Entropy and Gravity in Economics (draft)

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• 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)

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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)

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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)

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• 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