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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