“Symmetrical equations are good in their place, but ‘vector’ is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.”
Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis : The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120
The above quote has been bugging me recently. I know that number theory, for example, was seen as gloriously useless until modern encryption techniques were invented, but vectors are used in Newtonian physics. The simple case of a force acting in Euclidian space can be expressed as a vector with great economy of expression. Moreover, Maxwell used vectors in his famous equations (which lead directly to Einstein’s infinitely more famous work), work published well within Lord Kelvin’s lifetime.
Vectors are just as utilitarian as the differential calculus. What lead Lord Kelvin to say something so obviously at odds with reality?
I don’t know, but just judging from the quote, it would seem as though perhaps Lord Kelvin carried to vectors whatever baggage and prejudices he had acquired from his exposure to quaternions, whose uses are perhaps not nearly so apparent.
Not an answer to your question, unfortunately, but I can tell you that Maxwell did not use vectors when he first published electromagnetic theory. It was Oliver Heaviside who first wrote the four Maxwell equations as a group and in that notation, in 1884.
Yes, that’s still before Kelvin wrote that letter. If I had to hazard a guess, I’d say that physicists can be old-fashioned just like any other profession, and Kelvin may have believed that they way he had always done it was better because it had always worked.
IANAHOS (I am not a historian of science), but googling pulls up a couple more books that discuss Kelvin’s problem with vectors. For example, from “Degrees Kelvin” by David Lindley (via Google books):
‘Thomson [Lord Kelvin] disliked both quaternions and vectors, mainly for the same reason: To him they obscured rather than illuminated physics. He referred to “Heaviside’s nihilism,” and this opinion extended to the philosophy of the Maxwellians in general. He thought they embraced a kind of mathematical formalism that distanced itself further from true physics the more formal it became. He hankered still after mechanical models of the ether, as he had in Baltimore.’
(There’s a good deal more, but I don’t want to steal too much.) The suggestion is that he disliked the increasing mathematical formalism that vectors represented, taking physics away from the mechanical understanding he much preferred. Even though they simplified the math, over his use of Cartesian coordinates, he refused to use them.
What is meant by a “mechanical understanding”? Aren’t Cartesian coordinates also, and even moreso, a kind of extraphysical mathematical formalism? Nature has no preferred bases.
(Not an attack on your explanation; just wondering what Kelvin was thinking, exactly)
Again, just from a brief reading of a couple of pages from that book (starting on p. 273): It sounds like the argument over the mathematics was a proxy for a fundamental disagreement over the direction physics was taking, away from a more concrete, mechanical approach toward a more formal, mathematical one. This also seems to be tied up with questions about the nature of electromagnetics and the ether. (Of course, we now know that both sides were wrong about the latter.)
But now we’ve about reached the end of my understanding of the matter.
Fascinating; I would say that it’s vectors that get closer to the true physics, and that it’s a system of Cartesian coordinates that obscures it. When I’m looking at an actual phenomenon, the Universe doesn’t draw it on graph paper for me, and if I choose to put it on graph paper myself, it doesn’t matter how I orient the paper.
Really, though, Kelvin said a lot of things that were foolishly shortsighted or otherwise boneheaded. Coming from him, another such example really doesn’t surprise me.
Yeah, that’s what I was trying to say above, and part of what was confusing me about Kelvin’s views. From Topologist’s book link, though, I found a passage which somewhat satisfies my curiosity:
“That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.”
— Isaac Newton
We live in the Universe but none of us, not even the ones who have the mental tools, ever seem to understand it fully. Both Newton and Lord Kelvin refused to let go of their intuition and common sense, even when the physical universe was proving them wrong.
Interestingly enough, by coincidence, I had come across that Newton quote at the start of today’s morning, and had a very similar thought in response as you.