*sigh* after all the sex, drugs and trance music this is the 1% of my brain and knowledge I use to have that is left over to be barely able to process this. Chemistry, electron orbitals, polynomial maths, Newtonian physics, integration and differentiation. I've totally forgotten how to calculate acceleration/deceleration... Phew \
Well, all I want is to be able to go to my internet discussion forum for rumors about upcoming Apple Computer products without bumping into a bunch of nerds!
Whoa... Cool. Logarithms. Takes me back to high skool maths. Completely forgotten all that stuff. Don't do drugs, kids!! Now, hardeeharhar, can you answer the deceleration rate question?
Whoa... Cool. Logarithms. Takes me back to high skool maths. Completely forgotten all that stuff. Don't do drugs, kids!! Now, hardeeharhar, can you answer the deceleration rate question?
If I had a spread sheet in front of me (Kaleidagraph really, since it can do derivatives)...
In response to how would one calculate how many steps you would have to take to get 1 A separation:
log (10^10)/log(2) = 10*1/(log(2)) = 33.2192809 (looking up on a log table )
Ahhh. I see someone making assumptions about the motion!! (I thought scientists didn't do that in your world) Do we know if the motion is smooth, or is it really herky-jerky like the earlier mentioned kids who would take steps and pause??? You can only determine the part to the right of the decimal if you know the equations of motion hence my earlier answer that it is sometime between the 33rd and 34th second. Is it OK to be sloppy when the equations are "nice"? But all lingoistic when writing in prose?
Using a spreadsheet and "guessing" x and seeing how close it is to 10billion is kinda cheating though. Did you just do this?
Actually I already knew 2^33 is about 8 billion and 2^34 is about 16 billion. I used the spreadsheet to verify I hadn't screwed up my decimal places.
Three columns, one for n {looked at 28-42}, one for 2^(-n) and one for 1^(-10). Then did a quick visual comparison to double check the intervals where the values crossed.
Ahhh. I see someone making assumptions about the motion!! (I thought scientists didn't do that in your world) Do we know if the motion is smooth, or is it really herky-jerky like the earlier mentioned kids who would take steps and pause??? You can only determine the part to the right of the decimal if you know the equations of motion hence my earlier answer that it is sometime between the 33rd and 34th second. Is it OK to be sloppy when the equations are "nice"? But all lingoistic when writing in prose?
It doesn't matter if the steps are jerky or nice and neat and decimilic. The formula still works.
To some extent this is the rationale behind quantum mechanics, which is a subject where I'm not even a casual expert, and I won't make much of a claim.
But I will say that, at the subatomic level, energy tends to operate in quantized amounts. This has been observed in many classic experiments of the 20th century.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality. . .
The best part about math is that "imaginary numbers" are very much part of reality.
I'm just dumbfounded that a question about Zeno's Paradox went all sub-atomic and shit.
"all sub-atomic and shit" Well, we just came to a pragmatic approach. Two objects start moving at each other, 1/4 of the distance each second. Initial distance between two objects is 1 metre at 0sec. At 1sec, distance 0.5 metres, 2sec, distance is 0.25sec, etc.
Will they ever touch? Well, around 33seconds, the distance between the two objects is about 1 Angstrom, one-ten-billionth of a metre. Quantum mechanics start to come into play then. From 33seconds onwards that's where it gets "all sub-atomic and shit" because the definition of "touching" then comes into play.
Yeah, but a pragmatic approach is virtually pointless when tackling a mathematics problem. Sure the math problem is placed in the real world to make it more approachable, but it has no consequence whatsoever as to the actual explenation. Which is, of course, that an infinite addition of infinite small numbers does not get you an infinite large number. This may go against your language-based intuition, but should not go against you mathematical intuition.
The easiest way to 'prove' this, is trying to prove the opposite: that the number will grow to infinite. Well, let's try:
1 + .5 + .25 + .125 + ...
Now, everybody can see this number will never grow bigger than 10. Or 5. Or 2. But it will grow infinitely close to 2 (meaning you can prove it will grow bigger than any number smaller than 2, no matter how close to 2 it is), for all practical ánd mathematical matters (and here is where the two meet) making it equal to 2.
