Re: Predictions from Mathematical models

From: Mark Fergerson (nunya_at_biz.ness)
Date: 02/04/05 

Date: Fri, 04 Feb 2005 11:51:57 -0700

Mike Helland wrote:
> Mark Fergerson wrote:
>
>> Mike Helland wrote:
>>
>> < BTW, I got a new computer (and changed browser/newsreader) so I
>> lost track of the "To what do the laws of physics apply?" thread.
>> Any new thoughts on that?>

> Ah, indeed. The ball is still in my court wrt that thread. I'll
> revisit it.

   OK. I occasionally get sidetracked too.

>>> 2. Today, our mathematical models are relationships between
>>> values that represent measurement outcomes
>>
>> What else is there?

> There is what I've been trying to communicate to you for a while now
> :-)
>
> Leibniz, Zuse, Fredkin, they have all suggested something different
> from the above.
>
> Unfortunately, these are very very poorly understood, presumably
> because they are such radical departures from what you've been
> taught.

   Well, when we measure things we have to parse them in some way that
allows them to be compared so that we may see if they actually have any
relationship to each other, and mathematics has shown itself to be a
dandy tool for that especially as it allows us to predict the outcomes
of as-yet-unperformed measurements. What alternative tool set do they
offer? What utility has it been shown to have?

>>> 4. There is nothing about physics, or the scientific method, that
>>> says this is the one and only way of deriving predictions from
>>> mathematical models.
>>
>> Fine so far, except mathematical models must be based on
>> observations of physical systems. One makes observations and _then_
>> selects a mathematical formalism that fits the observations, then
>> looks to see if the mathematical formalism can predict
>> not-yet-observed properties of the actual physical system. One does
>> that by working the equations out farther than was used to parse
>> the original data.

> How can you say that premise 4. is "fine so far", and then say "one
> does that by working the equations"?

   Because we accept the validity of the formalism we used to parse the
original data. If we didn't, we wouldn't have used it in the first
place. Only by continuing to use it can we get it to make predictions
with which to _check_ its validity. Otherwise, you can't get from
hypothesis to theory (if it proves valid), or alternatively realize you
need a different formalism (if it doesn't).

> You either except that equations (relationships between observable
> magnitudes) are the *only* way to derive predictions, or you do not.

   You specified mathematical models. How else to derive predictions from
them than by working out the equations you selected to represent the
original relationships as far as possible to see what they say about
other possible arrangements of the original observables? It is indeed
the only sensible course to keep using a formalism that's already proven
its worth. Why change horses midstream when you don't know if the second
horse can swim or carry your weight?

> Which is it? And if you think equations are the only way, what sort
> of argument can you provide to support that opinion?

   You specified mathematical models. If you want some other kind of
relationship between observables, you need some other kind of formalism.

> I would agree that "tradition" certainly suggests that this has
> worked in the past, but inductive logic is not a response to critical
> inquirey.

   "Tradition" is irrelevant. Why change tool sets in the middle of the
process?

>>> What do I mean by that? Say you have some modeled electrons and
>>> protons and you arrange them into a mercury thermometer.
>>
>>> ___oo__oo___ooo ___oo__oo ___oo__oo___oo ___oo__oo ___oo++oo___o
>>> __oo++++oo __oo++++oo ___oooooo
>>
>> This is extremely unclear.

> It is supposed to be a thermometer, the "o" represents molecules
> making up the glass, and the "+" is the mercury.

   Ah, got it.

> In this simulation of particle physics, all the numeric values in the
> model represent properties of particles.
>
> The prediction here is that the temperature is "1 degree" of whatever
> the unit for the thermometer is (1 because the mercury is at the
> single "o" marker, if it had been at "oo" then the prediction would
> be 2).
>
> But the value "1" does not exist as a numeric value in the model. It
> is something that must be derived through analysis of the values. Not
> simply looked at and reported.

   Do you make all that serious a distinction between an explicit
prediction and an implicit one?

   Do you consider the fact that the Pythagorean Theorem is implicit, not
explicit in Euclidean geometry (Euclid had to prove it) to be evidence
that Euclid does not predict the Pythagorean theorem?

   You snipped an awful ot, like my noticing that your (extremely briefly
mentioned) model didn't mention anything about the properties of the
particles involved, or how you derived the concept of temperature, and
its possible limits. These factors would have allowed it to predict all
sorts of temperature values _implicitly_.

   You seem to be talking about an alternative to the scientific method
so powerful that it can state everything outright, not predict it. It's
gonna take a while to write down...

>>> Essentially, physics today describes a world of measurement
>>> outcomes.
>
>> What else is there?

> There is this:

>>> My new application for mathematical models describes a world
>>> where measurement takes place. I think it is more suited for
>>> quantum and relativistic behavior than the technique Newton
>>> established.
>>
>> What does this mean?

> It is so different from what you know, that you will not understand
> it unless you committ yourself to understanding it.

   Please don't try the old "you're blinded by the science conspiracy"
line on me. Either your stuff is compelling on its own, or it's not.

> If you are ready, you will read this web page several times, and get
> back to me with any specific questions:
>
> http://www.techmocracy.net/science/time.htm

   It isn't compelling on its own, and I have all sorts of problems with
the current scientific methodology. Your programming parallel to some
"new kind of physics" borrows so very many assumptions from the
scientific method that I can't list them all or my newsreader would puke
from overflow. Also, I do not see your Platonic "absolute space and
time" as anything new, rather something long discarded.

   Mark L. Fergerson

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