Re: [ Attn: Randy ] Ad-hoc Parsing?

From: Beth (BethStone21_at_hotmail.NOSPICEDHAM.com)
Date: 12/22/04 

Date: Wed, 22 Dec 2004 15:44:19 GMT

Evenbit wrote:
> Beth - /*
> keep saying "heads" and flipping a coin and,
> eventually, you're bound to get it right, if you just ignore how many
> times you got it wrong beforehand ;)...
> */
>
> I'll just happily ignore how many times you've gotten statistics wrong
> beforehand (as well as this hand).

No, not at all...reconsider the logic:

------------------------

repeat
    flip coin
until heads

eventually:

------------------------

Infinity is always a dangerous concept to play around with, though...as it
throws up logical connundrums such as this...can you flip a coin an
infinite number of times and always get "heads"? Theoretically, yes...but
can you execute the algorithm I was implicitly giving above and reach
"eventually:" without flipping a heads with your coin? Theoretically, no,
it's impossible...good old "infinity" is creating a logical paradox for
us...

I'm not wrong because I exactly stipulated that you keep on going "until
heads"...you're answering the question you want to be asked, not what was
actually asked...by the logic stipulated, if you flip an infinite number of
tails then, sorry, you flip another infinity and another infinity until you
_do_ flip a heads...the conceptual problem that's causing the paradox is
that "infinity" is impossible to actually reach (logically as well as
practically so)..."infinity + 1 = infinity"...so, in fact, you cannot -
even conceptually - actually flip an "infinite" number of tails because
it's impossible to actually reach "infinity"...this is why mathematics tend
to avoid "infinity" like the plague...it isn't actually a number, the
concept isn't actually mathematical, really...consistent logic flies out of
the window when it's involved...

A good statistician, in fact, would not go near the "infinities" you speak
of...you're falling for a "trick" of logic...smoke and mirrors...after all,
you're a coder so you know - presuming you had some theoretical machine
that could last forever itself to execute the program - then you know what
the _ONLY_ conclusion to the code could be:

------------------------

repeat
    flip coin
until heads

eventually:

------------------------

You cannot reach "eventually" without flipping a heads...a good
statistician would NOT be dealing with the "smoke and mirrors" of an
illogical concept of "infinity"...on the contrary, they would say "the
probability of flipping a heads tends towards 1.0"...and my algorithm
specifically states that you do not quit under any circumstances doing so
until it _DOES_ reach 1.0 (certainty; The event "flipping a heads" actually
happened)...

This does have the possibility that you run the above algorithm forever and
never ever flip a heads...in which case, you never reach "eventually", so
carry on going...

Statistics isn't quite as rigid as you may believe (it's pseudo-scientific
in some regards, even if it does deal with numbers ;)...for instance, what
if we reversed the question? Of all the possible infinite number of "runs"
of this loop, only _one_ instance can be "infinite number of tails"...the
probability of an event is "number of events / number of
possibilities"...meaning the probability of what you're talking about
actually happening is 1 / infinity (one "infinitieth" ;)...mathematics has
no answer to this...if we look at 1/2, 1/4, 1/8 then we can see it is more
and more approaching zero ("tends towards zero") but does it actually reach
zero at 1/infinity? As infinity is a concept and not actually a number,
mathematics simply ignores such a thing as if it were a "what is the
meaning of life?" kind of question..."infinity" is not a number - it's just
a concept - and, thus, cannot be manipulated sensibly
mathematically...after all, if "1 / infinity = zero" (your "it's possible
for it to never happen" assertion) and "infinity + 1 = infinity" then what
on Earth could "1 / (infinity + 1)" equal? You can't get more zero than
zero...hence, "1 / infinity <> zero" but, on the other hand, it must equal
zero...

This isn't really a paradox, mind you...the point is simply that "infinity"
is NOT a number...and you cannot sensibly deal with it statistically or
mathematically (indeed, a statistican would simply say "as x increases, the
probability _tends towards_ zero"...indicating a trend that it's becoming
more and more towards "impossible"...but as infinity cannot be reached, you
cannot actually say that it could actually become an absolute certainty at
any point)...

It's like accelerating to the speed of light...the more you accelerate, the
more energy it requires to go faster still until it requires an infinite
amount of energy to actually reach "lightspeed"...you can't even equal it,
let alone exceed it (though, this, interestingly, only applies to something
that needs to accelerate up to lightspeed...if it's already at lightspeed
or exceeding it, then this doesn't actually apply)...

You can never reach your stipulated "infinity" where it's possible to get
_zero_ probability...hence, unless it's exactly zero, however
astronomically unlikely, if it's even fractionally above zero then it could
happen...it's possible...

So, if you kept flipping that coin, then, eventually, you _WOULD_ get a
heads...you cannot, in fact, flip an "infinite" amount of tails, even
conceptually so, because "infinity" is impossible to reach...

"To everything there is a season;
A time to live and a time to die"

The joke is almost right...you can, in fact, avoid taxes (though,
admittedly, somewhat difficult to do while existing in the society we
create for ourselves because products have VAT tax on them and it would be
difficult to function without purchasing anything with VAT on it...not
impossible, mind you...as you could be born to hermits in the mountains and
live your entire life by what Nature provides and everyone else ignores you
and doesn't impose any taxes on you...but, in most societies, it's "as good
as" impossible and, in fact, it would actually make your life _more
difficult_ to attempt to avoid it than to just succumb and pay up :)...but
you cannot avoid death...this isn't only philosophically so, it's logically
so..."infinity" is only a concept, not an actual state that could be
reached (although, like "lightspeed", the bets are off as to whether
something could be "born" infinite (a question for philosophers to
ponder)...but if you start finite, then you can't "accelerate" to being
infinite)...

Beth :)

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