Scale As Dimension

[TheNick]

Thanks for the welcome, Laguna!

But seriously. Doesn't anyone have something to say about this? Attack me already, jeez.

Here's another one I've come up with that might help get things rolling:

In addition to the three dimensions of space and the dimension of time, it can be argued that, in the context of the physical universe, scale should be considered a fifth dimension, distinct from and perpendicular to the others.

[Gillianren]

In addition to the three dimensions of space and the dimension of time, it can be argued that, in the context of the physical universe, scale should be considered a fifth dimension, distinct from and perpendicular to the others.

Can it? Argue away, then.

Welcome to BAUT; I'm afraid I've not the scientific education to be useful to you.

[Bogie]

Can it? Argue away, then.

Welcome to BAUT; I'm afraid I've not the scientific education to be useful to you.Gillianren, are you stuck at 9,999 or will your next post be 10,000?

[TheNick]

It appears I may have screwed up the flow of this thread quite badly. I wrote the following when the quote below was the most recent post, and as I've written it now, I must post it. Perhaps this thread can be split so I may discuss both my proposed theories seperately.

Regarding my scale-as-dimension theory:

Can it? Argue away, then.

Very well, thus I argue:

Based on the things I do have a firm understanding of, I see a distinct pattern in the universe for natural objects to come into existence as a result of complex interactions of smaller, more fundamental objects. For example, a star, though at once being a single definable object, is at the same time a coagulation of many instances of a smaller object - namely the atomic particles. Although a star carries its own individual properties and behaviors, completely distinct from those of the atoms and particles that make it up (although I guess there probably aren't many intact atoms in a star), it is only because of the properties of the particles that a star ever comes into existence at all, and the star can only be said to exist when those particles have a specific arrangement. Imagine a hypothetical universe containing only our Sun. If you took all the particles that make up the Sun and redistributed them evenly across a cubic lightyear, what will have changed about this hypothetical universe? It will still contain all of the particles it did originally, but it would no longer contain a star. Lets define all the "objects" in the universe to be any instance of either a subatomic particle or a star. The total number of objects in this universe in its first state would thus have so many gazillions of objects + 1, the gazillions representing the subatomic particles, the +1 representing the star. In the second state, with the particles distributed, it would contain the same number of objects -1, the star no longer being in existence. So merely be redistributing the matter, without physically removing anything, you have in fact removed an object from this universe.

In the actual physical universe of course, in the forward direction of time, the opposite process is what happens naturally. Continuing with the star example, the actual physical universe will at one instant have widely dispersed subatomic particles dispersed over a finite region, and at a later instant these particles will have condensed, through their own individual behaviors, to form a star, effectively adding an object to the universe.

How can we define a star to be a distinct object? Primarily, a star carries its own distinct structure and behavior, none of which occur separately from each other anywhere ever. Additionally, we can confirm that there exists another type of object whose fundamental parts are stars. If the specific set of patterns that define a star did not come into existence, then those that define a galaxy would also not come into existence - in other words, if stars didn't exist, galaxies wouldn't exist. Likewise, if subatomic particles didn't exist, neither would stars. Conversely, it can be argued that because stars exist - because objects with the structure and behavior that define a star exist - galaxies must exist.

This last statement is incomplete as is. The existence of a galaxy is not dependent only on the existence of star, it depends also on the number of stars that exist, and their positions in space and in time relative to each other. If only one star exists in the universe, there are no galaxies in the universe. If several millions of stars exist in the universe, but they are spaced evenly in a perfectly straight line through space, a galaxy will probably not come into existence. If several million stars exist, but they each exist at different times, again the galaxy will not come into existence.

This is a basic summary of complex systems and emergence, the most beautiful and powerful concepts I personally have ever come across. The universe I observe around me, it appears, is defined by such complex systems - each complex system provides the medium for the next complex system to emerge, and conversely, each complex system emerges from another.

I have not stated it explicitly yet, but it should be obvious at this point that scale has an important place in this overall system. Each individual "member" of a complex system - i.e. an atomic particle, a star, or a galaxy - can only exist in a certain range of sizes. Starting with the radius of our Sun, for example, and reducing, we at some point reach a radius that is too small for any star. Getting larger, we at some point reach a radius that is too large for any star. Moreover, there is no way to define these sizes except by how they relate to the sizes of other things - there is no absolute measure of size in the physical universe, there is only scale relative to other fundamental objects. A star can only be so many times bigger than a proton, for example, or a star can only be so many times bigger than a cubic meter (which is also, ultimately, defined relatively). Thus there is between all emergent objects a certain "length of scale" between that object and next smaller class of object, and the same applies in the bigger direction.

In addition, there is a very similar temporal relationship between the different scales of objects. Given the distribution of subatomic particles used earlier, there is a certain "length of time" before these particles coagulate enough for a star to be said to exist. This length of time is a function of many variables, but knowing these variables it can still be quite precisely defined.

I have drawn on so many terms directly relating to dimension now that I'd almost think it was obvious what I'm trying to explain:The universe is defined by objects that occupy certain positions in space and time, and it is also defined by objects that occupy certain positions in scale. The position of things in any of these dimensions can be derived from its position in all of the others.

Here is a summary of the dimensional properties of scale:
-Like space and time, scale is defined by two opposite directions: smaller and bigger.
-These two directions appear to extend for ever.
-The position of an object in scale is called its size. Just as the position of an object in space or in time can only be defined relative to another object, the size of an object can only be defined relative to the size of another object.
-Most interesting to me: the nature of scale appears to be similar to that of time in that it has a direction of flow: larger objects appear after smaller ones, and not the other way around. In fact, this pattern is directly tied to the flow of time: larger objects emerge from smaller ones as time moves forward. I believe the ever-elusive definition of time could quite possibly be found somewhere in this relationship, such as by the converse of that last statement: Time moves forward as larger objects emerge from smaller ones.

Finally, let me point out what to me is a striking and compelling illustration of everything I have just described: Most of you are probably familiar with what a tesseract is: a four-dimensional cube. I have always preferred to represent a tesseract in the following fashion, as it has always been more comprehensible to me:
http://upload.wikimedia.org/wikipedia/commons/3/3f/Hypercubecubes.svg
Another common representation has never made much sense to me and has been difficult for me to relate to, but sometime after I formulated the above general theory, I ran across this representation again, and was dumbfounded:
http://upload.wikimedia.org/wikipedia/commons/6/69/Hypercubecentral.svg

I believe I've made a case.

[Jim]

Welcome to BAUT Nick!

