So many quantizations (memorandum)

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• DO NOT TRUST THE FOLLOWING
• glücklichneujahr!!!

QUANTIZATION

• mathematical form which represent infinite dimensional space
• must be separable (and summable) under certain restriction

INFINITELY MANY WAYS OF QUANTIZATION

• wave functions
• linear operators (hamiltonian, probability density, observations, ..)
• paths (in path integral)
• homotopies (might be used in generalization of path integral)
• wavelets
• triangulations of relativistic universe (simplicial decomposition)
• chain complexes (in homology algebra, as generalization of triangulation and observation, and these might be used in future categorical formulations)
• quantum sets (a la Takeuti and Ozawa, as parametrized boolean algebra and generalization of von Neumann's quantum logic)
• formulae valid in various systems of non-standard analysis allowing infinitely many infinitesimals
• (anything that forms topology and can be completed when bounded, given adequate interpretation)

What would be the "22nd century maths"?

• it looks just a matter of encoding (only after when throughly carried out, it should likely be realized that also old maths can be fully employed to formulate and solve)
• similarly in definition of Borel sets, it might include somewhat disguised (and likely finitized in properties of prime numbers) form of transfinite ordinals (order types) to order topologies
• it means: we might need meta-topology, which is just a topology itself, over topologies

Why?

• Since it must be a first-order approximation of "framework subsuming any possible mathematically-definable compatible and incompatible views as reflecting the only reality"
• "views" might be considered as topological spaces
• And it must eliminate infinities (poles) with finitization and interpretation

Completeness of probability measure and abstract 3-body problem (memorandum)

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multi-body system and probability

• what is probabilistic system?
• deriving virtual one-body approximation of multi-body system with probability
• or collapsing into one wave function
• complete measure turns many-body into one-body "falling" into incomparably large "ground"
• Lagrangian of the system make definite description for virtual one-body

future and incomplete probability measure

• sum of contributions from possible Feynman diagrams (no a priori completeness assured)
• estimating contributions from indistinguishable states as zero
• ignoring experimentally unobserved states
• completeness of cases might change over history and environment
• (added) e.g. solar neutrino density and probabilities of beta-decay or other phenomena involving weak forth
• expectation or Knightian uncertainty (tail risk that should be hedged only with longer-than-the-longest bond)
• abstract 3-body problem or game with indefinite sum

gravity or entropic force

• uncertain quantum entropy, indefinite radius of the universe
• Baysian gravity?
• is gravitational constant really constant?

TODO

• understand path integral, S-matrix and Wheeler-DeWitt theory
• relate them with gravity model of trade and transportation

unprepared for dinner yet (my wife just messaged)

unprepared for dinner yet:
lacking one thing for each menu to cook
no garlic for pasta
no celery for minestrone
no flour for chowder
no meat for stewed meat
and, only cabbage for casserole

Who's behind this silly site? (egocentric advertisement)

NOTICE

• Just Kidding
• Who's behind this silly site? The uneducated blogger answers. Ask me in English (Japanese question might be answered). Anonymous question is allowed, feel free to visit http://ask.fm/TuvianNavy

On Personal Matters and Forthcoming Posts (update November 2013)

For my and my family's health concern, I left Tokyo and moved to Kyoto from September 2013. For courtesy of my employer, my labor contract is kept unchanged. I have some heartache, headache, slightly high blood pressure and random pains but feel somewhat eased. My wife's throat turned well. We enjoy bigger rooms and now I have bookshelf!

I am preparing (at least) two essays, one on history of extensive thoughts for recent four centuries and the other on some biographical facts of ergodic theorist Shizuo Kakutani. Other subjects which have appeared in this blog would be rewritten in paper form.

There is no actual plan for forthcoming posts, but dimension theory (for cases of discrete and continuous dimensions) must be treated first.

(added) I also have a long-awaited plan for simple explaination of various versions of fixed point theorems in economical context, but I have no through understanding on this subject yet.

Shelah's Galois theory (memorandum)

"As an undergraduate, I found Galois theory beautiful, (more exactly what is in the book of Birkhoff-Maclane), and later I found Morley's theorem (with its proof) beautiful." -- Saharon Shelah, "The Future of Set Theory"

NOTICE

• DO NOT TRUST THE FOLLOWING

RESEARCH CONTEXT

• (added) Rather see Baldwin's slide on Abstract Elementary Classes
• (added) this paper might be helpful: An invitation to model-theoretic Galois theory
• (added) this might also be helpful: Une Théorie de Galois Imaginaire
• and my useless guessing follows

MOTIVATIONS

• Abelian variety is product of symmetric groups
• Galois theory states that solvable algebraic equations have their corresponding abelian groups
• Lie group is continuous, or infinite group
• Eigenvalue problem of (infinite dimensional) unitary operator should be "solvable" in certain meaning (gruppenpest)
• (added) Kakutani-Halmos: unitary oparator can be factorized as product of 4 symmetries, but not always as product of 3 symmetries
• What is Galois theory involving Lie groups?
• What is Galois theory involving groups of infinite degree?

HISTORY

• Sophus Lie and Friedrich Engel's Theorie Der Transformationsgruppen (1888) was motivated from Helmholtz' response to Riemann(1868)
• Cousin problems
• Whitehead conjecture
• Shelah's proof (V=L -> Whitehead group is free abelian group)

SPECULATIONS

• free group represents classical mechanics (zero curvature)
• non-free group represents "viscosity" of "elementary" mathematical objects
• regarding a cardinal as an infinite group which could be factorized into product of several symmetric infinite groups
• cofinality of singular cardinal might be degree of "normal subgroup" of this cardinal
• There's some arbitrariness in "factorization", or "cardinal division"
• (added) Such arbitrariness disappears when GCH holds (so under V=L too)

TODO

• clarify relations to Silver's works on singular cardinals (Silver was a pupil of Vaught, so his works also might have model theoretic implications)
• (added) "cardinal division" is inadequate. what is cofinality when GCH holds?
• (added) and how "ideal thoery of models" is?
• (added) clarify relations to entscheidungsproblem of transfinite functions (concerning complexity of elementary formula allowing recursively enumerable symbols of transfinite functions)

John von Neumann and computational fluid dynamics (memorandum)

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HISTORY

• (added) "Recent theories of turbulence" (von Neumann 1949), esp. chap. VI
• argument on analogy of "ultraviolet catastrophe" appears in chap. II
• (added) See Ryder and Mattsson's slide: CFD before CFD

