Your point?
Deeper than primes
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Your point?
doronshadmi
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1) Please define "immediate" and surrounding.
2) As long as a quantum element is defined in terms of a wave, its exact location is undefined.
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doronshadmi
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0-dimension ~= No-dimension
(By the way http://www.internationalskeptics.com/forums/showpost.php?p=6243183&postcount=11200 was edited).
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Yes, really, it does.
So it was. I'm not about to compare it with the original to see what you changed.
doronshadmi
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Please explain why do you think that 0-dimension = No-dimension.
My explanation, which shows that 0-dimension ≠ No-dimension, can be found in http://www.internationalskeptics.com/forums/showpost.php?p=6243183&postcount=11200.
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doronshadmi
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You don't have to.
All you need is to read the edited version http://www.internationalskeptics.com/forums/showpost.php?p=6243183&postcount=11200.
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doronshadmi
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n=1 to ∞
k=0 to n-1
X = "Dimension"
Y = "Dimensional element"
n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X
k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X
No_X - k_Y is an invalid mathematical expression.
k=0 to n-1
X = "Dimension"
Y = "Dimensional element"
n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X
k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X
No_X - k_Y is an invalid mathematical expression.
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How many dimensions does something of 0-dimension have?
This is a combination of Deliberate Error+intended Non Sequitur -- a reasoning last seen in the time of Spanish Inquisition.
Your quote of Wikipedia intentionally manipulates through generalization the property of the circle in question. A circle is considered 1-dimensional object only when its radius is given, such as in the case of the unit circle. A point on a circle can be located through Cartesian coordinates (x, y) as well as polar coordinates (angle, radius). Since the unit circle has r=1, one dimension is already assumed and therefore it takes only 1 coordinate (the angle) to locate a point drawn on the unite circle.
Here is the whole enchilada squeeky clean:
You better pray to the Holy Squirrel that The Man won't find out about your misquotes, coz if he does . . . I don't wanna be around when that happens.
tOMbstone
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Don't do it epix!!! I'm still waiting for doronshadmi to answer my questions that I'm presenting for the SEVENTH time:
The Man
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Well the point was for your to try to see the difference, but I guess you just can’t. So now you assert your “dimension 0” is a dimension? Again would that not make your line segment or ray 2 dimensional (being comprised of your “dimension 0” and your “dimension 1”) . Again the dimensional aspect is of the line (the dimensional space being considered in this case) as you assert your self “dimension 1 (dimension of a line)” not of any point along that line. You seem to be confusing, again perhaps deliberately, the dimensions of some space (like a line) with points in that space having a dimension themselves. If the space being consider was a plane as opposed to a point would that not make your “Dimension 0” locations two dimensional and thus your “points“ two dimensional. Also as you assert your “point” can include your “line” would it not also include your “surface”, “volume” “hyper volume” and an infinite number of dimensional objects?
Again this “dimension 0” is simply your fantasy, you evidently claim it to be a dimension. So again how many dimensions does your point or “dimension 0” have?
Even when I was a kid, I had no problem understand geometry.
We have been over this before Doron, again tell us what portion of that line does not have a location (a point). Again tell us how many dimensions your “dimension 0” “point” has? As you assert your “point” can include your “line” how do you determine which or how many “lines” it includes? What prompts you to seeming limit what your “point” can include to a 1 dimensional object as opposed to multi-dimensional objects or even a multitude of 1 dimensional objects?
Nope if that were “according to QM” you would not have had to use your nonsense “othe words”. Virtual particles and zero point energy have specific implications on quantum field theory none of which employ your nonsense “othe words” or the manifestation of your “un-manifested” fantasies.
They are your “uncomposed elements” Doron, if your “line” can not be completely covered by points (or locations if you will) or composed with the least upper bound property and no gaps between those elements (a Linear_continuum) then it is a discete space.
Again simply a result of the coordinate system being used (more precisely the dimensional space being considered). A single point has no location, the location (as the coordinates) thus the dimensional aspect comes from the space being considered. If you think not, then please give us the location of a single point in your “dimension 0”.
The Man
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“Nobody expects the Spanish Inquisition!!!”
Though we all have jumped on Doron’s evidently deliberate misquotes (or truncated quotes) and misrepresentations in the past, it never seems dissuade him from simply doing it again. So that, we have come to expect.
These days most of us (having be at this for about 2 years now) simply provide the actual quote in context, with perhaps some explanation, as you have done (thank you for that). Reserving the wrath of the Holy Squirrel for when he misquotes or misrepresents one of our own statements. Though I’ll still take the “comfy chair” over a Doron misrepresentation any day .
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What for? Do you have any problem with figuring the meaning of commonly used English words, such as "immediate" and "surrounding?" Given the fact that you weave non-existing terms, such as "non-composed element," through your arguments, your request really smells funny.
If you wrote that a banana needs to be peeled before consumption, the effect would be the same.
Btw . . .
I guess you need to prove (2) to smooth out the contradiction.
I kind of figured that Doron is not the first time offender, as far as a text manipulation is concerned, but I had to invoke the image of The Man, for I don't have the right disciplinary means for Doron to feel guilty for a sec or two.
