STATISTICS
“Statistical thinking will be as necessary for efficient citizenship as the ability to read and write.” — H.G. Wells
“Statistics is the grammar of science.” — Karl Pearson
“Then there is the man who drowned crossing a stream with an average depth of six inches.” — W.I.E. Gates
“Do not put your faith in what statistics say until you have carefully considered what they do not say.” — William W. Wyatt
“An approximate answer to the right question is worth far more than a precise answer to the wrong one.” — John Tukey
“All models are wrong, but some are useful.” — G.E.P. Box
“There are three kinds of lies: lies, damned lies and statistics.” — British Prime Minister Benjamin Disraeli (1804-1881)
“I am one of the unpraised, unrewarded millions without whom Statistics would be a bankrupt science. It is we who are born, who marry, who die, in constant ratio.” — Logan Pearsall Smith
Life is a school of probability. -Walter Bagehot Quoted in J.R. Newman (ed.) The World of Mathematics, Simon and Schuster, New York, 1956, p. 1360.
It has been pointed out already that no knowledge of probabilities, less in degree than certainty, helps us to know what conclusions are true, and that there is no direct relation between truth of a proposition and its probability. Probability begins and ends with probability.
-John Maynard Keynes The Application of Probability to Conduct
The excitement that a gambler feels when making a bet is equal to the amount he might win times the probability of winning it.
-Blaise Pascal In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988
He who has heard the same thing told by 12,000 eye-witnesses has only 12,000 probabilities, which are equal to one strong probability, which is far from certain. -Voltaire In J.R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
“Figures won’t lie, but liars will figure.” — Charles H. Grosvenor
“There’s little doubt that the Government figures are honest. The problem is that the things the numbers are supposed to measure cannot be determined with precision. Furthermore, the problem is compounded when the figures are reported to the public. Unless one is aware of the pitfalls — and few people are– the statistics can become extremely misleading.” — T.F. O’Leary, Jr.
“Statisticians … are much like lawyers. They do not need to remember every technique exactly, but must know where to locate it when needed and be able to understand it once found.” — S.R. Searle
“(Statistics is) the most important science in the whole world, for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, for only it gives exact results of our experience….to understand Gd’s thoughts, we must study statistics, for these are the measure of his purpose.” — Florence Nightingale
“It no longer suffices to know how things are constituted: we need to seek how things should be constituted so that this world of ours may present less suffering and destitution.” — 19th-century French statistician Eugene Buret
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EDUCATION
“I hear and I forget. I see and I remember. I do and I understand.” — Chinese Proverb (Confucius?)
“Those who can, do. Those who understand, teach.” — Lee Shulman
“The man who doesn’t read good books has no advantage over the man who can’t read them.” — Mark Twain
“The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.”
— William Arthur Ward
“If I had a child who wanted to be a teacher, I would bid him Godspeed as if he were going to a war. For indeed the war against prejudice, greed and ignorance is eternal, and those who dedicate themselves to it give their lives no less because they may live to see some fraction of the battle won.”
— James Hilton
“Educators have always known that learning and life are maximal where play and work coincide.” — L.W. Gibbs
“The pupil who is never required to do what he cannot do, never does what he can do.” — John Stuart Mill
“He is educated who knows how to find out what he doesn’t know.” — German philosopher George Simmel
“You can get help from teachers, but you are going to have to learn a lot by by yourself, sitting alone in a room.” — Theodore Geisel (Dr. Seuss)
“Spoon feeding in the long run teaches us nothing but the shape of the spoon.” — E. M. Forster
“The chief object of education is not to learn things but to unlearn things.” — G. K. Chesterton
“To teach is to learn twice.” — Joseph Joubert
“Who dares to teach must never cease to learn.” — John Cotton Dana
“Education is not the filling of a pail, but the lighting of a fire.” — William Butler Yeats
“A teacher affects eternity; he can never tell where his influence stops.” — Henry Brooks Adams
“Everyone who remembers his own educational experience remembers teachers, not methods or techniques. The teacher… makes or breaks the program.” — Sidney Hook
“Teaching is not a lost art, but the regard for it is a lost tradition.” — Jacques Barzun
“Teachers are expected to reach unattainable goals with inadequate tools. The miracle is that at times they accomplish this impossible task.” — Haim G. Ginott
“Most teachers have little control over school policy or curriculum or choice of texts or special placement of students, but most have a great deal of autonomy inside their classroom. To a degree shared by only a few other occupations, such as police work, public education rests precariously on the skill and virtue of the people at the bottom of the institutional pyramid.” — Tracy Kidder
“What is training? Training is preparing oneself to be able to do what one can’t count on having to do. In a football game, training is the thing that keeps one’s muscle from giving when the unexpected strain is applied, which means that little extra bit of wind when everyone’s wind is gone. Training of the mind is that which enables one to handle not the problem that we have been over — most of us can do that — but the problem we have never met before. Training of the heart is that kind of conditioning that makes one steady when he is sick in fear, or bewildered by strangeness, or hurt and bruised in the mind.” — Frank Ashburn, as quoted by Steve Forbes
“Who is wise? [One] who learns from all [people].” — Ben Zoma, Chapters of the Fathers
“Much have I learned from my teachers, more from my colleagues, but most from my students.” — R. Hanina (Talmud: Taanit, 7a)
“Through an act of tzimtzum [contraction], the teacher allows the child to be actively engaged and to learn by doing (na’aseh v’nishma). Through that same act, the teacher acknowledges that children are now and will more fully become images of Gd (tzelem clohim), each in his/her own unique way (ein domeh l’haverio).”