Edit: i never had to explain math in english so excuse me for any weird wording.
To some extent this is the rationale behind quantum mechanics, which is a subject where I'm not even a casual expert, and I won't make much of a claim.
But I will say that, at the subatomic level, energy tends to operate in quantized amounts. This has been observed in many classic experiments of the 20th century.
Gaaaaahhhh! Zeno's Paradox has nothing to do with quantum mechanics!
Here it is again, restated: Since an arrow flying towards a target must traverse half the distance, then half the distance remaining, and half again, and we can continue to halve the remaining distances forever, the arrow therefore can never reach its target.
This is not resolved by talking about quarks, or electron clouds, or the uncertainty principle, or anything in that neck of the woods. The arrow is not imagined to enter, in the last pico seconds before hitting the target, some kind of boundary ambiguity that resolves the paradox, because that is not remotely what the paradox is about-- unless somebody is prepared to argue that, in fact, the arrow never does reach the target and continues to move through an infinite series of bifurcations, forever.
Which it doesn't, and is in no way a condition suggested by quantum mechanics.
The paradox is simply, and again, about the difference between an infinite sequence tending toward limit x, where x is the distance to the target, and the real world movement of the arrow. The paradox hinges on the ambiguity of natural language being switched for mathematical description, not on some inherent ambiguity in the idea of "things touching".
Gaaaaahhhh! Zeno's Paradox has nothing to do with quantum mechanics!
Here it is again, restated: Since an arrow flying towards a target must traverse half the distance, then half the distance remaining, and half again, and we can continue to half the remaining distances forever, the arrow therefore can never reach its target.
This is not resolved by talking about quarks, or electron clouds, or the uncertainty principle, or anything in that neck of the woods. The arrow is not imagined to enter, in the last pico seconds before hitting the target, some kind of boundary ambiguity that resolves the paradox, because that is not remotely what the paradox is about-- unless somebody is prepared to argue that, in fact, the arrow never does reach the target and continues to move through an infinite series of bifurcations, forever.
Which it doesn't, and is in no way a condition suggested by quantum mechanics.
The paradox is simply, and again, about the difference between an infinite sequence tending toward limit x, where x is the distance to the target, and the real world movement of the arrow. The paradox hinges on the ambiguity of natural language being switched for mathematical description, not on some inherent ambiguity in the idea of "things touching".
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away. If I have some time, I'll dig up some of the papers I have on paleo-Zeno's Paradoxic change over time. You'll find, once you read up on the subject, that the "hockey stick" graph of the frequency of halfway points as the distance between objects decreases is actually a distortion and based on a limited number of experiments that have never been repeated.
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away. If I have some time, I'll dig up some of the papers I have on paleo-Zeno's Paradoxic change over time. You'll find, once you read up on the subject, that the "hockey stick" graph of the frequency of halfway points as the distance between objects decreases is actually a distortion and based on a limited number of experiments that have never been repeated.
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away.
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
Sorry, SpcMs, Midwinter is just having some fun with the tone of another thread about global warming. He's just really good at imitating the style of an obtuse loon. (Hmmmm....... or is he?)
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
And so it has begun. The post-objective truth era begins to spread through the forums.
Soon, we can question whether the "Mac" actually exists at all, or if it is just a liberal hobby-horse propped up by a cabal of MS hating terror lovers.
Comments
Quote:
*sigh* after all the sex, drugs and trance music this is the 1% of my brain and knowledge I use to have that is left over to be barely able to process this. Chemistry, electron orbitals, polynomial maths, Newtonian physics, integration and differentiation. I've totally forgotten how to calculate acceleration/deceleration... Phew
Well, all I want is to be able to go to my internet discussion forum for rumors about upcoming Apple Computer products without bumping into a bunch of nerds!
log (10^10)/log(2) = 10*1/(log(2)) = 33.2192809 (looking up on a log table
Originally posted by sunilraman
Whoa... Cool. Logarithms. Takes me back to high skool maths. Completely forgotten all that stuff. Don't do drugs, kids!!
