Shusaku Number
Table of contents |
The Shusaku number
Definition
Mathematicians brag about their Erdös number[1]. Go players can brag about their Shusaku number. This is the smallest number of games that link you to Shusaku. More explicitly, it is the first number in the following list which applies to you:
0. You are Shusaku (Shusaku has number 0).
1. You have played Shusaku.
2. You have played someone who has played Shusaku.
N+1. You have played someone with Shusaku number N.
Infinity. If there is no sequence of games linking you to Shusaku, your number is infinite. (see notes)
Notes
- A sequence of games linking you to Shusaku only gives an upper bound. In order to state your exact Shusaku number, you have to show that no shorter sequence exists. The games in the databases from the early 20th century come from a limited number of books (e.g. Igo Hyakunen) plus a few published game collections such as Shusai, Go, Kitani, and Hashimoto Utaro. This limits what we can demonstrate from the readily available sources, but realize that there are huge gaps in the information.
- If you've played a few dozen games online among disparate players, your Shusaku Number is probably finite. If your Shusaku Number is finite, it's almost certainly less than 10.
- Some people have difficulty with the notion of an infinite Shusaku number and prefer to say such a person has no Shusaku number. It all boils down to definitions, inspired by preferences and the old discussion of logical elegance versus usability for a large audience.
- Any kind of game will do but obviously having played a tournament game against a professional feels more valuable than having paid for a teaching game. It would be interesting to know your Shusaku number through a series of serious games, however that may be defined.
- A refinement of the idea would be your Winning Shusaku Number: which is one greater than the least Winning Shusaku Number of all the people you've ever defeated (at an even game, say).
- Another popular discussion is whether your Shusaku number can decrease even if you stop playing, because your earlier opponents go up the ladder. The answer commonly given is yes, although you are free to construct a system taking time dependency into account.
A few well known paths to calculate your Shusaku number
There are a couple of well known branches to get your Shusaku number with reasonable likelihood.
Via Iwamoto Kaoru (3)
If you ever had the honour of playing against Iwamoto Sensei it is at most 4. Based on games in GoGod (except the last one :))
- Honinbo Shusaku (0) -- Iwasaki Kenzo (1) -- Tamura Yasuhisa (2) -- Iwamoto Kaoru (3) -- Jan van Rongen (4)
Another path for Europeans is:
- Honinbo Shusaku (0) -- Iwasaki Kenzo (1) -- Tamura Yasuhisa (2) -- Iwamoto Kaoru (3) -- Ronald Schlemper (4)
- Shusaku (0) -- Iwasaki Kenzo (1) -- Shusai (2) -- Go Seigen (3) -- Takemiya (4) -- Alberto Rezza (5)
Via Kita Fumiko (2)
- Bob McGuigan: My number is at most 4 via an unusual path in that two of the players are female: Bob--Shiratori Sumiko--Kita Fumiko--Shuho--Shusaku.
- Anyone who has played the user "breakfast" on KGS has a Shusaku Number of 6: Honinbo Shusaku - Shuho - Kita Fumiko - Shiratori Sumiko - Michael Redmond - Alexandre Dinerchtein
Via James Kerwin
Evand: I'd be interested in knowing James Kerwin's Shusaku number. Is it low enough to provide a useful bridge? If someone with a database could look into it, I'd find it interesting. Thanks.
BobMcGuigan: Kerwin was a student of Iwamoto (see above) so he probably played at least one game with him.
Velobici: James Kerwin has a Shusaku number that is not greater than 4: Shusaku - Iwasaki Kenzo - Honinbo Shusai - Iwamoto Kaoru - James Kerwin.
FFLaguna: DrStraw has a Shuusaku number of 4 and a Go Seigen number of 2! Convo him for a game, or some such! ^.^
Via Cho Hun-Hyun
- Shusaku (0) -- Iwasaki Kenzo (1) -- Shusai (2) -- Segoe (3) -- Cho Hun-Hyun (4) -- Kim Jung-Jin (5) -- Usagi (6)
Does Cho Hun-Hyun have a Shusaku Number of 3? According to Jan van Rongen: "Segoe moved to Tokyo when he was 20 (1908) where he was promoted to 2 dan in the end of that year. So he might have played against Iwasaki or Shugen. Which would give all his pupils Shusaku number (3), including Cho Hun-hyeon. But again -- we need the game records to be sure."
senbazuru@DGS: Cho played several simul games at the European Go Congress 1979 in Germany, including one with me, which means my Shusaku Number is 5.
