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Article #661

Re: Measurement & Precision

#661
From: Derek Abbott
Date: Tue, 10 Nov 1992 12:13
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In article <1dck8fINNgie@agate.berkeley.edu> lizi@soda.berkeley.edu (Cosma Shalizi) writes:
>In article <1992Nov2.043143.24298@augean.eleceng.adelaide.edu.AU> dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott) writes:
>>Imagine you are a stone age philosopher. All you have are your big chunky
>>stone tools to work with to engineer with for everyday life.
>>You produce a persuasive argument that it is impossible to ever produce
>>tools, machines and measurements that are accurate to within micrometers
>>(or fractions of a camel's hair).
>>It is obvious to you that your coarse implements can't measure to any greater
>>accuracy than they are already and so engineering to greater precision
>>is philosophically impossible, by simple inductive reasoning.
>>Where is the flaw in his argument?
>   1. Induction is not valid. This has been known for some time. There are
>      many inductive arguments which are rational - the fact that all observed
>      crows have been black _is_ reason to believe that all crows are black -
>      but not valid, the way, "All men are mortal, and Socrates is a man,
>      therefore Socrates is mortal" is valid.
>   2. This is not a philosophical argument but an engineering one. "With our
>      current technology, it is impossible to make things finer than a
>      camel's hair, and we can think of no ways of improving things to get
>      around this limitation." This is a very sound argument. With stone age
>      techniques and science, there is no way to make tools or measurements
>      of the desired accuracy.

Exactly. If you are a stone age man with a measuring stick that is marked
off in certain intervals that are done as "accurately as can be," then it
is very difficult for you to see how to make them any more accurate
(as you would have done it in the first place).

The coarseness of your implements appear to be the absolute limit. The vision
to overcome this limit by use of a leveraging type principle (say) is not
forthcoming.

It is this limitation in mental vision that is interesting, not so much that
it was an engineering example.

>>I'm wondering to what extent we are tricking ourselves with words
>>(like the stone age man example did) today when we grapple with such
>>philosophical mysteries as quantum mechanics, mind-body problem,
>>determinism v. free will etc.

There maybe a concept lacking in our vision that that has yet to be found.



PS. BTW, it would be an interesting to put 5 or 6 scientists/engineers on
a desert island (rich in ores) with the goal of producing a 5um accuracy stepper
motor from stratch. They are allowed any text books they like and we feed them
well, so they can work on it full time.

It would be interesting to see if they could do it within their life time.

Do people think it would necessarily take a number of generations?

Also recording the minimum number of steps it took to "bootstrap" modern
precision out of stone age tools would be a fascinating bit of trivia.
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From: dabbott@augean.eleceng.adelaide.edu.AU (Derek Abbott)
Subject: Re: Measurement & Precision
Message-ID: <1992Nov10.121329.7384@augean.eleceng.adelaide.edu.AU>
Organization: Electrical and Electronic Eng., University of Adelaide
References: <1992Nov2.043143.24298@augean.eleceng.adelaide.edu.AU> <1dck8fINNgie@agate.berkeley.edu>
Date: Tue, 10 Nov 1992 12:13:29 GMT
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