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It doesn't postulate anything of the sort. For one thing gravitation is not quantized and a fundamental limit to size in spacetime at the low end would require that it be quantized. As yet however there is no evidence of this. A lot of physicists have tried but all have so far fallen short. Einstein still rules gravitation and his theory does not postulate that the gravitational field (which is spacetime) is quantized.
I remembered hearing about Planck Length and looked it up on Wikipedia, and came across this statement: "The Planck length is sometimes misconceived as the minimum lengthof space-time, but this is not accepted by conventional physics, as this would require violation or modification of Lorentz symmetry.However, certain theories of loop quantum gravitydo attempt to establish a minimum length on the scale of the Planck length, though not necessarily the Planck length itself"
So it does appear that there is currently no known "minimum length" of spacetime to speak of, other than theoretically, which is what Ed is saying.
But I liked what Dilip said about integers: "while the set of integers is 'potentially' infinite, each number within it is finite, and the 'potential' infiniteness is something we can dream about, but never realize in reality."
This is the essence of what I was saying about Cantor's supposed proof that one can create infinite strings that cannot be within pi. Once cannot create them because infinity goes on forever. Any string of digits you care to write out, NO MATTER HOW LONG, is finite and therefore must appear within pi... infinite times.
The notion of things (like the points on a line) being infinitesimally small (with their inverse being infinite), is no longer popular, as the quantum nature of reality postulates that at a certain level of smallness, you cannot further divide stuff!
Why are people on this thread confusing Mathematics with Physics? Just because in physics we talk about things like Planck length does not invalidate the mathematical concepts of ideal points, infinities and infinitesimals. Even Euclid acknowledged 2300 years ago that ideal points and lines did not exist in reality.
Mathematics is an entity unto itself. Physics uses mathematics to describe and model what we can observe of the universe. When we find our models in physics do not accurately describe our observations and predictions, we change our models, improve them. But that does not invalidate the mathematics that was used to describe the original models, only the model itself.
Why are people on this thread confusing Mathematics with Physics? Just because in physics we talk about things like Planck length does not invalidate the mathematical concepts of ideal points, infinities and infinitesimals. Even Euclid acknowledged 2300 years ago that ideal points and lines did not exist in reality.
Mathematics is an entity unto itself. Physics uses mathematics to describe and model what we can observe of the universe. When we find our models in physics do not accurately describe our observations and predictions, we change our models, improve them. But that does not invalidate the mathematics that was used to describe the original models, only the model itself.
I don't think there is any confusion going on, Garland. Dilip has been talking about reality, saying that infinity does not exist in our physical universe except possibly in the infinite recycling between big bangs and universal black holes. I don't think he said that infinity can't exist in math.
I think the vast unbridgeable chasm between an ideal mathematical world and our physical world is being respected here. In fact, I would say Cantor disrespected that chasm with his "proof" that you outlined for us earlier. He actually decided that we can create an infinite string of digits and then change the digit at the end of it, or maybe the fact that we can't do that just escaped him.
When mathematicians start religiously believing in concepts which can be labelled unrealistic, they leave the realm of an authentic discipline and distance themselves from even the charm of the game of chess...
When mathematicians start religiously believing in concepts which can be labelled unrealistic, they leave the realm of an authentic discipline and distance themselves from even the charm of the game of chess...
I'm not sure what you are driving at. Are you implying that because I defend that infinity exists as a concept even if it doesn't manifest itself in reality that I am being "religious"???
I don't think there is any confusion going on, Garland. Dilip has been talking about reality, saying that infinity does not exist in our physical universe except possibly in the infinite recycling between big bangs and universal black holes. I don't think he said that infinity can't exist in math.
I think he pretty clearly did say that. And you can't believe in an infinitely recycling universe and then claim that infinity cannot have any reality. At least not if you think you shouldn't believe two mutually contradictory positions at the same time.
I think the vast unbridgeable chasm between an ideal mathematical world and our physical world is being respected here. In fact, I would say Cantor disrespected that chasm with his "proof" that you outlined for us earlier. He actually decided that we can create an infinite string of digits and then change the digit at the end of it, or maybe the fact that we can't do that just escaped him.
There isn't any such vast unbridgeable chasm. In fact such purely mathematical ideas as the square root of minus 1 and infinity are all over modern physics. These and many ideas other ideas which originated as purely mathematical entities with no application to the real world when they were invented turn out to be absolutely necessary in physics, not to mention electrical engineering and computer science.
I would say Cantor disrespected that chasm with his "proof" that you outlined for us earlier. He actually decided that we can create an infinite string of digits and then change the digit at the end of it, or maybe the fact that we can't do that just escaped him.
Sigh.
No, Cantor did NOT say "change the digit at the end of it". His proof is based his constructed number having at least one digit different from every number listed in the original infinite list. Proof by contradiction.
