I had a random idea a while back and decided to chase it down. I saw that Gibbs method of statistical mechanics relies on operations of certain distribution functions, like the Gamma distribution or the Normal distribution. In my work I kept on coming across the Log-Normal distribution. It is everywhere. So I decided to have a look and see what I could derive. While I did this for the Log-Normal and Gibbs did it for the Gamma and Normal distributions, this approach is applicable to any other distribution.
Theory is no good unless you can test it and see it in our data. So I tested it on income distributions, reported in the the attached paper, bitcoin transactions (work in progress), and radiation exposure to cells (unreported work).
In my work, I derived the Cobb-Douglas function as a property of the Log-Normal distribution. Yesterday a friend tweeted a link to a blog The entropy of nations. If you have not read it I suggest you do. The author identifies maximum entropy as Adam Smith’s “invisible hand”. I emphatically agree with his analogy. The tendency towards maximum entropy is seen in the process of price discovery it is the invidible hand that drives arbitrage.
His work motivated me to finish mine and with a boring and non descriptive title to boot! Various Properties of the LogNormal Distribution. Can you say math fun? The policy stuff is in the last section if you are so inclined and the mathy stuff is in the front two sections. I found income distributions obey the second law of thermodynamics. This is great news! The bad news and what inspired my evocative title is that while we can propose policy and develop theories that say it will work, that no quantity of ink or PhD’s is going to change the second law. If you are not aware that it applies, so well. There is a chance you got the theory right, but its just not very likely. I had a Commanding Officer tell me, “Cal, Hope is not a plan. A plan is a plan.” Wise words. He left out that my plan actually better be possible. Hope as a policy is wishing for unicorns. That is my best description of any progressive policy, wishing for unicorns. It explains why what we get isn’t what we were sold. Somewhere along the line reality hit.
Here to any progressives that follow me or stumble across this blog, there is my gauntlet laid at your feet. I invite your responses.
Interesting and/or provacative blog. (I do wonder what your background is, since it seems to range from physics to political philosophy). I’m not sure what value my comments have, but for what its worth I’ll make some.
First, i discussed this with you already a bit on the RWER blog. You had mentioned Saslow, so I threw in Foley and Yakovenko among others. You said you were unaware of them, but it appears you had seen the Foley and Smith paper since its on your references from your ‘pre-alpha’ ‘econophysics’ paper.
It seems your view of Smith and Foley in the earlier paper is not the same as your view of them in the most recent paper on econophysics; I wonder if you’ve run it down with them (they think saslow is wrong, for example). I might add that there are maybe 50 other papers i know of that deal with tjhe same issues, some going back to the 40’s or before. (I will add that as I understand them, Foley’s 90’s papers are inconsistant with Smith and Foley 2005). (I also think its inexcusable to write papers like this with the most complex cases—-I have seen this in some economics books as well—when teaching a utility function, the author wants to impress and confuse you (so you don’t real.ize s/he doesn’t know what the f-k they are talking about) so rather than use something simple like Cobb-Douglas or better, additive, they throw in some sort hypergeometric form a zeta function coefficient with all sorts of parameters for discount rates, interest rates, mood, sexual orientation, whether a mac or apple user, sports team etc)..
Second, the idea that you have fouind that the income distributions obey the second law I think is ‘obviously well known’ though most popularized in the last 10 or so years by Yakovenko. It goes back at least to the 40’s or before in various forms. I have a derivation of a lognormal form from the 70’s by a very well known physicist (who now is also a global warming denier). One could argue that these are not really derivations from the second law, but rather maximum entropy, but to me the latter implies the former exists if one takes a dynamic view. There are other derivations in the journals ‘entropy’ and j. math. sociology from the 80’s to recently though they often use different formalisms, which are mathematically equivalent though not obviously so.
Most important, the idea that ‘maximum entropy’ represents or is equivalent to the action of Adam Smith’s ‘invisible hand’ to me is ‘wack’, as i mentioned on RWER. That is the ‘fatal flaw’ in the statistical mechanical approach and i explained why there. One can ‘fix’ this in 2 ways.
One is to assume ‘ergodicity’ (Keynes—in the long run we’re all dead) so everything (or everyone) really mixes (entropizes) over time, and current illusions about ‘class’, social stratification, lack of social mobility are due to the same problems seen by some who analyzed the first computer simulations of the second law by Fermi-Pasta-Ulam in the 40’s—-ie you just hand wave them away, and assume the infinite limit, and no long range correlations or phase transitions. . Similarily for the rest of the world, things like atoms, planets, life forms, water, protons etc. will all melt into photons because they really are just passing fads or illusions (like the passage of time and increase of entropy in the microcanonical ensemble, ior consiousness) because in maximum entropy we’ll find Boltzmann’s distribution—so called ‘heat death.
That may be correct, but some people are interested jn shorter time correlations.
The other way to fix it was assume people do have some ‘utlility function’ like cobbs-douglas. Yakovenko mentions and others went through the math. Unfortunately, from the intuitive perspective, this only works if you essentially slip in the same assumption used by Yakovenko and others—you have to assume a particular form of Cobb-Douglas (although its written the same) which is not what economists use, except when talking about ‘representative agents’. (Of course that is often the only way to solve things, and you get an answer but it assumes every individual is basically ‘average’, and I know this is false because i know i’m ‘above average’ because i’m partly from near Lake Wobegan where everyone is above average. (Mathematically this is possible and correct, because its possible or likely that then everyone else is below average—i believe that. Someone at Northwestern among others has written on this. But, this doesn’t explain what is so special about Lake Wobegon. Maybe its the water in the land of the 1000 lakes?
Physics can explain this, as the spontaneous polarization of the vaccum. It created the universe—E Tryon. But its just a fluctuation, so relax, and soon it will go away in the long.
Again, this is not satisfying to some. We may want some sureness that we’ll collect our pensions and social security before the light goes out).
One more complex way to fix it is viable, but too much to discuss here, and essentially revises the maximum entropy postulate (though you can still formulate it statistically—-you can put your constraints internally or externally). You can write the solution in gibbs form too—-exp(-bH)—but the devil is in the details, when you expand H. (Think ‘block spin method’ and ‘renormalization group’. )
I guess, in the tradition of E Verlinde’s ‘entropic gravity’ one can imagine this is as a second law phenomena too. (I actually do, in part). But it also shows the alternative is also possible—-preferences are real, and non random, and interactions are constrained because there is no perfect information and geography.matters, and the use of binomials or multinomials on distingishable or indistinguishable particles is really not defensible. ( Maybe it is—–increasingly the principle of gross substitution is seeming to hold—people are willing to sell or trade their spouses and children for example, for new ones or dope or property. The guy who desposed Ethiopia’s Helie Selassie (sic) for example seemed to be an innovator here).
In sum, so far as I am concerned (and maybe its just me) the maximum entropy and adam smith approaches to income distribution are completely orthogonal. Its possible to use the ME formalism, but you have to atart with a ‘prior’ set of assumptions. What is remarkable is that (as mostly simply shown by Yakovenko) assuming the simplest possible prior one can get remarkable (though not exact—-the income distribution is not exponential, especially at low incomes—though maybe he could fix that by counting under the counter transactions) agreement with data. He does assume one thing (via convoluting family incomes since that income is the most accesible data) so it may actually fail more than is apparent.
By the way, i made the same points to the people who wrote the papers mentioned above. I think they are (possibly like you) ‘right wingers’ so they didn’t like the message and cut off contact. Its easier just to maximize the entropy, and deny you are just arbitrarily curve fitting rather than explaining a mechanism. (Again as noted, there may be no difference fundamentally—-if i go to a store, while i may think i prefer some commodity bundle, in fact my preferences are due to billions of years of evolution, and so can be assumed to be random; similarily my fate—see the book ‘laws of chaos’). Of course normatively this means people like Senator Paul Ryan is an idiot who should be put on the food stamp and TANF rolls (since he already is actually) and then they should be cut so he can sleep on the street and eat out of dumpsters and the soup kitchen at his church.
I’m now going to see if I can find your derivation of cobbs-douglas from maximum entropy. (I think i know what you’ve done, since i have such a derivation, though its fairly implicit and sometimes almost explicit in the LITTERature). \
cheers. (ps i still like your blog, if not your conclusions).. .
I am very glad that you stopped by and took the time to leave such detailed feedback.
I am a nuclear engineer, and just a curious person in general. I started, a decade ago, to try and understand why the technology that I understood and appreciated was not very well appreciated amongst others. I wanted to understand why some very smart people were making policy recommendations that I knew to be physically impossible. How I understand it is that the political system is used to preserve a distribution of goods that preserves the status quo. Progressive and conservative policy’s are identical in execution, they just give a different bill of sale. By increasing barriers to market entry, in just about every market, the churn in the economy is limited and it becomes more rigid.
