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Re: [Phys-l] status of Occam's razor



On 08/02/2007 11:09 AM, chuck britton wrote:
An Historical Question concerning Occam's Razor -
Devil's Advocate Hat On:

When did the Copernican Theory of our Solar system become as precise
as the Ptolmeic Theory?
Did Newton work out the perturbations required - or am I totally
bonkers in believing someone who claimed that all the cycles and epi-
cycles DID give more precise predictions than did Copernicus (and
Kepler)?


There's an important distinction:
-- lots of parameters, versus
-- too many parameters.


I suppose you've heard the saying:
With four free parameters you can fit an elephant,
and with five you can wiggle his trunk.

That's amusing, but not true.

I once did what was effectively a curve fit with 100,000 independent
adjustable parameters. And it worked. It could make predictions
with 99.4% accuracy. The remaining errors were attributed to intrinsic
noise in the data. Highly skilled humans eyeballing the same data
could only score about 99%. This was a character-recognition task
where you would expect humans to excel.

Lots of parameters is not necessarily bad. If you have enough
training data, you can pin down all the parameter values.


Occam said entities should not be multiplied beyond necessity. He
didn't say (because he didn't know) what constituted "necessity".
Fortunately, there's been a lot of progress in the last 700 years.