If I had a spread sheet in front of me (Kaleidagraph really, since it can do derivatives)...
Originally posted by hardeeharhar
In response to how would one calculate how many steps you would have to take to get 1 A separation:
log (10^10)/log(2) = 10*1/(log(2)) = 33.2192809 (looking up on a log table
Ahhh. I see someone making assumptions about the motion!! (I thought scientists didn't do that in your world) Do we know if the motion is smooth, or is it really herky-jerky like the earlier mentioned kids who would take steps and pause??? You can only determine the part to the right of the decimal if you know the equations of motion hence my earlier answer that it is sometime between the 33rd and 34th second. Is it OK to be sloppy when the equations are "nice"? But all lingoistic when writing in prose?
Originally posted by sunilraman
Using a spreadsheet and "guessing" x and seeing how close it is to 10billion is kinda cheating though. Did you just do this?
Actually I already knew 2^33 is about 8 billion and 2^34 is about 16 billion. I used the spreadsheet to verify I hadn't screwed up my decimal places.
Three columns, one for n {looked at 28-42}, one for 2^(-n) and one for 1^(-10). Then did a quick visual comparison to double check the intervals where the values crossed.
Originally posted by Hiro
Ahhh. I see someone making assumptions about the motion!! (I thought scientists didn't do that in your world) Do we know if the motion is smooth, or is it really herky-jerky like the earlier mentioned kids who would take steps and pause??? You can only determine the part to the right of the decimal if you know the equations of motion hence my earlier answer that it is sometime between the 33rd and 34th second. Is it OK to be sloppy when the equations are "nice"? But all lingoistic when writing in prose?
It doesn't matter if the steps are jerky or nice and neat and decimilic. The formula still works.
Originally posted by CosmoNut
I've pondered this off and on since high school:
...
To some extent this is the rationale behind quantum mechanics, which is a subject where I'm not even a casual expert, and I won't make much of a claim.
But I will say that, at the subatomic level, energy tends to operate in quantized amounts. This has been observed in many classic experiments of the 20th century.
Originally posted by hardeeharhar
Not all math is applicable to "reality."
Period.
You can continue to deny this, but if you ever have had a conversation with a real mathematician doing research in modern topics, you will quickly realize that math has advanced far beyond simple descriptions of reality. . .
The best part about math is that "imaginary numbers" are very much part of reality.
Quote:
Originally posted by addabox
I'm just dumbfounded that a question about Zeno's Paradox went all sub-atomic and shit.
"all sub-atomic and shit"
Will they ever touch? Well, around 33seconds, the distance between the two objects is about 1 Angstrom, one-ten-billionth of a metre. Quantum mechanics start to come into play then. From 33seconds onwards that's where it gets "all sub-atomic and shit" because the definition of "touching" then comes into play.
Yeah, but a pragmatic approach is virtually pointless when tackling a mathematics problem. Sure the math problem is placed in the real world to make it more approachable, but it has no consequence whatsoever as to the actual explenation. Which is, of course, that an infinite addition of infinite small numbers does not get you an infinite large number. This may go against your language-based intuition, but should not go against you mathematical intuition.
The easiest way to 'prove' this, is trying to prove the opposite: that the number will grow to infinite. Well, let's try:
1 + .5 + .25 + .125 + ...
Now, everybody can see this number will never grow bigger than 10. Or 5. Or 2. But it will grow infinitely close to 2 (meaning you can prove it will grow bigger than any number smaller than 2, no matter how close to 2 it is), for all practical ánd mathematical matters (and here is where the two meet) making it equal to 2.
Edit: i never had to explain math in english so excuse me for any weird wording.
Originally posted by Splinemodel
To some extent this is the rationale behind quantum mechanics, which is a subject where I'm not even a casual expert, and I won't make much of a claim.
But I will say that, at the subatomic level, energy tends to operate in quantized amounts. This has been observed in many classic experiments of the 20th century.
Gaaaaahhhh! Zeno's Paradox has nothing to do with quantum mechanics!
Here it is again, restated: Since an arrow flying towards a target must traverse half the distance, then half the distance remaining, and half again, and we can continue to halve the remaining distances forever, the arrow therefore can never reach its target.
