# Hijack - from Dividing a Sphere re. Ideal vs Real

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Why a geometry of 3 planes or 3 "dimensions"? Because 3 orthogonal planes is the minimum number required to describe the physical dimension of volume, and is the simplest to visualize.

Again this is simply not true. Three orthogonal planes either meet in a point or in a series of lines. And anyway how are you intending to describe your object in these planes? Take a sphere centred at what I would call the origin - I can describe it very simply - how about your supposedly natural and simplest

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The universe has only one physical dimension which is what we call volume.

Riiight...

I want to meet you so I can give you the \$1,000,000 which this insight deserves. I suggest we meet at 4.75 gallons. OK?

That should tell you all you need to know. I don't know why GPS bothers with 4 dimensions when it only needs 1.

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This is getting nuts!!

Since I seem unable to cut and reply to quotes, let mesimply enumerate.

1. Orthogonality is a property of vectors. Specifically, 2 vectors are said to be orthogonal if their inner product is zero. So this is the incorrect term to use for planes that are mutually perpendicular

2. The mutualy perpendicular planes that Fred refers to are themselves 2-dimensional vector spaces. So that any space they enclose will be 6-dimensional. Such spaces do exist - they are called configuration spaces - but clearly this is not what is intended here

3. There is absolutely nothing special about the common use of the word "volume". I for one am quite happy to consider the area enclosed by the 1-sphere (i.e. circle) as a 2-volume (since it is a region of the 2-plane). Likewise the "area" enlcosed by any n-sphere (being a region of the embeddiding n+1 plane) as an n+1 volume

4. The universe, according to most people, is modelled as a 4-manifold. Being the "universe" there cannot be assumed to be an embedding space, so all statements must be intrinsic to this 4-manifold. Hence the term "volume", at least in the above sense, has no meaning.

5. Guess what..... we can aslo do intrinsic gemeotry on the 1-sphere, the 2-sphere etc

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Fred Champion,

I revisited the rendering Janus made of the second level build out of the 12 segment configuration and after building it out in clay, realized that in addition to what Janus says, the figure is a cubic octahedron. Not especially predicted that the second level of a sphere you are talking about, would produce a regular polyhedron.

The dual of a double tetrahedron is the cube. The dual of a cubic octahedron is a rhombic dodecahedron, but the point is, that the center of the twelve edges of a cube represent 12 points equal distant from the center of the cube, and if you put a ball in the center and surround it exactly with 12 balls of the same size, so that each ball is exactly on the center of each edge of the virtual cube, you would have a sphere like shape, that would have 6 four points and 8 three points. Build it out so that each of the twelve balls touching the center ball contact exactly 12 balls, maintaining the lattice arrangement of 4 hexagonal planes and 3 square planes, you AGAIN have a cubic octahedron, and the 42 resulting outside balls are arranged as Janus shows in # 16 of the parent thread.

I am thinking the layout of a spherical rhombic dodecahedron is a natural way that items fit together in 3 d space. No math required.

Regards. TAR

Several times in several ways, when figuring stuff about how the surface of a sphere can be physically divided up starting with the spherical rhombic dodecahedral configuration, I ran into the number 1.047 and its reciprocal .955. Particularly in reference to the ratio between the amount of square degrees in a sphere and the amount of TARadian divisions in a sphere. Being that 1.047 is a third of Pi, this gives me indication that Pi is a real physical thing.

and that there is a reason for the ratio

Edited by tar
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about 41,253 square degrees on a sphere

each diamond in the spherical rhombic dodecahedron is a segment in two intersecting hexagonal wheels around the sphere that can each therefore be considered as a 60 by 60 degree grid

60x60x12 segments is 43,200

Three times that is 3.14158968 which is close enough to 3.14159265 to consider that the exact amount of square degrees instead of about 41,253 would probably yield a ratio of exactly 1/3 pi.

