Spatial dimensions (Could there be an axing of the axes?)

[Amnon]

I'd just like to say that, before you get the wrong idea, this

thread does not concern dimensions that extend beyond the

human experience.

Human experience typically tells us that there are three spatial

dimensions - and why does the human experience tell us this? -

because it presents us with an idea that is really easy for us to

get our heads around. There's an a left and a right, an up and

a down and a forwards and a backwards. When we consider

the physical situation in which we find ourselves, this

description of dimensions could not be simpler.

The word dimensions comes from a Latin word that relates to

the action of measuring. The clue is in the word. However, the

dimensions of the dimensions has become an increasingly

tricky topic. There have always been problems related to the

so called dimension of time. We may make predictions for the

future but we can only really measure the past. Einstein then

added the complication of relativity to our conception of all the

perceived dimensions by saying that the dimensions of the

space-time dimensions are relative to quantities of mass that

would seem to weigh heavily into the fabric of experienced

existence.

Everything may already seem to be complicated enough and

yet I am forced to wonder whether our understanding of the

spatial "dimensions" has been crystallised in quite the right

way.

What is the direction of x? The same question might also be

asked of y and z? X gives us a left and a right but in which

direction are you meant to be facing? Y gives us an up and a

down and yet, when experience tells us that we live on a

rotating and roughly spherical planet, we find ourselves in a

situation in which we might still need to ask that most basic

questions: which way is up? Z gives us a forwards and a

backwards and, thankfully, the direction of this "dimension" is

easily understood. All we need to do is answer the first two

questions and, with the directive help of any massive objects

that may be in the local or the wider vicinity, a conception of a

third "dimension" will fall into place in a remarkably elegant way.

Having said all this it also occurred to me that an understanding

of the spatial dimensions might not be as easy as a-b-c or

even as x-y-z. When we think of crystals then certain images

come to mind. The standard view of space can be considered

to offer a kind of salt of the earth conception of the dimensions

for the natural reason for this is that Sodium-Chlorine is formed

on a cubic lattice with neat right-angled corners.

However, I would also be interested to know if it may be

possible that we may live within what I might describe to be

sugarland spatial "dimensions". Sugar is one of many forms of

crystal with a monoclinic lattice. The monoclinic description

basically means that the cube has gone lop-sided and that it is

only on only one of its sides that the lattice arrangement is

formed of 90 degree angles. We can also note that quartz, the

most common type of crystal on our planet, has a rhombohedral

in which none of the angles within the lattice framework are at

90 degrees. From our point of view it might seem that

everything has leaned over and it occurred to me that this habit

of sugar type crystals might offer an alternate view of any

fundamental lattice arrangement of space which we might

presume to exist. According to one conception it might be

considered that we might we could sit back and measure x, y

and z axes within a cosmological system that is based on a

fundamental lattice arrangement that is at angles to the x-y z

axes with which we commonly juggle. The other way of looking

at a monoclinic type view of the "dimensions" would consider

there to be three spatial "dimensions" that may be considered

to be at various angles to one another and yet, within the

system, everything might still seem to follow a neat x-y-z

format. This would mean that when you might turn from a

forward direction of travel so as to turn, for instance, left you

might actually be turning at an angle other than 90 degrees

even though, within the system, you could still have been

measured to have made a precise quarter turn.

A comparison to this kind of scenario might even be drawn from

the conventional cubic conception of the spatial "dimensions".

Imagine a 90 degree angle floating in space. There is a clear

corner point and, as far as I understand things, the two lines

would always be measured, within the system, to run

perpendicularly to one another. You could place a black hole

between the two lines with the mathematical effect that these

"dimension" type lines might really be pulled together and in a

way that dimensional distances might be profoundly shortened

and yet, within the system and according to my understanding,

the 90 degree angle would always be perceived to retain its

perpendicular nature.

It seems to me that other analogies may be drawn from an

understanding of crystals and be applied to potential

understandings of the spatial "dimensions". Analogy brings me

to wonder whether some of the "dimensions" may actually be

longer or shorter than they appear. Thinking back to crystals

perhaps we can take Turquoise as an example. This mineral is

formed according a fairly complex chemical structure with the

effect that one molecule within the crystal will extend further in

one lattice direction than in another.

Informed comments on all the above would be greatly

appreciated.

Things get more complicated when we consider crystals (such

as beryl) that are based on a hexagonal lattice arrangement.

This arrangement can be basically conceived by picturing a

hexagon laying on a flat horizontal surface with its nearest side

laying in the left to right orientation of the axis. Vertical lines

can then be pictured to rise from the corners of the baseline

hexagon so as to meet with a second hexagon above. These

vertical lines neatly fit the requirements of the y axis but then

things get interesting at z. The flat plane of the hexagonal

lattice stretches away from the x baseline in two directions

triangulated directions and the result, by analogy, would be a

model for four "dimensional" space.

Moving away from known crystals we can also consider other

geometric shapes. Let's stay with the idea of the hexagonal

base that we have recently looked at by consider that the lines

that rise from the corners of the base hexagon consistently

converge so that they meet at a central point above the middle

of the hexagon. These lines might provide a model for

conceptions of nine "dimensional" space.

Other geometric shapes that might be considered include the

square pyramid and the tetrahedron (triangular pyramid). The

square pyramid shape is commonly found within the Egyptian,

Mesopotamian and South American Pyramids. The lines of

this pyramid shape can be pulled outwards along any of the

planes of the pyramids to give a model for the conception of six

"dimensional" space.

The tetragon is well described as being a triangular pyramid in

a reflection of the triangular shape of its base. The lines of

this pyramid shape can be pulled outwards along any of the

planes of the pyramids to give a model for the conception of seven "dimensional" space.

Regardless of the direction of the "dimensions" in all of these models, they can still be considered to consistently provide frameworks for types of space that could still be measured within x, y and z axes. Nothing would necessarily change the experience of being in space. We may not necessarily have any direct phenomenological clue with regard to the lines upon which space was constructed. True realities may only be deduced by the maths ... and this is the bit where some informed guidance is greatly needed.

[Sisyphus]

When we say space is three dimensional, all we mean is that you need at least 3 parameters to describe a precise location. You could use length, width, height. You could use latitude, longitude, altitude. Or you could use something else.

[Amnon]

I appreciate that we need at least 3 parameters to describe a precise location. My concern was to raise a question regarding the type of lattice that nature might use to provide the space in which such a location might be found.

[Sisyphus]

Why does nature need to provide a lattice?

[Amnon]

Good question. In fact for all I know that may be a great question that may lead through to new potentially productive areas of research. The question might also be asked why do we need dimensions to allow us to have volumetric space? We have the xyz axes for the sake of measurement but does nature need this type of lattice to provide space with a structure? Any thoughts?