What does it mean for something to be "logically possible"?

[untermensche]

Your incredulity is noted, but I can think of multiple different ways that movement could happen without a smallest movement. Do you have an argument that shows why your claim MUST be true? Or is it just, "I can't see how that could happen..."?

Tell me.

How do you have movement that has no length?

A movement of zero length is not a movement. It is the lack of movement.

To have a movement it's length has to be greater than zero.

 

[beero1000]

Your incredulity is noted, but I can think of multiple different ways that movement could happen without a smallest movement. Do you have an argument that shows why your claim MUST be true? Or is it just, "I can't see how that could happen..."?

Tell me.

How do you have movement that has no length?

A movement of zero length is not a movement. It is the lack of movement.

To have a movement it's length has to be greater than zero.

Every movement has a non-zero length, but no movement is the smallest movement. Why is this so hard for you to comprehend?

 

[untermensche]

Tell me.

How do you have movement that has no length?

A movement of zero length is not a movement. It is the lack of movement.

To have a movement it's length has to be greater than zero.

Every movement has a non-zero length, but no movement is the smallest movement. Why is this so hard for you to comprehend?

I'm not talking about the imaginary concept "smallest movement".

I'm talking about the smallest movement possible for something real that moves to make.

A real movement has to be a length greater than zero.

If something moves it has to move a distance greater than zero.

The only question is: Which distance above zero is the smallest distance it is possible for something to move?

It has to be something.

And it has to be something greater than zero.

 

[beero1000]

Every movement has a non-zero length, but no movement is the smallest movement. Why is this so hard for you to comprehend?

I'm not talking about the imaginary concept "smallest movement".

I'm talking about the smallest movement possible for something real that moves to make.

A real movement has to be a length greater than zero.

If something moves it has to move a distance greater than zero.

The only question is: Which distance above zero is the smallest distance it is possible for something to move?

It has to be something.

And it has to be something greater than zero.

It doesn't necessarily have to be something. If you think it does, you should be able to give an argument as to why. Otherwise, you are still just question begging.

 

[untermensche]

I'm not talking about the imaginary concept "smallest movement".

I'm talking about the smallest movement possible for something real that moves to make.

A real movement has to be a length greater than zero.

If something moves it has to move a distance greater than zero.

The only question is: Which distance above zero is the smallest distance it is possible for something to move?

It has to be something.

And it has to be something greater than zero.

It doesn't necessarily have to be something. If you think it does, you should be able to give an argument as to why. Otherwise, you are still just question begging.

Tell me how you have a movement unless it has some length?

A movement has to be larger than zero.

 

[Kharakov]

A movement of zero length is not a movement. It is the lack of movement.

But a movement of zero length only implies no "movement of," not that there is no "movement within."

How far does a car moving 60 mph move in 0 seconds?

In 10^-100 hours?


One of the things you could ask is... what is the smallest meaningful movement in reality at the electromagnetically dominated scale. In other words, what is the smallest movement that can impact the evolution of a system at the electromagnetic scale over a relatively short period of time (say 10^5 years or so)?

This doesn't mean there aren't smaller movements in reality, it just means that they won't have a meaningful impact on the evolution of the system in the time the system is observed (whether or not they will have an impact in the far future remains to be seen).

 

[Speakpigeon]

Let's try to make sense of it all. Sorry, a bit of maths will come handy. Just a wee bit.

So, assume some movement, and assume some thing M doing the movement. I assume here that there's no movement if there is no thing doing the movement.

We also consider our idea of real space-time as suggested by our intuition, i.e. flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other.

We're interested in the kind of movement which is the succession or sequence in time of all the spatial positions occupied by some given thing M.

The idea is that we can try to formalise UM's idea of "first move". Not the "smallest first move" since we all agree it couldn't exist at all in any continuous space-time. But "first move" can certainly be formalised and investigated to try and prove the possibility or otherwise of the "smallest first move".

To simplify our investigation, we can think in terms of the distance covered during the movement. Since the movement considered is a sequence, it is clear that the distance covered increases with time, and this irrespective of whether the path followed goes more or less in a straight line or doubles back on itself. Considering the distance covered, we can think of any movement as having a starting point and an endpoint. The starting point is the point occupied by M at the time the movement starts, say, t1. The endpoint is the point occupied by M at the time the movement ends, say, t2. So far, so simple.

