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Cuito Cuanavale 7y

Garnet Garnet 6y

Cuito Cuanavale 6y

I didn't say, there is "just alphabet" in your logic signs. Their reflectional symmetry belongs to the logic in it. But the "Z" and "S" like signs for XOR and XNOR - displayed in the center of the rhombic dodecahedron - are more alphabet than logic, and not really symmetrical.

I think shorthands for linear bit patterns are more useful logic signs, as they dovetail with the common use of truth tables in logic, and can also be used to denote 3-ary or any other n-ary logical connectives, simply by combining them - quite alike hexadecimal figures.

Garnet Garnet 6y

When an asterisk stands for ANY connective, notice that (A * B), for example (A and B), can be subjected to four logical operations: Negate A, N*, NB, and convert-commute-interchange A and B. Next, the four logical operations become four symmetry rules, when the Logic Alphabet subjects EACH letter shape to the 16 possible combinations of the four symmetry rules, a different symmetry rule for EACH logical operation.

It follows that both Z and S (non-equivalence and equivalence) are each subjected to the 16 combinations of the four symmetry rules. Sometimes each (Zand S) stays itself, such as a half-turn rotation; and sometimes, as required by the logic, each CHANGES INTO the other, such as a left-right flip [so convenient at precisely this spot and this is good asymmetry!]. In keeping with the richness of the notation, it further follows that Z and S, as needed, have just the right symmetry in just the right places and just the right lack of symmetry (asymmetry) in just the right places.

Fortunately, as those at the Museum will tell you, to enjoy the Beauty displayed in the above cases, one does not have to understand how much logic has been built into the Logic Alphabet

Cuito Cuanavale 6y

И N

N И

have been a better choice?

Garnet Garnet 6y

The Logic Alphabet has been built so that the x-letter is telling us a short story. It is saying that the four Ts in (TTTT) have been placed at the corners of a square and, when x is placed inside the square, each stem on x comes close to but does not touch a T-corner. In effect, the x-letter has become a symbol for Tautology (TTTT).

Now comes the realization that the x-letter is loaded and dripping with symmetry. Flip it left-right and up-down. Flip it on both diagonals, Rotate it a quarter turn, a half, a three-quarter, and a full turn. No matter, it always ends up standing in its own home position. In effect, in the land of symmetry, the x-letter is a bit too willing to boast that it has a very high standing in the society of 16 letter shapes.

In fact, the social structure that governs the 16 letter shapes is marked by four levels of symmetry, from the highest to the in-between to the lowest. In reference to x-y axes, two letter shapes (o x) are two-way self-flippable (SF) and 180-degree self-rotatable (SR). Two (s z) are not SF but they are SR. Four (c u n back-c) are one-way SF but not SR. And eight (the odd stemmers) are neither SF nor SR. In effect, the count from top to bottom is (2 2 4 8).

The same pattern (2 2 4 8) shows up in two other places. First, when Ts and Fs are placed at the corners of a square, truth tables as such embody the same four levels of symmetry-asymmetry. This is the whole reason, right from the get go, for designing the shape-part of the letter shapes, so that it would MATCH EXACTLY the symmetries that inhabit square truth tables. Second, in what came tumbling out ot a moment of raw insight, the same pattern (2 2 4 8) also shows up in the power of chess pieces.

Two chess pieces with the most power are Queen and King. Two after that are the Rooks. Four next are the Knights and Bishops. And then eight are the Pawns. It follows that, when levels in the chess pieces are put into exact correspondence (2 2 4 8) with levels in the letter shapes, we can now say that the GREATER the power of a chess piece the GREATER the self-symmetry of the corresponding letter shape. Notice that the presence of chess pieces, at first glance, has been called: obscure, trivial, ridiculous, remote, spurious. This is also telling us that the less one knows about what is going on here the easier it is to miss the clear and vivid point that has been coded into the chess pieces.

Now for that lingering leaf on the tree. Could an N and a back-N be used instead of the present use of s and z? One reason says yes, because both pairs are self-rotatable at the same time that they are not self-flippable. Other reasons say no. (1) All of the letter shapes of the Logc Alphabet are lower case but N and back-N are uppercase. (2) A lower case n is already in the Logic Alphabet. (3) Uppercase N is already being used for Negation. (4) z, not back-N, is on the typewriter. Of course, knowing what is really going on in the deep structure of square truth tables is all it takes to become a sign engineer and design competing notations, many of them, provided that they are in the SAME CLASS as the Logic Alphabet.

Most of the above can be found in several places on the Internet, such as at the webpage called: logic-alphabet.net. The main point here is that, if one knows both how the Logic Alphabet is constructed and how it works, much easier it is for anyone to see-understand what is being displayed at the Museum of Jurassic Technology.

Cuito Cuanavale 5y

Alan Michelson 3y