Per your request, I have split your posts into two threads. Let me know if the title of this thread should be changed, or if I split the wrong posts.

[Noclevername]

Welcome to BAUT!

In addition to the three dimensions of space and the dimension of time, it can be argued that, in the context of the physical universe, scale should be considered a fifth dimension, distinct from and perpendicular to the others.


My first thought on seeing this was "Of course not!" Hard on the heels of that came the thought "...Or is it?" Scale does, after all, make a big difference in how matter and energy, basic forces, and even space/time act and interact. So maybe there is something to this idea.

I have no idea how such a "dimension" would relate to the other ones. But then I'm not even sure if Time belongs on the list (if it qualifies as a dimension, or a process, or both), let alone adding a new one!

[korjik]

To be a dimension, scale must be independent of the other dimensions.

namely, x dot scale equals zero.

However, since x dot scale = ax (where a is a vector indicating the size of the scale) then scale is not a dimension.

For a simple example is the scale desired is kilometers, then a equals .001 km/m, assuming that x is in meters.

[TheNick]

To be a dimension, scale must be independent of the other dimensions.

namely, x dot scale equals zero.

However, since x dot scale = ax (where a is a vector indicating the size of the scale) then scale is not a dimension.

For a simple example is the scale desired is kilometers, then a equals .001 km/m, assuming that x is in meters.

What is x here?

The concept here definitely still needs some work. I came to this theory because I noticed several things that reminded me of dimensions, but I'm still trying to figure out exactly what it means. For one thing, I can tell right away that if scale is to be considered a dimension, it is only in the context of physical material, as obviously no fourth dimension is required to define a small space and big space. Furthermore, the relationship to matter must be tied to the complex systems they produce in the universe.

Anyone who is not familiar with the concepts of complex systems and emergence would probably be unable to comprehend how I came to this proposition.

And as Noclevername hinted at, this dimension would likely be much more similar in nature to time than to space.

As far as the vector math is concerned, perhaps we can help solve that problem by remembering that the two directions of scale would be bigger (positive) and smaller (negative). Or, if you plotted a point on a 2D graph of x-position versus scale, what would that point be telling you?

Still, a lot left to figure out.

[Bogie]

This sounds like it could be a "Turtles all the way down" idea.

http://en.wikipedia.org/wiki/Turtles_all_the_way_down

I actually did a thread on this idea too, so we share the Nobel.

[hhEb09'1]

Anyone who is not familiar with the concepts of complex systems and emergence would probably be unable to comprehend how I came to this proposition.I'm a little familiar and I'm having trouble myself :)
And as Noclevername hinted at, this dimension would likely be much more similar in nature to time than to space.I looked over your OP, and it seems to me that you define the "dimensional qualities" in terms of other dimensions. In other words, without those dimensions, your "dimension" doesn't exist. We have plenty examples, especially in special relativity, where measurements in one dimension can translate into other dimensions, or other versions of dimensions. It doesn't increase the number of dimensions, merely their 'shape".

Like defining orbital parameters, which are defined by a certain number of independent quantities. The quantity definitions change, and take different shapes, but the total number ends up being the same no matter how you borrow from others to create a new one.

[Hornblower]

I would say no to considering scale to be another dimension.

The hierarchy of some of these fundamental structures is physically very real, but the limitations on the size ranges are consequences of physical properties that are fully described by means of mathematical constructions within the familiar dimensions.

[Jens]

In addition to the three dimensions of space and the dimension of time, it can be argued that, in the context of the physical universe, scale should be considered a fifth dimension, distinct from and perpendicular to the others.

What you wrote about hierarchies, like the sun being created out of atoms, etc., is quite an interesting thing, something that many of us think about, but it doesn't really have anything to do with dimensions. Just because you can measure something doesn't make it a dimension. Heat also has a scale, as does luminosity, as does anger for that matter. But it doesn't make them dimensions. I think a dimension is something like a direction in which you can travel. You can travel in three dimensions, and through time. But you can't travel in heat, or in scale.

[TheNick]

What you wrote about hierarchies, like the sun being created out of atoms, etc., is quite an interesting thing, something that many of us think about, but it doesn't really have anything to do with dimensions. Just because you can measure something doesn't make it a dimension. Heat also has a scale, as does luminosity, as does anger for that matter. But it doesn't make them dimensions. I think a dimension is something like a direction in which you can travel. You can travel in three dimensions, and through time. But you can't travel in heat, or in scale.

Every value you cited - heat, luminosity, anger - are all absolute quantities. This is of course a clear indication that those things are not dimensions. As I've stated, though, scale does not share this property.

The tone of your comment makes it clear that you have assumed I'm probably pretty naive. Let me take this opportunity to assure you I am no lazy thinker. I am not surprised at all that others have noticed the heirarchical nature of matter, but I believe in my bones that it would be foolish of me to think this means I can't possibly think of something nobody else has yet. I believe such an attitude would probably be healthier and more fruitful for some people (nothing to their detriment; I am very good friends with several such people), but I am not one of them.

This is certainly not meant to be offensive, and it is a statement I would direct towards many people on this forum, not just you.

As to your last statement: upon considering how to refute the argument that we cannot travel through scale, it occurred to me that indeed we can and all of us have. Even more, it was accomplished through the single most perfect example of complex systems and emergence known: life. At one point, your entire person occupied the space of a zygote, and your scale has moved very smoothly from that point to where it is now.

This leads me to another thing: although it may be perfectly possible to comprehend every lipid and protein, every cell, every tissue and organ, etc, that make up the human body, although it may be perfectly possible to precisely describe the structure and function of every part, I assert that it is intrinsically impossible to create a fully functioning replica of the human form other than by the same process by which each of us was created.

This is not just a statement about biology. This statement says something about the universe. And it definitely has something to do with what I'm talking about with scale and dimension.

[Noclevername]

This leads me to another thing: although it may be perfectly possible to comprehend every lipid and protein, every cell, every tissue and organ, etc, that make up the human body, although it may be perfectly possible to precisely describe the structure and function of every part, I assert that it is intrinsically impossible to create a fully functioning replica of the human form other than by the same process by which each of us was created.

A couple of points;

You can't prove something impossible. Just because it can't be done right now doesn't meant it can never be done.

I know of no physical property that makes it impossible to create a human body atom by atom. There's no basis that I'm aware of for thinking that there's some property of human beings that makes us unable to be duplicated. If you know of such a reason, please don't hesitate to share it, I love to learn new things.

