pmcgee
25th March 2013, 03:43 PM
I needed to get this down so it could settle to the back of the brain-pan, so apologies in advance.
Check out this video from the 1:44 marker ... it should start at the right spot ...
A taste of infinity - YouTube (http://www.youtube.com/watch?v=8zE-IZynfKM#t=104s)
Before going on to this very enjoyable video from numberphile ...
http://www.youtube.com/watch?v=XTeJ64KD5cg
As an aside ...
1. G is giganta-gorga-normously huge.
2. It is funny to watch them attempt to remember the committee analogy.
3. It is hilarious that the solution to the problem might be SANITY-THREATENINGLY LARGE ... or possibly 6.
Yes ... possibly larger than God himself ... but we're leaning towards single digits.
:D
_ _ _
You don't have to read on ... but I was trying to put some context or proportion to it ...
_ _ _
A couple of points of background first ...
The Planck length. This is (roughly speaking) the theoretically smallest measurable distance, and the size of the strings in String Theory (of which I know zip).
It is lp=1.616×10−35m. I'm gunna round a bit and refer to the Planck micro-poofteenth (pmp)=10-35m.
So a smallest three-dimensional volume of the universe or micro-poofteenth of volume (mpv)=10-105m3.
Ok?
Next the size of the observable universe. Some sources mention there being 1080 atoms in the universe ... but this wikipedia entry gives the *volume* of the universe as 1080m3. (Orders of magnitude (volume) - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Orders_of_magnitude_(volume)))
One of them is obviously wrong, unless atoms have gotten bigger than I remember.
... Ok ...
I just figured out where I was going wrong. A lot of the atoms in the universe are quite spread out, so I guess both could be "right".
So anyhoo ...
The number of mpvs in the observable universe becomes 1080 divided by 10-105 = 10185.
Now I will imagine a big drop of black empty goo - called Multiverse 1 - that will contain not one universe but a million trillion (1015) universes all the same size.
That gets us up to 10200 mpvs.
So far, so good.
Now zoom out to Multiverse 2 - same basic structure as the first one, but where every single tiny little building block of volume in this multiverse ... is a Multiverse 1.
So then it would contain 10400 mpvs.
Zoom out again to Multiverse 3 in the same fashion and we get up to 10800 mpvs.
Zoom out again to Multiverse 4 in the same fashion and we get up to 101600 mpvs.
Zoom out again to Multiverse 5 in the same fashion and we get up to 103200 mpvs.
10 ~= 32.1 so call this 36720 mpvs
38 = 6561 ... so close enough to saying 3(3^8) mpvs
This is less than 3^3^3^2 so less than 3^3^3^3 = 3^^4.
So waaaaaaaaaaaaaaaay less than 3^^^3.
And a fair bit short of G ... which is waaaaaaaaaaaaaaaay short of infinity. :U
Have a nice day. :D
Paul
Check out this video from the 1:44 marker ... it should start at the right spot ...
A taste of infinity - YouTube (http://www.youtube.com/watch?v=8zE-IZynfKM#t=104s)
Before going on to this very enjoyable video from numberphile ...
http://www.youtube.com/watch?v=XTeJ64KD5cg
As an aside ...
1. G is giganta-gorga-normously huge.
2. It is funny to watch them attempt to remember the committee analogy.
3. It is hilarious that the solution to the problem might be SANITY-THREATENINGLY LARGE ... or possibly 6.
Yes ... possibly larger than God himself ... but we're leaning towards single digits.
:D
_ _ _
You don't have to read on ... but I was trying to put some context or proportion to it ...
_ _ _
A couple of points of background first ...
The Planck length. This is (roughly speaking) the theoretically smallest measurable distance, and the size of the strings in String Theory (of which I know zip).
It is lp=1.616×10−35m. I'm gunna round a bit and refer to the Planck micro-poofteenth (pmp)=10-35m.
So a smallest three-dimensional volume of the universe or micro-poofteenth of volume (mpv)=10-105m3.
Ok?
Next the size of the observable universe. Some sources mention there being 1080 atoms in the universe ... but this wikipedia entry gives the *volume* of the universe as 1080m3. (Orders of magnitude (volume) - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Orders_of_magnitude_(volume)))
One of them is obviously wrong, unless atoms have gotten bigger than I remember.
... Ok ...
I just figured out where I was going wrong. A lot of the atoms in the universe are quite spread out, so I guess both could be "right".
So anyhoo ...
The number of mpvs in the observable universe becomes 1080 divided by 10-105 = 10185.
Now I will imagine a big drop of black empty goo - called Multiverse 1 - that will contain not one universe but a million trillion (1015) universes all the same size.
That gets us up to 10200 mpvs.
So far, so good.
Now zoom out to Multiverse 2 - same basic structure as the first one, but where every single tiny little building block of volume in this multiverse ... is a Multiverse 1.
So then it would contain 10400 mpvs.
Zoom out again to Multiverse 3 in the same fashion and we get up to 10800 mpvs.
Zoom out again to Multiverse 4 in the same fashion and we get up to 101600 mpvs.
Zoom out again to Multiverse 5 in the same fashion and we get up to 103200 mpvs.
10 ~= 32.1 so call this 36720 mpvs
38 = 6561 ... so close enough to saying 3(3^8) mpvs
This is less than 3^3^3^2 so less than 3^3^3^3 = 3^^4.
So waaaaaaaaaaaaaaaay less than 3^^^3.
And a fair bit short of G ... which is waaaaaaaaaaaaaaaay short of infinity. :U
Have a nice day. :D
Paul