Can we move at all?

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thinkandmull

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I TRULY wish someone can help me with this. Let’s say you are trying to get from A to B. You must first travel half of that distance, but half of THAT distance first, and HALF that ect ect ect. To infinity? How is that possible. It’s a finite segment. You can’t say you get to a point that cannot be divided, because then it has ZERO distance and is not a part of the line; a million zeros is ZERO. This is the greatest paradox around to me. ANY HELP!!!
 
thinkandmull said:
I TRULY wish someone can help me with this. Let’s say you are trying to get from A to B. You must first travel half of that distance, but half of THAT distance first, and HALF that ect ect ect. To infinity? How is that possible. It’s a finite segment. You can’t say you get to a point that cannot be divided, because then it has ZERO distance and is not a part of the line; a million zeros is ZERO. This is the greatest paradox around to me. ANY HELP!!!
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To truly address this without any hand-waving, you have to talk about the convergence of infinite series. Actually, I’ll just introduce the infinite series first, and we’ll proceed from there.

Suppose you are moving one meter per second for one second. Obviously you will travel a meter in this time. But as you point out, you don’t cover that distance all at once. You must first cover half of the distance, and then half of the remaining distance, and so forth. (This is just the reverse of your ordering. Framing the problem in terms of completing the motion rather than beginning it shouldn’t change anything, since we could just play a tape of someone running in reverse and get the same result.) So our one meter will be expressed as 1=1/2+1/4+1/8+… If you don’t have much of a background in math, you’ll just have to take my word for it that this works. If this seems surprising, remember that pi is 3.14159…=3+1/10+4/100+1/1000+5/10000+9/100000…

So the distance isn’t problematic, but what about time? Time also isn’t an issue because the time required to move a distance is proportional to the distance itself if you’re moving with constant velocity. So we would get the same series as before, giving us a total of one second.

Does any of this address your question?
 
thinkandmull said:
I TRULY wish someone can help me with this. Let’s say you are trying to get from A to B. You must first travel half of that distance, but half of THAT distance first, and HALF that ect ect ect. To infinity? How is that possible. It’s a finite segment. You can’t say you get to a point that cannot be divided, because then it has ZERO distance and is not a part of the line; a million zeros is ZERO. This is the greatest paradox around to me. ANY HELP!!!
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According to Berkeley (him again!), such paradoxes arise from thinking real distances and objects to be infinitely divisible. He says they aren’t- for example, he says that you can’t have 1/1000 of an inch- that it was nonsense to talk about something imperceptible as materially existing.

Because a real, perceptible distance, can’t be divided into infinite perceptible sections, what you are saying can’t happen.
 
I don’t think space is infinitely dividable. I think space is a creation with limits, but they are too small for us to perceive.
 
Nihilist said:
He says they aren’t- for example, he says that you can’t have 1/1000 of an inch- that it was nonsense to talk about something imperceptible as materially existing.
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This Berkeley sounds silly. So, according to him, the universe cares about our sensory limitations? If humans had exceptionally poor vision, would he deny that tenths of inches exist? Why is the “cut-off” from real distance to imaginary distance based on our perception?

And this has consequences for physics as well. If this is true, we shouldn’t be applying calculus to physics problems because position and velocity functions wouldn’t be continuous. In principle, algebra would be sufficient for physics.
 
Oreoracle said:
This Berkeley sounds silly. So, according to him, the universe cares about our sensory limitations? If humans had exceptionally poor vision, would he deny that tenths of inches exist? Why is the “cut-off” from real distance to imaginary distance based on our perception?

And this has consequences for physics as well. If this is true, we shouldn’t be applying calculus to physics problems because position and velocity functions wouldn’t be continuous. In principle, algebra would be sufficient for physics.
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No, he would say that you can’t treat ‘reality’ separately from our perceptions. If a certain particle is totally invisible, undetectable, unperceptible- then it basically doesn’t exist. For the same reason, at a certain point of smallness, distances become meaningless.

So, you either move x, or you don’t move at all (where x is the smallest limit of what you can be perceive).
 
Nihilist said:
So, you either move x, or you don’t move at all (where x is the smallest limit of what you can be perceive).
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Okay, so that would be the Planck length if I’m not mistaken. As I said, this would make calculus-based physics wrong and algebra-based physics possible because space and motion through it wouldn’t be continuous.

Loop Quantum Gravity predicts that space is discretized, although at a smaller scale than Planck lengths, so imperceptible motion is still possible in LQG. I don’t know enough physics to refute Berkeley on this. However, if he thinks he has overturned all of the physics that has developed since Galileo (all theories have assumed continuity thus far), then he should step forth to claim his Nobel Prize.
 
And then there is the old saw about the mathematician 🤓 and the engineer :hammering: at one end of a room, and the beautiful woman :love: at the other end.

