East meets West and Leibniz

Saipan doesn’t have a monopoly on meshing East with West, so today I’m going to turn a gimlet eye to ye olde Europe for this gig. And here we make the acquaintance of one of the most famous mathematicians in history, a German, Gottfried Wilhelm Leibniz (1646-1716).

Despite his fame in intellectual circles, I don’t think that history has been sufficiently generous to Leibniz. His legacy, at least in broad terms, has been eclipsed by the Englishman Isaac Newton (1642-1727). Well, Newton is one of history’s greatest luminaries, that’s for sure. Newton is the name associated with classic physics, and among other accomplishments, he calculated the orbits of the planets with a surprising degree of accuracy (it took Einstein to refine it), he invented the reflecting telescope, and, not so incidentally, he’s credited with inventing calculus.

Ah, calculus. Inventing it is quite the resume builder. As it turns out, though, Leibniz was developing calculus at the same time that Newton was. So these two geniuses were independently following the same path. As for who got there first, and as for who published what and when, well, that’s a subject for historians to ponder.

As for the calculus itself, I always regarded Leibniz’s form of notation superior to Newton’s, at least for the stuff I did. So I guess I’ve always had a soft spot for Leibniz and felt he was a bit under-appreciated.

He was, in fact, utterly ridiculed in one case. This facet of his legacy endures as a character named Professor Pangloss in a book entitled Candide. Pangloss is an absurd figure in this bitingly dark novel because he’s overly optimistic, saying, even in the most dire of situations, that he and other victims of circumstance were living in the best of all possible worlds. Candide was no one-hit wonder. Though it came out in 1759, it’s still easily avaliable and it’s still being discussed in college coffee houses.

This whole Pangloss thing was rooted in the reaction to some of Leibniz’s writing of the philosophical variety. I’ve never bothered to follow this trail. But I did notice that Leibniz wrote about how nature’s path is, sort of by definition, optimal. Or that’s what I think he was saying.

Here’s the quote: “…It is most clearly understood that among the infinite combinations of possibles and possible series, that one actually exists by which the most of essence or of possibility is brought into existence. And indeed there is always in things a principle of determination which is based on consideration of maximum and minimum, such that the greatest effect is obtained with the least, so to speak, expenditure. ..”

Two things struck me about this. The first thing is that this sounds very much like a mathematician, since math, including calculus, is very much concerned with concepts such as maximum, minimum and optimum. OK, he doesn’t actually say the word “optimum” here, but the term “greatest effect” is close enough.

The second thing that struck me was that this notion seemed very Eastern. Couched in this optimality is the concept of nature taking the path of least resistance, which is to say, the way of highest efficiency, sort of like water smoothly flowing down hill and around obstacles.

Well, as it turns out, Leibniz did, indeed, give some of his attention to the ways of the East. The Web has a photo of what is said to be a document owned by Leibniz, and this document is an array of Chinese characters and symbols rooted in an ancient Chinese work called the I Ching (also called the Yi Jing).

With that in mind, you can probably manage to get a glance at a South Korean flag on Saipan, and, if you do, you’ll notice that arrayed around the center image of the flag are four groups of black lines. Each group is a set of three lines, and each line is either unbroken or broken. These symbols are from the I Ching.

Since the I Ching symbology is comprised of combinations of just two symbols (broken line or unbroken line), it’s essentially a binary system. Binary systems are also what computers run on. Given that the I Ching is something like 3,000 years old, it’s certainly ahead of its time in this regard.

And Leibniz, for his part, was way ahead of his time, too. He’s credited with inventing a conceptual forerunner to the computer, a mechanical “math machine” that could perform multiplication.

Would you like to know another interesting fact about Leibniz? Well, I would, too, but I’ve just told you everything I know about the guy.

So we’ll have to end things here. We’ll conclude with one thought: Leibniz serves as an example of how Eastern and Western thought can come together in seemingly unlikely places.