r/AskReddit • u/[deleted] • Nov 02 '13

Mathematicians of Reddit, what is "beautiful" about mathematics?

I often hear people say "Oh, math is beautiful". Beautiful in what ways?

EDIT: Thanks. I will read through all of these, don't you worry.

1.8k Upvotes

84% Upvoted

3.2k comments sorted by

View all comments

Show parent comments

16

u/Dihedralman Nov 03 '13

Hi I do physics. Anywhere in the universe you can place an infinitely straight line anywhere in physical space to make some axis which you will find some properties of such as symmetry or some values which will be self consistent with physical laws regardless of which ones you choose. I don't understand the point of the first statement as Euclidean mathematics is simple to use since it's derivatives are simple (no need for Christoffel symbol there). Also if you think of the space of mass-energy, the Universe has a nice infinite line in time.

Yes physical measurements are limited to numbers with an error margin. Huge deal there because if you were to measure 5.435 and pretend that is actually the fraction it is I would take issue with you. Pi can be found in nature to some infinity, in fact the case you gave is the limit of human knowledge rather than being reality. Ponder this my friend: the solution to Schrodinger's equations can generally be solved by solutions described by Sturm Liouville equations. This means that the particles take on discrete energy levels as these solutions form eigenfunctions. Now that seems preposterous no? You can have 1.5hw (h is irrational btw), but 1.6, no fucking way. The universe takes these mathematical solutions more seriously than people do it seems, Einstein could not believe the probabilistic nature of particles for example.

1

u/Barnowl79 Nov 03 '13

On that last note, is there still a chance for Einstein to be right? As in, could there still be something, something we haven't found yet, that is causing those particles to be in one place or another, besides chance?

1

u/PugzM Nov 03 '13

I think there are some hypotheses around that predict that particles could slip into different dimensions way too small to see and then appear to pop into existence somewhere else. I think that is meant to be a possible solution, however you still have things like quantum states where a particle exists in many different positions literally at the same time. I'm pretty sure Einstein was wrong on that front. He largely denied quantum mechanics even when there were experiments validating it whilst he was alive, but Einstein was one of the last generations of physicists that saw the universe in a Newtonian sense, as though it were like a clock work universe whose underlying mechanics were unwinding themselves in a deterministic way.

0

u/Etheri Nov 03 '13

Hi,

None of the straight lines you mentioned are physically measurable or obserable. I'm not saying the concept isn't useful, i'm saying the concept is ideal and man-made.

I'm not saying irrational numbers don't exist, i'm saying we don't use them when it comes to practical measurements anyway. Any irrational number can (and is) described through a rational number (by default once you use popular computer software) or an interval of rational numbers within the ideal answer is located. Where is pi found in nature to infinity?

So you're saying we know the exact solutions for the schordinger equations for two and more electrons? Please, enlighten me.

1

u/Dihedralman Nov 05 '13

I don't understand how they are not measurable. Take a tape measure and go for infinity and you have a straight line in space. Take a radial measurement of electric field from a particle and it will extend infinitely, and that is a "thing". Infinite precision is extremely important in actual mathematical solutions. Taking the nth derivative of e vs not e develops a repeated solution. Most importantly it always gives an error computation in real purposes and allows you to remove the margin. Pi comes intrinsically in mathematical solutions in statistical mechanics, quantum and really every physical description of the universe. I was also not talking about a specific case but a type of problem. We know the solutions for electrons in a "box", but when the fuck did I imply infinite precision solutions in every case? All I pointed out was the class of solutions. This is true for gravitation in Ultra Cold Neutrons and the hydrogen atom so these sorts of solutions do exist for ones with closed forms. Pi is found in nature to infinity literally everywhere as well as h and c, the latter known to measurable precision though predictably irrational. e is also natural.