Excerpt from GENE515
This partly answers a question asked of me when I was 21 years old, by my doctoral thesis advisor Oliver G. Selfridge. When I say "Man" I am echoing and older text, and not excluding Woman.
Excerpt from GENE515What is Man, that he may know Number? What is Number that it may be known by Man ( Read more... )
Excerpt from GENE515What is Man, that he may know Number? What is Number that it may be known by Man ( Read more... )
"Of course God likes Math. That's because He's actually a Physicist."
Others opine similarly.
"[my] central theme ... concerns what I call the Big Four questions of existence:
(1) Why are the laws of nature what they are?
(2) Why does the universe consist of the things it does?
(3) How did those things arise?
(4) How did the universe achieve its organisation?"
"[As we proceed] ... tentative answers to these questions begin to emerge - answers based on the physicist's conception of nature. The answers may be totally wrong, but I believe that physics is uniquely placed to provide them. It may seem bizarre, but in my opinion science offers a surer path to God than religion. Right or wrong, the fact that science has actually advanced to the point where what were formerly religious questions can be seriously tackled, itself indicates the far-reaching consequences of the new physics.
[Paul Davies, preface to his book "God and the New Physics", 1983]
Bas von Frassen:
"... once atoms had no colour, now they also have no shape, place or volume...There is a reason why metaphysics sounds so passe', so vieux-jeu today; for intellectually challenging perplexities and paradoxes it has been far surpassed by theoretical science. Do the concepts of the Trinity and the soul, haecceity, universals, prime matter, and potentiality baffle you? They pale beside the unimaginable otherness of closed space-time, event horizons. EPR correlations and bootstrap models."
[Bas von Frassen, taken from Mary Midgley, "Science as Salvation: A Modern Myth and Its Meaning", Routledge, 1992, p. 107, via Anthony O'Hear's "The Element of Fire: Science, Art and the Human World", (Routledge, 1988) from "Empiricism in the philosophy of science", in Images of Science, ed. P. Churchland and C.A. Hooker, University of Chicago Press, p. 258]
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Who alterest all things with thy peering eyes.
Why prayest thou thus upon the poet's heart,
Vulture, whose wings are dull realities?
How should he love thee? or how deem thee wise,
Who wouldst not leave him in his wandering
To seek for treasure in the jewelled skies,
Albeit he soared with an undaunted wing?
Edgar Allan Poe
Sonnet-- To Science
1829
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"To speak algebraically,
Mr. M. is execrable,
but Mr. G. is
(x+1)ecrable."
--Edgar Alan Poe
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Ernest Rutherford
[1871-1937]
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Mathematics is inadequate to describe the universe,
since mathematics is an abstraction from natural phenomena.
Also, mathematics may predict things which don't exist,
or are impossible in nature.
-- Ludovico delle Colombe Criticizing Galileo.
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Among the minor, yet striking characteristics of mathematics,
may be mentioned the fleshless and skeletal build of its propositions;
the peculiar difficulty, complication, and stress of its reasonings;
the perfect exactitude of its results;
their broad universality;
their practical infallibility.
-- Charles Sanders Peirce, (1839-1914) "The Essence of Mathematics" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
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Mathematicians my flatter themselves that they possess new ideas which mere
human language is as yet unable to express. Let them make the effort to
express these ideas in appropriate words without the aid of symbols, and if
they succeed they will not only lay us laymen under a lasting obligation,
but, we venture to say, they will find themselves very much enlightened
during the process, and will even be doubtful whether the ideas as
expressed in symbols had ever quite found their way out of the equations
into their minds.
-- James Clerk Maxwell (1831-1879) [Scottish physicist]
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Physics professor is walking across campus, runs into Math Professor.
Physics professor has been doing an experiment, and has worked out an
empirical equation that seems to explain his data, and asks the Math
professor to look at it.
A week later, they meet again, and the Math professor says the equation
is invalid. By then, the Physics professor has used his equation to
predict the results of further experiments, and he is getting excellent
results, so he asks the Math professor to look again.
Another week goes by, and they meet once more. The Math professor tells
the Physics professor the equation does work, "But only in the trivial
case where the numbers are real and positive."
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Physics is not a religion. If it were, we'd have a much easier time raising money.
-- Leon Lederman, Nobel Prize in Physics, 1988
Leon Lederman is the recipient of fellowships from the Ford, Guggenheim, Ernest Kepton Adams and National Science Foundations. He is a founding member of the High Energy Physics Advisory Panel (to AEC, DOE) and the International Committee on Future Accelerators. He has received the National Medal of Science (1965) and the Wolf Prize for Physics (1982) among many other awards.
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"Mathematics began to seem too much like puzzle solving.
Physics is puzzle solving, too, but of puzzles created by nature,
not by the mind of man."
-- Maria Goeppert Mayer, (1906 -1972) J. Dash, Maria Goeppert-Mayer, A Life of One's Own.
