Transcript Percy Daniell and the British Probability Tradition(s0

“But You have to Remember P. J. Daniell of
Sheffield”
or
Percy Daniell and the British Probability
Tradition(s)
John Aldrich
University of Southampton UK
Séminaire d'Histoire du Calcul des Probabilités et de
la Statistique Paris February 2nd 2007
1
David Kendall on the origins of a British
probability tradition
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But you have to remember P. J. Daniell of Sheffield.
Daniell wrote his major papers in the US in the South—I
think.
Who taught him?
Sheffield does not have a portrait.
When he went to Sheffield he apparently gave up
probability and started working on the design of blast
furnaces.
2
Aims of this talk
Mainly
 to get the basic facts about Daniell straight
and to dispel some of the mystery
but also
 to show why Daniell should be considered in
the search for a British probability tradition
 to discuss whether he belongs …
Why consider him?
In books on measure & probability
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Daniell is often the only 20th century British
mathematician to appear.
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With de Moivre and Bayes he is often the
only British mathematician to appear.
Daniell and probability
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“Major papers”
Daniell integral
1918
Daniell Kolmogorov Extension theorem 1919
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Two unnoticed papers
Order statistics
Dynamic probability
1920
1921
Time series contribution
Daniell window
1946
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Percy John Daniell (1889-1946) in his 20s?
Main activities
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Theoretical physicist
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Pure mathematician
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Control theorist
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Applied mathematician
7
Percy John Daniell (1889-1946)
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Born 9th of January 1889 in Valparaiso Chile.
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First child of William and Florence.
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Family returned to Birmingham in 1895.
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William's occupation: export merchant's
buyer.
Places: education & employment
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King Edward’s
Trinity Cambridge
Liverpool
Göttingen
Rice Institute Houston
Sheffield
1900-1907
1907-1911
1911-1912
1912-1913
1913-1923
1923-1946
King Edward’s School “one of the great
schools of England”
yt
zt can be
King Edward’s and the Cambridge
connection
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The school was very successful at getting its
pupils into Cambridge
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Once there they did very well.
“The study of Higher Mathematics in the British
Empire is now practically concentrated at Cambridge”
The Times
Trinity College: biggest and best
Mathematics Tripos Part I
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The first class students wranglers were
placed in order of their marks
Senior Wrangler, Second Wrangler, Third
Wrangler, etc.
The order was published
Students labelled for life—e.g. Keynes
forever 11th Wrangler
MT Part I: retrospectives
J. E. Littlewood (1905, Senior Wrangler)
 I wasted my time except for rare interludes.
 One had to spend two-thirds of the time practising how to solve
difficult problems against time.
 The game we were playing came easily to me and I even felt a
satisfaction of a sort in successful craftmanship.
H. Hassé (1905, 7th Wrangler)
 the great absence from the teaching—what we now know as
analysis.
 The real mathematician ... will survive the effects of any teaching
and of any syllabus.
Daniell Last Senior Wrangler
“Killing a tradition”
Switch to Physics: Part II of the Natural
Sciences Tripos
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Teachers: J J Thomson and …
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First class degree
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Rayleigh Prize “Diffraction of light for the
case of a hole in a plane of perfectly
reflecting screen.”
Assistant Lecturer in Liverpool 1911-2:
high wrangler’s rite of passage
W. H. Young (1863-1942) part-time lecturer.
Possible influence?
To the new Rice Institute as Assistant
Professor in Applied Mathematics.
Sponsor J. J. Thomson.
Rice Institute—after a few years
But first to Göttingen for a year on a
$1000 travelling fellowship from Rice
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“studied under Born and Hilbert”
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published a paper on relativity with Ludwig
Föppl (one of Hilbert’s physics PhDs)
“On the Kinematics of the Born Rigid Body”
Then to Houston
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Houston not much more than an overgrown
commercial village seventeen hundred miles
away from the American metropolis
It is hard for an Englishman to realise that the
civilisation of the whole of the area west of the
Mississippi ... is to all intents and purposes the
product of the fifty short years since the civil
war
Julian Huxley "Texas and Academe"
Main colleague
Griffith Evans (1887-1973) ass. pro. pure mathematics,
integral equations & functionals. Sponsor Volterra.
Daniell’s research at Rice
Applied maths/ theoretical physics in 1915
 The Coefficient of End-correction (out of
Rayleigh and Cambridge)
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Rotation of Elastic Bodies and the Principle of
Relativity (out of Love and Born)
And then pure mathematics…..
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1918 A General Form of Integral (Daniell
integral)
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1919 Integrals in an Infinite Number of
Dimensions (Daniell-Kolmogorov extension
theorem)
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Etc., etc. …
A General Form of Integral: wonderful
prospectus
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[Earlier theories of integration] are based on
the fundamental properties of sets of points in
a space of a finite number of dimensions. In
this paper a theory is developed which is
independent of the nature of the elements.
