how to tile compact spacetime?

[AntonioLao]

From Kepler's sphere packings to the construction of group theoretic 24-dimension Leech lattice in 1965 with its applications for the design of error-checking codes for data transmission of modern telecommunications, continued discovery of mathematical patterns and structures are coming closer and closer to the eventual understanding of the fundamental structure of spacetime itself.

But one fundamental fact seems to emerge and that is the structure of spacetime is not easily understandable by just relying on common sense alone. Its complete realization requires the exactitude of mathematical logic. These logical formulations also must be supplemented with clear definitions of physical concepts such as density and its relation to mass and volume. Physically, density is defined as mass per unit volume. Here, the key word is ‘unit’ because mass per zero volume makes no sense (infinite quantity is not yet defined mathematically or for that matter, infinite density is not physically realizable).
On the other hand, zero length is physically and mathematically realizable and it also makes a lot of sense when it is applied to the microscopic domain of physics. Furthermore, zero length or ZL makes absolute sense when applied to a 1-dimension spacetime.

In 1934, H.F. Blichfeldt discovered some of the densest lattice packings in six and seven dimensions. But by using the same formula and working backward stopping at 1-dimension, it can be shown that the radius of the minor central hypersphere is zero, while the radii of the eight major hyperspheres remain at values of unity. This demonstrates the zero continuous density of spacetime and proved the emptiness of physical space without jeopardizing the finiteness of volume for matter and energy.

[mkirkpatrick]

A question Antonio,if we admit three or four dimensions,why not then an infinite
number of them,is this possible!How could we even draw a six dimensional shape
let alone a twenty two dimensional one.Is there alimit to dimensions,and if so
what isit that limits them,surely not being easy to draw!!



kind regards michael.

[harmonygirl]

Reducing 3 dimensions to 2 (a drawing) is difficult, but I can't even concieve of reducing 4 dimensions to 2. I don't believe there is a limit to them, but I can't concieve of any dimensions beyond 4, never mind drawing it.

[baudrunner]

If any of you have ever studied even the rudimentaries of computer programming then you must have at some point of your learning come across the multi-dimensional array. Computer technology has advanced far enough to provide the user with all the memory required of multi-dimensional arrays that allows them to be extended to virtually any depth. If one can think of multidimensional space-time then all one needs to do is to fill in the array subsets with the criteria for their being, and it becomes an exercise in imaginative mathematical proposition, but the fact is that all those theoretical dimensions are subject to the conditions established by the subsets' reasons for being and they still must exist in three dimensionall space were they to exist at all. Fact is, it's all just math - the abstraction of reality through mathematical theory. Only philosophers consider the possibilities inherent in the extra dimensions of being in some form of reality.
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[mkirkpatrick]

Reducing 3 dimensions to 2 (a drawing) is difficult, but I can't even concieve of reducing 4 dimensions to 2. I don't believe there is a limit to them, but I can't concieve of any dimensions beyond 4, never mind drawing it.

I agree,it wouldseem that in our minds eyewe know of many dimensions,but are unable to express them!Will that ever change I wonder.

kind regards michael.

[AntonioLao]

How could we even draw a six dimensional shape
let alone a twenty two dimensional one.

The dimension is here implied with the same meaning as the six degrees of freedom that each 3D object possesses.