I went back to school to learn public policy, but for time’s sake I am in a nuclear PhD program instead of public policy and just minoring in policy. I took a micro econ course saw very clearly the link between micro and macro. So I read through vNM Game Theory and used that to define a metric space for utility. As their work only applies to individuals, I needed a formal way to aggregate individuals. That is why I chose Gibbs’ formalism. At the time I was reading Jaynes and saw his appreciation of Gibbs, so I started with Gibbs. I showed my econ professor what I did and he promptly stopped talking to me. Additionally, my derivation does not assume a specific utility function, just that one exists and is at least once differentiable. This is a strong assumption and can be relaxed, but would result in mathematics that is much more complex as we would now have a quantized utility function and need to adopt von Neumann’s approach to deriving quantum statistical mechanics.
I do use an ergodic approach in the Elementary Principles paper. Formally setting is a statement that there is no change in information in the system, that every possible subspace has had the opportunity to explore the entire phase space available to it. This is a very presumptive (strong) assumption that can be relaxed. I used it because it made the math much easier. Jaynes’ work inspired the field Non-Equilibrium Statistical Mechanics which does not rely on such simplistic assumptions.
The reason why I don’t like Smith and Foley, is that I have a very clearly defined utility from Game Theory that I use to derive entropy from the formal aggregation of individuals. They think entropy is utility, when it is most clearly not. Saslow’s heuristics emerges as sound reasoning as my derivation supports his conclusions. I appreciate your view point on unnecessary complication used to hide lack of comprehension. It is utterly incomprehensible.
The physicist that you are referring to is Lienhard? He worked through the derivation of a generalized gamma distribution and applied it to a whole set of applications, including income distribution. The Gibbs derived the gamma distribution as a consequence of kinetic energy = mass times velocity squared. That begins on page 87 of his 1902 book in earnest. Gibbs canonical distribution is a gamma distribution, he also shows 5-years before Einstein’s Brownian motion paper that this results in a normal distribution if the number of degrees of freedom of the system are very high. Gibbs is very hard to follow, and his insights are profound. Getting there is quite painful…
Your statement “One could argue that these are not really derivations from the second law, but rather maximum entropy, but to me the latter implies the former exists if one takes a dynamic view.” is spot on. The second law is a derived law from the principle of maximum entropy, and the conservation of the density in phase (first law). The second law is the fundamental equation of thermodynamics, . As I understand this law it only describes how information within a distribution changes due to perturbations of its independent variables. The first law is a conservation of information. Information, knowledge of the system, cannot arbitrarily increase, although it can be lost. (this is a very poor explanation as it doesn’t have the nuance of the conservation of the density in phase)
I am not a right winger. I see little difference between the right and the left. Having been on both the right and left, I feel qualified to make that statement, along with the my observations here I see very little empirical difference.
The adoption of the principle of maximum entropy is one that says, given our knowledge of our measurements, that the system will be in a configuration that we know the least about. Any other assumption, presumes a quantity of information more than we observed in the data. By using the principle of maximum entropy, I formally say that I am only considering the data which I observe. This is why it is so important to not throw out data or restrict data from our consideration. In this regard the principle of maximum entropy is a theoretical maximum entropy of the system. The ultimate configuration will always result in a configuration with a lower entropy. If it does not, then there is a significant problem in our selected model which is not consistent with the physical world, eg assuming a normal distribution when a log normal is more appropriate.
On the topic of entropic gravity, I too am sympathetic to that argument. There is a paper floating around out there that shows general relativity as a specific set of assumptions under a PME framework on Riemann manifolds. PME is very powerful indeed. I am not a big fan of the word of randomness when thinking about probability theory. I much prefer to think of it as an expression of the information we have. So if we have additional information then we can build a more complete model that better explains the observed entropy. The point with PME is that it assumes the least. Jaynes justifies the approach of PME in the entropy conservation theorem. (Jaynes, E.T., Concentration of Distributions at Entropy Maxima, in E.T. Jaynes:Papers on Probability, Statistics and Statistical Physics, R.D. Rosenkrantz,Editor. 1989, Kluwer Academic Publishers: Boston. p. 317-336.)
Usually, people cut off their interactions with me. I started this blog because I wanted to have a forum where I could discuss these ideas, because when I discussed them with people directly, they would not respond to my emails. I apologize for the roughness of the blog. As I have thoughts I write them up, and more than often don’t clean them up. I am very glad that despite the warts you like the blog.
PS, Wisconsin has more lakes than Minnesota, we just let you think that you have more lakes out of politeness.
p.s. I couldn’t find any mention of cobb-douglas in papers linked to above, though a couple of formulas bear some resemblance though i’d have to look closer. maybe its in your longer paper (some of which seems written in gibbs’ formalism, which i dislike; jaynes is better though my glance of your discussions don’t exactly jog my memory of what i saw in his originals—on his web site). It can be mentioned i’ve seen a few papers apply stat mech to electrcity markets.
Thanks for your reply. I don’t have time to really read it now and haven’t gone through your papers in detail (i’m still somewhat confused on all this stuff, though i have my own approach conceptually (i haven’t really written it up except in parts).
I will just give you a few of the references i mentioned. The lognormal for income is discussed in an old 1974 book by Eliott Montroll and Wade Badger (it may be by Bruce West who works for the military and maybe jointly at Duke). Its reference 3 in Montroll’s paper PNAS #75 october 1978 ( http://www.pnas.org/content/75/10/4633.full.pdf ) . The entropy journal (mdpi.com) papers are on ‘fairness’ and ‘executive pay’ 2009 11 #4 and 2010 12 # 6 by ‘venkat’ (first name –you can probably search it). Foley has a ‘better’ paper in a 1994 journal but its still a wreck in my view (and conflicts with his smith collaboration). He wouldnt talk to me about it.
In general, David Wolpert’s stuff on game theory and stat mech i find close to the way i think http://www.arxiv.org/abs/cond-mat/040258 for example .
Another paper which mentions the ‘confusions’ is arxiv.org/abs/0903.4216 (‘statistical thermo of econ systems’) . You can also glance at entsophy.net. (a blog).
I’m just passing these along if you have time and curiosity. (There’s a ton of stuff out there, much of it redundant, but its hard to tell given the quantity.).
I come from the ‘boltzmann approach’—i see it as equivalent to Gibbs (and i distinguish them as one starting with the microcanonical ensemble, while the other focuses on the canonical). (There is of course a huge literature which discusses whether they are equivalent, with prominent physicists taking all views—‘equivalent’, not—boltzmann is right ‘, not-gibbs is). Yakovenko uses the boltzmann formalism. (I have read only a few Jaynes papers which used boltzmann form).(The economist Paul Samuelson has a couple of papers in PNAS (proc natl acad scis) in 1974 which are based on Gibbs formalism (he adopts it from previous models in biology). (on Marxism!!!).
There are papers applying this stuff to electrical power grids though i can’t remember where they are on arxiv.org
Last notes—‘free energy’ i do think is what is important (it combines entropy and energy). (There are lots of papers from various approaches promoting entropy; most deal with thermodynamics which i generally avoid—i like to start from microscopic level.) I will say i am almost more of a historian since i spend alot of time looking at what has been said on an issue, as opposed to just developing my own model. (The most intriguing part of your paper to me if i recall was discussion of euler-lagrange and action principles ).
Is this the Wolpert paper, http://arxiv.org/pdf/cond-mat/0402508v1.pdf ? Interesting. The derivation of both Gibbs and Boltzmann requires that the particles do not interact with each other. They are formally statistically independent. When covariance is considered, the entropy of the system is reduced by the covariance matrix. The problem comes in when considering these particle interactions the math is very very messy. I had to work through some of this in Plasma Physics. To say complex is an understatement. I need to look through this paper some more. I use a modified Metropolis Algorithm based on my derivations to help parallelize quadrature on my GPU’s. He has some similar outcomes and some other very interesting insights. Thanks for sharing this paper!
