Is mathematics something inherent to nature, or is it a purely human construct? Why do you think math is so effective in describing the physical world around us? Do you think math exists by itself without physics?
i) Maths is inherent to nature, so for example we can show retrospectively that maths applied before the human species evolved and before maths was discovered.
ii) Physical problems that can be expressed as maths problems can be analysed and potentially solved as applied maths problems.
iii) Some physics problems may not be expressible as defined or definable maths problems. This follows inter alia from completeness and computability theories.
iii) Potential maths can exist without physics, but actual maths is constrained by the physics of information processing, so one might argues that in this respect maths and physics are mutually-supporting.
Intuitively, maths should exist without nature. The predictions it can conclude in the physics community are commendable but maybe, we are seeking artificial patterns. Anyways, it is always great to see the dots connect and redefine the reality in a completely new way.
The problem here seems related, as far as I can think or grasp, since I’m not a mathematician, to the question: what do we mean by the word ‘nature’? Is there something else? Above? Different? As a materialist, I’m inclined to say that nature is all there is…wether it be ‘things’, minds, and so of course ‘human constructs’, products of our brains or neuronal organization…of a very high complexity, I agree, but nonetheless a ‘material’ complexity…so maths, or whatever, cannot exist ‘without nature’ because I don’t see how anything could exist without nature…It’s obvious to me that the physics community can use maths discovered long before physics…but mathematical human constructs belong intrinsically to nature just as physics does, and also the physics community and also any ‘human’ construct…Spinoza: Deus sive Natura…if you endorse a flat ontology, it’s not surprising then that maths has such effectiveness when it comes to describing or explaining the world in terms of physical laws…
Is mathematics something inherent to nature, or is it a purely human construct?
I prefer to frame this question as such: “Is mathematics something inherent to a universe void of beings that possess self-consciousness, or is it a purely an emergent behavior borne surreptitiously of a self-conscious beings language abilities?”. Either way, I tend towards the latter. I have the mindset that, although we have discovered/invented/evolved a certain flavor of math as humans (and other living species have likewise created (seemingly) less robust languages of math), there could be another universe with a similar paradigm as cause & effect in which a similar flavor of math could be invented/discovered/evolved. These disparate flavors of math I believe would be children of a higher mathematics. I wonder if this relates to Goedel’s proof that there are truths in math that are unprovable. If nothing exists as the vesicle by which mathematics emerges, is there mathematics? I don’t think so. I think at the core of math is observation. Would nature still exist? Sure, there just wouldn’t be a specific type of language to talk about it without the talkers.
Why do you think math is so effective in describing the physical world around us?
I believe that mathematics is very effective in describing the world around us for a few main reasons: its roots in the empirical, the rigor by which it is practiced, the proof building methodology that strengthens its incremental findings, and the continual abstractions that allow for more complex proof building on top of previous work. To me it seems to be the most extensive language we have developed to speak about the Physical world, so in that regard, it should be very effective at describing it certain aspects of it.
Mathematics is based on a set of elements and well-structured relationships (patterns), if for some reason these coincide with nature, the deductions also adjust that nature.
This works because nature has been shown to follow patterns.
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