They may be points in a space of a
denumerable number of dimensions or
curves in general or classes of events so far
as the theory is concerned.
Integrals in an Infinite Number of
Dimensions
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No probability application envisaged
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Daniell did not follow this up…
Where did this work come from?
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Analysis—out of Young, Radon …
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Strange that Daniell did this work but not
strange that somebody did it and did it then.
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Related work by Evans and a PhD, Hubert
Bray.
Unnoticed paper I “Observations
Weighted According to Order” 1920
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“at least thirty years ahead of its time, for it took that
long for his major results to be rediscovered.”
Stigler.
the ordinary average or mean, the median, the
discard-average … can all be regarded as
calculated by a process in which the measures are
multiplied by factors which are function of order.
It is the general purpose of this paper to obtain a
formula for the mean square deviation of any such
expression. The formula may be used to measure
the relative accuracies of all such expressions.
Unnoticed paper II “Integral Products
and Probability” 1921
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In many problems arising in statistical biology and
statistical economics time enters as an
indispensable factor.
the aim of this paper is to provide a form of analysis
suitable for such problems .... The first step in the
analysis is a search for some standard formula on
which may be built a more complex and general
theory.
It is found that … a functional equation is satisfied
which is expressed in terms of a Stieltjes integral
product. ... The Stieltjes integral product itself forms
a second nucleus for our paper
Where did it go ? Norbert Wiener (1894-1964)
1919 Wiener appointed instructor at MIT.
1920-22 Wiener writes 4 papers using the Daniell
integral—3 on Brownian motion.
1922 and -28 Wiener used Daniell as a referee for jobs.
Daniell & Wiener
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They probably met at the International
Mathematical Congress in Strasbourg 1920.
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They do not refer to each other’s work in
probability
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Their work was very different in intended
application and in technique.
Being a prof in England: Daniell to Wiener 1922
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I wrote to London university my opinion of your suitability for the
position and it was partly praise and partly otherwise. That is to say I
think highly of your promise as a mathematician but—and, I
naturally expect you to disagree with me on this—I feel that you
have not yet attained as established a position & have not had as
much experience as they try to get for such a position.
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A professor in England is not merely a man of professorial rank &
ability—he is a very active & sometimes autocratic head of a
department.
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I doubt it would be good for you if your application were successful,
You would be rather loaded down with work and would most likely
get stuck in a rut.
Daniell—the 20s and return to England
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1922 Cambridge ScD
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1923 To Sheffield as Professor of
Mathematics
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Analysis research continues but with less
intensity through the 20s
Sheffield
The city being an important centre of steel, electro-plate, glass, and
other manufacturing industries, and in the heart of an extensive
coal-mining area, students of Engineering, Metallurgy, Mining, Fuel
Technology and Glass technology have exceptional opportunities.
On being a prof continued
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In 1928 Wiener applied for a chair in
Melbourne. Daniell told Wiener
It's quite time I did some work myself but a
Chair in England involves a great deal of
business which is done in America by the
office.
The 1930s
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One publication
The Theory of Flame Motion, Proceedings of
the Royal Society of London, A, 1930
Related to work for Safety in Mines Research
Board in Sheffield.
According to Stewart (obit.)
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Daniell was a prodigious reader of scientific journals and was
conversant with the latest developments in Physics, Chemistry and
Biology as well as those in most branches of pure mathematics.
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he seldom gave his undivided attention to the systematic
development of particular lines of research and therefore the actual
number of his publications does not provide a true measure of his
intellectual powers of and activity.
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Much of his time and energy was expended in advising and
assisting research workers in many fields and it was only on rare
occasions that he troubled to make a permanent record of his own
contributions to the problems involved.
Stewart continued
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Lots of university committee work
Outside interests included the training of
teachers, the Mathematical Association, and
to the School Certificate Examination.
In one of the 5 letters Daniell writes to
Mordell saying he can’t make a meeting with
Hadamard because of press of school exam
business.
Activities in the War
Teaching continued—intensified in fact.
7 classified papers
 Mainly on fire-control
 Daniell worked with Arnold Tustin and Arthur
Porter important figures in automatic control
after the war
 Daniell translated American work by Bode
and Wiener so that British engineers could
understand it.
Arnold Tustin and the describing function
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The general method is based on unpublished
work of the late Professor P. J. Daniell, who
provided an analytical treatment of the effect
of backlash of which the present paper is
essentially an interpretation in geometrical
terms.