POINTS

• In the wide spectrum of John von Neumann's works, relation between early computational fluid dynamics (including explosives, atomic bomb and weather forecast studies), continuum geometry and other fundamental contributions to logic and quantum mechanics does not seem well explained
• continuum geometry is unclear to me, so I would consider later
• any real fluid (except superfluid helium) is somewhat compressible and have certain viscosity
• regarding fluid as quantum multi-body system, interaction matters
• Artificial viscosity, as convergence parameter in CFD computations, is one of JvN's inventions and he should have been aware of manipulation of AV is a form of ultraviolet cutoff
• Mathematical intuitionism (of Brouwer and Weyl) mandates "UV cutoff" to any mathematical objects (no such thing like non-measurable and null set of continuum cardinality might be permitted to appear in intuitionist reasoning): Intuitionist continuum is "viscous"
• Some efforts on Banach-Tarski paradox and two-dimensional analogues, topological/amenable(at first it was called "measurable") groups and regular rings preceding the huge theory of operator rings seems to be focused on defining "intuitionistically valid" objects in classical mathematics

TODO

• settle continuum geometry in above account
• examine Navier and Stokes' reasonings of FD

Determinacy of Macroeconomics

Abstract

In macroeconomics we have suffered to make closed models treating growth. From some field-theoretical speculation, we can not avoid to conclude relative unavailability of data which are needed to make such models work. For better market forecast, investors might even do extrasolar exploration.

My draft is downloadable: http://www.rr.iij4u.or.jp/~wataru-s/expectation.pdf

Duality in Descartes: Esprit Geometrique and Vortex Theory

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Summary

• Rene Descartes' natural philosophy had two incompatible views of nature in it: "esprit geometrique" (as named by Blaise Pascal), or geometric methodology, and the vortex theory. Two views should have appeared in separate books if there were no political problem with exposition of Heliocenterism
• Isaac Newton took the former, although Gottfried Leibniz took the latter
• Vortex would be naturally derived from a view regarding Keplerian system as a part of a whole system of various perturbations, rather than two-body system (so Newton's success was due to his cutoff of higher degree corrections)
• Pascal, as fluid mechanician, was probably aware of the limit of efficiency of geometric, or exact, method, but his alternative "esprit finesse" (spirit of sensibility) is unclear: In [DELETED:his rarely-known book On the Spirit of Geometry and on the Art of Persuasion, he admitted the limited efficiency of Cartesian view, and suggested use of somewhat obscure art of persuasion, and] his conclusive aphorisms in Pansee, he was turned into a thorough critic to Cartesian way, and looks even almost abandoned any model building
• His awareness to the limit of Cartesian view is still hypothetical, lacking evidences that Pascal had found Cartesian view is only appliciable to isolated fluid with no vortex
• With a broadest interpretation far beyond its proper limit, we might say that Pascal's view is well consistent to such methods that simultaneously use several granularities ("finesse") of approximation, as actually done in computer simulation of multi-scale physics
• Also with too much analogy, we surmise that Descartes himself was not troubled with the apparent incompatibility between his method and the vortex theory: we still can think, as John von Neumann did, any effective model to be a projection to finite-dimensional space from infinite-dimensional nature and all we can do is, in principle, [ADDED:multi-]linear approximation

TODO

• Show evidences of Pascal's fluid-mechanical thought on non-equilibrium systems
• [ADDED:Pascal's treaties on esprit geometrique deserve thorough analysis, the other essay by him on the art of persuasion looks like a sort of logical positivism]

Utility and Measurement (part 4)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• just a survey, no new claims intended
• This is the direct sequel to part 1

For Impatiants

• Quantitative sciences, or simply any sciences, are efforts to explain changes of intensive quality and non-propotional actions with values
• Phase space as orthogonal dimensions of extensive (additive) domain, or newtonian absolute space, is the space for any quantitative effective theories of physics and other somewhat exact mathematical sciences including economics
• i.e. exact abelian category (Mac Lane 1950, Grothendieck 1957)
• Harold Hotelling once said "But we all know the world is non-linear," and John von Neumann, advocating George Dantzig against him, "If you have an application that satisfies the axioms, well use it [linear vector space]. If it does not, then don’t,” (Dantzig 1991)
• How do we approach with locally linear (zero-curvature) space/spacetime to know globally/locally curved space/spacetime with mass singularities?
• Or how do we approach with iterative approximation with higher (or, projection to lower) finite dimensional vector space to (from) infinite-dimensional nature of quantum physics?
• Or how do we measure (integrate) any [DELETED:manifolds] sets with σ-algebra?
• Or how many points (cardinality) do we need in space, sufficient for any geometry?
• All we need is: non information-losing (faithful) duality between straight space [ADDED:of unbounded dimensions] and [ADDED:locally] curved spacetime: It's [ADDED:the central drive for continuum problem and] the very matter of advanced mathematics like non-archimedean fields, cohomologies, sheaves, models (Morley 1965) and also motivated domain theory (Suppes and Scott 1958, Scott 1958)

Least Metaphysics

• Category: A jargon for Aristotelean and Kantian philosophies
• Arisototelean: Basic classification (classes) of any object, like time, position, relation, and so on
• Kantian: Mental structure underlying any logical grasp (not mere sensing, rather cognition) of external events, which are thought as a priori to any grasp

Least Keywords in History of Physics (to be written)

• Cartesian coodinate system
• Newtonian absolute space
• Closed dynamical systems, phase spaces and symmetries
• Legendre transformation and projection [ADDED:(related to monotonity in the sense of domain theory)]

Somewhat Superfluous Guessing on History of Mathematics

• First-order axioms are not meant to show "what is talked about". According to David Hilbert, you axiomatic geometer may say "tables" "chairs" and "beer glasses" to do geometry consistently, instead of "points" "lines" "planes".
• What you are allowed to do is just relabeling objects consistently, or keeping things distinct (don't relabel both "point" and "line" with a new name "table")
• In other words, keep isomorphism unchanged
• Oswald Veblen introduced categoricity of, or, in early 21st century wording, uniqueness up-to-isomorphism of model of, the theory, with suggestion by John Dewey (Veblen 1904). Dewey, as a philosopher, was familliar to Kantian terminology
• Loewenheim-Skolem theorem says that generally there's no such uniqueness: You need second-order language to lock cardinarity of models
• On the train of model-theoretic exploration of the [ADDED:cardinality-relative version of] concept of categoricity, Micheal Morley, a student of Saunders Mac Lane, wrote a paper on "categoricity in power" (Morley, ibid) under additional supervision of a Berkeley model theorist, Robert Lawson Vaught
• In this paper, he introduced a concept of "totally transcendental theory", which sounds like Kantian metaphysics. It might not a coincidence
• [STILL NEED CONFIRMATION, NEVER TRUST] Mac Lane published the first(?) paper (Mac Lane 1965) having a word "category" in its title, on the series of papers expositing his developing general theory of natural transformation beginning in 1940s, in the same year to Morley's paper. Years later, he wrote the first textbook on the subject (Mac Lane 1971, "CWM")
• Mac Lane later wrote (CWM, pp.29-30): "Now the discovery of ideas as general as there is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from philosophers: "Category" from Aristotle and Kant, "Functor" from Carnap (Logische Syntax der Sprache), and "natural transformation" from then current informal parlance."

