My most recent piece for 3 Quarks Daily:
It’s about Miriam Yevick, a remarkable thinker. No one has conceptualized the phenomenon of human thought in technical terms more deeply than Yevick did in 1975 (see bibliography below). Her conception was certainly incomplete – she knew that. It may also be wrong, but that's something that has yet to be determined, through analysis and discussion.
Moreover, as I read her memoir, A Testament to Ariela, I realized that she was a remarkable woman as well. This essay is about both her ideas and her life and quotes extensively from one of her technical papers and from her memoir.
On women, Boston Commons, uninterrupted work
A Testament for Ariela consists of letters that Yevick wrote to her young grand-daughter, Ariela. In the following passage Yevick is reminiscing about visiting relatives in Boston and, in particular, about Harvard Yard.
I reminisced. I had entered this yard for the first time, Ariela, in l944, hand-in-hand with your grandfather [that is, Yevick’s husband, George]. We were two physics graduate students at MIT. I had fled a Europe under Nazi occupation a little more than three years before and he had left home in a steel town of Pennsylvania, immersed in the raw struggles caused by the depression. We were dreaming of a better world to come. We believed in science to help bring it about. We slipped into this yard deliberately hard of access, through one of the few entrances and left the monstrous world outside. Here all that ailed the world could be transmuted into abstractions, amenable to fascinating discussions. We listened awe-struck to debates and lectures by the giants of our time: the mathematicians, Norbert Wiener and John Von Neumann, who foretold the power of the computer in society; Niels Bohr, the physicist, who intimated what atomic energy was to create; Philip Frank, the philosopher of science, who stimulated us to argue about the meaning of science; Peter Debye, the biophysicist, who revealed the place of the quantum in biology. They projected to us a radically transformed post-war world, our world to be. We stood for hours with our fellow students on the steps of the bulky library building and commented to each other about what we had heard. Ideas were what made the world move, and if nothing is as powerful as an idea whose time has come, this yard with its old trees, its somewhat decrepit buildings, and its deep-furrowed scholars was to us the quintessential incubator of this new world. We were determined to study hard so we could give it our best!
More recent memories came to me as I sat in the yard: of helping your daddy in the fall of 1971 cart his numerous possessions into the dilapidated Harvard dormitory which was to be his home for the school year. He, too, was to master physics, he dreamed confidently.
We returned some six weeks later in pouring rain to a desperate young scholar. “Now you get into the driver’s seat,” your daddy would say to his father as they took turns in heroically confronting the murderous problem set, which yielded but slowly to their joint onslaught. We left behind a chastened but not defeated aspiring scientist when we said good-bye to our son, who was still bent on making his contribution to a world that one day would be yours, Ariela’s, and Catherine’s and Helen’s.
A bit later:
I lovingly thought of these, my female successors, and recognized my younger self in them. Once again I reminisced about the war years I had spent studying here in Cambridge. Hitler was raging in Europe, murdering my Jewish classmates who had been less lucky than I. America was united in a war effort to defeat this scourge of humanity. There was no time for niceties: Boston was disorderly, dilapidated and rambunctious. The city swarmed with soldiers on leave from the fronts, with sailors taking a respite on shore from the submarine infested oceans. Spirited, newly liberated women of all ages, working in factories and as technicians, replacing the men in combat, energetically mingled in the crowds. Love was made fearlessly in the Boston Commons, passions enhanced by the uncertainty of the service men’s return. Pregnant women stuck to their tasks; there was a job to be done!
Everyone’s life had a purpose. I, Ariela, was going to beat the men at their game and be a physicist. I was to be an independent woman: no man was to spread his protective cover over me again!
The spring term ended; the summer term followed close upon its heels. We had to learn hard and fast. The break between terms was of one week’s duration only. I felt that I needed a holiday from the intense pressures of my studies. My Master’s thesis adviser forbade me to leave: “There is no better way to produce results than by an uninterrupted week of work in the laboratory,” he said.
[Kindle Edition. Locations 663-699]
Remarks Yevick makes here and there make it clear that she often had to scramble for uninterrupted time in which to conduct her research.
Back when I was on the faculty at the Rensselaer Polytechnic Institute it would be two or three weeks after then Spring semester had ended before I’d be in a good frame of mind for research. My brain had to readjust the wiring on millions if not billions of synapses for that to happen.
Some of her papers (the ones I could find)
The Lebesgue Density Theorem in Abstract Measure Spaces, Ph.D. Dissertation, MIT, 1947. https://dspace.mit.edu/handle/1721.1/85715
Probability and Determinism, American Journal of Physics 25, 570 (1957); doi: 10.1119/1.1934551
Holographic or Fourier Logic, Pattern Recognition, Vol. 7, 1975, 197-213. https://doi.org/10.1016/0031-3203(75)90005-9
Two modes of identifying objects: descriptive and holistic for concrete objects; recursive and ostensive for abstract objects, The Behavioral and Brain Sciences, Vol.1, No. 2, 1978, 253-254, https://doi.org/10.1017/S0140525X00074458
Lipschutz-Yevick, Miriam (1991) "Mathematics for Life and Society," Humanistic Mathematics Network Journal: Iss. 6, Article 20. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss6/20
Powell, Arthur B. and Yevick, Miriam L., Letter to The New York Times, Humanistic Mathematics Network Journal: Iss. 19, Article 4, 1999, Available at: http://scholarship.claremont.edu/hmnj/vol1/iss19/4
A Mathematics Manifesto: Think Differently! Think Quantitatively!Quantitative Awareness as a Fresh Thinking Cap, Humanistic Mathematics Network Journal: Iss. 20, Article 20, 1999, Available at: http://scholarship.claremont.edu/hmnj/vol1/iss20/20
Use Your Head: Mathematics As Therapy, Humanistic Mathematics Network Journal: Iss. 22, Article 12, 2000, Available at: http://scholarship.claremont.edu/hmnj/vol1/iss22/12
Semiotic impediments to formalizations, Semiotica, 120(1-2), 1998, doi:10.1515/semi.1998.120.1-2.109
Social Influences on Quantum Mechanics? – II, The Mathematical Intelligencer, 23(4), 2001, 18-22. doi:10.1007/bf03024597
Memoir: To Agnes Berger (1916-2002) and Our Friendship, Newsletter, Association for Women in Mathematics, Volume 33, Number 1, January-February 2003, 7-10.
Poetic metaphor and mathematical demonstration: A shallow analogy. The Mathematical Intelligencer, 29(3), 2007, 11–13. doi:10.1007/bf02985683
More later.
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