Unfortunately, Doron doesn't cheat with the finesse of Henry Gondorff (The Sting). Instead, he waits when you go to the restroom so he can put a pinch of LSD powder to your drink. Once you start to see stuff like "non-composed elements" and other non-existing, non-dimensional shapes, Doron starts to deal the cards.
That Doron . . . LOL.
The Man
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Defiantly a “multitude” offender of exceeding “magnitude”, as we have been over the one dimensionally of a circle before. However, as he continues to just go around in circles the same things need to be explained again.
Just for clarification, technically a circle is one dimensional because by definition the radius is constant. As angles can be represented in radians (as they usual are in physics) a unique location on a circle does not depend on (or an assumption of) the value of the radius. An angle represents a unique location on any and all circles (not just a unit circle). What is does not do is represent that location on different circles as unique from each other in some two dimensional space, as a variation of radius is required for that. That is why in order to specify some unique location in a two dimensional space in polar coordinates both an angle, distinguishing a location on any and all circles, and radius, distinguishing a specific circle from other circles in that space and thus a unique location in that two dimensional space, are required. This is critical to the distinction of the dimensions of an object and that of the space it may be embedded in. Similarly the surface of a sphere is only two dimensional even though it might be embedded in a three dimensional space, also why a point remains zero dimensional even when embedded in a one or multi-dimensional space. So the one dimensionality of a circle, even when embedded in two dimensional space, in no way supports Doron’s assertions of some “dimension” for a point.
Here is the whole paragraph from the Wikipedia article on dimension.
The specific point of that paragraph was the independence of the dimensionality of some objects from that of the space they may be embedded in (as I have been trying to explain to Doron). So as usual the reference Doron cites and partially quoted actually was making the same point that I have trying to get across to him. A point embedded in a one dimensional space (a line) does no imbue that point with a dimension (even Doron’s imaginary “dimension 0”). Just as a circle embedded in a two dimensional space does not make that circle two dimensional nor does the surface of a sphere embedded in a three dimensional space become three dimensional.
Too bad that the Wikipedia contributor uses the term "unit circle" instead of "a circle" pointing the difference out, coz "unit circle" assumes given radius (one polar co-ordinate) and therefore it suffices to locate or define a point on the circumference with only one, the angular coordinate. But the usage of polar coordinates is limited, coz x=sin(0)= 0 or x=cos(0)=1 and that is where the first point of the circle appears. If you want to draw a circle on a plane with its center at x=10 and y=12, for example, you need to draw two semicircles using y1 = f(x) and y2 = -f(x), (or use parametric functions). That circle has always dimension 2 with no consideration of dimension 1, unless you offset its center to suit its definition expressed in the polar coordinates. It's a jungle out there . . . and Doron fevereshly works on converting it into a wasteland.
So Doron shouldn't be severely punished for manipulating the text the way he did, only for the analogy that he commited shortly thereafter.
I can't follow Doron in such a detail as you can, but that's a mistake easy to make. When it gets down to kinda abstract, esoteric stuff, impeccable definitions are a must, otherwise goulash. Since Doron's defining terms and his construction of definitions is an example of advanced cryptography, he also misdefines his own stuff here and there. Where exactly is the dificult part of Doronetics.
doronshadmi
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Again,
"How many dimensions?" is related the Multitude aspect of Quantity.
For example: "We have 0 elements, where each one of them has a magnitude of dimension 0 (which is a point) along an element that has a magnitude of dimension 1 (which is a line)".
As you can see, there is a difference between the Magnitude aspect and the Multitude aspect of the Quantity concept.
If you understand the difference between Magnitude and Multitude, and also understand that the concept of Dimension is defined by Magnitude, then "No dimension" means that there is nothing to be measured.
Again,
n=1 to ∞
k=0 to n-1
X = "Dimension"
Y = "Dimensional element"
n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X
k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X
No_X - k_Y is an invalid mathematical expression.
Persons like The Man do not understand the difference between the k_X and No_X.
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If you have 0 elements, how many elements do you have?
What do the quotes indicate? X is the string "Dimension", and Y is the string "Dimensional element"?
doronshadmi
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There is a difference between the value that determines the number of elements (where each one of them has magnitude 0) that can be located along a magnitude 1 element, because the first value describes Multitude (How many elements?) and the second value describes the Magnitude of a given element.
If you understand the difference between Magnitude and Multitude, and also understand that the concept of Dimension is defined by Magnitude, then "No dimension" means that there is nothing to be measured (there is no dimension at all, no point, no line, no plane, no fractal (which is an intermediate dimension between whole magnitude values), no sphere, etc …).
What is your problem to get? :
n=1 to ∞
k=0 to n-1
X = "Dimension"
Y = "Dimensional element"
n_X - k_Y = (n-k) coordinates that are used to determine k_Y location w.r.t n_X
k_X - k_Y = 0 coordinates that are used to determine k_Y location w.r.t k_X
No_X - k_Y is an invalid mathematical expression.
Persons like The Man do not understand the difference between the k_X and No_X.
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