Good is dead

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Irving John "Jack" Good, who died on April 5 at the age of 92, is best known to linguists as the author of a paper on mathematical ecology. The paper is I.J. Good, "The Population Frequencies of Species and the Estimation of Population Parameters", Biometrika 40(3-4) 237-264 (1953), and its abstract reads as follows:

A random sample is drawn from a population of animals of various species. (The theory may also be applied to studies of literary vocabulary, for example.) If a particular species is represented r times in the sample of size N, then r/N is not a good estimate of the population frequency, p, when r is small. Methods are given for estimating p, assuming virtually nothing about the underlying population. The estimates are expressed in terms of smoothed values of the numbers nr (r = 1, 2, 3, …), where nr is the number of distinct species that are each represented r times in the sample. (nr may be described as `the frequency of the frequency r'.) Turing is acknowledged for the most interesting formula in this part of the work. An estimate of the proportion of the population represented by the species occurring in the sample is an immediate corollary. Estimates are made of measures of heterogeneity of the population, including Yule's 'characteristic' and Shannon's 'entropy'. Methods are then discussed that do depend on assumptions about the underlying population. It is here that most work has been done by other writers. It is pointed out that a hypothesis can give a good fit to the numbers nr but can give quite the wrong value for Yule's characteristic. An example of this is Fisher's fit to some data of Williams's on Macrolepidoptera.

In 1953, it was not yet legal to reveal that the mathematics in question had really come out of the cryptological work at Bletchley Park during WW II, where Good had collaborated with Alan Turing on decoding German Enigma messages. The method described in Good's 1953 paper, which has come to be called "Good-Turing smoothing", was used in estimating the parameters of an n-gram model, which in turn could be used to assess the probability that a given letter sequence was really a fragment of German text.

My lecture notes on Good-Turing smoothing are here: "Statistical estimation for Large Numbers of Rare Events". Needless to say, this was by no means the only work Good ever did —  his "Shorter Publications List" runs to 61 pages — but it's the work that people like me know him best for.

A memorial page at Virginia Tech, where he worked from 1967 to 1994, is here, and a news release is here: "Virginia Tech professor, WWII code-breaker Irving Good dies".

I can recommend "A conversation with I.J. Good" from Statistical Science, 11(1): 1-19, 1996. A couple of sample witticisms:

Some statistical work by Donald Michie and myself, and my insistence that what is not checked is wrong (Good's law), led to occasional success …

When discussing complex systems, like brains and other societies, it is easy to oversimplify: I call this Occam's lobotomy.

Some obituaries: "Professor Jack Good", The Telegraph, 4/10/2009; "Jack Good", "Professor Jack Good: mathematician and wartime codebreaker", The Times, 4/16/2009; The Guardian, 4/29/2009. The NYT, the Washington Post, and other major U.S. papers don't have anything yet. If this represents an editorial judgment, it's an unfortunate one; if it's due to ignorance, that's unfortunate as well.  I'll continue to hope for the most charitable interpretation, which is that they're as far behind in writing obituaries as I am in working through my to-blog list.


  1. Antony Eagle said,

    April 29, 2009 @ 1:47 pm

    I am ashamed to say I thought he must already have been dead. Good did a lot of work on the foundations of subjective probability, for which I suppose he is best known in philosophical circles, and his work was characterised by a wit unusual for the area. His 1983 collection of papers on the topic, Good Thinking (, exhibits both his sense of humour and openness to lots of areas of inquiry. It contains his celebrated result that there are 46656 varieties of Bayesian, but it also contains much else of interest. In the index he quotes M.H. Newman to the effect that one reads an index to find out what a book is about. In that spirit, some index entries include: 'Clobbering of bad Bayesians', 'Doog, as Good's alter ego' (including the sub-entry on 'Doogianism, the elevenfold and twenty-seven-fold paths of'), 'Flying saucers, surreptitious', 'Horse, existence of, 167, 168; as kicker to death, 92', 'Homo sapiens, as not entirely irrational', 'Notations, good, as readable from left to right', 'Piglings, newly born, apparent beliefs of',' Science: as based on a swamp (like a baby)', and 'White shoe: qua herring, deep pink'. (This last refers to his well-known paper on Hempel's Raven's Paradox, 'The White Shoe qua herring is pink' (BJPS 1968, doi:10.1093/bjps/axm002).) They don't really make his like any more.

