Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby JudeMorrigan » Thu Nov 07, 2013 7:39 pm UTC

SecondTalon wrote:Unless you're saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2 on this other arbitrary measuring scale" to which the only answer is "..so?" or even the more abrasive "No shit?"

Based on my experience on this carosel, that's exactly what he means. And he refuses to believe that when we say "x' = x-vt", we are NOT saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2-vt on this other arbitrary measuring scale".

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby PolakoVoador » Thu Nov 07, 2013 8:10 pm UTC

JudeMorrigan wrote:
SexyTalon wrote:Unless you're saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2 on this other arbitrary measuring scale" to which the only answer is "..so?" or even the more abrasive "No shit?"

Based on my experience on this carosel, that's exactly what he means. And he refuses to believe that when we say "x' = x-vt", we are NOT saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2-vt on this other arbitrary measuring scale".


Yup. All this hundreds and hundreds of posts usually boil down to this. 'Round and 'round we go.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 2:08 pm UTC

JudeMorrigan wrote:
SexyTalon wrote:Unless you're saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2 on this other arbitrary measuring scale" to which the only answer is "..so?" or even the more abrasive "No shit?"

Based on my experience on this carosel, that's exactly what he means. And he refuses to believe that when we say "x' = x-vt", we are NOT saying that "a distance of 2 on this arbitrary measurement scale equals a distance of 2-vt on this other arbitrary measuring scale".

Well stated. This IS the issue. I am saying that since x is defined as the distance from S(0,0,0) to S(x,0,0)...
and x' defined as the distance from S'(0,0,0) to S'(x',0,0)
that this definition also applies to systems after any movement has occurred. That IS what x and x' are defined as.

I do grasp what you are NOT saying about x' = x-vt...and hence why I disagree with all of you.

Please tell me what equation you apply to the manifold? Is it S'(x',0,0) = S(x-vt,0,0)? If not, please tell me what equation does applies for the manifold? Noting that x represents a distance and that (x,0,0) represents a point. I am saying that x by itself, as in the equation x' = x-vt, is ALWAYS a distance and never just the point at S(x,0,0).

It seems you all grasp that even after vt was applied...and even totally agree that...
x [ the distance from S(0,0,0) to S'(x,0,0) equals x' [ the distance from S'(0,0,0) to S'(x',0,0) ]

and that you do not consequently mathematically extrapolate that this means x = x'...due to the fact that for you,
x' = x-vt is now exclusive ONLY to the manifold and thus makes x' = x-vt no longer pertinent to the given Cartesian systems definition for x and x'.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Chen » Fri Nov 08, 2013 2:45 pm UTC

steve waterman wrote:Well stated. This IS the issue. I am saying that since x is defined as the distance from S(0,0,0) to S(x,0,0)...
and x' defined as the distance from S'(0,0,0) to S'(x',0,0)
that this definition also applies to systems after any movement has occurred. That IS what x and x' are defined as.


You're defining x and x' in that manner. That is NOT the way they are defined in the Galilean Transform so any conclusions you are drawing from your definitions have nothing to do with the Galilean at all.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Nov 08, 2013 2:47 pm UTC

(x,0,0) represents a line, a point in potential, all of the possible values of X...but not a point. It represents ALL the points where your y and z values are 0. (5,0,0) represents a point.


Also, what the more math people say - that the Galiliean defines x and x' however it defines it, so if you're using different definitions you're going to get different conclusions.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 3:32 pm UTC

Mathematically, GIVEN Cartesian coordinate system S(x,y,z)... x is mathematically defined ( no choice ) as the abscissa of S. That means ( no choice ) that x is defined as the distance from S(0,0,0) to S(x,0,0). This is not just my way of looking at it, but the way that all mathematics defines x when given S(x,0,0).

The point that I seem to be having trouble getting across, is that it does NOT matter what/how the manifold works/functions. The point is that regardless, the relationship of x = x' IS maintained when one system gets moved from coincidence. So, not to be rude, but I do not care whatever the manifold does or does not do, as merely in saying
x' = x-vt says that the distance from S(0,0,0) to S(x,0,0) is no longer is equal to the distance from S'(0,0,0) to S'(x',0,0) WITH RESPECT TO the given condition for the two systems. What may or may not occur in the manifold has NO IMPACT upon the mathematical fact that x [ the distance from S(0,0,0) to S(x,0,0) ] =
x' [ the distance from S'(0,0,0) to S'(x',0,0) ]...indeed that x' = x after vt is applied.

