One Size Fits All Universe?

[Jay]

I was thinking about it, and I came up with the idea that our entire universe could fit into any 4-d object. Using the laws of analogy, of course:

A point, which has no x direction length, could fit into any linear object of of some x.

An infinite line, which has no y length, could fit into any planar object of some x,y combination, by folding infinite times.

An infinite plane, which has no z length, could fit into any realmic object of some x,y,z combination by folding it infinite times.

So our universe, with no w length, could fit into any tetra object of some x,y,z,w combination , by folding it infinite times.

In some other post someone I said we couldn't feel it if we were bent into the 4th dimnesion, so maybe it's possible that our entire universe is contained within some 4-d object as small as a 4-d atom!

[Aale de Winkel]

Yes, probably one could. Wheter or not our infinity can be folded into an infinite tetronian shape I don't know.
I think it all depends on the relative sizes (and timeflow) of the various universae, we could well be some picture on emilies wall, or a puny spot on her sons football, or as our universe is curved, be that football.
What we call infinite, might well be a finite length in tetronian space.

[alkaline]

I don't know about infinitely long n-planes fitting into (n+1)-planes. Maybe if the n-plane was curved in on itself (like an n-sphere), which to the beings inside it would be infinite, but not to an (n+1)-being.

[Keiji]

If an infinite n-plane has zero width in the (n+1)th dimension, it can easily be folded into an (n+1)-cube.

[alkaline]

not really - imagine a plane. You fold the plane in half, so that the plane extends infinitely in three directions (two of the original four directions point the same way within realmspace). It is still infinite. Then, ripple-fold it back along a line at some distance away from the original crease. It now extends infinitely into the opposite direction. You can go and fold it back and forth infinitely and you will never reach the end of planespace, because it is infinite. Thus, you could never fit it in a box. An unbounded object will never fit in a bounded one, no matter the dimension. You would keep folding forever. Even if it's mathematically possible to do so, it definitely isn't easy.

[Keiji]

infinity/infinity = 1

so therefore, by folding it infinately many times it is now a plane with zero thickness, infinite length and 1 width. repeat and you get a 1x1x0 object. then it's just a matter of folding it up until it's small enough to fit in the cube.

[alkaline]

looks like we have our first realmspace citizen, bobxp... congratulations :-) Aale is hot on your tail.

Anyhow, infinity is not a simple number, it is a symbol representing a concept. You can't merely divide infinity by infinity. There are actually infinities of different magnitudes - countable infinity, uncountable infinity, the powerset of uncountable infinity, powerset of that, on to an infinite number of infinities. If you have a countable infinity, and you take out every other element, it is still infinity, and paradoxically it still has the same number of elements. I've taken a course on abstract mathematics where we studied cardinality of sets, it was quite interesting, and we studied infinity, so that's how i know these things. If you abuse infinity and use it like a normal number, you can make zero x infinity = any number you want. The proof of this is on the appendix of the following page: http://www.geocities.com/vpanda/UnderstandingDimensions.html.

[Keiji]

i will beat aale to the fourth dimension

1/positive zero = positive infinity
1/negative zero = negative infinity

so 1/positive infinity = positive zero
so positive zero*positive infinity = 1

get it?

[alkaline]

1/zero = not a number/undefined. Infinity just represents the concept that the value is bigger than any actual number. You can't perform math like you are trying. Also, there is no such thing as negative zero/positive zero. There is only zero approached from the left side and zero approached from the right side.

[Aale de Winkel]

i will beat aale to the fourth dimension

1/positive zero = positive infinity
1/negative zero = negative infinity

so 1/positive infinity = positive zero
so positive zero*positive infinity = 1

get it?

