Dimensions, Numbers, and Aleph's

Dimensions, Numbers, and Aleph's

Today I looked back at a table and some assumptions I made- as just a working tool in candle design. I found it took awhile to make these abstract distinctions, and the idea was to find structures of wax in space that I may have overlooked in the ongoing evolution of my candle designs.

Interestingly, Cantor made the transfinites to pin down the idea of dimensions but did not succeed by his methods. The fact that aleph 2 contains in a plane infinitely more curves than lines drawn on it I just extended as an axiom into higher spaces up to 4 or so. The N for number also represents the color and content of what is actually arranged in space. Yet in a way these three abstract directions are all describing the same sort of general idea of what can be there structurally as dimensions. As you can see certain processes, as if we keep consecutive and contiguous questions in mind, that is a sense of a time direction or even do-first in a process, we acknowledge certain shapes such as the intertwining of units of volume, the compression of a blob along dimensional lines or its stretching, and all the warps and helical twists, knots in three space and there quasi analogs that in a sense result from these informal assumptions.

From an alternative view, we ask what is the Background (Cosmos), the information distilled into some concrete structure, and the meaning that resides in it. To extend it more than the 3-space pascal analog as I have done here may contain more variations such as the branching of natural shapes in the transmission of signals and energy. But I am not offering this treatment of the alephs as a conjecture. In the candle business as it evolved I have many times had to compete with my own designs and very rarely did some new principle arise- sometimes the designs arose because of the technology advancing. Sometimes old technology from the 1800's came back in force such as soft clear wax. I tried early on the soybean based waxes. A new design, and I do not dismiss at first glance any suggestion from the artists, seems to have a lifespan of two years on the market- and if not in production within that time sooner or later it occurs to someone who decides it worth making.

In a sense the idea of building up layers of things against the up and down and within and without of gravity without infinite steps is the mineral wax, ceresin, that forms layers that stack and in general can have warp symmetries as we build up the microcrystalline structures of such topologies in the liquid, hollows, and powdery forms of adding or removing heat so to achieve a given design. There are subtle variations in what is possible when given a choice of processes, some of which we kept even if labor intensive for the resultant arts sake.



Nevertheless, I have always had a view that into the depths of a smashed (flanged) hypercube beyond the orthogonal parts we have whole spaces of interconnections possible and these in a sense can be extended into the realms of transfinite numbers.