More remarks
Other bridges
- Dave Sigaty: There are probably better bridges than "Shusai --> XX". Iwasaki Kenzo died in 1913, Shuei died in 1907, Shugen died in 1917. Although they were too young to play any official games both Shuei and Shugen were sons of Shuwa and most likely knew Shusaku. There is an excellent chance that they played him as children. People like Segoe (d. 1972), Iwamoto (d. 1999), Hayashi Yutaro (d. 1983) directly spanned the gap between the beginning of the century and modern times.
- Bob McGuigan: It's interesting to speculate on who wouldn't have a Shusaku number. I'm sure there are such people. For example two people who "found" go in a game shop, bought a set, learned the rules from the enclosed pamphlet, and have only played each other. On the other hand, anyone who's ever played anyone who has ever played ...(iterate ad libitum) ... anyone who has ever played any pro, even in a simultaneous game, would have a Shusaku number (I'm sure the pros are all connected to Shusaku).
Thomas : I calculated by Shusaku number only through won, even and official games. It was a quite hard research, but I found the most ressourceful player who beat Shusaku was Murase Shuho (source : gobase). I calculated mine, which is astonishingly low (9) instead of 6 as normal Shusaku number :
0 Shusaku Honinbo
1 Murase Shuho(JP, B) vs. Shusaku Honinbo(JP, W) 1861-12-08 ; Black won by resignation
2 Honinbo Shuei (JP, B) vs. Murase Shuho (JP, W) 1885-03-05 ; Black won by 3 points
3 Honinbo Shusai (JP, B) vs. Honinbo Shuei (JP, W) 1903-08-16 ; Black won by resignation
4 Kitani Minoru (JP, B) vs. Honinbo Shusai (JP, W) 1938-06-26 ; Black won by 5 points
5 Otake Hideo (JP, B) vs. Kitani Minoru (JP, W) 1960-10 ; Black won by 16 points
6 Rui Naiwei (CHN, W) vs. Otake Hideo (JP, B) 1992-11-25 ; White won by resignation
7 Guo Juan (CHN, B) vs. Rui Naiwei (CHN, W) 1985-05-02 ; Black won by resignation
8 Groenen Geert (NL, W) vs. Guo Juan (CHN, B) 2003-05-31 ; White won
9 Debarre Thomas (FR, W) vs. Groenen Geert (NL, B) 2006-05-27 ; White won by 1,5 points
Note : some players are known as in different names (i.e. Murase Shuho is also known as Honinbo Shuho or Murase Yakichi, Honinbo Shuei as Hayashi Shuei, Shusai with Honinbo or Meijin or as Tamura Hoju...)
Shuei played Shuho providing additional "bridge" to Shusaku. Shuei, who died 1907, may provide a better bridge than Shuwa, who died in 1873. KariganeJunichi died in 1953, late enough to have played many of todays more senior professionals.
The earliest opponents recorded on http://www.GoBase.org
for Hayashi Yutaro (3) are Shusai, Kitani Minoru and Go Seigen. So, Hayashi Yutaro may not be a better 'bridge' to Shusaku.
Iwamoto's (3) connection to Shusaku suffers the same problem
per http://www.GoBase.org. Iwamoto (3) connects via Shusai, Kitani Minoru and Go Seigen as well.
Jan van Rongen: I tried the other connections too, but they all run into some problems. Of course there is the formal problem of the availability of a game record. On the other hand Iwamoto is very unlikely to have a lower Shusaku number. He did not arrive in Japan until 1911 and reached Sho-dan in 1917. Segoe moved to Tokyo when he was 20 (1908) where he was promoted to 2 dan in the end of that year. So he might have played against Iwasaki or Shugen. Which would give all his pupils Shusaku number (3), including Cho Hun-hyeon. But again -- we need the game records to be sure.
revo: Does anyone know the Shusaku number of Cho-Seok Bin 7d? My Bin number is 2, and since Bin was insei this could be my shortest connection to Shusaku.
