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  • feedwordpress 08:01:10 on 2018/11/04 Permalink
    Tags: , cell, fringe science, , Micrographia, microscope, , Probability, , Robert Hooke, ,   

    “Science is a process”*… 

     

    klee

    Paul Klee, “The Bounds of the Intellect,” 1927 (detail)

     

    When my grandfather died last fall, it fell to my sisters and me to sort through the books and papers in his home in East Tennessee. My grandfather was a nuclear physicist, my grandmother a mathematician, and among their novels and magazines were reams of scientific publications. In the wood-paneled study, we passed around great sheaves of papers for sorting, filling the air with dust.

    My youngest sister put a pile of yellowing papers in front of me, and I started to leaf through the typewritten letters and scholarly articles. Then my eyes fell on the words fundamental breakthroughspectacular, and revolutionary. Letters from some of the biggest names in physics fell out of the folders, in correspondence going back to 1979.

    In this stack, I found, was evidence of a mystery. My grandfather had a theory, one that he believed to be among the most important work of his career. And it had never been published…

    The remarkable– and illuminating– story of Veronique (Nikki) Greenwood’s quest to determine whether her grandfather was “a genius or a crackpot”: “My Grandfather Thought He Solved a Cosmic Mystery.”

    * T.S. Kuhn, The Structure of Scientific Revolution

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    As we note that the history of science is, effectively, the history of the instruments developed to help us “see” things smaller, larger, smaller, farther, or outside our human sensory range, we might recall that it was on this date in 1664 that natural philosopher, architect and pioneer of the Scientific Revolution Robert Hooke showed an advance copy of his book Micrographia— a chronicle of Hooke’s observations through various lens– to members of the Royal Society.  The volume (which coined the word “cell” in a biological context) went on to become the first scientific best-seller, and inspired broad interest in the new science of microscopy.

    source: Cal Tech

    Note that the image above is of an edition of Micrographia dated 1665.  Indeed, while (per the above) the text was previewed to the Royal Society in 1664 (to wit the letter, verso), the book wasn’t published until September, 1665.  Note too that Micrographia is in English (while most scientific books of that time were still in Latin)– a fact that no doubt contributed to its best-seller status.

     

     
  • feedwordpress 08:01:36 on 2017/07/20 Permalink
    Tags: , , Markov, Markov chains, Maryam Mirzakhani, , Probability, , stochastic processes,   

    “Mathematics, rightly viewed, possesses not only truth, but supreme beauty”*.. 

     

    Maryam Mirzakhani did not enjoy mathematics to begin with. She dreamed of being an author or politician, but as a top student at her all-girls school in Tehran she was still disappointed when her first-year maths exam went poorly. Her teacher believed her – wrongly – to have no particular affinity with the subject.

    Soon that would all change. “My first memory of mathematics is probably the time [my brother] told me about the problem of adding numbers from 1 to 100,” she recalled later. This was the story of Carl Gauss, the 18th-century genius whose schoolteacher set him this problem as a timewasting exercise – only for his precocious pupil to calculate the answer in a matter of seconds.

    The obvious solution is simple but slow: 1+2+3+4. Gauss’s solution is quicker to execute, and far more cunning. It goes like this: divide the numbers into two groups: from 1 to 50, and from 51 to 100. Then, add them together in pairs, starting with the lowest (1) and the highest (100), and working inwards (2+99, 3+98, and so on). There are 50 pairs; the sum of each pair is 101; the answer is 5050. “That was the first time I enjoyed a beautiful solution,” Mirzakhani told the Clay Mathematics Institute in 2008.

    Since then, her appreciation for beautiful solutions has taken her a long way from Farzanegan middle school. At 17 she won her first gold medal at the International Mathematics Olympiad. At 27 she earned a doctorate from Harvard University. The Blumenthal Award and Satter Prize followed, and in 2014 she became the first woman to be awarded the Fields Medal, the highest honour a mathematician can obtain.

    Before this particular brand of wonder became perceptible to Mirzakhani, she experienced feelings many of us can relate to: to the indifferent, her subject can seem “cold”, even “pointless”. Yet those who persist will be rewarded with glimpses of conceptual glory, as if gifted upon them by a capricious god: “The beauty of mathematics,” she warned, “only shows itself to more patient followers.”

    This concept of “beauty” found in maths has been referred to over centuries by many others; though, like beauty itself, it is notoriously difficult to define…

    For an experienced mathematician, the greatest equations are beautiful as well as useful. Can the rest of us see what they see?  “What makes maths beautiful?

    [From The New Humanist, via the ever-illuminating 3 Quarks Daily]

    Maryam Mirzakhani died last Friday, a victim of breast cancer; she was 40.  As Peter Sarnak (a mathematician at Princeton University and the Institute for Advanced Study) said, her passing is “a big loss and shock to the mathematical community worldwide.”  See also here.

    * Bertrand Russell, A History of Western Philosophy

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    As we accede to awe, we might spare a thought for Andrey (Andrei) Andreyevich Markov; he died on this date in 1922.  A Russian mathematician, he helped to develop the theory of stochastic processes, especially those now called Markov chains: sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors.  (For example, the probability of winning at the game of Monopoly can be determined using Markov chains.)  His work on the study of the probability of mutually-dependent events has been developed and widely applied to the biological and social sciences.

     source

     

     
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