Dear Eduardo,
Thanks for your reflections on Albert Einstein. Since this doesn’t
involve the question of first-order predicate logic and models of human
thought and reasoning, so I’m changing the subject header to
Einstein's Modes of Thought.
Your translation looks reasonable to me. You didn’t include a
reference, but it seem that you are translating from one of Einstein’s
three Rhodes Lectures at Oxford University. In one of the lectures, he
discussed Euclid, identifying Euclidean geometry as one source of the
theory of relativity.
Your comment on the reasons for Einstein’s interest in Euclid
doesn’t reflect Einstein’s own views one Euclid. It’s true that
Einstein wasn’t interested in ancient geometry or ancient geometers,
but he was interested in Euclid’s geometry and Euclid. There are
several reasons for this.
Some accounts I have seen state that Einstein saw Euclid’s geometry
as a key starting point for the theory of relativity. This is not as odd
as it may seem at first. Einstein did not claim that Euclid offered a
comprehensive contemporary description of the physical universe. Rather,
he saw Euclid’s geometry as an important starting point despite its
obvious weak points with respect to Einstein’s description of the
universe. In essence, Einstein saw Euclid as a beautiful and simple
description of geometry with weaknesses that modern mathematicians would
have to remedy. This is a gross over-simplification, but the point is
that Einstein actually used Euclid in developing relativity, at least as
a distant starting point.
Nevertheless, Euclid represented much more to Einstein. Euclid’s
powerful use of deduction from postulates inspired Einstein’s use of
rigorous deduction from hypotheses or theorems. He followed his theorems
to their conclusion, wherever they might lead. The principle of
conceptual rigor allied to simplicity was a central heuristic for
Einstein.
Einstein wasn’t simply interested in intellectuals as exemplars,
ancient or modern. Einstein saw Euclid as a predecessor and a
contributor to his work, in much the same as he saw Michael Faraday or
James Clerk Maxwell. In this sense, Einstein’s interest in Euclid had
very much to do with the particular way that Euclid thought.
John Stachel’s book Einstein’s Miraculous Year offers explicit
demonstrations of this thought process. Consider, for example,
Einstein’s paper on Brownian Motion. Stachel’s (1998)
introduction explains how this paper helped to demonstrate the physical
reality of atoms, showing that atoms were more than a convenient
heuristic device to assist physical calculations. Stachel’s
introductions to all the papers in the book show how Einstein thought,
and why. The book also contains Einstein’s doctoral dissertation on
molecular dimensions, still among the most frequently cited papers in
physics, the first papers on the theory of relativity, and a paper on
quantum theory that helped to win his Nobel prize by explaining the
photoelectric effect.
Hadamard’s (1996) book on the psychology of mathematical invention
contains the second Einstein quote on your post, but your quote is
slightly inaccurate and you’ve left out an issue that is decisive for
Einstein. The passage you presented addresses the logic of discovery:
“(A) The words or the language, as they are written or spoken, do
not seem to perform any role in my mechanism of thoughts. The psychical
entities which seem to serve as elements in thought are certain signs
and more or less clear images which can be ‘voluntarily’ reproduced
and combined.”
[NB: This passage describes “psychical” entities here, not
“physical” entities. But Einstein continues:]
“There is, of course, a certain connection between those elements and
relevant logical concepts. It is also clear that the desire to arrive
finally at logically connected concepts is the emotional basis of the
rather vague play with the above mentioned elements. But taken from a
psychological viewpoint, this combinatory play seems to be the essential
feature in productive thought – before there is any connection with
logical construction in words or other kinds of signs which can be
communicated to others.
[Next, Einstein writes a passage that points to the logic of
justification:]
“(B) The above mentioned elements are, in my case, of visual and some
of muscular type. Conventional words or other signs have to be sought
for laboriously only in a secondary stage, when the mentioned
associative play is sufficiently and can be reproduced at will”
(Einstein in Hadamard 1996: 142-143).
For Albert Einstein, generating physical, scientific, or mathematical
propositions was a matter of free play and imagination. Then, Einstein
used rigorous deductive logic and empirical proof to justify the free
and playful inventions of the mind.
