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FEYNMAN, RICHARD P. AUTOGRAPH MANUSCRIPT, BEING PLAYFUL NOTES ON ARITHMETIC, CA 1969
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招標截止
描述
- "System giving addition, defined via subtraction", ca 1969.
Autograph manuscript, 1 page (8 x 11 inches), in black ink on California Institute of Technology Interoffice Memo letterhead, creases where previously folded, some tanning and one small hole to fold.
拍品資料及來源
Amusing sheet, post-Nobel, that nonetheless speaks to Feynman's lifelong love affair with arithmetic, algebra, and symbolic manipulation. Here, the goal being to establish the commutative law of addition in, if you will, the absence of addition. The playfulness of it all recalls much from his youth- when at Far Rockaway High School he crafted his own version of Calculus for the Practical Man; then, in the 1936 summer preceding his sophomore year at MIT, trading algebraic manifestos with his classmate Ted Welton in the notebook that they shared, mailing back & forth (see Silvan Schweber's QED & The Men Who Made It; e.g., Fig. 17 there). Even at Princeton, with Wheeler in 1941, their joint work on the "Absorber Theory of Radiation," (Rev. Mod. Phys. 17, 157) a critical advance resulting from the seemingly preposterous algebraic gambit- R = [1/2(R)+1/2(A)] + [1/2(R)-1/2(A)]
where R & A refer to Retarded & Advanced fields. While this decomposition is algebraically trivial, it had a highly nontrivial physical interpretation since the 1st term in square brackets was related to the electromagnetic mass of the charged particle while the 2nd bracketed term, being asymmetrical in time, made the only contribution to the force of radiative reaction. Shortly thereafter, in Los Alamos, in his time during the Manhattan Project, Feynman delivered a 'public' lecture on "Some Interesting Properties of Numbers," constructing his arithmetic axiomatically from the bottom up- 'He invited his distinguished audience ("all the mighty minds," he wrote his mother a few days later) to discard all knowledge of mathematics and begin from first principles- specifically, a child's knowledge of counting in units.'- (Gleick, pp. 182-3). Those present included Oppenheimer, Bethe, Teller, etc- no ordinary 'public' lecture.
Unclear where Feynman's headed here, privileging subtraction over addition, but he no doubt enjoyed the diversion...
where R & A refer to Retarded & Advanced fields. While this decomposition is algebraically trivial, it had a highly nontrivial physical interpretation since the 1st term in square brackets was related to the electromagnetic mass of the charged particle while the 2nd bracketed term, being asymmetrical in time, made the only contribution to the force of radiative reaction. Shortly thereafter, in Los Alamos, in his time during the Manhattan Project, Feynman delivered a 'public' lecture on "Some Interesting Properties of Numbers," constructing his arithmetic axiomatically from the bottom up- 'He invited his distinguished audience ("all the mighty minds," he wrote his mother a few days later) to discard all knowledge of mathematics and begin from first principles- specifically, a child's knowledge of counting in units.'- (Gleick, pp. 182-3). Those present included Oppenheimer, Bethe, Teller, etc- no ordinary 'public' lecture.
Unclear where Feynman's headed here, privileging subtraction over addition, but he no doubt enjoyed the diversion...