why is math so fucked up? area used to have geometric meaning,

>>9081909
>work, energy, interest, and time. why is it so offputting to see it get so abstract?

Since when are work, energy and interest abstract?
What do you consider real?

>>9081914
that's not what i meant. i meant that having a geometric form to something that isn't related to occupying space.

saying you have a box that is 10x10x10 in centimeters makes sense. you can have area on the surface, makes sense. but when you start having curves that represents the change of something, then say what the total amount is through area, then some other quantity with volume, what are you looking at? what is this hulk of geometry? you are talking about the parts but what is the sum of the parts? there's no meaning outside this particular interval for a function because that's not what you're looking for, but that's not really an intuitive understanding that's rationalism.

>>9081920
>>9081909
Literally everything is geometry, you brainlet. Geometry is the soul of mathematics.

>>9081927
that's a vapid statement. if it's geometry then what is this nonsense about intervals over a curve? why not take the algebraic varieties of a given structure? why can't space and structure be enough to describe change? why is it that calculus is its own field?

>>9081931
>space and structure
That's what a fucking interval is you shithead.

>>9081933
>an interval is a given space and structure

except it's not it's the local subspace. you're only looking at a single part.

>>9081934
The whole point of manifolds is they are independent of any ambient space. A manifold can be a submanifold of some bigger manifold, but it is a priori independent.

>>9081960
So all or math can be generalized as manifolds?

>>9081927
But pi is in everything and is everything you dumbass. Science man told me so.

>>9081909
>area used to have geometric meaning, but now it can mean work, energy, interest, and time

no.

>>9081909
>area used to have geometric meaning
at this moment I honestly thought OP was gonna ramble about abstract measure spaces or whatever lmao

>>9082002
You rambling about potential rambling is even more autistic

>>9081909
>area used to have geometric meaning
no it didn't, area, and length and volume, were just understood intuitively, is wasn't defined and actually had no meaning whatsoever, math brought meaningful definition of area and it allowed us to reasonably discuss it

>>9081920
geometry is not just lines and squares on a plane, geometry copes with much more abstract concepts than area repreesnting work

>>9082156
Why? Arent lines enough?

>>9081927
I understand why you might say this, but I disagree with you sentiment. Algebra and set theory can describe everything Geometry does, but it can be done entirely symbolically. I find this to be a more powerful formulation, but that is only my preference, not absolute.

>>9082208
I'm not who you replied to, but I believe I can help. Consider the natural numbers. We normally write these like a number line. However, the only truly defining properties of the naturals are that they are:
-Countable
-Well ordered
-With no greatest element
(For more concrete details see Axiom of Infinity)
My point is that the details of this set are inherently not of any sort of visual. Considering the Cartesian product of the naturals with itself, we would get the positive quadrant lattice plane. Now this is certainly a geometric intuition, however the construction didn't really depend on any sort of geometry. The anon you were replying seemed to be getting at something slightly different, but the point remains. Geometry is not simply just lines and squares. There is a deeper construction.

>>9081909
>why has math left me behind
...bcoz you failed to keep up, brainlet.

>>9081909
Thanks for the laugh.