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Comment by hliyan | Hacker News Reader

This is very interesting.

One could take this further and claim that even the most rudimentary mathematical construct, the integer, is in the eye of the beholder. Counting relies on certain perceive regularities: "boundaries" that allow us determine where a the "identity" of an object, and "similarities" that allow us to group together objects into counts.

The concept of an integer seems to presuppose the concepts of identity (or distinctness) and regularity (for want of a better word). Whether all types of neurologies will have the same ideas of identity and regularities (or objects and classes?) and therefore the same concept of integers, is something that we probably could not imagine because we can't step out of our own neurologies...

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I don't understand this tendency to promote subjective experience from a process occurring in a physical universe to some property which constrains the universe and knowledge itself.

I prefer to believe the universe exists and whatever is possible is synonymous with being physical law. Conscious subjective experience is one of those phenomena not excluded by physical law.

But then this article claims and you also seems to claim something like:

> But what if somewhere else some consciousness has intuitive experiences about numbers which differ from our intuitive experiences.

I don't see why minds with intuitions creates any burden for numbers. From my perspective Mathematics is at bottom a game of string manipulation. Interpretations of those strings often can be applied to understand/predict/manipulate the physical universe. But the only real thing is the universe itself not the subjective interpretations in the minds.

The minds are real, obviously, they exist in the universe. Integers are an interpretation of a particular string. Suppose some other mind is incapable of an intuitive understanding an interpretation that we as humans have; I don't see how the "integers" could possibly be affected.

None of us are concerned that dogs don't understand math. Why we be concerned about the minds of aliens and what they find intuitive?

Well, there are multiple ways to interpret quantum phenomena, and some of our sensory organs (e.g. smell, taste, vision) seem to operate at the quantum level, so why should we assume that our sensing is in some global sense authoritative rather than simply being evolutionarily optimised for macro behaviour that's useful to us?

Although at the ground level the universe appears to be quantized (at least below the Planck limit, at our macro scale it's mostly continuous. In fact in most things, if not all real world things, integers live only in some platonic universe. Perhaps we do a disservice to children by starting them with discrete arithmetic.

> From my perspective Mathematics is at bottom a game of string manipulation.

I think this really can only be true of basic arithmetic. Even in arithmetic we can reason about strings too long to be constructed in your our universe.

> None of us are concerned that dogs don't understand math. Why we be concerned about the minds of aliens and what they find intuitive?

They don't? Leaping to catch a frisbee is pretty advanced mathematics. I do doubt that dogs understand integers. But these fundamental questions about alien species whether dogs or some extraterrestrial intelligence are pretty important epistemological inquiries.

The concept of "one thing and one thing makes two things" is orthogonal to what things you're actually counting. We use integers to count constructs belonging to the class of discrete things.

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