26-04-2002 00:38									#61
	Suffering from ads?

quote: Originally posted by orange would you say the same about 10100100010000100000......?

randomness implies that all possibilities are equally likely; 0-9. A truely random number would have both random pattern and distribution of the digits 0-9. You are artificially limiting 'infinite patterns' to predictable distribution.

	26-04-2002 00:38									#62
	Increase the size of your Attachments

ok wait
when i said repeat itself i didnt say it properly
im not saying pi contains pi i meant that pi will contain a repetion of any finite length u want
and that string of 0 and 1 orange will be contained an infinite number of times in pi if it is written in decimal OR binary

	26-04-2002 00:40									#63
	Support Apolyton, buy Civilization 2

yeah but since pi can be written as the limit of a series shouldn't there be a way to predict exactly where my phone number, or any other number will appear?

	26-04-2002 00:42									#64
	Inflate your Upload Space

quote: Originally posted by LulThyme ok wait when i said repeat itself i didnt say it properly im not saying pi contains pi i meant that pi will contain a repetion of any finite length u want and that string of 0 and 1 orange will be contained an infinite number of times in pi if it is written in decimal OR binary

Here's where I lose some of you.

I can understand if you say that it's possible for any finite string of numbers ( decimal or otherwise... ) to exist within pi, but to say that it must exist AND that it must exist an infinite amount of times sounds a little kooky to me.

Just because pi is random doesn't mean that EVERYTHING must occur within it.

For example: assuming the Universe is infinitely large, would you guarantee that there are an infinite amount of planets exactly like Earth within the Universe?

I'd say no, but from the sounds of things, simply because the Universe is infinite, you would make that guarantee.

	26-04-2002 00:43									#65
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

Since we are on the topic of random and infinite numbers:

You know that theory that states 'if you take a room full of monkeys, and give them each a typewriter, eventually (given an infinite amount of time) they will write a novel'? Another way to put it is to take a random number generator and infinite time: eventually, it will generate every number pattern possible... eventually.

The theory actually disproves itself.

Take an infinite number of random number generators; according to this theory (given infinite time to look for it), you will eventually find one that never produces the number '7'. So how can that particular number generator ever fulfill the theory?

	26-04-2002 00:43									#66
	Support Apolyton, buy Civilization 2

could it be possible to generate an algorithm or something to determine where a particular finite string of numbers will appear... and since it must appear an infinite number of times could it be written as a function?

then again what do i know...

	26-04-2002 00:44									#67
	Suffering from ads?

quote: Originally posted by Caesar the Great yeah but since pi can be written as the limit of a series shouldn't there be a way to predict exactly where my phone number, or any other number will appear?

Because prediction relies on order. If the order is not predictable... no prediction is possible. You could do a proof with a probability, but that would be different from an exact prediction.

	26-04-2002 00:44									#68
	Support Apolyton, buy Civilization 2

Slow down a bit, LulThyme... Let's assume two series of figures: First, some randomly chosen one, let's say 576456234. Second, all the numbers before some given point in the approximation of pi. Now, you say that the first has to be repeated infinitely many times in pi - in the second case, you say that it can only be repeated finitely.

* thinks *

Ah, of course, figured it out myself. In the first case we're speaking about occurrences - in the second case, repeats. Different things.

	26-04-2002 00:45									#69
	Support Apolyton

quote: Originally posted by orange Here's where I lose some of you. I can understand if you say that it's possible for any finite string of numbers ( decimal or otherwise... ) to exist within pi, but to say that it must exist AND that it must exist an infinite amount of times sounds a little kooky to me. Just because pi is random doesn't mean that EVERYTHING must occur within it. For example: assuming the Universe is infinitely large, would you guarantee that there are an infinite amount of planets exactly like Earth within the Universe? I'd say no, but from the sounds of things, simply because the Universe is infinite, you would make that guarantee.

is not NECESSARILY true that the universe is infinite. It may be. Then again, maybe its finite.

