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> Something to break a geeks mind., Maths geeks only.
Witless
post Aug 6 2007, 12:19 AM
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You clicked this link.. but still a second warning it takes a certain mind set to appreciate this (or even care about why this is mind boggling).

If you're a hardcore maths geek you probably already know about this.. but if you're decent at maths, but not a hardcore maths geek you may not be familiar with this thing which breaks my brain.

It's in the guiness book of records for being the largest number with a name in existence. It's called Graham's number, and it makes a googolplex seem like a miniature number. I didn't really appreciate the unconceivable nature of the number until I saw this step by step of how to make it.

Step 1) 3^3 means 3 cubed which is 3x3x3 which = 27. That's simple enough.

Step 2) So therefore 3^^3 means 3^(3^3) which means 3^27 which means 3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3x3 = 7,625,597,484,987. Quite a large number already.

Step 3) Ok.. still with me? Good cos it gets a bit hard to grasp the numbers now.

3^^^3 = 3^^(3^^3) basically means 3^^7,625,597,484,987 or 3^(7,625,597,484,987^7,625,597,484,987)

So to work that out.. multiply 7,625,597,484,987 by itself 7,625,597,484,987 times and multiply 3 by itself the number the number of times you got from that previous multiplication. The resultant number won't fit on a normal calculator.

Step 4) So if you can imagine 3^^^^3 = 3^^^(3^^^3). The number you'd get would be probably more than you could write given a year of constantly writing numbers.

Step 5) Ok.. not there yet.. consider 3^^^....^^^3 where there are 3^^^3 arrows between those two 3's. So a number of arrows beyond which you could ever hope to be able to write between two threes. Already broken any hope of writing this number down in any reasonable normal mathematical notation.

Step 6) Ok, now consider 3^^^...^^^3 where the number of arrows is the result of step 5.

Step 7) Right already beyond the imaginings of what our brains were meant to concieve of. However we're still far away.
Continue the process in step 6 of making the number of arrows in 3^^^...^^^3 equal to the resultant number you got the previous time you did it. Do this 63 times, and you will have finally arrived at graham's number.

The best way I ever heard of this number being described was: "If all the material in the universe were turned into pen and ink it would not be enough to write the number down."

The reason the number was named was because it is the largest number that's ever had a practical use. It use is something to do with Ramsey Theory which is theory to do with 'hypercubes'.

I was doing some reading about 3-D objects and after a few clicks I ended up on Graham's number because I was fascinated that such a large number could possibly have a use for anything. The world is odd indeed.


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Mata
post Aug 6 2007, 08:03 AM
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If I were that number, I'd ask for a new name. Something more glamorous, speaking of excitement and danger. How about 'Mata's Number'? biggrin.gif


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Novander
post Aug 6 2007, 10:24 AM
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Take apart your head
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As is far too often the case, it was xkcd that first made me aware of graham's number.


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gothictheysay
post Aug 6 2007, 02:13 PM
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Yeah, I think it was xkcd that enlightened me of it too. However, I didn't know exactly what it was until I read through your explanation. I feel all hardcore math geeky for knowing it beforehand though. biggrin.gif That's a biiiiig number.


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Moosh
post Aug 6 2007, 08:21 PM
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I heard about Graham's Number after reading The Man Who Loved Only Numbers, which is an excellent biography of Paul Erdos, who was good friends with Ronald Graham, of Graham's Number.

After reading this, I looked up some stuff on it, and I came across Knuth's Up-Arrow Notation, which is the easiest way to write numbers of these magnitudes, and I then used this notation to win a "write the biggest number you can using 3 numbers/symbols" contest, winning me chocolate.

So there you have it kids, Maths leads to chocolate. Do maths.


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mooooooooooopo
post Aug 6 2007, 10:32 PM
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: P>
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I think I heard about it first in Internet Security (read: cryptography and hacking) lectures. Fun times.


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{Gothic Angel}
post Aug 10 2007, 04:31 PM
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My direction
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I feel I should stick up for the dumbass side here.

The first place I heard about this number was here. I have a hard time visualising 6.022 x 10^23 (number of particles in a mole), and that is actually a small number. I am impressed with your huge number.

So there tongue.gif


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Daria
post Aug 11 2007, 11:40 PM
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Wait for the uprising
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*sides with her chemistry twin*
I got a B at GCSE maths and scraped by at that. I'm still not sure how I managed to do Logarithms for Chem A level. Some things are just meant to be a mystery.

That is a big number.


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