Journal of the IEEE 1947
Porter recalled in 1965
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Daniell's subsequent contributions to servo theory,
although not widely known because his reports and
memoranda were security classified, were of high
significance.
Daniell was the first man in Europe to ‘translate’
Norbert Wiener's work on the interpolation and
extrapolation of stationary time series
Daniell's interpretations of the early Wiener papers
on control theory are refreshingly elegant and make
a noteworthy contribution to the evolution of controlsystems engineering in Britain.
Illness and death. Stewart (obit.)
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The strain of the war years became evident during
the summer of 1945 when he was attacked by
serious heart trouble.
He recovered to some extent and decided to
undertake the work of the session 1945-1946, but
there seems little doubt that his life would have been
prolonged if he had made a different decision.
He continued with his many activities in a spirit of
great fortitude and determination, but early in May,
1946, he collapsed at his home and died a few
weeks later without fully recovering consciousness.
Daniell and the British probability
tradition(s)
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The “major papers” were canonised decades
after they were written and years after his
death.
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There was, though, one immediate
canonisation, commemorated in the eponym,
the "Daniell window."
“Daniell window” RSS Symposium January
1946. Daniell’s contribution begins
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My absence from this symposium is a grief to
me.
The work done in America has been based
on a fundamental study by N. Wiener of
integrals in an infinite number of dimensions,
corresponding to the values of the fluctuating
quantity at various instants. The work is not
behind that of the Russian school in time or
importance.
Maurice Bartlett (left) introduced Daniell
into the time series tradition
Probability/measure comes to Britain and
Daniell becomes known in the 50s/60s.
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Lévy (1925) knew Wiener’s work and
through it Daniell (1918).
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Doob (1934, 1953) refers to Daniell’s
1919 paper.
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Stone developed Daniell (1918)
Daniell’s Style
Daniell did pure maths, applied maths and physics
and wrote in the existing style of those subjects.
By contrast Wiener mixed up the styles
 “I saw as my habit, a physical and even an
engineering application, and my sense of this often
determined the images I formed and the tools by
which I sought to solve my problems...”
 “Paley and I attacked the problem of the conditions
restricting the Fourier transform of a function
vanishing on the half line. This is a sound
mathematical problem on its own merits, and Paley
attacked it with vigor, but what helped me and did
not help Paley was that it is a essentially a problem
in electrical engineering.”
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Puzzles
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Why did he switch to pure mathematics in 191518?
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Why did he stop writing when he went to
Sheffield?
As a person …
Daniell married Nancy Hartshorne in 1914. They had two daughters,
Frances and Mary, and two sons, David and John.
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Daniell impressed all who came into contact with him by his great
integrity of character and his sincerity of purpose.
He disliked publicity and his tastes were simple. He delighted in good
music, in books, in friendly discussion, in country walks and in the
quiet pleasures of a happy family life.
Stewart 1947
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I have very fond memories of him. He was charming, delightful, low
key, modest.
Arthur Porter phone conversation 20th October 2006
Works by Daniell: about 50 papers (Starred items not
in Stewart’s list.)
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*P. J. Daniell (1912) "Diffraction of light for the case of a hole in a plane of perfectly reflecting screen." Rayleigh Prize Essay. P. J. Daniell (1915) The
Coefficient of End-correction I, Philosophical Magazine, 30, 137-146. P. J. Daniell (1915) The Coefficient of End-correction II, Philosophical Magazine, 30,
248-256. P. J. Daniell (1915) Rotation of Elastic Bodies and the Principle of Relativity, Philosophical Magazine, 30, 756-761. *P. J. Daniell (1917)
Translation of E. Borel's 1911 Inaugural Address "Monogenic Uniform Non-analytic Functions," Rice Institute Pamphlet, 4, No. 1, P. J. Daniell (1917) New
Rules of Quadrature, American Mathematical Monthly, 24, 109-112. P. J. Daniell (1917) The Modular Difference of Classes, Bulletin of the American