[Jens]

The tone of your comment makes it clear that you have assumed I'm probably pretty naive. Let me take this opportunity to assure you I am no lazy thinker. I am not surprised at all that others have noticed the heirarchical nature of matter, but I believe in my bones that it would be foolish of me to think this means I can't possibly think of something nobody else has yet.


I'm not assuming you're naive. I'm interested in some of the same ideas, so I did not mean my message as an attack. I just think that the word dimension is not correct for what you're trying to say. It may well be that we grow, I won't dispute that, but to me, a dimension is something that you use to define the position of something. You say that something exists at time T, at position X, Y Z. And there may be other dimensions. But you don't mention its scale (or its heat) to locate it. But I don't know. It is true that dimension was originally used to refer to position in space, and then by analogy to mean time and also fractal dimensions. So I suppose my problem in a way is that "dimension" is really just a word, and I suppose you could define it in different ways. So I suppose it's not that important. Maybe the more important is why this would be important?

[Gillianren]

Every value you cited - heat, luminosity, anger - are all absolute quantities. This is of course a clear indication that those things are not dimensions. As I've stated, though, scale does not share this property.

Can you clarify this? It's obviously true that you can have more or less heat, luminosity, or anger; what makes them absolute quantities?

[TheNick]

You can also have no heat, no anger, or no luminosity. You cannot have no size. Not if you physically exist.

[hhEb09'1]

You can also have no heat, no anger, or no luminosity. You cannot have no size. Not if you physically exist.How do you have no heat (http://en.wikipedia.org/wiki/Absolute_zero), if you physically exist?

The comment about fractal dimension brings up a point--that things like orbital elements needing six independent quantities to define them is taken to mean that they have six dimensions. While some people say that there are 29 dimensions of compatibility, I think we've shown on BAUT that it's closer to a million five :)

[Aristocrates]

What can scale tell us about a shape that the usual space and time dimensions can't? Imagine I have two cubes, and you tell me one has scale = 1 and the other has scale = 2. I'll ask how that is measured. Is the measurement derived from anything other than the length, width and height of each cube? If not, then scale doesn't really describe anything that 3 spatial dimensions can't.

[Bogie]

TheNick, you are beginning to see that jargon is important and often the improper use of jargon will sidetrack a discussion of your idea. I am "jargon disadvantaged" meaning that I can discuss your topic in your jargon.

I’ve quoted from your above statements to put some scope on my reply.


In addition to the three dimensions of space and the dimension of time, it can be argued that, in the context of the physical universe, scale should be considered a fifth dimension, distinct from and perpendicular to the others.
…
The total number of objects in this universe in its first state would thus have so many gazillions of objects + 1, the gazillions representing the subatomic particles, the +1 representing the star. In the second state, with the particles distributed, it would contain the same number of objects -1, the star no longer being in existence. So merely be redistributing the matter, without physically removing anything, you have in fact removed an object from this universe.
…
[You mention particle to star to galaxy sequence.]
…
I have not stated it explicitly yet, but it should be obvious at this point that scale has an important place in this overall system. Each individual "member" of a complex system - i.e. an atomic particle, a star, or a galaxy - can only exist in a certain range of sizes.
…
Thus there is between all emergent objects a certain "length of scale" between that object and next smaller class of object, and the same applies in the bigger direction.
…
The universe is defined by objects that occupy certain positions in space and time, and it is also defined by objects that occupy certain positions in scale. The position of things in any of these dimensions can be derived from its position in all of the others.
…
Here is a summary of the dimensional properties of scale:
-Like space and time, scale is defined by two opposite directions: smaller and bigger.
-These two directions appear to extend for ever.
-The position of an object in scale is called its size.
-Most interesting to me: the nature of scale appears to be similar to that of time in that it has a direction of flow: larger objects appear after smaller ones, and not the other way around.
…
I believe the ever-elusive definition of time could quite possibly be found somewhere in this relationship, such as by the converse of that last statement: Time moves forward as larger objects emerge from smaller ones.
…You are talking about a progression of the size of objects from tiny particles to groups, to groups of groups, etc. right on up to the galaxies and beyond, all progressing on a forward moving time scale.

Several implications can be drawn. One is that the size/time relationship goes both ways, i.e. if we were to go far enough back in time there would be size “dimensions” smaller than the smallest particles that we observe, and if we were to jump forward in time there would be (or may already be) other “universies” (:)) on a larger scale than our own observable universe.

On your other thread I predicted that you were wrong about the positive/negative universes that remain separated by opposite charges but offered to discuss it. On this thread, in regard to a dimension we can call “scale” I see possibilities.

I would like to inquire that though you can (and have) linked “scale” to “time”, do they need to be linked? I see you view the universe from the perspective of an ongoing process of scale and time, but can it alternatively be viewed as a complete system now (and always)? Could it be a complete system and still be characterized by a full range of “scale dimension”, and could your range of scale be potentially infinite?


Most of you are probably familiar with what a tesseract is: a four-dimensional cube.I was not able to access your link to the tesseract.

[Gillianren]

"The fifth dimension is the tesseract."

--Madeleine L'Engle, A Wrinkle in Time

[Bogie]

"The fifth dimension is the tesseract."

--Madeleine L'Engle, A Wrinkle in TimeOh, thanks. I found it here. (http://setiathome.berkeley.edu/forum_thread.php?id=38687)

[Noclevername]

What can scale tell us about a shape that the usual space and time dimensions can't? Imagine I have two cubes, and you tell me one has scale = 1 and the other has scale = 2. I'll ask how that is measured. Is the measurement derived from anything other than the length, width and height of each cube? If not, then scale doesn't really describe anything that 3 spatial dimensions can't.

Nor does time. Scale might be considered a nonspatial, or "differently spatial", dimension.

[hhEb09'1]

Nor does time. Scale might be considered a nonspatial, or "differently spatial", dimension.Do you mean time "doesn't really describe anything that 3 spatial dimensions can't," neither?

That don't seem right

[Noclevername]

Do you mean time "doesn't really describe anything that 3 spatial dimensions can't," neither?

That don't seem right

Does it? How do length, width and height (without scale) lead you to a measurement of time? Movement along one of these axes can give you a demonstration of time, to show that it exists, but without knowing the objective scale, it cannot give an observer a measurement of time.

[Celestial Mechanic]

[Snip!] Just because you can measure something doesn't make it a dimension. Heat also has a scale,
Good so far ...

as does luminosity,
Still good ...

as does anger for that matter. [Snip!]
BZZZT!!! Looks like you've "jumped the shark" here. How does one measure anger? What units is it measured in? Furies, perhaps? So would a mild annoyance be several hundred milliFuries, a good venting be several kiloFuries, and a murderous rampage a megaFury?

