🚀 go-pugleaf

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).


A lovely counterexample to this is provided by the process of grinding
your own 6" mirror for a Newtonian reflector.  You start out with two
circular pieces of glass, and spend a great many hours walking round
and round grinding them together, checking the mirror's shape
occasionally with a simple optical setup that doesn't require any
high-accuracy components.  When you're done you have a mirror ground to
a highly polished paraboloid, "to within a fraction of a camel's
hair."  None of the tools used need have anything like that accuracy.
(It is true that you ordinarily do the grinding with meticulously
graded grit, but I would think one could do one's own separation
without fancy equipment by dropping what you have a long enough
distance to get the larger particles well below the smaller.  The key
thing is not have any large particles in with a lot of small ones; the
converse is ok.)

Another example is the resistor cloning problem.  Given an unknown
resistance R somewhere between 100 and 10K ohms, a Wheatstone bridge,
and a plentiful supply of 20% resistors of all 20% sizes (1, 1.5, 2.2,
3.3, 4.7, 6.8 between say 100 and 10K ohms), it is possible to clone R
to an accuracy of .1%.  That's 200 times more accurate than the
resistors you get to make it from, without using any equipment honed to
anything like that accuracy.  This is a cute exercise.
-- 
                                       |
Vaughan Pratt                          |                          ttarP nahguaV
Why do mirrors reverse words&not lettersrettel ton&sdrow esrever srorrim od yhW