Popularizing the Postulate

March 4, 2012 § 3 Comments


The Fifth Postulate (Bardi, Jason Socrates)

The Pop Science writer’s job is a difficult one. Scientists – practitioners of the very trade celebrated in Pop Science books – are likely to be put off by the extensive dumbing down of complex ideas that usually takes place in these books. On the other hand, laymen without a scientific education – the target audience for the books –get easily intimidated by jargon and formulae. So the Pop Science author is a harassed man, who knows he needs to tread very carefully, and on not a lot of ground.

At the same time, it is possible to write great pop science.  As I have observed elsewhere, pop science can be hugely inspirational and can transform the life of a teenager. In order to inspire, a pop science book needs three things. Most importantly, it has to be well-written. Like any other writer, you are telling a story, and you should be able to hold the attention of your reader from one end of the story to the other.  Second, you cannot sustain a narrative if the scientific theme you choose is not powerful in and of itself; if a sense of wonder and magic cannot be created out of a simple explanation of the philosophical and technological implications of the science. Finally, it never hurts for your narrative to have a liberal dose of human interest, in the form of the intrepid men and women in the midst of the action, who embody the spirit of adventure, the struggle for glory, the intense rivalries, selfless collaborations, the superhuman effort, the sacrifices – and ultimately, the triumphs and tribulations involved in the making of science.

Applying these yardsticks to the book at hand, my first observation is that Jason Bardi simply isn’t a very gifted writer. Even the subtitle of the book is clumsily worded: “How unraveling a two-thousand year-old mystery unraveled the universe.” With all this unraveling on the title page, it is a wonder the book isn’t about string theory!

And then there are paragraphs like the one below

Lobachevsky …stood at the edge of the cliff, just as many had done before, but instead of turning back or trying to find a way around, he plunged into the depths and discovered the secret that had eluded so many for thousands of years. He survived the fall and came back to tell all. His invention – non-Euclidean geometry – challenged the conventional notions of space and geometry. It was as if he had climbed the mountain to find a way down the other side and returned to claim that he could wave his arms and fly.

Did Lobachevsky climb a mountain or jump off one? Did he fall or fly? Bardi’s metaphors are all in a twist, and may need some unraveling of their own.

Do parallel lines meet? (Image courtesy scenicreflections.com)

Thankfully, at this point, mathematics comes to the rescue and supplies Bardi with an absorbing human interest story, which isn’t a complete surprise: mathematics has no shortage of brilliant characters and dramatic stories. To the small but intense fraternity that is mathematically inclined, being the first to solve a major mathematical problem is like winning the race to scale Mount Everest or to reach the Poles.  There is no glory in coming second, and the high stakes have always made for excellent drama. Hippasus of Metapontum and the Pythagorians; Bhaskaracharya and his daughter Lilavati; Cardano, Tartaglia and the solving of the cubic equation; Newton and Leibniz and the invention of calculus, of course, but also Roger Cotes, the obscure mathematician that Newton revered beyond anyone else; the romantic life and utterly romantic death of young Evariste Galois; and so much more come to mind. There is a book in practically every life dedicated to mathematics, and there have been many in every generation for the last 2,500 years.

Here, in the case of Euclid’s Fifth postulate, the cast of characters Bardi calls upon includes Giovanni Saccheri, Johann Lambert, FC Schweikart, FA Taurinus, Farkas Bolyai, Janos Bolyai, Nikolai Lobachevsky and Carl Gauss.  The story ends in tragedy for all except the last-named. The first five squandered their lives in the hope of solving the problem, but failed; their lives are tragic but not extraordinarily so.  The miserable ends of Janos Bolyai and Lobachevsky are more heartrending:  theirs is the tragedy caused by the complete failure of the world to recognize their Herculean achievement. It was as if Robert Scott had miraculously survived the -45 degree temperatures, the blinding blizzards and impassable terrain of the Antarctic, and had returned in triumph from the South Pole to London only to have people say, “Ah, there you are, Robert, my dear fellow. Where did you go pottering off to, this time? The South Pole, eh? But why would you want to do a dashed silly thing like that? Bournemouth’s got better pubs.”

If the most remarkable aspect of the human interest story behind the discovery of non-Euclidean geometry is the utter blankness and incomprehension with which it was received, its flip side is the immense, Copernican philosophical significance of the discovery in the history of science. The moment when the mystery of Euclid’s Fifth Postulate was solved (by rejecting the intuitive notion that lines that aren’t parallel will always meet somewhere) was the exact point in time when we decided that geometry did not need to make sense in order to work. Up until then, it was thought significant that you could write things like “1 + 1 = 3”, but you couldn’t depict on paper a triangle, one of whose sides was longer than the sum of the other two; or four straight lines in space that met at a single point and were at right angles to each other. In short, you couldn’t represent a single false idea in geometry – to many, this made it the purest possible form of mathematics. But non-Euclidean geometry doesn’t have anything to do with the way we perceive the external world, and it wasn’t long after Lobachevsky that books of geometry began to be published that didn’t have a single diagram in them.  Clever, but is this geometry? And of what earthly use is it? Never before had a single discovery caused so much schism and division among mathematicians, perhaps irrecoverably so.

It is droll to note that it was a problem concerning parallel lines that caused such divergence.  Physics and pure mathematics broke off at this point, but perhaps more significantly, so did the words Reality and Truth.  Reality continued to be defined by the universe as we sense it, but mathematical truth was now defined purely in terms of internal logical consistency, with no reference to the external world. So abstract is this concept that it has led many in modern times to decry mathematics as just a game with arbitrary rules that has nothing to do with either Reality or Truth.

One cruel consequence of this divorce from common sense is the increasing gap between mathematical scholars and the lay public. Modern mathematics, freed of compulsion to remain rooted in experience, rapidly acquired bewildering complexity in the 20th century, and you now need to devote a decade of study or more to come up to speed with the research in any of its sub-fields. Rocket scientists, brain surgeons and Presidents can explain, in broad but understandable terms, what they do for a living, to the general public. Not so a number theorist today. The gap is vast and growing, and this can be catastrophic both for science and for society. The famous Library of Alexandria, frequented by Euclid himself at one point, was burnt down when the esoteric texts within were deemed useless, incomprehensible and elitist by the angry mob outside. We cannot afford a repetition.

And this, precisely, is why there is a burning need for more popular science writers – even average ones like Bardi, whose selection of a good theme and competent biographical research makes up for other inadequacies.

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§ 3 Responses to Popularizing the Postulate

  • The 'Cruel Youth' says:

    I happen to disagree with the comment about his writing skills. Having never read him, I can’t argue that, but your examples are sadly lacking.
    Mixing a metaphor makes not a bad piece- in fact, I thought it was hooking.
    As for the unraveling… that is a fine metaphor. What would you say?
    ‘ Solving a mystery solved the universe’
    ‘unraveling a mystery solved the universe’
    and several others even worse.
    Finally, your comment on string theory- Strings are not ‘raveled’ if such a word exists. It is possible that they are not strings. Otherwise, they are strings geometrically shaped as to form a membrane.
    The last point, however, is merely the pedant in me 🙂

  • […] the history of mathematics, I recognize identical processes at play, for instance in the cases of non-Euclidean geometry and number theory. Most compelling are Kuhn’s descriptions of the period of crisis, when rival […]

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