TODO

• make the lengthy story brief
• add references

Regularity of Any Problem

NOTICE

• DO NOT TRUST THE FOLLOWING

Existence and Fixed Points

• We use Hilbert space daily and approximate it from finite dimension vector calculus
• Once our PDE problem is translated into maximization of infinite dimensional vector-valued function, logically the existence of solution is assured (even if it is not computable)
• Two fundamental problems still remain: (1) Is any thinkable PDE problem could be (with adequate topology which form $\sigma$-algebra) turned into finding fixed points in Hilbert space? (2) Can we always find, or does some transcendent principle assure adequate topology to settle arbitrary problem regularized?
• At least two Clay millennium problems are related to above problems: existence and smoothness of Yang-Mills and Navier-Stokes
• In other words, some transcendental version of fixed point theorem, which assures rigorous conservation of energy, is what we seek
• ZFC set theory might be too weak and insufficient to derive such principle

On Nodal Structure of Cofinallity of Cardinals and Dimensionality (part 1)

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"Je le vois, mais je ne le crois pas"

• In 1877, Georg Cantor found bijection between $\mathbb{R}$ and $\mathbb{R^2}$
• He was surprised that dimensionality of space does not matter for the number of points in space, or cardinality
• In reply to him, Richard Dedekind pointed out that $\mathbb{R^2} \to \mathbb{R}$ is not a continuous mapping
• Other than cardinality, what represents dimensionality in set theory?

Singular Cardinal with Countable Cofinality

• What are $\aleph_\omega$ and $\aleph_{\omega 4}$, which appear in a Saharon Shelah's well-known result of PCF theory?
• On the way of cardinal construction, $\aleph_0, \aleph_1, .. \aleph_\omega, \aleph_{\omega + 1}, .. \aleph_{\omega + \omega} = \aleph_{\omega 2} .. \aleph_{\omega 3} .. \aleph_{\omega 4} .. \aleph_{\omega \omega} = \aleph_{\omega^2} .. \aleph_{\omega^\omega} .. \aleph_{\epsilon_0} .. \aleph_{\Gamma_0} .. \aleph_{\omega_1} .. \aleph_{\omega_1+1} .. \aleph_{\omega_1 + \omega_1} = \aleph_{\omega_1 2} ..$
• For their cofinallity, singular cardinals form "nodes", or minima in cofinality graph: $cf(\aleph_\omega) = cf(\aleph_{\omega n}) = \omega = \aleph_0$

"But we all know the world is nonlinear"

• Halord Hotelling once questioned validity of linear programming in a presentation by George Dantzig (Dantzig 1991)
• John von Neumann adovocated for Dantzig, saying "If you have an application that satisfies the axioms, well use it. If it does not, then don't"
• To believe the validity of linear spaces, we need to ask the consistency of axioms of orthogonal linear domain
• So we need to prove existence of a model of othogonal n-dimension additive space and its geometry

On Repulsive Forces (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

MOTTO

• Different things attract each other and become alike
• Almost indistinguishably similar things repel each other
• Things tend to mixed up to positive (non-zero) volume of homogeneous matter

SUPPOSEDLY NATURE OF FORCES

• Any forces have duality (and any action have uncertainty)
• Any forces have two directions of action and effective lengths: attractive and repulsive resions
• Among basic fields, only electromagnetic field have a same effective length for attractive and repulsive actions, and we are aware of electricity-magnetism duality
• A quantity, which might be parameterized with combinatorial number of quantum states or number of paths to transit a quantum state to another, should be called as "Entropy" in a certain sense
• Functional forms of such "Entropy" characterize force fields as attractive or repulsive
• Superadditive (thermodynamical) entropy: $S = max \hat{S}$ for sum of entropy of each equiliburium subsystems $\hat{S}$
• Subadditive (combinatorial) entropy (which defined on quantum fields and non-equilibrium states): $S \leq \hat{s}$ for sum of entropy of each (generally) non-equilibrium subsystems $\hat{s}$
• In equilibrium, both effective entropy and energy are additive and mutually linear

Maybe Related Areas of Research

• Lieb-Yngvason theories of equilibrium and non-equilibrium entropy
• Rational Choice Theory (non-unique social wealth functions)
• Gravity models of spatial interaction and international trade
• Stability of firms (Industrial organization studies)
• Recent results in Lattice QCD

Entropy and Gravity in Economics (draft)

NOTICE

• DO NOT TRUST THE FOLLOWING

Perspective

• There's two basic extensive quantities in thermodynamics: energy and entropy
• In economics, analogy between energy and wealth was well acquainted (See Mirowski's More Heat than Light)
• When free energy (thermodynamic potential) goes to zero limit, total energy is maximum
• When marginal utility (economic potential) goes to zero limit, integrated total utility is maximum
• Gibbs-Fisher-Le Chatelier-Samuelson's thermodynamical economics is more or less explicitly built on this analogy
• Another analogy between entropy and demand was not so widely nor explicitly thought
• And underlying principle for origin of "gravity" between goods and people is still left unaccounted

Entropy

• Probably the most radical Samuelsonian was Nicholas Georgescu-Roegen
• His view was a revival of "limit of growth as steady state" concepts, like Ricardo's and Marx' "rate of profit to fall" arguments or Ramsey's "bliss", in the form of Boltzmann's thermodynamical apocalypse, "heat death"
• In his view, a notorious example in a DOSSO footnote is indeed the "breakdown of capitalism" (Georgescu-Roegen(1960))
• He was too radical to be understood seriously and economics is kept unchanged after him