I know that this is going to be difficult to accept, however, MY exclusive focus is to what x' = x-vt means wrt the abscissa distancing. Whether or not x' = x-vt applies to the manifold therefore has absolutely nothing to do with this/my line of reasoning/math/logic. This point never seemed to be understood by xkcd in several thousands of posts...and I will take the total blame for that, as I have not placed this concentrated focus onto this particular nuance, prior to this post.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Nov 08, 2013 3:53 pm UTC

Can you explain it like you'd explain it to a child? (Aka, someone under the age of 12)
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Chen » Fri Nov 08, 2013 4:05 pm UTC

steve waterman wrote:Mathematically, GIVEN Cartesian coordinate system S(x,y,z)... x is mathematically defined ( no choice ) as the abscissa of S. That means ( no choice ) that x is defined as the distance from S(0,0,0) to S(x,0,0). This is not just my way of looking at it, but the way that all mathematics defines x when given S(x,0,0).


x can be defined as the distance between S(0,0,0) and S(x,0,0). Similarly we can define x' as the distance from S'(0,0,0) to S'(x',0,0). In BOTH these cases S(x,0,0) and S'(x',0,0) represent points. If both are the same point, when S and S' are coincident, then yes x = x'. Say now S' "moves" (this isn't precise terminology, but its what you're using so lets use that for now). S(x,0,0) still represents the same point. However, S'(x',0,0) now represents a DIFFERENT point, if we still hold x = x'. If we want to still talk about the first point S(x,0,0) we need to change our coordinates of that point in the S' system. That is what the Galilean does.

Basically:
IF S(x,0,0)=S'(x',0,0) and S and S' are coincident, then x = x'
IF S and S' are NOT coincident and x = x' then S(x,0,0) ≠ S'(x',0,0)

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 8:01 pm UTC

SecondTalon wrote:Can you explain it like you'd explain it to a child? (Aka, someone under the age of 12)


That might be interesting to try.

Imagine you have two 12 inch rulers, but imagine that both rulers share the exact same locations in space.

Now imagine we place a red dot at the same number of inches on each of the two rulers, say at 4 1/2 inches.

Now, take of the rulers and hide one under your mattress and keep the other one in your hand.

What is your answer to these three questions???

Do you think that two red dots still are both at 4 1/2 inches with respect to their own ruler?

Do you think that the two dots still share the same location in space?

Do you think that the ruler under the mattress still even has its red dot, or did that red dot disappear when it was placed under the mattress?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Chen » Fri Nov 08, 2013 8:09 pm UTC

steve waterman wrote:
SexyTalon wrote:Can you explain it like you'd explain it to a child? (Aka, someone under the age of 12)


That might be interesting to try.

Imagine you have two 12 inch rulers, but imagine that both rulers share the exact same locations in space.

Now imagine we place a red dot at the same number of inches on each of the two rulers, say at 4 1/2 inches.

Now, take of the rulers and hide one under your mattress and keep the other one in your hand.

What is your answer to these three questions???

Do you think that two red dots still are both at 4 1/2 inches with respect to their own ruler?

Do you think that the two dots still share the same location in space?

Do you think that the ruler under the mattress still even has its red dot, or did that red dot disappear when it was placed under the mattress?


A good explanation of the point you're trying to make I think. The issue is the Galilean describes a situation where instead of putting the red dot on the ruler, you put the red dot on the floor. Then move the ruler. The question of how far the red dot is NOW from the ruler you moved. By knowing how fast the ruler moved with respect to the ruler that remains stationary, we can tell you how far the red dot is away from the moving ruler, without needing to measure the actual distance (using a third ruler).

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 8:37 pm UTC

Chen wrote:
steve waterman wrote:
SexyTalon wrote:Can you explain it like you'd explain it to a child? (Aka, someone under the age of 12)


That might be interesting to try.

Imagine you have two 12 inch rulers, but imagine that both rulers share the exact same locations in space.

Now imagine we place a red dot at the same number of inches on each of the two rulers, say at 4 1/2 inches.

Now, take of the rulers and hide one under your mattress and keep the other one in your hand.

What is your answer to these three questions???

Do you think that two red dots still are both at 4 1/2 inches with respect to their own ruler?

Do you think that the two dots still share the same location in space?

Do you think that the ruler under the mattress still even has its red dot, or did that red dot disappear when it was placed under the mattress?


A good explanation of the point you're trying to make I think. The issue is the Galilean describes a situation where instead of putting the red dot on the ruler, you put the red dot on the floor. Then move the ruler. The question of how far the red dot is NOW from the ruler you moved. By knowing how fast the ruler moved with respect to the ruler that remains stationary, we can tell you how far the red dot is away from the moving ruler, without needing to measure the actual distance (using a third ruler).


This does NOT assume, as the Galilean does, that the red dot on the moved ruler stays in the same location as it was before moving the ruler under the mattress. Indeed, that IS the premise SOLELY of the Galilean, and one that I say is contrived/bogus/fudged. EVERY damn 12 year old KNOWS the red dot is still on the moved ruler. For the 12 year old, there is no manifold, there is just these two damn rulers...um, where it makes no sense to have the red dot disappear from the ruler that gets placed under the mattress.

