Isaac Newton, Progress, and Patents

In my physics recitation class today, our recitation leader briefly digressed from the material at hand to discuss the history of differential calculus and the conflict between Isaac Newton and Gottfried Leibniz. Basically, Newton claimed to have invented differential calculus first (although, as with any other "invention", neither can truly claim to have invented calculus from scratch as they were building on the work of mathematicians before them (and I don't just mean 1 + 1 = 2 — I mean things like infinite series and tangent lines)), but as he kept his work secret for decades, he ended up publishing his work on calculus after Leibniz published his work. While both were initially on good terms, as Newton became more possessive of his own work and convinced of his own originality, the debate became progressively more heated, with Newton and his supporters accusing Leibniz of plagiarism. Follow the jump to read more.

So what does this have to do with progress and patents? (First of all, Newton couldn't possibly have patented his work, as copyrights and patents didn't exist before 1710; he would have had to have settled for a royal monopoly as a friend of the royal court, or something like that, I guess.) My teacher said (and this all can be verified by a quick search online) that England was very sympathetic to its countryman's arguments (after all, Newton was the first Lucasian Professor of Mathematics in Cambridge University and had other friends in high places), so it essentially banned the teaching of calculus in any other way but Newton's. Newton's notation for derivatives was a dot on top of the variable in question. Leibniz's notation was "d/d[independent variable]" of the dependent variable (e.g. "dy/dx" as opposed to "y" with a dot on top). Newton was primarily interested in calculus's applications to physics, hence the dot notation; Leibniz was more focused on expanding abstract math and geometry, so his notation more accurately conveyed the concept of dividing an infinitesimally small change in the dependent variable by a similarly small change in the dependent variable. The latter also ended up being easier to manipulate, as it could be manipulated like a regular fraction; Newton's dot notation was less intuitive in its manipulation. So what does this mean for mathematical progress? Leibniz's notation in continental Europe become much more widespread as it was more intuitive, easier to work with, and had a wider range of applications than Newton's notation; this allowed mathematics to flourish in continental Europe. On the other hand, as England had banned the teaching of calculus in any way other than Newton's way, mathematics remained stagnant in England until the government lifted the ban and allowed for Leibniz's notation to be taught. This is essentially the same thing that happens with patents: although the inventor reaps some rewards in the short-run (for Newton, this meant countrywide fame and lots of money), the forced lack of competition means the field simply cannot develop further than what the original inventor wants, leaving society as a whole worse-off.
What do you think? Feel free to leave comments below.

On a side note, my reviews of Sabayon 5.4 KDE and wattOS R2 have been included in DistroWatch's feed of new reviews, and my Sabayon review has even made it to its DistroWatch page! SWEET!

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