π: ratio of circle's circumference to it's diameter
we can generalize this concept to n dimensions
1_π: what we generally call pi, or the ratio of a 1-sphere's circumference to the line bisecting it: 2πr/2r = π
2_π: ratio of 2-sphere's surface area to the area enclosed by the 1-sphere bisecting it 4πr^2/πr^2 = 4
3_π: ratio of 3-sphere's surface volume to the volume enclosed by the 2-sphere bisecting it 2π^2r^3/(4pir^3/3) = 3π/2
in general, n_π is the ratio of an n-sphere's (n-1) bounding surface space to the space enclosed by the n-2 sphere bisecting it: given by the equation:
n_π = 2√π * Γ((n+1)/2)/Γ(n/2)
From this we can see that in even dimensions n_π is a rational number but in odd dimensions n_π is transcendental.
consciousness can only exist when π is transcendental, our space is conveniently 3 dimensions
you exist due to pure anthropic chance
>>7698735
lmao philosophy fag please leave
>>7698737
im a girl
>>7698735
look up vortex math
>>7698735
>consciousness can only exist when π is transcendental
[citation needed]
Where do you get this shit?
>>7698735
nice bait, made me angry.
>>7698832
http://www.megafoundation.org/CTMU/Articles/Langan_CTMU_092902.pdf
http://arxiv.org/ftp/math/papers/0211/0211337.pdf
>>7698735
>3-sphere's surface volume
what the fuck am I reading
ok
Gene ray is that you
>>7698735
But that's not extending the same concept to higher dimensions.
The first concept is:
The ratio of a distance to the size of the set of all points that distance from a point in two dimensions.
The second concept is;
The ratio of that set in n dimensions to that set in n-1 dimensions.
Of course the second one is going to be simple in even dimensions.
>>7699481
I thought that was a 4-sphere
>>7698938
>chris langan
CTMU is deliberately obfuscated bullshit
http://www.wolframalpha.com/input/?i=2sqrt%28pi%29+*gamma%28%28n%2B1%29%2F2%29%2Fgamma%28n%2F2%29%2C+n+from+2+to+20
wot is this
The fuck is a surface volume?
>>7699864
The surface of a volume
>>7699869
LOL RIGHT
>>7699481
What's the surface volume encapsulate?
>>7699864
3d analog of the surface area of a sphere
a sphere (or 2-sphere) is 2d, it has a volume of 0, but it encloses a 3 dimensional space (a ball) with a volume of (4/3) pi r^3
a 3-sphere is 3 dimensional but encloses a 4-dimensional space
Your confusion stems from the fact that people confuses circles and spheres with the area they enclose and use it synonymously in every day language. A disc has area, a circle doesn't, a ball has volume, a sphere doesn't.
>>7699888
Thanks, that clears things up. Whenever people talk about 4-spheres they're actually a dimension up from what I'm imagining...damn.
>>7699864
In 3 dimensional space, the set of points equidistant from one point (what you think of when you hear "sphere") is a 2 dimensional object. Think of a beach ball. So, it has a 2 dimensional measure of the space it takes up. This is called "surface area."
In 4 dimensional space, the set of points equidistant from one point is a 3 dimensional object, so, it takes up a 3 dimensional space. This space it takes up is it's "surface volume" (as volume is 3 dimensional).
>>7699888
Fucker already got it for me :P
>>7699864
this is the observable universe with earth as the center
pretend if you traveled to the edge of the universe you'd suddenly wind up on the other side like pacman
the volume of this universe is the "surface volume", it encloses a 4d hyperspace that you can't access because you can only move in 3 spatial dimensions
>>7699900
I can't fathom a perpendicular in 4-dimensional space. Can't a perpendicular point relative to a sphere's center exist at all possible points inside of a sphere??
Although that's also implying perpendicular = parallel.
