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

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

steve waterman wrote:vbkid
2 Quick questions.
Are you open to the idea that you are wrong and need to understand why you are wrong?

Are you simply frustrated because you know you are right, and you know that I am wrong?

These are rhetorical questions of course,

While they might be rhetorical, I'm happy to answer them as posed.

Yes, I am open to the idea that I am wrong. I have followed everything posted by both you and others, and have even gone to outside sources to brush on on stuff I was unsure of or hadn't known to begin with. I have learned a lot. However, all this learning has only supported my original stance, which is that it is clear where you are going wrong, which many people have happily pointed out and attempted to explain.

I am ALSO frustrated that I know both I and others are right, and you are not willing to learn.

Here's the thing, I can follow your 'logic' step by step and, as been pointed out by many, it is clear where your beliefs take a wrong turn. The reason I am frustrated is that while it has been spelled out clearly, you have not appeared to make an honest attempt to follow everyone elses logic.

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

"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve

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

steve waterman wrote:

Last edited by beojan on Mon Jul 29, 2013 3:47 pm UTC, edited 1 time in total.

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

steve waterman wrote:(new version)
Spoiler:
There is no "in physics". Also, we were not given v or t.

Granting what I think you mean, note that in math, even the math that physics uses, x'=x-vt when vt=0 also.

The x=x' equation is thus unnecessary.

x'=x-vt defines the relationship between x' and x.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

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

Thanks for the feedback, found the missing prime typo and got rid of vt...

"While statistics and measurements can be misleading, mathematics itself, is not subjective."
"Be careful of what you believe, you are likely to make it the truth."
steve

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

steve waterman wrote:Thanks for the feedback, found the missing prime typo and got rid of vt...

If Bob and Fred are in the same place, the distance between Bob and the Eiffel tower = the distance between Fred and the Eiffel tower.
In physics (and math, and everywhere else) if Bob and Fred are not in the same place, the distance between Bob and the Eiffel tower is not (necessarily) = the distance between Fred and the Eiffel tower.

This is a perfect example of a completely trivial statement.
No one is arguing with this.

(All assuming, as previously, S(x,y,z) = S'(x',y',z'))

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

Steve, we know that the Wikipedia article doesn't satisfy you, which is why we ignored it and built from the ground up. It's designed to communicate an idea in a simple manner, not a rigorous one. This is why we introduced 2D spacetime, so that we could show you what the transformation is like without requiring 'moving' spatial co-ordinates. What don't seem to realise is that you're making assumptions that no one else is making, and then saying this disproves what everyone else is saying. I am going to need your help to find where disagreement occurs, though.

Let's look at your latest post: "Given spatially coincident Cartesian systems S(x,y,z) and S'(x',y',z')"
Okay, under those assumptions, S(x,y,z) = S'(x',y',z') = S'(x,y,z), and so x'=x, y'=y,z'=z. Keep careful track of those primes. You now have two perfectly coincident co-ordinate systems, Cartesian or no. Now, nobody disagrees with this.

When we say 'initially co-incident', however (and so depart from your previous post), we are implicitly stating that there is a time dimension. That is to say our systems are S(x,y,z,t) = S'(x',y',z',t'). And so instead of the above equation, we have:
S(x,y,z,0) = S'(x',y',z',0) = S'(x,y,z,0), and so x'=x, y'=y,z'=z.
Again, no one you speak to will disagree with this.

However, if we've stated they are 'initially co-incident', that doesn't tell us the relationships between the two systems when t≠0. So we still have:
S(x,y,z,t) = S'(x',y',z',t'), but we cannot say that S'(x',y',z',t') = S'(x,y,z,t). We simply do not know what the relationship is between S and S' outside t=0.

Here we define the Galilean transform, which is a relationship between these co-ordinate systems that is initially coincident: we will have to test this, though.
We define S and S' such that:
S(x,y,z,t) = S'(x',y',z',t') = S'(x-vt,y,z,t); in short-hand, we can write this as: x'=x-vt; y'=y; z'=z; t'=t. Remember, this is short-hand for the expression at the start of the line.

Since we have stated that the systems are initially co-incident, we require that S(x,y,z,0) = S'(x',y',z',0) = S'(x,y,z,0). Let's test to make sure this is true:
S(x,y,z,0) = S'(x',y',z',0) = S'(x-v*0,y,z,0) = S'(x,y,z,0).

