riot of blind destructiveness. A way of looking at life (Lebensanschauung) confronts a way of looking at the world (Weltanschauung). Ethics is and remains a part of the Weltanschauung. Its special relationship with a life-focused point of view is only that of a particularly intimate contradiction, just because both seem to touch each other, indeed repeatedly claim mutually to solve the problems of the other together with their own. It remains to be shown in what sense this is actually the case. But the contrast of the life-centered and the world-centered points of view comes down so sharply to a contrast with the ethical portion of the world-centered view that one is inclined to designate questions of the life view as veritably meta-ethical." pg. 11
[Me: Lebensanschauung = Myworld, Weltanschauung = Ourworld]

Rosenzweig, Introduction to Star of Redemption

Franz Rosenzweig, Star of Redemption, Translated by William Hallo.

"Philosophy takes it upon itself to throw off the fear of things earthly, to rob death of its poisonous sting, and Hades of its pestilential breath." p.3
Me: Philosophy seeks to find, perceive, conceive something, anything, eternal; something immutable, immovable, unassailable. It then seeks to unconceal our relationship to this eternality, and, belatedly, my relationship to it and to us. Philosophy seeks a cosmically atomic aletheia. Whether this "bears us over the grave which yawns at our feet with every step" is besides the point, a secondary effect, a consequence, if that, of the search for safe harbor and dry land -- i.e., the search for certainty.

"Let man creep like a worm into the folds of the naked earth before the fast approaching volleys of a blind death from which there is no appeal; let him sense there, forcibly, inexorably, what he otherwise never senses: that his I would be but an It if it died; let him therefore cry his very I out with every cry that is still in his throat against Him from whom there is no appeal, from whom such unthinkable annihilation threatens -- for all this dire necessity philosophy has only its vacuous smile." p. 3
Me: True. Philosophy's embarrassment is that it can do nothing to alleviate the fact and fear of my ultimate annihilation; the fact and fear of eternal Nothingness before and after, of noise and noiselessness, of life well- or ill-spent but spent, of presence dissipating and diluting into past, to be ultimately lost and forgotten by a mindless, purposeless, unavailing and unobliging universe.

"For man does not really want to escape any kind of fetters; he wants to remain, he wants to -- live." p. 3

"It is presumably necessary for man to disengage once in his life. Like Faust, he must for once bring the precious vial down with reverence; he must for once have felt himself in his fearful poverty, loneliness, and dissociation from all the world, have stood a whole night face to face with the Nought." p. 4

"A way out of the bottleneck of the Nought has been determined for him, another way than this precipitate fall into the yawning abyss. Man is not to throw off the fear of the earthly; he is to remain in the fear of death -- but he is to remain." p. 4

"He is to remain. He shall do none other than what he already wills: to remain. The terror of the earthly is to be taken from him only with the earthly itself." p. 4
Me: A poor trade only if there is more to life than terror and pain.

"Only the singular can die and everything mortal is solitary. Philosophy has to rid the world of what is singular, and this undoing of the Aught is also the reason why it has to be idealistic...And it is the ultimate conclusion of this doctrine that death is -- Nought. But in truth this is no ultimate conclusion, but a first beginning, and truthfully death is not what it seems, not Nought, but a something from which there is no appeal, which is not to be done away with. Its hard summons sounds unbroken even out of the mist with which philosophy envelops it...And man's terror as he trembles before this sting ever condemns the compassionate lie of philosophy as cruel lying." p. 4-5

"Philosophy plugs up its ears before the cry of terrorized humanity. Were it otherwise, it would have to start from the premise, the conscious premise, that the Nought of death is an Aught, that the Nought of every new death is a new Aught, ever newly fearsome, which neither talk nor silence can dispose of. It would need the courage to listen to the cry of mortal terror and not to shut its eyes to gruesome reality...A thousand deaths stand in the somber background of the world as its inexhaustible premise..." p. 5

"We want no philosophy which joins death's retinue and deceives and diverts us about its enduring sovereignty by the one-and-all music of its dance. We want no deception at all." p. 5

On Kierkegaard: "This consciousness neither needed a blending into the cosmos nor admitted of it, for even if everything about it could be translated into universal terms, there remained the being saddled with first and last name, with what was his own in the strictest and narrowest sense of the word. And this 'own' was just what mattered, as the bearers of such experience asserted." p. 7
Me: What do I care if my 'energy' rejoins some cosmic stream? Or if my 'soul' gets reincarnated memorylessly. The silt, the 'detritus' left behind, will be "me", will be just what mattered to me.

