Angels on the head of a pin

Medieval European philosophers were not after all simple-minded:

“A glib speaker in the Brains Trust once entertained his audience (and reduced the late Charles Williams to helpless rage) by asserting that in the Middle Ages it was a matter of faith to know how many archangels could dance on the point of a needle. I need not say, I hope, that it never was a ‘matter of faith’; it was simply a debating exercise, whose set subject was the nature of angelic substance: were angels material, and if so, did they occupy space? The answer usually adjudged correct is, I believe, that angels are pure intelligences; not material, but limited, so that they may have location in space but not extension. An analogy might be drawn from human thought, which is similarly non-material and similarly limited. Thus, if your thought is concentrated upon one thing–say, the point of a needle–it is located there in the sense that it is not elsewhere; but although it is ‘there,’ it occupies no space there, and there is nothing to prevent an infinite number of different people’s thoughts being concentrated upon the same needle-point at the same time. The proper subject of the argument is thus seen to be the distinction between location and extension in space; the matter on which the argument is exercised happens to be the nature of angels (although, as we have seen, it might equally well have been something else); the practical lesson to be drawn from the argument is not to use words like ‘there’ in a loose and unscientific way, without specifying whether you mean ‘located there’ or ‘occupying space there.'” — The Lost Tools of Learning, by Dorothy Sayers, originally seen here.

It reminds me of the recent astonishing discovery that ninety percent of our genetic material is not after all “junk DNA;” scientists just hadn’t figured out its purpose.

Sayers’ essay has a number of other observations on educating children:

“…even a rudimentary knowledge of Latin cuts down the labor and pains of learning almost any other subject by at least fifty percent.”

That’s certainly true. Latin is also very easy for a native speaker of English, so the payback is pretty high.

Elementary mathematics “…is neither more nor less than the rule of the syllogism in its particular application to number and measurement, and should be taught as such, instead of being, for some, a dark mystery, and, for others, a special revelation, neither illuminating nor illuminated by any other part of knowledge.”

I wish that were more widely appreciated.

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6 Replies to “Angels on the head of a pin”

  1. Some 20 or 25 years ago, I recall having arguments with someone over that “junk”. I said that scientists could not possibly know that it was junk; there were simply too many possibilities for scientists to have ruled them all out. He was quite forceful and insulting about it. I wish I could remember who it was so I could give him a call…

    1. For extra fun, bring up the “humans are 98% genetically the same as apes” thing. The actual claim is that we have 94-ish% of the same genes, and it’s only comparing that 2% where we have the faintest clue what they do.
      Which is build proteins.
      Which is why we’re also 75% the same, in the same odd metric, as some kind of worm.

      Wow! The biological blueprints of two things that are vaguely the same– being mammals with four limbs, etc– look alike, if you kinda glance at the dark lines! /headdesk

      1. So “Man is 99% identical to an ape” should have been “At this point, geneticists can barely distinguish a man from an ape.”

  2. I still remember the shock when I took my logic class for “fun” and started identifying familiar shapes to things… it would’ve made it so much EASIER if I’d had that basic foundation!

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