Re: Razor and Anti-Razor

--- In cybalist@yahoogroups.com, Jens Elmegård Rasmussen <jer@...>
wrote:

> --- In cybalist@yahoogroups.com, "tgpedersen" <tgpedersen@...>
> wrote:
> >
> >
> > Popper (I forgot where) has a similar proposal: When having to
> choose
> > between two equally falsifiable theories, take the simplest one.
> He
> > does not propose a metric for measuring simplicity,

except "number

> of
> > symbols in the written representation of the theory" (this is not
> a
> > direct quote, but a rendition). Actually (I think) this points in
> the
> > direction why such a rule is necessary: Representability. The
> shorter
> > a rule is, the easier it is to represent, also (and especially)

in

> > your head. Panini (I've only seen one or two of his rules) or any
> > other grammarian in pre-literary times must have faced the same
> > problem: how to describe the whole grammar of a language as
> > succinctly as possible.
>
> Well, would anybody use that rule in a court of law? If you have

two

> possible killers, both claiming the other guy did it, would you
> seriously recommend that the one whose story whitewashing himself

is

> longer than that of the other guy be regarded as the guilty one and
> sentenced? Even worse: If they invent a third person, and A blames
> it on "some man", while B gives a detailed description of the
> supposed man C including his car and his gun, would you then feel
> entitled to conclude that, since the difference in their accounts
> shows that they are not both telling the truth, B must be sentenced
> because his story is longer?
>
> In this travesty, anyone can see that this is no valid way to get

at

> the truth. How then can it be good scholarly practice?
>
> In reality the principle (Occam's Razor) holds only for statistics:
> If we have a thousand problems and a million suggestions for their
> solutions, we are pretty sure to make fewer errors if we
> consistently choose thee simplest solution to them all than if we
> consistently choose a more complex solution. But we make even fewer
> mistakes of course if we investigate the particulars and discard
> suggestions that do not fit the additional observations we can

make.

> The last part has been crucial in the somewhat undignified debate

we

> have had on the list: A simple solution should not be agreed upon
> until there are no more particulars to be taken stock of. Am I the
> only one who can see this?
>

I think it's obvious too.

But note that in the absence of other evidence, we are inclined to
believe the guy with the simplest story.

I came to this line of reasoning since as a computer scientist I was
involved in several Artificial Intelligence programs in the eighties.
Representation of knowledge is important here. Example: to compute
the first derivative of cos x, you use either the symbolic
representation, in this case -sin x, or compute it by some iterative
approximate solution. Both will give you the right result, but using
(and storing the representation of!) the first one gives you insight
too which you wouldn't get using a numerical approximation. Besides,
it will shrink your storage requirement plenty much.

You might say that monotheism is the result of using mr. O's rule on
religion (understood as a theory-of-the-world); the result of using
the resulting theory is often right, sometimes fatally wrong, but
it's damned effective, and it doesn't require much intellectual
maintenance.

Torsten