Article in Wikipedia
Maria Goppert-Mayer (June 28, 1906 - February 20, 1972) was born Maria Goppert in Katowice (then in Germany, now part of Poland) and became one of the few women to receive a Nobel Prize in Physics.
Her family moved to Gottingen in Germany in 1910 when her father Frederick was appointed Professor of Paediatrics at the town's university. From a young age, Maria was surrounded by the students and lecturers from the University, intellectuals including future Nobel winners, Enrico Fermi, Werner Heisenberg, Paul Dirac and Wolfgang Pauli. In 1924 she passed the University's arbiter entrance examinations and enrolled there in the fall. Among her professors were three Nobel prize winners: Max Born, James Franck and Adolf Otto Reinhold Windaus. In 1930 Goppert married Dr. Joseph Edward Mayer, the assistant of James Franck. The couple moved to the United States, Mayer's home country. For the next few years, Goppert-Mayer worked at unofficial or volunteer positions at the university at which her husband was professor -- first at the Johns Hopkins University in Baltimore from 1931-39, then Columbia University in 1940-46, and after that the University of Chicago. During this time, Maria was unable to gain a professional appointment at Joseph's universities due in part to both sexism and strict rules against nepotism. However, she was able to find other research opportunities, including a part-time teaching opportunity at Sarah Lawrence College, a part-time research position with Columbia University's Substitute Alloy Materials Project and Opacity Project, and some time at Los Alamos Laboratory.
During Joseph's time at the University of Chicago, Maria was able to become a voluntary Associate Professor of Physics at the school. In addition, when Argonne National Laboratory came into existence on July 1, 1946, Maria was offered a part-time job there as Senior Physicist in the Theoretical Physics Division. It was during her time at Chicago and Argonne that she developed a model for the nuclear shell structure, work for which she received a Nobel Prize in Physics in 1963 together with Eugene Paul Wigner and J. Hans D. Jensen.
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[Maria] Goppert-Mayer's model explained why certain amounts of nucleons in the nucleus of an atom (2, 8, 20, 28, 50, 82, and 126, for example) cause an atom to be extremely stable. This had been baffling scientists for some time. These numbers are called "magic numbers". Maria postulated, against the received wisdom of the time, that the nucleus is like a series of closed shells and pairs of neutrons and protons like to couple together in what is called spin orbit coupling. This is like the Earth spinning on its axis as the Earth itself is spinning around the Sun. Maria described the idea elegantly:
"Think of a roomful of waltzers. Suppose they go round the room in circles, each circle enclosed within another. Then imagine that in each circle, you can fit twice as many dancers by having one pair go clockwise and another pair go counterclockwise. Then add one more variation; all the dancers are spinning twirling round and round like tops as they circle the room, each pair both twirling and circling. But only some of those that go counterclockwise are twirling counterclockwise; the others are twirling clockwise while circling counterclockwise. The same is true of those that are dancing around clockwise; some twirl clockwise, others twirl counterclockwise."
At the same time, there were German scientists working on exactly the same thing. After they had published their results, Maria sought to collaborate with them. One of the German team, Hans Jensen, worked with Maria to produce a book in 1950 called Elementary Theory of Nuclear Shell Structure. In 1963 both Maria and Hans Jensen were awarded the Nobel Prize for Physics "...for their discoveries concerning nuclear shell structure." Maria was quoted as saying, "Winning the prize wasn't half as exciting as doing the work."
During the 1940s and early 1950s, she computed equations on opacity for Edward Teller that would be used for Teller's investigations into the possibility of a hydrogen bomb.
Maria Goppert-Mayer died in San Diego in 1972.
After her death, an award in her name was set up by the American Physical Society to honour young female physicists at the beginning of their careers. Open to all female physicists who hold PhDs, the winner receives money and the opportunity to give guest lectures about her research at four major institutions. Two of Goppert-Mayer's former universities also honor her. The University of Chicago presents an award each year to an outstanding young woman scientist or engineer, and the University of California, San Diego hosts an annual Maria Goeppert Mayer symposium, bringing together female researchers to discuss current science.
In Literature
She has a small role in the novel Timescape by Gregory Benford.
External links
Maria Goeppert-Mayer
discoveries concerning nuclear shell structure.
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Speaking of Benford, here's Heinlein on Math:
"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house."
-- Lazarus Long, "Time Enough for Love" (Robert A. Heinlein)
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"Mathematics is the tool
specially suited
for dealing
with abstract concepts
of any kind
and there is no limit
to its power
in this field."
-- Paul Adrien Maurice Dirac (1902-1984) In P. J. Davis and R. Hersh The Mathematical Experience, Boston: Birkhauser, 1981.
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"God does not care about our mathematical difficulties.
He integrates empirically."
-- Albert Einstein
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"Do not worry about your difficulties in mathematics,
I assure you that mine are greater."
-- Albert Einstein, (1879-1955)
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