07 Feb 2016, 12:05 am
Deltaville wrote:
100000fireflies wrote:
Deltaville wrote:
What I wanted to bring into focus on this question was whether numerical fluxes occur near asymptotes that reasonably could bring about numerical uncertainty. Yet all I get are these negative responses from everyone. 
For the original question stated, it would be irrelevant. Jane is taller and the frog will half hop forever.
For the paradox version naturalplastic posed, i still don't see how it would matter? When i go from the couch to the fridge, whether i know the number of points i cross or not, there's a halfway to the destination. When i get there, there's another halfway ahead. And so on. Meanwhile, there are infinite points on any line. So whether i'm at point 999,556,743 or 12,456,465 how would it matter? I'd still have infinity to traverse.
How do you see it as influencing?
If there were finite points on a line, then the precise quantity would matter. But as there isn't, i don't see it. But again, as you mentioned it, maybe you're seeing a facet i'm overlooking??
Not sure what you mean by Jane is taller. Difference in magnitude is an incorrect premise in relation to this problem, although I am not exactly sure what you mean to be honest.
As I have mentioned numerous times on this thread, if you were to use the ratio limit test for convergence, you are right the limit as x->infinity is 1. That means you are correct, it would not be possible for the frog to every reach 1 in finite amount of moves as the distance does halve itself every subsequent step. This 'force field', as some call it, is known as an asymptotic barrier.
But these are two types of asymptotic for practical purposes, the other is a value where the denominator is 0 and it is impossible even theoretically to cross that threshold, because any value divided by zero is inheritable unknowable and undefined. If you were to find the limit of 1/x for instance, the function on the right would extend all the way up to infinity, and the function on the left would go all the way down to negative infinity.
However mathematician have long known that asymptotes can in fact be crossed, and thus are de facto regions in which functions cannot cross rather then de jure regions. For instance, some cubic functions do in fact cross the horizantal asymptote initially.
Therefore, some super computers, given the fact that 1 may not be in fact an absolute limit, have computed the so called Xeno's paradox and miraculously, after a gazillion (I cannot even write such a huge amount
) amount of subsequent steps miraculously, the value of 1 is crossed. Who knows why?Perhaps maybe you are right, they are nothing more then errors in decimal places, or perhaps, mathematics is a field that is more uncertain then we ever imagined.
This is the kind of discussion I wanted to probe in this thread, but it didn't go the way I hoped it would.
It had nothing to do with magnitude. It was in reference to my prior post's example (about the original post) that as stated, it's just a fact that the frog won't get there, the same as with the example, Mary is taller.
The zero denominator version is what i was referring to.
As i understand it (please tell me if i'm wrong because i easily could be), it approaches 1/0 as it approaches infinity. Based on that is why i said what i did - essentially that it would take so incredibly long to get to that point that while the numbers may be unknown (thou shall not divide by zero), that i'd still be dead long before i'd reach the fridge.
What i hear you saying is ..despite closing in on infinity, it can be crossed...which would mean that despite infinite points in a line, i potentially could get to the fridge before infinite time passes. Am i interpreting right?
Do you have a link to the computation work? I'm very curious to see it. I don't doubt it...many things we think we know are amazingly, progressively shown as wrong. And every time we learn something it seems to open a door into a greater unknown. In the end, there probably are no paradoxes, just holes in our knowledge.
A side question if you will, why did you transfer to law? You clearly think a lot and have a strong mathematical mind combined with a curiosity and thirst for understanding deeper meanings and truths. I would think law would be mundane by comparison.
07 Feb 2016, 2:47 am
100000fireflies wrote:
Deltaville wrote:
100000fireflies wrote:
Deltaville wrote:
What I wanted to bring into focus on this question was whether numerical fluxes occur near asymptotes that reasonably could bring about numerical uncertainty. Yet all I get are these negative responses from everyone.
For the original question stated, it would be irrelevant. Jane is taller and the frog will half hop forever.
For the paradox version naturalplastic posed, i still don't see how it would matter? When i go from the couch to the fridge, whether i know the number of points i cross or not, there's a halfway to the destination. When i get there, there's another halfway ahead. And so on. Meanwhile, there are infinite points on any line. So whether i'm at point 999,556,743 or 12,456,465 how would it matter? I'd still have infinity to traverse.
How do you see it as influencing?
If there were finite points on a line, then the precise quantity would matter. But as there isn't, i don't see it. But again, as you mentioned it, maybe you're seeing a facet i'm overlooking??
Not sure what you mean by Jane is taller. Difference in magnitude is an incorrect premise in relation to this problem, although I am not exactly sure what you mean to be honest.
As I have mentioned numerous times on this thread, if you were to use the ratio limit test for convergence, you are right the limit as x->infinity is 1. That means you are correct, it would not be possible for the frog to every reach 1 in finite amount of moves as the distance does halve itself every subsequent step. This 'force field', as some call it, is known as an asymptotic barrier.