SexyTalon...I cannot receive a private message because somehow my password changed. I cannot use the temporarily password either ( tried too many times according to that page ) and when I answer the damn number thingie...it too fails...when I tried that 3 different times.
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added - Huh, it seems that Ican see private messages now by clicking on ( 1 new message ) at page top.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby WibblyWobbly » Fri Nov 08, 2013 9:03 pm UTC

steve waterman wrote:This does NOT assume, as the Galilean does, that the red dot on the moved ruler stays in the same location as it was before moving the ruler under the mattress. Indeed, that IS the premise SOLELY of the Galilean, and one that I say is contrived/bogus/fudged. EVERY damn 12 year old KNOWS the red dot is still on the moved ruler. For the 12 year old, there is no manifold, there is just these two damn rulers...um, where it makes no sense to have the red dot disappear from the ruler that gets placed under the mattress.

That's not what the Galilean assumes. The Galilean does not say that the dots on the rulers disappear, it says that the dot you put on the moving ruler, once you move it under the mattress, is no longer interesting. Not something we're worried about anymore. That dot can be there and no one will care. Because what the Galilean is ACTUALLY INTERESTED IN IS NOT DOTS ATTACHED TO RULERS. It's POINTS IN SPACE. You know, those points, like basketballs, that exist whether you've got one ruler, no rulers, or fifteen goddamn billion rulers. No one cares. The dots being on the rulers before and after you move them is known to every 12-year-old because IT'S ENTIRELY FUCKING TRIVIAL.

Imagine your example, but now put one, single, solitary red dot on a basketball over on the desk. No dots on rulers, because the Galilean doesn't care. Now, take your two rulers, and put them at the same spot IN RELATION TO THE BASKETBALL. Note how far away the basketball is from the origin of each ruler. Now, take one of the rulers, and start walking backwards. How far away is the basketball from the origin of the moving ruler? We can figure it out by knowing how far the basketball is from the origin of the stationary ruler and how fast (and in what direction) the moving ruler is moving RELATIVE TO THE STATIONARY ONE. And that's the Galilean. No dots attached to rulers, because no one gives a fuck about them.

If you still think the Galilean is about disappearing dots, go the fuck back to school and learn something, damn it.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby JudeMorrigan » Fri Nov 08, 2013 9:15 pm UTC

I've always found it ironic that this all boils down to a map-territory confusion given the way that steve makes genuinely and unironically awesome maps.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Nov 08, 2013 9:23 pm UTC

steve waterman wrote:Do you think that two red dots still are both at 4 1/2 inches with respect to their own ruler?

Do you think that the two dots still share the same location in spaaace?

Do you think that the ruler under the mattress still even has its red dot, or did that red dot disappear when it was placed under the mattress?


1. Uh.. no duh? You put it on the measuring device, not the thing being measured, so of course the red dots aren't going to change.

2. No, because the dots never existed in space, they existed on the measuring device.

3. Again, as the dot is on the device, it's still there.

At no point is any of this useful for describing a point in space, merely for describing points on the measuring devices.

This does NOT assume, as the Galilean does, that the red dot on the moved ruler stays in the same location as it was before moving the ruler under the mattress. Indeed, that IS the premise SOLELY of the Galilean, and one that I say is contrived/bogus/fudged. EVERY damn 12 year old KNOWS the red dot is still on the moved ruler. For the 12 year old, there is no manifold, there is just these two damn rulers...um, where it makes no sense to have the red dot disappear from the ruler that gets placed under the mattress.


.. and every 12 year old knows that if you want to describe the relationship between two points in space, making marks on the measuring devices is useless.

Unless I'm mistaken, the Galilean is about taking a single point in space and - on two different measuring systems that overlap each other - describe the relationship between the different measurements.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby DaBigCheez » Fri Nov 08, 2013 9:28 pm UTC

Steve - there is absolutely no argument from anyone here about the claim that red-dots-on-rulers will stay at the same inch marker on the rulers no matter how you move said rulers. We've already agreed, we have no contention with that claim. Everyone agrees it is true. We just don't think that it's a particularly interesting claim, because it is obvious.

What the Galilean transform is discussing, and what we have generally been discussing, is not a situation where the red dot is placed on the two rulers, but rather where it is placed on the point on the ground, and then we wish to determine what inch-marker on each of the different rulers that dot will be at. For example, measuring to find how far from each of the walls of a room a nail you wish to hang a picture from is - it might be +4 feet from the left wall and -6 feet from the right wall.

The thing is, the "dot on the floor" isn't so much a "premise" of the Galilean, as just what it's talking about. What it's concerned with. If I say that I want a ham sandwich for lunch, because ham is tasty, but you insist that a loaf of bread is eighteen inches long, that doesn't mean the "ham is tasty" assumption is contrived/bogus/fudged. And if you keep arguing that I'm wrong to want a ham sandwich because a loaf of bread is eighteen inches long, then I would say "yes, it is eighteen inches long, but we're simply talking about two different things - my desire for a ham sandwich simply isn't concerned with the length of a loaf of bread, that's not what we're talking about here".