My thesis research is on state space modeling of reactor cores and optimizing control regimes in load following. The Wolpert paper is actually very useful in the time domain because of the formulation of the action integral. This allows time domain quadrature. Here is where I got the idea http://johncarlosbaez.wordpress.com/2013/11/11/quantropy-part-4/
The paper arxiv.org/abs/0903.4216 makes an arbitrary conserved quantity that is entirely unnecessary. The derivation is still capable of being done, only by conserving the density of phase (the phase space pdf). Additionally, the form of the exponent of that canonical distribution is a function of the statistics. In terms of ‘s and ‘s of a generic coordinate system, the statistics of the system are described by the relationship between these parameters. As an example the distribution of an ideal gas results directly from . When we get into quantum theory, different particles have different statistical distributions. You have fermions that obey Fermi-Dirac statistics and bosons that obey Bose-Einstein statistics. I have not gone back and determined the , relationship of a lognormal distribution. Interesting that their equation (23) is similar to what is in my work, just obtained from a different set of assumptions. They are quite right to study the phase transitions. They do their derivation from money, I start from utility. Their approach is limited to a single assumption and that is that the marginal utility of money remains constant. In a utility representation, entropy takes on different connotations, as does temperature. The concept of temperature as being carries more meaning as that is a measure of economic activity. Their paper is interesting, but misses some key things that I covered above.
I use Boltzmann’s approach directly in nuclear reactor analysis our entire methodology for modeling cores is based on solving that integradifferential equation. Boltzmann’s characterization is easier to determine how the system responds. Gibbs approach, is much simpler to understand what is happening and why. Both are useful.
Free energy is an ability to act. You are right to see its importance. It combines the freedom of the system (entropy) and the kinetic (income) to realize the extent and the number of different ways people in that economy can act. I don’t like thinking of entropy as disorder. I like to think of it as structure and complexity.
I do electrical grid modeling too and am familiar with the concept of flow entropy, It is quite useful.
Let’s keep the topic open this is extreamly interesting and informative. Thank you!
Thanks for responding—i like these discussions, so maybe they’ll continue. (Or maybe not after this one—it turned into a creative writing project, some possibly offensive to people (eg pc types) with no sense of humor. But there are serious points mixed in. You may not want it on your blog though).
(Of course there is an opportunity cost involved in responding —i think its almost 100% sure that if i walk up the street now and buy a lottery ticket, i can retire rich and devote myself to philanthopy—eg help the poor who squandered all their money playing the lotto, but didnt have the math background to win like me. But i don’t feel like it. I’m living with my New Year’s resolutions (same ones every year) to stop bad habits, squandering money, and to stop procrastinating—which means I operate ahead of schedule, and already have my next year’s new year’s resolution, which is ‘stop procrastinating’. If you can do it tomorrow why do it today?
Or how about you employ me to search the web for references—the invisible hand will optimize, so i’ll do the bibliography and sign my name to the author’s line, and you do the rst of the paper. i do need a job i have been told, but it doesn’t fair, nor compatible with the max ent solution.) .
A few comments:
—yeah thats the Wolpert paper (he has alot on arxiv). (i am bad at typing and dotting i’s—i would often mix up ‘-‘ and + signs, and it might take me hours to recognize the error because i’d keep repeating it, like a fly trying to get out of an open window which is stuck on the glass. Its interesting psyhcology, those blind spots.).
—-i agree your use of utility rather than money is more general. Money is sort of the ideal gas or simpest case. (have you heard that song ‘golddigger’ by kanye west ‘give me money, its all i need…’ Utility (functions) can be complex; so converting everything into standard units of money simplifies things—as they say, everyone has a price (capital, labor, human capital, natural capital, intellectual, social capital. ‘monetarize everything’ (some economist at GWU, maybe tyler cowan. If some say ‘can’t buy me love’ (Beatles) then they because they didn’t work hard enough.).
There are definately several different ways temperature is viewed in the econophysics literature; many of them however are (or seem to me ) somewhat conceptually equivalent—-eg average income of a society, average level of development, etc. (Sometimes however i suspect people took the way they characterize temperature from some other paper they read, and then say this is the meaning of the temperature in their derivation, though its not obvious and possibly false. I actually once talked with an economist who was peripjherally doing econophysics (and now is pretty much on it) and asked him about temperature in his model (since he was using some results from stat mech which involved temperature. He said there was no temperature in his model. Its like when i asked Cockshott about an equation in his book with Yakovenko—the fokker-planck equation (which at times is called the boltzmann equation—and he said he’d never heard of it.)
—-I looked at your discussion of the max ent approach to income distribution. As I mentioned, and its the same point i made to the person at Purdue who published in Entropy J (also on the lognormal), that is, just another convention or norm, as is Rawls’. You apparently claim that maximum entropy state is say, the most productive, or what i would call the state of ‘maximum social welfare’ (which some might say ‘best quality of life’ and others’ pareto optimal/gerneral equilibrium). On a simple level if maximum entropy were optimal than in my view (since i believe in cosmological and biological evolution) we should all be trying to turn the world into a photon gas. You have expertise here—‘drop the bomb, make earth a sun, let someone else, have some fun’. ‘Burn baby burn’—let the heat death (boltzmann) begin.
The economy is a nonequilibrium system which can be approximated locally by equilibrium and max ent (with Prigogine’s ‘dissipative structures’ or the ‘maximum entropy production’ or ‘edge of chaos’ principles, for example, being suggested for optimizing nonequilibrium states). Formally my view is one can write these so they look the same as the equilibrium case, but they have a different interpretation. (i.e. the boltzmann distribution applies to an ideal, noninteracting gas, but you can write a boltzmann form for ising miodels, spin glasses etc, which describe interactions, have phase transitions,etc.)—–Just as you can write down a diffusion or fokker-planck (or boltzmann, langevin, master ) equation desribing a stochastic process in a Hamiltonian or Lagrangian form.
I will say when i saw that it blew my mind.because i was always told hamiltonian/lagrangian dynamics are determinstic, conservative etc. unlike statistical evolutions, but then some tricks were done. Entropic gravity seems to be the culmination of the picture—newtonian/einsteinian determinism is the same as maximum entropy. Ariel Caticha in my view more or less already showed ‘entropic gravity’ before the recent work — Wolpert’s information geometry is in this school. )
I might almost say that the same is true for communism and capitalism (entropic gravity becomes communistic capitalism), –eg Rawls vs Hayek—-and I am not particularily impressed by either of them:
—-aside (interlude) for a brief rant: (You may want to skip this)
I don’t like Hayek because I don’t think he had much to say other than the calculation problem (which was one very good note—-i read his stuff debating lange/lerner, which paul cockshott, who has a book with Yakovenko, has ‘solved’ due to computers; the book emerged from a conference on Machover’s ‘laws of chaos’—see below). The rest of his stuff has been said better by anthropologists and evolutionary biologists—-it seems he would write 1000 pages saying what others had said better in 30. I guess Hayek’s appeal may rest in ‘spontaneous order, or catalyxess. I learned it as self-organization. (I guess this way he is called ‘eriudite’ or wise). (Some of other people if they write 300 pages more, turn the rest into rigorous math which starts from microfoundations and then gets the macro principles; the people i’ve run across who read hayek won’t do this, but are like people who love to talk about quantum theory but got it from watching the film the Matrix or Bleep somethig and don’t want to learn calculus.) .
I also read his ‘road to serfdom’ and I thought it was sortuh like a snarling rabid dog, like modern ‘hate radio’ (limbaufgh, michael savage, levin, etc.). Of course he had a point since the USSR and China made some mistakes and are not perfect communist utopias, just as Hitler did not turn germany into a perfect all blue eyed blond aryan nation, but he was a vegetarian who was kind to children (as was stalin) and had the t/rains run time. Idi Amin of Uganda, made a few mistakes, and George Washington only released his slaves after his death. But l still think criticisms of them are overblown, and there is no reason to be impolite. Reasonable people can agree to disagree. For example, in the case of Hitler, its unproven that there was a holocaust—and the fact is the ‘concentration camps’ actually were places where Einstein, Max Born, Heisenberg, and their students could concentrate in a beautiful natural environment, and go camping and hiking. Thats why they are called concentration camps. Mao’s ‘cultural revolution’ is well known to have produced most of the literature and music from the 50’s and 60’s, which culminated in the ‘summer of love’ at Tinamen’ square featuring the beatles, rolling stones, poetry by jack kerouac and allen ginsberg, the sex pistols, biggie smalls and NWA. Later, in the Chinese Invasion (which occured after china bought the UK, so some call it the british invasion) all these bands came to america and played at Altamont. .Then they went east (unlike William O Douglas–supreme court judge—who went west ) to the Plymouth Rock scene. where they were signed sealed branded and delivered by their manager, Niall Ferguson of Harvard( now NYU) on the highway to hell. (See Roadrunner by Jonathon Richman and the Modern Lovers on youtube). Niall Fetguson is famous for discussing ‘debt’ (see also S Keen and D Graeber) and also pointing out the maximum entropy solution for the optimal distribution of income in Africa was achieved by European colonization of Africa—the history of the Belgian congo, apartheid etc. may seem bad, just like WW2, but its part of the ergodic process, and one has to break a few eggs to achieve pareto optimality. Open borders and free trade in human organs maximize entropy. (I think this message could be turned into a jingle by the old SF hardcore punk band ‘intensified chaos’).
