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The logic alphabet is a shape-value notation. It has 16 signs, all cursives, arranged from left to right, as shown on a Flipstick. Again, to repeat the same pattern (1 4 6 4 1), the o-letter has no stems (all zeros) and the x-letter has four stems (all bent-in ones). These LSs have been selected with great care so that, as a total set, all of it is now serving as a new notation. It has been shape-specified to encode some fundamental properties in algebra, in geometry, in symmetry, and most of all, in logic. As a matter of high fidelity and in keeping with the requirements of good fit, the logic alphabet is very sensitive to the networks of interrelations that exist in layers throughout the 16 binary connectives. The logic alphabet introduces a shape-value alphabet that does its best to favor what happens when we activate logical operations. This is what makes the LSs like Arabic numerals. When we multiply Arabic numerals, we use symbols in such a way that the rules fit the calculations. Likewise, in what follows we will let the logic alphabet focus on four rules. By design, these rules will fit the logical operations. These rules introduce the game called flip-mate-flip and flip. This game, also called f-m-f and f, is a shorthand way of specifying how the four rules will operate on any LS in particular, such as (A d B), or on all of the LSs in general (A * B). R is for Rule, N is for Negation, and C is for Conversion. The C, also called Commuting, reverses the two sides, from (A, B) to (B, A), and vice versa. The four symmetry rules are as follows. R1 negates A. The NA flip is from left to right; (NA d B) changes to (A b B). R2 negates the LS. N* is the mate of any LS because all stem places are reversed; (A Nd B) changes to (A h B). This tells us that the end letters of "hand" are mates; also, the h-letter is the Nand gate, sometimes expressed as the S(h)effer stroke (A / B). R3 negates B. The NB flip is from top to bottom; (A d NB) changes to (A q B). R4 converts (A, B). This flip is along the dot-square diagonal that goes from upper-right to lower-left; (A d B) remains (B d A) because the dot in the d-letter dot-square in (3) stays in place. This example is testing the system. Obviously, under conversion, (A d B) must remain (B d A) because conjunction (A TFFF B) is commutative. One example will hint at what usually remains unsaid. It is inserted here to indicate how much sign engineering and architectural design went into the selection of the LSs. Those who use this notation may never notice that a super truth table (2 2 4 8) has been built into the Self-Flippable (SF) Self-Rotatable (SR) construction of the LSs. In other words, there are four levels of symmetry-asymmetry in the LSs. Extremely clarifying and visually uncanny, the four levels happen to line up exactly with the four levels of power in a chess set, when one chess piece is assigned to each LS. Not only introduced as stem-coded truth tables and not only serving as relational icons, the LSs are also topological cursives, at least to the extent that they must bend and twist, and stem, in just the right places --- or the system will not work. Two of the LSs are two-way SF and SR. Two of them are not SF but they are SR. Four of them are one-way SF but not SR. And eight of them are neither SF nor SR. Which LS belongs in which subset will remain an exercise. Likewise for specifying which chess pieces go in which subsets (2 2 4 8). |
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