Now, assuming a continuous space-time, we can always divide the distance covered in two parts, using a point P located on the path taken by M, somewhere in between, strictly in between, the starting point and the endpoint. If the path doubles back and crosses itself at P, we can always specify which part of the path point P is considered to belong to, for example "the first pass", or "the second pass", and so on. Since the movement considered is a sequence, there will be no ambiguity as to which element in the sequence point P corresponds to.

So, now we have the path taken by M divided in two parts by point P. Given a particular point P, we can talk of the first part of the movement as being the part from the starting point to P. It is also clear that we can choose P anywhere on the path taken by M (as long as we specify "first pass" etc. whenever required). To a given point P will correspond a given distance covered by M during the movement until it gets to P, i.e. from the starting point to P. Suppose we make a first choice of P as P1. P1 specifies the first part of the movement as the part from the starting point to point P1. And to P1 corresponds a specific distance covered by M from the starting point to point P1.

Now, can we make a different choice for P? That's where our assumption of continuity kicks in. If space-time is continuous and movement is continuous, whatever our first choice P1, we can always find another P, say, P2, corresponding to a shorter distance covered by M. And then again, we can find another point P, say, P3, corresponding to an even shorter distance. There is always the possibility of choosing another point P corresponding to a shorter distance. Trivially, this is because P is never chosen as identical to the starting point. And to each point Pi chosen, correspond a different 'first part' of the same movement. We will have as many "first parts" as we will choose P points.


So, the question is: can there be a smallest first part?

Suppose there is one. Call Psd the P point corresponding to this shortest distance. Psd is somewhere along the path taken by M, but it is different from the starting point and the endpoint, by construction. So, given that the space-time considered is continuous, we can in fact find a new P point, say, Pn, in between the starting point and the Psd point. Pn corresponds obviously to a shorter distance as covered by M and this distance will be smaller than the distance corresponding to Psd, which is contradicting our hypothesis that there is a smallest first part.

So, there is no smallest first part.


Please take the time to find holes in there but at the end of the day, I'd like all those who tried to talk UM out of insanity to take a view on this very nearly formal proof and express this view in non-ambiguous terms so I don't feel like I worked hard to no avail.
EB

 

[Juma]

Let's try to make sense of it all. Sorry, a bit of maths will come handy. Just a wee bit.

So, assume some movement, and assume some thing M doing the movement. I assume here that there's no movement if there is no thing doing the movement.

We also consider our idea of real space-time as suggested by our intuition, i.e. flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other.

We're interested in the kind of movement which is the succession or sequence in time of all the spatial positions occupied by some given thing M.

The idea is that we can try to formalise UM's idea of "first move". Not the "smallest first move" since we all agree it couldn't exist at all in any continuous space-time. But "first move" can certainly be formalised and investigated to try and prove the possibility or otherwise of the "smallest first move".

To simplify our investigation, we can think in terms of the distance covered during the movement. Since the movement considered is a sequence, it is clear that the distance covered increases with time, and this irrespective of whether the path followed goes more or less in a straight line or doubles back on itself. Considering the distance covered, we can think of any movement as having a starting point and an endpoint. The starting point is the point occupied by M at the time the movement starts, say, t1. The endpoint is the point occupied by M at the time the movement ends, say, t2. So far, so simple.

Now, assuming a continuous space-time, we can always divide the distance covered in two parts, using a point P located on the path taken by M, somewhere in between, strictly in between, the starting point and the endpoint. If the path doubles back and crosses itself at P, we can always specify which part of the path point P is considered to belong to, for example "the first pass", or "the second pass", and so on. Since the movement considered is a sequence, there will be no ambiguity as to which element in the sequence point P corresponds to.

So, now we have the path taken by M divided in two parts by point P. Given a particular point P, we can talk of the first part of the movement as being the part from the starting point to P. It is also clear that we can choose P anywhere on the path taken by M (as long as we specify "first pass" etc. whenever required). To a given point P will correspond a given distance covered by M during the movement until it gets to P, i.e. from the starting point to P. Suppose we make a first choice of P as P1. P1 specifies the first part of the movement as the part from the starting point to point P1. And to P1 corresponds a specific distance covered by M from the starting point to point P1.

