Comments on: The Clarkkkkson vs. the xkcd Number

By: video

video — Wed, 12 Nov 2008 17:40:28 +0000

the latest comic made me fall a little in love with you.

By: Danny

Danny — Wed, 29 Oct 2008 09:53:20 +0000

Ugh, my first post got messed up.

For example, define n(k) as the length of the longest possible sequence x[1],…,x[n] (of k elements) such that for no i < j less than or equal to n/2 is x[i],…,x[2i] a subsequence of x[j],…,x[2j].

It is easily seen that n(1) = 3 (AAA) and n(2) = 11 (ABBBAAAAAAA).

However, n(3) is between A(7183,158386) and A(A(5)). A lower bound for n(4), using Ludixkcdrous’ L(n) function, is L(A(187196)).

L(A(187196)). Now that is a very large number.

By: Danny

Danny — Wed, 29 Oct 2008 09:47:49 +0000

Also check out Jonathan Bowers’ website: http://www.polytope.net/hedrondude/array.htm

By: Danny

Danny — Wed, 29 Oct 2008 09:46:42 +0000

Some of the work by Harvey Friedman involves *very* large numbers:

http://www.math.ohio-state.edu/~friedman/pdf/EnormousInt.12pt.6_1_00.pdf

For example, define n(k) as the length of the longest possible sequence x[1],…,x[n] (of k elements) such that for no i L(A(187196)). Now that is a very large number.

By: Myoshu

Myoshu — Sat, 18 Oct 2008 01:26:27 +0000

I told a few people today about this argument and 4 of them said “infinity!!” to which i replied, “well, that’s not really a number”.. and the response was a disappointing “infinity minus one!”…. Seriously, try casting it first. lol

big_number = (int)#INF;

pwnd.

By: Aleph Infinity

Aleph Infinity — Thu, 02 Oct 2008 08:38:33 +0000

Associating power towers as ((((n^n)^n)^n)^n)… is inferior to right associativity because it fails to truly define a new function. For instance, a power tower of hyper4 (6, 6) (that is to say, 6 tetrated by 6) with the left associativity gives (((((6^6)^6)^6)^6)^6). When you work out some simple power math, that is the same thing as 6^(6^5). So when you get something like 100 tetrated by 100, rather than having a power tower too large to write, you have 100^(100^99).

By: Default

Default — Wed, 06 Aug 2008 22:04:51 +0000

Eh, someone beat me to the punch with using cardinals… I am quite the dilettant when it comes to sophisticated mathematics, and don’t know if this is valid, but I was going to suggest this “cheat”: aleph-null -1.

P.S. Can’t help but feel a bit disappointed that xkcd number lost, but I found it, somehow, satisfying to see people use the Conway chains to reslove it.

By: Bob D

Bob D — Mon, 14 Jul 2008 01:27:49 +0000

The Conway chained arrow notation, mentioned already, is astonishingly powerful. The simple expression 4 -> 4 -> 4 -> 4 is already far larger than Graham’s Number. In fact, it’s larger than the xkcd number itself.

I can’t tell whether or not it’s larger than the Clarkkkkson too…
but once the chain reaches a fifth term I’m certain it would be.

Therefore “Up” proposes a new number, in honour of the xkcd number, called the Upxkcd number:

http://azureworld.blogspot.com/2008/07/up-function.html

P.S. the uncomputables (such as busy beaver, see four comments up) will probably win this game hands down.

By: Wry Mouth

Wry Mouth — Sun, 06 Jul 2008 17:34:29 +0000

Sigh; just read this thread. In investigating *another* number theory problem, had developed a series of “hyperfactorials” just like the Clarkkksons — but last year (about 2007 Feb). I’d suspected they’d been fooled around with already, but now I’ve got a scintilla of evidence that someone else has been pondering the same number set. The author seems to be referring to another, previous person wwho’d dubbed them “hyperfactorial,” so now the hunt is on to find that person…

(I am a math teacher and by way of avocation, an amateur statistician/probabilist)

So, I get what he’s saying perfectly (once he gets beyond the “lynz” set up). Hyperfactorials get really, nicely huge fairly quickly. I think of them as mathematical poetry (no use for them, yet, although I can envision possible use in computer diagnotics).

By: m1omg

m1omg — Mon, 31 Mar 2008 20:28:11 +0000

Is this number larger than clarkkkson?

Let’s say that 9 pentated to 9, for example is 9 tetrated to 9 9 times , 9 sextated to 9 is 9 pentated to 9 9 times and so the steps go on.
Now, what if we have xkcd steps (name it xkcd-tation) and we xkcd-tate xkcd xkcd times?It is larger than the Clarkkkson?