Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Saturday, November 01, 2025

Easy Pieces: Reading Popular Books on Science

Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show.
- Richard Feynman [quoted in Genius, p.285]

Perhaps I should say: trying to read popular books on science. They tend to start off quite straightforwardly, then segue into some esoteric explanation of something mathematical, and after that I'm lost ...

But no-one gets anywhere without perseverance. The other day I bought a copy of the book above for a couple of bucks in a Salvation Army shop. I've been reading it ever since with steadily increasing interest. I don't really understand it, mind you. It still isn't quite clear to me exactly what Richard Feynman's "genius" consisted of. There's no obvious manifestation of it to be seen as yet, unlike Einstein's Theory of Relativity or Oppenheimer's atomic bomb. But at times I begin to think that even a scientific illiterate such as myself might be able to glimpse something of his achievements even at second-hand.



A few years ago, I bought a copy of the book above (also second-hand, in an opportunity shop). The title proved to be a bit of a misnomer, as I can't say I found any of the pieces particularly easy. But, as I recall it, that was also the point of the film Five Easy Pieces - which is presumably what the two editors, Matthew Sands and Robert Leighton, were thinking of when they gave their book of selections from Feynman's introductory lectures that title.


Bob Rafelson, dir.: Five Easy Pieces (1970)





William Blake: Newton (1795)
John Maynard Keynes ... spoke of Newton as "this strange spirit, who was tempted by the Devil to believe ... that he could reach all the secrets of God and Nature by the pure power of mind - Copernicus and Faustus in one. Why do I call him a magician? Because he looked on the whole universe and all that is in it as a riddle, as a secret which could be read by applying pure thought to certain evidence, certain mystic clues which God had laid about the world to allow a sort of philosopher's treasure hunt to this esoteric brotherhood."
- Freeman Dyson [quoted in Genius, p.317]

I suppose that the question I'm asking myself here is a fairly obvious one. Why do I keep on battering my head against the brick wall of books such as these? I clearly lack the background in mathematics - let alone physics - to make sense of them, and yet there's something attractive in the notion that a few ideas, a few precious gleams of knowledge might get through the barrier of my resolutely humanist education and give me a glimpse of what the universe is all about.


Banesh Hoffmann: The Strange Story of the Quantum (1947)


Some of the blame must be laid at the door of Banesh Hoffmann's The Strange Story of the Quantum. There's a tedious habit among us literary folk to try to sum up Einstein's famous theories as something along the lines of "everything is relative" - or (even worse) to make strained analogies between Heisenberg's Uncertainty Principle and the perilous lack of convictions underlying modern thought.

And as for all the stupid things we've said at one time or another about Schrödinger's cat! Don't get me started ...



Back in the days before Wikipedia, though, it wasn't so easy to get quick summaries of what such pat formulae really meant. Hoffmann's Strange Story of the Quantum gave me my first real glimpse into how these discoveries had actually been made, without all the clichés. I suppose, in a sense, I've been looking for a sequel as good as that ever since.



Way before that, though, I encountered a copy of the book above in the Rangitoto College Library. Its admittedly somewhat simplistic account of the history of astronomy fascinated me, and it wasn't long before I found myself reading Arthur Koestler's rather more testing exploration of the same territory, The Sleepwalkers:



Like most of Koestler's work, it's suffered a bit of an eclipse in recent times. There are certainly many eccentricities in his account of the birth of modern cosmology. His decision to end with Newton, on the rather flimsy pretext that we still inhabit an essentially Newtonian universe, is particularly frustrating.

What's great about the book is its engagé and even, at times, polemic tone. Koestler argues his case passionately, and he makes it clear that sticking to the comfortable concensus of opinion is not an option. He follows the evidence where it leads him - a strong encouragement to his readers to do the same. I've read the book so many times I practically know it by heart, but the lengthy account of his hero Kepler's life and times still gives me a thrill after all these years.



One of the advantages of having been a Sci-fi fan since my early teens is that boffin extraordinaire Alan Turing was well known to me long before the details of his wartime service at Bletchley Park were revealed. The "Turing test" was a frequent subject of discussion in the SF magazines I read, and his vital part in the creation of modern computers was common knowledge to us Sci-fi mavens long before the name "Enigma" ever strayed into print.

And, like everyone else, I stumbled through the pages of Douglas Hofstadter's Gödel, Escher, Bach with increasing bewilderment - until, that is, I made the reluctant decision to skip the pages of exercises and simply try to follow the text.






Leonardo da Vinci: Vitruvian Man (c.1490)


Do I feel better for having read all these books? Not particularly. They mostly just succeeded in underlining for me the gulf between my kind of knowledge and the mathematical, scientific kind.

At least I've ended up knowing a bit more about what I don't know, though. I get enough from them to see the bankruptcy of the simplified explanations we tend to rely on. So in that sense I do feel a bit better educated.