But these are two types of asymptotic for practical purposes, the other is a value where the denominator is 0 and it is impossible even theoretically to cross that threshold, because any value divided by zero is inheritable unknowable and undefined. If you were to find the limit of 1/x for instance, the function on the right would extend all the way up to infinity, and the function on the left would go all the way down to negative infinity.
However mathematician have long known that asymptotes can in fact be crossed, and thus are de facto regions in which functions cannot cross rather then de jure regions. For instance, some cubic functions do in fact cross the horizantal asymptote initially.
Therefore, some super computers, given the fact that 1 may not be in fact an absolute limit, have computed the so called Xeno's paradox and miraculously, after a gazillion (I cannot even write such a huge amount
) amount of subsequent steps miraculously, the value of 1 is crossed. Who knows why?Perhaps maybe you are right, they are nothing more then errors in decimal places, or perhaps, mathematics is a field that is more uncertain then we ever imagined.
This is the kind of discussion I wanted to probe in this thread, but it didn't go the way I hoped it would.
It had nothing to do with magnitude. It was in reference to my prior post's example (about the original post) that as stated, it's just a fact that the frog won't get there, the same as with the example, Mary is taller.
The zero denominator version is what i was referring to.
As i understand it (please tell me if i'm wrong because i easily could be), it approaches 1/0 as it approaches infinity. Based on that is why i said what i did - essentially that it would take so incredibly long to get to that point that while the numbers may be unknown (thou shall not divide by zero), that i'd still be dead long before i'd reach the fridge.
What i hear you saying is ..despite closing in on infinity, it can be crossed...which would mean that despite infinite points in a line, i potentially could get to the fridge before infinite time passes. Am i interpreting right?
Do you have a link to the computation work? I'm very curious to see it. I don't doubt it...many things we think we know are amazingly, progressively shown as wrong. And every time we learn something it seems to open a door into a greater unknown. In the end, there probably are no paradoxes, just holes in our knowledge.
A side question if you will, why did you transfer to law? You clearly think a lot and have a strong mathematical mind combined with a curiosity and thirst for understanding deeper meanings and truths. I would think law would be mundane by comparison.
There is no 'zero' asymptote in this case. f(x)= 1/x; XeR =/= 0 has a zero asymptote, as does f(x)= x/x-2; XeR =/= 2.
07 Feb 2016, 8:30 pm
07 Feb 2016, 9:07 pm
07 Feb 2016, 9:51 pm
07 Feb 2016, 10:11 pm
07 Feb 2016, 10:23 pm
07 Feb 2016, 10:46 pm
08 Feb 2016, 1:16 am
08 Feb 2016, 1:53 am
Tollorin
Veteran
Joined: 14 Jun 2009
Age: 42
Gender: Male
Posts: 3,178
Location: Sherbrooke, Québec, Canada
08 Feb 2016, 2:04 am
In the high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. A mathematician, a physicist, and an engineer were asked, "When will the girls and boys meet?"
The mathematician said: "Never."
The physicist said: "In an infinite amount of time."
The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."
http://www2.phy.ilstu.edu/~rfm/107_old/107F07/EPMjokes.html
Deltaville wrote:
Actually a degree does indicate higher intelligence then average, so it is not a far cry to claim that it gives you authority in certain disciplines. When I finished my undergrad I was given a chance to start work for my PhD in Theoretical Physics right away (skipping grad), although I declined to do so in favor of law.
You were on your way to probing the deep layers of reality, and instead you chooses to study law!? I don't get it.
08 Feb 2016, 2:09 am
Tollorin wrote:
In the high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. A mathematician, a physicist, and an engineer were asked, "When will the girls and boys meet?"
The mathematician said: "Never."
The physicist said: "In an infinite amount of time."
The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."
http://www2.phy.ilstu.edu/~rfm/107_old/107F07/EPMjokes.html
You were on your way to probing the deep layers of reality, and instead you chooses to study law!? I don't get it.
The mathematician said: "Never."
The physicist said: "In an infinite amount of time."
The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."
http://www2.phy.ilstu.edu/~rfm/107_old/107F07/EPMjokes.html
Deltaville wrote:
Actually a degree does indicate higher intelligence then average, so it is not a far cry to claim that it gives you authority in certain disciplines. When I finished my undergrad I was given a chance to start work for my PhD in Theoretical Physics right away (skipping grad), although I declined to do so in favor of law.
You were on your way to probing the deep layers of reality, and instead you chooses to study law!? I don't get it.
I know. Dumbest decision I made in my life.
08 Feb 2016, 2:20 am
08 Feb 2016, 9:38 am
08 Feb 2016, 11:27 am
12 Feb 2016, 9:07 pm