What kind of instrument can measure this? What is a reference anger that could allow us to calibrate it? :think:

[Maksutov]

"Scale" is not a separate dimension.

Instead, as it relates to size, area, and volume, it's the result of our assigning quantitative attributes to the three spatial dimensions. As it relates to speeds, velocities, rates, etc., it's the result of our assigning quantitative attributes to the three spatial dimensions and the one temporal dimension.

[Jens]

BZZZT!!! Looks like you've "jumped the shark" here. How does one measure anger? What units is it measured in? Furies, perhaps? So would a mild annoyance be several hundred milliFuries, a good venting be several kiloFuries, and a murderous rampage a megaFury?

What kind of instrument can measure this? What is a reference anger that could allow us to calibrate it? :think:

Yes, kilofuries. I'm surprised you never learned about it in physics. The instrument is called a furimeter, and I think it works by measuring the redness of the face or something like that. :)

OK, I went a little bit overboard with that one.

[hhEb09'1]

Does it? How do length, width and height (without scale) lead you to a measurement of time? Movement along one of these axes can give you a demonstration of time, to show that it exists, but without knowing the objective scale, it cannot give an observer a measurement of time.??

So, time does really describe something that 3 spatial dimensions can't. That was the point that I thought I was making. :)

[Aristocrates]

??

So, time does really describe something that 3 spatial dimensions can't. That was the point that I thought I was making. :)

I was just leaving time out to simplify. If I describe a moving object, then time will be involved, and scale still won't tell us anything new.

[Noclevername]

"Scale" is not a separate dimension.

Instead, as it relates to size, area, and volume, it's the result of our assigning quantitative attributes to the three spatial dimensions. As it relates to speeds, velocities, rates, etc., it's the result of our assigning quantitative attributes to the three spatial dimensions and the one temporal dimension.

It also relates to other factors, such as how physical laws apply, how objects behave, how energy behaves, uncertainty, and all the oddities of quantum mechanics. On the larger end of scale, it limits how much mass can be in one place without collapsing, and may effect things like how space acts and how gravity functions. So it's not just about measurements of volume.

I really wish I knew enough physics to express what I'm trying to say!

[Aristocrates]

But volume is still how scale is being described.

[Noclevername]

But volume is still how scale is being described.

That's just because of the limits of our terminology. And quantum mechanics takes its name from the measurement of energy, not from volume.

[TheNick]

Is there a standard explanation of what exactly the difference is between space and time? Is there any agreement on what the actual description of time is compared to space? That would be very useful for this discussion.

Perhaps we can agree that part of the difference is this: space does not depend on a physical universe, time does. If space was filled with only a static system, then there would be no time, and the universe would effectively be only geometry. Time is necessary to describe the actual physical universe. Scale shares this sort of property: if there is nothing of a physical nature to describe, then scale is meaningless.

I mentioned space filled with "only a static system." If we try to imagine what this would actually be like, I think it can be argued that it would not contain matter in the heirarchical arrangements we know. The concept of a static universe that contained atoms and stars is somewhat paradoxical. Such a scale-structured universe would imply time, as we are aware that the only way such structures come to be is over time. I think a "static-space universe" would be much more abstract and would be described in the more purely mathematical terms of geometry.

So scale is a property of the physical universe and loses its meaning when applied to a static system.

For the mathematically inclined here is a rough attempt at a mathematical description of how scale might be viewed. Lets say we choose an arbitrary standard unit of scale. I'll go with the second-cubic-meter (notice this is a unit of space-time). Now if we divide a certain system which we want to observe into any 4D grid of second-cubic-meters, and over the space-time volume enclosed in each second-cubic-meter of the grid, calculate a vector, or possibly a set of vectors, that describe the average change in each unit, we would effectively create a vector field, representing the behavior of that system at that scale, i.e. viewing the system at one second-cubic-meter. If we calculated a new vector field, this time defined by dividing the exact same system into a larger unit of space-time, such as the minute-cubic-kilometer, and calculated the new vector field from this new grid's average change for each unit, we would have a field describing the system at one minute-cubic-kilometer. We could make a third field describing the system from the view of one millisecond-cubic-micron, etc...if we compare the vector fields calculated for each scale, we will see that the patterns they exhibit from one unit of the grid to the next are not the same. In other words, the behavior of the system is different at different scales. A certain set of rules might describe the vast majority of the system at one scale, but become so vague and abstract when applied to a different scale as to be almost meaningless. A different set of rules is required to effectively describe the behavior of the system at this new scale. For example, the rules that describe the universe at scales near that of the solar system would include many equations of gravity and mass and so on, but equations of electromagnetic interactions, radioactive decay, or quantum mechanics would be more or less meaningless. On the other hand, if we tried to describe the universe at the scale of atoms, equations of gravity would not come in very handy. A different set of equations involving electromagnetics, nuclear physics, and quantum mechanics would be much more effective.

An important relationship between these vector fields is that, even though they are different, they can be derived from each other, at least in the bigger direction. That is, the vector field that best shows the universe at the solar-system level can be derived mathematically from that showing the universe at the atomic level. Deriving the atomic universe from the solar-system universe would be much more difficult, and is a question I would not be qualified to address currently.

I think you will find that there are almost no equations in the domain of physics that can be applied to all scales. Any equations that can would tell us something about the nature of scale and the universe as a whole.

Noclevername definitely appears to have a sense of what I'm trying to suggest. I share his frustration trying to describe these concepts, as they are quite abstract and are still developing in my own head.

[Noclevername]

Is there a standard explanation of what exactly the difference is between space and time? Is there any agreement on what the actual description of time is compared to space? That would be very useful for this discussion.
There are a number of theories, some of which can provide a partial expalnation for our observations. At present, IIRC none of them can explain all our observations. As you said, there are no equations that cover everything.

Perhaps we can agree that part of the difference is this: space does not depend on a physical universe, time does.
Uh, I don't agree with that. Space can't exist without a physical universe.

[TheNick]

Perhaps I need some help with this description, then. I based that statement on what can be represented conceptually on a piece of paper. Space can be represented quite easily without any processes occurring within it. This is just geometry. However, if you try to represent time on paper, it can only be done by describing something physical, and it also requires at least one dimension of space for the process to take place in.

Do you have some sense of what I'm getting at?

