Re: Correctness as a function of the number of hand-inserted parameters?

["Ralph E. Frost" <refrost@dcwi.com>]

Bjorn Wesen <bjorn@sparta.lu.se.NOSPAM> wrote in message
9qd8v6$4tu$1@merkurius.lu.se">news:9qd8v6$4tu$1@merkurius.lu.se...
> Ralph E. Frost wrote in message ...
> >I've been reading about the numbers of hand-inserted parameters in
> different
> >approaches and I am wondering if this count alone is a sufficient
criteria
> >with which to rank competing approaches?
>
>
> No, because the model itself consists degree of freedom.. There are
> infinitely many ways of combining, say, 5 parameters into a prediction of
a
> measurement (drawing on numerous external definitions, of course). The
> "algorithm" and the parameters are not two different things.
>
> So you'd have to add your other criterion:

Yes.  The clarification you add is a important one.    The different
model+parameter count pairs come about as a direct result of how one
initially partitions awareness.   The die is cast in the initial procedural
choice.    I sometimes think of this like that old BBS modem communication
protocol which was likened to a "sliding window" or some other moving frame
imagery. [Obviously, I don't know the details of it but may just barely
remember the concept...Hopefully, if ou are old enough to remember BBS and
modem protocols, you get the picture.]

In any event the frame is like a viewport down into the real data stream,
and if it is configured wrong, made of the wrong stuff,  and/or out of sync,
then  there is going to need to be a LOT of compensating parameters and
"error correction" added to the model (aka, inappropriate frame choice) to
give it a semblance of  "fitting" the datastream.  However, slide the frame
a bit one way or the other and Blammo!  the model fits the data and the
epicycles plus parameter count hits another minimum.   Moreover,
communication becomes easier, not more complicated, and  the improved signal
allows just about anyone to understand the datastream a bit faster and a bit
more completely, sort of. Maybe.

So, the root features of the model are  central.   It's my guess that
primary tenet (assumption) and the choice of symbol drives the entire
shebang and thus is central to minimizing  the assumption+parameter count
value on candidate trial theories.

No place is this distinction more evident and striking than in the current
move from the less unified to the more unified models.    It turns out that
unification is too big of an attribute to be anything but a primary
paradimatic tenet.  So the successful candiates for GUT, quantum gravity, or
unified what-have-you all must begin with the overt primary  tenet: "things
are unified".  Anything less and the model falls into the less unified
category which, in its subconscious roots flows back into the covertly
stated assumption, "things are NOT unified", embedded in the
subjective/objective Cartesian  assumption.

[As an interesting (imo) confirmation of Popper's ideas,  notice that the
emergence of  any more unified model, falsifies  the prior less unified
model.  The beginning of the more unified modeling phase IS the logical
conclusion of the less  (or non-) unified modeling phase as
ominant.  --Also, yes, I am aware you fellows don't like to think this
thought very much.  It can't be helped.--]

>
> >Now let's say both approaches deliver useful units of physical intution,
>
> I don't know exactly what you had in mind here, but something along the
> lines of Occams razor is probably what's needed.

>
> For example, in the standard model where neutrinos are massless and there
is
> a parity violation of right and left-handed weak interactions, you can
> either explicitely write and calculate with a difference in
> state-descriptions for left and right-handed states, or you can
parametrize
> this fact and say that the parameter responsible is zero (I guess, I
haven't
> seen this on paper). In either way, what you really are doing is
> incorporating a known measurement result into your theory, albeit in
> different ways (one which is more difficult to extend should the need
> arise... *cough*).

Sort of like adding an extra Ptolemic epicycle, huh?

What do you do with Occams Razor in the case where neutrinos aren't massless
but are unified and occillatory between more than a couple states?

>
> As another example, in the same way you can have theories where you try to
> explain some numeric property (a parameter) by high-dimensional geometry,
> but you need to choose _that_ geometry to make _that_ parameter come out
> according to experiment. Which is "best" ?

Gee, the approach that works in more cases and holds promise for more
openings in the future -- the one that works, I guess. Which approach would
you opt for, the one that didn't work?   ;-)    Maybe I am missing your
point.
In building the approximation called physics, folks move from trial theory
to trial theory as the approximation is improved.  You are not making an
arguement that Einstein should have or could have ignored Newton's picture
of gravitation, are you?

> I think occams razor, with a keen eye on the complexity of both the model
> and the parameters, would give you your desired metric of theories. I
don't
> know if there is a way to objectively measure the amount of abstraction of
a
> given theory. What you're really doing by making a theory more abstract is
> move some of the theoretic facts into assumptions of the reader instead...

To these criteria, I think one needs to also add in something like a
complexity factor, a comprehensibility index, and perhaps something having
to do with scalability, i.e., fitting as an easy introductory model that
also has the potential to scale, morph and bifurcate off into being more
sophisticated models.

This leading to a draft objective function to minimize akin to:

  assumption count + parameter count + raw symbol count

with qualifiers that relate to complexity index, fraction of local region
modeled easily, (total population  devided by those able to comprehend the
model) factor + minutes of education required to acquire communicable
physical inituition on, heh, heh, selected physical features...


Then one uses Occams Razor for what it is supposed to be used for:
determining which trial theory has the  lower "composite parameter count....


Something along that line?



--
Best regards,
Ralph E. Frost

Need out-of-the-box  front-end alignment on your next design project?

ralph@refrost.com

"...Love one another..." John 15:12