Dear Ken,
Thanks for more elements that confirm my intuition.
Two notes: My mistranslation is really a typo.
After reading the Einstein's apology for Euclid, and after underlying
the key words, do you really thought that my lyric interpretation of his
admiration was real?
My book is a collected essays book:
Einstein, Albert, /Como//Vejo A Ciência a Religião e o Mundo /[How do I
See Science, Religion and the World] Trans. José Miguel Silva & Ruth San
Payo, Lisboa: Relógio d’Água Editores, 2005
I like the Portuguese title.
On 22-06-2011 14:49, Ken Friedman wrote:
> 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
>
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