A friend sent me this link to an application of the laws of form. It refers to imaginary numbers, quaternions, and octonions. I have been thinking about imaginary numbers and quaternions and octonions for a bit. And have been confused by what they all mean. The names of things sometimes can confuse us from understanding what it is that they are pointing to. A case in point is imaginary numbers. Are they really imaginary, a fantasy? So I did a bit of web searching to try and understand these odd named numbers in a metaphorical sense. And I came across a great web page with a clear perspective / explanation of these imaginary numbers. And of course this led to some more cognitive wanderings and another way to think about these numbers. Those more mathematically and metaphorically gifted may see this as obvious.
Numbers are about quantizing entities (things). However, if we are really in a multidimensional universe (more than 4), then a simple (real) number is not enough to quantize a multidimensional thing. A real number only gets the quantity in the dimensions directly tangible / perceptible to us. Multidimensional things have quantities in other dimensions. Hence the a + bi, or a +bi + cj + dk in quaternion space and so on for octonion elements.
Our minds are limited by the complexity they can handle. So, it occurs to me that greater multidimensional minds would do their basic arithmetic with quaternions and octonions. A vista of a complexity I glimpse in pieces!
In Xanadu did Kubla Kahn
A stately pleasure dome decree:
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea. (Coleridge)
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