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While wandering about the ability of Large Language Models to understand, and the Chinese room argument (related question Is the "Chinese room" an explanation of how ChatGPT works?) I got into a mess with the very idea of understanding. Understanding something external to understanding looks like possible: we can somehow understand an ant by observing it, its shape, its behaviour... We study an object with a different object with no overlap.

Now, how about attempting to understand everything? In particular, what happens when one wants to understand understanding?

A reasonable object for understanding are understandable things. In particular, if understanding is understandable, a greedy agent would try to understand understanding. Now, if understanding is always understandable, understanding understanding is also understandable, so now the agent would be after understanding understanding understanding. Since for any order of understanding one can define a higher order understanding, there is no possible end to understanding, even with the single object of study $understanding$.

I am not sure whether we should compare this infinite chain of embedded $understanding^k$ to the natural numbers, where there is a final support (zero) for anything to be understood; or to the integers, where there is no first integer number to the left and thus no possible end to fully understanding understanding.

Is complete understanding impossible?

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The first issue is defining understanding. I don't want to go too deep here, but serious readers should likely go over some commonly accepted definitions and over the field of Epistemology. To make my point simple I will metaphorically define understanding as (theoretical) ability to draw on a piece of paper the inner workings on the object to be understood. Imagine a long, but finite, list of all the configurations of the object, all the behaviours in a given environment, etc.

According to this definition, is understanding an ant possible? Kind of. If we assume that the list is small, then yes. I suspect that, according to the specific definition of the list, the list may be so long that even an ant cannot be completely understood. The limitation is coming from the finite amount of resources available in our universe.

This applies similarly to understanding, for instance understanding a system of human+ant in which a human is understanding an ant. It's clear that this requires orders of magnitudes more "paper" than just understanding an ant.

Going up the hierarchy, while in principle nothing is stopping you from understanding everything, you simply run out of paper to write on. So it's not possible to understand everything.

If the universe is infinite (and so the resources) it gets more complicated. There can be a regime in which infinity is giving you enough resources to describe everything, if the infinity is "countable" in a sense, with your countable amount of paper sheets. Or the infinity may be "uncountable", and complexity is growing faster than you are able to write it down on paper.

Perhaps the ultimate strategy to understand everything (weird statement incoming) may be to become the whole universe and understand yourself (which of course I will leave as an exercise to the reader).

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  • $\begingroup$ Thank you for the answer. However, the question is whether a single property of understanding, composition, suffices to show full understanding is impossible, regardless particular definitions or world constraints. $\endgroup$ Mar 15, 2023 at 18:01
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    $\begingroup$ I still believe you need to fix a definition. Anyway, if understanding is idempotent the hierarchy you mention collapse. So I guess, is understanding idempotent? Which is hard to answer without a definition. $\endgroup$
    – Rexcirus
    Mar 15, 2023 at 20:44
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    $\begingroup$ I see... I guess I was somehow assuming it is not idempotent, but did not justify. Thanks for the links as well. $\endgroup$ Mar 15, 2023 at 21:14

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