The Gaussian-School of Higher-Arithmetic (1831, updated 2022); tutorial #4.

The founding father of the Gaussian School of Higher-Arithmetic was presumably blocked by radian fixation, this prevented him from completing his ideas.

The 2nd letter of JCF Gauss to the Royal Society, 1831. C. NOTICE ON THE THEORY OF BIQUADRACTIC RESIDUES.

Paragraph 24, the first three sentences in his last paragraph of a long tedious paper.

[24] "We have believed that we were doing the friends of mathematics a favour by this account of the principal parts of a new theory of so-called imaginary quantities. If one formerly contemplated this subject from a false point of view and therefore found a mystery darkness, this is in large part attributable to clumsy terminology. Had one not called +1, -1 and the square-root of -1, positive, negative, and imaginary (or even impossible) units, but instead, say, direct, inverse and lateral units, then there could scarcely have been talk of such darkness".

Translation from the original Latin by William Ewald within "From Kant to Hilbert Volume 1: A Source Book in the Foundations of Mathematics."  ISBN 0 19 850535 3. (Page 313 of the 1999 paperback edition). Once we have found that "needle in the haystack" there is no way back, no way to forget the secret hidden message engraved onto the magic Gaussian "needle".

Author's notes:

It is impossible to take away any real thing from nothing.

In other words, the nomenclature -1 (inverse-one) does NOT mean "take away one from zero"; it does not mean "minus one"; using this catastrophically false linguistic form of description for inverted numbers is very bad practice indeed.

ALL numbers with no physical or abstract units assigned to them are utterly imaginary. The number +1 (1.i0 or direct-one) is no less imaginary than are the numbers -1 (1.i2 or inverse-one) or i (1.i1 or lateral-one). ALL numbers with no units assigned to them must be thought of as a polarised quantity of non-existent imaginary units. The entire subject is so utterly abstract that it is generally beyond all human comprehension, until that is we add in an abstract unit. For example; the number of so-called "mathematical ideas" that are perfect nonsense. The purer the neo-Pythagorean School's "mathematics" (based upon their unhinged treatment of numbers) the more perfect the nonsense.

Author's notes (continued): 

Within the new Gaussian Unified Number Theory, every number expressed in the flat (finger counting) form MUST be expressed in the unified grammatical form "a.ir". "a.ir" means "a" (flat-magnitude) "dot" (times) "i" (a-rotation-of) r, where r is the left going (or right going) polarity rotation in quadrant units. The direction of rotational polarity change away from direct-unity (+1) has a hidden third binary property of left going (anticlockwise) or right going (clockwise) polarity rotation. The cypher "i" must always and everywhere be taken to mean "a rotation of" where the numerator that MUST always follow the "i" refers to any number in quadrant units of polarity rotation. In "flat earth arithmetic" (the neo-Pythagorean nonsense that you were indoctrinated into) multiplying a number by one makes no difference, but in Unified Number Theory, leaving out the two ones turns the valid unified number 1.i1 (one times a rotation of one quadrant) into unintelligible gobbledegook; the square-root of a number (minus-one) that does not even exist. One can only go so far with nonsense, nonsense can go on making sense for a very long time indeed, until one fine day it suddenly makes no more sense at all.

Two examples;

1) the nomenclature direct-one (+1) is stated in unified number theory as 1.i0

2) the nomenclature inverse one (-1) is stated in unified number theory as 1.i2, the square-root of which is 1.i1

Please note that 1.i2 (-1) is indifferent to the right or left rotational direction, where as 1.i1 is very particular to the rotational direction. Also please note that the flat number zero cannot and must not ever be stated in Unified Number Theory at all. Nothing (zero) as a flat finger counting or bean counting number is NOT even a number at all, where as zero in exponential counting means one (1) . Zero in exponential unified numbers is interpreted as e^0 (=1). Except that for that to refer to "direct one" (+1) rather than the whole circle of unity, we must specify (0 + i0). Therefore; +1 (i.e. 1.i0) and e^(0 + i0) are identical terms; that is the Bieżanek Unified Number Identity.

I jest of course, nobody needs to get their name honoured for first mentioning such a trivial and obvious fact. I mean for instance that Hans Christian Andersen does not even give his little boy in the crowd a name at all. The unnamed young boy just shouted out "the  Emperor is naked". BMJC Bieżanek, the author here, is just the 74 year old "boy" in your crowd who shouted out (on this website); our mathematical "Emperors" are naked.

Unified Number Theory is only tough for people indoctrinated into an illogical "number-dogma" (unfortunately that is presently everybody except for myself). The subject of Unified Number Theory is actually very simple. The problem for human-minds is only in unlearning  the absurd (religion like) number dogma drummed into us from primary school and onwards by so-called "math's" teachers. It is very hard indeed to get rid of deeply ingrained nonsense. Hence the association of both Quantum Relativity (qr) and the new Unified Number Theory with my fabulous meta-cybernetic model of the generic human mind.