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 SecondTalon » Fri Aug 02, 2013 3:50 pm UTC

eran_rathan wrote:Shouldn't the Axis notation be:

S(Germany, Japan, Italy) = S'(DPRK, Iran, Iraq)?
Nah, I'm not in to New Wave bands.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Fri Aug 02, 2013 5:13 pm UTC

SecondTalon wrote:
eran_rathan wrote:Shouldn't the Axis notation be:

S(Germany, Japan, Italy) = S'(DPRK, Iran, Iraq)?
Nah, I'm not in to New Wave bands.


I have been quite ill for the last couple of days...I have not read any messages since then at all.

I hope I will get a chance soon, but today seems like it might not happen.
I am hoping it is some kind of stomach flu and passes soon, as I am having real troubles eating
and the appetite seems vacant.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby SecondTalon » Fri Aug 02, 2013 5:19 pm UTC

No idea why you quoted me, but get better.
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.

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

Postby steve waterman » Sat Aug 03, 2013 11:27 am UTC

x axis and x' axis and y axis and y' axis and z axis and z' axis ALL intersect in the manifold at one point,
which is not an origin. I personally view this denial of these intersections as the origin as pure mathematical bullshit!
eSOANEM wrote: Everyone agrees that this is an origin.
Emphasis on "an". Where we disagree is that we know that this point is not inherent to the manifold, just the co-ordinate system we choose.

So, in your manifold M, the intersection point of all 6 axes is '"an" origin. Are your two systems in the manifold
"coincident" when t > 0 and P has two different sets of mapped coordinates?

In the manifold x is...??????????

eSOANEM wrote:Nothing.
x has no meaning to the manifold, only to the co-ordinate system (and only because we defined x as S(x,y,z)

Given S(x,y,z), x only has meaning to the coordinate system S. Given S'(x',y',z'), x' only has meaning to the S' system.
Neither x nor x' have any meaning in the manifold.

I placed the emphasis on eSOANEM's final quote.
"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."
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Sat Aug 03, 2013 11:43 am UTC

steve waterman wrote:x axis and x' axis and y axis and y' axis and z axis and z' axis ALL intersect in the manifold at one point, which is not an origin. I personally view this denial of these intersections as the origin as pure mathematical bullshit!


It's the origin of S and S', not the origin of the manifold.

steve waterman wrote:In the manifold x is...??????????


x is not in the manifold. x is a (placeholder for a) number, and an ordered set of numbers gets mapped by a co-ordinate system to the manifold. Our choice of axes is arbitrary.

steve waterman wrote:Given S(x,y,z), x only has meaning to the coordinate system S. Given S'(x',y',z'), x' only has meaning to the S' system. Neither x nor x' have any meaning in the manifold.


'x' has no special meaning beyond 'this is a placeholder name for the first co-ordinate in our co-ordinate system S which maps to our manifold M'.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Sat Aug 03, 2013 12:51 pm UTC

Steve, did you watch the videos I suggested?
If not, please go back and watch them. They will explain what the S(x,y,z) notation actually means, and, if you then re-read posts by, for example, Schrollini and ucim (this time seeing them as attempting to explain how the rest of are using notation, rather than as adversarial), you will hopefully being to understand why notation like M(x,y,z) and questions like "What does x mean in the manifold?" do not make sense.

Remember that you have chosen to challenge the Galilean transform (which is arguably a little like challenging cos or arctan). When the Galilean transform is stated, notation is used in a particular, predefined manner, and any challenge you may present is only valid if it uses the notation in the same way.

If I make the statement "Edinburgh is in Scotland", and you challenge it saying "Edinburgh is in England" because you have redefined Edinburgh to mean Rome, and England to mean Italy, your challenge is invalid, and repeatedly asking to "agree on a definition for Edinburgh" is pointless, because the statement you are challenging depends on the predefined definition of Edinburgh, so that is what any challenge must work with.

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

Postby steve waterman » Sat Aug 03, 2013 2:01 pm UTC

Please answer my question below or explain why you cannot answer it.
Also, I would appreciate a current posting giving YOUR definition of what "coincident" means wrt Cartesian coordinate systems S and S'.

So, in your manifold M, the intersection point of all 6 axes is '"an" origin.
Are your two systems in the manifold "coincident" when t > 0 and P has two different sets of mapped coordinates?

