Zapp is here :3

[Zapp]

hai guise :3

let me introduce myself, I am 17 years old and live in germany. I am currently attending the german equivalent to highschool and I still have 3 semesters ahead of me. I am interested in math and physics and I plan to study at least one of those subject after I graduate.
due to my great interest in math I stumbled across spikedmath, though I don't get some(read: most) of the jokes
in fact, I have a lot of questions concerning math, because, to be honest, the explanations on wikipedia are just to complicated and my other sources only explain how something works, but not why it works.

I am looking forward to awesome times with all of you

if you have any questions, feel free to ask ^_~

oh and my favorite number is 3

[SpikedMath]

My question would be ... why 3? There are so many numbers to choose from! Like 235884723.122, or i, or e, or pi, or phi, or ...

[Zapp]

for different reasons:
- in christian religion we have the trinity
- euclidean space has 3 dimensions
- in certain religions and philosophical beliefs, the human is composed of 3 parts: mind, body and soul
- the triangle is the most basic 2 dimensional shape
- :3 and <3

[xander]

- euclidean space has 3 dimensions

There is no one Euclidean space. There are Euclidean spaces of arbitrary dimensions exist, and arbitrary dimensional spaces that are locally Euclidean also exist (that's the whole point of manifolds, right?). A plane is a Euclidean space, as is a line, as are many higher dimensional abstract spaces that can't be easily visualized. A tesseract is an object that lives quite happily in a four dimensional Euclidean space.

xander

[theboss]

Welcome Zapp, hope to see ya around.

[Zapp]

- euclidean space has 3 dimensions

There is no one Euclidean space. There are Euclidean spaces of arbitrary dimensions exist, and arbitrary dimensional spaces that are locally Euclidean also exist (that's the whole point of manifolds, right?). A plane is a Euclidean space, as is a line, as are many higher dimensional abstract spaces that can't be easily visualized. A tesseract is an object that lives quite happily in a four dimensional Euclidean space.

xander

alright, thanks, I will have to study up on dimensions then
I'll probably do that next week, after I have taken a look at simple differential equations. ( I will probably have quite a few questions after that )
I always thought euclidean space would describe the 3 dimensions of our universe with which we can interact.

[xander]

Euclidean space describes space that follows the rules laid out by Euclid in the Elements. It has all of the straight lines and figures that we know and love from elementary and high school geometry. However, there are other geometrical and topological spaces that exist which are not Euclidean (consider the Klein disk where given a point and a line l, we can find infinitely many lines through the point that are parallel to l; or a spherical space, where no such parallels exist).

To get a better feel for things, you might want to read Edwin Abbott Abbott's Flatland, which gives you a really good feel for lower (≤3) dimensional Euclidean spaces.

xander

[Zapp]

I will keep that in mind, thanks!

[theboss]

Oh I loved flatland!
Great book and one of few which had a good sequel.

[Prunebutt]

I guess you didn't learnd about relativity yet. 4 dimensions are so much more fun that just three! (I'm still waiting for that hyper-rubics cube, Santa! ò.Ó)

BTW: Hi! ^^

[Zapp]

I guess you didn't learnd about relativity yet. 4 dimensions are so much more fun that just three! (I'm still waiting for that hyper-rubics cube, Santa! ò.Ó)

BTW: Hi! ^^

I did, but as far as I know, time is not a dimension of space

[theboss]

Well it's just the way that you look at it.
Width, breadth and highth are all dimensions that a lower dimensional being can go trough, like a graph "lives" in one dimension (the y axis) with the x-asxis as it's time. If you see our time in such a way then it is infact a spacial dimension.

[Zapp]

Well it's just the way that you look at it.
Width, breadth and highth are all dimensions that a lower dimensional being can go trough, like a graph "lives" in one dimension (the y axis) with the x-asxis as it's time. If you see our time in such a way then it is infact a spacial dimension.

so that means we are only able to interfere with length width and height, therefore we are 3 dimensional beings living in 4 dimensions?

[theboss]

Yes, here's a vid explaining the general idea;

[Zapp]

ok... let's say we would be 4 dimensional beings. wouldn't our body contain infinite copies of every state we experience as 3 dimensional beings?
let's even take this a step further, would our body then contain infinite copies of every state of every atom which was or will be part of our 3 dimensional states?

let's take this a step back: as 3 dimensional beings: does our body contain infinite copies of every state and every past and future parts for each individual state we would experience as 2 dimensionals?

[theboss]

To the first two yes, but it ofc would depend on the nature of their 4th dimension. If it is time, like we just discussed then yes, but if it is some other spacial dimension and they experience time like we do, then no.

Like 2D creatures (think of flatlanders) experience length, breadth and time but not hight.
So we would not contain infinite copies of every state they are in, unless they see hight as their time dimension, if we see graphs as living things though, then your argument would stand, as we can see its whole "life" from start to end in one picture, as itself can only see the Y coordinate that it is in at the given moment t=y.

I need to do some homework now, so I'll try to make a less disorganised picture once I'm done

[xander]

Dimensionality is an abstract mathematical concept. The equation w=x+y+z is four dimensional because it has four variables in it. You could graph in a four dimensional space in the same way that you might graph y=mx+b in a two dimensional space, or z=ax+by+c in a three dimensional space. A few years ago, I was given a problem to solve that had over 100 variables, hence the graphs of the various equations involved required many more dimensions than my poor brain can handle. Fortunately, they were just equations, and there are ways to deal with them.

Mathematics is a way of taking some essential properties about things, and running with those properties without any regard to how else the object might behave. When you try to apply those ideas to the real world, willy-nilly, you get nonsense like "time is a dimension." Mathematically, time can be modeled as a dimension. But mathematically a donut can be modeled as a coffee cup---they are both solid tori. The space that we move about in is like the abstract mathematical concept of three dimensional space, but that does not mean that it is the same as the abstract mathematical concept of three dimensional space.

xander

[Gary]

Just to confuse the issue a bit, as originally conceived, special relativity used a flat (ie not curved) but non-Euclidean 4-dimensional space. This idea of flat, and consequently of Euclidean as a special version of flat, is best approached using differential geometry (you want to be real comfortable with multivariate calculus first).