by iampunha | 7/01/2008 08:00:00 AM
There are 10 kinds of people in the world: those who know about the subject of Today in History and those who do not.

In teaching the history of calculus, including this man is integral, especially if you don't want to believe the old lie, published and pushed by Isaac Newton, that he and he alone is the father of the study.

If you want to study the history of evolutionary thought, you start not with Darwin but with 17th century thinkers like this man.

If you want to get to the core of the Earth's composition, read what this man proposed about it.

If you fancy the idea of a universal language based not on artificial, invented symbols but how people naturally conceive of things, such that language barriers are no longer formidable, check out his characteristica universalis.

I could go on much longer, but there is not time to fully catalog the plenitude of scholarly contributions made by Gottfried Leibniz, who was born on July 1, 1646.

When plf515 suggested in my visionary scientists diary that I make July 1's entry about Gottfried Leibniz, I thought, "OK, good idea. I've been doing a number of biologists and chemists, so a mathematician should be a nice break."

Well, that's one view -- that Leibniz was only a mathematician.

It's also a view that ignores a massive amount of Leibniz's work and subsequent scholarship on the man.

It is hard to find a nonspecialized field (i.e. particle physics instead of physics as a whole) that lacks Leibniz's fingerprints or name.

It is equally hard, given our separation from the 17th century and its academic culture, to understand and explain why today Leibniz is not celebrated with Gutenberg (who didn't invent the printing press), Shakespeare (who didn't dream up his plots on his own), Einstein (who wasn't the first to the relativity scene) and Edison (who was a far better businessman than scientist).

In my writing for this series, I have never tried to get the whole story, which I believe philosophically can never be told and which financially is simply not pursuable for a daily series like this written by someone with at best a rudimentary history education. (95 percent of what I have written on my Today in History subjects was not native knowledge.)

I mention this because in the case of Leibniz, attempting to get the whole story really is pointless. We don't even have a complete list of his writings, let alone anything approaching a full critical appreciation of the body of his work.

So instead, today's honoree is presented in a series of (sometimes faint) snapshots and the full and free admission that there is a hell of a lot more out there than I can access, understand and relay to you in the time I have reserved for this research.

Calculus and its notation
Do you like calculus, kids? If you've ever bothered with the subject (which is actually not that hard if you approach it with a nondefeatist attitude), you've used Leibniz's notation:

The Royal Society of London elected Leibniz a fellow in 1673. He studied mathematics and physics under Huygens, and read works by Pascal, Fabri, Gregory, Saint-Vincent, Descartes and Sluze. He began to study the geometry of infinitesimals. It was during this period in Paris that Leibniz developed the basic features of his version of the calculus. In 1673, he was still struggling to develop a good notation for his calculus and his first calculations were clumsy. In 1675, he wrote a manuscript using the integral notation for the first time. In the same manuscript the product rule for differentiation is given. By 1676 Leibniz had discovered the familiar power rule for both integral and fractional exponents.

At my sister's wedding, which some of you may have read about, some of the members of the bridal party (full of really hot geeks) took it upon themselves to write a calculus expression behind the couple's car.

In English, it was "the limit, from -heart to heart, of heart times the derivative of heart." They'd meant the solution to be heart^infinity, but it ended up being 2heart. (Either works, really.)

I did not tell them they were using symbols Leibniz had invented. (At that point, after 15 hours of wedding stuff, I was happy I could walk.)

(Many people are under the utterly incomplete, if not utterly misguided, Newton-born notion that Sir Isaac Newton invented calculus. While we will never know who had the first calculitic thought, that Newton stacked the deck with his supporters and himself wrote the "Newton got it first" decision lends itself, in my view, to the idea that Leibniz got there first and Newton understood the importance of stealing his contemporary's thunder. At any rate, we still use Leibniz's symbols, and whoever discovered the methods we use, ... we still use them.)


Do ya like computers, kids?

So did Leibniz:

Binary arithmetics based on the dual system he invented around 1679, and published in 1701. This became the basis of virtually all modern computers.

I think it's more accurate to say Leibniz exploded binary's use (the discovery, rather than the invention, was not his, as some sources have erroneously claimed, but perhaps that of Francis Bacon) than that he worked with a new way of counting all his own, but either way, every indication we have is that binary passed through Leibniz and grew up a ton. And our Boolean searches were born of that growth.

And here is a picture of some of the history behind the discovery (translation mine, not babelfish's):

[...] for example, that 111 or 7 is the sum of 4, of 2 and of 1. And that 1101 or 13 is the sum of 8, 4 and 1.

This expression of numbers being established, it is useful to do very easily all types of operations.

Do you like evolution, kids? Leibniz was thinking about it back in the day:

[Voltaire] proposed that although there were no living species to fill these gaps [in growth between the species], such gaps were real, perhaps caused by the extinction of species. In this respect Voltaire essentially echoed the thoughts of the philosophers Descartes (1596-1650) and Leibniz (1646-1716). Leibniz had even proposed evolutionary changes to account for these gaps, suggesting that many species had become extinct, others had become transformed, and different species that presently share common features may at one time have been a single race.

300 years later, some people are still struggling with this pretty basic thought: Stuff changes.

Do you like geology, kids? Leibniz thought our core was molten:

Leibniz proposed that the Earth cooled from an initially molten state and that the deep interior remained molten, a relic of its formation.

There's more. A lot more. This is a sampling of Leibniz's reach ... just in calculus. This gets into nothing of his philosophy (optimism, among other things), none of his universal/natural language, none of the many other things he worked on in his extremely prolific life.

And what is even more amazing is that I can find out about so much of this because not only did Leibniz have tons of ideas, so many of them worked. This computer is using binary like it's going out of style. Leibniz's legacy is self-perpetuating. In a way (and obviously not using the term in its traditional sense), Leibniz can be said to have invented his own makeshift perpetual machine.