TheGrobe wrote:
But if only one at a time, they can't play each other.
Two is also a finite number.
Infinite amount of monkeys playing chess
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I realize, I'm just (facetiously) pointing out that there's a lower concurrency limit in the case where you place an upper one.
Sep 4, 2011
0
#224
TheGrobe wrote:
I realize, I'm just (facetiously) pointing out that there's a lower concurrency limit in the case where you place an upper one.
My apologies. You make a good point which should be taken into consideration by all designers of infinite chess playing monkey experiments.
Elroch wrote:
Infinity is a feature of the mathematical structures which we find convenient to model the universe. For example, in all mainstream physical theories, space consists of infinite numbers of points. Try constructing a theory where space only has a finite number of points.
But the simplest place that infinity appears is in counting. You can ask the question, "do the natural numbers 1, 2, 3, 4 ... and so on, ever come to an end?" If the answer is no, you have concluded the number of natural numbers is infinite. But assuming the answer is yes seems absurd.
Although there are only a finite number of objects in the universe, we can make up concepts relating to these objects that require bigger and bigger numbers (eg (1) the number of electrons in the universe; (2) the number of possible subsets of the set of electrons in the universe; (3) the number of possible subsets of this set (ok, getting a bit tricky to picture, but definitely definable); and so on.
These concepts require there to be an infinite number of natural numbers to all make sense.
The problem is though, that numbers are not 'real.' Numbers are just imaginary concepts that we humans use to count and measure.
Can we have infinity exist as an abstract concept that is useful for some mathematcial operations? Yes. But can we come up with any practical examples of an infinite group of entities within our own universe bounded by space and time? No.
When you presume space and time are bounded right in the question, clearly not.
Won't there be an infinite number of tasks that the monkeys would never do, and why won't playing chess be one of those?
Well, there will bean infinite number of monkeys that won't do certain tasks, and an infinite number of tasks certain monkeys won't do, but an infinite number of tasks an infinite number of monkeys won't do? That's just not how this game works.
Sep 5, 2011
0
#229
Teary_Oberon wrote:
Elroch wrote:
Infinity is a feature of the mathematical structures which we find convenient to model the universe. For example, in all mainstream physical theories, space consists of infinite numbers of points. Try constructing a theory where space only has a finite number of points.
But the simplest place that infinity appears is in counting. You can ask the question, "do the natural numbers 1, 2, 3, 4 ... and so on, ever come to an end?" If the answer is no, you have concluded the number of natural numbers is infinite. But assuming the answer is yes seems absurd.
Although there are only a finite number of objects in the universe, we can make up concepts relating to these objects that require bigger and bigger numbers (eg (1) the number of electrons in the universe; (2) the number of possible subsets of the set of electrons in the universe; (3) the number of possible subsets of this set (ok, getting a bit tricky to picture, but definitely definable); and so on.
These concepts require there to be an infinite number of natural numbers to all make sense.
The problem is though, that numbers are not 'real.' Numbers are just imaginary concepts that we humans use to count and measure.
Can we have infinity exist as an abstract concept that is useful for some mathematcial operations? Yes. But can we come up with any practical examples of an infinite group of entities within our own universe bounded by space and time? No.
I already gave an example of an infinite set of entities in our universe. It comprises all of the electrons, all of the sets of electrons, all of the sets of sets of electrons and so on. Any problem?
It is currently believed that our Universe will expand for ever, especially as the expansion appears to be accelerating due to dark energy. How long is "forever"? Is is finite?
Elroch wrote:
Teary_Oberon wrote:
Elroch wrote:
Infinity is a feature of the mathematical structures which we find convenient to model the universe. For example, in all mainstream physical theories, space consists of infinite numbers of points. Try constructing a theory where space only has a finite number of points.
But the simplest place that infinity appears is in counting. You can ask the question, "do the natural numbers 1, 2, 3, 4 ... and so on, ever come to an end?" If the answer is no, you have concluded the number of natural numbers is infinite. But assuming the answer is yes seems absurd.
Although there are only a finite number of objects in the universe, we can make up concepts relating to these objects that require bigger and bigger numbers (eg (1) the number of electrons in the universe; (2) the number of possible subsets of the set of electrons in the universe; (3) the number of possible subsets of this set (ok, getting a bit tricky to picture, but definitely definable); and so on.
