[math porn] Quantum Booleans (Warning, XXX Rated)

So.....I ran out of Family Guy episodes to watch and elected to watching this instead and of course it made me think of 3-SAT for some reason, and I can't describe what was going on in my head for a while but I came up with an interesting idea.

However, as you'll find out shortly this is the mathematical equivalent of a threesome (the good kind) so please only read further if you are at least 18 years old.

Ok.  So lets take some boolean values.  If you don't know what a boolean is, just fuck off.  Here are some examples, and I'll throw in the equal signs:

True or False = True
True and False = False
True or True or True = True
True or False or False = True
True or False and False = die in a fire, you order-of-operations whorebag

Ok, now...lets make things simpler.  Instead of "True" i'm just gonna write 1, and instead of false I'll write zero, and I'll use a "v" for "or" and a ... ^ for "and".


1 v 0 = 1
1 ^ 0 = 0
1 v 1 v 1 = 1
1 v 0 v 0 = 1
1 v 0 ^ 0 = die in a fire, you order-of-operations whorebag

Soooo...this is where things get kinky.   Hello 2.

0 v 0 = 0
0 v 1 = 1
1 v 0 = 1
1 v 1 = 1

1 v 1 = 1
1 v 2 = 2
2 v 1 = 2
2 v 2 = 2

Oh yeah thats nice...that's so nice.  But zero doesn't want to be left out.  But wait, what relationship does zero have with 2?  Well, lets use the commutative property to decide that:

0 v 1 v 2 = (0 v 1) v 2 = (1) v 2 = 2

0 v 0 = 0
0 v 2 = 2
2 v 0 = 2
2 v 2 = 2

As you can see, the commutative property is basically the mathematical equivalent of that massage bullshit creepy guys use to start threesomes:

0 v 2 v 1 = (0 v 2) v 1 = (2) v 1 = 2

So that was "or" ...what about "and' ?

0 ^ 0 = 0
0 ^ 1 = 0
1 ^ 0 = 0
1 ^ 1 = 1

1 ^ 1 = 1
1 ^ 2 = 1
2 ^ 1 = 1
2 ^ 2 = 2

same trick:   0 ^ (1 ^ 2) = 0 ^ (1)  = 0

0 ^ 0 = 0
0 ^ 2 = 0
2 ^ 0 = 0
2 ^ 2 = 2

I like to think of 2 as a "super truth."


And here is the problem (for those of you who didnt know, "!" means "not," i.e. "opposite of":

!2 = ?

What the hell is the opposite value of this shit?  Because we need to satisfy:

2 = !!2
!2 = !!!2
!(2 ^ 0) = (2 v 0)
!(1 ^ 0) = (1 v 0)


I think we have three options:

•  !2 = 0 and 1 at the same time
• !2 = 0 or 1 (we dont know which, i.e. its a quantum state and we have to measure the value)
• !2 = a; !0 = b, !1 = c, and we also have "?" standing by

That last bullet point is the most interesting but instead of exploring it I decided to eat half a jar of pickles because I was hungry.  I now bid you good night.