Relevant xkcd as always
this post was submitted on 27 Aug 2024
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It is legitimately cool when a bunch of mathematicians get together in a room and say "Look at all the cool shapes and patterns we made," then show it to a physicist who goes all frantic and starts shouting "OMG! I understand how stuff works!"
Gotta love how the more "Applied" a field is, the more "Impure" it is.
The number of people having jobs is record low in this picture
There's a real gravity to that statement and it definitely adds up.
Because they are students? Both are high demand professions, I don't get it.
I guess that the commentor meant that those kinds of thoughts don't get you jobs, and doesn't know how easy it is to get a job with a degree in either of those fields. Same for the upvoters.
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Calling a made up construct "the absolute truth" is hilarious
The way I see it, axioms and notation are made up but everything that follows is absolute truth
Iβd say if your axioms donβt hold you wouldnβt go far in your quest for truth.
The thing that is absolute is a predicate of the form "if [axioms] then [theorems]".
And the fun thing about if statements is that they can be true even when the premise is false.
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That's not a gotcha. It's basically just the definition of an axiom.
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The test to know if anything is an absolute truth is if it is called an absolute truth. If it is called an absolute truth, then it isn't an absolute truth. If it isn't called an absolute truth, then it isn't an absolute truth. Absolute truths don't exist. If someone tells you something is an absolute truth, stop listening to them.
You could say it's an absolute truth that absolute truths do not exist.
What about my Sith friend?
They're made up constructs that reflect the absolute truth when applied correctly (from his perspective).
Well, it depends on your definition of truth and it could be the absolute truth by definition. A theorem is absolutely true in the same way that "a bachelor is an unmarried man" is categorically true.
"This line on the map is perpendicular to this other line on the map" is not a statement about the territory.
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Math is a tool!
Therefore mathematicians are tools? QED or whatever
They are tool specialist by career. As for themselves, that is an individual assessment.
Specifically, a language. It moves information from one place to another. It can reveal new information too, but that's more of a useful side effect imo.
I do see where you're going but I would consider language a tool for communication.
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You guys believe in objective reality?
Not as something we have access to but yeah!
Computer science, we use both of your tools to solve problems. And make an electronic canarys aka AI
Which dont solve much :/
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If someone needs another existental crisis here's a prompt:
- Is math universal or is it a system of thought invented by humans and it only makes sense to us?
Models. Humans hold models of the world in their minds, math helps you understand and create more complex and consistent models. You always exist in a simulation of your own construction to make sense of the universe.
My feeling is that no model can ever fully capture a complete description of reality, the information isn't compressible to such a degree that approximations or abstractions can be lossless.
Most of what we consider to be invention is merely combinatoric novelty.
How we express math is particular to us, though it'd be commonly decipherable. Math is more and more globally standardized as more of it gets globally acknowledged as "the most useful" way to do math. E.g. place holder 0 vs Roman Numerals. Ratios are conceptually universal to any species that bothers measuring. Quantification maybe less so. Especially if their comprehension of advanced sciences/engineering is somehow intuitive instead of formally calculated.
If a space faring species has a concept of proportions/ratios, but not individual identity of numbers, presenting Meters as a portion of the speed of light might be a universal way discern the rest of our math. Water as Liters might be more accessible, depending on how they think of water.
Sets and Axioms are purely conceptually representative and so viable as long as they're capable of symbolic abstraction at all.
Universal. How else would you calculate or solve equations?
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Theory without application is useless, isn't it?
BURN THE HERETIC!
But seriously though, yes, but useless isn't the same as pointless. Art by some definitions is useless, but it can still have a point, even if that point it just to be fun.
I agree. I'm pretty sure a bunch of stuff that Euler did was considered useless until it actually was used hundreds of years later. I'm pretty sure topology had a lot of people wondering what the hell to use it for until it was rediscovered multiple times.
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If something's fun, it isn't useless.
Very true, we're all really just splitting hairs about the definitions of words
Following from this, then math isn't useless!
Theories can be a stepping stone to other theories. Until we explore those chains, we don't know if there is anything useful at the end.
E.g. initially, lasers were a solution looking for a problem. An interesting quirk possible due to some interesting bit of physics.
Maths explores idea spaces. Much of that is purely of interest to other mathematicians. However, it sometimes intersects with areas of interest to other scientists, at which point it becomes extremely useful.
In social science, theory requires application. Otherwise, it's just a cool story, bro.
Theory without application is often the entire point in certain academic circles and if someone comes along and finds a practical use for their mathematically based philosophical musings they delve deeper looking for the pureness
Until is has a use, technically, it is useless.
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Bruhβ¦ then imagine how hard a philosopherβs world would be likeβ¦
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