Edited by tar
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Xerxes,

The seven planes in the matrix setup stacking the cannon balls as Janus did in #16 of the parent thread are not at nice right angles to each other. So I am not sure how you are using the various plane describers. The three square planes are at right angles to each other but the rows and columns of spheres are not at right angles to the rows and columns on the next square plane. And the four hexagonal planes are not even at right angles to each other. Seems to be more of a 60 degree thing going on.

Regards, TAR

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This is getting nuts!!

...

3. There is absolutely nothing special about the common use of the word "volume".

...

"Common use" is an interesting term. Perhaps you could provide us with another term for that portion of the universe occupied by individual physical entities such that we can put it into common use in place of "volume"? I think this term, or one which can replace it, is important, somehow, in the definition of matter and in what at least some believe is the basic thing that allows us to distinguish one entity from another.

Can you provide an example of a physical entity that does not occupy a volume?

How about a physical object that has only area and no volume, or one that has only length with no volume?

How about a physical entity that can merge with another physical entity in such a way that the two together occupy the same, or less, volume that either occupies by itself and still maintain their separate identities?

Xerxes,

The seven planes in the matrix setup stacking the cannon balls as Janus did in #16 of the parent thread are not at nice right angles to each other. So I am not sure how you are using the various plane describers. The three square planes are at right angles to each other but the rows and columns of spheres are not at right angles to the rows and columns on the next square plane. And the four hexagonal planes are not even at right angles to each other. Seems to be more of a 60 degree thing going on.

Regards, TAR

Certainly it is a 60 degree thing. The basic construct is an equilateral triangle. A geometry for this configuration would include a definition of the "right" angle or "perpendicular" as 60 degrees not 90 as in a cubic configuration. Note also that the labels for the 3 cubic coordinate axes, commonly x,y,z, would be replaced with labels for each of the 7 coordinate axes formed by the intersections of the 7 planes.

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How about a physical object that has only area and no volume, or one that has only length with no volume?

Make your mind up. You were talking about dimensions, not physical objects:

The universe has only one physical dimension which is what we call volume.

But, based on that comment, it seems you don't know what "dimension" means, anyway. So your opinions on the subject are pretty much moot.

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But, based on that comment, it seems you don't know what "dimension" means, anyway. So your opinions on the subject are pretty much moot.

I have such a hard time with people who didn't study science, but now find they have the ability to redefine it in such a way that it makes sense to them, and nobody else. They cherry-pick what they think makes sense, ignore the rest, and consider themselves very clever. Does this happen in other fields of study, or does science get a disproportionate amount?

"Bridges need to be rigid for strength, yet flexible when storms bring wind and rain. That's why the ONLY bridge-building material that should be used is pasta."

"I've never taken any dance classes, but I know you have to have a lot of rope to spin yourself that fast."

"It's clear to me that making food look good makes people fat, so my low calorie recipes are covered in dead bugs."

Again, the problem isn't not knowing the science. It's being so incredibly certain your wrongness is right that you assert things without checking.

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Before the onset of civilisation badly formed perceptions would often prove fatal. Today one can indulge ones stupidity in a broad range of subjects with little physical risk.

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The amount of crackpottery does seem to be proportional to the "purity" of the science. Physics attracts the most, life sciences fewer, the arts fewer still. Although, within each field, the same topics come up again and again ("Shakespeare didn't write the plays" is a recurring classic in literature crankery). And the symptoms and behaviour of cranks in every field are pretty much the same.

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Make your mind up. You were talking about dimensions, not physical objects:

But, based on that comment, it seems you don't know what "dimension" means, anyway. So your opinions on the subject are pretty much moot.

My posts have been consistent. I have posted only about physical objects and the physical world.

The term "dimension" can be used in a variety of ways, the length of a line in mathematics, the color of a woman's hair, the canon of a religion, and many others.

Since you don't like my assertion that volume is the only dimension inherent in physical objects and in the universe they comprise, please let us know what the three dimensions you and some others seem to believe are actually inherent in the universe.

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My posts have been consistent. I have posted only about physical objects and the physical world.

