Talk:Shannon number
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[edit] Number of Board Positions
Hmmm... well, it occured to me that the total number of posible board positions couldn't be more than 64!/32!... that is, the total number of ways of arranging 32 distinguishable pieces on a board of 64 spaces. But I didn't consider the affect of promoting pawns, and all the various choices that might be available in that case, and the extra board positions that this would create... still though, if promoting pawns was disallowed, it would limit the positions to 64!/32! (as well as noticably changing the dynamics of the game)... just a curious thought. (The Swami 08:36, 17 August 2005 (UTC))
- 64! / 32! = 482219923991114978843459072919892677776312893440000000, but that's not what Shannon's number is. Soo 16:01, 26 September 2005 (UTC)
- I know it's not, I was just posting some musings on the derivation of said number... but here's a few more while I'm thinking of it... I think the total number of board positions could not excede 64!/32! ^ 6^32; this would be the total thirty two pieces maximum on the board, each of which can be one of six types. The game-tree complexity may be larger than this, I'm just saying that the total number of board positions could not (I believe) excede this. (The Swami 02:53, 28 September 2005 (UTC))
[edit] Shannon Number
There are several possible problems with this page. First, "One novemtriginillion is known as the Shannon number." It seems like the Shannon Number is actually 90040, which is 1.478...×10118, for which 10120 is a poor approximation. If 90040 is indeed the Shannon Number, then that doesn't really belong in this article. Also, for the number of atoms in the universe: can that figure really be estimated with so much precision? Ardric47 05:18, 6 April 2006 (UTC)
- I've changed where it claimed that it was the Shannon number. While it might not be the Shannon number, it's pretty close in size to it. 152.163.100.10 00:55, 7 April 2006 (UTC)
- It only seems pretty close because the exponents are pretty close, but really it is larger than the Shannon Number by a factor of about 67...saying that this is pretty close would be like saying that pi is pretty close to 200 (3.14...×100 vs. 2×102). Ardric47 02:05, 8 April 2006 (UTC)
- Approximating 118 with 120 is hardly the same as approximating 0 with 2. A better picture is pi to 10 (100.5 vs 101) More importantly; when dealing with that large numbers approximating the exponent is usual, and frequently necesarry.
- It only seems pretty close because the exponents are pretty close, but really it is larger than the Shannon Number by a factor of about 67...saying that this is pretty close would be like saying that pi is pretty close to 200 (3.14...×100 vs. 2×102). Ardric47 02:05, 8 April 2006 (UTC)
[edit] Move?
This article is about the Shannon number. Now that it has been decided that the Shannon number is not 10^120, shouldn't the article be moved back to Shannon number? Melchoir 01:49, 8 April 2006 (UTC)
- In the googol article, it says "The Shannon number is a rough estimate of the number of possible chess games, and is more than a googol: 10120". Is it wrong? 64.194.43.49 13:02, 8 April 2006 (UTC)
- Yes, it's wrong, and I'll change it. While it is unclear exactly what the Shannon number is, whether it's 900^40 or some more accurate estimate, this article does not state that 10^120 is the Shannon number, so its title is misplaced. In general, you should trust the more specialized Wikipedia article above other articles mentioning it. Melchoir 19:23, 8 April 2006 (UTC)
[edit] Confusing redirects
Due to confusing redirects, this page has been mirrored (and then added to by me...) at Talk:10^120 (number). Ardric47 21:14, 8 April 2006 (UTC)
- Actually, as I type this, the page history is at 10^120. The redirect at 10^120 should be reverted and then moved on top of Shannon number. Melchoir 21:41, 8 April 2006 (UTC)
- Do you know offhand if there was ever anything about 10120 (and not the Shannon number) that might need to be moved to its own article? 10^120 (number) is now (as of 21:46, 8 April 2006 (UTC)) a redirect to Large numbers. Ardric47 21:46, 8 April 2006 (UTC)
- Not really. I'm actually now inclined to leave the redirect and this page as they are. As long as 10^120 (number) isn't deleted, it will retain a record of this page's early history, which includes so many moves that it might be best forgotten anyway. Melchoir 21:53, 8 April 2006 (UTC)
- The root of the problem is the first version, in which 10120 is equated with the so-called "Shannon number". Let me add though, that I'm sure the creator meant well. Ardric47 21:52, 8 April 2006 (UTC)
- Right. Melchoir 21:53, 8 April 2006 (UTC)
- Do you know offhand if there was ever anything about 10120 (and not the Shannon number) that might need to be moved to its own article? 10^120 (number) is now (as of 21:46, 8 April 2006 (UTC)) a redirect to Large numbers. Ardric47 21:46, 8 April 2006 (UTC)
[edit] Calculation error in refered page
This article refers to this site when mentioning the lower bound of an estimate of all the atoms in the universe. However, the following calculation on that page is incorrect: 1 * 1057 * 4 * 1011 = 5 * 1068. The correct answer is 4 * 1068, not 5 * 1068. This, in turn, affects the subsequent calculation and results in a different estimate of 3.2 * 1079 atoms in the universe.