I dont like . Rawls because he seems logically impaired, and/or pampered and lazy. He had many years to see what conclusions follow from his basic axioms which are fine as axioms (imagine your ideal world, etc. whether ayn randian or marxist or anarchist or libertarian or totalitarian or fascist ore theocratic…) , just as discovering that 1+0=1 and 1+1 = 2 is fine, but then maybe in the next 20 years you could see what happens if you try to solve 1+2=? . see if you can figure out induction. (start by helping the least of the least, and then step back, and iterate the process. Will you run out of the ‘least’ or is the system uncountable a la Cantor and Godel?) Or even see if you can try counting to ten, or solve reimann’s conjecture.
And then you have a whole Rawlsian industry of people (like Michael Sandel of Harvard, who is a deep ecologist (and sees all living things as equal, far beond Rawlsian equality) and so compassionately shares his entire income with his bank account) who dis/cuss in philosophy journals whether 0+1 is the same as 1+0, and whether the two 1’s in 1+1 are identical (a la gaussian particles) or indistinguishable (like bosons), and what that implies about 2—perhaps its a chiral number, occuring in left and right handed forms (like the nazi symbol) which don’t commute, so arithmatic is a quantum system, and may involve an aharanov-bohm effect, and there is a gauge symmetry.
And I especially hate the fact that he was some sort of bleeding heart moralizing self-righteous guilt tripping holier-than-thou dude who goes around preaching ‘i love the poor’ when all he was doiing was collecting a fat salary in an elite ivory tower, hanging out in the faculty club with the coeds, and also giving A’s to students who to go work as robber barons on wall street and pledge allegiance to Nozick or von Mises. He doesn’t walk his talk, like a bunch of preachers who are essentially con men. Of course that may be a good strategy—if you make your living talking about the poor and the least among us, its good to send your students out to dupe and then foreclose on people so you have something to alk about. Its like the people here who were reparing bus seats—after work, they’d go and slash alot of them up. the way a farmer must work to plant seeds to get a harvest. . (There’s a ton of people like this—lawyers in the hague teary eyed and seeking justice by prosecuting war criminals who will never be found, making fat salaries—and those war criminals did their crimes basically because they couldn’t get a cushy job in the hague since they weren’t on the govt payroll. All these ‘institute for peace’ people who want the US Government/taxpayer to fund their institute (which a few times a year will welcome the public for an inspiring talk on peace) so they can sit around and write policy papers citing John Rawls, Martin Luther King, Ghandi, Jesus, the Dahli Lama. We want a piece, and now we can afford to get one.
end of rant—————
As regarding the randomnness (entropy)/determinism equivalence, and the capitalism/communism equivalence, i would say 2 things—if one looks at general equilibrium theory in econ (arrow-hahn etc.) under certain reasonable assumptions (eg that people are basically the same, all self interested, all want the same thing, all have deep compassion for the poor and love of humanity, all believe some things have intrinsic value that can’t be monetarized (eg spirituality), all want to rule the world and also be able to buy anything or anyone money can buy or just take it if its not for sale, then the unique stable (obviously) pareto optimal equilibrium is an equal income society. Just as if x=1/x then x =+1 or -1, (own inverse) Adam Smith=Rousseau. (Of course you have to translate everything into cash values. A famous think tank, which funds a ton of famous scientists including noble prize winners—the John F Templeton foundation—has done this in their ‘spiritual economics’ track, as have many catholic economists i’ve read—i think they can show that good catholics, and christians in general, don’t believe in government (except of course when they fund with $millions so-called ‘catholic charities’ which serve the poor) believe people can and will, if they follow biblical principles, tithe and give to charity so there is no need for a government ‘safety net’ —for example, if people did the ruight thing and tithed 10% of their income the Catholic diocese would be able to pay off all the lawsuits brought against them by the children of their congregations.
(This would be an example of a conservative system in perpetual motion, though it can easily be generalizable to the nonequilibrium nonconservative case, since those who receive payoffs from the church for lawsuits can then give to charity, by tithing to the church who can then settle lawsuits against their children, and so on.)
(As noted, since max entropy solution is the same as the deterministic one—an apparent contradiction— you have to ‘break it down’ as they say, which is where the Gibbs/Boltzmann distinction comes up. The ‘unique stable equilibrium’ actually has ‘degeneracy’, so what looks like a single point in ‘mu’-space (boltzmann) is actually a huge number of points in ‘tau space’ (gibbs)—in fact the biggest part of that space when ‘coarse grained’. (I.e. its just an illusion like time. Its purely subjective, and a bias. Its like people who look at a billboard, and think it says something like ‘coke is it’, when actually if they took the time and care, they would realize there are many other interpretations if one uses a ‘fine grained’ microcanonical description. Coke is it may be the most probable interpretation but their are outliers in the list of all possible advertizements (or constellations, hallucinations, or configurations). ).
Machover’s book ‘laws of chaos’ makes the same point. If you assume maximum entropy is optimal, then actually over time (the system ergodizes, time averages equalling space ones) then everyone will have the same ‘lifetime income’. Molecules in an ideal gas are not stratified. At all times some will be poor and others rich, but over time they all go through the same phases (points)
(One can ‘fix’ maximum entropy’s inconsistancy with the empirical facts that people do inherit money and classes are often rigid with little social mobility, by saying something like lineages (ancestors and future generations) on average are all equivalent in income, which leads you into the mathematics of population genetics. Civilizations, like rock stars or wealthy families, rise and fall.l I am sympathetic to this idea in principle—rather than ‘races’ there are ‘clines’, and with genetic engineering in the near future every single person and animal will be able to mate with every other one, and even rocks and planets and bank accounts and hedge funds. That will be the maximum entropy solution. (Also, it permits the simplification of using money rather than utility, where money is seen as something like a superstring. All the different utilities are just different modes of vibration of the fundamental money particle.
A related idea is http://arxiv.org/abs/0902.4274 if you haven’t seen it.
I think Murray Gell-Man did a start on this with his quark theory, which if i recall has something like M1, M2, euros, yens, bitcoins, ithaca hours, etc. which go up and down but conserve color, charm, and other properties which enter into the utility function. (One conjecture is that supersymmetry exists, so there is also a futility function, referred to by people like Rush Limbaugh and Paul Ryan as lazy whiners, unlike them who talk hard for a living).
A couple of other points. I don’t think there is any real justification for preferring say, lognormal, pareto, exponential, beta or some other distribution of income (and i’d even say gaussian, or maybe popular opinion would aim for political correctness so i’d say ‘1 sided gaussian’ , though i could make an argument for the general case). There are reasonable ways to derive any of these—yakovenko gives 2 for the exp, one his own approach of max ent, and the other a more basic deterministic one (just as a fractal can be created purely deterministically or by a random process. Check out the prime numbers.)
The lognormal is seen to come from multiplicative processes, sometimes, and pareto from ‘preferential attachement’. (increasing returns). (Part of the differences are due to whether you consider income of individuals or households—do babies have any income?)
But there are hidden assumptions in these. For example, if one follows Yakovenko’s approach, but decides that not only individuals who reveive income are distinguishable by randomly exchanging money, suppose instead we take these indistinguishable individuals and randomly throw dollars at them—ie quantize the exchanges , and assume the dollars like people are distinguishable. Then you get a gauss distribution (urn model).
Gertrude stein i think said ‘a rose is a rose by any other name’. Is a dollar a dollar? (eg law of one price). is a job a job?
So maximum entropy solution is highly dependent on how you count your states (as you mentioned with fermions and bosons). For example 2 jobs which pay the exact same wage would be seen as identical and exchangeable according to Yakovenko’s model—they lie on the same energy surface. But some people might prefer a stipend as a grad student to working in fast food. They might follow Yakovenko and accept any job at a given wage, but then one would buy the others job and become poorer. (This fact is a basic one in economics—according to General Equilibrium theory, once the ‘walrasian engineer’ (invisible hand) has done ‘tattonement’ (calculated prices) there is no reason to actually do any exchanges. If I am starving and have 5$ to buy something you want to sell for 5$, according to the theory the utility or welfare of the system is the same whether you do the exchange or not. Econ is timeless just like equilibrium statistical mechanics.
