Re: Why the cards must have a memory
- From: Lute <lutelatner@xxxxxxx>
- Date: Fri, 18 Jan 2008 06:26:24 -0800 (PST)
Good question. At least you are thinking through the issue, not
throwing the blanket of assumption over it.
If infinity is endlessness, then you never cross the line from finity
to infinity.
However, physical reality so far as we know, is finite.
Probability assumes infinity, and therefore, the laws of probability
as they apply to a finite universe, but one which is unimaginably
large, might only mimic the theoretical.
In such a case, we must question whether, in a finite universe, there
can be true randomness, or only pseudorandomness.
Einstein himself never accepted the idea of true randomness. His view
on that never prevailed, as quantum physics is predicated on true
randomness in nature. However, Einstein may yet be proved correct.
True randomness leads to the possibility of truly absurd outcomes.
And while a line of reasoning might validly lead us to conclude chaos,
such conclusions have no practical value. One can prepare for limited
uncertainty, but not for limitless uncertainty.
On Jan 17, 5:35 pm, "WuzYoungOnceToo" <WuzYoungOnce...@xxxxxxxxx>
wrote:
On Jan 17 2008 2:02 PM, Lute wrote:
In my earlier post, I was careful to ask people to set aside their
large-universe bias when considering what I said. Few, if any of you,
did so. Indeed, the conventional bias was so immense, that I doubt
that any of you really differentiated between what I WAS saying, and
what I was NOT.
Part of it was my fault. To be honest, the cards don't literally have
a memory. That was just a symbolic intro to the underlying
assumptions of probability. My bad.
I simply said that probabilty theory assumes--- and this is a defining
assumption--- that if you flip a coin (truly randomly), it MUST come
up heads, half the time. Otherwise, you are not defining fifty
percent.
The smartest rebuttal I got was this:
***No. It doesn't.
***it assumes that the probability is heads half the time FROM NOW
ON.
***So, being probable at p<1 it is possible that it won't be 50% over
any span you might name.
Now that is a true statement, but it is somewhat misleading. Let us
see why:
The definition of the probability of fifty percent is axiomatic. If
you define fifty percent as anything else, you have contradicted your
initial terms. If fifty percent is NOT fifty percent, then you have a
pointless paradox.
Probability theory also assumes an infinite number of incidents (an
incident in this case being a coin toss).
But the assumption of infinite instances is, at least in the context
of our known universe, false. As presently understood, the universe
is finite, closed, and unbounded. That understanding is already being
seriously challenged (see M-theory), but for the moment, it is
workable.
Therefore, in any universe, where the laws of probability are in
effect, whether infinite or finite, probability assumes that if X has
a fifty percent likelihood, it WILL indeed occur fifty percent of the
time.
Again, this is a statement of definition.
Why is this important? Because according to those who believe that
literally anything is possible, it is literally possible for universes
to exist (if there are an inifinite number of them), in which every
single coin flip is zero. Forever.
Imagine the "people" who live in such a universe. They could spend
aeons in their futile, scientific quest for the universal principle
that REQUIRES every coin toss to be heads.
And if there are an infinite number of universes, then there MUST BE
an infinite number of them in which the most minuscule probable
outcomes must ALWAYS occur.
Indeed, our universe could itself be plausibly described as the
proverbial explosion in the printshop, resulting in the complete works
of Shakespeare. We could plausibly be nothing more than a continuin
series of unlikely, random events, giving rise to the illusion of
natural laws and logical principles. And such a universe might, at
any instant, revert to a bad Monty Python movie, or worse yet, to a
good Monty Python movie.
And if that is the case, then there is no ultimate orderly basis of
reality, but only a complex dice game in which ANYTHING can happen
(and eventually will). Science requires that the laws of nature be
orderly, or else, there is no point in seeking out natural principles.
The laws of probability may not be as we understand them to be. But
they are my starting point for this discussion.
Unfortunately, most people respond reflexively, based on what has
already been drilled into them, instead of investigating those tenets,
and testing them to see how valid they are.
What's 1/2 of infinity?
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