Mathematics is a way of the precision modeling of the relation. It is not the truth of the nature, but it is the finest approach that human know so far to make the model that close to the nature.
For something to "escape" from Mathematics, it should escape from Reason, too. In fact, it would disprove the Church-Turing thesis. Mathematics is a sophistication of Reason.
Insering a comment here that I made in the Ed Witten video on the same topic. "I humbly disagree with Eugene Wigner's claim that mathematics is unreasonably effective. In fact, there are cases where mathematics lacks effectiveness, and in many cases, mathematical models are approximations. In addition, one would expect within reason, that mathematics would be effective in modeling the processes of the natural world. Thus far, mathematics is not doing too well to model, described, and explain "mind", "self," and "consciousness," all of which are part of the natural world. That said, I love mathematics and physics having taken a degree in both. Both are quite powerful and amazing at times, but not unreasonably so."
you should have a talk with Edward Frankel (and may be with Edward Witten) on deep interconnections between physics and mathematics, which are under investigation within the Langlands program -- as a grand unification of fundamental sciences.
I disagree with the statement that math isn't linguistic. Any communication is linguistic, for if any mathematics was non-linguistic how could it be taught? Metaphor and simile in language lies at the root of mathematics. Geometry is algebra, probability theory is quantum mechanics, nodes and links are optimizations, linear algebra is string theory. Anything which can be thought or taught is linguistic or The Word of God. For if one can make relationships between lines and curves:pi, what can't one make relationships out of?
My question is this, if humans were predominantly an aquatic species, would our mathematics be different? Would our physics be different? For a fish does 1+1=2? I agree with what she says about physics, each branch of science needs to produce its own language. The beauty in math lies in its flow and precision, where this falls short, as in quantum theory and engineering, problems tend to suffice.
Language and Programming Channel - I think math is just a formalized, precise form of logic, and logic has kind of the same relationship with reason. But I think math gives rise to _everything_ else. It’s a “primitive” because it’s existence is explained by pure logical necessity, unlike the laws of physics, which are emergent and _contingent_ - they don’t _have to_ exist. I actually kind of think math is really all that exists-that is, I think physical structures are literally made of math. Physical structures are _identical_ to the mathematical structures that give rise to them. edit: Okay...maybe I’m taking things too far... 🤔🤔🤔🤯
@@BugRib IMHO, Math and Logic are contained in or at least are a facet of Reason. For me the most important principle of the Universe is that there is Order and from that Order all things follow, so Reason = Reality.
That's what I think: Mathematics is a concept of the mind to imagine and derive structures. No if you conceptualize the universe as a huge mind the same happens in our physical reality. That's why mathematic so tied to physics.
There is plenty of mathematics with zero link to physics. And presumably mathematical facts such as the infinitude of the primes would remain true regardless of how humans conceptualized it and what sort of universe they inhabited. This is in reality a deep and difficult question
Why don't physicists invent their own mathematics, they are about to, they train artificial intelligence how to describe itself and walk as we speak. Mathematics deal in abstract, physicist must stick with material. But there's a new player now, AI powered by quantum computers is a bridge between those two concepts. Super computers are not kinda same thing, they still use switches, 1 and 0, but numbers doesn't have precise meaning or location in quantum states. People can't do math if things doesn't have exact value or position, but for abstract entity as self aware quantum computer will be, those paradoxes will come as natural.
@@nschulz5698 I'm a huge fan, Wolfram mathematica is my favorite scientific tool, couldn't do philosophy without it and i have no doubt first self aware AI will also depend on it. It's a very important research and i have no doubt he will succeed, his ideas will power first conscious being created by humans.
What a legend. Bless up!
Mathematics is a way of the precision modeling of the relation. It is not the truth of the nature, but it is the finest approach that human know so far to make the model that close to the nature.
mathematics is about relation.
For something to "escape" from Mathematics, it should escape from Reason, too. In fact, it would disprove the Church-Turing thesis. Mathematics is a sophistication of Reason.
