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.
Oh it's far worse than that, my friend. Postmodern mathematicians are destroying traditional liberal education and indoctrinating our children with their so-called "mathematical relativism." All you have to do is look at the debate over Fermat's last theorem to see it in its fullest flowering, where it's become a kind of Rube Goldberg-esque game to see how complicated the answer can be. Anybody with half a brain knows the solution is "equals 4."
We must be ever-vigilant about this if we are to preserve our way of life, because these people truly do hate America and all she stands for.
Oh it's far worse than that, my friend. Postmodern mathematicians are destroying traditional liberal education and indoctrinating our children with their so-called "mathematical relativism." All you have to do is look at the debate over Fermat's last theorem to see it in its fullest flowering, where it's become a kind of Rube Goldberg-esque game to see how complicated the answer can be. Anybody with half a brain knows the solution is "equals 4."
We must be ever-vigilant about this if we are to preserve our way of life, because these people truly do hate America and all she stands for.
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.
When did I ever mention Zeno's Paradox? I was responding to the author of the thread, and happened to notice that none of the physics-based answers really touched upon the basic idea that energy is released in distinct packets.
Beyond that, if there's a universal speed limit, i.e. the speed of light, and it happens to be a quantifiable amount, then what prevents the quantization of minimum amount of energy? If I'm not playing along with your little game, I apologize, but I'm not interested in Zeno.
You're discovering the difference between mathematics and physics.
Mathematics is ONLY concerned with being consistent with itself.
Physics is concerned with explanations of physical phenomena that is consistent with our observations.
Quote:
Originally posted by CosmoNut
I've pondered this off and on since high school:
I understand the principle behind the assertion that decimals never end and that you can (theoretically) infinitely halve the space between two objects and they'll never touch. A parabolic curve works on this principle, but really...
If two objects are travelling at each other, at some point the space between them must end so that there is NO space left and they are touching, right? By this notion, I'd think that a value of their distance apart MUST end. So it seems that at some point 0.00000000000000000...1 must become simply 0 when the objects finally touch.
--> <--
Surely someone way smarter than I am can explain this. What am I missing here?
Just asking this again because the question was buried in a post above:
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.
What is the rate of deceleration of each object in metres/(second squared) ?? I Just can't bloody remember how to calculate it.
The distance between objects at time = t (sec) is 1/ (2^t) meters.
Acceleration is second derivative of distance function.
When did I ever mention Zeno's Paradox? I was responding to the author of the thread, and happened to notice that none of the physics-based answers really touched upon the basic idea that energy is released in distinct packets.
Beyond that, if there's a universal speed limit, i.e. the speed of light, and it happens to be a quantifiable amount, then what prevents the quantization of minimum amount of energy? If I'm not playing along with your little game, I apologize, but I'm not interested in Zeno.
Sigh.
Please read CosmoNut's original post again. It's in two parts:
1) CosmoNut notes that he understands that the distance between two objects can be halved repeatedly, forever, yielding a number that constantly approaches, but never reaches, zero (or, to put it another way, the sum of these numbers approach, but never equal, the original distance).
2) He then wonders how that it is that objects may be observed to traverse this seemingly "infinite" space (the space getting smaller between two objects approaching each other part isn't necessary, the principle is the same for any finite interval).
This is Zeno's paradox. Sorry it doesn't float your boat, but that's what it is. It isn't a physics problem, and pointing that out isn't "my little game". Everybody is free to talk about anything they want, but CosmoNut's original question is very definitely "So, what's up with Zeno's paradox?"
edit: Zeno's paradox is somehow related but Let's go back to CosmoNut's question and the title of this thread.
"Physics: Decimals can't be infinite because the space between must end."
[QUOTE]Originally posted by CosmoNut
I understand the principle behind the assertion that decimals never end and that you can (theoretically) infinitely halve the space between two objects and they'll never touch. A parabolic curve works on this principle, but really...
[QUOTE]Originally posted by CosmoNut
If two objects are travelling at each other, at some point the space between them must end so that there is NO space left and they are touching, right? By this notion, I'd think that a value of their distance apart MUST end. So it seems that at some point 0.00000000000000000...1 must become simply 0 when the objects finally touch.
You all are arguing in a totally different space of thought as to what CosmoNut is saying. In the first part he is talking about a series of infinitestimally small numbers, then jams on the idea to a real world physical idea.
Thus any discussion here should involve both physics and applied maths
In CosmoNut's second part, he confuses the issue further by saying that he makes an assumption 0.0000.....0001 must equal zero, therefore two objects extremely super-close to each other must therefore also have zero space between them.