As i mentioned any distribution of income can be achieved as a maximum entropy solution by choosing your constraints (i think this is well known for exp, pareto, gauss, long normal etc.). In generasl econ, the same idea results from the ‘first’ and ‘second’ fundamental theorems of welfare economics if i recall—any distribution of income can be achieved—and it will be a unique pareto optimal general equilibrium—if at the beginning you set up the endowments (original incomes of people) the right way. Or you can transform any pareto optimal income distribution into any other by redistributing it. Since both are pareto optimal only some other criteria can be used to distinguisah betwen them.
This Rawls’ ‘original position’ concept, which is the same as that of equal a priori indistinguishable used in maximum entropy.
In some ‘coordinates’ a uniform distribution of income, or one where the Gini=0 will appear to be exponential or whatever. If you have an urn and distribute balls into them, you might just ask how many balls per urn exist; or you might say hiow many light ones versus dark ones, or how many of some color. Does it matter if you have N rather than M balls in an urn, or do you have to consider if you have some N, and also that the N conists of A dark balls, and B ligjht balls, or X, Y,Z… balls of different colors?
This is also why ‘phase transitions’ are important (interactions). You may think a maximum entropy is the most ‘productive’ (eg catalytic, considering chemistry). But thats questionable. ‘Optimal inequality’ may not be or always be say, lognormal. And, besides empirically it isnt. I guess we could have government fiscal policy orient towards this say, G=1/2 point, like 0 inflation. (You also seem to have a bit of that anti-tax libertarian streak—the government is stealing our money. Well, the government did more or less develop the internet, and most higher education in some way is dependent in part on taxes.
I’d also say, as far as i am concerned, much of private enterprise steal my, or ‘our’ money, because they are con men who sell crap and are as coercive as the IRS and police indirectly. )
Last, i actually read Azimuth (baez’ blog), off and on. I saw that article (i note he mentions a possible type in Lisi’s path integral).
The points I mention above regarding how you count states in statistical mechanics (the simplest situation when considering distinguishable particles versus quantum ones–ie bose and fermi stats) actually are sort of the topic of another john baez post on the front page—-chemical reaction networks, Thats closer to the way economic systems should be dealt with in my mind. y. These are very constrained interactions. (This is the kind of thing that got me interested in stat mech besides the fact that it was required classwork—i did an undergrad research project using max entropy to figure out aspects of the immune reponse—how different antibodies react with different antigens—-its not an ideal gas nor a simple random graph (where any 2 things can be connected to each other). There are mutliple constraints and multiple optima.
The same thing with income. If one is simply seeking any distribution with a Gini=1/2 one could do it deterministically —first in line gets the most, last gets the least (and also actually in quite a few ways—both who gets what positijn in line and how the portions are doled out). .
So the normative question is open. Facts=/Values. Is=/Ought. I think we need a variety of currencies which are mutually inconvertible. (One is going to have maximize a function of several variables, which means most likely multiple optima. You are for freedom and liberty—-in what? Freedom to take a walk without getting hit by a car, or freedom to buikl a highway where ever i feel like? Maximize income like in china, but have no clean air?) I am an ‘environmentalist’ so my view of maximizing ‘growth’ is not the same as what others mean by it.
(I started in math biology, as I noted; i wandered around and found a research project (with a visiting prof from Santa Fe institute); when i showed my prof in my math bio courses what i was studying he stopped talking to me, cuz he didn’t like the chaos and complexity approach)..
anyway. obviously i havent looked much deeper at your stuff.
A short reply. I had some thoughts on Baez paper and of looking at quantum systems. I like classical mechanics very much. There is a very simple elegance. However the domain in which it is applied is important. I was taking a course in nuclear physics and couldn’t help shake the notion that the system of a nucleus if its relaxation time is much shorter than our observation time scale, then what we observe at our macroscopic level will be a fixed number of quanta with defined probabilities of occupancy. I haven’t gone down that rabbit hole to even test the hypothesis, it is conjecture. What interested my about the quantropy post is that formalism strikes me as well suited for a variational approach to tease out the allowed quantum states. But this is dependent on a suitable mechanical model.
As for maximum entropy and the issue of path dependance. I agree those have impacts on the outcome and would provide greater insight. However, without that detailed information, and the construction of a suitable model to explain that information, arriving at a state of knowledge that included that information is impossible. The affect of including this information, only acts to lower the system’s entropy. These are restrictions on the actions of the individuals within that group. by assuming logical independence, indistinguishably, and time invariance the model provides a theoretical maximum on the entropy of the system. Only by the inclusion of extensive forces (not intensive constraints), can the entropy of the system increase. What is important to note in all of this is that the impact of those constraints is small, as the relative entropy from my very crude and simple model is close to that of the observed data.
For the path dependent data to be included it has to first be collected and analyzed with an appropriate amount of rigor. This has very real costs. In my simple model I looked at the data and sought a model that explained with the greatest parsimony. It happened also to have a wider applicability, including species distribution, and one that I found, in the distribution of Radiation Induced Foci in post irradiated cells. To me, the parsimony and the widespread applicability give this distribution better aesthetics over others. I chose it out of aesthetics really. However, as I noted in a previous comment the defining distribution defines the relationship between the ‘s and ‘s of the internal coordinate system. So while it may be aesthetics that guided me, there may be a deeper understanding to be gained.
If not the principle of maximum entropy then what other assumption do you propose as a guiding principle that assumes less. Yes the tendency of a system to the point of maximum entropy is a tendency toward ergodicity. This is clear that the change in information of the system with any increase in time is zero, . It is a formal statement of what is ergodic. An ergodic system is one where our knowledge of the system does not change the longer we observe it. I recall mentioning something like this in Elementary Principles.
This is a very gross assumption, it does however, greatly simplify the math and provide an avenue for increased insight. What surprises me, is that even with all these terrible assumptions I can still explain the data with some fundamental insights. Increased sophistication and complexity often times makes it difficult to comprehend. This is why when we teach new nuclear engineers how a reactor works we use a one-speed time independent reactor under diffusion theory. What is really funny is that if we are very careful of how we compute the integrals for the cross sections we actually have a very accurate representation of the flux distribution in the core. When we look at the adjoint flux, we see that the location where the neutrons are “born” in the core has a significant impact on their importance in the system. In fact, we call the adjoint flux the importance. So, my brutally simple model that provides reasonable insight into income distribution and inequality shows very clearly the fundamental drivers of why it is the way it is. This approach and my experience guided my logic in selecting an appropriate model.
So what will the tendency be for society, to achieve a state of higher entropy. This will be through increased energy consumption and/or increased liberty. That is not a normative statement, that is positive. I am not a logical positivist either. I can just say what direction humanity is going. I can also say that ANY policy acting to restrict this tendency will create a force to overcome it. Why I like higher entropy is that it ensures survival. You could construe that as a positive statement, however I think self preservation is a normative value, as it tends toward a point of maximum entropy for the individual.
The current set of policy that we have, that I critique in my blog, tends to restrict our entropy. As a result our societal entropy is stagnating. This is very dangerous, as pressure is building to affect change and increase entropy. I had a very dear friend tell me, “There is no such thing as good or bad. There is only consequence.” I seek to understand the consequences. Here is my first law of public policy: restricting individual freedom increases societal pressure against the agency causing the restriction. impulse=>reaction. So as I said in a blog if we want to end global poverty, we must increase individual liberty and increase our energy consumption. The goal of ending global poverty is used to do some really wacky stuff that has no forbearance on the outcome and constitutes pouring money down a rat hole.
So here normative goal “end global poverty” has a defined set of policy outcomes, increase liberty and energy consumption, and that everything else is just mental masturbation.
Another normative goal “income inequality is a scourge on our society and we must have those who do pay their fair share” has a defined policy outcome where the stability of the system is reduced due to increased social stress due to a reduction in specific entropy in the developed nations. This lowers the overall societal wealth embrittling society making a extensive shock potentially catastrophic.
These are consequences of policy design choices. As an engineer I am constrained in my design choices by what I have available and the laws of thermodynamics. It is no different in public policy. Their problem is that they don’t understand that they are constrained. I’m reminded of a quote from The Hunt for Red October, the second officer to the commanding officer (Rameus’ old pupil) as a torpedo he shot performed a circular run after he ordered the ACR safeties removed, “You’ve killed us all you arrogant ass!” The policy makers removed the ACR safeties on a presumption of knowledge, just like that CO did. The safeties on the economy are free and unfettered markets with a strong common law. Just about every single policy we have disables each of these safeties.
There is only consequence.