"Schopenhauer was the first of the great thinkers to inquire, not into the essence but into the value of the world...This man no longer philosophized in the context of, and so to say as if commissioned by, the history of philosophy, nor as heir to whatever might be the current status of its problems, but 'had taken it upon himself to reflect on life' because it -- life -- 'is a precarious matter.' ... He declares the content of philosophy to be the idea with which an individual mind reacts to the impression which the world has made on him....Man, 'life,' had become the problem, and he had 'taken it upon himself' to solve it in the form of philosophy." p. 8

On Nietzsche: "Poets had always dealt with life and their own souls. But not philosophers. And saints had always lived life and for their own soul. But again -- not the philosophers. Here, however, was one man who knew his own life and his own soul like a poet, and obeyed their voice like a holy man, and who was for all that a philosopher." p. 9
Me: A pointed, and almost certainly intended, irony; Nietzsche wrote in Ecce Homo, "I have a terrible fear that some day one will pronounce me holy."

More: "For the great thinkers of the past, the soul had been allowed to play the role of, say, wet nurse, or at any rate of tutor of Mind. But one day the pupil grew up and went his own way, enjoying his freedom and unlimited prospects. He recalled the four narrow walls in which he had grown up only with horror. Thus mind enjoyed precisely its being free of the soulful dullness in whch nonmind spends its day...For Nietzsche this dichotomy between height and plain did not exist in his own self: he was of a piece, soul and mind a unity, man and thinker a unity to the last." p. 9

"Philosophy ceased to be a negligible quantity for his philosophy. Philosophy had promised to give him compensation in the form of mind in return for selling it his soul, and he no longer took this compensation seriously. Man as philosophizer had become master of philosophy...philosophy had to acknowledge him, acknowledge him as something which it could not comprehend but which, because powerful over against it, it could not deny. Man in the utter singularity of his individuality, in his prosopographically determined being, stepped out of the world which knew itself as the conceivable world, out of the All of philosophy." p. 10
Me: Heidegger, in his lecture "The Way Back into the Ground of Metaphysics", writes: "Insofar as a thinker sets out to experience the ground of metaphysics...his thinking has in a sense left metaphysics. From the point of view of metaphysics, such thinking goes back into the ground of metaphysics. But what still appears as ground from this point of view is presumably something else, once it is experienced in its own terms -- something as yet unsaid, according to which the essence of metaphysics, too, is something else and not metaphysics."
Me: This relates to Godel's essay "What Is Cantor's Continuum Problem?", where he writes: "But despite their remoteness from sense experience, we do have something like a perception of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense percpetion, which induces us to build up physical theories and to expect that future sense perceptions will agree with them." This is a weak claim; there is no reason why we should have "less" confidence, rather than the strong claim that confidence in either is justified by and after a finer-grained resolution of the problem.
Me: Thus, underlying the systematic reasoning of Heidegger's animal rationale (which is inseparable in fact from the animal metaphysicum) are truths that can only be intuited, perceived, experienced as truths which force themselves upon us; logically ineffable, formally irreducible, describable only indirectly, metaphorically, sensationally, if at all.
Me: This also tracks Quine and his "blending of analytic and synthetic, empirical and metaphysical [intuitional] knowledge" into a type of epistemic pragmatism. As Godel writes:
"Evidently, the 'given' underlying mathematics is closely related to the abstract elements contained in our empirical ideas (e.g., the idea of object itself). It by no means follows, however, that the data of this second kind, because they cannot be associated with actions of certain things upon our sense organs, are something purely subjective, as Kant asserted. Rather they, too, may represent an aspect of objective reality, but, as opposed to the sensations, their presence may be due to another kind of relationship between ourselves and reality."