The Galilean transformation is concerned with "measuring the distance to a dot on the floor using two non-co-located rulers". Your concern with how far along a pair of rulers a set of dots on those rulers will be is noted, but that's a) a different question, and b) an uninteresting question, since it is immediately obvious to anyone that of course the dots will stay at the same inch-marker on the rulers no matter how you move them. And if you misuse terminology and try to use the Galilean transformation with "dots on the rulers", then of course you're going to come up with bogus answers - just like I wouldn't get a very tasty sandwich by trying to use an entire eighteen-inch loaf of bread in place of a slice of ham. It's not what it's for, it's not what the notation means, and disputing it by trying to use things it's simply not concerned with is akin to announcing someone is wrong because, in a new language you've just invented, "a loaf of bread is eighteen inches long" actually means "ham is made of deadly poison" - no matter how frantically you try to warn us not to eat the ham because a loaf of bread is eighteen inches long, we will continue to be confused as to why you think that's even relevant, because we're simply not speaking the same language.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 10:13 pm UTC

ST,

I have been told over and over and had forced upon me many times..."points do not move as the coordinate system moves". That is, only the coordinates move but NOT the red dots/points. That is the problem. The red dots/points I say do move, and up to now, you/the Galilean declares that points/red dots do not move with the moving system.

This is what the Galilean does...it moves one system but DOES NOT move any points. That is EXACTLY what I object to. Do not confuse the coordinate locations wrt a moving system, which DO move as the system moves, with POINTS/red dots, which according to the Galilean, do not move with the moving system.

Hence why this example of rulers and red dots directs us to the Galilean's already well-beaten-to-death assertion that points do not move as the system moves...only the relative coordinates move as the system moves. So, that was forced down my throat for hundreds of pages and now you contend that the red dots DO move with the system but are "uninteresting". I can only assume then, that you make no distinction between a coordinate and a point.

recap...every 12 year old knows that the red dots do move with the ruler under the mattress. Like it or not, the Galilean does premise that their red dot never moves with the moved system. That is why you get x = 2 and x' = -1 when vt = 3...because you simply ignore/"are uninterested" in the moved red dot. You simply compare point locations S'(x',0,0) to S(x,0,0) -vt and totally ignore that the distances of x' and x-vt are not equal.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Nov 08, 2013 10:21 pm UTC

I'm saying that if you mark a ruler and then move the ruler, the point you marked is on the ruler no matter how you wave it around, unless you marked it with jelly or clay or something, and it flies off in your waggling.

I am also saying this is completely and utterly meaningless in any application that is not explicitly paint application to measuring devices.


In the application of our tool, the ruler with the mark, that's not the coordinate system. The coordinate system starts where we are putting the 0 of the ruler. The ruler is simply a tool to let us know how far 3cm is from whatever we decided the point of origin was.

This is only remarkable to the point of origin. If we choose a different point of origin, the spot will - in almost all cases - no longer be 3cm along, but maybe 5cm, or 20cm, or -5cm.

Because the point is not moving, we're moving between different coordinate systems. Every time we slap the ruler down at a different spot, we're using a different coordinate system to measure to our point that's not on the ruler.

The way you are describing it is not unlike hooking a speedometer to the spare tire in the back of the car, doing 90 in a 35 and exclaiming "But I'm not even moving according to this dial!" when the cop arrests you. If you move your measuring device, any measurements you tie explicitly to the device remain on the device. This is in no way remarkable, unusual, or notable.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby DaBigCheez » Fri Nov 08, 2013 10:23 pm UTC

steve waterman wrote:Do not confuse the coordinate locations wrt a moving system, which DO move as the system moves, with POINTS/red dots, which according to the Galilean, do not move with the moving system.

Alright. Could we ask you to do the same, then? The Galilean is only concerned with points. Trying to apply the Galilean to "coordinate locations" will get you nowhere. Objecting to the use of the Galilean on "coordinate locations" will likewise get you nowhere, because nobody applies the Galilean when dealing with "coordinate locations", they apply it when dealing with points.
steve waterman wrote:So, that was forced down my throat for hundreds of pages and now you contend that the red dots DO move with the system but are "uninteresting". I can only assume then, that you make no distinction between a coordinate and a point.

*rubs temples*
I was/we were trying to demonstrate that we understood what you meant by your coordinate locations - that if you take your coordinate location (a point defined by a vector from the origin of its coordinate system), and you move the coordinate system it's defined by, it will move with the coordinate system. Sure! Great! That's true by the very definition of what you're defining as a coordinate location! That's fantastic, that's true, and that's utterly irrelevant to the Galilean, because the Galilean deals with points.
steve waterman wrote:Like it or not, the Galilean does premise that their red dot never moves with the moved system. That is why you get x = 2 and x' = -1 when vt = 3...because you simply ignore/"are uninterested" in the moved red dot.

If the "moved red dot" is referring to a 'coordinate location'...yes. Exactly. So, we're done here then?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Nov 08, 2013 10:27 pm UTC

SecondTalon wrote:... the spare tire in the back of the cat...


...

Well played, whoever. Well played indeed.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 10:53 pm UTC

Round and round.

x is defined as distance...you all insist upon comparing points. You focus exclusively upon the end point of the vector distance. You say the red dots do move but are uninteresting. I tire of this arguing technique of avoidance by saying the dots are uninteresting as your manner of dismissal.