	26-04-2002 00:46									#70
	Increase Your PM Length

orange... that depends wether you mean space itself or matter? if there is only a finite ammount of matter there may only be 1 planet like earth, but with an infinite ammount of matter (which creates all kinds of problems) there would have to be an infinite number of planets exactly like earth, not to mention an infinite number of planets with an extra oxygen molecule and an infinite number of planets with an extra nitrogen molecule etc....

	26-04-2002 00:47									#71
	Support Apolyton buy from Amazon

quote: Originally posted by MrBaggins is not NECESSARILY true that the universe is infinite. It may be. Then again, maybe its finite.

I said that it was an assumption for my analogy. I never made the claim that the universe actually is infinite.

quote: quote: For example: assuming the Universe is infinitely large, would you guarantee that there are an infinite amount of planets exactly like Earth within the Universe?

	26-04-2002 00:47									#72
	Suffering from ads?

quote: Originally posted by Caesar the Great orange... that depends wether you mean space itself or matter? if there is only a finite ammount of matter there may only be 1 planet like earth, but with an infinite ammount of matter (which creates all kinds of problems) there would have to be an infinite number of planets exactly like earth, not to mention an infinite number of planets with an extra oxygen molecule and an infinite number of planets with an extra nitrogen molecule etc....

only if formation of matter worked to include dupes... its possible that such a universe would have infinite variation too.

	26-04-2002 00:48									#73
	Get a bigger avatar today!

quote: Originally posted by Caesar the Great orange... that depends wether you mean space itself or matter? if there is only a finite ammount of matter there may only be 1 planet like earth, but with an infinite ammount of matter (which creates all kinds of problems) there would have to be an infinite number of planets exactly like earth, not to mention an infinite number of planets with an extra oxygen molecule and an infinite number of planets with an extra nitrogen molecule etc....

Why?

	26-04-2002 00:49									#74
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

quote: Originally posted by Caesar the Great orange... that depends wether you mean space itself or matter? if there is only a finite ammount of matter there may only be 1 planet like earth, but with an infinite ammount of matter (which creates all kinds of problems) there would have to be an infinite number of planets exactly like earth, not to mention an infinite number of planets with an extra oxygen molecule and an infinite number of planets with an extra nitrogen molecule etc....

No, there is no proof of that; see my post about the monkeys a few paces back.

And there is no such thing as random anyhow; the system generating the randomness determines the pattern.

That's how high-tech crooks can win at digital Keno everytime. And it is also true in nature.

	26-04-2002 00:49									#75
	Suffering from ads?

i'll assume there has to be

	26-04-2002 00:52									#76
	Inflate your Upload Space

quote: Originally posted by Caesar the Great i'll assume there has to be

Just because there is an infinite amount of space OR matter does NOT mean that there has to be an infinite repetition of everything possible.

It is possible that there could be an infinite number of earth repilcas, and no this could not be disproven assuming an infinite universe, but I don't see why it MUST be true.

	26-04-2002 00:53									#77
	Support Apolyton, pre-order Civilization IV

quote: Originally posted by Caesar the Great i'll assume there has to be

Ahh! Modern science at work.

	26-04-2002 00:54									#78
	Support Apolyton, buy Civilization III: Complete

i no see no monkey...

infinity has to be the most messed up number... well besides e^pi*i

	26-04-2002 00:56									#79
	Got spare money?

quote: Originally posted by Anunikoba No, there is no proof of that; see my post about the monkeys a few paces back. And there is no such thing as random anyhow; the system generating the randomness determines the pattern. That's how high-tech crooks can win at digital Keno everytime. And it is also true in nature.

Not entirely true. Humans have difficulty of conceiving random systems, due to the limitations of what we have to work with.

QED provides us with, in every demonstratable behavioral study, random behavior.

	26-04-2002 00:57									#80
	Tired of ads?

quote: Originally posted by orange Just because there is an infinite amount of space OR matter does NOT mean that there has to be an infinite repetition of everything possible. It is possible that there could be an infinite number of earth repilcas, and no this could not be disproven assuming an infinite universe, but I don't see why it MUST be true.

because if infinity doesn't contain everything it isn't infinity...

of course the counterarguement is does infinity contain itself which leads to a very interesting proof about the non-existance of the universe...

