Re: PI random? Debate running in circles (you try making math jokes)


Martin Winer wrote:
All of mathematics seems to progress according to an "assumed"
underlying bedrock of determinism somehow. It seems that randomness is
a kind of oddity which does not really fit in smoothly anywhere because
it's like mixing oil and water. Disorder and determinism just dont seem
to mix.

I think that this pessimism has thwarted the imaginations of those who
probably should have formalized this area 70 years ago.

Ok, but particles and waves are seemingly completely different things,
but when wave particle duality was introduced, physicists were quick to
embrace it. This is perhaps because physics rests on coming up with
working (tenable) theories whereas mathematics rests on coming up with
formalized theories. Physicists are sort of gunslinger mathematicians,
quick on the draw.


Yeah - the gunslingers are having a hard time with whichway
information. They cant quite figure out how such a simplistic thing
would make perfect sense. They have no explanation of it, even when you
present them with one they prefer to stay confused.

I think that they use confusion like a cheap drug because it wont show
up on a urinalysis test. Many of them appear quite addicted to it.


Here's an interesting theory for you. Suppose we have a pattern
recognizing box. This machine is the most robust, fastest possible
pattern recognizing box imaginable (even possible). Suppose too that
at the beginning of the universe quantum mechanics was NOT random at
all. Finally suppose that quantum mechanics is subject to a
recursively self complicating pattern generation, such as the primes.
(See Pat(n) at http://www.rankyouragent.com/primes/primes.htm for more)
Here's the cool part, anyone with such a box who was also present at
the beginning of the universe, would be able to know the entire fate of
the universe for all time because their box would always be able to
answer the question... what happens next. However for anyone who
developed such a box after the beginning of the universe, they would
never be able to answer absolutely what happens next because their
pattern recognizing box could never 'catch up' with algorithm
generating the complexity of quanta.

Thus, the bedrock of determinism mathematics rests upon is intact and
in effect in our universe. However, our ability to see this
determinism is blocked due to the fact that we came along after the
ball started rolling -- we can't catch up.


Here I disagree. The universe cannot be considered completely
deterministic, nor can mathematics. The indeterminacy which you
described so well below proves this, a * 0 = 0.

Physicists know that indeterminacy exists in the quantum realm, but
they cannot understand why the universe dosent simply "fly apart".
After all, if the fundamental components behave randomly, then so
should larger things.

But there is order in this universe, because the disorder is confined
to the quantum scale - it is the result of an existential boundary
condition. Extreme differences in scale confine the disorder and keep
it in it's place.





But we DO know how to create genuine indeterminacy,
by trying to solve for a where a * 0 = 0 .

This is genuine indeterminacy. Why are they not teaching this ?

They do teach this. I distinctly remember my Grade 11 math teacher
drawing the following on the board.

a*b=0; b!=0, a=0
a*0=1, a is undefined
a*0=0, a is indeterminate


So, we know how to construct indeterminacy analytically !!! Do you know
what this means for understanding randomness ?

I seem to remember hearing someone say that as well - but it seems that
there is a huge chunk of math which should be present, but it is
mysteriously absent.

I'd like to hear what Chaitin or Wolfram have to say about it. We know
that this is a genuine example of indeterminacy - and obviously it must
have some bearing on randomness.

I think it's absolutely fascinating.


Suppose you have something like

a * t_1 = t_2

If t_1 and t_1 both get "very close" to zero, can this equation become
similar to a * 0 = 0 ? This might allow a to become nearly
indeterminate.

Of course, a is a constant, but you could easily sibstitute another
variable for a such as t_3, or y_n or something, and this might explain
why certain maps seem to mimic randomness.

I feel like slapping myself in the face to make sure I'm not dreaming
or something - never in my wildest dreams did I suspect that it might
make any sense to see how randomness and indeterminacy would make sense
analytically.

Well - these are just hunches and speculations.

It would be REALLY interesting to devise some experiments or run some
simulations to play around with it.

.

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