Shindo Hikaru
Stefan: How do deshi feel about Shindo Hikaru as a bridge? He has played Shusaku's Go engine on multiple occasion, and therefore carries a 1. The problem probably is to find a game between Shindo and somebody with us here in meatspace.
BlueWyvern: How would you define meatspace? (BTW, Maybe Umezawa Yukari has a Shusaku # of 2)
Jared: Meatspace is a term from Gibson's novel Neuromancer, and refers to real life, the opposite of cyberspace.
C.S. Graves: Using a cartoon character as a bridge? Wouldn't this be like saying you studied martial arts with Masaru Hananakajima?
Anonymous: Oh, so are you saying Sexy Commando doesn't work?
Velobici: Umezawa Yukari can't have a Shusaku number of two via Shindo. She has never played a game with Shindo, much less Sai.
About Paul Erdös and the Erdös number
[1] The practice for Erdös numbers is that Paul Erdös has uniquely the Erdös number 0. Then everybody else has Erdös number defined to be one greater than the minimum of their co-authors' Erdös numbers. As in graph theory the reflexive edges are discarded: one does not consider either the papers under Erdös' single authorship or, analogously, Shusaku's solitaire games.
Sandy Harris A fairly serious page on the Erdos number is http://www.oakland.edu/enp/.
MrMoto: To clarify the mechanics of the Erdös number:
Let G be a graph with vertices labeled by people. Vertices P and Q are adjacent if and only if P and Q have co-authored a paper. Then the Erdös number of person P is the distance from P to Erdös.
Fwiffo: Both Erdös numbers and Bacon numbers are based on the work of
Stanley Milgram which inspired the book and movie "Six Degrees of Separation".
Rafael Caetano: Really? Erdös and many of his colleagues studied graph theory. It would be surprising if they had to see Milgram's work to come up with the idea of a collaboration graph.
ilan: The co-author graph is actually a hypergraph. In fact, you can take the general co-authors + papers situation as a definition of hypergraph. The "six degrees of separation" hypothesis alluded to above is that any two people in the world can be linked by a chain of 6 people where any two consecutive members of the chain have met each other. Mathematically, I believe that this can be interpreted as follows: the diameter of a random hypergraph is of the order of the logarithm of the number of vertices.
Anonymous: It's only a hypergraph if you choose to define it as such. There's nothing wrong with defining it as a graph.
About Erdös and Go
I've been told that Paul Erdös enjoyed playing go -- in fact, that it was his only hobby aside from visiting other mathematicians. Can anyone corroborate this? Any idea how strong a player he was? Do we have any readers with a Erdös Go number of 1 (played a game of go with Paul Erdös)?
Charles Matthews: Yes, I played him twice. The first time was probably around 1975. He was around 2 kyu then. I played him a few years later, and he was perhaps a little stronger; but given his habits that might not be significant. There is even a photo I've seen of him playing, in an AMS publication - sadly he was in Hane at the head of three stones bad shape there.
Matt Noonan: In Budapest there is an annual Erdös Pal Go tournament (as of 2001). Too bad he can't make it...
enel: Unfortunately my Erdős Go Number is 2 only (Erdős-Göndör-enel). I saw him sometimes while he playing in Budapest. He has a "famous" saying related to the go game.
"May play go wrong, but must not play slow". Erdős played very quickly.
Chad Miller: I wonder what Erdős' ShusakuNumber was.
- Paul Clarke: I don't know, but I imagine it was lower than Shusaku's Erdős Number.
- DrStraw It is at most 6 based on the fact that Charles Matthews has played both me and Erdős (mine is 4). If Charles ever played Iwamoto then it would be at most 5.
functor: I know that Herb Doughty, who plays at the Berkeley go club, played Erdös and also once played Go Seigen in a simul. If this is counted (which I think it should be) Erdös' Shusaku number is no more than five.
Thomas : I have a Shusaku number of 6 through a fairly unusual path Shusaku - Iwazaki Kenzo - Shusai - Go Seigen - Takemiya - Alexis Welvaert - Thomas Debarre. Alexis is a friend of mine who has gone to Japan with me and has played Takemiya sensei. Perhaps I am another path for European players ? Boris: i Have a shusaku number of 5 Paul Anserson-Go Seigen-Shusai-Kenzo-Shusaku I am O on KGS .