Posts Tagged ‘Frank Drake’
“Pure mathematics is, in its way, the poetry of logical ideas”*…
Alexander Grothendieck is revered in the world of math; outside of it, he’s known for his unusual life, if he’s known at all. Konstantin Kakaes outlines his actual mathematical contributions…
What Albert Einstein was to 20th-century physics, Alexander Grothendieck was to 20th-century mathematics. He is much less well known because math gets technical even more quickly than physics does. But as with Einstein, Grothendieck’s impact came not just from his own results, revolutionary though they were. His work also reoriented his entire discipline in radical new directions.
Grothendieck was intense and ascetic from his early days. Starting in the early 1950s, when he was in his 20s, he produced thousands of pages of formal and informal notes that changed the course of mathematics. Then in 1970, he quit. He left his post at a prestigious research institute just outside of Paris to teach at the provincial university in Montpellier where he studied as an undergraduate. He mostly stopped talking to other mathematicians. In the early 1990s, he moved to a small village in the Pyrenees, where he lived as a hermit.
Mathematicians are still grappling with the innovations he made half a century ago. His work pushed mathematics to a new level of abstraction by focusing on the relationships between objects rather than the objects themselves. “If there is one thing in mathematics which fascinates me more than any other (and undoubtedly always has), it is neither ‘number’ nor ‘size,’ but invariably shape,” he wrote in his memoirs. “And among the thousand and one faces under which shape chooses to reveal itself to us, that which has fascinated me more than any other and continues to do so is the structure hidden in mathematical things.”
His revolutionary mathematics centered around that search for hidden structure…
Read on: “How Alexander Grothendieck Revolutionized 20th-Century Mathematics,” from @kkakaes.bsky.social in @quantamagazine.bsky.social.
For more, see the section on Grothendieck in Benjamin Labatut‘s remarkable When We Cease To Understand the World.
* Albert Einstein
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As we study shape, we might send speculative birthday greetings to a man who, while not technically a mathematician, nonetheless created a famous equation: Frank Drake; he was born this date in 1930. An astronomer and astrophysicist, he formulated the Drake Equation in 1961 to estimate the number of technological civilizations that might exist in the Milky Way galaxy, N = R* × fp × ne× fl × fi × fc × L. Using plausible guesses for the parameters, Drake concluded perhaps 10 planets in our galaxy may have life originating detectable signals. In 1960, Drake led the first search, the two-month Project Ozma to listen for patterns in radio waves with a complex, ordered pattern that might be assumed to represent messages from some extraterrestrial intelligence.
Carl Sagan and Drake designed the plaques on Pioneer 10 and Pioneer 11 for the purpose of greeting and informing any extraterrestrial life that might find the vessels after they left the solar system.
“The commonality between science and art is in trying to see profoundly – to develop strategies of seeing and showing”*…
Working with her scientist husband, Orra Hitchcock produced illustrations on bolts of linen that manifest original knowledge about extinction, stratigraphy, and their evidentiary features in the surrounding landscape– and trained eager young students to recognize and describe geological and natural-historical phenomena…
After meeting and falling in love with Edward Hitchcock, her employer at Massachusetts’ Deerfield Academy, Orra (née White) married him in 1821, beginning a lifetime of professional collaboration while raising a family amid piles of rocks and research tomes. Highly trained, white, and wealthy, she was far from an oddity in nineteenth-century education. Like many other women of her class, Hitchcock received extensive instruction in the arts and sciences, making a name by working alongside, not beneath, a man who had easier access to academic opportunities. Variously lauded as “an anomaly” and “the most remarkable” of their era, her scientific illustrations have rarely been considered on their own terms — admired for the natural historical and religious knowledge they contain — without being made an exemplar of the broader category of “women’s work”.
Moving to Amherst when Edward was appointed Professor of Chemistry and Natural History, the couple embarked on a decades-long exploration of the Connecticut River Valley’s botany and geology. While Edward lectured to eager young students about the principles of nature, from the depths of oceans to the granite veins of the earth, Orra produced more than sixty hand-colored scientific illustrations on poster-sized linen swaths designed to be hung on classroom walls.
Ranging from extinct mammals like Megatherium (a genus of giant ground sloth [below]) through lithic strata to fossilized footprints, the collection is striking for its modern abstraction, anticipating the later works of George Maw. Although some of Hitchcock’s geological illustrations seem far from “accurate” in their specificity (or lack thereof), her devotion to clear and concise visual communication bespeaks a deep-seated understanding of complex scientific principles…
An appreciation: “Orra White Hitchcock’s Scientific Illustrations for the Classroom (1828–40),” from @PublicDomainRev.
* Edward Tufte
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As we picture it, we might send sharply-observant birthday greetings to Cecilia Helena Payne-Gaposchkin; she was born on this date in 1900. An astrophysicist and astronomer, she was the first– in her Radcliffe (Harvard) PhD thesis in 1927– to apply the laws of atomic physics to the study of the temperature and density of stellar bodies: the first to conclude that hydrogen and helium are the two most common elements in the universe and the first to suggest that the Sun is primarily (99%) composed of hydrogen. During the 1920s, the accepted explanation of the Sun’s composition was a calculation of around 65% iron and 35% hydrogen. Her thesis adviser, astronomer Henry Norris Russell, reached a similar conclusion via his own observations several years later, and (while he made brief mention of Payne’s work) was for a time credited with the discovery. But in 1947, astronomer Fred Hoyle confirmed her original claim.
She spent her entire career at Harvard. In 1956 she became the first woman to be promoted to full professor from within the faculty at Harvard’s Faculty of Arts and Sciences. Later, with her appointment to the Chair of the Department of Astronomy, she also became the first woman to head a department at Harvard.
Her students included Helen Sawyer Hogg, Joseph Ashbrook, Paul W. Hodge, and Frank Drake (the creator of the Drake Equation)– all of whom made important contributions to astronomy.
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