Originally posted by Coletti I think there is something in what you say. But we may be begging the question when we say that time and space are continuous. But still, this may be the correct answer. One might even ask, if there is anything that is truly finite. (I'm really pushing my limits here.)
Question: has anyone proven that the value of Pi is an infinite number? We know tha ...[text shortened]... know exactly ether the radius or the circumference of a circle, but not both at the same time.
You have reached a new height of mathematcial absurdity with this post.
You simply make a fool of yourself anytime you post regarding anything related to numbers or logic.
It seems we can know exactly ether the radius or the circumference of a circle, but not both at the same time.
That is quite possibly the most ridiculous mathematical claim I have ever encountered.
Originally posted by Palynka I'm just thinking out loud here, and probably wrong, since I've almost no knowledge of physics and my mathematical knowledge is mostly in the realm of statistics.
Anyway.
The constructs of mathematics are obviously independant to applications to the real world but Pi is derived from a geometric result, so it's not a merely abstract construct like the r ...[text shortened]... y divisible, then I don't see how it's possible for a surface or a length to be irrational.
Mathematics is abstract and pi is derived from mathematics.
In the real world time and distance may or may not be discrete, however this will not affect pi in any way.
If time and distance are discreate then a circle (as defined in mathematics) simply cannot exist in the real world and your apparent paradox will not be a problem.
Originally posted by Coletti I think there is something in what you say. But we may be begging the question when we say that time and space are continuous. But still, this may be the correct answer. One might even ask, if there is anything that is truly finite. (I'm really pushing my limits here.)
Question: has anyone proven that the value of Pi is an infinite number? We know tha ...[text shortened]... know exactly ether the radius or the circumference of a circle, but not both at the same time.
Pi is defined in mathematics and yes it has been proven to have an infinite number of digits when written in decimal notation as it is an irrational number (cannot be written as a fraction).[/b]
It seems we can know exactly ether the radius or the circumference of a circle, but not both at the same time. This depends on what you mean by "know". Yes, one of them will be irrational and therefore impossible to write down in decimal notation or as a fraction. But does this mean we dont know it? Do we not know pi?
We can still use both the radius and circumference in calculations and write one or both of them in terms of other irrational numbers such as pi or e. what about the square root of 2? Is that unknowable?
This is similar to complex numbers in that despite being impossible to map to the real number line, they are still immensely useful in doing calculations and still definable in terms of real numbers.
Originally posted by DoctorScribbles That is quite possibly the most ridiculous mathematical claim I have ever encountered.
It is not rediculous but rather dependant on your definition of knowledge.
Do I know the number 2? Never met him.
Can I know and irrational number? Does defining something provide knowledge of it? If so then I know infinity! Does this give me infinite knowledge?
Originally posted by twhitehead It is not rediculous but rather dependant on your definition of knowledge.
Do I know the number 2? Never met him.
Can I know and irrational number? Does defining something provide knowledge of it? If so then I know infinity! Does this give me infinite knowledge?
You are so confused, I don't even know where to begin.
Let's start here. If you think irrational numbers are not knowable -- whatever that term means to you -- what distinguishes them from rational numbers with respect to knowability?
Is it the fact that rational numbers can be expressed in a finite number of symbols? Guess what...so can pi.
Originally posted by Coletti Actually I'm debating someone on the infinity of God's knowledge and I came across Zeno's Paradox.
I don't have a problem with saying God's knowledge is infinite, but the complaint was that infinite knowledge implied there was always something beyond what is known (or something like that). I didn't quite understand the complaint.
Anyhow, I'm trying ...[text shortened]... ook - I haven't departed from the realm of logic. But 3 more posts might do it. 😉
Since 'god' has only given you a bible, written by men about three hundred years after Jesus, the information contained within is very finite. And since 'god' has not given you any knowledge of infinity, it seems to me the height of arrogance to assume ANYTHING about such a god. You don't know for a fact that it TAKES an infinite being to make our universe, if in fact such a being did make it. You can only repeat assumptions made with no basis in fact for the last two thousand years. I suspect a very powerful being with the right equiptment could bring forces together strongly enough to kick-start a universe, say some extremely advanced beings a million years ahead of us in science might generate new universes all the time but the individuals involved may be nothing more than the equivalent of high school students. That is not my personal belief, just pointing out a possibility.
Originally posted by sonhouse I suspect a very powerful being with the right equiptment could bring forces together strongly enough to kick-start a universe, say some extremely advanced beings a million years ahead of us in science might generate new universes all the time but the individuals involved may be nothing more than the equivalent of high school students. That is not my personal belief, just pointing out a possibility.
