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Jakub Smékal

Regression as holism

GEB2 min read

Upon reading the Ant Fugue chapter in Gödel, Escher, Bach by Douglas R. Hofstadter, I am left with a number of impressions that I’ll try to convey here. I was particularly intrigued by the analysis of ant colonies as agents and also the interesting link between ant colonies, the brain, and even consciousness. An individual ant does not know what the emergent message of the ant colony is, similarly an individual neuron doesn’t know how its firing results in me pondering about the nature of consciousness. On some level, in order for something to “emerge”, it needs to be a self-referencing system, which forms a kind of infinite recursion. I am conscious, but for me to be conscious, I have to be conscious of the fact that I’m conscious, the question on which came first is omitted.

The brain tease really took another turn when the characters in the Ant Fugue actually went into a form of dialogue that was representative of a “fermata” from a musical fugue. One of the characters was taking active part in producing this piece, yet was unaware of it, while others noticed what just happened, nicely demonstrating both reductionism, where the whole was fully explainable from its constituent parts, and holism, where the fine-grained details cannot account for the properties of the whole, which is actually a nice contradiction. This somehow reminded me of another part of the book that discussed GOD, or GOD Over Djinn, where the acronym contains itself in its definition, effectively forming an infinite sequence. Yet in the story, that sequence was actually fully unfolded, as a limit, so I’m wondering, is holism just taking the limit?

If you consider a sequence 1/n where n is a positive integer, it is pretty obvious that it approaches zero as n goes to infinity, yet it never reaches it, nevertheless, what you often do in math is take the limit, which outputs the number that the sequence approaches, yet never gains. But if we take a look at the informational content of the sequence 1/n as n goes to infinity, the number zero tells us all we need to know, that is the ultimate goal of that sequence, regardless of whether it’s attained. So in this sense, perhaps reductionism is like taking the sum, but holism is like taking the integral (which is defined through a limit of an infinite sum). The thing is, where does the regression end? And does it at all? The activity of neurons in our brains produces our lived experience without us having to consider the fine-grained detail of their function, are we also “neurons” of some greater entity? I think the evidence points to yes, perhaps it’s not even that complicated, we might just call that entity society, but what’s incredible is that this means that even society itself would form a fundamental computational unit of something greater, so in effect, “emergence” itself might form an infinite sequence. The question then becomes, what is the limit?