Turns out it's true! The Galilean transform is a relation between the two co-ordinate systems, and meets the requirement that they are initially co-incident, which is all that we said it would do.
cemper93 wrote:Dude, I just presented an elaborate multiple fraction in Comic Sans. Who are you to question me?

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

It was my birthday vacation this weekend, so I made a present for Steve that I hope the rest of you can enjoy too.

Steve, please watch it all the way through (until it loops) and tell me what you think about it, I put a lot of work into this gift for you.

Forrest Cameranesi, Geek of All Trades
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yurell
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Nice image, where's that damn Like button?
cemper93 wrote:Dude, I just presented an elaborate multiple fraction in Comic Sans. Who are you to question me?

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

If that doesn't settle it in a way Steve can understand, then Steve is intentionally misunderstanding. Not understanding is not a problem; choosing not to understand is - it's intellectual dishonesty. And I think Steve's guilty of that. I imagine he'll ignore the animation and re-post his "word picture", demanding to know xkcd's definition of a clearly defined term.

Excellent work, Pfhorrest. And happy (belated, I presume) birthday.

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

WibblyWobbly wrote:If that doesn't settle it in a way Steve can understand, then Steve is intentionally misunderstanding. Not understanding is not a problem; choosing not to understand is - it's intellectual dishonesty. And I think Steve's guilty of that. I imagine he'll ignore the animation and re-post his "word picture", demanding to know xkcd's definition of a clearly defined term.

Well, there's that quote of him in his signature...
steve wrote:Be careful of what you believe, you are likely to make it the truth.

I wonder if he is purposely distorting his impression the truth, or even trolling.
And happy birthday to Pforrest. Nice animation, too.

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

Pfhorrest wrote:post with animated graph

Very treeish! That was an awesome way to put it all together - lots better than I could have done. Much kudos!

Steve - watch that animation... many times.
This is what we are talking about! I don't see how it can be made any clearer.

Come back to it tomorrow and watch it again. And again.

Questions? Watch it again and then ask.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

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

brenok wrote:
WibblyWobbly wrote:If that doesn't settle it in a way Steve can understand, then Steve is intentionally misunderstanding. Not understanding is not a problem; choosing not to understand is - it's intellectual dishonesty. And I think Steve's guilty of that. I imagine he'll ignore the animation and re-post his "word picture", demanding to know xkcd's definition of a clearly defined term.

Well, there's that quote of him in his signature...
steve wrote:Be careful of what you believe, you are likely to make it the truth.

I wonder if he is purposely distorting his impression the truth, or even trolling.

Yeah, I thought about that quote, too. It seems ironic that Steve doesn't seem to see where he's failing in that regard.

FWIW, I don't think Steve is trolling, personally. He's done too much work, put up websites and YouTube videos and carried on this argument for more than a year. If it's a troll, it's the mother of all trolls. As someone mentioned or alluded to earlier, Steve's thing is his Waterman polyhedra; shapes based on a sweeping-out of close-packed spheres. Steve even went as far as to "re-derive" the basic constants of physics with his spheres; he thinks the universe is really based on the interactions of close-packed spheres, evidently. And when someone told him that his sphere theory doesn't align with relativity, he decided to go all-in on his belief, and made "relativity must be wrong" his own truth. But he found that the math for relativity works. So, clearly the only option is to challenge math itself, because he's absolutely CONVINCED that if his theory and relativity are contradictory, relativity must be to blame. But the math still works! So the last line of defense for sphere theory is to distort basic terminology in order to fit his worldview. And he picked the Galilean as the place to make his stand, as if the Galilean is actually what relativity is founded on.

So yeah, TL;DR is that he's royally and completely twisted his worldview to demand the Galilean is wrong, and he can't admit that the hole he thinks he found is just his "truth" getting in his own way.

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

steve waterman wrote:vbkid
2 Quick questions.
Are you open to the idea that you are wrong and need to understand why you are wrong?

Are you simply frustrated because you know you are right, and you know that I am wrong?

These are rhetorical questions of course,

Those are tough questions.

It is up to a Vote?
If 9 out of 11 Math Guys say That is Outside;
Then, That is Outside.

I hope it is a vote of 9 to 2.
If there is One More Person that sees it Steve's Way;
They can Start a Church!

I know I can't do the Math.
The Joke?

Three guys. An Engineer; A Mathematician; A Physicist.

The Task was: Enclose the most area using the least fencing.
I thought the Math Guy Won.

