Re: World's noise

["John S. Denker" <jsd@MONMOUTH.COM>]

At 05:20 PM 9/8/01 +0300, Muhsin Ogretme wrote:
> [The student] actually was looking for if
> there was such a cause and effect relation.

OK.

> Do you think that all the
> sounds (except the ones created by human activities such as speaking,
> concerts etc.) like the crashing waves on the earth has a symetrical
> relation with the rotation?

I didn't say that, and I didn't mean that.

There are four main possibilities.

Suppose we have a dataset with two columns (A and B) and many rows
(observations).  In this case A might represent the binary proposition "it
rotates" and B might represent the binary proposition "it makes noise".

The four main possibilities are:

1) We might observe that in this dataset A implies B.  That is, the
proposition
        B or not A
is upheld.  A weaker version of this would be to observe a high probability
        P(B|A)

2) We might observe the converse, namely B implies A.

3) We might observe both of the above, in which case there would be a
symmetric relationship between A and B, namely equivalence.  The weaker
version could be called "near equivalence" or "high correlation".

4) Or we might observe none of the above.  We might find that the database
contains so many examples of
        A and B
        A and not B
        not A and B
        not A and not B
that it contradicts any hypothetical nontrivial relationship.

  Weird tangential remark:
  Actually you could define a trivial "uncorrelatedness"
  property if you were desperate.  You could say that A and B
  have the property of being uncorrelated.  But it would be an
  abuse of language to say that they are "related" by this
  property, since the whole point is that they are unrelated.

  This uncorrelatedness property is symmetric, but that
  does NOT make it comparable to the equivalence property.
  An equivalence relation is (by definition) symmetric,
  reflexive, and transitive.  Uncorrelatedness is neither
  reflexive nor transitive.

==========================

Finally:  For reasons discussed at
  http://mailgate.nau.edu/cgi-bin/wa?A2=ind0010&L=phys-l&P=R32554
even if we could discover a nontrivial asymmetric relationship between A
and B (A implies B or vice versa) it would !not! mean that A causes B or
vice versa.

It is easier to prove non-causation than causation.  To prove
        A does not cause B
it suffices to exhibit examples of A without B.

In the case of ordinary household rotating objects, A (rotation) is always
associated with B (big noise), so the student's hypothesis, while not
proved, is not disproved either.  It remains a viable hypothesis.  Call it X:
        X = "world's rotation implies big noise"
which is the Boolean equation
        X = Conjunction(over all rows) B or not A

So the next step is to look at the physics.  A household object such as a
spinning wheel makes noise because the bearings are imperfect, and/or
because the spokes stir up the surrounding air.

If we now shift our attention to solid objects rotating in empty space, we
find that we must totally re-examine the physics.  Such objects have no
bearings, and they have no surrounding air to be stirred up.  So
proposition X receives no support whatsoever from the analogy to household
objects.

At this point, hypothesis X is not disproved.  But it is so lacking in
support that the opposite hypothesis is becoming plausible and must be
considered, namely the hypothesis that
        X is false.
In other words, let us shift focus to proving proposition Y
        Y = not(X)
        Y = not(for all rows, B or not A)       ## definition of X
        Y = for some row, (not B) and (A)       ## by DeMorgan's theorem
        Y means "there exists an object that rotates while
                making no big noise"
If we can prove Y, we have rigorously disproved X.

Because statement Y is a disjunction (unlike X which was a conjunction),
all we need to prove Y is to find an example of Y.  The example is easy
enough to find:  Consider a solid object (large or small) spinning all
alone somewhere in empty space.  By a simple change of coordinates we can
calculate the forces on every subpart of the object.  In the rotating frame
we find that the forces are not time-dependent.  You can't generate noise
without having some sort of time dependence.  If there's no noise generated
in the rotating frame, there's no noise generated in any frame.

We conclude that things make noise if they spin WHILE IN CONTACT with
something else (specifically, something that is not spinning at the same
rate on the same axis).  There is absolutely no reason (theoretical or
experimental) to believe that spinning is the important idea, and there is
every reason to believe that the following are important ideas:
 -- Contact while in relative motion generates noise.  This applies to
household object but not planets (not usually, not primarily or directly).
 -- Solar heating of the bottom of the atmosphere generates instabilities
that make wind, which in turn makes noise.  Rotation changes the details,
but the main instability would be there even without rotation.  There is
every reason to believe that the sun, not the rotation, is the primary
causative factor.