Computation by a Population

[This is part of my series on Thomas Malthus’ “Essay on the Principle of Population,” first published in 1798. You can find an overview of all my posts here that I will keep updated: “Synopsis: What’s Wrong with the Malthusian Argument?”]

This post is a bleg, where I ask a question and hope that someone has an answer or can point me to one. Any help very much appreciated. The question is somewhat technical, but in my view so interesting that I guess I am not the first one to ask it. But maybe it is also beyond what can be answered.

My starting point is that I am thinking about a non-Malthusian explanation for population dynamics. It has two parts:

• A population sets a target for population size. That should be reasonable, ie. achieve some goal for the population like keeping it away from distress, but not so much that the population just decides to go extinct. When opportunities arise, the population should grow into them, and when they fade away also shrink back to a smaller size.
• The population then tries to achieve the target size. That would work via pursuing fertility over time. But that also depends on mortality, which determines the replacement level where a population stabilizes.

Now, what I am thinking of in the first place are human populations. But it could also be other species, even pretty dumb ones. My suspicion is that not only humans behave in this way, setting a target size and pursuing it, but also many other species. They do not grow their numbers until they are stopped, but only to some reasonable target size.

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The challenge is this, especially in view of other species than humans: Obviously, the population will not do mathematics, write down an optimization problem for the target size, solve it, then design a schedule for fertility, and implement it. Still I think it can achieve such an outcome nonetheless.

What can it use?

It can estimate inputs from observations. Aggregating them via a social process may lead to some “wisdom of the crowds” where errors are suppressed and the estimate becomes rather precise. To achieve this, it is not necessary that everybody gets together. It would be sufficient if such information propagated through a network. Even rather dumb species could do something like this if they infer knowledge others have from their behavior.

You could also have some operations on the inputs, eg. exponential smoothing where you update a value with incoming information. That need not be only for a mean over time. You might also try to estimate a variance or even a correlation in such a way.

Next, the population could perform some operations on these inputs. It could apply a rule to them and get a result. Basic operations would probably have to be very simple. There could be some constants that are innate, “embedded in hardware” so to speak. Then operations like addition and subtraction seem feasible. Ratios and multiplication are harder, but probably doable. The auditory system can also effectively calculate logarithms. So why not that, too? Logical operations seem basic, maybe some rules for handling probabilities. And you could also have programs where you can plug different such operations together.

However, there should also be stringent constraints. For example, the population could not keep track of many inputs. There should not be too many estimations going on either. And as for the computations, these might not be in principle, but only over a certain range. There could also be constraints on how many you can do in a formula or how you can plug them together into a program. Can you have loops with an index or stopping rules? If/then/else-branching? Recursivity?

Humans can communicate rather directly what they have found out. Other species might be able to do that indirectly by signals and cues. Once the population has calculated some output, it can then use it to drive its behavior. There might be alignment, so also those who do not have the results, learn from those who do. This again could propagate through a network. A species might also take hints from other species.

All the steps would perhaps be overlayed with noise. Especially, inference from others should suffer from errors. But also calculations might be imperfect and deteriorate when they go beyond a familiar range. Storing information over time could be another problem if memories fade away. And also how the results are implemented might suffer from random interference by other processes.

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All in all, such a population would work like a huge computing machine. However, that would have a rather strange infrastructure compared to a computer that can do some basic stuff with perfect precision and has only a few constraints on computing time, memory, storage, and can execute very complicated programs , but doesn’t have constraints like fading memory, imperfect computation or inference, etc.

What can such a population compute in this way?

On the one hand, you can be very optimistic: Practically anything. Populations could basically do all the math: Set up optimization problems, solve them, then put the results to good use. Economics is full of such assumptions. Of course, that has been criticized, and people have pointed out how humans fall short of such expectations and commit systematic errors versus ideal beings, how aggregation may go wrong, etc.

But that is only a negative result, which shows that some things might not be possible. How about a positive approach? For example, if I threw a set of basic procedures of the above types at you, what could a population achieve with them?

My intuition is that you have emergent properties here. You need at least a set of basic procedures to achieve certain goals. There might be critical parts here that are make-or-break. For example, if a species lacks any form of memory, that should put stringent constraints on what it can do. It would basically only be able to react to things on the fly. If there cannot be any form of inference from others, then aggregation would fail. But again, those are negative results.

Maybe the problem is too hard on this level because it is so broad. But can you still draw some conclusions nonetheless? Is there some hierarchy for computing capabilities? Or is there at least an idea about what basic procedures there are and which species have them? Can you calculate a sine or a square root? Humans are far ahead of other species with language that makes so much possible. However, what does that imply? Can other species obtain similar results also with other procedures?

All this is admittedly very vague. I can add no more to it so far than asking the question and this vision of viewing a population as a computing machine. But maybe there is something already there?