Gravity

• Timbergen's gravity model is standard equipment in international economics

TODO

• refer entropic gravity, relativity and quantum gravity
• asymptotic extensivity of von Neumann entropy and determinant

Towards Justificaton of Say's Law (preliminary)

NOTICE

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Summery

• Principal axiom of classical economics: Say's law (S = D)
• Neo-classical generalization: Walras' law ($\Sigma{ps} = \Sigma{pd}$)
• Supply might be estimated as total wealth (in equilibrium theories, assumed somewhat constant, except on unpredictable changes of tastes and technologies)
• Demand might be formulated as utility function (might be usually function of price of goods, expectation, with any other endogeous parameters)
• Usually, tangible affections (shocks to technologies and tastes) to equilibrium is usually formulated in supply function, and demand is determined with markets alone
• Note that: Technology seems to be supply factor, but tastes are not supply factor for non-economists

Supply - Wealth - Exchange Value - Demand - Welfare - Utility - Use Value

• If you think all these words above have same meaning, you need only one word
• We use such words vaguely but quite differently
• These must not be confused each other
• And indeed Say's (Walras') law need theoretical justification

TODO

• State an acceptable definition for demand

Conservation of Wealth (part 1)

NOTICE

• I do not intend to deny or criticize current study disciplines
• NEVER TRUST THE FOLLOWING

Conservation of Wealth and Equilibrium

• Any economics have proper limit of explanation
• In equilibrium theories, the limit is wealth-conservative system, or closed economy
• Like as energy conservative systems in physics, we isolate the region of economic interest from rest of the world, and keep the total amount of wealth invariant within (before-after) the observed period
• But wealth is not equivalent to physical energy: What we call economics is, always models of (usually) market-part of (regions of) whole global economy, which is a part of earth system continuously in (physically) non-equilibrium steady state with heat and ray energy from the sun
• Just as in thermodynamics, there is two levels of isolation: closed but outside information (exogenous variables) can affect, and completely isolated
• In other words: partial equilibrium vs. general equilibrium
• For present purpose, we regard money as synonym for wealth (detailed argument is later)
• Game: zero-sum (Note: non zero-sum N-player game can be rewritten as limited form of zero-sum N+1 player game)
• Microeconomics: Paleto efficiency (no better off)
• Finance: self-financing (always bet your own money only)
• Macroeconomics: autarchy (no foreign trade)
• International: limited number of (usually two) nations (often endogenous exchange rate, and >2 nations could be unsolvable)
• For financial models, you may lose or gain your assets, so apparently it looks non-conservative, but for every contract you did, the counterpart gain when you lose, lose when you gain. To summerize, what you lose(gain) is always what the rest of the market gain(lose)
• For macroeconomic models, we must distinguish "flow" from "stock". In any dynamic macroeconomic model we state national wealth (stock) as integrated income (flow) but wealth have arbitrariness with initial amount of wealth, or integration constant

TODO

• define and explain open economy and its stability
• define and explain "equilibrium" with growth or other endogenous changes
• define and explain money and tangible asset

Revolution of Understanding (joke)

NOTICE

• I'm just joking

History

• "Mon cher Blaise, Je suis sick et bored et gazing at ceiling. On ceiling grid over my bed, the fly goes from one block to another. Donnes any movements on the grid, quoi do they look?"
• (years after) "Hey, you saw the apple fall?" "Yep, Isaac, why?" "I wonder why the globe does not fall into the apple contrary."
• (years too) "Why lights go the shortest path? Why balls go the shortest path? For me, they look similar. They look, somewhat, stationary." "Billy, I don't understand what you say. Are you talking about physical action?" "Yes."
• (years too) "Currently known calculations of black-body radiation fail at each sides. I need the formula valid at both siden, IR und UV." "What about thinking intensities as countable, Herr Wien?" "Herr Planck, what did you say?" "Not my idea. Mein EnglischKollegen proposed to do so."
• (leaped)
• (centuries after) "And our possibility to talk about things like inertia, mass, force, and so on, is about 0%. We are expected nully to talk about truth and false in logic. We have an unified and well-tuned theory and almost definitely know how fields work."
• (leaped)
• (tens of centuries after) "Hey, did you certainly know about an ancient good phenomenology of massive entropy? People in 15th century perhaps used obscure and ambigous concepts about 'force'. It's curious, hard to understand, but I find it might be useful for accounting ordinary reality with almost 100% of certainty."

TODO

• add xkcd-like cartoon

Subjective Time and Perception (memorandum)

NOTICE

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Subjective Time

"Why are things so heavy in the future?"

• Augustine of Hippo (when asked), Heidegger (boredom) and Bergson (sugar cube) thought about it
• Seems to be a somewhat outdated subject of metaphysics in modern days, after SR/GR
• In modern days, GPS receiver and other devices need precise internal clock
• Of course, such clocks work under gravity and relative latency from GR matters in GPS
• No interaction other than planetary scale effect of GR is assumed
• Periodical signal inside brain cortex could be affected from other sources
• For some drugs which might suppress excitement in cortex (carbamazepine, benproperine) anomaly in pitch perception is reported (said to be lower about half-tone)
• Some drug might cause even observable EEG slowing down
• In virtuallized computing environments, emulated "hardware clock" of guest virtual machine is a source of mysterious troubles - it unpredictablly jumps
• How interpolate missing values of such signals? Mentally, boring or painful tasks take time (you'll feel wallclock as slow) and interesting tasks does not take time (you'll find wallclock goes too fast)
• Some long computational processes and psychological trauma which take time to overcome (forget, forgive..) are often called "heavy"

Pseudo-Relativity

• Suppose you were a bat flying in a cave with no help of light
• Some people support human echolocation training
• bats or human doing echolocation might experience "pseudo-relativistic" view of the world
• how much can "sound" be sped up with extremely low density (vacuum-like) media?
• "sound cone" effect exists
• for reliable location, sound speed compensation with humidity and temperature is needed (bats actually do it)
• sound-light analogy apparently broken, as far as we think on ordinary sound wave and relativistic light
• We usually assume frequency of sound is measured with wallclock (proper time) cycles
• In GR, there is nothing like wallclock
• With certain machinery of internal clock correction might recover complete sound-light analogy

TODO

• So what? Implications?

