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?

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.

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.