  2. Mark Liberman said,

    April 29, 2009 @ 3:21 pm

    Antony Eagle: In the index he quotes M.H. Newman to the effect that one reads an index to find out what a book is about.

    The "Subject Index of the Good Thinking Bibliography" can be found here. The author introduces it this way:

    Good Thinking contains two subject indexes. One is to the bibliography (pages 251-266) and the other index is to the book itself. The present index covers only those publications listed in the bibliography (that are not republished in Good Thinking). The references in the index of Good Thinking as such are to publication numbers. Occasionally, there are other numbers in parentheses that refer to pages within the publications. There are many keywords that appear also in the index of the book itself rather than to the index of the bibliography. Items beyond #1457 are not yet indexed (as of August 24, 2002).
    A.P.Dempster, on p. 81 of the 1970 Waterloo conference proceedings (see #659), commented that an information retrieval system for my work would be helpful. The following index, combined with that for the book, should go a long way in that direction, although the bibliography is not comprehensive.

    I believe that this is a different index from the one you're quoting; but it contains (just after "Dons, as also human") entries for "Doog, K. Caj: introduced as a joint author to justify the use of 'we' in a publication", and "Doogian, all things are Doogian to a".

    Another Good quote, from his paper on Rational Decisions: "There may be occasions when it is best to behave irrationally, but whether there are should be decided rationally."

  3. Nathan Myers said,

    April 30, 2009 @ 12:17 am

    I'm partial to the quote, "A 'hard science', by definition, is one that makes use of the FFT."

  4. Charmed Reader said,

    May 2, 2009 @ 11:07 pm

    The link for lecuture notes to
    "Statistical estimation for Large Numbers of Rare Events"

    …seems to not be responding. I'm interested.

  5. Bletchely Park Slates 2009 Alan Turing Memorial Soiree said,

    May 28, 2009 @ 12:01 pm

    […] Good is dead ( […]

  6. Christian Sütterlin said,

    June 7, 2009 @ 4:57 am

    Dear sir,

    We were very sorry to learn Pr. I.J. Good passed away. We know him as a strong support of SRT and GRT (relatity theories) until he changes his mind further the major problems met since 2007 by GRT (Strings theory failure especialy).

    We would like to add his photo you have in your page in the NPA database. Is it covered by any copyright? If it is the case could we have the related authorization. NPA is a US registered non profit association of scientists all over the world.

    I belong also to Jean de Climont associates Ltd, also a non profit organization. But our database of dissident scientists includes only homepage reference and scientific data. We don't need the photo for us.

    thank you very much

    Christian Sütterlin

  7. Dr. Jochen L. Leidner said,

    November 14, 2009 @ 12:02 pm

    Isadore Jacob Gudak (alias "Good"), Alan Mathison Turing, Donald Michie (founder of the Edinburgh "Machine Intelligence Laboratory", whom I had the honor of meeting just in the week before he tragically died in a car accident), and all the other remarkable people at Bletchley Park were true heros of science and helped end the Second World War earlier.

    It was Gudak/Good who best characterized Turing's contribution to code-breaking best, namely that he made the *automation* of crypto-analysis much more efficient (the principles were uncovered by a Polish trio, who shared their results). In lay persons' imagination, code-breaking is a one-time activity, but in WW II (due to the nature of the parametric codes), it was actually a continuous, semi-industrial process.

    It is sad that many people (including computer scientists) are not familiar with most of Good's, Turing's (did you know that during's PhD thesis under Alonzo Church extended Turing machines with Oracles so as to enable them to do things that are beyond the computational power of Turing machines/type 0 Chomsky grammars?) and Michie's work.

    May they rest in peace and their contributions to computation and peace never forgotten.

  8. David Frazier said,

    November 1, 2012 @ 10:55 am

    How sad to see that this page has been sullied by a comment by a nutter from the Jean de Climont gang. Those people are not fit to comment on real science and mathematics. It is a mere trick to call crackpots 'dissident scientists', as they do. True dissidents question every detail of the foundations of science. Crackpots always concentrate on things ('free energy', 'antigravity', cancer cures) which will attract media attention …. and money from gullible investors.

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