Given S(x,y,z), what if we mathematically let x = 2,
then x = 2 has no meaning in the manifold, ( since there is no S origin in the manifold) x = 2 only has meaning in S.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Sat Aug 03, 2013 2:30 pm UTC

steve waterman wrote:Also, I would appreciate a current posting giving YOUR definition of what "coincident" means wrt Cartesian coordinate systems S and S'.
Two 3D systems S and S' are coincident if for every x, y, and z, S(x,y,z) = S'(x,y,z) Note the lack of primes on the second system. When the same numerical coordinates are applied to system S and to system S', and the result always is that each system refers to the same point in the manifold, then those two systems are coincident. This can be generalized to any (positive integer) number of dimensions.

In this definition I am (of course) using x, y, and z as placeholders for actual values. If the use of x, y, and z is confusing to you in this case, then an equivalent definition can be written thus:

Two 3D systems S and S' are coincident if for every a, b, and c, S(a,b,c) = S'(a,b,c) Again, note the lack of primes on the second system. As above, the definition says that when the same numerical coordinates are applied to system S and to system S', and the result always is that each system refers to the same point in the manifold, then those two systems are coincident. In this definition (which is functionally equivalent to the one above), a, b, and c are placeholders for real numbers.

steve waterman wrote:Are your two systems in the manifold "coincident" when t > 0 and P has two different sets of mapped coordinates?
t has not been defined. But no matter... the test is to look at the numerical result of the calculation it is used in. If systems are coincident, then the numeric values of the coordinates will be the same in both systems (for any point P in the manifold). If systems are not coincident, then there will be some points for which this is not true - that is, in order to identify such a point, you will need different numerical coordinates in different systems. An example is for a system S' which is offset from S by (only) being moved two units to the right.

If P=S(3,5,6), then P=S'(1,5,6). Thus, S(3,5,6)=S'(1,5,6) and both expressions refer to the same point P in the manifold. These two systems (S and S' from this example) are not coincident, since different numerical coordinates are needed to refer to the same point.

Note that S'(3,5,6) refers to a different point in the manifold from S(3,5,6). Thus, S(3,5,6) =/= S'(3,5,6)

steve waterman wrote:Given S(x,y,z), what if we mathematically let x = 2,
then x = 2 has no meaning in the manifold, ( since there is no S origin in the manifold) x = 2 only has meaning in S.

Correct. x=2 means nothing to the manifold. However, S(2,y,z) does have meaning in the manifold. It is the set of points in the manifold which is parallel to the y-z plane, and two units away in the +x direction.

Equivalently, S(x,y,z) where x=2 means the same thing. Note that the x=2 part specifically is referring to S, and it is only the combined (bolded) phrase that refers to M.

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

Postby steve waterman » Sat Aug 03, 2013 4:05 pm UTC

In the recent depiction,

when red S and blue S' systems are not coincident, the x axis and the x' axis are coincident at t > 0.

Given S(x,y,z) in solid red...then the solid red axis IS the x axis in S...which appears to me, to be being
refused to label as such. The x axis is inherent to S, and not inherent to the manifold. To simply place the x axis in the manifold is cheating, imo.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Schrollini » Sat Aug 03, 2013 4:31 pm UTC

steve waterman wrote:Given S(x,y,z) in solid red...then the solid red axis IS the x axis in S...which appears to me, to be being
refused to label as such. The x axis is inherent to S, and not inherent to the manifold. To simply place the x axis in the manifold is cheating, imo.


Remember this picture?
Image
And a bit later, I said,
Schrollini wrote:I'm a bit inconsistent later, when I use the expression f(x,0) to indicate the points for all values of x. What I should write there is {f(x,0) | ∀ x ∊ ℝ}, which is math-speak for "the set of points f(x,0) for all real numbers x". But both of these seemed too long to write, so I abbreviated.

So the x-axis we're drawing for the coordinate system S is the set of points S(a,0,0), for all values of a.

Also, I'm going to repeat this post, because you're still making this mistake:
Schrollini wrote:
steve waterman wrote:1 Given S(x,y, z)...