1. To me ‘free market’ is too vague. Like max ent it works in ideal cases, but once you add in long term dependencies it becomes say ‘NP-complete’ if not undecidable (as is seen in evolutionary game theory) . And the common law is also NP complete or undecidable (Arrow’s theorem, condorcet, Donald Saari, S Brams…)
Maybe there is a common law (presumably the maximum entropy solution since its the most common or probable state of the union) and all the other ones are just fluctuations which will dissapear in the fossil record or universe. In a nonequilbium world, you may not know when you are there,
(As an aside regarding your idea about decay of the nucleus, i guess i dont understand it, but that seems to me to be the accepted wisdom. A nucleus is a long lived (long in the sense that supposedly even protons decay) metastable state, like everything else we see. Thats why we see it. There may be ET’s who can’t see it, or the earth, because like rocks who don’t notice biological evolution , its not on their time scale. I bird watch sometimes, but unlike some others i have a hard time seeing them because they dissapear fast, like the mice in my apartment. I even missed the recent eclipse, and the Higgs boson.
The Ferm-Pasta-Ulam simulations (FPU) from the 40’s to test the ergodic hypothesis with a slight modification of the ideal model (ie they added a quartic interaction to couple harmonic oscillators) seems on point here—they didn’t find equipartition of energy (signature of ergodicity), ahnd that led to chaos, KAM, etc. theory, More recent work however suggests mayvbe they just didnt wait long enough. In other words, one could say the system has path dependendence, and there are several attractors of the system (which actually are all part of the same ergodic system) but it takes a long time to get from one to another.
Phase transitions, like plant succession and evolution of species, are really just phases the universe goes through, the way people go through adolescence, senility, etc, and then come back again (after quantum mechanically tunneling out of the cemetary; Count Dracula published on this in the 20’s, and modern crionics has rediscovered it. As an aside i was looking at a biography of famous serbian scienctists (many of whom seem to all have the same name) who include Tesla, and there was one around 1900 who wrote a book discussing economics and thermodynamics (who supposedly was very obscure).).
You say ‘the safeties on the economy are free markets with a strong common law’. (So unlike some ‘market anarchists’ (David Friedman, son of Milton, at UCLA i think) you believe in some form of ‘minimal’ governemtn (as opposed to private ones like he believes—private armies, police, etc.— a sort of ‘tribalism’ though internationally the world operates the same way, as a set of tribes).
the question is ‘what is the common law’? Do you try to use, say, Coase’s theorem (do anything you want but compensate anyone for the costs your actions impose—-which as he noted is practically impossible to enforce, since people die in court). Should it be US or Universal Declaration of rights, the consitution, Sharia, 10 commandments or what?
Is the common law unchangeable? If not, is it ok for rich people to buy legislators to make the common law favor their interests (eg use ‘takings’ to bulldoze neighborhoods so they can build a sports stadium for rich m-frs, and the common law will also require that local government pay for the stadium, and also that players who get hurt within the first 3 years are not owed a dime.)?
Usually or often the common law is not for ‘commoners’ in some sense, though likely its named ‘common’ as a way to deceive people so they think it is for them. ‘Ask not what your country can do for you…’ Of course, people do love walmart, as do the rich people who own it. (They just built one near me, with a big fight over their minimum wage policy, and also the fact that local small businesses would be effected. They of ccourse gave tones of money to buy off local politicians and community leaders)..
Should GMO modified foods be labeled, cigarettes have warnings, we have laws about dumping toxic materials, regulations on nuclear power plants to avoid Cherbonyls (or high utility bills duem to having to replace reactors like Harrisonburg, Pa).
Does the market include ‘natural capital’—should we put a price on clean air, or should we permit the world to be like in China (or Pittsburgh and London in the 1800’s) and not force polluters to clean up their emissions? Do we regulate speech like in France where holocaust denial is a crime, or via FCC regulations on what is permitted to be seen or said on radio and TV, and also how you decide who gets a ‘ownership’ or lease’ of some frequency , and under what conditions you lose the liscense? Should there be a ‘fact check’ rule (beyond ones on nudity and profanity) so that if someone proposes that 911 was an ‘inside job’, or denies it, that AIDS is not caused by a virus (or is) and autism is (or isn’t ) caused by vaccinations, that evolution is false (see F Tipler.and Freeman Dyson’s signing of the discovery institute’s petition on ‘intelligent design’ ) or true, etc.
‘Should there be a ‘core curriculum’ in education, and should intelligent design be taught in biology? Should people be required to attend school, and should parents be required to provide for their kids? Is universal healthcare required by ‘common law’, and littering prohibited?
Is the US Consitution or US declaration of human rights, or Universal declaration (which differs from the US one because it does not require that people vote, serve in the military if asked, and some other things) the common law? Does it require that one let people of other races into your business or public school (eg civil rights movements), or that Catholic hospitals must perform abortions?
People say ‘your rights extend to the edge of my face’, but in a networked, non-ideal gas society there are long interactions—-should people be permitted to put on facebook private communications (eg pictures of your ex-freinds in compromising positions, or to ‘out’ gays )
or violent scenes (eg beating someone up ) or does common law prohibit this because it breaks the peace? Do free markets include speech? Should we tax carbon, or include it in the market? should there be regulations on elected officials requiring them to go out and shovel snow in atlanta?
The devil is in the details. ,
———–How many regulations? I like the idea in congress—first, you pass the law, then you read it. In education too—First i get the PhD, and then i do the research, and then i write the thesis. Following Herbert Spencer (libertarian) every baby when born should be endowed with a grant (including a bank account with their entire lifetime expected earnings, a full of academic degrees, honors, prizes, certificates for qualification as expert plumber, winning lottery cards, and valid id, property titles and driver’s liscense. Then they are abandoned and are ‘free to choose’ (milton friedman) in the unfettered free market (and then one sees if maybe they are ‘born to (o) lo(o)se’ (New York Dolls, a band on youtube—Frankenstein is my favorite—the US military shouldah used that in Iraq to torture people). Babies could then follow Marx and sell themselves to increase their grant (though it becomes impossible to determine whether, say, education is something you buy or instead is an income generator). Maybe employees employ their manager and company, and dogs own their masters.
Can max ent determine how many books should be in the library of congress or local one, and how many pages should be in the tax law, or steps in a proof of a theorem?
(An article in Parade Magazine by the genius May Savant (or something) actually solved this, by calculating how much energy is required to publish tax law and math journals, or store them in ‘the cloud’, see http://www.cs.nyu.edu/pipermail/fom/2013-November/017696.html
and the entire thread (esp 677 and 684) . It turns out Eugene Wigner discovered the common law (unless its ‘constructal theory’ by some engineer in NC which may be the same thing)..
Maybe we need another huge buerocracy to study how big the beurocracy, court system, etc should be— and maybe its required, by supersymmetry. As Ernst Mach and David Mermin (in qantum theory) showed, people need mirrors, and the moon needs people, to exist and shine, and this is why prohibition laws failed because we need moonshine (i used to get some from some ‘hillbillies’ i knew ‘up in the holler’.) (I met ‘mersol’ last nite— spanish for ‘sea sun’ when i was foolish enough to walk up the street at nite. Saw one of my ‘hoodlums’ selling dope on the corner; i gave him a beer to pass the time and deal with the ice and cold).
Interestingly, it turns out one possible solution among many for optimal lengths of tax codes, using an energy metric (eg H T Odum, R Constanza,etc. in ecological economics) is that ‘MOre can be better’!! because if one cuts all the trees and turns it into legislation one can then sequester it (like carbon) and then grow more trees, and keep doing the process, and soon you will get oil reserves, and life is happy ever and in perpetual motion. AS Say (actually didn’t) say, ‘supply creates its own demand’, and the reverse. (That was Keyne’s interopretation of Say, while what Say said was that using the perron-froebenius theorem you can find the fixed point of general equilibrium. Sonnenshein among others showed that just as its not unique for some set of fixed preferences and endowments, but also there is no way to assign a unique set of preferences.
Like max ent, its just a convention.
(Bitcoin is interesting in part because apparently consumers, or users, play the part of the Fed—they set the exchange rate. One day you use Haldane’s rule and value your family by genetic relatedness—your identical twin being more valuable than your nonidentical one, whose is more valuable than your brother and sister, who are worth more than your cousin, etc. and really valuable .
Next day you sell them all for a low price to buy heroin.
You say increasing entropy and energy use should be the goals. (And that seems to follow from your ideas, as well as the equations).
I’m sort of an environmentalist, and also as noted have a different set of math asumptions (which actually are implicit in your work in nuclear power—-maybe on one scale you are increasing energy and entropy by liberating bound photons from their atomic prisons, but in the short run, to achieve this commonly accepted goal so people can heat their houses, entropy is lowered (since the math used to design does not follow zipf’s law in some coordinates and also is temporarily trapped in homes and bodies).
