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Turing on intelligence versus accuracy

2007-11-12 17:40:14.841104+00 by Dan Lyke 4 comments

Yet another Alan Turing[Wiki] quote, from Alan Turing: The Enigma[Wiki], by Andrew Hodges[Wiki], p378:

It is related that the infant Gauss was asked at school to do the addition 15 + 18 + 21 + ... + 54 (or something of the kind) and that he immediately wrote down 483, presumably having calculated it as (15+54)(54-12)/2.3 ... One can ... imagine a situation where the children were given a number of additiuons to do, of which the first 5 were all arithmetic progressions, but the 6th was say 23+34+45+...+100+112+122...+199. Gauss might have given the answer to this as if it were an arithmetic progression, not having noticed that the 9th term was 112 instead of 111. This would be a definite mistake, which the less intelligent children would not have been likely to make.

[ related topics: Children and growing up Mathematics Education ]

comments in ascending chronological order (reverse):

#Comment Re: made: 2007-11-12 18:39:33.116245+00 by: ebradway

That might be better stated as "intelligence vs. precision"

One of the "problems", in my mind, with the way math is taught is that rote methods for generating precision (getting exactly the "right" answer) is rewarded, while intuitive methods for quickly reaching accurate, but not necessarily precise, (like not showing intermediate steps) is punished.

What's funny is once one gets far enough into Physics and Engineering, "precision" becomes a relative concept (i.e., maintaining the same number of digits in the mantissa).

And in Math, once you hit infinite series, you start having to operate on values that can't be precisely calculated. So you use things like the Squeeze Theorem (function f is always less than g and more than h, therefore if we can know g and h, we can limit the bounds of f and if g and h approach some value as we let their domain approach infinity, we know that f also approaches that same value - the stuff that Gauss actually did...)

#Comment Re: made: 2007-11-12 21:50:39.884157+00 by: jeff [edit history]

Heuristics, by definition, are never guaranteed to be exactly precise?

#Comment Re: made: 2007-11-13 03:40:18.59354+00 by: meuon

Heck, I'm trying to figure out how the less intelligent people even survive. I keep think we, as a society, have done too good of a job making it had to fail, starve and drop out of the gene pool.

Oh, did I say that out loud? Oh well.

#Comment Re: made: 2007-11-14 16:02:39.336712+00 by: petronius [edit history]

Its interesting that many of our technologies have made mental math unnecessary. Does anybody use logarithms any more? The secret of the slide rule was that you had to keep the decimal places straight in your own head. When I was in 8th grade there were newspaper stories about Trachtenburg Speed Airithmatic, which I never quite picked up, being a real math dummy. Does anybody do serious long number addition or multiplication mentally anymore?

On the other hand, I would love to own a Curta.