I'm going to stop you right there, because I suspect what you wrote isn't what you mean. What you wrote is essentially, "Given a point". I think what you mean to say is, "Given a coordinate system and some coordinates." Or, if you want to introduce some symbols, "Given a coordinate system S and coordinates x, y, and z." But again, this is assuming that you're using conventional notation. To avoid confusion, you should specifically say what each symbol you introduce means.

(Note that sometimes we refer to a function f, and sometimes we refer to a function f(x). In the latter case, the x is just acting as a dummy, indicating that f takes a single argument. It has no meaning. I will try to avoid this notation, and I encourage everyone else to avoid it as well.)
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby beojan » Sat Aug 03, 2013 6:11 pm UTC

steve waterman wrote:So, in your manifold M, the intersection point of all 6 axes is '"an" origin.
Are your two systems in the manifold "coincident" when t > 0 and P has two different sets of mapped coordinates?

Such a point, where all 6 axes intersect, does not exist, unless your two coordinate systems are coincident (which, given the other constraints, essentially means the two coordinate systems are really two names for the same coordinate system, and hence there are only three axes).

If 'P has two different sets of mapped coordinates' which I can only assume means 'if P has different coordinates in each coordinate system' then the two coordinate systems are by definition not coincident.

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

Postby ucim » Sat Aug 03, 2013 7:29 pm UTC

beojan wrote:Such a point, where all 6 axes intersect, does not exist, unless your two coordinate systems are coincident...
... or differ solely by a rotation around their common origin. But if the axes are aligned, then yes, the existence of such a point implies coincidence.

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

Postby Pfhorrest » Sat Aug 03, 2013 7:31 pm UTC

Steve, did you read this?

Note particularly the differentiation between the x axis and the number x. And likewise with x' and the x' axis.

Pfhorrest wrote:Steve, did you miss this? This explains exactly what we mean by x in your own setup, and how it differs from what you mean by x. Also x' and vt (or d if you like).

Since you asked for it "in words" specifically today, I'll put it in text here too:

When we are considering a point P and its coordinates in two coordinate systems S and S'

x' = the place on the first axis of S' (the x' axis) which lines up with P
x = the place on the first axis of S (the x axis) which lines up with P
vt = d = the place on the first axis of S (the x axis) which lines up with the origin of S'

In your first setup depicted below (the non-coincident one), that means:

-1 = x' = the place on the first axis of S' (the x' axis) which lines up with P
2 = x = the place on the first axis of S (the x axis) which lines up with P
3 = vt = d = the place on the first axis of S (the x axis) which lines up with the origin of S'

In your second setup depicted below (the coincident one), that means:

2 = x' = the place on the first axis of S' (the x' axis) which lines up with P
2 = x = the place on the first axis of S (the x axis) which lines up with P
0 = vt = d = the place on the first axis of S (the x axis) which lines up with the origin of S'

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

Postby steve waterman » Sat Aug 03, 2013 8:08 pm UTC

beojan wrote:
steve waterman wrote:So, in your manifold M, the intersection point of all 6 axes is '"an" origin.
Are your two systems in the manifold "coincident" when t > 0 and P has two different sets of mapped coordinates?

Such a point, where all 6 axes intersect, does not exist, unless your two coordinate systems are coincident (which, given the other constraints, essentially means the two coordinate systems are really two names for the same coordinate system, and hence there are only three axes).

If 'P has two different sets of mapped coordinates' which I can only assume means 'if P has different coordinates in each coordinate system' then the two coordinate systems are by definition not coincident.

Does anyone grasp that the above is a contradiction? Both conditions exists simultaneously:
P has different coordinates and all 6 axes intersect in the manifold at a singular point.

Hence, coincident systems having point P with different coordinates. That is not a good thing, mathematically.

Schrollini -
http://www.mathsisfun.com/data/cartesia ... nates.html
There are many more url, that need to be posted...last time I did, they were merely blown off, as unimportant, or trivial, or saying that the internet, was not always right, or the like..

Why does the Galilean say given S(x,y,z,t) and does not say, given f(x,y,z,t) = S(x,y,z,t)?
You believe that f(x,y,z,t) means just the one point to be enumerated, it appears.

btw, still really feeling ill, and struggling to post anything at all today. I would be so happy should this health issue fade away over the next few days.

