A footnote on the exponential nature of existence and a New Note

A footnote on the exponential nature of existence. 

The Ancients knew the transcendental number PI, and had a well developed understanding of circular relationships.  Most of us who study any Mathematics at school learn Trigonometry, that is based on circular relationships and the number pi.  It was only a couple of centuries ago that people came to recognise an equally significant transcendental number, e.   This number is associated with a separate form of Trigonometry based not on the circle but the hyperbola, which is the inverse relationship. 

We live in a hyperbolic universe.   There are many illustration of the Hyperbolic Perabola, the curved surface that divides three dimensional space.  It is saddle shaped, like a Pringle Chip.  It is harder to imagine the four dimensional equivalent.  But we must exist in it.  Instead of the “z” axis, where z=x^2-y^2 we have the unreal axis “I”, that exists mathematically and provides explanation and restriction to our real world as if it existed.

What does this mean?  How would it feel?  Just as if we were on the surface of the Hyperbolic Perabola, we would think it was flat except that when we measure larger areas or lengths, they become bigger, because the surface increases in size due to the curvature going both ways.

We live in a universe of increasing magnitude.  We perceive it as an expanding universe, but perhaps that is an illusion because of the curvature.  

New Note Sunday, 1 November 2015

Started out browsing on Wikipedia.  What a trap.  Knowledge is expanding so fast.  I am astonished at what is known.  I wanted for a long time to know how the protein recipies that make up DNA end up as actual bodies, with organs that are so similar etc.   I started with The Chemical Basis of Morphogenesis, which seemed to explain things so amasingly well.  But of course there were difficulties in my understanding of the article, because they were explained by the mathematics of Reaction–diffusion systems, but they depended on a type of differential equation, in particular.  I ended up reading about solitons, and had to revise my hyperbolic trigonometry in the process. 

During the process of all that, I made myself a fried egg and two cups of coffee.  I was very sad for a lot of the time as it just brought home to me how deficient my education was at the early age when it mattered.  One needs to learn the discipline and art of learning when young.  I never did.  It is not what we learn in school that matters, but learning how to learn.

I should have done the combined Law-medicine double degree.  I should have read the Aeneid in Latin and memorised the written Torah in Hebrew.  Others can do it.  I should be able to play the great piano works for myself, and composing my own music.  By now, I should have had a diverse career in Public Office, contributing to the wellbeing of mankind, and of course I should be a Great-Grand-Parent by now. 

What ever I was reading, and supposedly learning, and whatever I was writing a paragraph back, all came to an end with a major coughing fit.  The Plane Trees are shedding their fibres, or whatever.  I foolishly had the doors and windows open as it was such a lovely day.  I’m closed up in the house now.  What a pathetic waste of a morning, though I did finish two sudokus  for last week, both marked easy, but one requiring some guess work, and then it had an alternative ending with two parallel pairs of numbers.  I don’t feel like cutting the Nature Strip grass tussocks, or anything else outside, or doing vacuuming or cleaning bathrooms or even the washing up. 

It is just a down, miserable day.