The mathematician conceives the infinite series and despairs that try though he might, he would never be able to reach the beautiful woman. :crying:

The engineer realizes, however, that he can get close enough for practical purposes. :rotfl:

tee
 
Oreoracle said:
Okay, so that would be the Planck length if I’m not mistaken. As I said, this would make calculus-based physics wrong and algebra-based physics possible because space and motion through it wouldn’t be continuous.

Loop Quantum Gravity predicts that space is discretized, although at a smaller scale than Planck lengths, so imperceptible motion is still possible in LQG. I don’t know enough physics to refute Berkeley on this. However, if he thinks he has overturned all of the physics that has developed since Galileo (all theories have assumed continuity thus far), then he should step forth to claim his Nobel Prize.
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Is there any experiment, evidence that the LQG is valid?
It seems it’s not a valid concept/model as of now.
 
abucs said:
why Galileo?
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Galileo was, as far as I know, the first to clearly state the relationship between math and physics, and apply this relationship. The tradition of discovering “laws” experimentally and then manipulating them mathematically to derive other laws began with him.

Before him, most of physics still followed the Aristotelian tradition, which was mostly qualitative rather than quantitative.
Jaaanosik said:
Is there any experiment, evidence that the LQG is valid?
It seems it’s not a valid concept/model as of now.
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No, it is untestable in its current form as far as I can tell. But it is the closest thing I can think of to what Berkeley describes that would be consistent with our observations.

Of course, LQG was designed to be consistent with what we already know about physics, so it reproduces the predictions that have already been made by Quantum Mechanics. However, there are many possible theories that can do this, such as String Theory, and we have no way of telling which, if any, is correct.
 
Even the longest journey begins with a single step. Just put one foot in front of the other, and soon you are there. No need to overcomplicate things.
 
Oreoracle said:
Galileo was, as far as I know, the first to clearly state the relationship between math and physics, and apply this relationship. The tradition of discovering “laws” experimentally and then manipulating them mathematically to derive other laws began with him.

Before him, most of physics still followed the Aristotelian tradition, which was mostly qualitative rather than quantitative.

No, it is untestable in its current form as far as I can tell. But it is the closest thing I can think of to what Berkeley describes that would be consistent with our observations.

Of course, LQG was designed to be consistent with what we already know about physics, so it reproduces the predictions that have already been made by Quantum Mechanics. However, there are many possible theories that can do this, such as String Theory, and we have no way of telling which, if any, is correct.
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The LQG has good ideas but it starts with a false assumption that it’s background independent.
Logically, the wrong conclusions will follow.
 
thinkandmull said:
I TRULY wish someone can help me with this. Let’s say you are trying to get from A to B. You must first travel half of that distance, but half of THAT distance first, and HALF that ect ect ect. To infinity? How is that possible. It’s a finite segment. You can’t say you get to a point that cannot be divided, because then it has ZERO distance and is not a part of the line; a million zeros is ZERO. This is the greatest paradox around to me. ANY HELP!!!
Click to expand...
Yes, we can move because there exist a subjective quantity so called speed.
 
Bahman said:
Yes, we can move because there exist a subjective quantity so called speed.
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The speed as a scalar quantity is a math construct that describes reality. That reality objectively exists.

What is subjective about the speed?
 
Jaaanosik said:
The LQG has good ideas but it starts with a false assumption that it’s background independent.
Logically, the wrong conclusions will follow.
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It’s untested, but we can’t really say that it’s wrong either. Indeed, to falsify it, you would need to be able to test it, hence the problem. If it had any obvious flaws, surely it would have been discarded by now.
 
Bahman said:
Ok.

No, since the reality is subjectively exist too.

We perceive speed as perceive time and position. There is no guarantee that there exist a unique map between the form that we perceive and what exist out there.
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Well, get out of your chair, run towards a concrete wall and ram it with your head.
We’ll talk about a guarantee after, fair enough?
 
Oreoracle said:
It’s untested, but we can’t really say that it’s wrong either. Indeed, to falsify it, you would need to be able to test it, hence the problem. If it had any obvious flaws, surely it would have been discarded by now.
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It has flaws.
edge.org/3rd_culture/smolin_susskind04/smolin_susskind.html

There is also evidence that the relativity does not work all the time and therefore the biggest flaw is the assumption of the background independence.
 
Oreoracle said:
Galileo was, as far as I know, the first to clearly state the relationship between math and physics, and apply this relationship. The tradition of discovering “laws” experimentally and then manipulating them mathematically to derive other laws began with him.

Before him, most of physics still followed the Aristotelian tradition, which was mostly qualitative rather than quantitative.
Click to expand...
Not an expert but you may want to look at John Buridan, Nicole Oresme, Domingo de Soto and Albert the Great regarding inertia and velocity and the use of mathematics in natural science.
 
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