Insering a comment here that I made in the Ed Witten video on the same topic.
"I humbly disagree with Eugene Wigner's claim that mathematics is unreasonably effective. In fact, there are cases where mathematics lacks effectiveness, and in many cases, mathematical models are approximations. In addition, one would expect within reason, that mathematics would be effective in modeling the processes of the natural world.
Thus far, mathematics is not doing too well to model, described, and explain "mind", "self," and "consciousness," all of which are part of the natural world.
That said, I love mathematics and physics having taken a degree in both. Both are quite powerful and amazing at times, but not unreasonably so."
you should have a talk with Edward Frankel (and may be with Edward Witten) on deep interconnections between physics and mathematics, which are under investigation within the Langlands program -- as a grand unification of fundamental sciences.
I disagree with the statement that math isn't linguistic. Any communication is linguistic, for if any mathematics was non-linguistic how could it be taught? Metaphor and simile in language lies at the root of mathematics. Geometry is algebra, probability theory is quantum mechanics, nodes and links are optimizations, linear algebra is string theory. Anything which can be thought or taught is linguistic or The Word of God.
For if one can make relationships between lines and curves:pi, what can't one make relationships out of?
My question is this, if humans were predominantly an aquatic species, would our mathematics be different? Would our physics be different? For a fish does 1+1=2? I agree with what she says about physics, each branch of science needs to produce its own language. The beauty in math lies in its flow and precision, where this falls short, as in quantum theory and engineering, problems tend to suffice.
We can replace "Mathematics" by "Reason" : Why the 'Unreasonable Effectiveness' of Reason?
Good insight! I think I agree. 🤔
Language and Programming Channel - I think math is just a formalized, precise form of logic, and logic has kind of the same relationship with reason.
But I think math gives rise to _everything_ else. It’s a “primitive” because it’s existence is explained by pure logical necessity, unlike the laws of physics, which are emergent and _contingent_ - they don’t _have to_ exist.
I actually kind of think math is really all that exists-that is, I think physical structures are literally made of math. Physical structures are _identical_ to the mathematical structures that give rise to them.
edit: Okay...maybe I’m taking things too far... 🤔🤔🤔🤯
@@BugRib IMHO, Math and Logic are contained in or at least are a facet of Reason.
For me the most important principle of the Universe is that there is Order and from that Order all things follow, so Reason = Reality.
@Language and Programming Channel I tend to think that Mathematics is a sophistication of Reason. It is like laser guide for Reason.
That's what I think: Mathematics is a concept of the mind to imagine and derive structures. No if you conceptualize the universe as a huge mind the same happens in our physical reality. That's why mathematic so tied to physics.
There is plenty of mathematics with zero link to physics. And presumably mathematical facts such as the infinitude of the primes would remain true regardless of how humans conceptualized it and what sort of universe they inhabited. This is in reality a deep and difficult question
This dude is really interested in this phrase huh?
Why don't physicists invent their own mathematics, they are about to, they train artificial intelligence how to describe itself and walk as we speak. Mathematics deal in abstract, physicist must stick with material. But there's a new player now, AI powered by quantum computers is a bridge between those two concepts. Super computers are not kinda same thing, they still use switches, 1 and 0, but numbers doesn't have precise meaning or location in quantum states. People can't do math if things doesn't have exact value or position, but for abstract entity as self aware quantum computer will be, those paradoxes will come as natural.
Stephen Wolfram is in a sense proposing a new mathematics for physics; the computational universe
@@nschulz5698 I'm a huge fan, Wolfram mathematica is my favorite scientific tool, couldn't do philosophy without it and i have no doubt first self aware AI will also depend on it. It's a very important research and i have no doubt he will succeed, his ideas will power first conscious being created by humans.
All those languages, if expressive enough, will be equivalent.
You should contact the guys at Numberphile. They breathe mathematics
Why don’t you rename this show to “the smug elites”?