The term "dimension" can be used in a variety of ways, the length of a line in mathematics, the color of a woman's hair, the canon of a religion, and many others.

Since you don't like my assertion that volume is the only dimension inherent in physical objects and in the universe they comprise, please let us know what the three dimensions you and some others seem to believe are actually inherent in the universe.

OK. So you don't know what the word dimension means in physics. It helps to know that.

The simplest, informal description is the number of pieces of information you need to define an event in space-time. (Hence my joke about meeting at a specified volume.) In reality, you cannot use your single dimension (volume) to specify a meeting, you need to use four dimensions. For example, these could be latitude, longitude, altitude and date/time. (Anything else you choose, such as a street address, is just another way of "encoding" these dimensions.)

The important point about these dimensions is that they are "orthogonal"; in other words you can't express one of them in terms of the others.

It would be impossible to arrange a meeting by just defining a volume; "Lets meet at 13 litres" ?? (But you could use the three spatial dimensions to say where in that volume to meet)

I think you would struggle to calculate the trajectory of a ball using only volume, and not time plus at least two spatial dimensions. But please feel free to prove me wrong.

And after that, perhaps you could rewrite Einstein's field equations using only volume instead of 4 space-time dimensions.

Edited by Strange
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The important point about these dimensions is that they are "orthogonal"; in other words you can't express one of them in terms of the others.

I have heard it say that c is the conversion factor between space and time.

Does this mean that space can be expressed in terms of time?

If so, are the space dimensions orthogonal to the time dimension (and vice versa obviously) ?

Hope the question makes sense.

Edited by geordief
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I have heard it say that c is the conversion factor between space and time.

Does this mean that space can be expressed in terms of time?

Well, c is the "conversion factor" when, for example, a Lorentz transform rotates between space and time coordinates. Actually, "conversion factor" isn't quite right as implies some sort of linear relationship and it is a lttle more complex than that.

If so, are the space dimensions orthogonal to the time dimension (and vice versa obviously) ?

Yes, all four dimensions are orthogonal.

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OK. So you don't know what the word dimension means in physics. It helps to know that.

The simplest, informal description is the number of pieces of information you need to define an event in space-time. ...

The important point about these dimensions is that they are "orthogonal"; in other words you can't express one of them in terms of the others.

...

When you say the information needed to define an event, as used in physics, aren't you really saying the information required to describe our observations of an event? If we limit physics to describing what we observe, then your definition is quite adequate.

What then are we to do if we want to describe our experience of a thing and not just relate what it appears to be? What I have tried to get across is that the one thing we experience with all physical things is volume; there is no other "dimension" inherent in an object. The volume of an object, and the exclusive occupation of that particular volume, is the basis for displacement which is the basis for all physics.

The identification of an object, which is our most basic and limited description of that object, depends not at all on the position of that object relative to any other object. The event we describe by identification of the object is our recognition of the object's existence. Any other information about our observations of the object are relative.

I think I have said all I need to say about this. I give you and others the last words. Peace.

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When you say the information needed to define an event, as used in physics, aren't you really saying the information required to describe our observations of an event?

No.

What then are we to do if we want to describe our experience of a thing and not just relate what it appears to be?

How are those different? We only know what a thing appears to be from our experience of it.

What I have tried to get across is that the one thing we experience with all physical things is volume; there is no other "dimension" inherent in an object.

This is plainly wrong. I know how long my garden or my drive to work are. But I have no idea what their volume is.

And again, I invite you meet me at 17.36 litres.

The volume of an object, and the exclusive occupation of that particular volume, is the basis for displacement which is the basis for all physics.

As you have failed to calculate the ballistic trajectory of an object using only volume, I assume you can't. So it is odd (and somewhat dishonest) to keep repeating the same drivel.

I think I have said all I need to say about this. I give you and others the last words.

Last words: none of that has anything to do with the fact that your claim "volume is the one and only real physical dimension of real physical objects" is just ignorant nonsense.

It is sad that you are not honest enough to either back up your assertions or admit they are wrong.

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