1/9 can be written as 0.1111111... to infinity
2/9 can be written as 0.222222... to infinity.
I know that every digit after the decimal place is different in these two numbers. I don't have to go to the "end" of either number to know this.
When mathematicians start religiously believing in concepts which can be labelled unrealistic, they leave the realm of an authentic discipline and distance themselves from even the charm of the game of chess...
The world is not required to bend itself to your fantasies of what it should be.
The 'infinity' in the above example is another way of saying that the decimal numerical system cannot accurately adapt to the fraction under consideration (fractions are not restrictive like each of the various numerical systems unfortunately are). For this particular fraction, the nonary numerical system would work better, giving an accurate and finite answer...
Last edited by Dilip Panjwani; Thursday, 18th June, 2020, 05:26 PM.
I think the vast unbridgeable chasm between an ideal mathematical world and our physical world is being respected here. In fact, I would say Cantor disrespected that chasm with his "proof" that you outlined for us earlier. He actually decided that we can create an infinite string of digits and then change the digit at the end of it, or maybe the fact that we can't do that just escaped him.
I guess I don't get what I'm missing here. <removed inflammatory comment, apologized>?! You seem at times obsessed with discrediting a man who died over a hundred years ago. On the one hand, I do find it plausible that many minds are in a more advanced place than a century ago. But regardless, why would you explicitly disrespect specifically one of the greatest mathematicians, ever?!
Why not just stick to your actual arguments, and have people judge them on their own merits? It seems at times that you need to discredit others to make an opening for your new "insights"?!
Last edited by Aris Marghetis; Wednesday, 12th August, 2020, 10:52 AM.
I guess I don't get what I'm missing here. What did Cantor DO to you or your family?! You seem at times obsessed with discrediting a man who died over a hundred years ago. On the one hand, I do find it plausible that many minds are in a more advanced place than a century ago. But regardless, why would you explicitly disrespect specifically one of the greatest mathematicians, ever?!
Why not just stick to your actual arguments, and have people judge them on their own merits? It seems at times that you need to discredit others to make an opening for your new "insights"?!
Pargat, Now you know why Southerners in the USA feel the way they do when someone suggests bringing down the statues of their brave generals from the past...
I guess I don't get what I'm missing here. What did Cantor DO to you or your family?! You seem at times obsessed with discrediting a man who died over a hundred years ago. On the one hand, I do find it plausible that many minds are in a more advanced place than a century ago. But regardless, why would you explicitly disrespect specifically one of the greatest mathematicians, ever?!
Why not just stick to your actual arguments, and have people judge them on their own merits? It seems at times that you need to discredit others to make an opening for your new "insights"?!
Please take your psychological analyses somewhere else, they aren't wanted or needed here.
You most definitely ARE missing something. I AM sticking to my arguments, against Cantor's PROOF, not against Cantor the PERSON. I haven't said ANYTHING about Cantor the person, how in hell did you make that mistake?
Is it something about my name that you keep trying to discredit me? Get lost! Please leave this thread and don't come back unless you can lose the attitude.
I'm genuinely curious here (psychology is so fascinating): because the logic seems, to you, to break down, are you leaning towards the logic being suspect, or your perception of said logic?
This is a RIDICULOUS question. Why do you keep personally attacking the people you don't agree with?
It would be like asking Trudeau if he is leaning towards Progressive Conservative party policies breaking down, or leaning towards his "perception" of them breaking down. It is a joke of a question.
You really don't like people with certain types of names, do you? (you were responding to Dilip)
Oh dear, this is really nasty! I suppose it happens when a few people who seem to know what they're talking about try to debate with others who haven't a clue. My problem is that I have lost track of who is in which camp......pity, but probably time to call it quits.
Oh dear, this is really nasty! I suppose it happens when a few people who seem to know what they're talking about try to debate with others who haven't a clue. My problem is that I have lost track of who is in which camp......pity, but probably time to call it quits.
Fred, I"m glad if you were enjoying this thread. I was not (despite Aris' claims) trying to discredit others so that I could claim new insights. I even realized that I was in error to think that a string of infinite 7's must appear within pi, and I admitted it. This thread was more to get everyone thinking during their covid shutdown, that's all it was about.
I didn't claim anything about Cantor's proof until I read Garland's explanation of it, and then I realized that it doesn't work. I'm not claiming to be some super genius, so I've outlined my explanation of why I think it doesn't work and maybe someone can prove ME wrong, and that's fine. So far I haven't seen that, but I'm open to the possibility it might happen.
We were just straightening out the differences between math and physics and how they describe (respectively) ideal world and the real physical world. Garland thought we were confusing the two, but I don't really think so, but maybe Garland can show a specific example.
I hope Aris stops his harassment and even continues to contribute, as long as he doesn't get personal. There was no need for his behavior.
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