“The extension of common sense by other means”


Abraham Wald, late in his life
Tragically, Abraham Wald and his wife died in a plane crash while on a lecture tour in India in 1950. He was only 48 years of age.  (Wikimedia Commons public domain)


I’ve been reading a few pages every few days in Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking (New York: Penguin Books, 2014).  Jordan Eilenberg is the Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin at Madison.  Here are a couple of items from his book:


“To paraphrase Clausewitz:  Mathematics is the extension of common sense by other means.”  (13)


“Mathematics is not settled.  Even concerning the basic objects of study, like numbers and geometric figures, our ignorance is much greater than our knowledge.  And the things we do know were arrived at only after massive effort, contention, and confusion.  All this sweat and tumult is carefully screened off in your textbook.”  (14)


And here’s an anecdote from the Second World War that Eilenberg tells and that I enjoyed and thought quite significant:


Abraham Wald and the Missing Bullet Holes”




A few other quotations about mathematics, which Carl Friedrich Gauss (a mathematician, naturally) called “the queen of the sciences”:


“Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”  (Bertrand Russell)


“You do not study mathematics because it helps you build a bridge. You study mathematics because it is the poetry of the universe. Its beauty transcends mere things.”   (Jonathan David Farley)


I actually began my undergraduate studies at Brigham Young University as a mathematics major.  I decided fairly quickly that there were other things that stirred my passions more, but I can’t say that I haven’t occasionally regretted my change of major.  And I retain a more than wistful interest in the subject.  Life is short — but all of the roads not taken fill me with enthusiasm for the eternities ahead.




Some news flashes from the world of science:


“Clumps of dark matter could be lurking undetected in our galaxy: A hypothetical ‘dark’ force could allow clouds of invisible particles to collapse into small structures”


“We Might Need to Redefine ‘Planet’ Again”


“Robust research needs many lines of evidence: Replication is not enough. Marcus R. Munafò and George Davey Smith state the case for triangulation.”


This one is consistent with what I’ve been posting about consciousness and “mysterianism” lately:


“Is Science Infinite?  Science will never tell us who we really are, and that is why it will last forever” 




A nice explanation, for those who’ve wondered:


“What’s So ‘Anti’ About Antimatter?”



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