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what is the mathematics of the universe

sushi

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what do you think are the underlying mathematics of the universe

mathematics describe increase, decrease change.

I think is addition and division is most universal. (mutiplication and subtraction, exponential seems to be no go)
 

Animekitty

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symmetry in self-feedback code
 

sushi

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i read from Max tegmark that the universe is made of mathametical code, implying that god is either a programmer or mathematician

therefore, there must be some sort of math underlying the universe.

in terms of mathmatical operators, increase and change seems to be addition, while decrease seems to be subtraction and division
 

Viaterum Orbis

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As a mathematician myself (or at least an undergraduate student), I find hard to believe that the universe is made of math, since math is a human abstraction.

Sure, we can describe certain phenomena and model things with math models, but if anything, the universe is made of physics rather than math.

I mean, math is more about proving and analyzing structures than reality, and most ideas will never have a real equivalent. You can calculate volumes with integrals, but what do you do with number theory?

I like to think that the universe and reality can behave under certain criteria, but it's the result of chaos and randomness and we identify it with human-made models, like seeing a smile on the sky made of clouds, and that we can use those models to have a better understanding of things around us, but thinking about math only in terms of reality is really just limiting the real power of itself.
 

Viaterum Orbis

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PD: If we are talking of mathematical operations, sum and multiplication seem 'natural' to us because of its meaning (we can describe the sum of two numbers as the cardinal of the set formed by the union of two disjoint sets whose cardinal equal to the original numbers, respectively); and multiplication as the cardinal of x times a set of y elements (if we assume disjoint sets).

The trend now is to logically connect all math to the set theory, and even if this seems to be a good idea, check out the axioms for the theory and you'll see the abstraction taken into account. There's no way the universe can be born out of human-made math.

Can we describe the universe with it? Yes, but that's a totally different story.
 

sushi

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what subject of math are you specialize in?

the counterarguement is that Isacc Newton publish the principia mathemtica to describe how mathematics influence or govern the universe, leading to the birth of physics, but i am also open to the possibility that it could all be randomness

I think number and quantity in universe increase due to addition, mutiplication and exponential is very rare.


decrease is usually division, like cell division.

maybe i should just focus on increase only.
 

Viaterum Orbis

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Right now I'm a few periods before getting to actually specialize in anything, but so far I'm way more into algebra and logic than analysis or geometry.

Topology is interesting too, and it has lots of algebra.

The thing with Newton's Principia is that before of them pretty much every serious scientific study was faith-biased or plain discarded. Without Galileo and Kepler, however, there would be no Newton.

Newton does start real physics and thus a rigourous study of the universe, and also "invented" calculus (some of his ideas weren't new, from Pithagoras to Fermat, there was a "basic" idea of it; and there's the Leibniz dilemma) in order to help with the calculations, but it's more about physics than it's about math.

Math is what the physicists use to study the behavior of a system, and both disciplines have influenced each other heavily, altough for me, math is more than reality modeling, there's creation and proofing of things wich may or not exist. "Quoting" G. Hardy, there are two kind of math: "pure" math, which has nothing to do with reality, and "real" math, which can be used for something. The true geniouses, according to him, cared not about reality but about the consistency and correctness (and therefore the invention) of theorems and ideas.

I'm more into "pure" than "real" math.
 

Grayman

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Vectors. Everything is a vector through space and/or time.
 

Serac

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Newton himself made the point in Principia that he makes no claims as to what actually drives the various phenomena and that the math was just a tool to describe things.

So there’s your answer; there’s no “mathematics of the universe”, just formalization of human perception.
 

sushi

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I just really hate the number 0 for some reason, since it imply nothing.
 

Niclmaki

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0 = 0

The sum of all things is zero. But you can have one hell of a time modifying both sides of that equals sign.
 

Viaterum Orbis

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We need the number 0 for a lot of things. Without it, negative numbers make no sense, since we define the negative number -x as the number such that

x + (-x) = 0

Also, we need it to prove certain properties about the sum, such as is there a number such that the sum of any number plus the unknown is the same as the original number? Or even equations like "is there a number equal to its double?"

The 0 is a "recent" number in western culture because of its meaning, but think of it via set theory. One of the axioms of this theory is that an empty set exists. Without the empty set a lot of modern math is just... nothing. 0 can be defined as the number of elements of the empty set.

So, how can we think of the empty set? For many years we used to think of sets as the collection (yeah, what is a collection? A set? I know it's a little circular, that's why we need axioms for the set theory) of elements that verified certain condition. For instance, the set of red cars is the set formed by every car that is red.

Now, what clause can we choose to define the empty set? There are many who might appear to be paradoxes, but only if we think about one element veryfing it; such as "every x such that x is not equal to x", or "every positive number less than 0", or "the ammount of pink elephants in the moon". Those are some of the ways to construct the empty set, and therefore, the zero.
 

sushi

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How does 0 becomes infinity, or how does infinity becomes 0 in the universe?

through arithmetic or geometric progression. my personal belief is that Arithmetic series is more likely.

the problem of 0 is another matter which i do not want to discuss here, i only brought it up because i believe 0 is an impossibility in this universe. the closest thing might be a black hole singularity or absolute vaccum and even then it may not be the case.
 
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