Wednesday, November 4, 2015

Statistical mechanics of ants

I like to say that the IT model looks at human behavior as so complex that it looks like randomness at the micro level. Basically, there is so much going on that statistical mechanics kicks in (most of the time [1]) and the macro behavior is well-described by a gas or fluid.

In this video (article here) from Georgia Tech, the behavior of individual ants is very complicated, but at the macro level the ants behave as a fluid (or more accurately a state that has properties of solids and fluids):


The decision process in each tiny (but still too complex to model with a computer!) ant brain of what force level to let go and "play dead", to stick together or not, is aggregated into a single number: a viscosity coefficient.

Footnotes:

[1] Recessions and other mass coordination events are the exception, but most of the time, the economy is not in a recession.

15 comments:

  1. A good post for me to ask about something I have been wondering about: subdiffusive movement. (As a liquid, the ants seem quite viscous.) An example in economics might be "sticky" wages at the micro level. It seems like mucosal stickiness is adaptive for some viruses. ( See http://www.pnas.org/content/112/44/13675.abstract . I have not been able to download the paper before now, so I do not know much about this.) I know that you have derived a macro form of stickiness, but it may well be that sticky wages are adaptive at the micro level. What do you think? Thanks. :)

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  2. The difference with humans is that the 'gas or fluid' is intelligent and learns. That's the bit that is always missing when you try and use physical analogues. Which is why you really need to go to large aggregates of neural nets.

    The essence of the Lucas critique still holds. Policy works on individual entities, not the whole. Which is why macroeconomics still fails to help.

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    1. "The difference with humans is that the 'gas or fluid' is intelligent and learns."

      Whereas humans stubbornly cling to their views. Good one. ;)

      P. S. I know what you meant. Just a joke. ;)

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    2. Hi Neil,

      The thing is that you need some kind of evidence that micro-level learning leads to macro-level learning. To say an individual human learns therefore an aggregate of humans learns is the fallacy of composition.

      In general, each human is described by say, a million variables (say ~ 10⁶). Very complex. The macro economy (made up of millions of humans, say ~ 10⁶) seems to be described by a few variables like the price level, nominal output, interest rates, etc. Say there are 100 of those.

      The aggregate human problem represents a 10⁶ x 10⁶ = 10¹²-dimensional space. The nominal economy represents a 100-dimensional space.

      My question to you (and anyone else who thinks human brains have a significant impact on macroeconomics): Where are the trillions of missing macroeconomic aggregates?

      You can't parameterize a 10¹² dimensional space with 100 dimensions. Fractals can sometimes parameterize a 2-dimensional space with 1-dimension (see here).

      But I can't just take "humans learn therefore the macroeconomy learns" without some kind of evidence.

      Not that humans as neurons in an emergent Earth-brain isn't an interesting idea.

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    3. I don't think that there is any question that social adaptation, and hence, economic adaptation exists. Regulatory capture is a good example. But the time frame for most such adaptation seems to be largely limited to two generations, i. e., when the grandparents' generation dies off. The prehistory of the recent financial crisis is a case in point. In the U. S., starting in the 1980s, the institutions put in place to help prevent another Great Depression began to be dismantled. That's almost 50 years, around two generations, afterwards. This dismantling continued over time, despite the warning signal of the S&L crisis, and was largely completed with the dismantling of Glass-Stiegel protections under Clinton. This adaptation to the socalled "Great Moderation" was a form of social and economic forgetting. Enough was remembered, however, that a great deal of money was poured into the economy by the Bush administration, and there was some economic stimulus under Obama. Without that influx of money we could well have had another Great Depression.

      I don't hold much truck with the idea of Kondratieff Waves, but it is a model of social and economic forgetting with a time scale that is about right. Batra's prediction of a depression in 1990 was way off, however. ;)

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    4. Jason, this statement of yours:

      "To say an individual human learns therefore an aggregate of humans learns is the fallacy of composition."

      got me thinking... I know you wrote that in regards to economics, however I wonder if it might be applicable to other human endeavors such as teaching and learning about science and the natural world for the supposed good of humanity.

