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Gen. Marshall

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Infinity is one of the most useful tools in physics, which is the study of... reality. One example that's rather easy to visualise is the repelling force of opposite charges; how large would you expect that force to be if they are right on top of each other? Besides values that can obviously be (-)infinity, there's also theories about infinitesimally small particles and an infinitely large universe. Infinity is not a mathematical construct, and I'm not entirely sure how you could claim that infinity has no basis in reality.

Only when coming from the positives. And I've heard it's even worse on the complex plane, but I've not looked at that myself.

Oh, right. I'm used to other solutions being redundant or useless, to be honest :rolleyes:
 

LatinKaiser

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64364407.jpg
Don't worry; it'll be great.
 

EnvyDemon

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I think I want to give you a hug for both of these posts, and/or nominate either one for PoTM.

How does math prove itself, though?


If you've looked into formal logic, then I think that you might be able to recognize the value of things with no application to reality. Or if you have ever enjoyed a well-written fantasy novel with a well-developed magical system. Or if you have ever looked into Locke's ideal of natural rights and the social contract, which did not mirror reality at the time very well.

And if there is no concept of a nonexistent thing, then there is a concept of a nonexistent thing. The concept of a nonexistent thing itself would be a concept of a nonexistent thing.

Even word problems aren't real things. I have never had to make it so that two ships don't collide in the middle of a foggy sea, but it was immensely satisfying to have completed that and to have it with everything in its proper place.
Look, something is either real or it isn't. Even thoughts are real, and are representable in reality. In order for you to have a thought, something has to happen in your brain to cause that thought. There is nothing, literally nothing, that isn't real, that we can sense, conceive, interact with, etc. If it wasn't real, you wouldn't be able to think about it, because your thought is a thing, with physical representation in reality.
 

jeray2000

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Look, something is either real or it isn't. Even thoughts are real, and are representable in reality. In order for you to have a thought, something has to happen in your brain to cause that thought. There is nothing, literally nothing, that isn't real, that we can sense, conceive, interact with, etc. If it wasn't real, you wouldn't be able to think about it, because your thought is a thing, with physical representation in reality.

How big is the universe, as in its diameter? I've been given to understand that size is infinite, and thus infinity is real.
 

npstr

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Look, something is either real or it isn't. Even thoughts are real, and are representable in reality. In order for you to have a thought, something has to happen in your brain to cause that thought. There is nothing, literally nothing, that isn't real, that we can sense, conceive, interact with, etc. If it wasn't real, you wouldn't be able to think about it, because your thought is a thing, with physical representation in reality.

This is not completely on topic, and not even in English language, but I think it is one of the best visualization I've seen of dimensions, so I'm going to post it. It also demonstrates there are probably things out there that we won't be able to understand or comprehend.

 

Rovsea

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Just as the representation is not the thing, we can represent things that aren't things. Case in point Twilight: even the "humans" in it aren't really human in any meaningful sense.

Mathematics makes no attempt to prove itself against the world. It proves itself against itself. All of it's concepts are equally as valid in any universe we can conceive of, and likely those we can't. I would suggest they're equally as valid in the absence of a universe too. Many of them are outright impossible to produce in our world. But we know those things because we stopped worrying about how the world is, stripped away all the tangible, and asked what the nature of the abstract concept is.

That doesn't mean there's no application, as many a pure mathematician has suffered the indignity of their utterly useless work being used for something. The mathematician behind modern internet banking went to his grave proud that there was no conceivable use for his work. His ideas had nothing to do with cryptography at the time; but because they were so abstract, people could look at them away from preconceptions and think of all the things they were similar to.

I will note that mathematics has essentially proven that there's no such thing as a logically complete and consistent description of anything meaningful anyway, so it's not like anything can say anything about anything in the first place.

I'm also curious if you're using the same Kantian arguments of the 18th century mathematicians who refused to believe in non-Euclidean geometry's validity, or if it's something of its own. They held that mathematics arose naturally from the mind as we expressed our perception the world around us. But in the face of mutually exclusive but mutually valid alternative axioms it was recognised mathematics was in no way an empirical science, and it thus became purely rational. Something of a neat reverse from the antiquity positions on it and "natural philosophy"...
Doesn't the lack of application deprive them of meaning?
This is not completely on topic, and not even in English language, but I think it is one of the best visualization I've seen of dimensions, so I'm going to post it. It also demonstrates there are probably things out there that we won't be able to understand or comprehend.

It doesn't exist if we can't comprehend it, or observe it's result, or in any way detect it.
 

Capt. Kiwi

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Doesn't the lack of application deprive them of meaning?

Of course not. Because this:

comprehend it

Does not require this:

or observe it's result, or in any way detect it.

We can comprehend vampires and infinite sequences quite easily without measuring them.
 

Cliges

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What does this even mean. How do you know this.

Aren't you going to be a doctor? Well, marty, when a man and a woman love each other very much, and all that...

The state of Irish medicine can't be as primitive as you're making it appear.
 

Cliges

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The augur interpreted the flight of birds for them, obviously.

I sacrificed a kiwi to ensure a favorable augury, too.

It's also notable that I'm thus far outbreeding the entire Chemist clan-so much for Catholic fecundity!
 

LatinKaiser

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Birds? Pigs? Pfft. Only the feasting of the sacred chickens guides my destiny.