I don't know whether this is a serious philosophical proposal but it makes a certain amount of sense to me. I haven't sen this on the forum so forgive me if it's old hat.
We use lots of computer simulations in our work and play, with varying degrees of complexity. Imagine a vastly more technically advanced civilisation with far superior computing resources. I'd bet that if they had the resources, they would would simulate universes (for research, for play, whatever). Any simulated beings within such simulated universes are unlikely to be aware of their true nature. In such a situation it is quite possible that there would be many such simulations created. Indeed if simulated beings became advanced enough, they may gain the ability to create their own simulated universes.
Obviously this is pure speculation and begs the question, as people like to say here. But if it is possible, what are the odds against us being real as opposed to simulated?
Originally posted by Penguin I don't know whether this is a serious philosophical proposal but it makes a certain amount of sense to me. I haven't sen this on the forum so forgive me if it's old hat.
We use lots of computer simulations in our work and play, with varying degrees of complexity. Imagine a vastly more technically advanced civilisation with far superior computing resource ...[text shortened]... s possible, what are the odds against us being real as opposed to simulated?
--- Penguin.
Why does everyone always assume that for the universe to be created, every single atom must be tracked an moved by some unseen power?
A simple mathematical formula can be used to create the Mandel Bro set, an infinitely detailed and beautifull pattern. All you need to run a universe is one very simple law of physics. Why simulate etc every single atom?
Originally posted by twhitehead Why does everyone always assume that for the universe to be created, every single atom must be tracked an moved by some unseen power?
A simple mathematical formula can be used to create the Mandel Bro set, an infinitely detailed and beautifull pattern. All you need to run a universe is one very simple law of physics. Why simulate etc every single atom?
I would not think you would need to simulate every single atom and every quark, etc., only pockets of reality simulation, such as every mind of whatever level, mouse, insect, human. Around each of those minds is an environment but out of its environmental sphere, there would be no need of simulation because it would not effect the nearby environment of each mind. So an ant in a colony would have its volume of influence and senses, chemical or whatever, and there would be no need to simulate for that particular ant the actions of a volcano 10,000 miles away. So the simulations would be pocket intensive with gaps that would be invisible because as each mind moves around, the simulated environment would respond to include that particular mind but beyond that the simulation would not need continuity. The sum total of all the simulations could lead to a continuity of the whole when the pockets overlap, like venn diagrams.
Originally posted by sonhouse I would not think you would need to simulate every single atom and every quark, etc., only pockets of reality simulation, such as every mind of whatever level, mouse, insect, human. Around each of those minds is an environment but out of its environmental sphere, there would be no need of simulation because it would not effect the nearby environment of each ...[text shortened]... imulations could lead to a continuity of the whole when the pockets overlap, like venn diagrams.
Although I wasnt actually refering to simulations but rather God concepts, your ideas have been covered in various forms in science fiction (The matrix for example).
However you miss the most likely and easiest simulation possibility of all. That it is only you that is simulated in full and all the rest is only simulated as required.(The was a good movie, I have for gotten its name, which revolved around the single city simulation concept. Then someone in the city simulated another world.
Are we a simulation? Not in a world identical to ours. In some other reality? Who cares? - if it is a complete simulation.
Some of the people on this forum would fail the turing test though.
Originally posted by twhitehead Although I wasnt actually refering to simulations but rather God concepts, your ideas have been covered in various forms in science fiction (The matrix for example).
However you miss the most likely and easiest simulation possibility of all. That it is only you that is simulated in full and all the rest is only simulated as required.(The was a good movie ...[text shortened]... t is a complete simulation.
Some of the people on this forum would fail the turing test though.
I'm trying to make the solution as rigorous as I can.
I think the solution to Zeno's will have to do with the definition of motion and time.
Also, one can divide a line up into any number of sections, but the sum of the sections will always add up to the same amount. So even though there can be infinite divisions of a line - the ...[text shortened]... ... and so on.
Any one know if I'm heading in the right direction to solving the paradox?
if it is really a paradox than there is no real answere, it will just go on and on. i belive it may be a paradox and there fore unsolvable, if thats a word
Originally posted by laxman38 if it is really a paradox than there is no real answere, it will just go on and on. i belive it may be a paradox and there fore unsolvable, if thats a word
The apparent paradox is based on the assumption that space dimensions can be mapped directly to the real numberline which we dont know for sure (hence the talk about space being discrete or not). It is also (and this is more important) based on the imposibility of dividing infinity by infinity. However as calculus shows, it is not as imposible as it first seems.
The claim is that you cannot cover infinite divisions of space in finite time. However if you have an infinite number of pieces of finite time to use then maybe you can!
Zeno's Paradox and God's Infinite Knowledge
20 Oct '06 03:271 edit
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