      For example, I'm of the opinion that the more people who learn about science and critical thinking and come to embrace the inherent values of those pursuits the better.

      However, I have no proof of that. Perhaps such evidence exists. I've certainly never even tried to find any.

      But what if my supposition is fundamentally flawed? Perhaps we have no reason to suspect that increasing the number of individuals learning those skills carries over to the aggregate (i.e. society). Put crudely, perhaps there's no reason to think that increasing the ratio of smart people to dumb people in society increases the smarts of society as a whole.

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    5. Hi Bill,

      That theory implies that e.g. the repeal of Glass-Steagall has a significant effect on the economy. However the IT model shows that the economy would be where it is today with or without Glass-Steagall (IT model predicts low inflation and interest rates in the 2000s using just data from 1960-1980, we are now on the NGDP-M0 path that could have been inferred from the data from 1960-1980).

      I wouldn't go so far as to say Glass-Steagall didn't contribute to how the recession manifested, but our situation today seems to be largely path-independent.

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    6. Hi, Jason,

      My understanding of Glass-Steagall (Thanks for the spelling correction. :)), such as it is, is that it and other measures enacted in the wake of the Great Depression reduced the variability (increased the stability) of the economy by erection of the analogs of fences and speed bumps. A good ecological analogy might be prey sanctuaries, which dampen the predator-prey population swings. That does not mean that we would not have ended up where we are in terms of inflation and interest rates, but would we have had a return to a succession of financial crises such as we saw in the 19th and early 20th centuries?

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    7. Tom,

      One thing is that if everyone was "smart" in economics, we'd end up with highly correlated movements in markets, and lower overall entropy. It takes people with diverse views to make an economy run ... and diverse views can't by definition all be considered "smart".

      And another aside: few people are smart in every domain, so in a diverse economy, a typical sample of people won't be smart on the subject at hand.

      The issue at hand is the mechanism by which individual ideas are translated into group ideas. What tends to happen is not some kind of averaging, but rather 'wavefunction collapse' to one of the ideas represented. Sometimes that's a smart idea, but 'dumb' people won't necessarily herd around a smart idea, so its not a foregone conclusion.

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    8. Thanks Jason.

      I think I understand what you're saying with regards to economics.

      To make my comment more concrete, let's take the climate change issue. Suppose human caused climate change is real, and it has negative consequences and legislation can have some positive effect.

      Now say the Koch brothers and Rupert Murdoch and a few other billionaires have a change of heart and donate all their money to do an all out media blitz to try to educate people on the issue, and they are largely successful: they substantially improve the ratio of people who have some meaningful understanding to those who don't.

      Does that necessarily change the trajectory of the aggregated electorate on the issue?

      It sounds like you're saying that it might improve the chances that this "wavefunction collapse" ends up with society as a whole adopting the view of the now larger fraction of society that is informed on the issue. However, there's no guarantee, we're just dealing with probabilities. So these hypothetical education efforts could very well appear to do no good at all (from the perspective of society as a whole) for a very long time.

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    9. I would agree that such a media blitz could influence the wavefunction collapse around a new equilibrium. However, the change of heart is doubtful :)

      I think we've seen a recent re-collapse of the wavefunction around gay marriage; there was a sudden transition from one state to another.

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  3. Jason, this might be an interesting analogy to use to highlight how a micro-founded model might try to tackle this ... a single ant perhaps? Does the fidelity of the model of the ant's brain matter? Or is it simplified?

    What about multi-agent models? Would they try to improve their model by adding fidelity to the ant-brain model? A wasted effort, if what you're after is their aggregate behavior?

    What of Neil's objection about learning? Is the process of learning subsumed into aggregation if done properly?

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    1. In other words, if the analogies are strong enough, it might be amusing to poke some fun at different economic schools by writing a line or two summarizing the approach they might take to studying these ants.

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