On Conservatism and Evangelism in Social Sciences

NOTICE

• Divided as another post from the previous post

A Report of Social Experiments held in Biblical Era

Having eyes, see ye not? and having ears, hear ye not? and do ye not remember? When I brake the five loaves among five thousand, how many baskets full of fragments took ye up? They say unto him, Twelve. And when the seven among four thousand, how many baskets full of fragments took ye up? And they said, Seven. And he said unto them, How is it that ye do not understand? *1

An Economic Account

• Apostles and theologians just thought reasonably: aggregate amount of bread fragments can not exceed initial amount of the bread loaves under the assumption of total bread conservation
• The prophet meant differently: "yeast" of divine truth made an economic growth: the people might just have shared their own stocks of bread and have brought newly baked in a while. Accumulation estimated from the surplus of bread ex post was greater where smaller initial supply would have existed (5/5000 initial supply in loaves per capita produced 12/5000 surplus in baskets per capita, whereas given 7/4000 produced 7/4000)
• We can easily see both types of economists
• Coerced donation as an alternative form of taxation might be seen in religious states

Footnotes

1. Mark 8:18-21

Banach-Tarski Paradox: A Physical Interpretation (updated)

NOTICE

• NEVER TRUST THE FOLLOWING
• Almost irrelevant economic argument in an early version of this post is now divided to another post
• Addendum: some corrections due to misunderstandings to measure theory (Aug 29 2013)

Paradoxical Decomposition

Having eyes, see ye not? and having ears, hear ye not? and do ye not remember? When I brake the five loaves among five thousand, how many baskets full of fragments took ye up? They say unto him, Twelve. And when the seven among four thousand, how many baskets full of fragments took ye up? And they said, Seven. And he said unto them, How is it that ye do not understand? *1

• Banach-Tarski (1924) stated: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of non-overlapping pieces
• Such pieces must have measure zero (CORRECTED Aug 29 2013: do not have any measure) to make the ball recomposed from certain congruence transformations (motions) of them having arbitrary positive measure
• von Neumann (1929) further stated a 2-dimensional analogue of above
• Some said that just blame the (abuse of) axiom of choice, which assure zero-measured (CORRECTED Aug 29 2013: unmeasurable) subsets of the continuum having same cardinality of the continuum
• Others think that the concept of continuum is an idealization beyond physical reality

What do we mean to say "zero-measured" in QM/QFT?

• Measure is (classical) volume
• Measure is also (quantum) probability
• So "it's zero-measured" just means "physically such state can't be realized"
• But it is still possible to think mathematically about direct sum decomposition (hence diagonalization) of a fermion into several bosonic fields which can not actually exist with interactions
• Such bosonic fields might be, if realized, like holographic images projected with extremely high energy coherent light sources
• Even if such projection were (approximately) possible, you would not see even one of such images
• It would need just sub-femto seconds for extreme pressure of coherent light to make everything around evaporated

Addendum (Aug 29 2013)

• I was confusing "measure zero" with "unmeasurable"
• Unmeasurable sets in standard ZFC set theory are non-member of any σ-algebra, whereas zero-measured (null) sets are valid member
• Why unmeasurable subsets could be constructed? Probably, because of lack of sufficient determinacy - under ZF+AD (implies countable choice, but not full AC), no such subset exists. ZFC+certain large cardinal axioms also works somewhat alike.
• For any decomposition to be definite, we need strong orthogonality far beyond the degree that standard ZFC set theory assures
• The full story should be written: wait for me or publish your much better conception

Footnotes

1. Mark 8:18-21

Rubber Elasticity Reconsidered

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Rubber Elasticity

• Elastic (stretchable) polymer chains of approximately infinite length
• Approximately no characteristic length scale (except the UV-cutoff below monomer scale - Silicone rubber is transparent to visible light)
• Tension relaxation is endothermic, that is, it takes heat from the environment as it shrinks

Scale Invariance

• One of conformal symmetries
• In economics, perfect competition concludes constant return to scale
• In economies with such property, any exogenous shocks are soon absorbed
• Wage stickiness and social discrimination are thought as imperfectness
• Economists have called above property as "elasticity" for a long time

Gravity

• De Sitter black holes behave like rubber lumps - endothermic contraction
• Existence of specific structural length scale (as in solid crystals) may cause negative curvatures in certain energy levels
• AdS-CFT seems to be ineffective for "rubberlike" matters

TODO

• What does it mean the nonnegative constraint of interest rates in economics?
• Action of relaxation on rubberlike universe is called quintessence, or fifth interaction. What is it?

Physical Applications of Heterogeneity (preliminary)

NOTICE

• NEVER TRUST THE FOLLOWING
• All ideas which sound good are already concerned

Almost Raw Ideas

• On the boundaries of different substances, energy converts in one form of modes to another
• Such conversions are costly - in conversion, non-ignorable amount of energy dissipates as almost uncorrelated phonons (just heat)
• Lattice defects in crystal of pure substance might work similarly
• Rubber, activated carbon and zeolite are such substances - these dephase stable coherent modes
• In absorption of external radiations and particle beams, such incoherency and heterogeneity in structures might make difference in absorption (heat conversion) efficiency, almost regardless however wavelength of external radiations short

TODO

• How refrigerate such absorbers?
• Find literature
• Design experiments

How Facts Emerge: Subject, Self-fulfllment and Stability

NOTICE

• NEVER, NEVER and NEVER TRUST THE FOLLOWING

Subject

If you want to know the taste of a pear, you must change the pear by eating it yourself. *1

• There is a basic distinction of objective versus subjective values
• In economics: exchange value versus use value (market price versus individual utility)
• Use value of consumer goods is hedonic utility, use value of capital might be net outcome of investment
• Exchange values are guess (with or without theoretical reasoning and statistical assumption)
• Some theory-based measurements are still guess but reliable guess (with stable measurements and sound statistical assumption)
• We define "subjectivity" as "reliance to sense data", or ratio of energy loss
• Subjective observation might be called "consumption" and objective guess relies on assumptions
• More subjective measurement is more disturbing (causing more state changes)
• Less subjective measurement has weakness to heterogeneity (surface effect), singularity and noise
• Experts in various disciplines often talk about their versions of degree of subjectivity (hence, residual degree of guessing)
• In electronics: input impedance, high or low
• In engineering: (non-)destructive inspections
• In medicine: invasive or not (for operations and inspections)
• In QM: observables on the lattice of projections, having true "wave function" as its ideal
• In other words: Subjective measurement is recovering whole spectrum from IR eigenvalues and less subjective measurement is recovering from UV eigenvalues
• Sometimes, objective values, or guesses, might be far from being precise, when we guess with wrong theoretical foundation or wrong statistical assumption