Each one I pick up still gives me a shiver of hope, however. As Liza Minnelli once put it: "Maybe this time ..." In any case, it seems to be enough to keep me filling in these gaps in - at the very least - my knowledge of the history of science.


Minnellian Woman: Cabaret (1972)


I wonder, too, if any of this fascination has manifested itself in my own work? My first novel, Nights with Giordano Bruno, for instance, concludes with the diagram below - chosen, I suppose, as a kind of distorted mirror-image of Da Vinci's Vitruvian man.

The novel itself is ordered according to a mad numerological scheme, inspired principally by the Memory Palaces described in Frances Yates' classic account The Art of Memory (1966). I suppose that the simultaneous fascination and distrust I feel for such ways of ordering the mind has been influenced also, by all this reading about modern science: its apparently chaotic and arbitrary nature, combined with its inability to find a way out of its dialectic structures, are continually belied by the practical success its towering edifices of thought continue to achieve in the (so-called) "real world".

What else can a poor humanist do, under such circumstances, than construct a Don Quixote-like parody of the kinds of rabbit-hole thinking which have become more and more dominant over the past 25 years?


Jack Ross: Nights with Giordano Bruno (2000)





NAASP: Stars

Cosmology, Mathematics & Physics

  1. Nicolaus Copernicus (1473-1543)
  2. Albert Einstein (1879-1955)
  3. Richard P. Feynman (1918-1988)
  4. Galileo Galilei (1564-1642)
  5. Stephen Hawking (1942-2018)
  6. Douglas R. Hofstadter (1945- )
  7. Johannes Kepler (1571-1630)
  8. Isaac Newton (1643-1727)
  9. J. Robert Oppenheimer (1904-1967)
  10. Ernest Rutherford (1871-1937)
  11. Alan Turing (1912-1954)
  12. Anthologies & Secondary Literature



    Nicolaus Copernicus (1473-1543)

  1. Gingerich, Owen. The Book Nobody Read: Chasing the Revolutions of Nicolaus Copernicus. 2004. Arrow Books. London: The Random House Group Limited, 2005.

  2. Rosen, Edward, trans. Three Copernican Treatises: The Commentariolus of Copernicus / The Letter against Werner / The Narratio Prima of Rheticus. Second Edition, Revised with an Annotated Copernicus Bibliography, 1939-1958. 1939. New York: Dover Publications, 1959.


  3. Albert Einstein (1879-1955)

  4. Einstein, Albert. Relativity: The Special and General Theory. A Popular Exposition. 1916. Trans. Robert W. Lawson. 1920. London: Methuen & Co. Ltd., 1977.

  5. Bodanis, David. E = mc2: A Biography of the World's Most Famous Equation. Macmillan. London: Macmillan Publishers Limited, 2000.


  6. Richard Phillips Feynman (1918-1988)

  7. Feynman, Richard P. Six Easy Pieces. 1995. Harmondsworth: Penguin, 1998.

  8. Gleick, James. Genius: Richard Feynman and Modern Physics. 1992. An Abacus Book. London: Little, Brown and Company (UK), 2000.


  9. Galileo Galilei (1564-1642)

  10. Santillana, Giorgio de. The Crime of Galileo. 1955. Time Reading Program Special Edition. 1962. Alexamdria, Virginia: Time Life Books Inc., 1981.

  11. Sobel, Dava. Galileo’s Daughter: A Drama of Science, Faith and Love. London: Fourth Estate, 1999.


  12. Stephen William Hawking (1942-2018)

  13. Hawking, Stephen. The Illustrated A Brief History of Time: Updated & Expanded Edition. 1988. A Labyrinth Book. London: Bantam Press, 1996.

  14. Hawking, Stephen. Black Holes and Baby Universes and Other Essays. London: Bantam Press, 1993.


  15. Douglas Richard Hofstadter (1945- )

  16. Hofstadter, Douglas R. Gödel, Escher, Bach: An Eternal Golden Braid. 1979. Harmondsworth: Penguin, 1981.

  17. Hofstadter, Douglas R. Metamagical Themas: Questing for the Essence of Mind and Pattern. 1985. Harmondsworth: Penguin, 1987.

  18. Hofstadter, Douglas R., & Daniel C. Dennett, ed. The Mind’s I: Fantasies and Reflections on Self and Soul. 1981. Harmondsworth: Penguin, 1982.


  19. Johannes Kepler (1571-1630)

  20. Banville, John. The Revolutions Trilogy: Doctor Copernicus; Kepler; The Newton Letter. 1976, 1981, 1982. Picador. 2000. London: Macmillan Publishers Ltd., 2001.

  21. Connor, James A. Kepler’s Witch: An Astronomer’s Discovery of Cosmic Order Amid Religious War, Political Intrigue, and the Heresy Trial of His Mother. With Translation Assistance by Petra Sabin Jung. 2004. HarperSanFrancisco. New York: HarperCollins, 2005.

  22. Koestler, Arthur. The Sleepwalkers: A History of Man's Changing Vision of the Universe. Introduction by Herbert Butterfield. New York: The Macmillan Company, 1959.


