# Shusaku Number

Keywords: Culture & History, Humour

# The Shusaku number

## Definition

Mathematicians brag about their Erdős 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)

# 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 Honinbo Shusai (2)

If you ever had the honour of playing against Iwamoto Sensei it is at most 4. James Kerwin, Jan van Rongen and Ronald Schlemper are in such a position. There must be many other people who have played teaching games against Iwamoto Kaoru, including myself Harry Fearnley – these would seem to count.

Honinbo Shusaku (0) — Iwasaki Kenzo (1) — Honinbo Shusai (2) — Iwamoto Kaoru (3)

Also through Go Seigen and Kitani Minoru you can reach 4. Many professionals have played these two. Examples include:

Shusaku (0) — Iwasaki Kenzo (1) — Shusai (2) — Go Seigen (3) — Takemiya (4) — Alberto Rezza (5)
Shusaku (0) — Iwasaki Kenzo (1) — Shusai (2) — Kitani Minoru (3) — Kobayashi Chizu (4) and Kobayashi-sensei lived in Vienna, Austria, for many years, teaching widely in Europe and the West.

Through Cho Hun Hyun you can reach at least 5.

Shusaku (0) — Iwasaki Kenzo (1) — Shusai (2) — Segoe (3) — Cho Hun-Hyun (4)

Of interest to KGS players, lloyd, who gives many teaching games in the Beginner's Room says he has played Miyashita Shuyo, a pupil of Shusai.

Shusaku (0) — Iwasaki Kenzo (1) — Shusai (2) — Miyashita Shuyo (3) — lloyd (4)

## Via Shuho (1)

Bob McGuigan's number is at most 4 via an unusual path in that two of the players are female:

Shusaku (0) — Shuho (1) — Kita Fumiko (2) — Shiratori Sumiko (3) — Bob McGuigan (4)

The same goes for Michael Redmond. Another one through Oscar Korschelt:

Shusaku (0) — Shuho (1) — Oscar Korschelt (2) — Bruno Rüger (3) — Christian Zak (4).

## Via Iwasaki Kenzo (1) Karigane Junichi (2) Kikuchi Yasuro (3)

Dave: Iwasaki (as Ebisawa Kenzo) played Shusaku a number of times. GoGoD lists two games between Iwasaki and Karigane Junichi played at Hoensha meetings (1900 and 1904). Karigane played many major names that reach into the modern era (Go Seigen, Kitani Minoru, Hashimoto Utaro, etc.). In addition, he played a teaching game with Kikuchi Yasuro, then amateur 4d, published in July 1952 (1952-07-00b in GoGoD). Various people who have played Kikuchi in the WAGC over the years thus will have Shusaku numbers of 4 through this path.

In my case, I was the lone non-Japanese person to send in a postcard to Go Weekly when the Ki-in recruited the local team for the goodwill match held as part of the opening festivities before the 8th WAGC in 1984. Naturally I was paired against the Japanese WAGC representative - Kikuchi. Sadly but not surprisingly I was gently but thoroughly crushed, thus missing my chance to also achieve a Winning Shusaku Number of 4! :-)

# The Shusaku-tree

The following tree summarises data from the rest of this article and perhaps elsewhere. These should be treated as maxima – there may be shorter paths in some cases:

# Notes

## Definition

• 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.

## Variants

• 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.

## Application

• 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.

### Islands

• 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).
• Tas: It is virtually certain that there is no larger groups who is not connected to the go world, and thus to Shusaku. For such a group to be disconnected, the knowledge of the game would have to have spread by text (like the pamphlet in the set under the tree at Christmas). Such groups can surely nucleate, and indeed I started as part of one, when my friend was given a go set. However they are highly unlikely to grow beyond 10 people or so before someone gets a game with an outsider and thus gives everyone in the group a Shusaku number. It is not just the pros, anyone who has played more than a the same couple of people is surely connected to Shusaku.

