[michel123456]

jajrussel, on 29 March 2011 - 01:16 AM, said:

I am a little late to this thread...
I agree that there is a relationship between time, distance and speed; but why do you imply that distance and space are the same thing?

Wiki's definition is

Quote

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria (e.g. "two counties over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific set of rules, and provides a concrete way of describing what it means for elements of some space to be "close to" or "far away from" each other.

"numerical description" means "measurement".(description has a broader meaning, but they are basically the same)

My definition would go like this:
Distance is a one dimensional measurement of space.

If you accept the above, you can say that distance is the measurement of space reduced to one dimension.

And if you accept the above, the next step consists at saying that measurement coincides with reality.

Then you obtain distance = [one dimensional] space.

This is my syllogism.

This post has been edited by michel123456: 29 March 2011 - 06:11 AM

[lemur]

michel123456, on 29 March 2011 - 06:10 AM, said:

Wiki's definition is


"numerical description" means "measurement".(description has a broader meaning, but they are basically the same)

My definition would go like this:
Distance is a one dimensional measurement of space.

If you accept the above, you can say that distance is the measurement of space reduced to one dimension.

And if you accept the above, the next step consists at saying that measurement coincides with reality.

Then you obtain distance = [one dimensional] space.

This is my syllogism.

I'm not so sure that dimensionality is the same thing as "space." E.g. if you travel in a straight line in any direction on a sphere, you eventually end up where you started. If all space worked like this, what would that imply about "space/volume?" Further, if spatial dimensionality on the surface of a sphere can be deconstructed by recognition of the sphere as the dominant reality, who is to say there's not yet another level that is even more dominant, which renders sphericism itself a function of some other "truer form?"

[jajrussel]

Distance is a physical measurement. Point A to point B. Point A and point B can always be said to have a physical relationship even though as separate systems they may seemingly act independent of each other. There is their synchronic relationship to time; there is their gravitational relationship, etc… Space though difficult to define is to some degree defined. We expect certain things of it. It shares a synchronic relationship to time; it takes shape or is shaped by matter. It is as much a thing, as point A and point B is, in that it is independent of A and B, but is so correlated to A and B that either A or B would not exist except for space. I will grant that most of spaces properties, if not all, are implied, but most of those implications are accepted and generally expected. We say that space is expanding and accept the statement as fact, because we can not conceive matter moving through an area where there isn’t space. More important for this discussion, we can measure sections of space using the same system we use for matter, and we express the measurement as distance.
Your argument concludes that one dimensional space exists; there would be no measurement.

I apologize for the statement that there would be no measurement. I tend to see a line as a string of multiple points. I forget that most people see a line as a representation of a single dimension.

I still question if one dimensional space exist?

This post has been edited by jajrussel: 29 March 2011 - 09:16 PM

[Mike Smith Cosmos]

TaoRich, on 4 March 2011 - 09:27 AM, said:

Back in my University days - during Maths I and Physics I - for some reason I was deeply uncomfortable with the "foundation on which the higher-level arguments" were built.

I always felt there was something missing - that there was something "shaky" at the root.

Somehow I had this (intuitive) feeling that I was being led into a house of cards, but I could never quite work out from whence exactly my discomfort stemmed.

That's what started me off on this 15 year track of investigation.

I am sure you have probably come across Lee Smolin A lecturer ( Prof or Dr ) at the Peninsular Institute Canada ( an offshute of Princetown University ) He came up with Loop quantum gravity as a link from/between quantum mechanics and relativity. He found that space rather than being a backdrop to " things" came out of, and with, the loops and knots . See The road to reality by Lee Smolin

This post has been edited by Mike Smith Cosmos: 30 March 2011 - 09:05 PM

[lemur]

Mike Smith Cosmos, on 30 March 2011 - 09:03 PM, said:

I am sure you have probably come across Lee Smolin A lecturer ( Prof or Dr ) at the Peninsular Institute Canada ( an offshute of Princetown University ) He came up with Loop quantum gravity as a link from/between quantum mechanics and relativity. He found that space rather than being a backdrop to " things" came out of, and with, the loops and knots . See The road to reality by Lee Smolin

Thanks for posting this reference. I googled it and read the Amazon preview pages. There is a nice quote that I'd like to copy and paste but I can't. I don't want to retype it word for word so I can just paraphrase it as basically comparing space to a sentence where if you would take all the words and phrases and subject-predicate-object relationships out of it, you wouldn't be left with an empty sentence - you'd be left with nothing. That's a pretty good (and original) analogy for space, I think.

This post has been edited by lemur: 31 March 2011 - 01:22 AM

[matterdoc]

Space is a functional entity, envisaged by rational beings, where real entities exist. It is a container without form or structure. Space extends to infinity means that you can find matter bodies (real entities) however far you go.