[Noclevername]

Perhaps I need some help with this description, then. I based that statement on what can be represented conceptually on a piece of paper. Space can be represented quite easily without any processes occurring within it. This is just geometry. However, if you try to represent time on paper, it can only be done by describing something physical, and it also requires at least one dimension of space for the process to take place in.

Do you have some sense of what I'm getting at?

I think so, but representation isn't reality. Space isn't just the measurements of space. Space without time is an abstract concept, I don't think it's possible in any real sense.

[TheNick]

So lets take two abstract concepts: space without time, and time without space. Which can you better comprehend? Which is easier to describe on paper?

Which comes first, space or time? I say space.

[Noclevername]

So lets take two abstract concepts: space without time, and time without space. Which can you better comprehend? Which is easier to describe on paper?

Which comes first, space or time? I say space.

I doubt either can exist. They are both needed to define each other. Space without time is unmeasureable and unobservable, since the act of observing itself takes time. So what you're left with isn't really space. And as you pointed out, time requires space to exist. As the song says, "You can't have one without the other".

[TheNick]

I agree with you entirely when it comes to reality. Neither space nor time exist independently of each other in the actual universe. But maybe it can be shown that one can still be imagined without the other, without the reverse being true. I am making a purely conceptual distinction here, which may not even be important, but which on the other hand may help us describe the nature of space and time, and, eventually, of scale.

There must be other threads on this forum that have dealt with this issue extensively. Perhaps someone can provide a link to one?

[hhEb09'1]

But maybe it can be shown that one can still be imagined without the other, without the reverse being true. No, I have your counterexample right here in my head. :)

[Noclevername]

One problem conceptually is that "holding still" is about the closest we can really imagine to "no time". Or alternately, "there and gone in a blink". Neither is really a good representation of existence without time.

[TheNick]

Okay, but can we not mathematically represent a space without involving time? This is what geometry is all about.

[Noclevername]

Okay, but can we not mathematically represent a space without involving time? This is what geometry is all about.

Geometry does not represent space without time, it represents volumes within space (which requires measurement, which requires time). And it has limits to its accuracy when it comes to representing anything but localized space.

[Aristocrates]

Time is generally regarded as being as geometrically "real" as space, so that one could describe processes involving space and time using geometry only. If this were not the case, general relativity could not describe spacetime as a geometric cause of gravitation. If I recall correctly, time is perpendicular to the spacial dimensions, but with a negative metric relative to them, causing equations regarding spacetime to be hyperbolic in general. Someone correct me if I'm wrong.

That isn't the whole story, and nobody knows the whole story, but we do know that time isn't as different from space as it appears to the casual observer.

[north]

Time is generally regarded as being as geometrically "real" as space, so that one could describe processes involving space and time using geometry only. If this were not the case, general relativity could not describe spacetime as a geometric cause of gravitation. If I recall correctly, time is perpendicular to the spacial dimensions, but with a negative metric relative to them, causing equations regarding spacetime to be hyperbolic in general. Someone correct me if I'm wrong.


That isn't the whole story, and nobody knows the whole story, but we do know that time isn't as different from space as it appears to the casual observer.

its not so much " time " as it is the energy of the object(s) IN space.

space is the consequence of energy/matter or energy/matter is the consequence of space . you can't have neither without the other .

the confusion about the relationship between space and time is about how one affects the other , is in the geometric , alone . but not in the fundamental root reality of the difference between space and time .

space is fundamental too the ability of energy/matter too manifest in the first place , which then leads to the geometric of time. time is a resultant consequence of space not the other way around

[Bessler007]

Hello The Nick,

I have an idea to put on the table. It might be described as half-baked. I'd like you and others to bake it if you'd be so kind. Maybe we can make a meal of it.

Conceptualize reality as digital and atoms as the building blocks. The atoms are either in a distinct space or not. If you look at the geometry of space in this manner, it can be represented by a binary 3 dimensional array.

Time can be looked at in terms of the interval or cycle you look at the 3 dimensional digital array of space. It is a dimension of the array outside it but effects the information between the data or atoms occupying or not the 'holes' or 'positions' within the data base of space.

The difference between a universe where the constituent parts of a binary star are spread evenly throughout it compared to one where the stars are formed could be viewed in terms of the information between the parts and between larger parts also; existing between the moments we look at the data. The relationships of information wouldn't be infinite but they would be very large.

The scale-as-dimension theory you mention is a dimension of information. As the data base of space clumps together or organizes, it does so at an ever increasing rate. Also the rates of change represent a mathematically defined scale that could be a little fuzzy around the units but might have a pattern.

Should this idea go back in the oven?

[Bessler007]

1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


This is a rough representation of the idea. The first interval of time is on the left and the second interval is on the right. Mass is conserved in the four part two star formations. I might have put more atoms in the stars and put them further apart but this was very tedious as it was. This is well before collisions and atoms splitting. I could never draw that. I didn't represent the information (eg gravitational attraction, kinetic energy, power, magnetic attraction, etc.)

It was next to impossible to do this in 3-d.

The more organized the system becomes the faster it tends to organize?

[Hornblower]

Hello The Nick,

I have an idea to put on the table. It might be described as half-baked. I'd like you and others to bake it if you'd be so kind. Maybe we can make a meal of it.

Conceptualize reality as digital and atoms as the building blocks. The atoms are either in a distinct space or not. If you look at the geometry of space in this manner, it can be represented by a binary 3 dimensional array.

Time can be looked at in terms of the interval or cycle you look at the 3 dimensional digital array of space. It is a dimension of the array outside it but effects the information between the data or atoms occupying or not the 'holes' or 'positions' within the data base of space.

The difference between a universe where the constituent parts of a binary star are spread evenly throughout it compared to one where the stars are formed could be viewed in terms of the information between the parts and between larger parts also; existing between the moments we look at the data. The relationships of information wouldn't be infinite but they would be very large.

The scale-as-dimension theory you mention is a dimension of information. As the data base of space clumps together or organizes, it does so at an ever increasing rate. Also the rates of change represent a mathematically defined scale that could be a little fuzzy around the units but might have a pattern.

Should this idea go back in the oven?

*****


1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


This is a rough representation of the idea. The first interval of time is on the left and the second interval is on the right. Mass is conserved in the four part two star formations. I might have put more atoms in the stars and put them further apart but this was very tedious as it was. This is well before collisions and atoms splitting. I could never draw that. I didn't represent the information (eg gravitational attraction, kinetic energy, power, magnetic attraction, etc.)

