Societal Path Integral by Douglas Alexander Singleton

P.S., You've probably read it, but if you haven't, I think you'll love Feynman's lecture on the principle of least action, Vol. 2, Ch. 19 of his [link:selfdefinition.org/science/25-greatest-science-books-of-all-time/20.%20Feynman%20et%20al.%20-%20The%20Feynman%20Lectures%20on%20Physics%20Volumes%201%20-%203%20%281963%29.pdf]Lectures on Physics[/link].

Doug,

I found your essay very readable well-thought-out and relevant. Far be it for me to judge how humanity should steer the future (I have made Einstein say as much in my essay) and particularly the very reasonable and logical multiple path search optimisation method you have suggested.

My instincts however are that in social and political action people just go ahead and do what they know best, the tried and true, the easiest, or in a society like Japan, what is least likely to be criticised by friends and neighbors. In other words searching out different possible paths may go against the grain of human nature.

Or indeed of physics, Feynman notwithstanding. In my Streamline Diffraction Theory the streamline is the path integral along which energy flows as light diffracts. And according to my Beautiful Universe theory, nature follows these streamlines to propagate energy, form atoms and all sorts of fields. In all these cases, Nature finds a unique path from A to B. Perhaps humans have evolved to act that way too. Picasso said "I do not seek, I find". Perhaps for humanity to get out of its present difficulty, such confidence, even arrogance and sense of venturing linearly along a a single path (and I do not mean that Bali bridge!) is needed.

Yours is certainly the safer way, though!!

Best wishes

Vladimir

Hi Vladimir,

Thanks for having a look at my essay and your comments.

Yes, whether my proposal or any proposal would be implemented is a big question. The people entrusted to enact laws for society and provide direction are often driven by the desire to stay in office which is a very poor motivator for (or at least is uncorrelated to) building a well functioning and logical society. This was the point of my ending story in the essay. In any case I agree that coming up with some plan and actually implementing it are very different beasts.

Also since you use Einstein in your essay (which I will try to read soon) let me say that he is an example, in the scientific realm, of going straight toward a goal rather than trying out different paths. Einstein had a fixed set of concepts in mind of how Nature should work and he was vindicated in his choice of concepts with special relativity and general relativity. However, later in his scientific life this dogged adherence to these fixed concepts lead him only to dead ends (apparently, since it could still be that when we really understand QM Einstein's adherence to his idea of how Nature should work may be proven correct). So if I take your meaning correctly you would suggest that having a social/political version of Einstein would be better than the slow trial and error method suggested by my path integral metaphor. I agree with this but (i) Einstein's in any field are extremely rare (ii) even Einstein was (apparently) wrong after some point in his life by his strict adherence to certain fundamental concepts. The path integral suggested approach is a way to have built in flexibility and openness to new directions once old directions have taken one as far as one can go. It has the disadvantage of being much slower than an inspired move in the right direction, but it also would avoid "inspired" moves in the wrong direction (e.g. Pol Pot's turning Cambodia into an agrarian communist "paradise").

I will get to your essay soon. Best regards,

Doug

Hi Doug,

Thanks for bringing some basic physics into tbe essay mix. Calculating the best probabilities for the future is the method to steer to desired goals.

I advocate a technique to use when the goals are fuzzy... universal education. Take a look, I think you will find it interesting.

Thanks,

Don Limuti

Hi Doug,

Thank you for your thoughtful comment on my thread. And I have a reply you may want to see. And I'll love to know you did see it.

Bests,

Chidi

Doug,

A Da Vinci quote that I like is "the greatest misfortune is when theory outstrips performance" - so whether the theory is your many-paths exploration or my single-streamline to the goal, the devil is in the details and in the actual working out of these generalised ideas. The 'genius' leader leading his country to glory or to infamy is an extreme case of this singular path concept and it is not what I have in mind - what I am saying is that things are so complex and intertwined (society with economics with the environment with media etc etc.) that one does not have the luxury of cool testing this or that path, but is - in a way - forced by circumstances to adjust the aims and methods in real-time, keeping the goal in sight.

Best wishes,

Vladimir

Doug,

Your reply to my comments above:

"My suggestion for how to choose a path for some particular societal question would be to run as many small scale "experiments" as possible and see which ones work best and then scale up to see if they still work at a larger scale, etc. For example if one wants a health care system try various health care systems at a small scale and see which works best according to criteria such as mortality rate, cost effectiveness, timeliness, patient satisfaction, etc. and then expand those health care experiments to a larger scale which work best according to the criteria that are picked. Of course unlike physics the choosing of criteria will be a bit subjective and different groups may weight things differently and thus choose different systems/paths."