[Imparticle]

I have a different approach.
A dimension is a facet of being. Dimension describes one imaginary line among numerous imaginary lines that, in tandem, provide the building of reality in which any given "being" may exist in the universe. Within reason, these dimensions must exist. I find that logically, dimensions are built upon each other; that is to say, dimensions aren't randomly meshed together, they are perfectly built so that each point in each dimension can be congruent, and allow the being represented by said point to be a conclusively congruent being. For example, if there was even one dimension that was not built upon the others, a being's point in that dimension would cause the being in its entirety to be out-phased from the universe. It would be stuck in a crack of hypothesis, between the void of chaotic randomness and the dimensions of the universe. So, each of the real dimensions are built on each other. For common thinkers, this is obvious. Length, width, and depth are plainly built on each other, and if you attempted to build one separately, or to separate one from the others, you would find yourself wedged into something hypothetical--you'd land into the Flatland universe.

Moving on, I find that logically one dimension is built upon the previous one. That is to say, a point in one dimension, is a line in the next. For example, a given point in Length, is interchangeably a line in Width. A further point in Width, is a line in Depth. Furthermore, the point in Depth describes a line in Continuity (or, the dimension of time). The issue here is, if dimensions are built this way, then logically they build from innumerable dimensions into further innumerable dimensions. However, we observe that the universe seems to have a beginning and end, in terms of "beings". An apple does begin and end in the universe, we do not observe an apple infinitely unfolding itself into hypothetical dimensions. Again, logically, if anything were to have "innumerable dimensions", it would not be contained within a universe, and would only exist in its own universe of exponential tangents. But since we exist in the universe and can observe beings which do not consist in their own universe of exponential tangents, we must apply this to our dimensional logic. The result: The dimensions do in fact have beginning and ending points.
So, logically, the first dimension would have to be self-containing, that is to say, a line in the first dimension must also represent the first dimensional point. Conversely, the final dimension would have to be self-terminating, a point in this dimension must also represent a line in this dimension. In short, a line in the final dimension represents the end of the point in the first dimension. A point in the first dimension expands into further points in lines that are unfolded from those, until the point only further expands into itself, and any line unfolded from this point would lie on the same line. That is the final dimension. This can be demonstrated by unfolding a piece of paper. Once it is completely unfolded, any further attempts to unfold it result in tearing it. And since we observe that the universe is not dimensionally torn, this must logically be the end point.

So, we begin with the first dimension, the self-containing one. In this dimension, a point is also a line. That means, mathematically, a line in this dimension always begins and ends at this same point. This is an "abstract" line, it is not a concrete dimension. This dimension is called Singularity. Without this dimension, there would be no singularity to any given being, and the universe would not be able to remain a singular collective. All beings would be out-phased into the void of chaotic randomness. This dimension describes the dimension of all beings that places us in the same unified universe, and allows any and all relativity and interaction.
The second dimensional point lies on a line, that is unfolded from a point in the first dimension. So, a point in Singularity is a line in Length. We all know what Length is. It is the first spatial dimension. If you try to first unfold the Width or Depth of a being in space, logically you will actually unfold its Length. Again, imagine unfolding a piece of paper. You cannot unfold the third or fourth fold without first unfolding it a second time, no matter how hard you try. Width and Depth unfold from this point and so forth.
A point in Depth, is a line in Continuity. It is the dimension of time. This dimension describes the dimension of all beings that places us in the universe as it is changed, as it reproduces. It is a reproductive point, on a circular line, figuratively. A point in the fifth dimension is actually represented by two interchangeable points. On a circular line, any given point has a polar opposite. This opposite point describes the polarity of time--past and future. This is the figurative representation of the fifth dimension.
If we imagine all the dimensions figuratively unified, it would look like this: Singularity would be a point in the center. Length width and depth are represented by lines expanded into a cube. If you imagine any given point in time, you see an infinite number of circles around the other dimensions, forming a sphere. This sphere is the fifth dimension, and the volume of the sphere represents space, in its three dimensions. Mass is also described in this figure, where it is visualized displacing the volume of the sphere, hence the involution of space and relativity of time.
That said, there are still further dimensions yet to unfold. Logically, the fifth dimension does not terminate itself, because a point in Continuity unfolds into a line that does not lie in Continuity--in the fifth dimension. This line is the sixth dimension, Simultaneity. Figuratively, this line lies between the two interchangeable points in the fifth dimension. It is the line between time. Without this dimension, beings would continue through time in their own mutually exclusive passages. To put it simply, in order for you to continue to be reproduced within the universe, there must be a facet of you that is built from Continuity onto Singularity. Figuratively, this line contacts the central point that visualizes the first dimension. This dimension describes the dimension of all beings that places us in the universe as it is reproducing and changing in unification, in an interrelated web of cause and effect.
A point in the sixth dimension is a line in the seventh. But what could this line unfold as, and where could this line be? It unfolds from the point of Simultaneity, and builds from the point of Singularity. Figuratively, is lies between the first point and the sixth line, thus, it cannot be seen as it is an abstract line. The abstract dimensions are all unable to be represented 3-dimensionally, naturally because they do not pertain to those 3-dimensions. We have no method of drawing them as lines relative to 3-dimensional lines, except as abstract points. The seventh dimension is Infinitude. This dimension describes the dimension of all beings that places us in our self-congruency. That is to say, any given object is self-congruent, it is infinitely identical to itself. Without the dimension of Infinitude, any given being would not be self-congruent and would be out-phased due to a lack of agreeing with its own reality. Logically, this means that each being is infinite in its own congruency.
The eighth dimensional line is a seventh dimension point. This line unfolds from the seventh dimension, and builds on the fifth. This dimension between Infinitude and Continuity is called Potentiality. Figuratively, if we were to bisect the six-dimensional sphere, so that we could see the seventh dimension as a line between the two halves, the eighth dimension would appear as two interchangeable lines stemming from the seventh line to the two interchangeable points on the circumference of the semi-sphere. This dimension describes the dimension of all beings that places us in a mathematically feasible universe.
Boggling, the further dimension is abstracted from the initial abstraction. This dimension is highly abstract. It is a line between the two interchangeable points in Potentiality. A point in Potentiality is a line in the ninth dimension, which is built on the interchangeability of that point. The ninth dimension is Possibility. This dimension describes the dimension of all beings that places us in a universe of infinitely conclusive feasibility. Figuratively, this line is visualized between the two points of the eighth dimension, intersecting the dimensional line of seventh dimension. In a 3-dimensional representation, the ninth dimension is a disc with the geometric "cone" of the eighth dimension. Now, what happens if we try to unfold a line from this ninth dimensional point? Any line drawn out of Possibility cannot build onto anything else. Beyond the infinitely conclusive feasibility of the universe, logically there can be nothing, no further point of dimension. Any line unfolded from a point in Possibility lies on the same line of said point. Alas, we have come to the end of the universe.