It was next to impossible to do this in 3-d.

The more organized the system becomes the faster it tends to organize?
If I had the foggiest idea what these two posts are trying to say, I might be able to make an informed reply as to whether it should go back to the oven or down the garbage disposal. Otherwise no dice.

[Bessler007]

Hello Hornblower,

The idea is one that came from a frustration of a simulator. It's an attempt to reduce reality to what is real to the degree of resolution I'm able to.

The model presumes there is something in space or there isn't. Also there can't be two point masses in the same space.

The next assumption is about the nature of time. Analysis is constrained by time but reality isn't. There's not much we can do about that. In other words we can only look at information that exists between two frames of time. Reality is looking infinite times between any two frames we're considering.

As the left matrix is translated to the one on the right there exists information that describes the translation. There is also information that causes or determines the change. Here is another way to consider it. There are forces in both matrices and the information between those two frames describe energy and power. Stating the obvious, both quantiles are dependent on the duration between our look at them and the distance they move in the translation.

If one point mass moves further between looks as another we describe it as having more power. If it can move twice as far what are the forces causing that movement? What is the cause? This is an assumption reality has a cause. There is no Santa Cause.

Now as this relates to the topic: Is it possible to consider reality as mass organizes or collects in an effort to support the concept there is a dimension termed 'scale'? There are usually any number of ways to look at the same thing.

When you think about the critical density of the universe you can see there isn't a whole lot of matter out there. We're fortunate here on earth to have a lion's share of it piled up.

Then when you consider the nature of matter there really isn't much there either. We think about the particle of an electron has having mass as a function of it's motion as it orbits in a wave being almost every where at once around a nucleus. It's a Tasmanian devil cloud.

This is a little off topic but consider electrons. They've been busy spinning around nuclei for a very long time with an excellent track record. No accidents. So what do we do? To understand what they're made of we make a track or accelerator and send one particle one way and another the other way and let them meet on the other side in a collision! What is this?? They've had an excellent record for a very long time of 'no accidents' but we're not happy with that. We want an accident so we can examine the pieces to see what they're made of! Amazing.

So back to the topic one more time. Is it possible that the collection of matter (that is very sparse in the universe) exhibits a dimension of scale as it organizes in clumps. I find it very noteworthy this same matter isn't much to speak of either.


I am suggesting if there is any dimension termed 'scale', it might be seen by looking at the change in information that exists between frames of reference and that time is a human construct that might be expressed as a distance between cycles of two perspectives or frames.

Not much to organize or collect (matter) and not much substance forms our reality. It is interesting.

[Bessler007]

1 0 0 1 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 1 0 1 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 0 1 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 0 0 1 0 0 1 time/distance 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 0 1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 time/distance 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 1 time/distance 0 0 0 0 0 0 0 0 0 0 0 0



The model is an attempt to look at the information between frames of a digitized reality with a relational data base. What isn't shown is that data base of information between the frames as time cycles.

I don't know if the idea would be useful in uncovering a dimension termed 'scale'.

[TheNick]

Bessler,

I think I know what you are getting at. You have hit upon a lot of the very concepts that led me to the idea that scale behaves like a dimension, and I have lots and lots to say about several related subjects. Unfortunately I don't have time at the moment to write a full response. For now, tell me if you agree with this statement, and whether or not it represents your motivations for this idea:

By breaking down a real, physical system into pure information, we should be able to analyze it completely mathematically, and thus minimize the amount of guesswork involved in deciphering the nature of the system.

[Bessler007]

The Nick,

I never thought about it until I read your description. Scale might be a property definable by some set of measurements.

I do think I agree.

[north]

So lets take two abstract concepts: space without time, and time without space. Which can you better comprehend? Which is easier to describe on paper?

Which comes first, space or time? I say space.

your right

space is not about measurement , as so many have mistakenly claimed , space is about ROOM to manifest energy/matter.

time is about measure . which is secondary. since it plays NO part , in and of its self to any consequence in this Universe. time has NO substance

[north]

Originally Posted by TheNick
So lets take two abstract concepts: space without time, and time without space. Which can you better comprehend? Which is easier to describe on paper?

Which comes first, space or time? I say space.


I doubt either can exist. They are both needed to define each other. Space without time is unmeasureable and unobservable, since the act of observing itself takes time. So what you're left with isn't really space. And as you pointed out, time requires space to exist. As the song says, "You can't have one without the other".

ahh I see , so that if the mathematication finds space " unmeasureable " space then becomes " unobservable " . this is a case of logic rather than Reason , obviously .

I ask you this question " what came first reality or mathematics ? "

[north]

further scale is not a true dimension .

a true dimension is defined as ( by me ) that which ALLOWS an object the possibility too manifest. hence height , depth and breadth. 3D

scale is about " size " within a 3D space.

[Noclevername]

I ask you this question " what came first reality or mathematics ? "

Reality. Mathematics is a human invention to describe some aspects of reality.

[Noclevername]

further scale is not a true dimension .

a true dimension is defined as ( by me ) that which ALLOWS an object the possibility too manifest. hence height , depth and breadth. 3D

scale is about " size " within a 3D space.

You didn't read the thread, did you? It shows. Go back and read the whole thing before slinging comments on what's already been covered.

[Michael Noonan]

I am sorry I haven't made a comment yet but have read this a couple of times. Does this seek to remove the rubber sheet effect of the curvature of time and space for the passage of light?

That is for each point viewing outwards through the mass distribution of the universe the density of matter per cubic unit of space needs to be calculated to determine the amount of space a photon must travel through to reach an observer.

In that case wouldn't each point in space need to be determined with the three spatial dimensions and the one time dimension and the one linear adjustment dimension and two radial dimensions to determine direction of light source.

I could be wrong here but using this idea (and I probably don't have the concept properly in my mind that you have), where does the curvature of light from a source get calculated if dimension of size is warped in a sideways movement between point of transmitting and point of receiving?

[north]

Is there a standard explanation of what exactly the difference is between space and time? Is there any agreement on what the actual description of time is compared to space? That would be very useful for this discussion.

the difference between space and time , is that space is necessary for the manifestation of energy/matter.

time is merely the measurement of movement of energy/matter within space itself.


