Societal Path Integral by Douglas Alexander Singleton

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.

(continued) However, your essay's use of path integrals as a metaphor leads to a different, and independently interesting, connection. You refer to the importance of allowing small-scale experiments to build up evidence and social momentum for larger-scale social changes. By itself, this is just a matter of advantageous information-gathering (along multiple subsystem paths) partway through a situation. Therefore, it does not directly relate to the special advantages of path-integrals for planning, which are mostly about able to cleanly decompose the calculations you want to make, about the multiple possible paths, in advance of getting into a situation. But path integrals are, notably, a basic tool in high-energy physics, and high-energy physics is notably full of situations with physical laws which are invariant under specifically tuned combinations of rescalings of the physical quantities involved. This could be connected, along the metaphor, to the points you were making about findings from allometry and about hypothetical scaling laws applicable to interpreting the results from social experiments.

It might be possible to make a tighter connection than this between physical scaling laws and social experiment scaling laws, but it would require a better understanding of the role of information-as-a-state-variable. Most problems in stochastic control don't just involve outward states, but also hidden information that one can acquire depending on one's actions. Therefore, planning can't just be about what outward states to get into, but about which information to potentially acquire and what use that information might have once acquired. Mathematically, this is represented by expanding the state space to include possible states of knowledge or belief about the hidden state of the world (an operation that resembles quantization, and that usually leads to state spaces too intractably large for exact solutions). Social experiments are unavoidably about getting information, so whatever the scaling laws are that apply to social experiments, they would have to accommodate this alteration to the state space to account for information. (The metaphor here seems to suggest, unsettlingly, an analogy between renormalization group calculations and the modeling of scaling laws applicable to nested social experiments.)

Another connection between path integral-style planning and social experiments is that path integrals lend themselves to thinking in terms of, "What kinds of mistakes would be likely to happen if the behavior was random? Those mistakes will probably mostly happen anyway, so I should notice which paths are robust and which ones are fragile." Kappen, in his discussion of path-integral control, compares this to a drunken spider that prefers to go around a lake rather than try to cross a narrow bridge that it would fall off, even if, in the expected-value (in your terms "classical") path, it wouldn't fall off.

You may be interested in the work of Hilbert Kappen and Karl Friston, who try (in different ways) to draw explanatory connections between cognitive psychology and statistical physics, both on the level of "how do neural systems exploit statistical phenomena to plan efficiently in combinatorially complex situations?" and the level of "is the purposeful action of living creatures a coherent class of physical phenomenon, like 'heat' or 'superconductivity', for which we can find unifying modeling principles?". Perhaps some of their ideas generalize to decision-making processes outside of individual brains.

Our own contest entry is about the possible importance of developing theory to generally identify abstract processes that affect the decision-making of societies as physical phenomena, including the processes that have given rise to our moral perspective. The purpose would be to try to make it possible to avoid steering the future in ways that disrupted unrecognized dynamical sources of morally positive decisions, including decisions about how to steer the future.

Steven Kaas & Steve Rayhawk

Hi Doug,

I'm so happy with the great success of your essay here. It is so well-deserved. As this this the last day of the forum, there is no time for the discussion I still would very much like to have with you. I suggest that we can communicate via email, at your convenience. When you have a chance, I would welcome an email from you to initiate that. You can reach me at the following address:

foreknowledge.machines{AT}{g.m.a.i.l}.{c.o.m}

All the very best to you! Congratulations on your fantastic win.

Warmly,

Aaron

P.S., Later tonight, there will be some posts at the bottom of my page that I have reason to believe you will enjoy.

dear Douglas,

Congratulations with your high score and place in the finalists pool.

I hope that the discussions are not at an end so I have the pleasure to sent you the link to my essay "STEERING THE FUTURE OF CONSCIOUSNESS" and hope for a comment on my thread.

best regards and good luck

Wilhelmus

Doug

Congrats on 3rd spot, I really hope it converts to a place better than my 2nd spot last year!

Following from our interesting conversation I had an epiphany re-reading Bell (p146). He validates the model I use, of spin direction relating the detector spin, but the different assumption he used, of entirely random spin axis in all planes, becomes clear as the problem causing the Wigner-d'Espagnet inequality limit. I use propagation on the axis, consistent with quantum optics, and only detector electron orientation freedoms, which also then give the 'intermediate value' distribution.

I wonder if you'd be so kind as to have a look at this short (2 page) updated summary and comment for me.

"> Classical_reproduction_of_quantum_correlations_popular_summary B.](https://https://www.academia.edu/6525547/Classical_reproduction_of_quantum_correlations_popular_summary_B_

)

Many thanks, Best of luck, and Best wishes

Peter

PS; if you prefer do reply direct to; peter.jackson53@ymail.com