Monday, 16 March 2009

WUCC15 Number Proposal - The Chess Equivalent of The Erdős Number?

Paul Erdős (1913-1996)
Hungarian Mathematician

The eccentric Hungarian mathematician Paul Erdős (1913-1996) was one of the most prolific publishers of papers in mathematical history (apparently second only to Leonhard Euler). Erdős wrote around 1,500 mathematical articles in his lifetime, with 511 direct collaborators.

The Erdős number describes the "collaborative distance" between an individual and Paul Erdős, as measured by authorship of mathematical papers. Paul Erdős is the only person having an Erdős number of zero. The lowest Erdős number of a coauthor is 1.

Diagramatic explanation of Erdős number [by user:h2g2bob, Wikipedia ]

Other similar number ratings include:
  • Bacon number - as in the game Six Degrees of Kevin Bacon. [link]
  • h-index - index quantifying both the actual scientific productivity & apparent scientific impact of a scientist. [link]
  • Kibo number - someone who has received e-mail from Kibo either directly or through shared contacts.
  • Shusaku number - "distance" between a Go player & Honinbo Shusaku, measured in Go opponents. [link]
  • Small world experiment - comprised several experiments conducted by Stanley Milgram examining the average path length for social networks of people in the USA. [link]
  • Stringfield number - application of the same idea to the field of ufology - connecting ufologists with the late Leonard H. Stringfield.
Proposed WUCC15 Number:
Now the hard part, doing the calculations. My prediction is that the lowest WUCC15 score will go to Victor Korchnoi or Boris Spassky. I would be interested in any comments.

Claude Shannon - Chess & The Shannon Number

Claude Shannon:

Claude Shannon (1916-2001) was a mathematician and electrical engineer. He is considered the "father of information theory" and also known for founding both digital computer and digital circuit design theory. Chess was a hobby of Shannon's - publishing the important paper Programming a Computer for Playing Chess (1950). Shannon used his knowledge of information theory, and its applications to game theory, to make fortunes at both Blackjack (Las Vegas) and on the stock market. Unfortunately, in the later parts of his life he was affected by Alzheimer's disease. [Wikipedia]

Claude Shannon calculated the possible number of chess moves to be around 10120. This being known as the Shannon Number. The calculation was published in his 1950 scientific paper - Programming a Computer for Playing Chess (download pdf here). The relevant section of the paper quoting the result is below:
With chess it is possible, in principle, to play a perfect game or construct a machine to do so as follows: One considers in a given position all possible moves, then all moves for the opponent, etc., to the end of the game (in each variation). The end must occur, by the rules of the games after a finite number of moves [4] (remembering the 50 move drawing rule). Each of these variations ends in win, loss or draw. By working backward from the end one can determine whether there is a forced win, the position is a draw or is lost. It is easy to show, however, even with the high computing speed available in electronic calculators thiscomputation is impractical. In typical chess positions there will be of the order of 30 legal moves. The number holds fairly constant until the game is nearly finished as shown in fig. 1. This graph was constructed from data given by De Groot, who averaged the number of legal moves in a large number of master games (De Groot, 1946, a). Thus a move for White and then one for Black gives about 103 possibilities. A typical game lasts about 40 moves to resignation of one party. This is conservative for our calculation since the machine would calculate out to checkmate, not resignation. However, even at this figure there will be 10120 variations to be calculated from the initial position. A machine operating at the rate of one variation per micro-second would require over 1090 years to calculate the first move!
In comparison to the Shannon Number, the number of atoms in the observable Universe, is estimated to be around 1080.

Claude E. Shannon [Bell Telephone Laboratories, Inc., Murray Hill, N.J.]
XXII. Programming a Computer for Playing Chess
Philosophical Magazine, Ser.7, Vol. 41, No. 314 - March 1950.
[Received November 8, 1949]

Chess Quote - Samuel Johnson & John Denham - Chess & Puppets

Samuel Johnson (1772):
[Painting by Joshua Reynolds]

"CHESS. n.s. A nice and abstruse game in which two sets of puppets are moved in opposition to each other." Denham
- from A Dictionary of the English Language By Samuel Johnson (link)

Dr Samuel Johnson (1709-1784) was an author and "arguably the most distinguished man of letters in English history" (Rogers, 2006). Johnson wrote the Dictionary of the English Language, which was first published in 1755. Some authorities believe that Johnson's behaviour and mannerisms were consistent with a diagnosis of Tourette syndrome.

The above chess quote appears to have been attributed to Sir John Denham, whom Johnson held in very high regard.

Sir John Denham:

Sir John Denham (1615-1669) was a poet, born in Dublin, and educated at Trinity College Oxford, initially training as a lawyer. After the Restoration, under the rule of Charles II, Denham was politically appointed in 1661 as the King's Surveyor. Sir Denham's last years were troubled with insanity, and on his death Christopher Wren (Denham's deputy) succeeded him as King's Surveyor.

A Dictionary of the English Language By Samuel Johnson - Google Books link
Rogers, Pat (2006), "Johnson, Samuel (17091784)", Oxford Dictionary of National Biography (online ed.), Oxford University Press.
Wikipedia Articles - Dr Samuel Johnson - Sir John Denham - Christopher Wren

Matthew Flinders Chess Set (1810)

Matthew Flinders Chess Set (1810):
Full size image ... here
[Courtesy State Library of NSW]

Matthew Flinders RN (1774-1814), the famous cartographer and navigator, was born in Donington, Lincolnshire, England. He joined the Royal Navy at the age of 15 years, at least partly as a result of being "induced to go to sea against the wishes of my friends from reading Robinson Crusoe". Flinders is remembered for suggesting the name of Australia, for what was then known as Terra Australias, though the name was only gradually taken up over the next 10 years after his death. As a mariner, he sailed at one time with the infamous William Bligh.

Matthew Flinders attempted to return to England in 1803, on the schooner Cumberland, but was forced to dock in French-controlled Mauritius for repairs. Unfortunately war had broken out between Britain and France (1803-1814, one of the Napoleonic Wars). The French governor of Mauritius, Charles Mathieu Isidore Decaen, detained Matthew Flinders on the island until 1810.

During his detention Flinders was taught the game of chess by a M. Chazal. The diaries of Flinders document many chess playing sessions whilst on Mauritius. Before leaving the island he was presented with a chess set (pictured above) by M. Labauve (source).

Matthew Flinders (1774-1814)