It does feel, however, that we are finally getting down to why there has been SOOOO much confusion. We are getting to the bottom of a few remaining terms/notations...and need to be 100 percent clear about their meaning
f(x,y,z)
S(x,y,z)
x
coincident
given

hopefully, now completely clear are...
point P
manifold M
transformation
origin
coordinate
x abscissa
separated systems
repositioned system
t = 0
t > 0

Yup, that was quite long, and I should stop all computer stuff for the rest of the day.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby JudeMorrigan » Sat Aug 03, 2013 8:48 pm UTC

steve waterman wrote:Does anyone grasp that the above is a contradiction? Both conditions exists simultaneously:
P has different coordinates and all 6 axes intersect in the manifold at a singular point.

Hence, coincident systems having point P with different coordinates. That is not a good thing, mathematically.

The six axes don't intersect at a single point for non-coincident system. Furthermore, coincident system's don't have different coordinates for a given point P. That, however, is not true for systems that are not coincident. And you can't take a coincident system, break that condition, and expect the same results.

And in case this is where the first point of confusion crept in, let me reemphasize that the purple lines in this picture are NOT axes:

Image
We're calling the red and blue lines axes the same as you. (And as you can clearly see, they do NOT all intersect at a single point.) 'x' and 'the x-axis' are not the same thing.

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

Postby ucim » Sat Aug 03, 2013 8:57 pm UTC

steve waterman wrote:
beojan wrote:
steve waterman wrote:So, in your manifold M, the intersection point of all 6 axes is '"an" origin.
Are your two systems in the manifold "coincident" when t > 0 and P has two different sets of mapped coordinates?

Such a point, where all 6 axes intersect, does not exist, unless your two coordinate systems are coincident (which, given the other constraints, essentially means the two coordinate systems are really two names for the same coordinate system, and hence there are only three axes).

If 'P has two different sets of mapped coordinates' which I can only assume means 'if P has different coordinates in each coordinate system' then the two coordinate systems are by definition not coincident.

Does anyone grasp that the above is a contradiction? Both conditions exists simultaneously:
P has different coordinates and all 6 axes intersect in the manifold at a singular point.

Hence, coincident systems having point P with different coordinates. That is not a good thing, mathematically.
The problem is that you are treating t as if it were a coordinate, and treating t as if it were not a coordinate, at the same time.

If you treat t as not a coordinate, then your only coordinates would be x, y, and z - the three dimensional space coordinates. In that case, each different value of t will create a different Cartesian system. There will be S, S', S'', S''', S'''', etc, each corresponding to a unique value of t. The mapping S will not be the same as the mapping S' and that will not be the same as the mapping S'' and that will not be the same as... well, you get the idea.

What you call "moving the coordinate system" is the same as looking at a different system with (however many) primes, that corresponds with the value of t in question.


if on the other hand you treat t as an actual coordinate then you are dealing with a four-dimensional manifold, and a four-dimensional coordinate system. I'll use the old convention of putting t at the end: There will be just one system: S(x,y,z,t). There will not be an S' or an S''. If you just look at the space part you are looking at a (3D) slice of that very same S, at some given value of t.

What you are calling "moving the coordinate system" is in this case really just looking at a different slice in time of the (immobile) S(x,y,z,t).


That is where your words and notation differs from standard math, and what is leading you astray.

Hope you feel better soon.

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

Postby Schrollini » Sat Aug 03, 2013 9:08 pm UTC

steve waterman wrote:Schrollini -
http://www.mathsisfun.com/data/cartesia ... nates.html
There are many more url, that need to be posted...last time I did, they were merely blown off, as unimportant, or trivial, or saying that the internet, was not always right, or the like..

Yes, that is a URL. Congratulations? Whatever your point is, I've missed it.

steve waterman wrote:f(x,y,z)
S(x,y,z)
x

Symbols have no inherent meaning. If you write a sentence that includes S or f or x, you have to tell us what you mean by that. You're the only one who writes things like "Given S(x,y,z)"; the rest of us have been very careful to write, "Given a coordinate system S on a manifold M", which tells you exactly what S and M are (a coordinate system and manifold, respectively).