Mathematical Society, 23 446-450. P. J. Daniell (1918) A General Form of Integral, Annals of Mathematics, 19, 279-294. P. J. Daniell (1918)
Differentiation with Respect to a Function of Limited Variation, Transactions of the American Mathematical Society, 19, 353-362. P. J. Daniell (1918)
Integrals around General Boundaries, Bulletin of the American Mathematical Society, 25, 65-68. P. J. Daniell (1919) A General Form of Green's Theorem,
Bulletin of the American Mathematical Society, 25, 353-357. P. J. Daniell (1919) The Derivative of a Functional, Bulletin of the American Mathematical
Society, 25, 414-416. P. J. Daniell (1919) Integrals in an Infinite Number of Dimensions, Annals of Mathematics, 20, 281-288. P. J. Daniell (1919)
Functions of Limited Variation in an Infinite Number of Dimensions, Annals of Mathematics, 21, 30-38. *P. J. Daniell (1919) 2738: Solution to a Problem
posed by W. D. Cairns, American Mathematical Monthly, 26, 321. P. J. Daniell (1920) Further Properties of the General Integral, Annals of Mathematics,
21, 203-220. P. J. Daniell (1920) Stieltjes Derivatives, Bulletin of the American Mathematical Society, 26, 444-448. P. J. Daniell (1920) Stieltjes-Volterra
Products, Comptes Rendus du Congrès International des Mathématiciens, 22-30 Septembre 1920 / Publiés par Henry Villat . 1921 P. J. Daniell (1920)
Observations Weighted According to Order, American Journal of Mathematics, 42, 222-236. *P. J. Daniell (1921) The Integral and its Generalizations, The
Rice Institute Pamphlet, Volume Eight, No. 1. pp. 34-62. P. J. Daniell (1921) Integral Products and Probability, American Journal of Mathematics, 43, 143162. P. J. Daniell (1921) Two Generalizations of the Stieltjes Integral, Annals of Mathematics, 23, 168--182. *P. J. Daniell (1923) Review of An
Introduction to Electrodynamics by Leigh Page. 39. P. J. Daniell (1924) The Setting of a Proposition, Annals of Mathematics, 26, 65-78. P. J. Daniell
(1926) Derivatives of a General Mass, Proceedings of the London Mathematical Society, 26, 95-118. P. J. Daniell (1926) Disussion of "Theory of Mine
Ventilation," Transactions of the Institute of Mining Engineers, 71, 39-45. P. J. Daniell (1926) Orthogonal Potentials, Philosophical Magazine, 7, 247-258.
P. J. Daniell (1927) A Note on Schrödinger's Wave Mechanics, Journal of the London Mathematical Society, 2, 106-108. P. J. Daniell (1928)
Transformations of Limited Variation, Proceedings of the London Mathematical Society, 29, 537-555. P. J. Daniell (1928) Stieltjes Derivatives,
Proceedings of the London Mathematical Society, 30, 187-192. P. J. Daniell (1929) Boundary Conditions for Correlation Coeffcients, British Journal of
Psychology, 20, 190-194. P. J. Daniell (1930) The Theory of Flame Motion, Proceedings of the Royal Society of London, A, 126, 393-405. P. J. Daniell
(1940) Ratio Tests for Double Power Series, Quarterly Journal, 2, 183-192. P. J. Daniell (1940) Remainders in Quadrature and Interpolation Formulae,
Mathematical Gazete, 24, 238-244. *P. J. Daniell (1942) Analogy between the Interdependence of Phase-shift and Gain in a Network and the
Interdependence of Current and Potential Flow in a Conducting Sheet, Report in Servo Panel Library B. 39. *P. J. Daniell (1943) Interpretation and Use of
Harmonic Response Diagrams (Nyquist Diagrams) with Particular reference to Servomechanisms, Report No. 1 and pp. 1-12 of Selected Government
Research Reports Volume 5: Servomechnisms, London, Her Majesty's Stationery Office 1951. *P. J. Daniell (1944) Operational Methods for Servo
Systems, Servo Panel Report S1, July 1944 published as Report No. 2 and pp. 13-33 of Selected Government Research Reports Volume 5:
Servomechnisms, London, Her Majesty's Stationery Office 1951. *P. J. Daniell (1944) Digest of Manual on the Extrapolation, Interpolation and Smoothing
of Stationary Time Series with Engineering Applications, by Norbert Wiener, OSRD Report 370, Servo Panel Library, p. 47, circa 1944. *P. J. Daniell
(1944) Backlash in Reset Mechanisms, C. S. Memo 199, 16 March 1945. *P. J. Daniell (1944) An Explanatory Note on H. W. Bode's Paper on the
Relation between Phase-lag and Attenuation (Bell Journal 19 (1940) p. 421), C. S. Memo 201, 21 March 1945. *P. J. Daniell (1946) Contribution to
Discussion in the Symposium on Autocorrelation in Time Series, Journal of the Royal Statistical Society, Supplement, 8, 88-90. *Föppl, L. & P. J. Daniell
(1913) Zur Kinematik des Bornschen starren Körpers, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische
Klasse, 519-529.
Production
People who have helped.
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Birmingham
Cambridge
Göttingen
Rice
Sheffield
MIT
Physics
Control engineering
F. J. Daniell
Jonathan Harrison Jonathan Smith
Ulrich Krengel
Lee Hecht Lisa Moellering
Helen Mathers Matthew Zawadski
Silvia Mejia
Scott Walter Andrew Warwick
Stuart Bennett
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