Here is bionian proof of the statement: 0 * infinity = -1:
When two lines are perpendicular their directional coefficients (dy/dx) multiply to -1.
The x-axis has directional coefficient 0, while the y-axis has coefficient infinity.
Those axes are perpendicular.
Henche 0 * infinity = -1 Q.E.D. (ain't math fun )

I don't think I'll ever reach the fourth dimension, neither as a visitor, let alone as a citicen. Far too steep an ascent
So don't reserve for me some tetrapolean quadruplex, since by that time I assume my warp-engines warped me out of this realmspace anyway

[Jay]

I'm can't really follow your reasoning as well as I would like to, Alkaline b/c I'm only taking Pre-Cal right now. But let me try to approach my idea from a different light. Instead of imagining an infinite (n) dimensial object fitting into a finite (n+1) dimensional object, try to imagine the n-dimensional object as originating at a point an expanding.

I'll try to draw it out: we start with a point, contained within a finite 2-d object (the o's).

000000
000.000
000000

Then, the point begins expanding 1-dimensionally, into a line.

000000000000
000000000000
000 ______000
000000000000
000000000000

When it reaches boundaries, it folds in on itself. The right side folds up, and the left side folds down.

00000000000000
00000000000000
0 ___________\0
0\000000000000
00000000000000

The layers can get infinitely close to each other and the process can continue when the expanding line reaches the boundaries again. (The line you see now is now 3 lines with an infinitely small space between them)

0000000000000000
0000000000000000
0/_____________0
00000000000000/0
0000000000000000


Then yeah, apply the laws of analogy to this until you reach 3-d within 4-d. If our universe started from a singualr point, then this should hold true.

[Keiji]

that's how i was describing it aswell

[Jay]

I was actually thinking about wha I drew out and now I'm wondering if the laws of analogy do apply. I mean, it's hard to conceive an expanding plane within a box. Witht the line inside the square, it had two ends that could easily just fold over in two opposite directions.

But with an expanding plane, you have four enclosing sides, with only two ways to fold: upwards or beneath the starting plane. I think it should be possible, although the folding pattern would become very complicated very quickly.

The folding of our universe might be ridiculously complicated then.

[Keiji]

damn right you are - so a plane of any size could be folded into a 4-cube or higher, and a realm of any size could only be folded into a 6-cube or higher

[alkaline]

I was just thinking - if a plan is infinitely thin, and you fold it over on itself, then it wouldn't be any thicker than before. Thus you could fold forever and not make it any thicker. Thus, by your assertion that you could fit an infinite line within a square, you could fit an infinite line within a line segment. This is obviously obsurd. Thus, i don't think it's possible to fit infinite hyperplanes into n+k hypercubes. You can't fit the infinite into the finite.

[Keiji]

ah, the thing here is that although you can fold lines in such a way that they become as thick as only one line, as soon as you let go, air currents will take action and put a small amount of air between the parts of the line.

[alkaline]

it was a mathematical argument, not a physics one - thus you can't bring air currents into it.

[Keiji]

bah, you can't describe rl with math

[Jay]

I understand what you're trying to say about fitting the infinite into the finite, alkaline, so I changed my argument:

Imagine something forever expanding, instead of something infinite. At all times it does have a "finite" measurement.

A line of of 4 inches can fit into a square 4 inches in length. If it expanded to 8 inches, it could be folded over itself. It could keep extending and folding indefinitely within the square, don't you think?

Our universe isn't infinite, but it is expanding. It can be folded over indefinitely too, can't it?

[Keiji]

Precisely.

[alkaline]

If something is forever expanding, you will never successfully fit it in the box, because it *keeps expanding*. When you stop expanding to see if it will fit in, then it is finite, and it will fit. You will never reach the point where it won't fit in, just like you will never reach infinity.

I have no idea if our universe could be folded infinitely.

[RQ]

I agree with Aale's proof that indeed on a graph a slope zero times a slope x/0 should equal -1, but 0 times infinity isn't only that since if we define infinity as x/0 times zero we get that -1 is 0/0. If we are to further prove -1/1=0/0, now 0/0=0/0/0 since zero times 0/0=0 so 0/0=0/-1 and that equals 0/0=0 and therefore -1=0

...so far, I have not found the science...