He built a little tiny area and declared that area Outside.
The rest of the Universe was Inclosed within His Model.

Those guy were listened to: Once upon a Time.
It is so funny.

It may look like In To You.
It may look like In To Me.
If He says it's Out; It's Out.

yes. I know it sounds like a Fairy Tail.

If the Question was Asked, "Who are You?"
If the Answer was, "A Scientist."

No one messed with a Scientist.
Why would they? They don't tell the Police.

Never did. Just people.

What? My Mom worked on a Dude Ranch.
Those things need staff.

My Mother worked in The Restaurant.
I think there were Three Kinds.

A Bar. A Dinner House. A Breakfast-oh, Are you Hungover? Cafe part.
It was a Great Place to be a child. People did not argue much.

I like listening to people talk about Math. It is like an organic Thing.
They usually Agree! What is Up with You People?!

Why do you Not Agree? Is it Too Hard to do The Math?
I can't blame you, there. Math is hard! And; To What End?

165 different dimensions? Who Needs 165?! I don't have Three under control!
Knotts? How Viruses Tie themselves in Knots and how to talk them into untieing?!

Math People! You people have Got To agree!
For some reason you explain things no one else can.

After you are finished with The Math.
You have Computers.

In the Dark Ages people did Math.
Why?! By Candle Light!

I Know! It sounds Fanciful and Horrible!
Why would some Mad Mind climb the stairs with candles and ink and paper and Work on Math in The Quiet of a Medieval Night while the Owl Calls. "Come out into the Moonlight."

Some people, just, like Math. Besides; It Rained a lot.
Were there many, many people that lived and died thinking they had It All figured out?
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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

Pfhorrest wrote:It was my birthday vacation this weekend, so I made a present for Steve that I hope the rest of you can enjoy too.

Steve, please watch it all the way through (until it loops) and tell me what you think about it, I put a lot of work into this gift for you.

[img]

When defining X and Y, you missed a golden opportunity to temporarily rename them Moose and Squirrel to further prove the point that they could be anything (and rename the point Zombo.Com)

So I can only give you an A-.
heuristically_alone wrote:I want to write a DnD campaign and play it by myself and DM it myself.
heuristically_alone wrote:I have been informed that this is called writing a book.

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

brenok wrote:I wonder if he is purposely distorting his impression the truth, or even trolling.

Alas, no. Read his posts and interactions with daan Strebe in the Map Projections thread. This is just how Steve is.

Awesome animation, btw, Phorrest. And I hope you had a happy birthday.

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

SecondTalon wrote:When defining X and Y, you missed a golden opportunity to temporarily rename them Moose and Squirrel to further prove the point that they could be anything (and rename the point Zombo.Com)

Good point (except that I never gave the point under consideration a name at all, besides its various coordinates).

I've updated the animation to feature an extra "page" where moose and squirrel get renamed x and y.
Forrest Cameranesi, Geek of All Trades
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bluebambue
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Pfhorrest, thank you for the gif. I had been half reading the thread and not really understanding what the argument is about. I now know what is being argued about.

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

bluebambue wrote:Pfhorrest, thank you for the gif. I had been half reading the thread and not really understanding what the argument is about. I now know what is being argued about.

yes. Thank you, Pfhorrest.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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

As a now long time lurker of this thread I thank you as well!
I've been following the thread since its creation but didn't want to add another voice to the choir of of fear of confusing things further.
I believe this gif makes things as clear as they possibly can be.

It's a tricky transformation since it's so intuitive that it's difficult to fix it in your mind.
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beojan
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Applause to Pfhorrest.
Now if only Steve would watch the animation.

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

Pfhorrest wrote:I've updated the animation to feature an extra "page" where moose and squirrel get renamed x and y.

For your convenience: a LaTeX to BBCode converter

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

Pfhorrest wrote:
SexyTalon wrote:When defining X and Y, you missed a golden opportunity to temporarily rename them Moose and Squirrel to further prove the point that they could be anything (and rename the point Zombo.Com)

Good point (except that I never gave the point under consideration a name at all, besides its various coordinates).

I've updated the animation to feature an extra "page" where moose and squirrel get renamed x and y.

A+
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heuristically_alone wrote:I have been informed that this is called writing a book.

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

Pfhorrest wrote:I've updated the animation to feature an extra "page" where moose and squirrel get renamed x and y.

I appreciate the amount of work invested to make the animation. I have watched it several times now.

