Re: consistent, overdetermined facts

[John Denker <jsd@MONMOUTH.COM>]

At 7:48 PM -0700 8/19/00, I wrote:

> >Science is not serial.  It is a very high-dimensional tangled latticework
> >of facts.  There is no natural ordering of the facts.

At 08:54 AM 8/20/00 -0700, Leigh Palmer wrote:

> this tangled latticework is *self consistent*,

An excellent point.

Not only is the structure consistent, but it is overdetermined -- in a way
that preserves and strengthens the consistency.

Have all of you played with a Hoberman sphere?  If not, I recommend
it.  The thing is like a geodesic sphere, but it leaves one degree of
freedom undetermined over a wide range, so you can increase and decrease
the size of the sphere.

Now imagine adding one strut to a Hoberman sphere.  All the shape
coordinates are now determined, but just barely.  Note that the length of
this strut is arbitrary, over a wide range.

Now imagine a Hoberman sphere with N added struts.  The shape is now
overdetermined.  The length of N-1 of the struts is NON-arbitrary, to
preserve consistency.  If you accidentally lose a few of the struts, you
can reconstruct them exactly;  their length is determined by the remaining
struts via the consistency requirement.

The analogy to science is fairly close:  The struts represent facts.  We
know enough facts to make the overall structure strongly overdetermined in
most places.  That means if you forget a few facts, there are usually a
great number of ways of rederiving those facts.

Occasionally there are corners of science that are underdetermined, like
the unadorned Hoberman sphere.  For instance, before Millikan came along,
people knew the charge-to-mass ratio of the electron, but they didn't know
the charge or the mass.