This is not resolved by talking about quarks, or electron clouds, or the uncertainty principle, or anything in that neck of the woods. The arrow is not imagined to enter, in the last pico seconds before hitting the target, some kind of boundary ambiguity that resolves the paradox, because that is not remotely what the paradox is about-- unless somebody is prepared to argue that, in fact, the arrow never does reach the target and continues to move through an infinite series of bifurcations, forever.
Which it doesn't, and is in no way a condition suggested by quantum mechanics.
The paradox is simply, and again, about the difference between an infinite sequence tending toward limit x, where x is the distance to the target, and the real world movement of the arrow. The paradox hinges on the ambiguity of natural language being switched for mathematical description, not on some inherent ambiguity in the idea of "things touching".
Originally posted by addabox
Gaaaaahhhh! Zeno's Paradox has nothing to do with quantum mechanics!
Here it is again, restated: Since an arrow flying towards a target must traverse half the distance, then half the distance remaining, and half again, and we can continue to half the remaining distances forever, the arrow therefore can never reach its target.
This is not resolved by talking about quarks, or electron clouds, or the uncertainty principle, or anything in that neck of the woods. The arrow is not imagined to enter, in the last pico seconds before hitting the target, some kind of boundary ambiguity that resolves the paradox, because that is not remotely what the paradox is about-- unless somebody is prepared to argue that, in fact, the arrow never does reach the target and continues to move through an infinite series of bifurcations, forever.
Which it doesn't, and is in no way a condition suggested by quantum mechanics.
The paradox is simply, and again, about the difference between an infinite sequence tending toward limit x, where x is the distance to the target, and the real world movement of the arrow. The paradox hinges on the ambiguity of natural language being switched for mathematical description, not on some inherent ambiguity in the idea of "things touching".
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away. If I have some time, I'll dig up some of the papers I have on paleo-Zeno's Paradoxic change over time. You'll find, once you read up on the subject, that the "hockey stick" graph of the frequency of halfway points as the distance between objects decreases is actually a distortion and based on a limited number of experiments that have never been repeated.
Originally posted by midwinter
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away. If I have some time, I'll dig up some of the papers I have on paleo-Zeno's Paradoxic change over time. You'll find, once you read up on the subject, that the "hockey stick" graph of the frequency of halfway points as the distance between objects decreases is actually a distortion and based on a limited number of experiments that have never been repeated.
Originally posted by midwinter
What utter horeshit. Clearly, you have only been getting one side of the Zeno's Paradox debate, and that, no doubt, is coming from mainstream math, which has a vested interest in maintaining its hegemony. And they will brook no dissent, as your snarky look down your nose just indicated. Whether you like it or not, teh relationship between Zeno's paradox and quantum mechanics is a subject of debate, and sticking your fingers in your ears isn't going to make it go away.
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
Originally posted by SpcMs
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
Sorry, SpcMs, Midwinter is just having some fun with the tone of another thread about global warming. He's just really good at imitating the style of an obtuse loon. (Hmmmm....... or is he?)
Originally posted by addabox
I would send you one, but it would never get there.
Originally posted by SpcMs
I'm sorry, but that's just bull. Zeno's Paradox was all about the 'mainstream math' problem as discribed by Addabox and myself, and has nothing to do with mechanics. Sure, today it is used to illustrate some theoretical concepts about things 'touching', but is completely unrelated. It's an interesting and worthwile topic, but does nothing to 'solve' or 'answer' Zeno's Paradox.
See? This is how it starts.
a) "You are not qualified to question math,"
b) "All mathematicians say X; therefore, anyone who questions X is not of math,"
c) "You must be motivated by political loyalties, economic vested interests, or religious beliefs if you question X,"
d) "You must be ignorant or lacking intellectual honesty if you question X,"
e) You desire a personal insult that demonizes you and casts you in the role of a monster, an enemy, or a fool.
I see you've added a new one:
f) you don't seem to know what the hell you're talking about.
Soon, we can question whether the "Mac" actually exists at all, or if it is just a liberal hobby-horse propped up by a cabal of MS hating terror lovers.