Yes Zeno's paradox is related in some way, but it is a bit different in that it talks about an arrow flying to the air, at each stage (slice of time) it is not moving, therefore on the whole it never moves at all. The paradox is proven false in general by looking at it and saying, you can't just decide that time is discrete and slice it up the way you might do with an infinitely small series of numbers. Ie. 0.00000000....0000000001 sec is not equal to zero.
So we go back to try and explain in a way that deals with the *PHYSICS* aspect of CosmoNut's question, eg 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.
Similar in a way to disproving Zeno's paradox of the arrow is saying that just because you can split numbers into superbly small amounts doesn't mean that space or time in "the real world" works that way. Physics people are still exploring what the smallest amount of space is (they don't just say 0.000000....00000000001 metres must equal zero) because subatomic space just doesn't work that way. Similarly, they don't just cut up time into superbly small amounts and then say 0.0000000.....0001 seconds must be zero. If they did this, then it would create a situation where time did not exist at all. First and foremost this violates Newtonian physics. It also affects quantum mechanics because for example, the position of an electron in an atom is not static. It pops here and there (mostly within the electron orbital) OVER a certain amount, however small, of time.
So essentially, we go back to the point that in Maths you can do a lot in pure maths that doesn't have to relate to the real world. However, when you use certain aspects of Maths and try and apply it to the real world, eg. CosmoNut's question and Zeno's paradox, it comes straight up against the Physics view of the world. Whether you're coming from the Maths side of things or the Physics side of things the moral of the story is that when combining the two you can't just simply BASH TOGETHER one idea from Maths and another idea from Physics and hope it flies (pun unintended wrt Zeno's arrow)
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
Not if there are any kinks in the derivative curves, or if accel is non-linear between sample points.
In my question, I was asking how long it takes for the distance between the two objects to equal 1 angstrom. 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.
For the sake of the problem, it was assumed that the pattern of movement as described above is constant. No kinks
The acceleration between points doesn't matter (remember the pathway independence concept in all physical sciences)...
But really whatever.
Now you just exposed yourself as espousing bullcrap. How much else have you made up? Lingo can't save you from that gaffe.
The fatal counterexample: an acceleration step function. No movement until 33.5 sec (later than your log result), then constant velocity (instantaneous infinite accel) and immediate decel back to zero velocity. Your log function computes an incorrect time because it implicitly assumes a smooth non-kinked acceleration function. It can't take into account that movement may not even commence until after the smooth functions result, leading to an obvious contradiction.
The fact infinite accel is theoretically impossible is of little consequence since there are still an infinite number of other accelerations that can also be applied after 33.5 sec that will get our object to the correct point at 34 sec, but it only takes a single counterexample to prove your statement false.
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
The acceleration changes over time.
The proof of this goes something like this (and it's easier to shof for the whole system rather than one side at a time):
If we assume constant acceleration the equations of motion are as such:
The total collective distance traveled is 1-2^(-t); 1/2 at t=1, 3/4 at t=2, etc
also distance travelled = Vo + 1/2At^2
making 1-2^(-t) = Vo + 1/2At^2
Vo happens to be zero as no motion at time zero so that term drops out leaving 1-2^(-t) = 1/2At^2
simplifying gets us
2 [ 1- 2^(-t) ] = A
t^2
Here we see A changes as t changes. A contradiction of the equations assumption that acceleration is constant.
I don't remember off the top off my head how to derive the integrated acceleration equation which would allow us to solve for an instantaneous acceleration and velocity. I'll leave that exercise to other brave souls. Maybe hhh wants to redeem himself.
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
I'm sorry I have no idea what your talking about. I haven't actually started college yet, I've just left secondary school! So what you're asking is beyond the scope of a GCSE textbook by the sound of it. I hope someone else has managed to answer your question. (I meant sixth form college, I'm only 16 on the 21st!!!, college means uni over there doesn't it? Ask me in two years time and I may be able to tell you )
Comments
Originally posted by addabox
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.
Oh it's far worse than that, my friend. Postmodern mathematicians are destroying traditional liberal education and indoctrinating our children with their so-called "mathematical relativism." All you have to do is look at the debate over Fermat's last theorem to see it in its fullest flowering, where it's become a kind of Rube Goldberg-esque game to see how complicated the answer can be. Anybody with half a brain knows the solution is "equals 4."
We must be ever-vigilant about this if we are to preserve our way of life, because these people truly do hate America and all she stands for.
Originally posted by midwinter
Oh it's far worse than that, my friend. Postmodern mathematicians are destroying traditional liberal education and indoctrinating our children with their so-called "mathematical relativism." All you have to do is look at the debate over Fermat's last theorem to see it in its fullest flowering, where it's become a kind of Rube Goldberg-esque game to see how complicated the answer can be. Anybody with half a brain knows the solution is "equals 4."
We must be ever-vigilant about this if we are to preserve our way of life, because these people truly do hate America and all she stands for.
Two keyboards.