— R. Elana Kanter
“Before going in to teach, R. Nehunia ben Kana would say: May it be Your will, my Gd, that no misunderstanding or confusion arise through my teachings. May my colleagues and students value my learning; and may I value theirs.” — Talmud (Berakhot 28b)
MATH-AND-MUSIC
“Music is the pleasure the human soul experiences from counting without being aware that it is counting.” — German mathematician and philosopher Gottfried Wilhelm von Leibniz (1646-1716) who co-discovered calculus
“Mathematics and music, the most sharply contrasted fields of scientific activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind, and which leads us to surmise that the manifestations of the artist’s genius are but the unconscious expressions of a mysteriously acting rationality.” –19th century German physician and physicist Hermann von Helmholtz, Vorträgeund Reden, Bd. 1 (Braunschweig, 1884), p. 82
“May not music be described as mathematics of the sense, mathematics as music of the reason?” –19th century English mathematician James Joseph Sylvester, On Newton’s Rule for the Discovery of Imaginary Roots; Collected Mathematical Papers, Vol. 2, p. 419
“If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.” – Spanish philosopher/writer George Santayana (1863-1952)
“Musical training is a more potent instrument than any other, because rhythm and harmony find their way into the inward places of soul, on which they mightily fasten, imparting grace, and making the soul of him who is rightly educated graceful…” — classical Greek philosopher Plato (428-348 BCE), The Republic, III
“Educators have always known that learning and life are maximal where play and work coincide.” — L. W. Gibbs
“In the future, we can expect that not much difference will exist between education and entertainment. We just have to put intelligence behind the entertainment.” — North Carolina State University’s James Lester, quoted at the 12th International Conference on College Teaching and Learning
“It is harmony which restores unity to the contrasting parts and which moulds them into a cosmos. Harmony is divine, it consists of numerical ratios. Whosoever acquires full understanding of this number harmony, he becomes himself divine and immortal.” –20th century Dutch mathematician B. L. van der Waerden, describing the beliefs of the followers of Pythagoras
“We do not listen with the best regard to the verses of a man who is only a poet, nor to his problems if he is only an algebraist;
but if a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic music.” —19th century American philosopher/writer Ralph Waldo Emerson, Society and Solitude, Ch. 7, Works and Days
“Mathematics is on the artistic side a creation of new rhythms, orders, designs, harmonies, and on the knowledge side, is a systematic study of various rhythms, orders, designs and harmonies.” — William L. Schaaff, author and mathematics education professor
“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made of ideas. His patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way.” — English mathematician G. H. Hardy (1877-1947)
“Music and math together satisfied a sort of abstract ‘appetite’, a desire that was partly intellectual, partly aesthetic, partly emotional, partly, even, physical.” –music critic/composer Edward Rothstein (p. xv of his 1995 book Emblems of Mind: The Inner Life of Music and Mathematics)
“We can no more come to understand mathematics by examining its final product than we can understand the experience of music through simply looking at a score or an analysis of one; there is an experience that lies underneath and behind the systematic organization of the material.” –music critic/composer Edward Rothstein (p. 38 of his 2006 book Emblems of Mind: The Inner Life of Music and Mathematics)
“Each time I’ve learned a little bit more about the inner structures of music, the math of it and the shape of it, my joy in it has increased.” — recording artist Peter Mulvey, in the Nov. 2000 Performing Songwriter
“Music is true. An octave is a mathematical reality. So is a 5th. So is a major 7th chord. And I have the feeling that these have emotional meanings to us, not only because we’re taught that a major 7th is warm and fuzzy and a diminished is sort of threatening and dark, but also because they actually do have these meanings. It’s almost like it’s a language that’s not a matter of our choosing. It’s a truth. The laws of physics apply to music, and music follows that. So it really lifts us out of this subjective, opinionated human position and drops us into the cosmic picture just like that.” — recording artist James Taylor, in the May 2002 Performing Songwriter
“The syntax and the grammar of the language of music are not capricious; they are dictated by the texture and organization of the deep levels of the mind, so with mathematics.” – mathematician H. E. Huntley
“The most distinct and beautiful statement of any truth (as of music) must take at last the mathematical form.” –19th century American writer/philosopher Henry David Thoreau, A Week on the Concord and Merrimac Rivers (Boston, 1893), p. 477
“You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves.” — Alfred North Whitehead (1861-1947), English mathematician
“Musical form is close to mathematics — not perhaps to mathematics itself, but certainly to something like mathematical thinking and relationship.” — 20th century Russian composer Igor Stravinsky