Now, can we make a different choice for P? That's where our assumption of continuity kicks in. If space-time is continuous and movement is continuous, whatever our first choice P1, we can always find another P, say, P2, corresponding to a shorter distance covered by M. And then again, we can find another point P, say, P3, corresponding to an even shorter distance. There is always the possibility of choosing another point P corresponding to a shorter distance. Trivially, this is because P is never chosen as identical to the starting point. And to each point Pi chosen, correspond a different 'first part' of the same movement. We will have as many "first parts" as we will choose P points.


So, the question is: can there be a smallest first part?

Suppose there is one. Call Psd the P point corresponding to this shortest distance. Psd is somewhere along the path taken by M, but it is different from the starting point and the endpoint, by construction. So, given that the space-time considered is continuous, we can in fact find a new P point, say, Pn, in between the starting point and the Psd point. Pn corresponds obviously to a shorter distance as covered by M and this distance will be smaller than the distance corresponding to Psd, which is contradicting our hypothesis that there is a smallest first part.

So, there is no smallest first part.


Please take the time to find holes in there but at the end of the day, I'd like all those who tried to talk UM out of insanity to take a view on this very nearly formal proof and express this view in non-ambiguous terms so I don't feel like I worked hard to no avail.
EB

Eh. If spacetime is discrete in small 4dimensional cubes of side p then p is the smallest distance that all motion has to start with. since there obviously no logical contradiction in that assumption (motion is still totally possible) your proof seems to be dust...

 

[Speakpigeon]

Let's try to make sense of it all. Sorry, a bit of maths will come handy. Just a wee bit.

So, assume some movement, and assume some thing M doing the movement. I assume here that there's no movement if there is no thing doing the movement.

We also consider our idea of real space-time as suggested by our intuition, i.e. flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other.

We're interested in the kind of movement which is the succession or sequence in time of all the spatial positions occupied by some given thing M.

The idea is that we can try to formalise UM's idea of "first move". Not the "smallest first move" since we all agree it couldn't exist at all in any continuous space-time. But "first move" can certainly be formalised and investigated to try and prove the possibility or otherwise of the "smallest first move".

To simplify our investigation, we can think in terms of the distance covered during the movement. Since the movement considered is a sequence, it is clear that the distance covered increases with time, and this irrespective of whether the path followed goes more or less in a straight line or doubles back on itself. Considering the distance covered, we can think of any movement as having a starting point and an endpoint. The starting point is the point occupied by M at the time the movement starts, say, t1. The endpoint is the point occupied by M at the time the movement ends, say, t2. So far, so simple.

Now, assuming a continuous space-time, we can always divide the distance covered in two parts, using a point P located on the path taken by M, somewhere in between, strictly in between, the starting point and the endpoint. If the path doubles back and crosses itself at P, we can always specify which part of the path point P is considered to belong to, for example "the first pass", or "the second pass", and so on. Since the movement considered is a sequence, there will be no ambiguity as to which element in the sequence point P corresponds to.

So, now we have the path taken by M divided in two parts by point P. Given a particular point P, we can talk of the first part of the movement as being the part from the starting point to P. It is also clear that we can choose P anywhere on the path taken by M (as long as we specify "first pass" etc. whenever required). To a given point P will correspond a given distance covered by M during the movement until it gets to P, i.e. from the starting point to P. Suppose we make a first choice of P as P1. P1 specifies the first part of the movement as the part from the starting point to point P1. And to P1 corresponds a specific distance covered by M from the starting point to point P1.

Now, can we make a different choice for P? That's where our assumption of continuity kicks in. If space-time is continuous and movement is continuous, whatever our first choice P1, we can always find another P, say, P2, corresponding to a shorter distance covered by M. And then again, we can find another point P, say, P3, corresponding to an even shorter distance. There is always the possibility of choosing another point P corresponding to a shorter distance. Trivially, this is because P is never chosen as identical to the starting point. And to each point Pi chosen, correspond a different 'first part' of the same movement. We will have as many "first parts" as we will choose P points.


So, the question is: can there be a smallest first part?