"One has always realized the 'contingency of the world,' its state of 'that's the way it is.' But the point is that this contingency had to be mastered. In fact, this was precisely the function of philosophy. In the process of being thought about, the contingent changes itself into something necessary...There is, to put it very crudely, a nonidentity of being and reasoning which has to show itself in being and reasoning themselves. It cannot be harmonized by a third party, will, stepping in as a deus ex machina which is neither being nor reasoning." p. 12

"Reason is entitled to a home in the world, but the world is just that: a home; it is not totality...Thus the world is beyond as against what is intrinsically logical, as against unity. The world is not alogical; on the contrary, logic is an essential component of the world, rather literally, as we shall see, its 'essential' component. It is not alogical, but, to use the term coined by Ehrenberg, metalogical." p. 13-14

"For the world, truth is not law but content. It is not that truth validates [bewahrt] reality, but reality preserves [bewahrt] truth. The essence of the world is this preservation (not validation) of truth. "Outwardly" the world thus lacks the protection which truth had accorded to the All from Parmenides to Hegel. Since it shelters its truth in its lap, it does not present such a Gorgon's shield of untouchability to the outside. It has to expose its body to whatever may have happened to it, even if that should be its--creation. Yes, we might well grasp the concept of the world in this new metalogical sense rather completely if we would venture to address the world as creature." p.14-15

"Logic and ethics had once, it seemed, been locked in ceaseless combat for pre-eminence: metalogic, however, left room beside itself for metaethics. The world as a multiplicity united into an individual unicum and man, by nature an individual unicum, now confronted each other and they could breathe side by side." p.15

"Metaethical man is the leaven which causes the logico-physical unity of the cosmos to fall apart into the metalogical world and the metaphysical God." p.16: The science of God is called metaphysics.

"That the metalogical concept of the world succumbed to, say, confusion with the concept of nature was equally unavoidable...For if metaethical man, in spite of that designation, could be equated with the moral personality, then there remained for the metalogical cosmos only the equation with the critical concept of nature." p.16

"We sought to distinguish...our concept of the world from the critical concept of nature...[encompassing] on principle all the possible contents of a philosophical system, provided only they meet one condition: they are to appear as elements not of 'the' but only of 'an' All." p.17

"The metaethical in man makes man the free master of his ethos so that he might possess it and not vice versa. The metalogical in the world makes the logos a 'component' of the world entirely emptied into the world, so that it might possess the logos and not vice versa. Just so, the metaphysical in God makes physis a 'component' of God." p.17

"Philosophy fed theology on the identity of reasoning and being as a nurse might prop a pacifier into the mouth of a babe to keep him from crying." p.17

"The history of philosophy had not yet beheld an atheism like Nietzsche's. Nietzsche may not negate God, but he is the first thinker who, in the theological sense of the word, vey definitely 'denies' him or who, more precisely still, curses him. For that famous proposition: 'If God existed, how could I bear not to be God?' is as mighty a curse as the curse with which Kierkegaard's experience of God began. Never before had a philosopher thus stood, as it were, eye to eye before the living God." p.18

"Plato already discovered that mathematics does not lead beyond the Aught and the any; it does not touch the real itself, the chaos of This. At most it touches upon it...This thus-far-and-no-further was already ordained for mathematics at its birth." p.20

"The differential combines in itself the characteristics of the Nought and the Aught. It is a Nought which points to an Aught, its Aught; at the same time it is an Aught that still slumbers in the lap of the Nought. It is on the one hand the dimension as this loses itself in the immeasurable, and then again it borrows, as the 'infinitesimal,' all the characteristics of finite magnitude with the sole exception of finite magnitude itself...Thus it draws its power to establish reality on the one hand from the forcible negation with which it breaks the lap of the Nought, and on the other hand equally from the calm affirmation of whatever borders on the Nought to which, as itself infinitesimal, it still and all remains attached." p.20-21

"Thus it opens two paths from the Nought to the Aught -- the path of affirmation of what is not Nought, and the path of the negation of the Nought. Mathematics is the guide for the sake of these two paths. It teaches us to recognize the origin of the Aught in the Nought." p.21

"[Kant] undermined those three 'rational' sciences with which he was confronted without himself by any means returning from this undermining to a one-and-universal despair over cognition. Rather he ventured on the great step -- albeit hesitantly -- and formulated the Nought of knowledge as no longer uniform but triform. At the very least, two discrete Noughts of knowledge are designated by the thing-in-itself, the Ding an sich and the 'intelligible character,' the metalogical and the metaethical in our terminology. And the dark terms in which he occasionally speaks of the mysterious 'root' of both are presumably attempts to grope for a fixed point for the metaphysical Nought of knowledge too." p.21
Me: The "intelligible character" is the open ended set of possible meanings each "thing-in-itself" might register on an observer.

"The Nought of our knowledge is not a simple but a triple Nought. Thereby it contains within itself the promise of definability." p.22
Me: Algorithms, via reification, compartmentalization and logical operation, elide these three fundamental Noughts in favor of threshold functionality, in favor, i.e., of technique.