“The most important
questions of life are indeed,
for the most part, really
only problems of
probability.”
X
Pierre Simon Laplace
Théorie Analytique des Probabilités, 1812
“The theory of probability as a
mathematical discipline can and
should be developed from axioms in
exactly the same way as geometry
and algebra.”
Andrei Kolmogorov
Foundations of the Theory of Probability,
1933
“I think you’re begging the question,’’ said
Haydock, “and I can see looming ahead one of
those terrible exercises in probability where
six men have white hats and six men have
black hats and you have to work it out by
mathematics how likely it is that the hats will
get mixed up and in what proportion. If you
start thinking about things like that, you would
go round the bend. Let me assure you of that!”
Agatha Christie
The Mirror Crack’d
“There is no problem in
all mathematics that
cannot be solved by
direct counting.”
Ernest Mach
I’m very well acquainted too
with matters mathematical,
I understand equations, both the
simple and quadratical.
About binomial theorem I’m teeming
with a lot o’ news,
With many cheerful facts about the
square of the hypoteneuse.
Gilbert and Sullivan,
Pirates of Penzance
“Suam habet
fortuna rationem.”
(Chance has its reasons.)
Petronius (First century, A.D.)
“The conception of chance enters into the
very first steps of scientific activity in
virtue of the fact that no observation is
absolutely correct. I think chance is a
more fundamental conception than
causality; for whether in a concrete case,
a cause-effect relation holds or not can
only be judged by applying the laws of
chance to the observation.”
Max Born, 1882-1970
“Iacta alea est.”
(The die is cast.)
Julius Caesar,
Upon crossing the Rubicon
49 B.C.E
“How many really basic mathematical objects are there? One
is surely the ‘miraculous jar’ of the positive integers 1, 2, 3, . .
Another is the concept of a fair coin. Though gambling was
rife in the ancient world and although prominent Greeks and
Romans sacrificed to Tyche, the goddess of luck, her coin did
not arrive on the mathematical scene until the Renaissance.
Perhaps one of the things that had delayed this was a
metaphysical position which held that God speaks to humans
through the action of chance. . . . The modern theory begins
with the expulsion of Tyche from the Pantheon. There
emerges the vision of the fair coin, the biased coin. This coin
exists in some mental universe and all modern writers on
probability theory have access to it. They toss it regularly and
they speculate about what they ‘observe.’”
Philip Davis and Reuben Hersh,
The Mathematical Experience
“It is remarkable that a
science which began with the
consideration of games of
chance should have become
the most important object of
human knowledge.”
X
Pierre Simon Laplace
Théorie Analytique des Probabilités, 1812
“The odds? A dissertation may be needed in the
mathematical journals, but it seems the odds may be
1 in 10 million (from a U. of Rochester math
professor), to 1 in 1,890 trillion (according to a
Harvard math professor), to 1 in 8.7 million
(according to the National Hole-in-One Foundation
of Dallas), to 1 in 332,000 according to Golf Digest
Calculator, who added that, statistically, this will not
happen again in 190 years.”
Boston Globe, 1989, reporting on the U.S. Open when 4
golfers, all using 7 irons,
scored holes-in-one on the 6th hole of the course,
in less than two hours
“Coincidences, in general, are great
stumbling blocks in the way of that class
of thinkers who have been educated to
know nothing of the theory of
probabilities---that theory to which the
most glorious objects of human research
are indebted for the most glorious of
illustrations.”
Edgar Allen Poe
The Murders in the Rue Morgue
“A striking example was the number of
soldiers killed by horse kicks per year per
Prussian army corps. Fourteen corps were
examined, each for 20 years. For over half the
corps-year combinations there were no deaths
from horse kicks; for the other combinations
the number of deaths ranged up to four.
Presumably the risk of lethal horse kicks
varied over years and corps, yet the overall
distribution was remarkably well fitted by a
Poisson distribution.”
International Encyclopedia of the Social Sciences entry for
Ladislaus Josephowitsch Bortkiewicz,
The Law of Small Numbers, 1898
“Misunderstanding of
probability may be the
greatest of all
impediments to
scientific literacy.”