Now if there's a statement wherein you can't figure out what we mean by a symbol, you should ask about that statement. But we can't answer in general because there is no answer in general.

steve waterman wrote:coincident

ucim wrote:
steve waterman wrote:Also, I would appreciate a current posting giving YOUR definition of what "coincident" means wrt Cartesian coordinate systems S and S'.
Two 3D systems S and S' are coincident if for every x, y, and z, S(x,y,z) = S'(x,y,z) Note the lack of primes on the second system. When the same numerical coordinates are applied to system S and to system S', and the result always is that each system refers to the same point in the manifold, then those two systems are coincident. This can be generalized to any (positive integer) number of dimensions.

In this definition I am (of course) using x, y, and z as placeholders for actual values. If the use of x, y, and z is confusing to you in this case, then an equivalent definition can be written thus:

Two 3D systems S and S' are coincident if for every a, b, and c, S(a,b,c) = S'(a,b,c) Again, note the lack of primes on the second system. As above, the definition says that when the same numerical coordinates are applied to system S and to system S', and the result always is that each system refers to the same point in the manifold, then those two systems are coincident. In this definition (which is functionally equivalent to the one above), a, b, and c are placeholders for real numbers.

Did you not bother to read this, or were you just hoping for another definition?

steve waterman wrote:given

This is just a short-hand way of saying, "for the purposes of this discussion, I will use these symbols to represent these objects". Sometimes we say "let"; it means the same thing.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Pfhorrest » Fri Aug 09, 2013 7:16 pm UTC

Anyone know what happened to Steve? This thread has been dead for nearly a week now. Hope whatever was making him sick didn't turn out to be worse than expected...
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Fri Aug 09, 2013 10:22 pm UTC

Pfhorrest wrote:Anyone know what happened to Steve? This thread has been dead for nearly a week now. Hope whatever was making him sick didn't turn out to be worse than expected...
I don't know, and I'm also a bit concerned. But the thread is also hard for him in some ways and he may be taking a break.

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

Postby steve waterman » Mon Sep 02, 2013 9:32 pm UTC

Had some troubles. Triple bypass and valve replacement then some complications and a pace maker. Been in hospital for almost a month. Will perhaps write later when better.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Dark Avorian » Mon Sep 02, 2013 9:41 pm UTC

Holy hell, feel better.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby JudeMorrigan » Tue Sep 03, 2013 3:02 pm UTC

Oh, my. Glad the doctors had the opportunity to do their thing. Hope you get better, steve!

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

Postby WibblyWobbly » Tue Sep 03, 2013 5:32 pm UTC

steve waterman wrote:Had some troubles. Triple bypass and valve replacement then some complications and a pace maker. Been in hospital for almost a month. Will perhaps write later when better.

Best wishes for a speedy recovery, Steve.

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

Postby ucim » Tue Sep 03, 2013 5:57 pm UTC

Welcome back Steve - hope you recover fully and quickly!

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

Postby ivnja » Wed Sep 04, 2013 3:13 pm UTC

I'm glad you're back and doing okay! I hope your recovery has been and continues to be uneventful.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby PM 2Ring » Thu Sep 05, 2013 2:37 am UTC

Hope you feel well soon, Steve.

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

Postby addams » Thu Sep 05, 2013 3:25 am UTC

Goodness! That is a lot.
Take care and come back.

You may have new questions.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby oauitam » Thu Sep 05, 2013 11:50 am UTC

Best wishes, Steve.

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

Postby steve waterman » Thu Sep 05, 2013 1:06 pm UTC

Thanks for all the good wishes, they are quite appreciated.

Too soon yet, to get into any Relativity "pressure" for me.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Thu Sep 05, 2013 3:15 pm UTC

steve waterman wrote:Too soon yet, to get into any Relativity "pressure" for me.
No prob.... I'm good at Waiting For It. :)

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

Postby Vetala » Thu Sep 05, 2013 3:34 pm UTC

steve waterman wrote:Had some troubles. Triple bypass and valve replacement then some complications and a pace maker. Been in hospital for almost a month. Will perhaps write later when better.

Some troubles? There's an understatement - wow. That's a lot to go through. Hope things are going smoother now and you're feeling better.

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

Postby SecondTalon » Thu Sep 05, 2013 4:22 pm UTC

I'm going to second the "Holy hell, feel better" sentiment, because..

Holy Hell, dude. Rest.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Schrollini » Sun Sep 08, 2013 3:45 pm UTC

Hey Steve -- Sorry to hear about your troubles, but I'm glad to hear you made it through! My father had bypass surgery a decade ago, and it took him months to recover. You'll probably need a similar time to recuperate, and you should take it. Don't get yourself riled up with us idiots until you're feeling good.

