Irving J. Good
I.J. Good was born in London in 1916 and became proficient in mental arithmetic
by the age of nine. Lying in bed with diphtheria, he turned over in his mind
his sister's lesson on square roots. On his own, he realized the irrationality
of the square root of two and solved Pell's equation. The impressive feat of
reaching these conclusions as a young boy is not compromised by the fact that
they had been reached by others long before he was born.
In secondary school, Good distinguished himself in mathematics, often finishing
all the problems before the other boys had finished the first. He enjoyed mathematical
puzzles, and would decide upon an answer and then trace his way back to the
problem. In this way, Good stumbled onto the principle of mathematical induction.
Cambridge University was a shock to Good, who was accustomed to being the best
math student in the room. At 19, Good was surrounded by brilliant students.
Still, he excelled at Cambridge and obtained his PhD in mathematics in 1941,
distinguishing himself and writing a thesis on the topological concept of partial
dimension based on the ideas of Henri Lebesgue. G.H. Hardy, Fellow of the Royal
Statistical Society, advised Good on his thesis. Good also won Cambridge's Smith's
Prize for a mathematical essay by a graduate student.
In World War II, Good served the British government as a cyptanalyst in Bletchley
Park, decoding German messages in which numbers or symbols were assigned to
each letter in a pattern. Cryptanalysts looked for patterns in the messages;
they would notice repeated numbers or symbols and work from those to decipher
the message. Toward the end of the war, the encrypting was done with a machine
that would switch the code with each new letter. This prevented cryptanalysts
from solving the code by watching for repeated characters, but they could use
watch for statistical patterns and regularity.
The codes got more complicated when the cryptographers began shifting the codes
by a fixed plan, then a superfixed plan, and so on. Since the intended recipient
has to be able to crack the code, however, it was possible to find a final level
of encryption by using a hierarchical Bayes model. Max Newman, also of Cambridge,
recruited Oxford linguist Donald Michie to help develop linguistic methods of
solving the codes electronically. Good joined them, working toward the development
of the Colossus machines, which were considered the first operational, special
purpose computers, and had a direct impact on the "Fortress Europe"
invasion in 1944.
After the war, Good had a brief teaching career at the University of Manchester.
There. Good worked with Tom Kilburn and Fred Williams on the "Manchester
Mark I," considered the first computer in the world to operate from an
internal program. Good posited the idea of "Machine Building," which
may have been the same as what we now know as microprogramming. It was during
this time that he published his first book, Probability and the Weighing of
Evidence, expanding on Alan M. Turing's ideas on measuring the smallest weight
of evidence possible.
Good returned to British Intelligence in 1948 and earned an Sc.D. from Cambridge
and a D.Sc. from Oxford. He later spent several weeks consulting for IBM, followed
by three years at Admiralty Research Laboratory. Good went on to consult for the
Communications Research Division of the Institute for Defense Analysis, after
which he became the Senior Research Fellow at Trinity College, Oxford, and Atlas
Computer Laboratory. In 1967, Good moved to the United States, where he was Virginia
Polytechnic Institute's University Distinguished Professor until he retired in
An avid student of coincidence and the occurrence of numbers, Good became more
and more philosophical in the later part of his career. "I arrived in Blacksburg
in the seventh hour of the seventh day of the seventh month of the year seven
on the seventh decade, and I was put in apartment 7 of block 7
all by chance,"
Good said of his arrival in Virginia. Good turned his thoughts to the meaning
beneath the models used in mathematical statistics, which became more apparent
in his later papers and books.
Good's efforts in the war led to a lifelong interest in the theories behind
mathematical statistics. He was instrumental in implementing computer analysis
to examine numbers and possible combinations. Good was named a Fellow of the
Institute of Mathematical Statistics in 1958. In 1972, he and R.A. Gaskins won
the Virginia Academy of Science Horsely Prize for the best scientific paper
presented at that year's annual meetings. The ASA recognized Good as a Fellow
in 1973; the American Academy of Arts and Sciences followed suit in 1985. Good
was a member of the New York Academy of Sciences and an honorary member of the
International Statistical Institute.