You talk about point equality whereas I talk about distance equality. I say x is distance, you say x is (x,0,0). The Galilean equation x' = x-vt says x and not S(x,0,0). I hear two scenarios about red dots...they do move and they do not move. This makes arguing most frustrating, and logic impossible to agree upon. I think I need another break, as you all insist that x' = x-vt is about points ( that never move ) and I stick with x as defined by the distance from S(0,0,0) to S(x,0,0). You say points/aka red dots are not IN a coordinate system...only in the manifold

The Galilean equation x' = x-vt has an x but has no S(x,0,0).
The manifold has no distance x but has an S(x,0,0) and yet needs no S(0,0,0).

added -
when vt = 3, I wonder if we now finally all agree that
S(2,0,0) and S'(-1,0,0) share the same location in space in the manifold.
the distance x from S(0,0,0) to S(2,0,0) does not equal the distance x' from S'(0,0,0) to S'(-1,0,0).
the distance x from S(0,0,0) to S(2,0,0) equals the distance x' from S'(0,0,0) to S'(2,0,0).
x is defined as the distance x from S(0,0,0) to S(x,0,0).
x' is defined as the distance x' from S(0,0,0) to S'(x',0,0).
Last edited by steve waterman on Fri Nov 08, 2013 11:14 pm UTC, edited 1 time in total.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby PolakoVoador » Fri Nov 08, 2013 11:11 pm UTC

steve waterman wrote:Round and round.

x is defined as distance...you all insist upon comparing points. You focus exclusively upon the end point of the vector distance. You say the red dots do move but are uninteresting. I tire of this arguing technique of avoidance by saying the dots are uninteresting as your manner of dismissal.

You talk about point equality whereas I talk about distance equality. I say x is distance, you say x is (x,0,0). The Galilean equation x' = x-vt says x and not S(x,0,0). I hear two scenarios about red dots...they do move and they do not move. This makes arguing most frustrating, and logic impossible to agree upon. I think I need another break, as you all insist that x' = x-vt is about points ( that never move ) and I stick with x as defined by the distance from S(0,0,0) to S(x,0,0). You say points/aka red dots are not IN a coordinate system...only in the manifold

The Galilean equation x' = x-vt has an x but has no S(x,0,0).
The manifold has no distance x but has an S(x,0,0) and yet needs no S(0,0,0).


C'mon Steve! It's been pointed out to you before. The equation x'=x-vt is a shorthand for S'(x',y',z')=S'(x-vt,y,z)=S(x,y,z) because who the hell has time to type all this stuff? Can you understand this? Are you OK with this?
Last edited by PolakoVoador on Fri Nov 08, 2013 11:52 pm UTC, edited 1 time in total.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Nov 08, 2013 11:28 pm UTC

PolakoVoador wrote:
steve waterman wrote:Round and round.

x is defined as distance...you all insist upon comparing points. You focus exclusively upon the end point of the vector distance. You say the red dots do move but are uninteresting. I tire of this arguing technique of avoidance by saying the dots are uninteresting as your manner of dismissal.

You talk about point equality whereas I talk about distance equality. I say x is distance, you say x is (x,0,0). The Galilean equation x' = x-vt says x and not S(x,0,0). I hear two scenarios about red dots...they do move and they do not move. This makes arguing most frustrating, and logic impossible to agree upon. I think I need another break, as you all insist that x' = x-vt is about points ( that never move ) and I stick with x as defined by the distance from S(0,0,0) to S(x,0,0). You say points/aka red dots are not IN a coordinate system...only in the manifold

The Galilean equation x' = x-vt has an x but has no S(x,0,0).
The manifold has no distance x but has an S(x,0,0) and yet needs no S(0,0,0).


C'mon Steve! It's been pointed out to you before. The equation x'=x-vt is a shorthand for S'(x,y,z)=S(x-vt,y,z) because who the hell has time to type all this stuff? Can you understand this? Are you OK with this?

Total bullshit. Then why isn't the Galilean equation written in ALL the textbooks as S'(x,y,z) = S(x-vt,y,z)...because EVERY Physics textbook for over 100 years only has the time to write x' = x-vt, ???
You are joking, right? ( rhetorical )
Finally some comic relief, thanks, Polako I needed that, dude! ( where "dude" is not gender specific! )
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Fri Nov 08, 2013 11:32 pm UTC

steve waterman wrote:Round and round. x is defined as distance...you all insist upon comparing points


Damn straight, because that's what the Galilean transform is talking about. Whatever are the brilliant ideas are created by your singular genius that will revolutionise maths forever, they are not related to the Galilean transform because they're talking about something different than the Galilean transform, as we have informed you on numerous occasions.

PolakoVoador wrote:C'mon Steve! It's been pointed out to you before. The equation x'=x-vt is a shorthand for S'(x,y,z)=S(x-vt,y,z) because who the hell has time to type all this stuff? Can you understand this? Are you OK with this?