Originally posted by hardeeharhar
It doesn't matter if the steps are jerky or nice and neat and decimilic. The formula still works.
Not if there are any kinks in the derivative curves, or if accel is non-linear between sample points.
I find the debate on Zeno's utterances infinitely, even limitlessly more satisfying at the moment though.
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 halve the remaining distances forever, the arrow therefore can never reach its target.
When did I ever mention Zeno's Paradox? I was responding to the author of the thread, and happened to notice that none of the physics-based answers really touched upon the basic idea that energy is released in distinct packets.
Beyond that, if there's a universal speed limit, i.e. the speed of light, and it happens to be a quantifiable amount, then what prevents the quantization of minimum amount of energy? If I'm not playing along with your little game, I apologize, but I'm not interested in Zeno.
Mathematics is ONLY concerned with being consistent with itself.
Physics is concerned with explanations of physical phenomena that is consistent with our observations.
Originally posted by CosmoNut
I've pondered this off and on since high school:
I understand the principle behind the assertion that decimals never end and that you can (theoretically) infinitely halve the space between two objects and they'll never touch. A parabolic curve works on this principle, but really...
If two objects are travelling at each other, at some point the space between them must end so that there is NO space left and they are touching, right? By this notion, I'd think that a value of their distance apart MUST end. So it seems that at some point 0.00000000000000000...1 must become simply 0 when the objects finally touch.
--> <--
Surely someone way smarter than I am can explain this. What am I missing here?
Originally posted by sunilraman
Just asking this again because the question was buried in a post above:
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.
What is the rate of deceleration of each object in metres/(second squared) ?? I Just can't bloody remember how to calculate it.
The distance between objects at time = t (sec) is 1/ (2^t) meters.
Acceleration is second derivative of distance function.
That's twice the deceleration of each object.
I'll let you ponder the simple derivative. :-)
Originally posted by Hiro
Not if there are any kinks in the derivative curves, or if accel is non-linear between sample points.
I find the debate on Zeno's utterances infinitely, even limitlessly more satisfying at the moment though.
The acceleration between points doesn't matter (remember the pathway independence concept in all physical sciences)...
But really whatever.
Originally posted by Splinemodel
When did I ever mention Zeno's Paradox? I was responding to the author of the thread, and happened to notice that none of the physics-based answers really touched upon the basic idea that energy is released in distinct packets.
Beyond that, if there's a universal speed limit, i.e. the speed of light, and it happens to be a quantifiable amount, then what prevents the quantization of minimum amount of energy? If I'm not playing along with your little game, I apologize, but I'm not interested in Zeno.
Sigh.
Please read CosmoNut's original post again. It's in two parts:
1) CosmoNut notes that he understands that the distance between two objects can be halved repeatedly, forever, yielding a number that constantly approaches, but never reaches, zero (or, to put it another way, the sum of these numbers approach, but never equal, the original distance).
2) He then wonders how that it is that objects may be observed to traverse this seemingly "infinite" space (the space getting smaller between two objects approaching each other part isn't necessary, the principle is the same for any finite interval).
This is Zeno's paradox. Sorry it doesn't float your boat, but that's what it is. It isn't a physics problem, and pointing that out isn't "my little game". Everybody is free to talk about anything they want, but CosmoNut's original question is very definitely "So, what's up with Zeno's paradox?"
The distance between objects at time = t (sec) is 1/ (2^t) meters. Acceleration is second derivative of distance function.
That's twice the deceleration of each object.
I'll let you ponder the simple derivative. :-)
Sorry skatman, can't process this stuff. Why can't anyone tell me what the deceleration of the object in metres per second squared?
*All I remember is that if you have an acceleration curve, you differentiate at a certain point you get velocity.... or something like that.
Two keyboards.
[QUOTE]Originally posted by midwinter
I would send you one, but it would never get there.
ROFLMAO
"Physics: Decimals can't be infinite because the space between must end."
[QUOTE]Originally posted by CosmoNut
I understand the principle behind the assertion that decimals never end and that you can (theoretically) infinitely halve the space between two objects and they'll never touch. A parabolic curve works on this principle, but really...
[QUOTE]Originally posted by CosmoNut
If two objects are travelling at each other, at some point the space between them must end so that there is NO space left and they are touching, right? By this notion, I'd think that a value of their distance apart MUST end. So it seems that at some point 0.00000000000000000...1 must become simply 0 when the objects finally touch.
You all are arguing in a totally different space of thought as to what CosmoNut is saying. In the first part he is talking about a series of infinitestimally small numbers, then jams on the idea to a real world physical idea.
Thus any discussion here should involve both physics and applied maths
In CosmoNut's second part, he confuses the issue further by saying that he makes an assumption 0.0000.....0001 must equal zero, therefore two objects extremely super-close to each other must therefore also have zero space between them.