Self-fulfillment

• Some philosophers talk about "speech act", "performative utterance" etc. Naming ships is an example of "speech act", which effect through mere announcement. (cf. Austin(1962))
• Some sociologists talk about "self-fulfillment" (cf. Merton(1949))
• Some financiers, managing hedge funds or central banks, may fail to make reliable forecast on future balance of their accounts (e.g. bankruptcy of Long-Term Capital Management) *2
• In various situations, announcement of authorities matters or does not matter. What makes difference of success and failure of prophecy/forecast?
• Some statement classified "self-fulfilling prophecy" might be regarded as "energy-collectors" or "recyclers of social wealth" in certain bosonic field

Stability

• Correct forecast might be on stable (and even self-stabilizing) phenomena
• Stable phenomena (excitement) have certain amount of energy which can not be easily dissipated
• Stable phenomena allow more observations (i.e. numerous dephasings and substantive energy losses) than unstable phenomena
• Even most stable phenomena can break under excessive observations (classical intervention)
• Vulnerability to observation may depend on "effective surface" and sureness depend on "volume"
• If certain type of "phenomenological" argument works, it might be stable

Observation of excitement in group of cells in clinical contexts

• In early stage, low volume cancer might be actually superposition of low probability cancer and high probability non-cancer, and fortunately, almost all of such "quantum cancer" *3 soon disappear, but some evolve to "classical cancer"
• Is unnoticed subclinical cancer exist? (Berkeley's argument)
• Inflammation is observation over itself *4 : how about just suppressing it?
• Some refusals of inspections and denials of symptoms might be indeed therapeutic (but I do not know how to design refutable experiments on such hypotheses)

Generally, whether wishful thinking works or not

• Some sorts of wishful thinking are just against stability, just ignoring substantial energy and may fail
• In certain critical situations, it might be fundamentally unclear ante post

Footnotes

1. Mao Zedong, On Practice
2. Robert C. Merton, an LTCM board, is the son of Robert K. Merton
3. Japanese anesthetist Makoto Kondo writes about "gan-modoki", which translates literally "pseudo-cancer" in English. It is a pun on "gammodoki", which is Japanese tofu pudding fritter
4. Neil Gaiman(1990): "Notoriety wasn't as good as fame, but was heaps better than obscurity". These words originate from Oscar Wilde's talk in 1883, "If it took Labouchere three columns to prove that I was forgotten, then there is no difference between fame and obscurity" (remember his infamous popularity). I do not know who first derived the "hauptsatz" of viral advertisement stating that "notoriety is more valuable than obscurity". Corresponding Japanese phrase "aku-mei ha mu-mei ni masaru" is a popular proverb

Integrable Systems: Do They Exist?

NOTICE

• DO NOT TRUST THE FOLLOWING

History

• Kepler found integrable systems and elliptic orbits
• Priority for the principle of least action is not so clear but Leibniz found early
• Hamilton investigated the principle of least action, or rather he called it the principle of stationery action, and analogy between lights and planets in the form of calculus of variations
• Poincare investigated three-body problem and found that no analytic solution other than the Lagrange points. With his recurrent theorem, energy-conserving orbits go arbitrary near the starting point
• (Supposedly) von Neumann might have asked himself: There's no such thing like thermodynamically isolated system, other than possibly the whole universe. The second law is solid and Boltzmann's "heat death" look so inevitable. We can see that Haar invariant measure exists iff the universe is uniform and eternal. But it does not seem the general case. Why can we calculate the time-evolution of orbits as if they were ergodic?
• Kuramoto says that pull-in synchronization is observed perversely in chemistry and biology

Answer?

• Even blackholes are predicted to evaporate someday, but gravity works against dissipation, radiation for a while
• Lucretius' mystic clinamen works for both directions: heavy mass point might be somewhat self-stabilizing in its orbit, bend everything, including radiation from itself, slightly toward itself and steal momentum even from the (vacuum?). Orbits of lighter ones only emit photons, loss energy, get smaller, more uncertain and disappear earlier

TODO

• Isaac, after all, what is gravity?

On Economic Phenomenologies (memorandum)

NOTICE

• Related investigations on the line of Pareto and Mandelbrot are not treated
• DO NOT TRUST THE FOLLOWING

Examples

• Irving Fisher(1907) stated that nominal interest rate is approximated with sum of real interest rate and inflation rate
• When bookkeeping, we always sort incomes and expenses then add them up without worrying about non-extensiveness of value in money
• Also we compare profit of this quarter with previous quarter without worring about non-extensiveness of months in calender
• A phenomenological production function presented in Cobb-Douglas(1928) fitted well to actual statistics over 1899-1922 with correction coefficient 1.01: 1st degree homogeneity of production function requires constant return to scale
• (added) I'm still not sure but duality between price and quantity follows from usual convexity requirement of economic optimization (KKT condition)

TODO

• rewrite all above more formally

Towards the Theory of Tangible-Financial Relation (preliminary)

NOTICE

• quite preliminary: DO NOT TRUST THE FOLLOWING

Directions

• To complete field-theoretic theory of financial asset prices, some consideration on interrelation with tangible constraints is inevitable
• Financial assets can grow exponentially apart from its tangible backs, or dissolved, like bosons could be stretched (divided) into more bosons with lower energy (wavelength)
• When tangible assets are more utilized and circulate with accelerations, indeed "high-powered" money, or demand for short-term bonds, grows
• Once amount of wasting assets recognized, as shown in Choate and Walter(1981), economy would be "pulled-in" to real investment cycle
• Real turbulence strongly alters brain states of economic subjects and invoke massive recalculation of preference order
• Currently macroeconomics avoids bankruptcy with boundedness assumptions like cash-in-advance or money-in-utility, which date back at least in Walras' Éléments
• Bankruptcy, or collapse of economic agents, should have adequate place in monetary economics
• Irving Fisher's debt-deflation theory looks so similar to Dirac's hole theory
• Fermionic substances could not multiplied: excluded and charged
• In principle, despite it is difficult to see what is really tangible in economic context, we can not avoid consideration on conformal symmetries, or "electrodynamic" constraints, in addition on "bosonic" free field, as the basis of theory of tangible constraints
• And it must ultimately determine the curvature of economy, also called as "productivity" or "inflation rate"

TODO

• learn classical electromagnetic field theory

Logic, Measure and Universe (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING
• I do not intend to make any "alternative" or "abuse" of well-established results in related areas