Just to avoid confusion, this should read x'=x-vt is a shorthand for S'(x',y',z')=S'(x-vt,y,z)=S(x,y,z)

steve waterman wrote:when vt = 3, I wonder if we now finally all agree that
S(2,0,0) and S'(-1,0,0) share the same location in spaaace in the manifold.

Correct: they map to the same point.

steve waterman wrote:the distance x from S(0,0,0) to S(2,0,0) does not equal the distance x' from S'(0,0,0) to S'(-1,0,0).

Correct: the origins are also separated in this case.

steve waterman wrote:the distance x from S(0,0,0) to S(2,0,0) equals the distance x' from S'(0,0,0) to S'(2,0,0).

Correct if you have three-dimensional Cartesian co-ordinate systems in the four-dimensional space (and not four-dimensional co-ordinate systems which we were using to help avoid this confusion) and the co-ordinate systems have the same unit size.

steve waterman wrote:x is defined as the distance x from S(0,0,0) to S(x,0,0).

One could define x=d(S(0,0,0), S(x,0,0)); note this does not necessarily hold for non-Cartesian systems

steve waterman wrote:x' is defined as the distance x' from S(0,0,0) to S'(x',0,0).

False. By our previous definition it would be the distance between S'(0,0,0) to S'(x',0,0) parallel to the x' axis.
Last edited by yurell on Fri Nov 08, 2013 11:51 pm UTC, edited 1 time in total.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Fri Nov 08, 2013 11:45 pm UTC

steve waterman wrote:Total bullshit. Then why isn't the Galilean equation written in ALL the textbooks as S'(x,y,z) = S(x-vt,y,z)...because EVERY Physics textbook for over 100 years only has the time to write x' = x-vt, ???
You are joking, right? ( rhetorical )
Finally some comic relief, thanks, Polako I needed that, dude! ( where "dude" is not gender specific! )


We have discussed this before, both with and without the condescension dripping from your post. We don't need to use manifold notation because most physicists (or even high school students) understand intuitively the assumptions being employed. However, you have demonstrated that you don't understand the implication by this very post, which is why we've been going a more formal route. If you want formal, precise language, physicists are not the people to go to — mathematicians are. They build these things from the ground up, which is why Schrollini first introduced you to manifold notation.
As for why the longer notation isn't written in every textbook? Because trying to teach an idea using subjects the students haven't learnt is completely stupid.

Edit: Sorry for the double-post, mods; my internet is about 5 kB/s at the moment, so I can barely tell what's going on
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby PolakoVoador » Fri Nov 08, 2013 11:50 pm UTC

yurell wrote:
PolakoVoador wrote:C'mon Steve! It's been pointed out to you before. The equation x'=x-vt is a shorthand for S'(x,y,z)=S(x-vt,y,z) because who the hell has time to type all this stuff? Can you understand this? Are you OK with this?

Just to avoid confusion, this should read x'=x-vt is a shorthand for S'(x',y',z')=S'(x-vt,y,z)=S(x,y,z)


Thanks yurell! I will fix it.

steve waterman wrote:Total bullshit. Then why isn't the Galilean equation written in ALL the textbooks as S'(x,y,z) = S(x-vt,y,z)...because EVERY Physics textbook for over 100 years only has the time to write x' = x-vt, ???
You are joking, right? ( rhetorical )
Finally some comic relief, thanks, Polako I needed that, dude! ( where "dude" is not gender specific! )


The justification of "who the hell has time to type all this stuff" was indeed kinda of a joke, but I forgot you are unbelievably literal when reading, and can't parse context. Which, by the way, is the reason why the Galillean is mostly written in the "short" form: context. Using it, everyone can understand what is meant by x, x', etc.

EDIT: also, what yurell said. It's a better answer.

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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Sat Nov 09, 2013 1:10 pm UTC

x' is defined as the distance x' from S'(0,0,0) to S'(x',0,0)
Oops...I made a typo, obviously, as I have said/typed this definition properly like perhaps a 100 times before, so I corrected the above statement.

Now, I wish to focus upon the assertion that although the Galilean equation is always written as x' = x-vt, it really means that S'(x',y',z')=S'(x-vt,y,z)=S(x,y,z). Specifically the assertion that the textbook equation is written as x' = x-vt because everyone knows that x' = x-vt is about points in the manifold and not about distances from an origin.

Also, it seems that xkcd agrees that given S(x,y,,z) = S'(x,y,z'),
x is defined as the distance from S(0,0,0) to S(x,0,0) and that
x' is defined as the distance from S'(0,0,0) to S'(x',0,0)

and the Galilean denies that after vt is applied, that x = x',
insisting that x' = x-vt no longer refers to distance from their own origin, which becomes "uninteresting" and rather is all about a singular point P and NOT a shred to do about the distances x and x'.


