Notes on 2-Color Numbers

Notes on 2-Color Number

Dear Blog Readers
I have to add some notes to the dialogue on 2-color numbers

1. Si Nessa discovered that there are two kinds of 2-color number. One type is 2-color numbers with Red number unit which is squared to unity and the other type is 2-color numbers with Pink number unit which is squared to minus unity. The Red 1 and the Pink 1 is respectively represent counter-imaginary unit e and imaginary unit i of the counter-complex and complex numbers system.

2. Color symbology is more economic because we do not have to use new letter symbols for new non-real units. We are just coloring the real number symbol to represent the non real number. Of course the color chosen is arbitrary. This color symbology will make the hypercomplex number system more intuitive and comprehensible for primary school students.

3. It can be proved that Black-Red numbers or countercomplex number, while does not form a field arithmetic, can be regarded as direct sum of two fields, each is isomorphic to real number field, form by by real multiples of idempotent because the the two idempotents are zero divisors.  That's why it does not have many interest from mathematician. On the other side, the black-pink numbers or complex numbers are very useful to physics and engineering.

4. But it can also be proved that complex and countercomplex number system is just two of three binary or duplex number systems in which non-real units is following quadratic equation. The other one is dual number system where its non real number unit d is squared to zero. This number system can be realized as another 2-color number, say Black-Brown  number, with multiplication checker board.

where the white box represents zero.

5.In the mythical Numberland, Black-Brown numbers more likely to populate the Dichromic Zero province that has not  been visited by Si Nessa. The Dichromic provinces are in the many dimensional number country: Polychromic. The polychromic country is the mythical symbol for higher dimensional number domain: the hyper-complex numbers. Discussion of hypercomplex number can be found in hypercomplex@yahoogroups.com maintained by Jens Koeplinger. Anybody who are interested to  many dimensional numbers can join the egroups to discover how binary numbers itself is just special kind polyplex numbers that was discovered by my creative friend  Marek Ètrnáct.

6.The Black-Red or Counter-complex numbers and Black-Pink or complex numbers are only parts of the more mysterious hypernumbers discovered by late logician and philosopher Charles Muses that was discussed in hypernumber at yahoogroups.com maintained by myself. I create the egroup to continue the discussion in hypernumbers@yahoogroups.com that was extinct because it was closed by the owner Kevin Carmody, an informal student of Charles Muses, has been redirect his attention from the study of hypernumbers to the study of science of consciousness in the context of Maharishi Mahesh Yogi Transcendental Meditation in scienceofconsciousness@yahoogroups.com.