Monday, August 17, 2009
Hyper-, Ultra-, and Meta-complex Numbers
My thoughts lately with my sons weddings within two weeks there is not much time to post- but I have had thoughts on the geometry of things again, of art and mathematics.
So it takes a whole plane to map the imaginary numbers. Aleph2, perhaps, the number of curves greater than the lines in a plane. But what is the next step where the significant dimensions seem to be four rather than the expected three? And so on. There is after all a level of insight to which some seem not to be aware and frankly it is not my loss they they remain uninformed and think my words are obscure- after all I played at the wedding and was surprisingly drunk underestimating the champagne and wine. And people danced to my music (for the first time)and held each other close and I made so mistakes, the band loaning me the guitar probably wondered what was happening with all the attention and cheers (they are a nice laid back blues and funk band at their first wedding gig). I told my son I was sorry I was so drunk but he did not warn me I would have to play- no problem everyone said, they were all drunk too :-)
Maybe those on the frontier of complex analysis can extend things a bit- well beyond the idea of quaterions and octonians and the roots of unity of hypercomplex numbers- after all the world seems to decisively reflect this as well our Platonic dreams that border on the downright mystical after all- and well, a little more where all this comes or will come together. The e pi phi i relationships are well advanced and an achievement as well the idea of what so limits logic to some rational plane but these are a little dated, as well the idea of recursive adding on to a sequence of the sum of previous ones fractal like, such that such information say in the DNA is conserved. Of course we need new but careful notation of these methods similar to sigma summing and pi products- perhaps qoppa or Q quasic foundational chi like origins. Dont understand- np - one day we will and our detractors be long left behind- I expect more from those who claim they teach and do such work- but I do not expect them to have the desire to reach a hard life of such awakening. Yet, you ghosts you cannot stand in the way of the ghost I am, ye without faith and belief can harm not the wine nor have drought forever with the chaf you shun even if it is wheat. The sin of alcohol, well the rivers flow with it in Islamic heaven yet no one drinks when in the fulfilling presence of God- and the woman like me feeling so old yet seeing my portrait Oscar Wild like forever young stay so he knew of life as given and eternal as art and not that we dance, walk the moon to our songs and mimic love and desire and deep knowing- we of the simple earth and metaphors and of the mystery of dreams.