## Specific cases

### Another Path to Europe

• I would like to mention a path into Europe, which seems to be unknown by the most players. It is Shusaku->Kenzo->Shusai->Felix Dueball->Günther Cießow. Mr. Cießow, a former European champion who is living in Berlin now, has played a lot of people during Go evenings and events. He has learned the game from Dueball and written a book about him.

### Cho Hun-Hyun

• 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."

### Better 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.
• Shuei played Shuho providing additional "bridge" to Shusaku.

Shuei, who died 1907, may provide a better bridge than Shuwa, who died in 1873. Karigane Junichi died in 1953, late enough to have played many of today’s more senior professionals.

Shusaku (0) — Shuwa (1)
Shusaku (0) — Shuho (1) — Shuei (2) — Karigane Junichi (3) (PJT: KariganeJunichi has a number of 2 via Shusai)

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.

## Purity ranks?

bugcat:I had an idea for categorising Shusaku numbers into four different ranks of purity.

These are as follows:

(A "formal game" here is a castle game, match game, tournament game or a game in another serious event. It does not include teaching games or simuls, but does include blitz games.)

• First rank: The games are all formal, even, face-to-face and consecutive.
• Second rank: The games are all face-to-face and consecutive.
• Third rank: The (possibly online) games are all consecutive.
• Fourth rank: The games are non-consecutive.

## Shindo Hikaru

Stefan: How do deshi feel about the character Shindo Hikaru (protagonist of Hikaru No Go) 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.

Velobici: Umezawa Yukari can't have a Shusaku number of two via Shindo. She has never played a game with Shindo, much less Sai.

C.S. Graves: Using a cartoon character as a bridge? Wouldn't this be like saying you studied martial arts with Masaru Hananakajima?

## Paul Erdős and the Erdős number

[1] The practice for Erdős numbers is that Paul Erdős has uniquely the Erdős number 0. Then everybody else has Erdős number defined to be one greater than the minimum of their co-authors' Erdős numbers. As in graph theory the reflexive edges are discarded: one does not consider either the papers under Erdős' 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 Erdős 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 Erdős number of person P is the distance from P to Erdős.

Fwiffo: Both Erdős 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? Erdős 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.

## Erdős and Go

I've been told that Paul Erdős 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 Erdős Go number of 1 (played a game of go with Paul Erdős)?

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 Erdős Pal Go tournament (as of 2001). Too bad he can't make it...

enel: Unfortunately my Erdõs Go Number is 2 only (Erdős–Göndör–enel). I saw him sometimes when he played in Budapest. He has a ‘famous’ saying about Go:

May play go wrong, but must not play slow” – Erdõs played very fast.

Chad Miller: I wonder what Erdõs' ShusakuNumber was.

Paul Clarke: I don't know, but I imagine it was lower than Shusaku's Erdõs Number.

DrStraw It is at most 6 based on the fact that Charles Matthews has played both me and Erdõs (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 Erdős and also once played Go Seigen in a simul. If this is counted (which I think it should be) Erdős' Shusaku number is no more than five.

### Shusaku-Erdős number

freehold: So, who has the lowest Shusaku + Erdõs number?

What about Charles Matthews? No idea what his actual number would be but he has played Erdõs and he is a mathematician?

Howard Landman: Not sure but my Erdõs number is at most 5. I may possibly get my Erdõs number down to 2 if I ever publish a paper with Avi-ezri Fraenkel; we have related interests in combinatorial game theory. My Shusaku number is at most 5 because I've played Herb Doughty, but I've also played many pros including Abe Yoshiteru and Ishida Yoshio, so it might be lower. (Also, my Erdõs movie number is at most 5, since I was in the movie Little Fauss And Big Halsey with Robert Redford, and Erdõs was in the movie N Is A Number (about himself).)

That would also mean you have a Shusaku- Erdős-Bacon number of at most 13: 5 for Erdős, 5 for Shusaku, and 3 because you were in a movie with Robert Redford, who has a Bacon number of 2.

Jim Hlavka: I played a go game with Erdős in the mid 1970's, when he came to a conference at U. of Wisconsin. I've often wished I had instead spent the time discussing a math problem with him, I might have gotten an Erdős number of 1.