it's not possible to program infinity, is it?

[Domski]

There are a few things that spring to mind.

- Why am I here after 5:00pm?
- Should I go for a pint?
- Steak or pizza for tea?

That's about all that springs to my mind at the moment.

Dom

 

[kylefoley76]

“if you create a universe and if you have the power to do it, you can assign any property to any object and the choices at your disposal are infinite.”
Certain elements are attracted to each other to form bonds, there isn’t an infinite number of combinations."

you misunderstand me. if you create something, let's say, a language, you can attach an infinite number of arbitrary symbols to it. you could come up with a 1000 types of horse, a 100 types of snow, etc. you're looking at something after it has been done and saying it's limited.

someone mentioned the anthropic principle. they're misunderstanding it. you could say the same thing about stonehenge:

stonehenge exists, therefore it could come about at random.

just because something exists, does not follow that it is random

 

[mikerickson]

i've listening to about 200 chomsky lectures in my life, but only about 5 of them were about language. so i just have the watered down version of his language theories. but nevertheless, the sentence: "human can utter an infinite amount of sentences" is straight from chomsky."

i'm not saying that humans can utter sentences for an infinite amount of time, but their choices are infinite.

The references at http://en.wikipedia.org/wiki/Chomsky_normal_form should give you somewhere to go.

 

[mikerickson]

"A Human can utter an infinite number of sentences" is different than "There are an infinite number of sentences that can be uttered by a human."

But both are wrong. Both for the same reason.
The first avers that a human can utter, but the death thing shows that this is false.
The second avers that the set of sentences that can be uttered (once) by a human is infinte.
But..If we define length of a sentence to be the number of seconds it takes to utter, then the second hypothisis is that there are in infinite number of utterable sentences i.e. that there are an infinite number of sentences that can be uttered in less than "3 score and 10" years.

I question that implication. (If there are a fintite number of sounds that the human mouth can utter, then it is false.)

 

[PaddyD]

It is not clear to me why "There are an infinite number of sentences that can be uttered by a human" should take the limited interpretation "...the set of sentences that can be uttered (once) by a human is infinite."<?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>
<o></o>
If this is taken to mean something like "It is possible to construct a grammatically correct sentence of arbitrary length." then the set of possible sentence is straightforwardly infinite (E.g. Keep on adding a he said / she said to a sentence of the form "He said that she said that he said that she said it was raining"). The fact that only a finite number of them could ever be uttered in a finite universe is true, but a different issue surely. (Or at least if you don't think the set of possible sentences is infinite then you can't think the natural numbers are either). <o></o>
<o></o>
But all of this is moot given what the OP’s is apparently trying to do:<o></o>
“…if you create a universe and if you have the power to do it, you can assign any property to any object and the choices at your disposal are infinite. So I'm very skeptical that the properties of the objects in our universe were assigned to them at random.”<o></o>
There is a confusion here, especially given where OP’s trying to head re ‘coordination’. Randomness is, as a starting point, about the distribution of things. How you choose among a (possibly infinite) number of sets with randomly distributed characteristics is something totally different. One obvious solution has been implied by earlier post from Lewiy – simple allow there to exist an infinite number of universes and just stipulate that you happen to live in this one. <o></o>
p.s. thanks Mike for picking up the ‘reals are countably infinite’ slip J<o></o>
p.p.s. “…but I think this is heading towards one of the 3 subjects that forums generally try to avoid (race, religion & politics)” Concur. Let’s be careful here – any fights over creationism etc and this thread gets shut down J. <o></o>

 

[Taul]

Can a computer "understand" infinity?
MatLab can find the limits of functions as x>>infinity, so apparently computers can work with infinity as well as humans can.

Original question was; “a computer can't understand what infinity is, can it?”

Based on what I have read in the threads and in particular Mike’s comment:-

Computers Understand infinity = no (not wishing to imply computers can undersatand)
Work with infinity = yes

 

[Greg Truby]

“…but I think this is heading towards one of the 3 subjects that forums generally try to avoid (race, religion & politics)” Concur. Let’s be careful here – any fights over creationism etc and this thread gets shut down J. <?xml:namespace prefix = o ns = "urn:schemas-microsoft-comfficeffice" /><o></o>

Thus far this thread has inspired a lot of good posts regarding math theory and some general philosophical thoughts on computers and "comprehension". If it does veer off into religion then one of us moderators will just move any nettlesome posts off the thread. But so far I think we've done a great job of staying out of the brambles. So, back to discussion at hand:

I would say that - if one goes with the ever-expanding universe, i.e. no Restaurant at the End of the Universe dinner, and one assumes that humankind can indeed conquer interstellar travel to defeat the sun's eventual burnout and one assumes that language will never cease to evolve, then yeah, I can buy into the number of sentences that humankind can create could indeed be infinite while still obeying some form of grammatical structure. But wouldn't that still qualify for the "there are as many even numbers as there are numbers" thing, i.e. there are as many sensical sentences as there are sensical + gibberish sentences?

 

[arkusM]

Not to drag this down to the knuckle draggers (I have enjoyed this where I can follow it) but I do think that people can utter an infinite amount of ...strange.. things. Generally, take a look at our respective counties politicians, there seems no end to the most mind numbing drivel the spews forth from their mouths. (Sorry to dance near one of the 3, but no names, and none blameless)

Didn't Einstain say something about mans foolishness....

 

[arkusM]

Ahh got it.
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."

 

[ZVI]

It is possible to program infinity in terms of its declaration.

Operations with infinite values are defined in IEEE floating point standard.

Some mathematical software uses the special values to represent of positive and negative infinity.

For example MATLAB represents infinity by the special value inf. Infinity results from operations like division by zero and overflow, which lead to results too large to represent as conventional floating-point values. MATLAB also provides a function called inf that returns the IEEE arithmetic representation for positive infinity as a double scalar value. There are some other functions which operate with infinite values.

MAPPLE supports operations with infinite values as well:

• infinity is a name in Maple which has several special properties.
  
• infinity is used to denote a mathematical infinity, and hence it is usually used as a symbol by itself or as -infinity.
  
• Several functions accept infinity as a parameter or produce it as a result of computation. The to part of the for loop statement accepts infinity as an argument, which will cause it to loop forever.
• The kernel can compare infinity or -infinity to any other numerical value. Hence, infinity can be used in boolean expressions (for example, max, min, etc.).
  
• In the floating-point computation domain, infinity is represented as Float(infinity), and -infinity is represented as Float(-infinity) or -Float(infinity). (The exponent fields are both the symbol infinity, while the mantissas are 1 and -1, respectively.) For completeness, these can be entered as Float(n, infinity), where n is a non-0 integer. Float(n, infinity) automatically simplifies to sgn * Float(infinity).
  
• Float(infinity) cannot be assumed to represent the mathematical concept of infinity, as it may also arise from non-infinity operations, such as overflows. Care must therefore be taken when converting between computation domains (e.g., via round()) that spurious information is not artificially created.
  
• The quantities infinity, -infinity, infinity*I, -infinity*I, infinity + y*I, -infinity + y*I, x + infinity*I and x - infinity*I, where x and y are finite, are all considered to be distinct in Maple. However, all 2-component complex numerics in which both components are infinity are considered to be the same (representing the single point at the "north pole" of the Riemann sphere).
  
• Similarly, different floating-point infinities are generally considered to represent distinct entities, except that the four infinities Float(+-infinity+-infinity*I) are considered to be the same.