In my tiny little counter-proof depiction, there was/is no point P!

1. All we have is S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, it is true that x = x'.
3. When S or S' are repositioned to non-coincidence, (noting that there is no point P), x ≠ x', in the manifold.
4. Given x = x', therefore x = x'.

As a mathematician, we do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

btw, my sphere packing math is NOT the basis of my physical constants suggested values. I dare say, that story is longer than these x' = x-vt threads. Sphere packing is why I looked at nuclear structure, but very very little to do with any math scheme for the the physical constants. Sphere packing is not involved at all, in the x = x' challenge.
Sphere packing makes sphere clusters and those are interpreted as convex hulls. So, these issues are stand-alone;
x = x', physical constant values, sphere packing (which lead to cartography).
Last edited by steve waterman on Tue Jul 30, 2013 3:26 pm UTC, edited 1 time in total.
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steve

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

All we've done Steve is what is the logical process of introducing universal quantification (which means "for all").

The way this works is that, if you can prove something about an arbitrary example then it is true for all such examples.

The point chosen here is entirely arbitrary and thus this proof can be extended to all points which is what you're trying to talk about.
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ucim
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

steve waterman wrote:In my tiny little counter-proof depiction, there was/is no point P!
and that is what is wrong with your counter-proof.
steve waterman wrote:1. All we have is S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, it is true that x = x'.
No. A thousand times no.

"coincident" means that,
WHEN x=x' AND y=y' AND z=z'
THEN S(x,y,z) refers to the same point as S'(x',y',z').

That is what it means. If there are no points, then the entire idea of coincidence is bereft of meaning.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

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

As a mathematician, I do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

Given S(x,y,z) coincident S'(x',y',z'), therefore x = x'; whereas in manifold M, x ≠ x'.

Should you have counter math logic, I will certainly listen and will really desire to hear your related thoughts.

Noting - There is presently too many notions for what the concept of coincidence is, still floating around.
We have two stand-alone conditions/cases ...
case 1 S(0,0,0) and S'(0,0,0) share the same spatial location = coincident
case 2 S(0,0,0) and S'(0,0,0) do not share the same spatial location = not coincident
Of course, other things are also implied by "coincident", such as same demarcation units and same orientation of axes.
Last edited by steve waterman on Tue Jul 30, 2013 4:34 pm UTC, edited 3 times in total.
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bluebambue
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Could someone give me the definition of coincident? Would it mean completely overlapping coordinate systems?

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

bluebambue wrote:Could someone give me the definition of coincident? Would it mean completely overlapping coordinate systems?

Two coordinate systems, f and g are coincident if, for every a,b,c,..., f(a,b,c,...) = g(a,b,c,...). That is, both coordinate systems assign the same coordinates to a given point.

Note that the Galilean transformation does not involve coincident coordinate systems (although the spatial parts are coincident at t=0), and the translated coordinate systems of Pfhorrest's example are not coincident. Steve's continual invocation of coincident systems only serves to muddy the waters.
For your convenience: a LaTeX to BBCode converter

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

steve waterman wrote:As a mathematician, we do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

GIVEN S(x,y,z) coincident S'(x',y',z'), therefore x = x'.

Please stop pretending like you speak for all mathematicians. There are plenty of people here speaking as well-qualified mathematicians who have tried very hard to explain how you're misunderstanding things. You are very, very, very wrong if you think that the issue here is that there's some sort of divide between how mathematicians and scientists do things here.

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

steve waterman wrote:As a mathematician, we do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

GIVEN S(x,y,z) coincident S'(x',y',z'), therefore x = x'.
This is not a statement of mathematics. It is a statement of religion.

Jose
Order of the Sillies, Honoris Causam - bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith - bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me - you really made a difference.

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

steve waterman wrote:As a mathematician, we do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

GIVEN S(x,y,z) coincident S'(x',y',z'), therefore x = x'.

No, we require all points to do that.

To prove something about all points, we prove it about a single arbitrary point and can therefore generalise.
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

JudeMorrigan wrote:
steve waterman wrote:As a mathematician, we do not require some point, say point P, in order to manifest/set the condition of S(x,y,z) coincident S'(x',y',z').

GIVEN S(x,y,z) coincident S'(x',y',z'), therefore x = x'.

