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Subject: John Nash apparently did not independently invent Hex rss

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David Bush
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https://boardgamegeek.com/blogpost/59630?commentid=6742048#c...

If true, the description on the Hex page should be edited. I have not done this yet because, without more solid references to back me up, such action would likely generate lots of controversy. So, I'm waiting for Cameron to get back to me with more details. If you, dear reader, happen to know more about this, or can afford to access the ICGA journal, 38:2, pp.126-7, any verifiable detail would be appreciated.
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Rex Moore
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I don't think there would be a problem making note of this in the description where it mentions Nash independently discovering it.
 
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Rex Moore
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And while we're at it, how do you feel about "REIMPLEMENTED BY: THE GAME OF Y"?

I guess I'm not quite sure what that's supposed to mean, but to me it implies some sort of new version or superior version to an original. It would be like the chess entry saying "reimplemented by [my own bad chess variant]."

So I'd vote to remove that.

<Later> Ah... I just looked, and chess is "REIMPLEMENTED BY: 3 MAN CHESS + 10 MORE."

So this is a thing.
 
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Jason Breti
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"Hex was first invented by Danish mathematician Piet Hein. The first published description of the game can be found by Hein in the December 26, 1942 edition of the Danish newspaper Politiken, in which he describes a game called Polygon. The 11x11 hexagonal board and the rules described by Hein are identical to those of Hex today.

The game was also invented independently by American mathematician John Nash in 1948 while he was a graduate student at the Princeton mathematics department [Nasar 1994]. This version of the game was named Nash in his honor, and sometimes called John due to the tendency of students to play it on hexagonal bathroom tiles. Thus Hex can boast an exceptional pedigree -- its inventors are among the most acclaimed mathematicians of this century."

Browne, Cameron, "Hex Strategy: Making the Right Connections", A.K. Peters, 2000, ISBN 1-56881-117-9, pg 3

Ref: Nasar, S. (1994) "The Lost Years of a Nobel Laureate", New York Times, November 13th.

"Piet Hein invented this game [Hex] in 1942. It was reinvented by Nash in 1948. People say that he had the idea while contemplating the hexagonal tiling in the men's room of the Princeton mathematics department. There were indeed hexagonal tiles there, but Nash tells me that he doesn't recall finding them at all inspiring."

Binmore, Ken, "Game Theory: A Very Short Introduction", Oxford University Press, 2007, ISBN 978-0-19-921846-2, pg 39
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Rex Moore
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jayzen wrote:
"Hex was first invented by Danish mathematician Piet Hein. The first published description of the game can be found by Hein in the December 26, 1942 edition of the Danish newspaper Politiken, in which he describes a game called Polygon. The 11x11 hexagonal board and the rules described by Hein are identical to those of Hex today.

The game was also invented independently by American mathematician John Nash in 1948 while he was a graduate student at the Princeton mathematics department [Nasar 1994]. This version of the game was named Nash in his honor, and sometimes called John due to the tendency of students to play it on hexagonal bathroom tiles. Thus Hex can boast an exceptional pedigree -- its inventors are among the most acclaimed mathematicians of this century."

Browne, Cameron, "Hex Strategy: Making the Right Connections", A.K. Peters, 2000, ISBN 1-56881-117-9, pg 3

Ref: Nasar, S. (1994) "The Lost Years of a Nobel Laureate", New York Times, November 13th.

"Piet Hein invented this game [Hex] in 1942. It was reinvented by Nash in 1948. People say that he had the idea while contemplating the hexagonal tiling in the men's room of the Princeton mathematics department. There were indeed hexagonal tiles there, but Nash tells me that he doesn't recall finding them at all inspiring."

Binmore, Ken, "Game Theory: A Very Short Introduction", Oxford University Press, 2007, ISBN 978-0-19-921846-2, pg 39


This is the information that's now in dispute. See the thread linked in the original post.
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Nathan James
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If there is any doubt, simply changing the description to "may also have been independently invented" should suffice.
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Jason Breti
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orangeblood wrote:
This is the information that's now in dispute. See the thread linked in the original post.


I understand. I was providing samples of the current sources, since I haven't seen anyone quoting them, just talking about them. Cameron, the author of both "Connection Games" and "Hex Strategy" is discussing in the other thread, but I didn't put it there because that thread covers people asking Cameron to consider adding new connection games to a requested second edition of the book. (A fine book "Connection Games", BTW.)

I forgot to write that in though. Thanks for pointing it out.
 
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Dr Caligari
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twixter wrote:
....access the ICGA journal, 38:2, pp.126-7...


Just curious: what is in the ICGA journal that will clear this up?

Also: we may have better chances at getting the journal by posting the question to a wider audience, say the Abstract Games forum here on BGG.
 
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David Bush
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jayzen wrote:
"Hex was first invented by Danish mathematician Piet Hein. The first published description of the game can be found by Hein in the December 26, 1942 edition of the Danish newspaper Politiken, in which he describes a game called Polygon. The 11x11 hexagonal board and the rules described by Hein are identical to those of Hex today."

