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?
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
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
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
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
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
