How's Infinity looking now? (Graham's number)

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

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
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You don't have to read on ... but I was trying to put some context or proportion to it ...
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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 l_p=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)
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 ~= 3^2.1 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

Ben Hur's number > Graham's number :D

Actually Ben Hur's number > Graham's number ^ ^ ^ ^ ^ infinity :U

Now my head hurts!:wink:

This looks like a problem that should be sent to Sheldon Cooper of "The Big Bang Theory"

6 is a number I can cope with!!!:D

Infinity is still outa sight!!

My head has officially imploded. I was going well about 20 seconds after the start of 1:44, then I started to dribble.

Johns number = 556.
The number of seconds I wasted watching that video. Life's too short to worry about things like this

I'm with GJ, when your personal number is up (PNIU) it's up.
To illustrate here is a photo taken from near infinity of an elephant whos' PNIU being consumed by jackals in darkest Africky.

Geoff.

That's one hairy effluent!

Sort of reminds me of the one pane cartoon. (Which I can't find on the web)

A picture of two students, one holding a slide rule.
The slide rule is broken in half and smoking.
The caption says, "All I tried to do was divide infinity by zero."

I showed it to my Trigonometry teacher in High School and his comment was, "Just try to find infinity and zero on a slide rule." My comment was "No sense of humor?" His comment was, "Get out of here and spend the class time in the office." At least the Principal thought that the cartoon was funny.

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Originally Posted by rrich

Sort of reminds me of the one pane cartoon. (Which I can't find on the web)

A picture of two students, one holding a slide rule.
The slide rule is broken in half and smoking.
The caption says, "All I tried to do was divide infinity by zero."

I showed it to my Trigonometry teacher in High School and his comment was, "Just try to find infinity and zero on a slide rule." My comment was "No sense of humor?" His comment was, "Get out of here and spend the class time in the office." At least the Principal thought that the cartoon was funny.

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Infinity (+ve or -ve) add or subtract 1 then loop.....what did you get......

e to the power if i and pi and from this result then add one and this equals 0...maths ... the only true brain teaser (my brain now hurst ...it's easter)

e = base of natural logs
i = square root of minus 1
pi = ratio of the diameter of a cricle to its circumfrence
1 = basis of all counting
0 = starting point

since i is imaginary, e and pi are non repeating (unable to be fully qualified) where is inifinity in this scale?

i had an imaginary friend once. We hae not seen each other since high school. :C

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Originally Posted by Wongo

i had an imaginary friend once. We hae not seen each other since high school. :C

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Maybe his number was up!!!:D:p

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since i is imaginary, e and pi are non repeating (unable to be fully qualified) where is inifinity in this scale?

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Just past infinity - 1, and before infinity + 1.