Yes Zeno's paradox is related in some way, but it is a bit different in that it talks about an arrow flying to the air, at each stage (slice of time) it is not moving, therefore on the whole it never moves at all. The paradox is proven false in general by looking at it and saying, you can't just decide that time is discrete and slice it up the way you might do with an infinitely small series of numbers. Ie. 0.00000000....0000000001 sec is not equal to zero.
So we go back to try and explain in a way that deals with the *PHYSICS* aspect of CosmoNut's question, eg 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.
Similar in a way to disproving Zeno's paradox of the arrow is saying that just because you can split numbers into superbly small amounts doesn't mean that space or time in "the real world" works that way. Physics people are still exploring what the smallest amount of space is (they don't just say 0.000000....00000000001 metres must equal zero) because subatomic space just doesn't work that way. Similarly, they don't just cut up time into superbly small amounts and then say 0.0000000.....0001 seconds must be zero. If they did this, then it would create a situation where time did not exist at all. First and foremost this violates Newtonian physics. It also affects quantum mechanics because for example, the position of an electron in an atom is not static. It pops here and there (mostly within the electron orbital) OVER a certain amount, however small, of time.
So essentially, we go back to the point that in Maths you can do a lot in pure maths that doesn't have to relate to the real world. However, when you use certain aspects of Maths and try and apply it to the real world, eg. CosmoNut's question and Zeno's paradox, it comes straight up against the Physics view of the world. Whether you're coming from the Maths side of things or the Physics side of things the moral of the story is that when combining the two you can't just simply BASH TOGETHER one idea from Maths and another idea from Physics and hope it flies (pun unintended wrt Zeno's arrow)
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
Originally posted by sunilraman
therefore two objects extremely super-close to each other must therefore also have zero space between them.
Is "extremely super-close" some high-falutin' technical math/physics term?
Not if there are any kinks in the derivative curves, or if accel is non-linear between sample points.
In my question, I was asking how long it takes for the distance between the two objects to equal 1 angstrom. 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.
For the sake of the problem, it was assumed that the pattern of movement as described above is constant. No kinks
Is "extremely super-close" some high-falutin' technical math/physics term?
Originally posted by hardeeharhar
The acceleration between points doesn't matter (remember the pathway independence concept in all physical sciences)...
But really whatever.
Now you just exposed yourself as espousing bullcrap. How much else have you made up? Lingo can't save you from that gaffe.
The fatal counterexample: an acceleration step function. No movement until 33.5 sec (later than your log result), then constant velocity (instantaneous infinite accel) and immediate decel back to zero velocity. Your log function computes an incorrect time because it implicitly assumes a smooth non-kinked acceleration function. It can't take into account that movement may not even commence until after the smooth functions result, leading to an obvious contradiction.
The fact infinite accel is theoretically impossible is of little consequence since there are still an infinite number of other accelerations that can also be applied after 33.5 sec that will get our object to the correct point at 34 sec, but it only takes a single counterexample to prove your statement false.
Quote:
Originally posted by max_naylor
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
The acceleration changes over time.
The proof of this goes something like this (and it's easier to shof for the whole system rather than one side at a time):
If we assume constant acceleration the equations of motion are as such:
The total collective distance traveled is 1-2^(-t); 1/2 at t=1, 3/4 at t=2, etc
also distance travelled = Vo + 1/2At^2
making 1-2^(-t) = Vo + 1/2At^2
Vo happens to be zero as no motion at time zero so that term drops out leaving 1-2^(-t) = 1/2At^2
simplifying gets us
2 [ 1- 2^(-t) ] = A
t^2
Here we see A changes as t changes. A contradiction of the equations assumption that acceleration is constant.
I don't remember off the top off my head how to derive the integrated acceleration equation which would allow us to solve for an instantaneous acceleration and velocity. I'll leave that exercise to other brave souls. Maybe hhh wants to redeem himself.
Originally posted by midwinter
Is "extremely super-close" some high-falutin' technical math/physics term?
This thread is seriously in need of the proper engineering terminology, which is:
"Close Enough".
I say to Hell with Math... I'm an art major.
Originally posted by sunilraman
Quote:
Originally posted by max_naylor
I'm glad I've given up maths in college. Although I am doing physics. Poo.
Can you answer my deceleration question please? Nobody else here feels like doing it: 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.
What is the rate of deceleration of each object in metres/(second squared)?
I'm sorry I have no idea what your talking about. I haven't actually started college yet, I've just left secondary school! So what you're asking is beyond the scope of a GCSE textbook by the sound of it. I hope someone else has managed to answer your question. (I meant sixth form college, I'm only 16 on the 21st!!!, college means uni over there doesn't it? Ask me in two years time and I may be able to tell you