Re: Why the cards must have a memory

I like it.
You regurgitate well.
But I am NOT saying what you think I'm saying.
Probability theory assumes uncertainty, but it also DEFINES its
terms. And the term of 50 percent probability is an expectation of
that specific outcome.
Whatever semantic contortions one may wish to use, the expectation of
an uncertain outcome, albeit a self-contradiction in terms, is
nevertheless definitive.

This is why I used the "tiny universe" scenario, a concept that eludes
most people until they really dwell on it for awhile. That concept is
necessary to understand how one applies this self-contradiction to an
elemental case.

Our mental conception of probability assumes the infinite. But
physical reality, on the other hand...
...well, we've been over that.

Once one gets beyond all the assumptions and ingrained biases, we
arrive at the real meat of the discussion, which is whether true
randomness can actually exist in the real world.

Some people hold that the universe is deterministic, others that it is
random. Either scenario leads to inevitable absurdities, to
conclusions that are of no practical use.

The third alternative is a universe that contains the aspect of free
will, which is neither deterministic nor random.

However, if one cannot wrestle with the paradox of probability theory,
without resorting to emotional tantrums, then there is no hope of
discussing the broader issue.

I accept, by the way, that I am an idiot. The greatest human
intellect is finite, and the least of truth is infinite. Using that
scale, the difference between a genius and an idiot is minuscule. I
accept my lot as an idiot.



On Jan 17, 6:33 pm, Jason Pawloski <jpawlo...@xxxxxxxxx> wrote:
On Jan 17, 1:49 pm, Lute <lutelat...@xxxxxxx> wrote:


I'm glad you found humor in it.
So did I.
I'm neither trolling, nor trying to pass myself off as of more than
average intelligence (which actually is quite low, as I'm sure you've
observed).
I'm presenting an unconventional idea, and one which while suspect,
has just a tiny bit more merit than you may think, since I perceive
you're hamstrung by a lifetime of unquestioned assumptions.
I've been proved wrong before, and never found it humiliating.
On the contrary.  Quite exhilarating.
:)

On Jan 17, 4:04 pm, Jason Pawloski <jpawlo...@xxxxxxxxx> wrote:

This is the funniest post I have ever read in my entire life.
Mathematical nonsense serendiptiously mixed with inapplicable physics
combined with a poster's IQ of 75 made me print this out and hang it
in my cube at work.

Let me explain something to you, Lute. You are not a smart person. At
all. Please just give up. If you really want, I can go through this
line by line with you, in public (so that I publicly humiliate you),
but I assume you are either (a) trolling or (b) trying to pass
yourself off as a sophisticated intellectual by using mathy-like words
when you, in fact, have no math training, or (c) a complete idiot. In
these three cases, you would not be interested in a rebuttal at all,
so I'll pass.

On Jan 17, 12:02 pm, Lute <lutelat...@xxxxxxx> 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.- Hide quoted text -

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That's a cute move, ignoring my post about finding something that
satisfies the "finite, closed and unbounded" criteria. Do you
understand that you said something completely stupid? Or are you still
feigning that that is something meaningful.

Let me explain something to you. Let A_h be the event that a coin is
flipped and heads is the result. Now let A_t be the event that a coin
is flipped and tails is the result. Likewise, define A_hh to be a coin
is flipped and heads is the result, and the coin is flipped again and
heads is again the result. Take A_ht to be a coin is flipped and heads
is the result, and the coin is flipped again and tails is the result.

Now consider all possible infinite sequences of this event:

A_hhh....
A_ht....
...
A_t.....

Let A be the set containing all of these sequences. Its not hard to
see that the cardinality of A is uncountable. Then the probability of
any ONE of these happening is 0. That's right, 0%. Impossible. What
does this do to your multiverse horse*** that you were spewing?

You study things like this in a subject called "math." Using "math"
you can prove such results above and disprove idiots on Usenet. I
could prove the above result, for instance, by finding a morphism in
the category of measure, map the above set to [0,1], and use basic
results from measure theory to show that a singleton has Lebesgue
measure 0. I won't write a rigorous proof because, frankly I don't
think you're up for it.

Let me try this again.

Suppose you flip a coin and it comes up heads 500 times in a row. Now
assume this is a fair coin and this is just a gross statistical
anomaly.

Now, let's say the coin acts fair again after these 500 coin flips.

After two more flips, you are expected to get heads 99.80% of the time
((500+1)/(500+2)).

After 2,000 flips after this 500, you are expected to get heads 60% of
the time.

After 200,000,000 flips after this 500, you are expected to get heads

50.000124999687500781248046879883% of the time

Even though the coin has no "memory", it is clearly going to 50% as
the number of heads goes to infinity, in spite of this huge
statistical anomaly.

Got it, you idiot?- Hide quoted text -

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