As noted, it might be optimal to build a lot of nuclear bombs and start using them—get a whole lot of energy and entropy. Make earth a sun, so some ET’s can get a suntan.
As an environmentalist, ‘free energy’ is what is important (the original helmholtz version, since pressure and volume are not inuitive for me , except in the sense of music—‘lets get small y’all’ (troublefunk) or ‘its like a jungle outside and i reaslly weonder how i keep from going under’ (grandmaster flash) or ‘submission ‘ (sex pistols) or ‘once in a lifetime’ (talking heads).
Energy conservation should be the priority. I’m not hardcore (though i have participated in some EF! and Sierra Club, 350.org protests etc As a precautionary princiiple, before trashing the earth by the Keystone XL, offshore drilling, etc. see if you really need it.
I don’t think alot of suburban sprawl is desirable, and all these truck drivers listening to rush limbaugh on publicly owned hate radio who are delivering cigarettes and guns and bottled water and junk food maybe should get off the road and stay home and find something to do like get a m-fing grip by reading some science. Maybe an ‘unfettered free market with a strobng commobn law’ would achieve that goal, but, as Johnson said about socialism—‘we could have it tomorrow if we had the votes’.
I looked over your longer paper up front. I don’t understand equn 8 (i think—multiply by 1, etc.) but i don’t think i really need all the first part to understand probability or definition of utility, in a general sense. Your thermodynamic derivations remind me of why i don’t like the Gibbs approach (which i glanced at in the original, and also saw it in Tolman’s book on stat mech and in ‘Gibbs Ensemble, Biological ensemble’ by E Kerner (a Feynman PhD,who also had a VSL thoery in the 60’s). .
I haven;t looked at this stuff in a while, but the Utility you identify as E (or H) somehow to me seems to be not quite what i was thinging of—-i was thinking of ‘individual utility’ (eg my cobbs-douglas or other function) while you are looking at the whole economy. I’ll have to think about it and look some more. I guess in a retarded view, one just sums the individual utilities to get the global one (which i think of as the ‘social welfare function’—utility of the whole society.
From that view, which is how I interpret stuff like Wolpert or spin glass/ising models or S Kauffman’s / S Wrifght’s ‘fitness landscapes’ you end up due to multiple competing interactions a whole lot of possible configurations in the maximum entropy solution, but its multimodal not gauss, exp, lognormal, pareto etc (except in the way that the earth’s surface is normal or gaussian—sure, if you list mountains, heights of people, lengths of sentences and books,you can get a common distribution (most of which in my view are actually almost the same—there’s a paper by Snyder (israeli econo/physicist) which points out ‘power laws’ are canonical ones in disguise, as is also true for lognormal (depending on choice of utility function, as shown in one of the papers I mentioned). (This also seems to be ‘elementary probability’—in various limits (choose your prior of greatest utility) various distributions become equivalent.
The Gini may be 0.5 at maximum entropy, and that may be most desirable state of affairs, but that leaves out some details, like geography—maybe the world’s mountains (and incomes) are distributed optimally but people might prefer to hasve the himalayas over there, the appalachians over here, McLean virginia and madison avenue somewehere else, and the ‘hood down there.
I am actually theoretically open to the idea of a jmax ent income distribution (exp, logN etc.) but think maybe it should be randomly distributed, maybe by lottery, and maybe there should be ‘term limits’ (or as was done with some alternative US currencies in the past, currency would be like coupons or fruiit, and expire or rot—you’d lose it if you dont use it). .
——-I guess i wonder whether you have an agenda or idea with your papers—maybe just free markets and increasing energy use (more (and) freer is better, ) I actually believe that, if that also means we include ‘more’ things in the more. I’d like more wilderness for example, since i use it to use up (my personal) energy. I’d like more people highly educated in math/sciences, and less garbage talk whether on radio, the street, CSPan, etc.
Possibly, for example, regulations conerning degrees and credentials like PhDs should be abolished, and everyone could just set up shop for a free market in ideas….(the blogosphere is in that direction). ola (as some say around here).
You are quite correct that in the real world (non-equilibrium) that our knowledge of the equilibrium condition will be fuzzy, never knowing precisely where you are.
Common Law is an emergent process that is discovered. It exists only as an aggregate of individual action. It does not contain the information of the microscale interactions but is instead a macro phenomena. This is congruent with Hayek’s take on the law. Every individual is bound by it, but is not necessarily aware that they are bound by it. Additionally the discovered law (written by judges) does not contain the full depth of the actual law. It comes back again to the knowledge problem. The law exists without the constraints of government. While, government can exert pressure to influence the law, through legislation and the coercive threat of force, it can not subvert it. The extent to the divergence between the legislation of government and the emergent law is a direct measure of the amount of force the government must exert to maintain it’s control.
For the record, common law was the law of commoners. Nobility was subjected to a separate set of constraints.
You have a misunderstanding of Coase’s theorem. His work was a reaction to Pigou’s arbitrary method of price internalization. What Coase does, is to establish a market to discover the price of the externality, without the presumption of knowledge of the price. The main way that he does this is through the creation of a property right. To quote Coase “I’m just a person who thinks that the government should give up everything. How much the government should give up will be found by studying how the government operates. But the assumption that governments always do the right thing is not true. They make lots of errors, and where they are most likely to make errors can be found by studying how governments operate. My approach to the subject of what governments should do is to be based on studies of how governments actually operate. And I’ve had a lot of experience. I worked for the British government for many years, and I saw how decisions are made. And stupidity is very common.” http://www.econtalk.org/archives/2012/05/coase_on_extern.html His approach is to deal with the world as it is, not as we wish it would work. Coases’ solution to the price discovery problem actually has a limited applicability (wide enough to be significant). It only applies to situations where the cost of establishing the property right are low enough and the social harm high enough to warrant creation of a market.
Should GMO’s be labeled? Only if they want to be. If somebody wants to dictate their own marketing by all means, but to dictate the marketing to society, that’s unclear. So far, there has been no reproducible harm from GMO’s. That may change, but it is not a reason to not use them. The precautionary principle is just a simple means to force your beliefs onto others. It is used to inhibit innovation and restrict competition to existing firms. As for cigarettes, I think that should have been settled in the court system not in regulations. I have no issue against another individual for voluntarily entering agreements with knowledge of a potential harm to themselves.
Actually there was a great deal of common law that governed the handling of toxic materials. Taking Love Canal as an example the disposal of the waste exceeded EPA standards when the standards went into affect almost 25-years later. Common law and proof of damages would provided an incentive for them to limit their liability to the extent that they could. The issue was with the school board (government) wanting cheap land to build a school and ignoring the warnings of the chemical company. So who was at fault? What role did government presume to take in this. What did the resultant regulations solve?
I think it is presumptive for government to regulate what Adam Smith refers to as “propriety”. Propriety is much too complex to put into regulation. Let’s look at how the market would resolve censorship. Say a broadcaster had a vulgar show that the advertiser was looking at placing an add. Let’s say a large number of the advertisers customers complained saying that they wouldn’t buy the advertiser’s product anymore, because of the chosen venue. The advertiser would pull their advertising to prevent the loss of customers. This would impact the revenue to the producers of the show as the network would pay them less. Giving the producers less of an incentive to produce the show. Their reputation would be harmed and they would be less likely to land a pitch. This is just a simple example of Bastiat’s seen and unseen.
You underestimate in your examples the social repercussions of trollish behavior. I saw on a number of blogs the impact of social constraints on individuals who behaved in thuggish behavior. I also witnessed backlash on Facebook and Twitter watching people be ostracized for their behavior. There are also repercussions with employers who search social media. If someone is brutish in an unsupervised media what will happen in your work force if that individual is left unsupervised. They will likely have a negative impact on productivity. Again it is the seen and the unseen. Be very careful about what you presume. You seem to have a lack of faith in humanity. The devil is indeed in the details. The details are in fact so complex that any well intentioned presumption to do good, paves the road to hell.
You also misunderstand what maxent is and what insights it provides. First let’s look at what entropy is within a society. Entropy as popularized is not about disorder. It is complexity. Entropy is a descriptor of the complexity of the internal structure of the system being observed. While complexity may initially be perceived as disorder. It is not. Let’s take the nuclear bomb example. To illustrate the point. A bomb is detonated over a city. and it levels the city. First looking at the biodiversity, most life that was in the city is greatly reduced, plant, animal, and human. With only a hardy species and some other lucky survivors left. The entropy of the biodiversity is now much lower. Looking at the height of the buildings in the city, the entropy there too is greatly reduced. There is no more complex topography, it is leveled. Measuring the economic activity, where was once a vibrant city is now nothing, but some survivors caring for the dying and burning the dead. Again a much lower entropy.