  23. Isaac Newton (1643-1727)

  24. More, Louis Trenchard. Isaac Newton: A Biography, 1642-1727. 1934. New York: Dover Publications, 1962.


  25. Julius Robert Oppenheimer (1904-1967)

  26. Bird, Kai, & Martin J. Sherman. American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer. 2005. London: Atlantic Books, 2009.

  27. Monk, Ray. Inside the Centre: The Life of J. Robert Oppenheimer. Jonathan Cape. London: Random House, 2012.


  28. Ernest Rutherford (1871-1937)

  29. Campbell, John. Rutherford: Scientist Supreme. Christchurch: AAS Publications, 1999.


  30. Alan Mathison Turing (1912-1954)

  31. Hodges, Andrew. Alan Turing: The Enigma of Intelligence. 1983. London: Unwin Paperbacks, 1989.


  32. Anthologies & Secondary Literature

  33. Abbott, Edwin A. Flatland: A Romance of Many Dimensions by A. Square. Illustrations by the Author. 1884. Classic Science Fiction. Harmondsworth: Penguin, 1986.

  34. Casti, John L. Paradigms Lost: Tackling the Unanswered Mysteries of Modern Science. 1989. Avon Books. New York: The Hearst Corporation, 1990.

  35. Crombie, A. C. Augustine to Galileo. Volume 1: Science in the Middle Ages, 5th – 13th Centuries. 1959. A Peregrine Book. Harmondsworth: Penguin, 1969.

  36. Crombie, A. C. Augustine to Galileo. Volume 2: Science in the Later Middle Ages and Early Modern Times, 13th – 17th Centuries. 1959. A Peregrine Book. Harmondsworth: Penguin, 1969.

  37. Duncan, David Ewing. The Calendar: The 5000-year Struggle to Align the Clock and the Heavens – and What Happened to the Missing Ten Days. London: Fourth Estate, 1998.

  38. Euclid. The Thirteen Books of the Elements / Archimedes. The Works, Including the Method / Apollonius of Perga. On Conic Sections / Nichomachus of Gerga. Introduction to Arithmetic. Trans. Thomas L. Heath, R. Catesby Taliaferro, & Martin L. D’Ooge. 1926 & 1939. Great Books of the Western World, 11. Ed. Robert Maynard Hutchins. Chicago: William Benton, Publisher / Encyclopaedia Britannica, Inc., 1952.

  39. Greene, Brian. The Fabric of the Cosmos. 2004. London: Penguin, 2008.

  40. Hoffmann, Banesh. The Strange Story of the Quantum. 1947. A Pelican Book. Harmondsworth: Penguin, 1963.

  41. Kuhn, Thomas S. The Structure of Scientific Revolutions: 50th Anniversary Edition. 1962. Introductory Essay by Ian Hacking. Chicago & London: University of Chicago Press, 2012.

  42. Landes, David S. Revolution in Time: Clocks and the Making of the Modern World. 1983. Rev. ed. 1998. Viking. Harmondsworth: Penguin, 2000.

  43. Popper, Karl R. The Logic of Scientific Discovery. 1934. Trans. by the author with Dr. Julius Feed & Ian Feed. 1959. Mansfield Center, CT: Martino Fine Books, 2014.

  44. Poundstone, William. Prisoner’s Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb. New York: Doubleday, 1992.

  45. Ptolemy. The Almagest / Copernicus. On the Revolutions of the Heavenly Spheres / Kepler. Epitome of Copernican Astronomy: IV & V; The Harmonies of the World: V. Trans. R. Catesby Taliaferro, & Charles Glenn Wallis. Great Books of the Western World, 16. Ed. Robert Maynard Hutchins. Chicago: William Benton, Publisher / Encyclopaedia Britannica, Inc., 1952.

  46. Rucker, Rudy. The Fourth Dimension, and How to Get There. Foreword by Martin Gardner. Illustrations by David Povilaitis. 1985. Harmondsworth: Penguin, 1986.

  47. Segrè, Gino. Faust in Copenhagen: The Struggle for the Soul of Physics and the Birth of the Nuclear Age. 2007. Pimlico. London: Random House, 2008.

  48. Singh, Simon. Fermat’s Last Theorem: The Story of a Riddle that Confounded the World’s Greatest Minds for 358 Years. Foreword by John Lynch. 1997. London: Fourth Estate, 2002.

  49. Singh, Simon. Big Bang: The Most Important Scientific Discovery of All Time and Why You Need to Know About It. 2004. London: Harper Perennial, 2005.

  50. Teresi, Dick. Lost Discoveries: The Ancient Roots of Modern Science - from the Babylonians to the Maya. New York: Simon & Schuster, 2002.

  51. Thiel, Rudolf. And There was Light: The Discovery of the Universe. Trans. Richard & Clara Winston. London: Andre Deutsch, 1958.




Erik Desmazières: The Library of Babel (1997)