Perhaps we can agree that part of the difference is this: space does not depend on a physical universe,

I disagree

space does depend on the physical Universe . I have contended that in order for an atom to exist it needs a certain amount of space in order to manifest.

inotherwords space and energy/matter go hand in hand . you cannot have one without the other.




time does. If space was filled with only a static system, then there would be no time, and the universe would effectively be only geometry. Time is necessary to describe the actual physical universe. Scale shares this sort of property: if there is nothing of a physical nature to describe, then scale is meaningless.

time in and of its self is does not have have any inherent energy . time merely describes the energy within atoms and their consequences of interactions amoung themselves. hence movement and therefore time.

[Hornblower]

further

I disagree with Albert

Albert suggests that as a mass approaches the speed of light that the mass increases . so therefore can not reach the speed of light .

I think the other way , as the mass increases its speed the more energy like it becomes.

inotherwords mass > reaches speed of light > energy.What does this have to do with the OP?

[north]

What does this have to do with the OP?

I'll just start a new thread

[autumn1971]

"Scale" is defined by the other dimensions. Length cannot be described by width or height, height cannot be described using width and length, and time cannot be described by using length, width, height, etc..
Yes, the dependence of scale upon the ability of humans to describe particular interactions is sensitive, but I fear that it is much more sensitive than your notion of scale is. Dirac's equations can precisely model a proton-electron system, but require significant fudging with the addition of one more particle. Also note the three-body gravitational problems.

To be blunt, North, the fact that you have defined a "star" as existing at a particular "scale", and then have posited that the disappearance of the "star" at a different "scale" can be turned on its head very easily. I define a "star" as the structure occurring when a group of particles is evenly distributed in a universe, and your assertion in the OP is reversed.
Tweaking definitions to suit your ideas is not without value and interest, but it is called "philosophy", and is not amenable to rigorous study.

[Bessler007]

Hello autumn1971,

Philosophy or sophistry?

[Noclevername]

"Scale" is defined by the other dimensions.

That's exactly the problem; we now know that scale effects a lot more
than just measurements. It has to do with how the laws of physics apply, how particles. energy, forces, and even space and time all act and interact. Just because we're currently stuck with an outmoded primary definition doesn't make an accurate definition. It needs an update to account for new data and observations.

[autumn1971]

That's exactly the problem; we now know that scale effects a lot more
than just measurements. It has to do with how the laws of physics apply, how particles. energy, forces, and even space and time all act and interact. Just because we're currently stuck with an outmoded primary definition doesn't make an accurate definition. It needs an update to account for new data and observations.

Nope. Right now, inside of you, the Sun, and an isolated atom, there is a whole lot of quantum physics going on. The difference in you and the Sun is that the quantum effects are hidden by their number, and the macroscopic effects are the ones that are more interesting and easier to investigate.
If I am studying a shoreline, to do so by examining every individual grain of sand would be hypothetically possible, but very impractical. Scale has absoloutly no effect on the way physics works, only on the methods used to investigate it.

Oh, and sorry about the dig on philosophy. It just annoys me sometimes that people with all those logical tools use them to wonder about things rather than to actually investigate things (darn, that's probably just as much a dig as my first comment. Sorry, I have a problem communicating without being snarky).

[Noclevername]

Nope. Right now, inside of you, the Sun, and an isolated atom, there is a whole lot of quantum physics going on.

Yes, at the same scale. Which is my point.

[TheNick]

First off, autumn, I posted the OP, not North, so please direct your snarky remarks my way.

Noclevername hit it on the head. As you say, autumn, quantum mechanics apply everywhere in space and time, but it does not apply at all scales. At the scales where gravity shows itself, quantum mechanics does not show itself. I need zero knowledge of quantum mechanics to accurately describe the orbits of the planets mathematically.

I am recognizing a simple truth - stars exist. If the entire universe was only quantum mechanics, it would be pointless to make the assertion that a star exists. And yet, stars exist, and effect things in predictable ways. There is a singularity of information that exists at the scale of stars that cleanly separates larger physical systems such as galaxies from smaller ones such as atoms. This is a simple fact that I doubt you will argue with. Our differences seem to be mainly in how much significance we assign to this fact.

[Hornblower]

First off, autumn, I posted the OP, not North, so please direct your snarky remarks my way.

Noclevername hit it on the head. As you say, autumn, quantum mechanics apply everywhere in space and time, but it does not apply at all scales. At the scales where gravity shows itself, quantum mechanics does not show itself. I need zero knowledge of quantum mechanics to accurately describe the orbits of the planets mathematically.For physical property reasons that can be described within the familiar dimensions of space and time. Still no convincing demonstration of any need to treat scale as an additional dimension.

I am recognizing a simple truth - stars exist. If the entire universe was only quantum mechanics, it would be pointless to make the assertion that a star exists.Why? Please show us, in concise mathematical terms, why you think this is so.
And yet, stars exist, and effect things in predictable ways. There is a singularity of information that exists at the scale of stars that cleanly separates larger physical systems such as galaxies from smaller ones such as atoms. This is a simple fact that I doubt you will argue with. Our differences seem to be mainly in how much significance we assign to this fact.
Can you tell us, in concise mathematical terms, what you mean by "singularity of information"?

Can you show us, mathematically, why you think there is a clean break somewhere? If so, where is that break?

Once again, there is no denying that a star, for example, cannot be scaled up or down beyond certain limits. In my opinion the reasons for that are fully describable in the familiar space/time dimensional construct, with no need to treat the scaling factor as an additional dimension. So far I have seen nothing that comes close to convincing me otherwise. Please try to show us a mathematical demonstration of where you think I am going wrong.

Perhaps you are thinking of "dimension" in a sense that is clear enough within your thought process, but defies attempts to communicate it in plain English.

[Argos]

Perhaps you are thinking of "dimension" in a sense that is clear enough within your thought process, but defies attempts to communicate it in plain English..

Perhaps we´re in need of a formal definition of 'dimension', as in here (http://mathworld.wolfram.com/Dimension.html) and here (http://en.wikipedia.org/wiki/Dimension).

[TheNick]

I admit the concept is still quite fuzzy. The idea come to me from studying the nature of information and organization in the universe, not from studying any of the geometry of the universe, so I still am not sure how a geometrical dimension of scale could actually be described or observed. Like you, I get the impression I am missing something important, and that this something relates to the nature of matter, and possibly relates to some sort of number theory.

Still, it is extremely interesting to me that, from an information perspective, scale exhibits some highly "dimensionish" properties. It is comprised of two opposite directions. These both appear to extend forever. Further, when observing the physical universe, there are clearly positions of scale that are "occupied". Just as an object can be said to occupy a position in space or a position in time, it can also be said to occupy a position in scale. Finally, just like with space and time, a position in scale can only be defined relative to another position in scale.