I wonder also, if I could ask for xkcd posters to include their age. I was quite surprised to see the tally from the "AGE" thread. The average age was way below what I had envisioned it to be. This is just personal curiosity, and will not be used an argumentative wedge/ploy as justification against anyone. I have found almost a unified front of logic exhibited by all
( younger and older ) xkcd people. It surely does not matter if someone is say, under 14, in order to be quite logical. If you wish to keep this your secret, that is surely up to you. I thought I would ask, and for the record, I will turn 66 this month; being part of the 2 percent of the group of over 41.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Sat Nov 09, 2013 1:25 pm UTC

What is the point of distance to origin? What purpose does it serve to single it out and work with it while explicitly not using points for the exact same data?

And the age information in my profile is accurate.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Sat Nov 09, 2013 1:37 pm UTC

SecondTalon wrote:What is the point of distance to origin?

Because in the given Galilean equation x' = x at t = 0, x was defined as distance and x' was defined as distance.
Regardless of what one may think the manifold point equation might be, the fact is that these definitions for x and x' do not chance because vt got applied. That means that distance x = distance x' always, and that x' = x-vt only if vt = 0.

btw, I notice that very very few people have included the age in their profile.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Sat Nov 09, 2013 1:40 pm UTC

The origins (of the 3D Cartesian systems at time t≠0) are in different places, so the fact that we end up with two different distances when measuring how far it is from each to a defined point is unsurprising and uninteresting.
When we use the 4D system, we see that there's a component of the t' axis that's parallel with the x' axis — that is to say, the axes aren't all orthogonal and thus the system isn't Cartesian — and so the vector distance becomes even more meaningless than it was before.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Sat Nov 09, 2013 1:59 pm UTC

yurell wrote:The origins (of the 3D Cartesian systems at time t≠0) are in different places,


It is part of the given for the Galilean, at t = 0, S and S' are coincident.
That means that S and S' are in the same exact place at t = 0.
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The notation below describes the relationship under the Galilean transformation between the coordinates (x,y,z,t) and (x′,y′,z′,t′) of a single arbitrary event, as measured in two coordinate systems S and S', in uniform relative motion (velocity v) in their common x and x’ directions, with their spatial origins coinciding at time t=t'=0:

x'=x-vt,
y'=y ,
z'=z ,
t'=t ,
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Sat Nov 09, 2013 2:20 pm UTC

steve waterman wrote:
yurell wrote:The origins (of the 3D Cartesian systems at time t≠0) are in different places,


It is part of the given for the Galilean, at t = 0, S and S' are coincident.


What's your point? I say that at t≠0 the two are in different places, and so you're measuring two different distances, and your response is to insist that they're in the same place at t=0? I don't contest that! How about the infinite amount of time it's not the initial time; that is to say, the time I was talking about?
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Sat Nov 09, 2013 2:53 pm UTC

yurell wrote:
steve waterman wrote:
yurell wrote:The origins (of the 3D Cartesian systems at time t≠0) are in different places,

It is part of the given for the Galilean, at t = 0, S and S' are coincident.

What's your point? I say that at t≠0 the two are in different places, and so you're measuring two different distances, and your response is to insist that they're in the same place at t=0? I don't contest that! How about the infinite amount of time it's not the initial time; that is to say, the time I was talking about?

The Galilean given commences at t = 0, then t becomes > 0, where that time gets multiplied by velocity to achieve a distance, representing the separation distance between the S origin and the S' origin along the common x /x' axis. So, certainly at t > 0, the two origins do not share a common location in space.
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Carry on my wayward son

Postby Schrollini » Sat Nov 09, 2013 4:44 pm UTC

What devilry is this? Steve Waterman, late of these parts, vowed ne'er to return, doth appear. Speak, O specter -- what tidings doth ye bring? What witchcraft hath doom'd thy soul to haunt this message board?

My friends, my compatriots, who I hold to my breast, remember ye this: For as the sun need not a cloud to shine, neither doth a coordinate system need a metric. Verily I tell you, thou mustn't consider distances whilst transforming thy coordinates. And while thy coordinate systems and metric spaces are oft together, as the sun and the cloud doth share the heavenly sphere, thou must keep them separate in thy thoughts, lest foul tidings befall you!

Good day, and thus, good bye.
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Re: Carry on my wayward son

Postby PolakoVoador » Sat Nov 09, 2013 6:29 pm UTC

Schrollini wrote:What devilry is this? Steve Waterman, late of these parts, vowed ne'er to return, doth appear. Speak, O specter -- what tidings doth ye bring? What witchcraft hath doom'd thy soul to haunt this message board?

My friends, my compatriots, who I hold to my breast, remember ye this: For as the sun need not a cloud to shine, neither doth a coordinate system need a metric. Verily I tell you, thou mustn't consider distances whilst transforming thy coordinates. And while thy coordinate systems and metric spaces are oft together, as the sun and the cloud doth share the heavenly sphere, thou must keep them separate in thy thoughts, lest foul tidings befall you!

Good day, and thus, good bye.