Please stop pretending like you speak for all mathematicians. There are plenty of people here speaking as well-qualified mathematicians who have tried very hard to explain how you're misunderstanding things. You are very, very, very wrong if you think that the issue here is that there's some sort of divide between how mathematicians and scientists do things here.

Yes, I need to tone that down and will dump the "we mathematician" thoughts.
I see now that it came off as way arrogant. My wording was quite shitty as what I have always been trying to say was just "from a strict mathematical approach". I apologize, I should have latched on to that much earlier.

I was trying to say something more like...
No point, say point P, is required using a strictly mathematical approach, in order to set the condition of S(x,y,z) coincident S'(x',y',z').
Given S(x,y,z) coincident S'(x',y',z'), therefore x = x'; whereas in manifold M, x ≠ x'.
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

And that statement is incorrect.

In order to say S(x,y,z) is coincident with S'(x',y',z') we need to consider all points. Not one, not two and definitely not none. The way we consider every point is by considering a single arbitrary point and then saying "since that point was arbitrary, this proof applies to any other point as well".

This is an important concept in predicate logic and its application to proofs like here is something you should look into because it might help move this along.
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

From a strictly mathematical approach a coordinate system is defined as a mapping between a set of points and a set of coordinates. If you do not have any points, you do not have a coordinate system, and if S and S' are not coordinate systems, all your discussion of S and S' being coincident is so much gibberish. It's like saying that two circumferences are equal while denying that circles exist.

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

eSOANEM wrote:And that statement is incorrect.

In order to say S(x,y,z) is coincident with S'(x',y',z') we need to consider all points. Not one, not two and definitely not none. The way we consider every point is by considering a single arbitrary point and then saying "since that point was arbitrary, this proof applies to any other point as well".

This is an important concept in predicate logic and its application to proofs like here is something you should look into because it might help move this along.

So, are you saying that it is mathematically impossible to have a Cartesian system with no point(s)?
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

steve waterman wrote:Cartesian system with no point(s)?
Isn't that kinda like a hamburger with no meat, no bread, no additives, no sauces, no plate and no table?

And I mean that seriously - I was under the impression the points were the entire point, and the whole X/Y/Z nonsense was so we could talk about them by specifically pointing out particular points, so.. by not having points, the thing doesn't exist.
Last edited by SecondTalon on Tue Jul 30, 2013 5:13 pm UTC, edited 1 time in total.
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

steve waterman wrote:1. All we have is S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, it is true that x = x'.
3. When S or S' are repositioned to non-coincidence, (noting that there is no point P), x ≠ x', in the manifold.
4. Given x = x', therefore x = x'.

1. We begin with x and y coincident (i.e. x = y). For a concrete example, lets say x = y = 5
2. When x and y are coincident, it is true that x = y
3. When x and y are repositioned to non-coincidence x ≠ y. For the concrete example, lets add 3 to y. Now, x = 5, and y = 5 + 3 = 8
4. But given that we started with x = y, how can this be? 5 ≠ 8 so x ≠ y.

Answer? We changed y. What we said about x and y is no longer true once we change y.

It's the same with coordinate systems.
Once we change (reposition) one or both of S and S', what we said about them before we changed them is no longer (necessarily) true.

Note: For all those confused by the numbered statements, I deliberately used Stevean terminology, which may be a little nonsensical to everyone else.

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

Mathematically,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x.
3. When S or S' are not coincident, x' = x.

Galilean transformation,
1. S(x,y,z) coincident S'(x',y',z').
2. When S and S are coincident, x' = x because vt = 0.
3. When S and S' are not coincident, x' = x -vt.
Last edited by steve waterman on Tue Jul 30, 2013 8:33 pm UTC, edited 1 time in total.
"While statistics and measurements can be misleading, mathematics itself, is not subjective."
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### Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

steve waterman wrote:
eSOANEM wrote:And that statement is incorrect.

In order to say S(x,y,z) is coincident with S'(x',y',z') we need to consider all points. Not one, not two and definitely not none. The way we consider every point is by considering a single arbitrary point and then saying "since that point was arbitrary, this proof applies to any other point as well".

This is an important concept in predicate logic and its application to proofs like here is something you should look into because it might help move this along.

So, are you saying that it is mathematically impossible to have a Cartesian system with no point(s)?

Yes. It is mathematically impossible to have a Cartesian (or any other sort of) coordinate system with no points. Not having an underlying manifold (again, feel free to just consider the cases of euclidean surfaces if it makes you feel better) defeats the entire purpose of having a coordinate system.