When Einstein published the general theory of relativity, he proposed
three predictions that followed from it that would prove the theory to
be correct. He stated that these predictions constituted tests of the
theory, stating further that all three predictions must prove to be
correct. He stated that if any of the theory failed any of the three
tests, the theory would be shown to be incorrect, at least in the form
he published it.
There is much more to be said on all these topics. You can read
Einstein’s (1969: 1-94) own view of his philosophy and his view of
thought in Paul Schilpp’s excellent collection. If you want to read a
full and well developed biography of Einstein, try Abraham Pais’s
(1982) Subtle is the Lord. Many have been written since, but Pais – a
physicist and friend of Einstein – wrote one of the best.
Where it comes to Euclid, Einstein believed that every scientific,
physical, or mathematical proposition must lead to necessary
conclusions. The origin of the proposition might arise in a million
imaginative ways – inductive, abductive, creative. From any
proposition or series of propositions, a range of necessary consequences
must follow. For a physicist, these consequences take the form of
physical predictions. We can use these predictions as the tests that
permit us to determine which among our imaginative propositions are
correct. It is from Euclid that Einstein learned to deduce from each
proposition the necessary consequences. The combination of profound
physical intuition, vast imaginative power, and powerful deductive
capacity made Einstein what he was. From Euclid, Albert Einstein learned
to follow propositions to their logical conclusion, whatever that might
be.
But I will refer to the earlier thread on logic to note, as Einstein
himself asserts, that logic was not how Einstein thought. Logic and
deduction were tool that Einstein used to test the consequences of his
thought. Your post quite correctly captured the playful, generative
quality with which Einstein created (or discovered) his ideas.
Yours,
Ken
--
References
Einstein, Albert. 1969 [1949]. “Autobiographical Notes.” In Albert
Einstein. Philosopher-Scientist. Third Edition. Edited by Paul Arthur
Schilpp. La Salle, Illinois: Open Court Press, 1-94.
Hadamard, Jacques. 1996 [1945]. The Mathematician’s Mind. The
Psychology of Invention in the Mathematical Field. With a new preface by
P. N. Johnson-Laird. Princeton, New Jersey: Princeton University Press.
Pais, Abraham. 1982. Subtle is the Lord. The Science and the Life of
Albert Einstein. Oxford: Oxford University Press.
Stachel, John. 1998. “Einstein on Brownian Motion.” Einstein’s
Miraculous Year. Five Papers that Changed the Face of Physics. Edited
and introduced by John Stachel. Princeton, New Jersey: Princeton
University Press, 73-84.
--
Eduardo Corte-Real wrote:
—snip—
[Eduardo’s translation of Albert Einstein back into English from
Portuguese]
“We revere the Ancient Greece as the cradle of western science.
There, for the first time, the world witnessed the miracle of a logical
system that moves forward step by step with such precision that each one
of its prepositions is totally certain. I’m referring to the Euclidean
Geometry. This admirable triumph of reason gave to the human intellect
the necessary self confidence for its forthcoming achievements. … If you
weren’t thrilled by Euclid in your teens, then you were not born to be
a scientist.”
—snip—
For Einstein (this was part of a speech at the University of Oxford),
the Euclidean Geometry was the first argument to explain that
theoretical physics was mostly mentally constructed rather than based in
empirical observations. I will risk that what fascinated Einstein was
the mental construction of Euclid for being intellectual and not for
being intellectual in that particular way. The speech is mostly devoted
to Einstein’s ideas about contemporary Physics and, obviously, not
about ancient geometry.
—snip—
In 1945 responding to Jacques Hadamard in an enquiry about mathematical
thought, he wrote: “The words or the language, as they are written or
are pronounced, don’t seem to perform any role in the machine of my
thoughts. The physical entities that look like elements in thought are
certain signs and images more or less clear that can be
‘voluntarily’ combined or reproduced”
—snip—
Professor Ken Friedman, PhD, DSc (hc), FDRS | University Distinguished
Professor | Dean, Faculty of Design | Swinburne University of Technology
| Melbourne, Australia | [log in to unmask] | Ph: +61 3
9214 6078 | Faculty www.swinburne.edu.au/design
Fluxus and the Essential Questions of Life | University of Chicago
Press |
http://www.press.uchicago.edu/presssite/metadata.epl?isbn=9780226033594
|
