gaps between the numbers


I had thought that I would use a neat little passage by McLuhan on “zero” for today’s blog. I read it yesterday and liked it. But this morning I got up and continued reading and found that he weirdly attributed the notion of infinity to Gutenberg. He also said that the Greeks and Romans had no idea of infinity. I thought to myself, hey what about Euclidean geometry?

Sure enough a little poking around online showed me that Euclid had ideas of infinity (even if they were a bit qualified).

Wrong, McLuhan. Makes one wonder what other things he was simply mistaken about.

Nevertheless, here is his passage on “zero.”

“Before the advent of ordinal, successive, or positional numbers, rulers had to count large bodies of soldiery by displacement methods. Sometimes they were herded by groups into spaces of approximately known area. The method of having them march in file and of dropping pebbles into containers was another method not unrelated to the abacus and the counting board. Eventually the method of the counting board gave rise to the great discovery of the principle of position in the early centuries of our era. By simply putting 3 and 4 and 2 in position on the board, one after another, it was possible to step  up the speed and potential of calculation fantastically. The discovery of calculation by positional numbers rather than by merely additive numbers led, also, to the discovery of zero. Mere positions for 3 and 2 on the board created ambiguities about whether the number was 32 or 302. The need was to have a sign for the gaps between the numbers. It was not till the thirteenth century that sifr, the Arab word for “gap” or “empty,” was Latinized and added to our culture as “cipher” (ziuphrium) and, finally, became the Italian zero. Zero really  meant a positional gap.”

Marshall McLuhan, Understanding Media: The Extensions of Man

McLuhan is essentially correct about this. He neglects mathematical history in the non-Western civilizations. This probably reflects the ethnocentricity of the time. But still it’s a lucid description of the need for zero in decimal positional numbers.


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