There's some dispute about that as well, inasmuch as no evidence is shown that Hein included the pie rule.
andre_sand wrote:
twixter wrote:
....access the ICGA journal, 38:2, pp.126-7...


Just curious: what is in the ICGA journal that will clear this up?

In the original link, Mr. Browne makes a further comment:

"I didn't read about it, I heard it from a colleague who had researched some of Hein's original correspondence. He hasn't released the full story yet, although the incident has been alluded to in the ICGA journal, 38:2, pp.126-7."

So it seems likely we will have to wait for this colleague to publish about it before we have a reference for Wikipedia.
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Russ Williams
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2017-01-12 Ingo Althöfer commented in the littlegolem thread

https://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&to...

kindly giving a link to a post in another forum (at dgob.de) with scans of the text from ICGA journal, 38:2, pp.126-7.

http://www.dgob.de/yabbse/index.php?topic=6053.msg208773#msg...

The 2 key scans seem to be the last 2 of the 4:
http://www.dgob.de/yabbse/index.php?PHPSESSID=9b1r2ika3b37qj...;topic=6053.0;attach=5607;image
http://www.dgob.de/yabbse/index.php?PHPSESSID=9b1r2ika3b37qj...;topic=6053.0;attach=5609;image

that part of Ingo Althöfer's Obituary of John Nash wrote:
It is difficult to investigate a priority question after about 70 years, especially when the main characters - Piet Hein and John Nash - are no longer alive. Ryan Hayward allowed me to cite his assessment of the origins of Hex.

"It is not clear whether Nash invented the game independently, or whether he first learned of the game from someone from Denmark. In any event, he described the game to David Gale, probably in the later winter 1949, and mentioned that he could prove that the first player wins. Gale thought the game would be interesting to play, built a board, and left it in the common room of Fine Hall, where Princeton math people often gathered to play games. The game became popular among that crowd. Eventually Martin Gardner heard about the game, and wrote about it in Scientific American.

"By the way, when Gardner was writing his first column on Hex, he was corresponding with Piet Hein... it is clear that Hein was aware of the strategy-stealing proof that there is no draw in Hex, but of course he did not publish anything on this, so Nash is credited with the result." (Sources mentioned by Ryan Hayward are: A Beautiful Mind (Nasar), Gardner's columns, and Gardner and Hein correspondence.)


(FWIW: To me, that text does not really do much for proving or disproving whether Nash independently invented Hex.)
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Jason Breti
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I have contacted Dr. Hayward and asked him if he has any further details.

If he has a chance to respond to me I will attach it to this thread.
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Jason Breti
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Hello Everyone,

Dr. Hayward has kindly responded to me. He writes:

Quote:
yes, it's not clear that Nash's invention of Hex was independent of Hein's. there is evidence for and against.

I hope to have a book on hex finished in about a year (I have a sabbatical that starts in July, when I can work fulltime on finishing the manuscript).


So it appears his forthcoming book may shed some more light on the subject.
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Todd Neller
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I saw your query at:
https://en.wikipedia.org/wiki/Talk:Hex_(board_game)#John_Nash_apparently_did_not_independently_invent_Hex

Here's what I've added to that discussion:

Here are two relevant Martin Gardner Sci Am sources:

Martin Gardner's article first popularizing Hex:
Gardner, Martin 1957. "Mathematical Games" Scientific American 197, no.1, July 1957, pp. 145-146, 148, 150. Accessed September 25, 2017.

In this first article, Piet Hein is credited as the inventor, having presented it at the Neils Bohr institute in 1942. Neils Bohr's son, Aage, then introduced the game at the Institute for Advanced Study in Princeton in 1949. The game was said to be called "John" by Princeton students because it was played on hexagonal tiles on bathroom floors. However, later the same year, Gardner writes of John Nash's independent invention of the game in 1948.

Later issue mention of John Nash's independent invention:
Gardner, Martin 1957. "Mathematical Games" Scientific American 197, no.4, October 1957, pp. 138 Accessed September 25, 2017.

So there are two possible lines of interpretation as I see it: (1) Piet Hein presented it at the Neils Bohr Institute (while Neils Bohr still lived), then through the Institute or from his father Neils, Aage learned the game and communicated it to Princeton where it then was learned of and analyzed by John Nash. (2) John Nash independently devised the game, given his interest in Go and the hexagonal tiles on Princeton bathroom floors. The date of Nash's reported invention seems so close to Aage's propagation of the game to Princeton that it would seem that Piet Hein is likely the sole inventor. I would be interested in which sources support Nash's independent invention given the Piet Hein -> Neils Bohr Institute -> Neils Bohr -> Aage Bohr -> Princeton Institute for Advanced Study connection that would also explain Hex's popularity in Princeton in the late 1940s. The Wikipedia article on Aage Bohr notes that "In early 1948, Bohr became a member of the Institute for Advanced Study in Princeton, New Jersey.", i.e. Aage arrived on the scene at Princeton early in the year Nash is said to have independently invented Hex.

Unless we can find solid evidence of Nash's independent invention, all other evidence points to Piet Hein as the sole independent inventor.

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