Stephen Jay Gould
“There are two times in
a man’s life when he
should not speculate;
when he can’t afford it,
and when he can.”
Mark Twain
Hugh: I'll get the dictionary.
Lisa: Why?
Hugh: You'll see when you get there: the
word ‘stochastic’.
Lisa: “Pertaining to a process involving a
randomly-determined sequence of
observations.”
(Laughs. They look at each other, then
embrace passionately.)
The Simpsons
Lisa's Wedding
“The ‘Law of Frequency Of Error’ . . .
reigns with serenity and in complete selfeffacement amidst the wildest confusion.
The huger the mob . . . the more perfect
is its sway. It is the supreme law of
Unreason. Whenever a large sample of
chaotic elements are taken in hand
. . . an unsuspected and most beautiful
form of regularity proves to have been
latent all along.”
Francis Galton
“The world of science lives fairly comfortably
with paradox. We know that light is a wave,
and also that light is a particle. The discoveries
made in the infinitely small world of particle
physics indicate randomness and chance, and I
do not find it any more difficult to live with
the paradox of a universe of randomness and
chance and a universe of pattern and purpose
than I do with light as a wave and light as a
particle. Living with contradiction is nothing
new to the human being.”
Madeline L'Engle (author of A Wrinkle in Time)
“Steinhaus, with his predilection for
metaphors, used to quote a Polish
proverb, ‘Forturny kolem sie tocza’
[Luck runs in circles], to explain why π,
so intimately connected with circles,
keeps cropping up in probability theory
and statistics, the two disciplines which
deal with randomness and luck.”
Mark Kac, Enigmas of Chance
“The record of a month’s
roulette playing at Monte
Carlo can afford us
material for discussing
the foundations of
knowledge.”
Karl Pearson
“Probability does pervade the universe, and in this
sense, the old chestnut about baseball imitating life
really has validity. The statistics of streaks and
slumps, properly understood, do teach an important
lesson about epistemology, and life in general. The
history of a species, or any natural phenomenon, that
requires unbroken continuity in a world of trouble,
works like a batting streak. All are games of a
gambler playing with a limited stake against a house
with infinite resources. The gambler must eventually
go bust. His aim can only be to stick around as long
as possible, to have some fun while he’s at it, and, if
he happens to be a moral agent as well, to worry
about staying the course with honor!”
Stephen Jay Gould
“It is difficult to understand why
statisticians commonly limit their
inquiries to Averages, and do not revel in
more comprehensive views. Their souls
seem as dull to the charm of variety as
that of the native of one of our flat
English counties, whose retrospect of
Switzerland was that, if its mountains
could be thrown into its lakes, two
nuisances would be got rid of at once.”
Sir Francis Galton
“Ideal Toy Company stated on the
package of the original Rubik's cube
that there were more than 3 billion
possible states the cube could attain.
This is analogous to McDonald's
announcing that they've sold more
than 120 hamburgers.”
John Allen Paulos, Innumeracy
“I dreamt that I was in Hell, and that
Hell is a place full of all those
happenings that are improbable but not
impossible . . . There is a special
department of Hell for students of
probability. In this department there are
many typewriters and many monkeys.
Every time that a monkey walks on a
typewriter, it types by chance one of
Shakespeare’s sonnets.”
Andre Bumblowski’s nightmare
as related to Bertrand Russell
“Therefore, this is the problem
which I now set forth and make
known after I have pondered over it
for 20 years. Both its novelty and its
very great usefulness, coupled with
its just as great difficulty, can exceed
in weight and value all the remaining
chapters of this thesis.”
Jacob D. Bernoulli, Ars Conjectandi
(concerning the Law of Large Numbers)
Dilbert writes a poem and presents it to
Dogbert:
Dogbert: I once read that given infinite
time, a thousand monkeys with typewriters
would eventually write the complete works of
Shakespeare.
Dilbert: But what about my poem?
Dogbert: Three monkeys, ten minutes.
Scott Adams,
Dilbert comic stripe, May 15, 1989