	26-04-2002 00:59									#81
	Put an end to popups!

quote: Originally posted by Caesar the Great because if infinity doesn't contain everything it isn't infinity... of course the counterarguement is does infinity contain itself which leads to a very interesting proof about the non-existance of the universe...

how many times do I have to say this... no. Infinity contains merely itself. Just a singular unreal infinite set.

	26-04-2002 00:59									#82
	Support Apolyton buy from Amazon

Does the "what do you look like" thread contain a picture of Caesar? No!

	26-04-2002 01:01									#83
	Lose 30 kilos (of popups)

quote: Originally posted by MrBaggins Not entirely true. Humans have difficulty of conceiving random systems, due to the limitations of what we have to work with. QED provides us with, in every demonstratable behavioral study, random behavior.

the only way the universe can be random is if it is infinite... if you had a finite universe you could simply take a really really powerful computer and input all the variables and you'd be able to predict the future (which of course only brings up more problems)

	26-04-2002 01:03									#84
	Help yourself to an AD-FREE life

Quanta exist in Quantum fields which are infinite.

There are forwards-recursive infinite states. Everything happens, and keeps on recursively happening.

We only perceive one of those realities.

	26-04-2002 01:03									#85
	Tired of ads?

quote: Originally posted by MrBaggins how many times do I have to say this... no. Infinity contains merely itself. Just a singular unreal infinite set.

question... are there more rational or irrational numbers? (i know the answer i'm just not sure why its true)

	26-04-2002 01:04									#86
	Support Apolyton, buy Civilization III: Complete

what do you mean more?

	26-04-2002 01:05									#87
	Support Apolyton

quote: Originally posted by MrBaggins Quanta exist in Quantum fields which are infinite. There are forwards-recursive infinite states. Everything happens, and keeps on recursively happening. We only perceive one of those realities.

i guess we're just taken from one of those realities to another and that is consciousness... although wouldn't an exact copy of you be stuck somewhere (or more appropriately somewhen) at a point in time for eternity....

	26-04-2002 01:07									#88
	Remove this text

A number that can be expressed as a fraction where p and q are integers and , is called a rational number with numerator p and denominator q. Numbers which are not rational are called irrational numbers. The set of all rational numbers is referred to as the "rationals," and forms a field that is denoted Q. Any rational number is trivially also an algebraic number. The set of rational numbers is denoted Rationals in Mathematica, and a number x can be tested to see if it is rational using the command Element[x, Rationals].




The elementary algebraic operations for combining rational numbers are exactly the same as for combining fractions.




It is always possible to find another rational number between any two members of the set of rationals. Therefore, rather counterintuitively, the rational numbers are a continuous set, but at the same time countable.




For a, b, and c any different rational numbers, then




is the square of a rational number (Honsberger 1991).



The probability that a random rational number has an even denominator is 1/3 (Salamin and Gosper 1972).




It is conjectured that if there exists a real number x for which both and are integers, then x is rational. This result would follow from the four exponentials conjecture (Finch).

Last edited by MrBaggins on 26-04-2002 at 02:05

	26-04-2002 01:07									#89
	Support Apolyton buy from Amazon

quote: Originally posted by MrBaggins what do you mean more?

say you have a number line from negative infinity to infinity and you made a point for each rational number and each irrational number, the set of points for the rational numbers is A and the set of points for the irrational numbers is B. are there more elements in set A or set B?

	26-04-2002 01:13									#90
	Enter the AD-FREE zone

quote: Originally posted by MrBaggins Quanta exist in Quantum fields which are infinite. There are forwards-recursive infinite states. Everything happens, and keeps on recursively happening. We only perceive one of those realities.

Sooo.. if a tree falls in a forest, and no one is around to hear it, then does it make a sound?

Or, if a Quanta exists in a different reality, and we can't percieve that reality, does it exist at all?