[/thread]

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Re: Carry on my wayward son

Postby lokar » Sat Nov 09, 2013 11:58 pm UTC

Schrollini wrote:What devilry is this? Steve Waterman, late of these parts, vowed ne'er to return, doth appear. Speak, O specter -- what tidings doth ye bring? What witchcraft hath doom'd thy soul to haunt this message board?

My friends, my compatriots, who I hold to my breast, remember ye this: For as the sun need not a cloud to shine, neither doth a coordinate system need a metric. Verily I tell you, thou mustn't consider distances whilst transforming thy coordinates. And while thy coordinate systems and metric spaces are oft together, as the sun and the cloud doth share the heavenly sphere, thou must keep them separate in thy thoughts, lest foul tidings befall you!

Good day, and thus, good bye.


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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Sun Nov 10, 2013 3:35 am UTC

Steve, when you say x=x', you must also staple your two rulers together at that point.... x in (ruler) S gets stapled to x' in (ruler) S'. This ensures that x will always equal x'.

Now move the rulers around.

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Re: Carry on my wayward son

Postby addams » Sun Nov 10, 2013 3:54 am UTC

Schrollini wrote:What devilry is this? Steve Waterman, late of these parts, vowed ne'er to return, doth appear. Speak, O specter -- what tidings doth ye bring? What witchcraft hath doom'd thy soul to haunt this message board?

My friends, my compatriots, who I hold to my breast, remember ye this: For as the sun need not a cloud to shine, neither doth a coordinate system need a metric. Verily I tell you, thou mustn't consider distances whilst transforming thy coordinates. And while thy coordinate systems and metric spaces are oft together, as the sun and the cloud doth share the heavenly sphere, thou must keep them separate in thy thoughts, lest foul tidings befall you!

Good day, and thus, good bye.

Nice. Very nice.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Sun Nov 10, 2013 12:41 pm UTC

ucim wrote:Steve, when you say x=x', you must also staple your two rulers together at that point.... x in (ruler) S gets stapled to x' in (ruler) S'. This ensures that x will always equal x'.

Now move the rulers around.

Jose

The Galilean example however would do this...
1 commence with the two rulers imagined to be in the same place ( coincident )
2 moves one ruler
s since x is the distance from the zero inches location and not just the point at x, at that same vector head,
then of course that ensues that x will always equal x'.

Care to mention you age?

btw, the red dot on the ruler ( or not on the ruler ) under the mattress is critical, and of infinite interest.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Sun Nov 10, 2013 12:56 pm UTC

I have no idea what your contention is at this point.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby quetzal1234 » Sun Nov 10, 2013 4:24 pm UTC

DaBigCheez wrote:
Spoiler:
Steve - there is absolutely no argument from anyone here about the claim that red-dots-on-rulers will stay at the same inch marker on the rulers no matter how you move said rulers. We've already agreed, we have no contention with that claim. Everyone agrees it is true. We just don't think that it's a particularly interesting claim, because it is obvious.

What the Galilean transform is discussing, and what we have generally been discussing, is not a situation where the red dot is placed on the two rulers, but rather where it is placed on the point on the ground, and then we wish to determine what inch-marker on each of the different rulers that dot will be at. For example, measuring to find how far from each of the walls of a room a nail you wish to hang a picture from is - it might be +4 feet from the left wall and -6 feet from the right wall.

The thing is, the "dot on the floor" isn't so much a "premise" of the Galilean, as just what it's talking about. What it's concerned with. If I say that I want a ham sandwich for lunch, because ham is tasty, but you insist that a loaf of bread is eighteen inches long, that doesn't mean the "ham is tasty" assumption is contrived/bogus/fudged. And if you keep arguing that I'm wrong to want a ham sandwich because a loaf of bread is eighteen inches long, then I would say "yes, it is eighteen inches long, but we're simply talking about two different things - my desire for a ham sandwich simply isn't concerned with the length of a loaf of bread, that's not what we're talking about here".

The Galilean transformation is concerned with "measuring the distance to a dot on the floor using two non-co-located rulers". Your concern with how far along a pair of rulers a set of dots on those rulers will be is noted, but that's a) a different question, and b) an uninteresting question, since it is immediately obvious to anyone that of course the dots will stay at the same inch-marker on the rulers no matter how you move them. And if you misuse terminology and try to use the Galilean transformation with "dots on the rulers", then of course you're going to come up with bogus answers - just like I wouldn't get a very tasty sandwich by trying to use an entire eighteen-inch loaf of bread in place of a slice of ham. It's not what it's for, it's not what the notation means, and disputing it by trying to use things it's simply not concerned with is akin to announcing someone is wrong because, in a new language you've just invented, "a loaf of bread is eighteen inches long" actually means "ham is made of deadly poison" - no matter how frantically you try to warn us not to eat the ham because a loaf of bread is eighteen inches long, we will continue to be confused as to why you think that's even relevant, because we're simply not speaking the same language.

Irrelevant, but props to DBC on a good post that went fairly ignored. I actually understand what you all are talking about now.
That's all I wanted to say, I'll let you get back to it now.
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