Quote:
Originally Posted by Profpat  I think our numbering system is arbitrarily set as a base 10. We could have just as easily set it as a base 8, or a base 2, or some other base.
When we look at the octant cube, I come up with 10 things. 8 small cubes, 1 large cube, and 1 area in which that cube occupies. |
I have a tiny hole in my way of communicating, too, Pat. The tiny hole is actually the essence of what I am trying to convey; not an easy job.
Our numbering system is not set arbitrarily at 10, just like the dimensions are not arbitrarily set. We may disagree whether we call the three divisions the three dimensions, or the underlying two aspects the two dimensions, but the spatial aspects they portray are real, and cannot be altered.
Depending on what you want to achieve, one can choose a numerical concept, and there are several concepts out there to choose from. Computers function okay already in the binary system (but interestingly enough, the jump to bits and bites was made quickly). Or we may place everything in a hexagonal system with its clear benefit for easy division of matter (used, for instance, in ancient trade, but our clock is still based on it as well - 24 hours - and math uses 90 degrees and 360 degrees, not 100 and 400).
The reason to see that the decimal concept is the best representation of the toe, is that it contains all other concepts (even when the singular concept rejects/ignores the importance of the decimal concept) and also contains the correct appropriation of zero.
The singular concept does not have a significant zero; the binary system gives zero an all important spot, but is also totally dependent on it; the hexagonal concept only acknowledges zero in a pyramidal delivery; the decimal system does all this and more.
We have come to understand that the decimal system is most appropriate to use, all over the world. That we don't know how we have come to this is human behavior: we forget - if a concept allows us to forget. It is the decimal system that allows us to forget the importance of zero, while using it where needed without thinking much about it. The hexagonal concept kind of does this, too, but is in many respects not as easy to use.
I can go on for a long time, Pat, but I also don't want to become an unwelcome guest in your thread. However, if you feel that the decimal concept is still an arbitrary one, you are then obliged to provide information that shows this indisputably. I know I am a guest, but I can ask you to verify the truth inside your words without it being an insult. And if you can achieve a fundamental reason why the decimal is not most appropriate for the toe, then you have my eternal admiration.
P.S. I hope you did see that the hexagonal system (the pyramid) and the decimal system are like half and whole (or like whole and double-whole), just like the binary system contains the pyramidal structure inside itself, but becoming visible only in the results (see JAK's previous post on neurons)! This latter concept is where the ether is and isn't.