If the six-dimensional sphere is bisected, and the first point and sixth point are represented as interchangeable, then the complete figure looks like a sphere and two opposite cones with the circumference of the sphere as their bases, and meeting at the point of Infinitude. This forms a sort of conical "infinity" symbol.

[TaoRich]

matterdoc, on 4 December 2011 - 10:17 AM, said:

Space is a functional entity, envisaged by rational beings, where real entities exist. It is a container without form or structure. Space extends to infinity means that you can find matter bodies (real entities) however far you go.

I see space as the "context within which things exist and interact".

The problem I have - or should I say the reason I started pursuing this line of questioning - is that the definitions I find mostly tend to "jump" into descriptions of "the things that exist and the way that they interact" while glossing over a (necessary) formal description or definition of "the context within which they interact".

I'm trying to put together a definition "from first principles" which accurately describes what this "context" is.

In my opinion, it is not without form or structure ... I'm leaning towards the conclusion that all the characteristics of our reality (physical attributes, properties of interaction, and time itself) emerge from the underlying form and structure of the context of our reality (space).



Rich

[granpa]

space is made of 'events'.

events usually interact is a space-like way but they dont have to do so.
they can interact in other ways too.

http://en.wikipedia....um_entanglement

[michel123456]

TaoRich, on 5 December 2011 - 09:42 AM, said:

I see space as the "context within which things exist and interact".
(...)

That could be space-time, not space.
In space only, things cannot interact.
And I suspect that in space only, things cannot even exist.

[URAIN]

"What is the space ?" Now it is main topic of discussion in everywhere.





Now there are three views about space.



1) Space is notion

2) Space is entity and It is empty.

3) Space is entity and It is filled.





Do experts say what is the space?



And how it is?




Is it empty or filled?

This post has been edited by URAIN: 7 January 2012 - 04:44 PM

[matterdoc]

TaoRich, on 5 December 2011 - 09:42 AM, said:

I see space as the "context within which things exist and interact".

The problem I have - or should I say the reason I started pursuing this line of questioning - is that the definitions I find mostly tend to "jump" into descriptions of "the things that exist and the way that they interact" while glossing over a (necessary) formal description or definition of "the context within which they interact".

I'm trying to put together a definition "from first principles" which accurately describes what this "context" is.

In my opinion, it is not without form or structure ... I'm leaning towards the conclusion that all the characteristics of our reality (physical attributes, properties of interaction, and time itself) emerge from the underlying form and structure of the context of our reality (space).



Rich

Afunctional entity is visualized to fulfill functions assigned to it by rationalminds. Function of space is only to provide a place for existence ofmatter-bodies. Space is required only when and where matter-bodies are present.Being functional entity, it requires no form or structure. It exists only inrational beings’ minds. That is why it is a container without form orstructure.

Distanceis the separation between two matter-bodies (or between two points on amatter-body). It is not a measure of space. Area and volume are degrees ofdistance.

Spacehas any meaning only when it is filed entirely (without voids) by a realentity. Matter is the only real entity in nature. As and when we discover anall-encompassing universal medium, made of matter and which fills thespace, space will have a form and structure. Without form and structure,provided by real entity, space cannot deform. Only in a space, filled withuniversal medium, “all the characteristics of our reality(physical attributes, properties of interaction, and time itself) emerge fromthe underlying form and structure of the context of our reality (space)”.