10 May 2007

Derbyshire & Clifford

I've recently been reading a book by John Derbyshire on the history of algebra, called "Unknown Quantity." It's a follow-up of sorts to his book on the still unproven (and unfalsified) Riemann Conjecture concerning prime numbers, which I believe I mentioned earlier in this blog.

Anyway, in the more recent Derbyshire book, I came across a brief passage about the 19th century English mathematician William Kingdon Clifford.

Clifford is an important name for those of us who admire William James. Not for his mathematical accomplishments (which are undoubted) but for his venture into philosophy (which was unfortunate). It was Clifford who wrote that it is our general duty to our species to guard our minds from unproven beliefs, even if they should happen to be true. Believing something on insufficient evidence is like accepting into one's body "a pestilence which may shortly master our own body and then spread to the rest of the town."

James thought this simply ridiculous, with "too much of robustious pathos in the voice" as he said, and it inspired him to write the famous/notorious essay "The Will to Believe."

But Derbyshire's passage doesn't mention any of that. He's interested in Clifford as a mathematician, one responsible for generalizing "Hamilton's quaternions into a whole family of n-dimensional algebras."

I won't explain here what that means, what Hamilton's quarternions are. It is fully discussed in the context of the book. I was simply impressed by this example of what seems to have been a general 19th century truth. One could still get a reputatiuon as a considerable philosopher without any academic credentials in the field, but one did have to have academic credentials in some field.

Clifford earned his bones in math, as James did in psychology.

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Knowledge is warranted belief -- it is the body of belief that we build up because, while living in this world, we've developed good reasons for believing it. What we know, then, is what works -- and it is, necessarily, what has worked for us, each of us individually, as a first approximation. For my other blog, on the struggles for control in the corporate suites, see www.proxypartisans.blogspot.com.