This is kinda related to an idea I've been "struggling" with.
Some numbers represent real things. Like my little kid saw a pair of oven mitts and said 'two gloves'. Like, he was seeing a literal manifestation of two-ness in front of him - which is different than the logical idea of 1+1 or the symbol 2.
So you can physically see two of something. You can see ten of something. You can see a billion of something (sand on a beach). But at some point numbers get disconnected from concepts. We can easily say "ten to the power of million" as easily as "ten to the power of two" but the former is literally more than the number of particles in the universe. You can never encounter anything and say "oh, that's one with a million zeros of something."
Basically it seems like some numbers represent physical concepts (twoness, which can be manifested by a pair of mittens) and some numbers are purely theoretical.
You might be interested in reading some mathematical philosophy.
Here's an excerpt from Bertrand Russell summarizing Gottlob Frege's answer to "What is a number" [1]:
> A trio of men, for example, is an instance of the number 3, and the number 3 is an instance of number; but the trio is not an instance of number. This point may seem elementary and scarcely worth mentioning; yet it has proved too subtle for the philosophers, with few exceptions.
> A particular number is not identical with any collection of terms having that number: the number 3 is not identical with [page 12] the trio consisting of Brown, Jones, and Robinson. The number 3 is something which all trios have in common, and which distinguishes them from other collections. A number is something that characterises certain collections, namely, those that have that number.
The idea that "3" is not the same as a group of three things seems fairly straightforward, in the same way that a seeing a red ball and a red shirt next to each other and describing them as "red" is not the same as the concept of "red". The "weirdness" of numbers is that seeing 3 balls in one place and 2 balls somewhere else lets you say "3 + 2 is 5, so there are 5 balls"; we don't have a system of "composing" most descriptions of a shared category in a universal way. While we might be able to come up with a way of composing some of them, like "horizontal striped shirt plus vertical striped shirt equals plaid shirt", we don't (at least right now) have a system that makes it simple for two people to independently come up with consistent answers (does red shirt plus white shirt equal red and white striped shirt, or pink shirt, or something else entirely?)
The difference is the complexity of the concepts involved. There are predictable results when you e.g. combine and filter light spectra, stack several lenses and mirrors to make a telescope, mix two chemicals, put electric circuit components together, or perform a well-defined sequence of knitting stitches, but describing them is more difficult than whole-number arithmetic.
> Some numbers represent real things. Like my little kid saw a pair of oven mitts and said 'two gloves'. Like, he was seeing a literal manifestation of two-ness in front of him - which is different than the logical idea of 1+1 or the symbol 2.
Yes but even then you are using an abstraction. The two gloves forming a pair are a good exemple because they are not even actually identical: there is a left one and a right one. Yet, we can abstractly see them as a kind of glove.
Great point. I kinda snoozed on the article and didn't catch this idea but yes I see what you mean
But actually, does it stop being a pattern at some point? Is anything real. Like is h^2o really 3 atoms? Can we say that's a number. Can we count electrons?
It is naive (no offense indended) to think that only things that can be seen in our "human" reality exist (think of viruses etc.). But even if this was the case with numbers, what is the problem? Natural language allows us to entertain abstract thoughts with no immediate realization, and numbers are just one of these things.
No offense taken and I am kinda amused that I triggered you into being defensive about numbers (not saying you are, it's just a funny image in my head)
So to be clear, there's no problem but there's clearly a difference between things that are solely abstract and things that also have a physical manifestation.
I'm abstract, we can talk about "Napoleon's invasion of Russia," "Napoleon's invasion of Japan," and "Napoleon's invasion of the nucleus of an atom" as concepts on the same level, but it still matters is that one is a historical fact, one is a thing that didn't happen but logically could have existed, and one is a purely abstract idea without meaning.
Same pattern. "3 has definitely happened. There's definitely been 3 of something", "739163859115 may have happened. No guarantee that this exact number of anything was ever present but obviously could have", "10^1,000,000,000,000,000 isn't possible because it's more than countable things in the universe."
But I agree with you that this is just a human perspective. To the infinite G-d, no number is abstract :)
All numbers are purely theoretical; an abstraction.
There are no "two gloves", just as there are no "two stones". There's energy in certain configuration and if this configuration matches a certain macroscopic criteria, we call it "a stone".
So, even though you see ten of something, the "ten" is only in your head.
This really ties in to how brains and neurons work. A cluster of neurons will be primed with some sensory input. It might be the sound of the word that represents the number, or the visual impression of two items (and a sense of visual symmetry), etc...
Over time, neurons accumulate associations to other neurons associated to other stimuli that are related. Which trigger reinforcement as they are validated.
The number 10, might make you think of your fingers. The number 21 might make you think of Blackjack, 2 turtle doves, that 4 is related to "Four" written, 7 makes 8 when combined with a "counting" neuron impulse, etc...
Ultimately, we are a product of the inputs we are given, and a set of fundamental pre-wired associations (like visual symmetry detection).
This is similar to how AI neural nets in large language models can learn to create complex word associations just by inputing mountains of texts.
And that is why even though Mathematics aptly represents the nature, it, at least to me, is a different thing entirely. Which again begs the question, why should Mathematics be so good at depicting natural phenomenons.
Some numbers represent real things. Like my little kid saw a pair of oven mitts and said 'two gloves'. Like, he was seeing a literal manifestation of two-ness in front of him - which is different than the logical idea of 1+1 or the symbol 2.
So you can physically see two of something. You can see ten of something. You can see a billion of something (sand on a beach). But at some point numbers get disconnected from concepts. We can easily say "ten to the power of million" as easily as "ten to the power of two" but the former is literally more than the number of particles in the universe. You can never encounter anything and say "oh, that's one with a million zeros of something."
Basically it seems like some numbers represent physical concepts (twoness, which can be manifested by a pair of mittens) and some numbers are purely theoretical.