Speculations

• Logic and probability was united in Boole's time
• Jevons' intertemporal consumption optimization model naturally used probabilistic measure as utility
• Semantics of classical logic is measure theory
• Models corresponding theories form topological groups
• Banach-Tarski theorem on paradoxical decomposition must have metamathematical correspondent in forcing theory. Free group F_2 (i.e. propositions) plays crucial role in both arenas
• Measure (or truth value) may vary, difference of measure could be zero or some
• Independent statements, like existence of certain kind of real numbers, reside as "edge" of certain ergodic ensemble of orbits. Reflecting its dissipative nature, truth value for it may vary
• Central orbits, which should have relations to "center" factors in operator ring theory, is computable, or integrable
• Everyone knows (or should know) that anyone who rigorously relies on well-specified model is just searching under the street light
• Complete probability measure is such street light
• We always are able to build another street light
• Why our universe ever grow? (in both QFT and logical sense)

Remarks (added)

• Banach-Tarski and slightly similar theorem in 2-dimension was considered by John von Neumann. He also wrote a descriptive set theory paper with Kuratowski, I think that's not unrelated
• Topology of operator space, or lattice, reflect its computational hierarchy
• There are some studies on descriptive set theory in relation with ergodic theory
• A talk by Clive Newstead on a recent result by Andreas Blass: "Models of set theory from topological groups" (pdf) (video)

TODO

• learn everything to state all above correctly

On Farthest Infrared Interactions

NOTICE

• Just regard as I am joking (it is sorry, too late to April fool's day)
• I do not intend to expose any "alternative" views on current research

Summary

• History and Social studies treat causality, or vague correlations, between past, present and future events and acts
• Against philosophical realism, evaluation of historical events can vary or be revised
• In principle, No reason for exempting human-scale events from physics
• From physical point of view, historical/social correlations could be viewed as "farthest infrared interactions"
• unit of accounting time is a day. 1.16E-5 Hz, or 4.8E-20 eV, or 7.67E-39 J
• longest term of sovereign bond I know is 100 years, 3.2E-10 Hz or 1.3E-24 eV, or 2.1E-43 J
• Not few historical causes, like "thoughts", can span even longer
• Such farthest infrared mode appear as "pennies for change" or "heterodyne beat" in absorption of higher energy and perverse with diffraction
• "subtraction of frequencies" occurs just as exchanging bonds of different maturity in bond futures market
• the whole process of mollification of thermal singularity is similar to resolution of "contradiction" a la Hegel-Marx
• In its late consequences, it looks like "prolonged social contradiction"
• Such interactions are easily stretched (redshift) under gravity so if we could measure the energy of such interaction, it might help our understanding of general relativity
• in absorption, deviation from resonance peak might be emitted as such far infrared photons.
• Cosmological local structures are excitation of same order, e. g. solar system spanning several light-days. angular momentum of planets too.
• Cosmological large-scale structures have even much longer (darker) wavelength

TODO

• show interesting implications

Role of Information in Market Price Convergence (half-baked)

NOTICE

• still half-baked: DO NOT TRUST THE FOLLOWING

Basic Ideas

• On applying field theoretic ideas to economics, we must be aware that most of economical information which appears in each transactions or estimations (emission, scattering, absorption or observation of wealth) corresponds to internal states of physical matter, which is experimentally unmeasurable and have no thermodynamical meaning
• Also some properties, which seemed definite in macro-scale, is aggregate (market mean) and turn into uncertain: e. g. relative price (mass)
• Buyers' information about sellers' status can lower the price: it means information (boson) can convey substantial proportion of the price (special relativity assures that)
• Majority in price of rare and inseparable goods is just knowledge about who own them (imagine poker players)
• Such "bosonic" interaction between peers is strongest at cross trade and vanishes in the limit of market participants goes to infinity, as pointed out in Edgeworth's Mathematical Psychics
• Why? In larger market, our weak seller can seek unacquainted buyer who offer "fair" value
• In equilibrium of complete market, total wealth (energy) of system is properly direct-sum-decomposed into wealth of each participants, so Paleto optimal.
• Sellers can manipulate price with fake information in certain degree
• Buyers, who "sell" demand, can also manipulate price of demand
• Such interaction also plays a role in market convergence in its speed and character
• Slow settlement algorithm (like as assumed in classical mechanics) corresponds to no interaction setting: eventual collision between buyers and sellers is only chance of exchanging "momentum", or portfolio
• Consumer markets with ordinary money may converge fast
• Slower algorithm which corresponds to ordinary bazaar with bargaining
• In modern stock market with ticker and some boundedness constraints still have such "off-market" interaction and manipulation is still effective
• In translating various information to money, phase information might be lost. It seems that money behaves like phonons

TODO

• I heard but not confirmed yet that Yasutomi(1995) gives experimental observations on convergence of various settlement algorithm, with and without money and argue emergence of money

Utility and Measurement (part 3a)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• For this vast and vague subject, even a course survey is not presented
• Sorry for Jeremy Bentham and ethical thinkers all time who take heterogeneity seriously, little treatment given for social contexts

Far Historical Landscape of Decision and Social Choice Theory

• There is impressive contrast between slow development of decision (voting) theory, which treats ordinal utility, or preference, and fast development of utility theory, which treats mainly cardinal utility
• Despite that we compare one with another everyday, and discrete and abstract argument of preference looks well intuitive, ordinal utility could not be well understood without complete foundation of measure theory, topology and set theory. Any interesting (or dismal) choice in reality faces on opposition and uncertainty, both requires utility calculus based on sets and measures, and defined utility make various such conditions comparable
• Bernoulli(1738, trans. 1954) considered St. Petersburg paradox and gave modern notion of risks and utility with uncertainty, left unconsidered before von Neumann-Morgenstern(2/e, 1947)
• (aside) Essentially also by von Neumann, together with some other mathematical abstractions, general topology were introduced to economics
• Condorcet(1785), known for voting paradox, was the first systematic treatise on decision theory, using order-theoretic argument built on probability theory. Simply it was too early for the human race in pre-Bourbaki age
• Essentially no disciplinary landmark before Arrow(1951, 1963)
• For detailed exposition, see Duncan Black(1958, 1998)
• Game theory give a way to describe operations to partial-ordering of consistent social preference. Discrete conception of preference and game made microeconomic arguments applicable to areas where no explicit or continuous quantity and price is given: these span for fundamentals of several disciplines in economic (off-market competition), social and political studies.

