From Abstract to Discrete and vice versa

This crazy old uncle, Octonion, was giving me a hard time. I had been working all long holiday on a discrete part. I had tough problem facing such brutal computation that i did not know how to handle it. But suddenly i found that, there is a standard formulae in the literature, god knows how useful was that, exactly for easing my difficulties. Indeed by few identification, the computation and the whole set up become very clear. Now I am done, I am so happy. Now following my two last posts, I can now play with this crazy old uncle. My passion is getting more accessible.

Algebraic Structure Corresponds to Geometric Axioms!

It is interseting that one can prove all the algebraic properties like distribution and associative law, etc, by introducing an algebra of segments in the plane geometry. The associative law correspond to the Desargues's theorem, see elegant text of Hilbert; Foundation of geometry. If you choose the geometric axioms so that the Desargues's theorem does not hold, you get kind of non-associative algbera,That is it, the Octanions. and the geometry is projective geometry of OP^2 constructed by Ruth Moufang. This projective geometry can be used vastly to describe physical model in quantum mechanics.

Description of four normed division algebras given by John C. Baez:

Description of four normed division algebras given by Baez:
There are exactly four normed division algebras: the real numbers (R), complex numbers (C),
quaternions (H), and octonions (O). The real numbers are the dependable breadwinner of the
family, the complete ordered eld we all rely on. The complex numbers are a slightly
ashier but
still respectable younger brother: not ordered, but algebraically complete. The quaternions, being
noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the
octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative.

Storm , cloudy, hopefully sunny

These few days was sort of storm in my life, Thanks god, now it is cloudy, i hope monday afternoon will be sunny!

spark of life, sprout of passion and moving towards them

One i was reading a post from : The Enchanted Soul . I used it in the preface of my dissetation:

We could say that everyone's life has several layers. The surface layer is constantly changing and sometimes it transmutes into a storm.
This layer, usually deals with daily life happenings, tasks, and responsibilities. The exterior layer, tends to draw great deal of attention
towards itself: the semester is starting, deadlines are pushing, tasks are lining up, moving to a new apartment is on the way, and many more.
However, I have learned to focus, and see beyond the surface layer, deeper into my inner life and what I consider to be of more importance to me.
For the last four years, I have been able to track the inner progress of my personality and the changes that happen in the state of my mind. Every now
and then, while sitting behind my desk and sipping coffee, I look into the progress and the new challenges on my way, which provide me with
fresh perspective. The droplets of formulas and equations open their way through this arid soil of technical jargon.
I wait for a spark of life, for a sprout of passion to appear, but i kept in mind that I should move to see them as Albert Einstein says :``Life is like riding a bicycle.
To keep your balance you must keep moving.''.

Defence, Odyssey and ...

Next week will be my Ph.d defence. Alhamdolellah i get to this point after passing all those difficult times, anxieties. But i still need the reader's pray.
It was kind of Odyssey. I had a file i named it Odyssey.tex. I wrote all progress and challenges with. I wish i could continue it. Anyway, I love to read the real Odyssey of Homer, maybe i should find english version and read it, that would be much enjoyable.

The Hen or the Egg?

During last 6 months, i have encountered many times to the following problem:
The egg is created first or the hen or which Came First: The Hen or the Egg?
Dont think about Christianity, Islam, Darwin's theory or even Mr rooster.
Here is my intention of asking this question:
How many times I gave the wrong answer which resulted in waste of my time and energy. God bless me!