Such small scale experiments are a great idea. In fact, Vermont has taken this ACA ("Obamacare") opportunity to try a one payer system in Vermont with the state as the one-payer. This will offer a contrast to the for-profit ACA.

Having had browser problems with ratings, I am rechecking those I've read and found that I rated yours on May 12th.

I would like to see your thoughts on my essay: http://www.fqxi.org/community/forum/topic/2008

Jim

Doug,

I appreciate the time you took to read my essay and your constructive remarks. Such an honest effort with insightful suggestions is very helpful to the author.

Regards,

Jim

Dear Doug,

I seize the opportunity of this extension to employ you to read my article-You did promise to do so but I have not seen you on my thread. I read yours and even added to increase your leadership by rating you accordingly. I hope to read your comments and rating as well.

STRIKING A BALANCE BETWEEN TECHNOLOGY AND ECOSYSTEM using this direct link http://fqxi.org/community/forum/topic/2020

All the very best for your assiduous contribution in the contest so far.

With high regard

Gbenga

DAS

I liked your essay as well. Yes. I see the similarity.

Hodge

Doug,

I wrote the paragraphs following this one on my blog site. I read your essay quite some time ago and scored it. I remember being favorably disposed to your paper, but I don't remember what I gave it. I was going to write something about whether this idea of a path integral is a Euclideanized form and is then really a sort of neural network "Boltzmann machine" idea. However, I never got back to writing about this. I have been rather occupied in the last month or so.

The solution a ~ t^{1/2} is the matter dominated result and t^{2/3} is the radiation dominated result. If you have

da/dt = a*const*sqrt(ρ)

then for a ~ t^n, then for ρ ~ a^{-3} matter density you have

t^{n-1} ~ t^n t^{-3n/2}

this means that n -1 = -3n/2 + n === > n = 2/3, and for ρ ~ a^4 for radiation, this gives n - 1 = -2n, so n = 1/2. This is a fairly standard result. I did write e^{3t/2} and I really meant t^{2/3} and t^{1/2}. This is a rather curious mistake, and I am not sure why I wrote this. This appears to be a rather embarrassing brain fart.

Your comments about interactions and entanglements are interesting. It is a bit late for me to go into this, so I will do so tomorrow. There is something odd occurring with entanglement is that the gravity field is not local in the way other fields are. The nonlocality of gravity, or really quantum gravity, changes the nature of entanglement. Most QFTs are local, such as the Wightman canonical quantization condition and causality one gets in basic QFT texts. Gravitation is different, and I think entanglement monogamy and such may no longer apply.

Cheers LC

Doug,

I posted a response to your very objective and clear questions.

Regards,

John Merryman

Path integrals have surprising applications in optimal stochastic control -- the engineering field normally most closely associated with "steering" in uncertain situations. ("Normally", because some situations are so uncertain that you don't even know things like the dimensionality of the state space, in which case you have to use the even more general optimal sequential decision theory.)

In particular, if a control problem is one with perfect state information, continuous time, Brownian-motion-type random forcing, and a quadratic cost rate for control effort which is inversely proportional to the local Brownian-motion volatility, then the Hamilton-Jacobi-Bellman control equations (which describe a consistent assignment of values and strategies to reachable states) can be transformed to equivalent Fokker-Planck equations. (The reason this works is that, under the given conditions, the desirability of a state becomes proportional to the log of a probability density of reaching that state. This result (as far as we can tell) is due to H. Kappen (2005) or W. Fleming (1978).) After that transformation, path integral calculation techniques can be used to determine the value or best strategy from a given state.

(More surprising, to us at least, is the claim that there is a stochastic control problem whose solution correctness criteria are equivalent to the Schrödinger equation! In terms of Madelung's decomposition of the wavefunction Phi=sqrt(rho)*exp(iJ/hbar), the gradient of J is the strategy or "control", and, if we remember correctly (we haven't been able to find the reference beyond discussions of Nelson's mechanics), J is the state-desirability or "cost-to-go", the density rho has a straightforward meaning, hbar is a Brownian forcing, and the Hamiltonian is the state-dependent cost. Path-integral treatments of the Schrodinger equation then apply equally to solving that control problem.)

These specific points of intersection between path integrals and optimal stochastic control can be expanded, to motivate heuristics for planning in more general control problems. A review of the techniques invented so far can be found in Horowitz et al. 2014 ("Linear Hamilton Jacobi Bellman Equations in High Dimensions"). And of course path integrals and optimal stochastic control both involve dependencies on spaces of random trajectories, so maybe the event that someone trying to think about developing strategies for an uncertain situation hits on a metaphor involving path integrals isn't actually that surprising.