Death and destruction are characterized only by their ability to reduce entropy. The use of nuclear weapons does not increase entropy, it reduces it. It is why I cannot stand nuclear weapons. They are vile things. On the other hand the use of nuclear energy greatly increases societal entropy. It also increases biodiversity as the quantity of fauna supported by the rejected heat is prodigious. Nature is very good at taking waste and making it into something beautiful. I too am an environmentalist. You should read my paper on Rational Sustainability, posted on this blog.
Energy conservation as a mandated social value is used only as a tool to fund boondoggles. It ignores the cost of replacement, the impact on existing assets, and presumes one metric as the measure by which firms and individuals should direct their resources. As an engineer, I am obsessed with efficiency. However, if I make something so efficient that nobody ever buys it, it has no value to society, or to me for that matter.
Our goal should be to expand our energy consumption, not reduce it. Here, I will be proved right. The global poor, those without, will want what we have and the energy we consume. They are markets that are untapped. Their energy use will skyrocket, and be predominantly fossil based, initially. This will put price pressure on our fossil resources. Fossil cannot scale much further, because it lacks the needed energy density. Density and the ability to scale are directly related. For this reason alone, the developed world will shift to nuclear energy and synthetic fuels or it will bifurcate.
Again my question to you is, “If you choose not to adopt maximum entropy as a proposition for logical inference, then what metric do you propose that presumes less?” I’d like to know, in case there is some other form of inference that I am as of yet unaware of. All of the conclusions and examples that I used above are consequences of a system that tends toward maximum entropy. You continue to presume too much.
thanks for responding—-i looked over my comment, and it was pretty incoherent plus alot of typos. i will say you are a ‘real person’ who knows your stuff (nuclear engineer).
i figured out your paper—and that’s why i cited david wolpert. (and there are a few others—i could cite john baez/azimuth but thats not the way to go–he gets lost in the details.). you could always read a book on statistical mechanics. (i can’t reccomend any, but try ‘fokker-planck equation’ by risken, ‘handbook of stochastic methods’ by gardiner, stuff by h haken (synergetics), or even landau and llfshitz from the 20’s or 40’s.
you don’t seem to understand max ent. (and i didn’t see any derivation of cobb-douglas or lognormal in your papers—you ignore or just assume it; some derivations exist, but i don’t see it it in your papers).
the metric is in the wolpert paper, though not explict. (like i said, they are other ones, but they get into heavy math—-though its actually simple—i worked with some of em)
it doesn’t appear you even understand coase or pigou. you have to include the transaction costs—thats why they have energy efficney—or, what i call (helmholtz) ‘free energy’.
as a disclaimer i have so many family members involved in university of chicago that stuff is like coase’s . theorem was elementry school.we just focus on rg wilson (renormalization group) and stuff by leo kadanoff.
Thank you for the feedback and suggestions. I will read through them. I started with Gibbs, as his was to me the most intuitive explanation, , of constraining the variational problem. You are quite right, there is much in there I don’t understand, especially with non-equilibrium discrete cases. My method is very blunt and not nuanced and as a result it misses much finer grain detail. You have no argument with me there.
My selection of the density function is similarly crude. The Cobb-Douglas function is a polytropic process (equation 20 in the various properties of log normal). Power law also falls out of the more standard Maxwellian distribution. The process defines the thermodynamic path of the system (how entropy is gained/lost).
The establishment of markets carries transaction costs, Coase went into that in his first paper “The Nature of the Firm”. The issue is with the relative transaction costs. Based on the Helmholtz free energy of the system (wealth, or measure of the potential for action) the relative transaction costs become a much smaller fraction of the total value gained. This is why, I think, problems in the commons in the past had to rely on social mechanisms, because the relative transaction costs were quite high. Whereas today, the overall increase in wealth changes the relative transaction costs and provides a different set of options, where the use of markets to establish prices becomes the most effective option. I will look at those references that you suggest.
This is also part of my critique of the Rawls. He assumes that the concept of justice is a fixed ideal. I see justice as defined by the system and must be considered within the context of the constraints on that system (such as resource availability and path history). Justice, in my understanding is the internal structure of the system that provides the greatest entropy. The path is critical here, because of the local entropy maxima. These have barrier potential to get to a more global maxima. Funny, when I think about this these state transition barriers act as social transaction costs, much like when evaluating the potentials around critical points. As we approach the entropy barriers between the states lessens allowing simultaneous existence of both states. Or when we think about phase transitions like the transition form water to steam, the process of boiling can be thought of as the emergence of mixture distribution, where the relative probabilities determines the quality factor of the system. My most recent post (Nuclear and Cryptographic Renaissance) you can see the dromedary emerge from the mixture “camel” distribution.
I have Gallaghar’s “Stochastic Processes” but have not had time to read it. I don’t have a solid grasp yet on how to handle the time domain with enough rigor. So, I greatly appreciate your suggestions. To understand QM models and Stat Mech from a different perspective I have Landau-Lifschitz and am working on that. Interestingly, Lev Landau has a tremendous appreciation for Gibbs approach. I gained a much greater understanding of Gibbs and Jaynes from Landau’s insights. As I read Landau it seems the Markovian process of the evolution of a system is an evolution of the system’s density function. I am going to go through the Wolpert paper as that seems cogent and well thought out. I agree, Baez is interesting but overly complex. His complexity has complexity which makes it difficult to understand.
One more comment on how I use entropy to evaluate and develop models. I copied Jaynes. This paper he goes through the construction of a model of Rudolph Wolf’s dice experiment http://bayes.wustl.edu/etj/articles/entropy.concentration.pdf, beginning on Page 11, although the rest of the paper is well worth a read. If you don’t mind, I’d like to resolve what the difference that we have in what entropy and more specifically what is the principle of maximum entropy. While there is a possibility that we are both right, that would also imply that to a certain measure we are both wrong. You asked earlier what my agenda is, my only answer that it is to understand.
Thanks for responding. (I had some hostility in my comments, so i apologize for that (unfortunately i still have the mentality of a 4 year old who explains ‘im going to take you all out( not to a restaurant, but beat you up) because i disagree'(and i couldn’t back it up—see ‘wobble baby’ v.i.c (your part of town—of course i live off georgia avenue (dc’s maximum entropy solution) and we donated this name to the south because they needed an extra quantum state. )
i’m not sure if you have revised your main paper or i missed it, but from my perspective its looking better). (you have something like a louiville equation in there, plus the basic formula for utility maximization. i’ll have to look at equation 20 in your lognormal paper. i am more of a historian—i have many many papers on this sort of issue; wolpert is more close to your issue, and i cant find the other one (someone with a polish name—free energy of graphs with a chemical potential ).
(landau and lifshitz stat mech was one of my bibles—i also like george mackey on group theory (he’s on wikipedia and his classic paper on ‘harmonic analyses as the exploitation of symmetry’ in Bulletin of Am Math Assn 1980—free on web) is also one, plus stuff like on the FOM-list (foundations of math).. Also, i was thinking of C W Gardiner ‘s book ‘handbook of stochastic methods’. (i just google searched it, and downloaded it—someone put it on the web cuz i couldnt afford to buy one—its actually mostly fairly basic but has some stuff in the end which is more state of the art—-path integrals a la dirac/feynman/kac).
the jaynes paper you cite also is one my influences (plus a few other ones). (ariel caticha (on arxiv), golan (info-metrics institute at american university in dc —duncan foley is part of that too are in that way of thinking–but i call that boltzmann as distinct from gibbs—they count ‘particles’ (eg n factorial) rather than dealing with tau space (microcanonical ensemble)).
well it looks several feet of snow and i have to out. also, since i’m almost from dc (i moved here from arkansas where we produce presidents and garbage (walmart, faubus, tyson foods) i have to catch a plane to hawaii tomorrow for a family visit, and see if obama has a valid green card, and if not i can go see some of those green mountains up there and try not fall.
I don’t think we necesarily disagree. But i do have a big agenda, though i can’t recall what it i—maybe if read these thousands of papers i i’ll remember. Now i work for a local equilibrium as opposed to global (shower, hit the store quickly if its open), pack, clean up this joint, shut everything down, and try to make it to my staging ground for the airport (my brother’s house) (some think they have a serial killer there in alexandria va because of some recent murders so i’m hoping they can get rid of that person or persons). peace, out. i may not be on internet much for awhile but i’ll check back, to see if we stil have a conversation.