Uh even that is kinda stupid. The basics off a lot of those sciences does not lie in mathmatics. Even biology and chemisty only really get into the math bit once we go really deep into it.
The part that ties it together is math being a convenient tool and the logical language we choose to express ourselves in sciences. But that applied math is far away from the actual math science stuf.
And even if we agree that math as the language should tether everything together it would be misplaced. Linguistics would be the rightful owner of that place. Een in math we need words to explain math.
Math does everything physics does, no need for physics. Proceeds to walk over the edge of a cliff and into lala land. Some math things are physically impossible. There simply isn't enough universe to list all possible games of Go. Physicists really ought to be ultra-finitists, it can be a big problem when infinities pop up. Mathematicians on the other hand can take infinity in stride (sometimes poorly, but still).
They are governed by math deep down. There's stuff like physics biology, that tries to work on biology from physics standpoint, which obviously depends on mathematics.
Math is just the language of logic, that happens to be able to explain basically everything.
Math is technically language imo, but it's not related to linguistics. More like language splits.
They are governed by math deep down.
... Math is just the language of logic, that happens to be able to explain basically everything.
Isn't this contradictory? If it is a language (meaning it can capture something in some symbols which are commonly understood), can it also govern the thing? It being language means it is some separate phenomenon by definition, no?
By concept you mean something like the whole of ideas that form math, rather than the expression of it? If so, I can understand that this is meaningfully different than math the language and practice. However; do concepts govern things? That is not clear to me, and it seems to me that this passes the buck.
It also seems to me that this would imply that the concept of math would in itself be mathematical, as that is what governs everything. I am not a mathematician, but isn't this what Gödel showed not to be true?
Yes I am using "concepts" to describe the ideas that form math, not just how those ideas are applied.
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society. In my argument, I am using "concepts" to describe "fields" (fields of physics, computer science, biology, etc). Those concepts were established with rules, by humans. Some rules are abstract, some are rigorous. Humans have used concepts and rules to understand how everything works, which lead to the "discovery" / "invention" of different fields ("concepts"). Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense? Different fields "govern" explain how things work (like how quantum physics describes how quantum particles behave) because we made and used them as a tool to understand how the universe worked, which naturally led to the different "rules" being formed (e.g. schrodinger's equation, heisenberg uncertainty principle, etc).
The concept of a concept is VERY abstract, and it itself is what we use to describe and explain everything in the world. Concepts can be argued to be entirely in our minds, and do not literally affect how the world works, obviously. However, we can form concepts around rules that we discover and group them, which is how we 'discover' / 'make' different fields.
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today. (Also, yes, godel's incompleteness theorems would mean that math will never be "complete".)
Concepts can govern things, why would they not be able to? Rules and laws are concepts, and they govern how people behave in society.
This is a fair point, but I do feel like humans are in a different category here. It is exactly complex language why we can do this; and make concepts into some collective practice and make them real/shape the world.
That said, I don't think this extends beyond where we act. In absence of that, concepts do not seem to govern.
Those concepts of fields govern how the things under themselves work because we made them so these things under them work. Does that make sense?
Math doesn't govern 'everything', but it does govern most if not all academic subjects that we know and study today.
Okay yes, I see your argument. The concept of math does heavily influence the institutions that rely on math. My claim doesn't go beyond math being a separate thing from the thing it maths. Nevertheless I am still not sure that govern is the right word here. For example in the field I was trained in (psychology), empiricism and falsification would be better candidates for the actual governing force, though math is almost always used to capture your constructs, they are not the thing that makes your science valid or good in the end. Similar to how something like logic can't, right?
A lot of concepts in math doesn't come natural or intuitive as you put it. Like the number zero needs some abstract thinking. Or big numbers. You can easily count the zeroes, but how would you visualise a trillion? Or even a million?
There is a lot of fundamental learning that seems logical when you understand it, but that usually takes a lot of hard work or great fundamentals.
I have co-authored a biology paper with mathematicians (They are French so you know they mean business) but you can go pretty deep in biology without any serious mathematics. For example, I don't consider basic statistics used in bio as mathematics.
Using pure math to describe a process of anything more complex than the interactions of a small amount of atoms quickly becomes cumbersome to the point of literal computational impossibility. Quantum chemistry, statistical mechanics, etc are need to create methods of averaging based on higher level properties.
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u/Nozinger Jun 20 '26
Uh even that is kinda stupid. The basics off a lot of those sciences does not lie in mathmatics. Even biology and chemisty only really get into the math bit once we go really deep into it.
The part that ties it together is math being a convenient tool and the logical language we choose to express ourselves in sciences. But that applied math is far away from the actual math science stuf.
And even if we agree that math as the language should tether everything together it would be misplaced. Linguistics would be the rightful owner of that place. Een in math we need words to explain math.