Jason Socrates Bardi’s book, The Calculus Wars, about the disputed invention of Calculus surprised me most in this way… that I was able to pry apart the covers in spite of the immense vacuity of substance between them.
There is barely a hint of all the philosophical exertion and mental mining and mountainous-knowledge-climbing that assuredly occurred as Newton and Leibniz, mostly independently, went about creating a new branch of mathematics. Instead, we get gossip and he-said, he-said.
This book could have been constructed as a detective story of sorts– the author guiding us through the mysteries and accusations surrounding the creation of this new style of math (Newton and Leibniz both claimed to be the inventor of Calculus). The author could have peered over the shoulder of each man as he worked through equations and readings during their contemporaneous quests to determine the calculations most penetrating and elegant to use when considering curves.
The Calculus Wars aspires to be another Wittgenstein’s Poker (by John Eidinow and David Edmonds)– that book is an example of how the popularization of philosophy and philosophical history can be done well. In that book, some of the great ideas of the spotlighted philosophers are examined at a deeper than epidermal level. I mentioned Wittgenstein’s Poker positively in my Wittgenstein posts (here, and here). But Bardi does not come close to this level of accomplishment.
Bardi’s book also has a further distinction: it is the worst-edited book so far completed of the near-100 books perused to date on my Self-Doctorate Reading List. Now, as a HORRIBLE editor myself (which this site all too well makes manifest), I have to pull my punches a bit here. On the other hand, no one’s paying me to edit anything, and most writers would agree that no one edits their own work very well– you tend to skim over errors, seeing what you know is SUPPOSED to be there, or at least what was there in your head when you wrote it.
Some quasi-edited, mind-bending gems that I can’t NOT mention from the book:
“he tried unsuccessfully but failed”
“neither were not there to defend themselves”
In defense of the author, many of the errors smacked of the intrusion of an editor who rephrased a few sentences without adequately deleting all the remnants of the original construction. At least, that’s one guess.
As to the content, itself…
I came away with two things from the book, neither of which I trust very much, my confidence undermined by the book’s failings…
1) Newton probably deserves the majority of the credit for inventing Calculus
2) Newton was not modestly exaggerating when he said he that he merely stood on the shoulders of giants, philosophically speaking– at least when it comes to Calculus… much of the legwork seems to have already been done or was being worked-out by others at about the same time.
Taking the last of my “take-aways” first…
According to Bardi, the following mathematical inventions had already occurred before Newton and Leibniz started their wrestling match for credit:
* Fermat had discovered a method for finding maxima and minima– an important part of differential calculus. Fermat’s method involved drawing tangents to curves.
* Johann Hudde advanced along similar lines (or curves) as Fermat
* Pascal did some important work concerning Conic Sections
* de Robernal, Issac Barrow, and de Sluse also worked on finding tangents to circles
* Torricelli had developed a method of coping with the “infinitesimals” created as one divides the area beneath a curve into smaller and smaller sections
* James Gregory was integrating trigonometric functions. Gregory and Torricelli’s work would have presumably been precursors to the “Integral” side of Calculus
* And the immensely talented Huygens had not only worked with maxima and minima, but had explored the math of points of inflection.
As far as my first take-away from the book (that Newton deserves the greater share of the credit for Calculus), I base this on Bardi’s narration of events.
According to Bardi, Leibniz was teaching himself higher math when came across the mathematical work of Newton (not yet made public)… In October 1676 Leibniz read some of Newton’s Calculus notes while perusing the papers held by a certain Mister Collin, the librarian of England’s Royal Society. Whether Leibniz would have arrived on his own at his version of Calculus (pretty much the same as Newton’s they tell me) will forever be mere conjecture. From the moment that he saw Newton’s work– whether it helped him or not– he could not “unknow” what he had seen.
Leibniz went on to publish, in Bardi’s words, “the first calculus publication anywhere in the world.” And for decades afterward, Leibniz was acknowledged by most of continental Europe (that cared about such things) as the inventor of “Calculus” (the term Leibniz came up with for the new math; Newton called it Fluxions or some-such).
But as Newton can take much credit, he must also absorb much blame. If he had only allowed his work on Calculus to be published, he would have avoided the whole messy situation.
The Calculus Wars, disappointingly, offers very little concerning HOW Newton and Leibniz produced Calculus. I was very much hoping to get clued-in as to PROCESS of creating a new math.
I’ll have to leave it to other books in The 300 to educate me upon the following fields that I’m still hungry for: 1) a REAL history of the origins of Calculus, 2) a quality overview of the philosophy of Leibniz, 3) some insight into Newton’s alchemy work.