Additionally, all the structures that appear to have naturally settled into a stable position of scale - atoms, stars, galaxies - form either a circular or spherical shape. There is then no longer a need to use three spacial parameters to define its shape. The shape of these structures can all be defined with a single parameter - a radius.

I am fully aware that this is all very abstract. But you must admit there is an interesting pattern here that is not as simple as it might appear at first.


I am recognizing a simple truth - stars exist. If the entire universe was only quantum mechanics, it would be pointless to make the assertion that a star exists.
What I mean by this is that it is worth noting that, to understand what is going on in the space occupied by, say, Sirius, it is not infact necessary to go to Sirius and study the quantum field in that space. Indeed, to understand what is going on inside a star billions of lightyears away, that we have never seen but who's existence we can predict, it is not necessary to go to that point in space and study it. Does it not seem fortunate that, to understand what goes on at every point in space and time, we are not required to study every point in space and time?


Can you tell us, in concise mathematical terms, what you mean by "singularity of information"?
Yes indeed I can, and this pertains directly to the above paragraph:
Once we understand how one star works, we know, to a high degree, how every star works. Only one complete set of information is needed to understand a multitude of independently-formed objects.

I doubt you would try to tell me the nature of information in the universe - the arrangement and behavior of truth - was not of interest or import to scientific study. The desire to understand the patterns in what can and cannot be said to be true is what motivated me to put this concept forth.

[Michael Noonan]

I admit the concept is still quite fuzzy. The idea come to me from studying the nature of information and organization in the universe, not from studying any of the geometry of the universe, so I still am not sure how a geometrical dimension of scale could actually be described or observed. Like you, I get the impression I am missing something important, and that this something relates to the nature of matter, and possibly relates to some sort of number theory.
(snip)


First for me if I can see a star it did exist, it may not be in the exact position that I am looking or looks anything like it did when the light left it but was there ... somewhere.

Next geometry. I am guessing this is like the five dimension geometry of space before general relativity. If so then it is what the best minds in existence before Einstein came up with, so a good start.

Take five cubes of space, line them up along line x and call them A, B, C, D and E. Now C is in the middle ... evenly and thinly spread with matter. B and D have large central galaxies in them. The linear geometry between them is line x and the parallel planes y,z.

What happens to the line x in cube C if the galaxies in B and D move to A and E? What happens to the series of y,z planes that C is full of as a result?

Now if C is to keep its exact cube shape then how does that affect those results? That is the geometry I am thinking about or is that not what you meant. No problems TheNick fuzzy or not it is interesting.

[Hornblower]

I admit the concept is still quite fuzzy. The idea come to me from studying the nature of information and organization in the universe, not from studying any of the geometry of the universe, so I still am not sure how a geometrical dimension of scale could actually be described or observed. Like you, I get the impression I am missing something important, and that this something relates to the nature of matter, and possibly relates to some sort of number theory.
I think the physical properties of the matter that makes up objects at all scales has everything to do with it. The important thing that you may be missing is that these properties impose limitations on the range of possible sizes of various types of objects, for reasons that can be analyzed and interpreted unambiguously in the familiar dimensions of space.


Still, it is extremely interesting to me that, from an information perspective, scale exhibits some highly "dimensionish" properties. It is comprised of two opposite directions. These both appear to extend forever. Further, when observing the physical universe, there are clearly positions of scale that are "occupied". Just as an object can be said to occupy a position in space or a position in time, it can also be said to occupy a position in scale. Finally, just like with space and time, a position in scale can only be defined relative to another position in scale.
Are you trying to convince us that a change of "position in scale" is something fundamentally above and beyond merely changing the range of spatial positions of the parts that make up the whole object?

Additionally, all the structures that appear to have naturally settled into a stable position of scale - atoms, stars, galaxies - form either a circular or spherical shape. There is then no longer a need to use three spacial parameters to define its shape. The shape of these structures can all be defined with a single parameter - a radius.
Woefully simplistic, in my opinion. Suppose a star is spinning. It will not be spherical, and additional parameters will be needed. Besides, this does not address the question of whether or not to treat scale as an additional dimension.

I am fully aware that this is all very abstract. But you must admit there is an interesting pattern here that is not as simple as it might appear at first.
No, I see no reason to admit any such thing, any more than I see anything more than a coincidence behind the beautiful pattern of Orion's seven brightest stars.


What I mean by this is that it is worth noting that, to understand what is going on in the space occupied by, say, Sirius, it is not infact necessary to go to Sirius and study the quantum field in that space. Indeed, to understand what is going on inside a star billions of lightyears away, that we have never seen but who's existence we can predict, it is not necessary to go to that point in space and study it. Does it not seem fortunate that, to understand what goes on at every point in space and time, we are not required to study every point in space and time?
What does this have to do with the question of whether or not to treat scale as an additional dimension?


Yes indeed I can, and this pertains directly to the above paragraph:
Once we understand how one star works, we know, to a high degree, how every star works. Only one complete set of information is needed to understand a multitude of independently-formed objects.

I doubt you would try to tell me the nature of information in the universe - the arrangement and behavior of truth - was not of interest or import to scientific study. The desire to understand the patterns in what can and cannot be said to be true is what motivated me to put this concept forth.Yes, by recognizing patterns, we can extrapolate from our in-depth studies of representative objects and make good inferences about numerous similar ones. This tells me nothing about the question about scale as an additional dimension.

[TheNick]

You are telling me you don't see any connection between these things. I am telling you there is one and it might be difficult to see at first.

The universe has a clear tendency to create large numbers of extremely similar objects, repeating patterns if you will. Each class of objects is created in a specific range of sizes. Nothing like a star is possible in the volume of an atom. Nothing like an atom is possible in the volume of star. Obviously we can take the highly-complex route to explaining why this is true, as we know the vast majority of the physics that cause atoms to form into stars and stars into galaxies. But the supreme simplicity of this pattern suggests there is a more fundamental truth at work here. Each class of objects - atoms, stars, galaxies, what-have-you - is utterly different from the others, and yet the pattern persists.

[Hornblower]

No, I see no reason to admit any such thing, any more than I see anything more than a coincidence behind the beautiful pattern of Orion's seven brightest stars.
I see now that I was not completely clear here. Of course I can see a pattern of hierarchy of structures ranging from small to large. What I do not see is your assertion that it is not as simple as it might appear at first. It appears to me that relatively simple principles of physics tie it together over the whole observable range, with no need to add additional dimensions to our mathematical conceptual construct.