Suppose there is one. Call Psd the P point corresponding to this shortest distance. Psd is somewhere along the path taken by M, but it is different from the starting point and the endpoint, by construction. So, given that the space-time considered is continuous, we can in fact find a new P point, say, Pn, in between the starting point and the Psd point. Pn corresponds obviously to a shorter distance as covered by M and this distance will be smaller than the distance corresponding to Psd, which is contradicting our hypothesis that there is a smallest first part.

So, there is no smallest first part.


Please take the time to find holes in there but at the end of the day, I'd like all those who tried to talk UM out of insanity to take a view on this very nearly formal proof and express this view in non-ambiguous terms so I don't feel like I worked hard to no avail.
EB

Eh. If spacetime is discrete in small 4dimensional cubes of side p then p is the smallest distance that all motion has to start with. since there obviously no logical contradiction in that assumption (motion is still totally possible) your proof seems to be dust...

For God sake, JuJu, focus!

I said, "flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other".

Ok, my post was a bit long, but you can't stay alert and focused beyond the first TWO lines?!
EB

 

[Kharakov]

Eh. If spacetime is discrete in small 4dimensional cubes of side p then p is the smallest distance that all motion has to start with. since there obviously no logical contradiction in that assumption (motion is still totally possible) your proof seems to be dust...

For God sake, JuJu, focus!

I said, "flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other".

Ok, my post was a bit long, but you can't stay alert and focused beyond the first TWO lines?!
EB

The above is TLDR, but I'd say that if people could post terse comments...

 

[Speakpigeon]

For God sake, JuJu, focus!

I said, "flat space, linear time, continuous space and time, and we can always assume that there is another point strictly in between two given points distinct from each other".

Ok, my post was a bit long, but you can't stay alert and focused beyond the first TWO lines?!
EB

The above is TLDR, but I'd say that if people could post terse comments...

MDR.
EB


Sorry, guys, it's all French to me and there's no translation service provided.
The Moderator

 

[Kharakov]

That was TLDR, or 'too long, didn't read' used as an adjective.

 

[fast]

But a movement of zero length only implies no "movement of," not that there is no "movement within."

How far does a car moving 60 mph move in 0 seconds?

In 10^-100 hours?


One of the things you could ask is... what is the smallest meaningful movement in reality at the electromagnetically dominated scale. In other words, what is the smallest movement that can impact the evolution of a system at the electromagnetic scale over a relatively short period of time (say 10^5 years or so)?

This doesn't mean there aren't smaller movements in reality, it just means that they won't have a meaningful impact on the evolution of the system in the time the system is observed (whether or not they will have an impact in the far future remains to be seen).

Atoms are all always in motion, even the atoms of a train, but if the train isn't traveling then the train (as a whole) isn't in forward or backward motion, even if there is vibrating motion or other movement to the trains components. If I'm perfectly still, it's kinda weird to deny it based on the fact my blood is flowing and heart is beating. If the train begins to go forward, then the smallest possible distance is (I suppose) somewhere near 1 to the negative 37 meters (something like that). That would not be the initial movement, but it would be the initial movement of the train. The initial movement of the train would be because of another movement-the movement within the train.

 

[Kharakov]

I think untermensche is going for his (begging the question) smallest possible movement in reality(/begging the question)- not smallest detectable movement (Planck scale).

I mentioned it because I figured it might be something that he is confused about- the difference between smallest detectable movement and any size movement in continuous reality (smallness is really scale based in the continuum).

 

[untermensche]

I think untermensche is going for his (begging the question) smallest possible movement in reality(/begging the question)- not smallest detectable movement (Planck scale).

I mentioned it because I figured it might be something that he is confused about- the difference between smallest detectable movement and any size movement in continuous reality (smallness is really scale based in the continuum).

My points are nothing but truisms.

A movement must have a length greater than zero.

So there must be some movement that is greater than zero that is the smallest possible movement something can make.

And that movement is not necessarily the same thing as the smallest detectable movement.

Are you saying there is no smallest possible movement?

How could something move without having a movement greater than zero? How could you have movement without a smallest possible movement to begin it?

 

[ryan]

I think untermensche is going for his (begging the question) smallest possible movement in reality(/begging the question)- not smallest detectable movement (Planck scale).

I mentioned it because I figured it might be something that he is confused about- the difference between smallest detectable movement and any size movement in continuous reality (smallness is really scale based in the continuum).

My points are nothing but truisms.

