AI and cognitive psychology rant (getting more and more OT - tell me if I should shut up)

[Andrew Dalke]

Me:
> >  (Eg, QCD could be used to
> > model the weather on Jupiter, if only we had a currently almost
> > inconceivably powerful computer.  Running Python.  ;)

GrayGeek:
> Weather (3D fluid dynamics) is chaotic both here on Earth and on Jupiter.
> As Dr. Lorenz established when he tried to model Earth's weather,
prediction
> of future events based on past behavior (deterministic modeling) is not
> possible with chaotic events.

Weather is chaotic, but you misstate the conclusion.  Short term predictions
are possible.  After all, we do make weather predictions based on
simulations, and the "shot in the dark" horizon is getting more distant.
We're even getting reasonable models for hurricane track predictions.
Orbital mechanics for the major planets are also chaotic, it's just that the
time frame for problems well exceeds the life of the sun.  (As I recall;
don't have a reference handy.)

Also, knowledge of history does help.  Chaotic systems are still
subject to energy conservation and other physical laws, so
observations help predict which parts of phase space are accessible.
And if the system is only mildly chaotic (eg, Lyapunov exponent is
small enough) then an observation which is "close enough" to the
current state does help predict some of the future.

> In a chaotic system changing the inputs by even a small fractional
> amount causes wild swings in the output, but for deterministic
> models fractional changes on the input produce predictable outputs.

To be nit-picky, that should be "... amount eventually causes arbitrary
differences in the output .. " (up to the constraints of phase space).
The two values could swing wildly but still track each other for some
time.

> The charge of an Electron is a case in point. Okkam's Razor is the
> justification for adopting unitary charges and disregarding fractional
> charges.   But, who justifies Okkam's Razor?

Quarks have partial charges, and solid state uses partial charges
for things like the fractional Hall effect.

The justification is that without Occam (or Ockham)'s razor
then there is no way to choose between theories with the same
ability to describe observed data.

In a simple case, consider
  x  y
 -----
  1  1
  2  2
  3  3
  4  4
  5  5

This can be modeled with y = x or with the osculating

y = 1*(x-2)*(x-3)*(x-4)*(x-5)/( (1-2)*(1-3)*(1-4)*(1-5) ) +
      2*(x-1)*(x-3)*(x-4)*(x-5)/( (2-1)*(2-3)*(2-4)*(2-5) ) +
      3*(x-1)*(x-2)*(x-4)*(x-5)/( (3-1)*(3-2)*(3-4)*(3-5) ) +
      4*(x-1)*(x-2)*(x-3)*(x-5)/( (4-1)*(4-2)*(4-3)*(4-5) ) +
      5*(x-1)*(x-2)*(x-3)*(x-4)/( (5-1)*(5-2)*(5-3)*(5-4) )

(Hope I got that all correct.  BTW, I remember this as the
an osculating function, because it wobbles back and forth
so much it 'kisses' the actual function.  However, the term
'osculating curve' appears to be something different and the
term 'osculating function' is almost never used.  Pointers? )

Both describe the finite amount of data seen.  Which
do you prefer, and why?


Me:
> > For a simpler case .. what is the center of the universe?  All locations
> > are equally correct.  Is it mystic then that there can be multiple
> > different answers or is simply that the question isn't well defined?

> "All locations are equally correct" depends on your base assumptions about
> the Cosmological Constant, and a few other constants.  Event Stephen
> Hawkings, in "A Brief History of Time" mentions the admixture of philsophy
> in determining the value of A in Einstein's Metric.

I was refering to my earlier statement that I could designate my house
as the center of the universe and still have all my calculations come
out correct.  I somewhat overstepped that when I made the above
statement.

I looked in my copy of ABHoT but didn't see mention of "A".
It's been about a decade since I last looked at Wheeler, and I
never took a GR course, so I don't recognize the term.  Web
searches don't find anything relevant.  (Do you really mean
"a Lorentzian manifold whose Ricci tendor R_(ab) in the
coordinate basis is a constant scalar multiple of the metric
tensor g_(ab)."?  Perhaps you mean the Robertson-Walker
metric, which appears to meet that definition.  But there
doesn't appear to be an A term in the formulations I found.
Perhaps it's the a in the cosmic scale factor of the Friedmann
equation?)

How does the cosmological constant affect things?  I don't
recall that having an implication on isotropy and homogeneity.

In any case, you are refering to the observed large-scale
isotropy and homogeneity of the universe.  There is a bit in
ABHoT on that, but it's pre-COBE, and definitely pre-brane and
the statements of Hawking are more of a "this may explain things
but it's untested."  Then again, that's about the current state of
the art too.  ;)

So it's still pretty safe to say that my house is the center
of the universe.

                    Andrew
                    dalke at dalkescientific.com
P.S.
  When you quote someone else's post, please take care to
trim the paragraphs you are not responding to.  That makes
it easier to find the text you added.