🚀 go-pugleaf

In <1992Oct6.030213.20215@galois.mit.edu> jbaez@riesz.mit.edu (John C. Baez) writes:

>In article <1992Oct5.154211.21663@ecrc.de> micha@ecrc.de writes:
>>In article 24242@access.usask.ca, choy@skorpio.usask.ca (I am a terminator.) writes:
>>>How do you know that the line you draw is really straight? What
>>>defines straightness?
>>
>>This is something I've been wondering about since a long time. Although we can
>>make a circle as precise as we want, I think we cannot make a really
>>precise straight line - every straight line is made from another one or from a tool
>>that has been made using some older straight lines - so it all comes down to
>>copying a line that has been made thousands years ago. Although we have precise
>>instruments and tools, we can only make better and better lines (so that eventually
>>the error is less than an atom, and we are there), but IMHO there is no
>>process to create a straight line directly. Or is it?

>The compass is nice because it works straight from the definition of a
>circle, while a ruler, as you note, is not so nice since it does not
>work from the definition of a straight line as the shortest path between
>two points.  However, there is a machine that has been built which draws
>straight lines "by definition."  Alas, I forget how it works.  Maybe
>someone can remind us or reinvent it.  Of course this is not to say it
>really is better than a good ruler but it is philosophically satisfying.
>I seem to remember that it was built, not for practical reasons, but
>just to show it could be done.  Back in the age of mechanical (as
>opposed to electronic) ingenuity they did this sort of thing.  Some of
>you may know how to built a device which will measure the area of a
>shape if you trace the outline of the shape.  Others may enjoy figuring
>it out.  Nothing electronic allowed!  Big clue: Green's theorem.
>Disclaimer: I would have to figure out the details myself so don't ask....

How about pulling a piece of string taut?  Won't that give a straight line?

Stephen