A movement must have a length greater than zero.

So there must be some movement that is greater than zero that is the smallest possible movement something can make.

And that movement is not necessarily the same thing as the smallest detectable movement.

Are you saying there is no smallest possible movement?

How could something move without having a movement greater than zero? How could you have movement without a smallest possible movement to begin it?

Then these "movements" would be just jumps that jump 0 distances (if we assume the smallest movement is the smallest unit of space); it becomes a paradox. Or we can accept infinitesimals even though they aren't easily imagined but are logically consistent.

 

[Kharakov]

I think untermensche is going for his (begging the question) smallest possible movement in reality(/begging the question)- not smallest detectable movement (Planck scale).

I mentioned it because I figured it might be something that he is confused about- the difference between smallest detectable movement and any size movement in continuous reality (smallness is really scale based in the continuum).

A movement must have a length greater than zero.

You're fine here.

So there must be some movement that is greater than zero that is the smallest possible movement something can make.

Noop. No logical reason to assume there has to be a smallest possible movement. You can divide that movement into 2 smaller movements, ad infinitum. Unless you claim to possess knowledge of reality that is unavailable to current generation humans? Are you a subatomic scale being?

Are you saying there is no smallest possible movement?

How could something move without having a movement greater than zero? How could you have movement without a smallest possible movement to begin it?

There is no "smallest amount of time elapsed since a movement began". The length of the movement is the velocity of the movement multiplied by the time elapsed (this is the simplest semi accurate description of movement).

So if something is moving 1 meter per second, the length of the movement is determined by the amount of time moved. If you wait 1 second, the length is 1 meter. If you wait .00000000000001 seconds, the length of the movement is .00...01 meters.

Capiche?

 

[Speakpigeon]

How could something move without having a movement greater than zero? How could you have movement without a smallest possible movement to begin it?

Then these "movements" would be just jumps that jump 0 distances (if we assume the smallest movement is the smallest unit of space); it becomes a paradox.

That would be because you have the wrong, and indeed paradoxical, conception of distance.

In a discrete or quantified space, the distance between any two neighbouring space locations is not zero but one. So, a zero distance movement would be staying put on the same space location and then we can agree it's no movement at all. The smallest movement then becomes any movement where the distance covered is one, i.e. from any one location to any neighbouring location.

In other words, distance can only be a function of the space locations attained by the moving thing different from the starting location. In particular, in a discrete space, there's nothing in between neighbouring space locations and that 'nothingness' cannot be allowed to count in how we compute the distance covered.

Unless you really like paradoxical conceptions.

Or we can accept infinitesimals even though they aren't easily imagined but are logically consistent.

Your conception of infinitesimals don(t seem logically consistent.
EB

 

[Speakpigeon]

No logical reason to assume there has to be a smallest possible movement. You can divide that movement into 2 smaller movements, ad infinitum. Unless you claim to possess knowledge of reality that is unavailable to current generation humans? Are you a subatomic scale being?

Well, it works both ways.

In an infinitely divisible space all you can hope is achieve a smaller movement than the previous one without any certainty that you will be able to do it again and again. And yet, if at some point you are unable to do it again it doesn't mean it can't be done in principle. And then we're left not knowing what kind of universe we're in.

If the universe is that with a discrete space, we may perhaps get to the smallest movement achievable, i.e. from one location to one of its neighbouring locations. But I don't see why we would know we'd have achieved the smallest movement possible. We may well think we have but how would we know for sure? And then, we're stuck.

To know the result would be in effect as if we could travel to the end of infinite time. We couldn't do that, presumably.

Although, who could know until we do it?
EB

 

[untermensche]

My points are nothing but truisms.

A movement must have a length greater than zero.

So there must be some movement that is greater than zero that is the smallest possible movement something can make.

And that movement is not necessarily the same thing as the smallest detectable movement.

Are you saying there is no smallest possible movement?

How could something move without having a movement greater than zero? How could you have movement without a smallest possible movement to begin it?

Then these "movements" would be just jumps that jump 0 distances (if we assume the smallest movement is the smallest unit of space); it becomes a paradox. Or we can accept infinitesimals even though they aren't easily imagined but are logically consistent.

They don't "jump" anywhere.

They slide right into that smallest possible movement smoothly. The only problem is they can't stop sooner.