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/sci/ - Science & Math

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12775437 No.12775437 [Reply] [Original]

>study higher math. algebraic number theory, topology, representation theory
>slowly become a finitist

h-help me bros. i'm becoming a brainlet

>> No.12775644

>>12775437
functional analysis

>> No.12775668

>>12775437
When I first took PDEs back in the day my professor would always say things like "nothing in the universe is infinite and there are no actual infinitesimals, we use these things because they're better to work with mathematically etc." and other such things.
I don't agree with him.

>> No.12776463

>>12775668
what exactly do you disagree with?

>> No.12776653
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12776653

>>12776463
Well. I don't think for example that just because you have a really big numer, for example googol, that this somehow prooves infinity. Also, for example, even if it seems like there is infinity, doesnt mean it actually is. Just like for example even if 1+1 = 2 in reality, when you do it in python you get 2.00000000002, which is not the same. Does this prove 1 plus 1 is not two? No, but it proves that it might not be exactly how we think it is, but just that we ignore it if it doesnt fit our, "oh so rational", "theories" (mathematics doesnt have theories, only ideas".

>> No.12776697

>>12775668
Your professor was an arrogant autist.

>> No.12776704

>>12776653
The python example is fucking stupid and out of place

>> No.12776709

>>12776653
Are you trying to prove something about the concept of infinity by concluding that floating point arithmetic has an intrinsic inaccuracy?

>> No.12776922

>>12775437
infinity = indefinite, mass produced.
finity = definite, unique, precious, creation.

>> No.12776934

That's ok OP, the world needs ditch diggers too.

>> No.12776997

https://www.youtube.com/watch?v=E_dGqavx5AU

>> No.12777128

>>12775437
It seems to me that a large part (or all) of the ongoing human obsession with finitism, can be boiled down to a sort of neocatholic addiction to the concept of underflow.

https://en.wikipedia.org/wiki/Arithmetic_underflow

Some people need a "too small to be represented" or "too large to be represented" in order to make sense of the human condition.

>> No.12777259

>>12776653
this is not me, i don't know why you'd post this just to pretend to be and then act dumb

>> No.12777278

>>12777259
welcome to the internet. if you want to be unique, tweet on twitter

>> No.12777308

>>12775668
Prof was based, shoulda listened to him.

>"nothing in the universe is infinite"
infinity is not a thing or a number, it is an abstraction identifying an open-ended process. A completed infinity, ala Cantor, is a self-contradiction. It would be an open-ended process that has ended.

>"there are no actual infinitesimals"
the "ghost of departed quantities" are buried in limits and integrals. Pi, e, etc. are not actually numbers per se but symbols that stand for these methods that can generate a number to whatever precision is required. Infinity is necessary in math so we can advance beyond counting things, it is all about the measurement of continuous quantities. Any valid, real measurement results in a rational number but infinity allows mathematicians to abstract from the process of getting actual numbers, i.e. "infinite" precision, and identify relationships by treating Pi, e, et.al. as if they were numbers.

Nobody uses Pi to infinite decimals, it is indefinite by definition. To buy enough tile to cover your circular patio Pi is 3.14 but to get to Mars you need to use more decimals but not an "infinity" of them. Gotta stop counting at some point or you'll never leave the planet.

>> No.12777730

>>12777308
>it is indefinite by definition
π is perhaps the worst example other than √2 you could have picked for that claim. it’s one of the vanishingly sparse irrational numbers which is quite well-defined. over-defined, even.

>> No.12777738

>>12775668
>we use these things because they're better to work with mathematically etc.
They said the exact same thing about heliocentrism. Galileo wasn't arrested for teaching the model, but for telling his students it wasn't JUST a model.

>> No.12777904

>>12777730

>Any valid, real measurement results in a rational number...
Talking measurement here not math. Math won't get you to Mars only measurement will, don't change the subject.

>> No.12777954

>>12777904
Really? How does “measurement” get you to Mars? What did you measure?

>> No.12777958

>>12776653
Based Python fixing the gyromagnetic ratio for you

>> No.12777968

>>12777904
>anyone on /sci/ actually cares about getting to Mars
Why do you feel the need to *do* things?

>> No.12778618

>>12777954
Baby steps for you...mars is too abstract. tiling your patio is much simpler and probably in your reach, start there.

>> No.12778655

>>12777968
who said I wanted to go to mars? I think it is a dumb idea. It was just an example, think up your own if you are smart and understand my point. Or switch gears and claim that no one cares about patios either.

>Why do you feel the need to *do* things?
life is action, motion or decay, life or death, which do you choose? Math is a tool that helps us choose the right actions.

>> No.12778927

>>12775437
I think finitism is fine to some degree.
In fact, I'd argue that all mathematicians are finalists in some sense (but, yes, not in the conventional sense).
If you study logic and proof theory, you'll see that only finite sequences of finite statements are considered valid proofs.

Even proofs about infinite sets and sequences and shit have to be finite sequences of finite statements. It's just that we accept inference rules (like universal generalization) and axioms (like the axiom of infinity in ZFC or induction from the Peano axioms) that lets us talk about "infinitely" many things while still using finite statements.

At the end of the day though, I think formalism is the way to go for pure math. (Finitism or other philosophies might be better if you need to apply the math in physics or something.).

>> No.12779006

>>12778618
No, tell me what you think we’re “measuring” when we calculate how to explode a ball of metal up and have it land on a little red sky dot. (Or admit that you’re talking out of your ass, and don’t have an answer.)

>> No.12779169

>>12779006
Elliptical orbits are too advanced for you. Stick to understanding tiling your patio first. You can do it! Don't give up.

>> No.12779178

don't assume anything to be true unless you yourself understands it as true.
otherwise you'll fall victim to dogma.

>> No.12779248

>>12779169
Yep, you’re talking out of your ass, as expected on /sci/.

>> No.12779975

>>12779178
what you understand to be true is just a part of dogma though

>> No.12781074
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>> No.12781674
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12781674

>>12775437
>>12781074

>> No.12781696
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12781696

>>12775437
>>12781074
.

>> No.12782468

>>12781674

this makes me self-conscious

>> No.12785121

>>12775437
Welcome to the geocentric model of the world my friend. You are in for a rough ride.
You probably will take some time. Most take a lot of time. But I will give you some hints. What is the deep meaning of the three-body problem. Why did Einstein have to come up with special relativity. Or better, which experiments showed a scientifically disturbing truth that had to be explained away.
Good luck my friend.

>> No.12787366

>>12785121
take your meds lol

>> No.12788974

bump

>> No.12789018

>>12775437
the only way to live with maths is to acknowledge they are a mental construct. Be careful, atheists hate this.