V is for Vendetta, Q is for Queer.

So I've been thinking about the language I wrote about last week, attacking it like I attack any problem, decomposing it into smaller an simpler parts. With something like a programming language, this always reduces down to the old 1 and 0, True and False; Boolean logic.

The language I was talking about was based on Codd's relational model, which is formally based on a three valued logic; True, False and Null, where null means the truth value of the predicate is not known. It was a little new to me, so I drew out the truth tables of this logic. I was shocked to see how simple it was: NOT Null = Null, x AND null = False if x== False, Null otherwise, Null OR X == True if x == True, Null otherwise, and so on for IMPLIES, EQUALS, and XOR. Relational 'purists' claim that Null never should have been part of the model at all, but after deep contemplation I conclude that these people are fucking dicks. If a database user doesn't know a customer's address, they should just enter that into the database as Null. If these purists had their way, the user would have to construct multiple tables, to deal with all the contingencies of unknowns, just so things would be a little easier for these 'purists'. Purist, of course, means lazy ass: Its been show that an n-valued logic is always reducible to a 2-valued logic, so the only reason anybody would reject a 3 valued logic is that they are too lazy to reduce it to 2 valued logic to make a proof based on boolean theorems, though they are more than happy to pass hardships on to end users.

Anyway, I am digressing. This blog post is about a concept I came upon in my reductions to the boolean spheres,(not 3 valued, but boolean) something slippery I finally reduced down to that realm. I call it q-logic. You could call it "quantum logic" and it would be dead on accurate, but I prefer the term "queer logic". Less intimidating, right? Nobody is afraid of queer, right? It deals with the hidden function 'v' in the old school boolean model.

Quick summation: ask the question, is 'True' == 'True OR False'? (T==T|F) The quick mind answers 'yes', thinking of the OR logic table, but what we are formally asking is: "is the expression 'T' == the expression 'T|F'? The answer is no, the two strings are different. In formal logic, the function 'v', which stands for "eValuate" is used to reduce logical expressions down to their end values, so that (v(T) == v(T|F))

its like asking: does "5" == "3+2", no, the two strings are different. "5" is a different 'word' than "3+2". One has 1 character, 1 has 3 characters. But v(5) == v(3+2), where the function v actually adds the two terms in the string of characters "3+2", so the two resulting strings "5" and "5" actually are equal.

So it turns out, the function 'v' plays a secret and critical role in logic and math, one taken for granted. Anyway, the long point is, my reductions of the logic I am picturing have lead me down to changing the nature of the function 'v'.

My q-logic works thus: Values can be either collapsed or in superposition. The values that are collapsed are the traditional logic values T and F. The easiest way to explain intuitively here is to depart into a metaphor. While 'v' eValuates, the function 'q' Queries. Let us consider two chat rooms, Gaga chat, and Sports chat. You log into the chat rooms, and to find out what they are talking about, you must ask (query) the people who have been there. The predicate you ask is, "are you talking about Lady Gaga?" Gaga Chat users will answer "True", while Sports Chat users will answer "False". If you ask the opposite, "Are you NOT talking about Lady Gaga here"? The answers will be opposite. For the predicate given, these two answers conform directly to the traditional logic concepts of True and False, and support the Law of the Excluded Middle needed by Boolean logic. However, q-logic introduces two new chat rooms: The Lonely hearts club, and The Snobs.

If you go into the Snobs and ask them if they are talking about Lady Gaga, they will answer "False", even if they were: They want you to go away. If you ask the opposite, "did I find a room where people AREN'T talking about lady Gaga"? They will answer that they were talking about her. They just want you to leave.

The lonely hearts club is quite the opposite. They will answer that they WERE talking about her even if they weren't, just to get you to stay. And they will answer that they weren't talking about her even if they were, if you ask the negation of your original predicate. In other words, they tell you what they want to hear, they just want to talk to you.

So, for the predicate, the Gaga chat room = T, the sports chat room == F, the snobs == NOT and the lonely hearts == IDENTITY. For the last two, the answer you get depends on the question you ask. You "collapse the superposition" by querying them.

I HAVE COME TO DROP BOMBS

So in the 'q' rather than 'v' context, what is the q() Russel's paradox? T? F? No, SNOB. Assume S, the set of all sets which do not contain themselves contains S. Is my assumption correct?

"False".

Assume S, the set of all sets which do not contain themselves, does NOT contain S. is my assumption correct?

"False".

Russel's paradox, like the snobs, just wants you to leave. It negates your predicate. "Lonely hearts" paradoxes are out there as well, they are just harder to detect, as the human ego is more inclined to notice its unconditional rejections than its unconditional acceptance.

The real question is, just as Russel's paradox = NOT, is there a paradox which == IMPLIES, AND or OR? Such a paradox would make paradoxes under Q Turing complete. You could construct, for instance paradoxes that add numbers, based on the truth values you assumed for the original predicates. using q(). (remembering you must assume initial values with q and ask if they are indeed correct).

But lets take this back to the ground, what am I really talking about with this queer/query/quantum business? We are talking about observations where the result of the observations is entangled with the state of the observer. The observer must choose to ask if P is correct, or ask if P is incorrect, and the answer they get depends on which of those two choices they make. The choice they make defines their state, which is entangled with the state of the outcome.

Now given the 4 "chat rooms", it seems obvious to me that all of this is reducible, like n-valued logic, to boolean logic. but when 3 valued logic is integrated, with Null, an interesting possibility becomes part of it all: A fifth chat room, where asking the question reduces the answer to either T or F for the predicate, but which one will be chosen is unknown (Null) and undefined: Its a roll of the dice.

This is the thing that is fundamentally new, and not reducible to 2-valued logic: because it is here where the system must shrug, and admit the unknown, which makes that choice. This atomic concept is fundamentally new, and powerful, and beautiful.

Selah.

Addendum: Consider the two-slit experiment: the evaluation/query (v|q) of a particle going through one slit will collapse it down to either the slit observed or the other one, (T|F but NOT Null, the outcome is known) but there's no telling how that choice is made, its made by factors beyond the predictive capability of the system. Meher Baba: "There are four levels"

1) Ignorance of Ignorance: You think you know it all, but your model is completely fucked. You will fail.

2) Ignorance of knowledge: You've learned humility, but you still aren't aware of what your missing, what it is you don't know.

3) Knowledge of Ignorance: You know exactly what you don't know, and this is extremely empowering.

4) Knowledge of Knowledge: You've filled in those gaps you identified, you are profoundly powerful.

In this schema, 3 is a damn good target.