🚀 go-pugleaf

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.

>>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.

>   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.

	Induction IS valid, it is the basis of all science.  It just
isn't LOGICALLY valid (i.e. an inductive argument is not a logical
proof).  Just to further complicate matters, a 'proof by induction'
is the name of an argument which is not inductive, and which is
logically valid.

>   2. This is not a philosophical argument but an engineering one.

	Yep.
	For instance, a lathe (consisting of two fixed centers)
can spin its workpiece about a line which is as perfect as the
flexing of the support of the centers allows: there is NOTHING
to limit the circularity of work on the lathe that relates in
any way to the 'accuracy' of the centers.

	To take a second example, one can run two wheels on 
parallel axes and make a centerless grinding rig; such machinery
produces (routinely) hardened steel rods with .0001" accuracy,
from grinding wheels which are considerably coarser than the
accuracy to be attained (again, it is the rigidity of the
centers that matters most).

	The caveman's measuring tools include flakes of stone
with sharp edges (obsidian knives are VERY nice tools in 
many respects), with which accurate marking onto a scale
is possible; the limit of caveman measurement accuracy is just
about the limit of his visual ability to see differences,
and I'm sure he could achieve hundredth-of-an-inch 
comparisons.

	Lastly, it is possible to scale down a machine by
pantograph-like methods: a large accurate screw can be used
thus to make a small, even-more-accurate screw... and
thus one can bootstrap from crude mechanisms to more accurate
ones.  Getting back to the larger scale is just a matter of 
stacking the small, accurate devices atop each other, like
Johansson blocks.

	John Whitmore