Another perspective could be that we are creatures emergent out of the physical and chemical processes of the universe.
There is some similarity or equivalence to some of these processes with mathematics, which allows us to model a subset of physics/chemistry with mathematics.
Because physics/chemistry can create us using rules that follow math (or even some undiscovered rules), this same physics/chemistry gives us the faculties of reason that lets us think about and apply math in some universal way
The physical, chemical, and mathematical substrate to which we are born allow us to even discover that the rules of math can be applied to some subset of the laws (or chaos?) of the universe.
> Do we really know if adaptation is responding to discrete classifications of environmental pressure?
Yeah we do know.
Take any system of variables that interact, and change them smoothly, and inflection points will emerge. This is true literally any way you look at it. In space. In time.
Heck aggregate states of matter represent "categorical adaptation" of matter to smooth alteration of temperature.
Point being this process happens even before we even can call a system "thinking". It's absolutely inevitable.
We can keep our options open forever and say "I don't know", that's fine. But if we analyze what we do know... turns out we DO do know.
You are just saying that interacting systems have phase transitions.
I think this is a far cry from "emergent numbers".
Edit:
Maybe self organizing matter that lives on a phase transition boundary benefits from being aware of the boundary? Thats the only analogy I could think of that could logically connect.
> You are just saying that interacting systems have phase transitions.
Right.
> I think this is a far cry from "emergent numbers".
Because it was just a clarification remark on everything else I said before that, which did connect it to numbers.
> Maybe self organizing matter that lives on a phase transition boundary benefits from being aware of the boundary? Thats the only analogy I could think of that could logically connect.
That's also what I initially said, but think about it a little more broadly. Whether you "live on a boundary", or you live in a system that experiences such boundaries, or your own system internally has such boundaries, or the INTERACTION between you and your environment creates these boundaries, it doesn't matter. You benefit from being aware of them.
And here's the thing. You will experience such boundaries, because it takes infinitely more "resistance" to change, in order to survive a changing environment without changing yourself, than it takes energy to adapt to a changing environment so you resist less, and it resists you less (you become more compatible).
When leaves drop in winter it doesn't matter there's a specific day and hour and second we switch from summer to winter, but trees do benefit from recognizing the overall "shift" over time and adapting to it through its own shift. I'm deliberately using "non-thinking" adaptations to show that categories are precursors to how thinking works, rather than thinking inventing the idea of categories for no fundamental reason.
Our recognition of objects and entities are the same phenomenon. We recognize a boundary (inside and outside the entity/object) where there's a shift of overall behavior in that local timespace, compared to its surroundings. We benefit tremendously from recognizing that a field of grass looks and acts more like a hungry lion in a specific region of it. Technically objects/entities are not a perfectly defined thing. A lion is in consistant exchange and interaction with its environment, it's not a closed system. And anyway I don't feel like repeating the rest of this again.
TLDR; There be phases/categories in N dimensions/parameters. There be instances of them (repetition of patterns). There be adaptation by recognizing the phases/categories and their repetition and counting and measuring them, in order to optimize our predictions quality.
Do we really know if adaptation is responding to discrete classifications of environmental pressure?
There could be other ways to describe how systems adapt. You are ascribing a lot to how you think it emerged.
I think your opinions are great, but I just have a hard time having beliefs about things that are as fundamental as numbers.