TODO

• write the latter half of part 3 (may treat development of utility theory and unnamed open sets inside indifference curves)

Price Index, Monetary Redenomination and Discounting (half-baked)

NOTICE

• still half-baked: DO NOT TRUST THE FOLLOWING

Outlines

• Sometimes total reform of numerical structure of economic quantities needed
• Components of consumer price indexes and of market indexes like Dow Jones need to be changed time after time: there was no GOOG before 2004, no AAPL before 1980. Such components are basis in certain vector space but can not stay adequate over time
• Even monetary redenomination is needed rarely, usually as a process in aftermath of hyperinflation
• In econometrics, time-series data require unit root test. Time-evolution of such data could be non-unitary and should be detrended before calculating correlation. Two pro-cyclical data would have unit root in common, which is equal to inflation rate
• It might not so inadequate to call such act of reform of economic quantities system as renormalization
• Discounting factors, or inflation rates might be called as curvature
• There's no constant approximate wealth functional (and no orthonormal basis) even after discounting of inflation rate (was the key issue in Cambridge capital controversy)
• In other words, space of goods grows: infinite dimensional, not compact and non-separable
• Hence, maximization of certain wealth functional, or intertemporal substitution, might not make sense in long-run

TODO

• find physical analogues of Paasche, Laspeyres, and etc.
• explain what real interest rate is (or is not), and when Irving Fisher's approximation i = r + p (and neutrality of money) breaks
• examine index number requirements with the theory of measurement
• explore relations to FPTs and other well-known results in functional analysis (may take years)

On Personal Matters and Forthcoming Posts

Since I'm living near Tokyo and for ongoing Fukushima reactor crisis as of 19th March 2013 and curious arrhythmia, high blood pressure and thyroid enlargement noticed after June 2012, I have little hope to survive coming five years or even less. Around home and office, almost everyday I hear ambulance siren. My wife daily evacuates slightly reddish mucus and I don't know what to impute, her vice of smoking or Radioaktivität in the air for you and me.

In forthcoming posts, treatment of these subjects is planned.

• As previously annonced, Utility and Measurement part 3, treating history of utility theory in economics and interrelation with topology, order theory and measure theory
• von Neumann's contribution to social sciences and to other diciplines
• Hamiltonian dynamics and Samuelson's economics

Sorry for irregular grumbling.

Utility and Measurement (part 2 beta)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• just a survey, no new claims intended
• Blame my wife if this post is more insufficient than previous posts :)

History in Physics

• Like other metaphysical categories (space, time, whole vs. part), distinctions between quality (or intensity) and quantity (or extension) is soon relativized after clarification
• I don't know the very first appearance of "Intensive" and "Extensive" in thermodynamics literature
• Gibbs(1876) introduced "Intensive" concept, but no inclusive concept for extensive values: he just enumerated values which are proportional to volume in equilibrium
• Helmholtz(1887) explicitly referred to old metaphysicians' conception of "Extensive" and "Intensive" contrast, respectively adding "Mr. P. du Bois-Raymond named former as linear magnitude and latter as non-linear"
• Hölder(1901) presented axioms for theory of measurement
• Duhem(1911) assured mediæval roots of this metaphysical distinction (mentioned in part 1)
• Textbooks of thermodynamics: In Duhem(1902) and Planck(1903) these concepts do not appear as such
• (Added Sep 17 2013) Richard C. Tolman proposed terminology of "Extensive" and "Intensive" properties in 1917, as reported in O. Redlich(1970)
• Enswiler(1921), as an product of transitional period, use "intensity factor" and "distribution factor"
• Enswiler(1921), as an product of transitional period, use "intensity factor" and "distribution factor"
• Fermi(1937, 1956) avoids use of "Intensive-Extensive" and use homogeneity (of 0th or 1st degree) instead

History in Mathematics

• After Helmholtz and Hölder, it was widely understood that extensivity is additivity
• Measure in general needs to be built on set theory. Affected by Cantor, Henri Lebesgue and his fellow French researchers tried to define measure
• After WW2, from a order-theoretic viewpoint, Dana Scott and Patrick Suppes contributed to theory of measurement (incomplete differentiation, non-monotonic change of variables, or projection, causes information loss - probably that's the motivation for domain theory)

TODO

• detailed bibliography
• or total refinement of Math part
• Scottish Metaphysician Sir W.Hamilton (1788–1856), who appear in OED entries "Intensive" and "Extensive" is not Irish Physicist Sir William Rowan Hamilton (1805–1865)
• preview for forthcoming: How economists once abandoned ordinal/cardinal utilities and still use them today? Stay tuned

Utility and Measurement (part 1)

NOTICE

• May contain errors: DO NOT TRUST THE FOLLOWING
• just a survey, no new claims intended

Least Philosophy

• Affection: In Kantian philosophy, Ding an Sich (thing as itself) is not accesible to human mind. Things just affect.

History in Philosophy

• (Pierre Duhem's finding) mediæval French philosopher Nicole Oresme's conception: latitudo (width), or intensio, and longitudo (length), or extensio
• In Cartesian philosophy, followed by Leibnitz and Spinoza, extension is very central concept (if interested to the linkage between Descartes and mediæval thoughts, Étienne Gilson's Index might be helpful)
• Pascal's Pensées: mysterious criticism against Cartesian way (algebraic models): "useless and uncertain"
• Cartesian coodinate is one of Leibnitz' inventions (putting aside similar ideas independently used). Another one is optimism
• Kant's Critique of Pure Reason: Euclidian space (space of extensive values) as a priori, perception and intension (to be written)
• Hegel's Orbits of Planet: over 200 years after Principia, argued against Newtonian synthesis of theories of conservative (Keplerian) system and dissipative (Galilean) system
• Common underlying insight of Pascal's and Hegel's (and later Duhem's) critiques (even if they were not aware): How the nature decide directions of changes?
• Leibnitz' solution was optimism, but it was insufficient then
• Vitalism was also insufficient
• Energetics was needed, but there was no thermodynamics yet
• pre-thermodynamical investigations in Hegel's Science of Logic: (1) Instant freezing of supercooled water as an example of transition from quantity to quality, (2) confused and "contradict" as usual, noticed on the fact that intensive values can always be represented as extensive values (example: temperature or pressure and length of mercury)

TODO

• clarify Kant's contributions with footnote about Deleuze on intensity and affection
• clarify relation to Bergson's "sugar melt" argument in Creative Evolution