These concepts require there to be an infinite number of natural numbers to all make sense.
The problem is though, that numbers are not 'real.' Numbers are just imaginary concepts that we humans use to count and measure.
Can we have infinity exist as an abstract concept that is useful for some mathematcial operations? Yes. But can we come up with any practical examples of an infinite group of entities within our own universe bounded by space and time? No.
I already gave an example of an infinite set of entities in our universe. It comprises all of the electrons, all of the sets of electrons, all of the sets of sets of electrons and so on. Any problem?
It is currently believed that our Universe will expand for ever, especially as the expansion appears to be accelerating due to dark energy. How long is "forever"? Is is finite?
No, you didn't give a practical example of infinity--you started with a pratical example, but then veered off into abstract mathematical concepts with no grounding in the real world.
If you could be God for a day, stand outside of the known universe and take an instantaneous measure the total number of electrons, then you would invariably end up with a real (albeit seemingly incomprehensibly large) number. But just because something is incomprehensibly large doesn't make it infinite.
Are you so sure?
TheGrobe wrote:
Are you so sure?
That question would be more useful if asked of a proponent of a universe unbounded by space and time, where monkeys can magically transform into computers and unicorns fart rainbows.
But Teary is a realist, and a realist sees the universe as having a fixed amount of energy and real boundaries (even if expanding). And in such a bounded universe, it is simply not possible to have an infinite amount of anything that is composed of either matter or energy. Boundaries of any kind contradict the basic concept of infinity.
Actually, you need boundaries of every kind to contradict the instantiation of infinity.
As has already pointed out, in bounded space, infinite time still allows for infinity, just as the reverse is true.
In addition, even in bounded space and time the concept of infinity is safe and sound. I think that's also been shown, and it's an invaluable abstraction that allows us to perform some pretty impressive logical and mathematical feats. It's the instantiation of infinity that remains restricted.
The heart of my questions, though, was how you can be so sure that the universe is bounded in both space, time and energy?
TheGrobe wrote:
Actually, you need boundaries of every kind to contradict the instantiation of infinity.
As has already pointed out, in bounded space, infinite time still allows for infinity, just as the reverse is true.
In addition, even in bounded space and time the concept of infinity is safe and sound. I think that's also been shown, and it's an invaluable abstraction that allows us to perform some pretty impressive logical and mathematical feats. It's the instantiation of infinity that remains restricted.
The heart of my questions, though, was how you can be so sure that the universe is bounded in both space, time and energy?
And what makes you so sure that space and time are infinite? That is an age old debate that neither side is very close to winning, so it is rather arrogant of you to defend one side so vehemently.
But of course, we can always do this in terms of conditionals...
Assuming that you are using the definition of:
Instantiantion - (Philosophy / Logic) the representation of (an abstraction) by a concrete example
If space and time are finite, then the instantiation of infinity cannot happen.
Space and time are finite,
Therefore, the instantiation of infinity cannot happen.
I also liked a quote that was posted on a forum discussion of this very topic:
"I am a novice but it appears to me that you guys confuse actual infinites with potential infinites. We live in a finite universe, finite space, finite matter, and therefore finite time. While the idea of actual infinites can be postulated and theorized none can, in actuality, be experienced since we ourselves are finite beings."
I never made a claim one way or the other. I'm questioning how you can, not whether you're right or wrong.
I can be means of conditionals.
If one is true then there is a certain conclusion.
If the other is true then there is a different conclusion.
For the side the says that space and time are finite, then an instantianized ifinity cannot exist and therefore the whole example of infinity monkeys is utter bologna.
If this whole thing is about the practicality of getting an infinite number of monkey pairs to play an infinite number of chess games then there are far easier ways to highlight why such an idea is ludicrous.
You keep dodging the question though: How can you be so sure?
"How can you be so sure?"
You don't have to prove conditionals (that is the entire point of using them). Conditionals allow you to explore multiple possibilities.
I'd refer you back to your post #257 -- you didn't present it as a conditional....
Helium is a good, simple, practical choice. I meant ideal in the sense of having no confusing behaviour (such as ionising or forming molecules). This is a minor point. Of course all real gases (even the most inert ones) have some such behaviour.