My other piece of advice would be to start exercising as soon as you can (and the doctors allow). My father only did this grudgingly, and to this day he gets winded easily. So as soon as the docs give you a green light, start walking, biking, climbing stairs, or whatever tickles your fancy.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby Pfhorrest » Thu Sep 19, 2013 3:39 am UTC

So I just saw this article which made me think of Steve and some of his theories, thought I would share. (Posted here since this is the current Steve-and-his-theories thread).
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby yurell » Thu Sep 19, 2013 6:17 am UTC

I'm looking forward to said "forthcoming paper".
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby steve waterman » Thu Sep 19, 2013 1:08 pm UTC

Pfhorrest wrote:So I just saw this article which made me think of Steve and some of his theories, thought I would share. (Posted here since this is the current Steve-and-his-theories thread).

For the record -
My own theory is that unit spheres form clusters to manifest all matter; themselves possessing no inherent charge. Charge would be determined by the clusters external field shape, which in general are either formatted as a plane of squares or a plane of triangles. Also, that the cluster volumes have a pertinence. So, akin to Newtonian spheres only way way smaller, as would be say, dark matter. So...what if all matter was composed of equal spheres is my singular conjecture. However, my issue remains the whole x = x' thingie.

Sorry to post and not really be ready to respond quite yet. btw, do not confuse my x = x' thrust with anything at all to do with spheres or sphere packing or to my challenge to existing values for the fundamental constants...these are stand-alone concepts. I am desperately trying NOT to think of x = x' logic now, and just need to avoid going down this path for a few weeks more. Hence, I am not trying to evoke any feedback yet upon any of the thingies mention above.
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Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Postby ucim » Thu Sep 19, 2013 6:20 pm UTC

Pfhorrest wrote:So I just saw this article which made me think of Steve and some of his theories, thought I would share. (Posted here since this is the current Steve-and-his-theories thread).
As Spock would say... "Fascinating!". I found the article a little vague, but after some digging around came up with the following understanding:

Feynman diagrams are simple diagrams that represent particle interactions:
particles go in,
a miracle happens,
particles come out.

Step two looks simple; the trick is that there are many ways the miracle can happen, and each one is its own Feynman diagram. They all have to be calculated and added together to get a final result. Further, inside any given part of the miracle, fundamental laws of the universe do not have to hold strictly, so long as it all evens out in the end.

That bit always bothered me. It seemed too much like cheating, and I couldn't bring myself to believe the universe cheated. It seemed just too dodgy, even for QM.

So, it turns out there's a kind of geometric shape that manages to embody all of the non-cheating miracles all by itself, and "adding all the miracles together" is equivalent to "finding the volume" of this kind of geometric shape. Being as this family of shapes (essentially, this geometry) represents all the possible non-cheating interactions, it is a fundamental property of the universe, in a way that has not been seen before.

Do I have this more-or-less close?

Oh, and welcome back Steve. No prob about laying off the x=x' stuff. We'll wait for it. :)

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

Postby PM 2Ring » Fri Sep 20, 2013 7:30 am UTC

Perhaps we should discuss the amplituhedron in its own thread, on the Science forum.

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

Postby steve waterman » Fri Sep 20, 2013 2:14 pm UTC

To all at xkcd,

I may be jumping the gun a bit...I am curious if xkcders all agree with me, in that -

when t = 0, where S and S' are coincident Cartesian systems,
1 the distance from S(0,0,0) to S(x,0,0) = the distance from S'(0,0,0) to S'(x',0,0), regardless of the value for x?

when t > 0 is applied to the S' system of this set of coincident S and S' systems at t = 0,
2 the x' axis = x axis - vt?

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

Postby SecondTalon » Fri Sep 20, 2013 3:37 pm UTC

Steve,

I don't know you personally. This is no big shocker. I also don't know your doctor nor the medical advice you've been given. I also don't know how worked up you get while reading and debating in this thread.

I do know that a triple bypass and valve replacement with a pace maker (and some complications on the side) is not something you just bounce right back from, even after a month stay in the Hospital.

So, with that being said and with your remark about jumping the gun - we aren't going anywhere anytime soon. Can this wait another couple of weeks?
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