I’m currently attempting to break myself of caffeine addiction, and seem to be suffering from caffeine withdrawal, so please forgive any grammatical errors or the like.

But to the subject matter posthaste: I’m, again, writing about Time Cube. I have a perverse fascination with it, largely because it’s like reading the thought processes of a lunatic. I mean, that’s pretty much what it is.

Gene Ray, Doctor of Cubicism, has followed in the footprints of James Randi, and offered the sum of $1000 to the first individual to show his theory to be incorrect. Sadly, the majority of it appears to be non-falsifiable, and therefore, no one has, thus far, claimed this prize. However, he makes one claim that is easily demonstrated to be true or false, which is that (-1)^{2}=+1. This, being a simply formulated mathematical statement, can be concisely and conclusively proven wrong. This is what I shall proceed to do, with the enhancement of lovely graphs. I don’t know if this will qualify me for the prize, or whether or not he’ll actually pay me if it does, but in the event that I do, and he follows through, I will donate 70% of the money to charity.

This proof is predicated upon the axiom that, a function applied to both sides of a valid equation does not change the true/false evaluation of said equation. I’m not sure what the technical term for this is (assistance, anyone?) and I feel to lazy to look it up at this time, so let us call it “axiom 1”. This proof is also predicated upon that fact that (-1)(1)=-1, which shall call “axiom 2”. I doubt that even Gene Ray will dispute this.

Let y=-x. Graphed on Cartesian coordinates, this appears as the following:

Taking into account axiom 1, if the same operation is applied to both sides, the graph should remain the same. If it does not, then the equation is fundamentally different. Therefore, let us multiply both sides by -1. If (-1)(-1)=+1, then the equation now reads as -y=x. This graphs as the following:

You’ll notice that the two are the same. However, if we assume that (-1)(-1)=-1, as Mr. Ray suggests, then the equation should read -y=-x. In addition to the obvious inconsistency between the first equation and this (they used to be opposite signs, but now they’re the same? And this is valid how?), it graphs as the following:

This is obviously vastly different from figure 1, therefore, (-1)(-1)≠+1. Q.E.D.

Note that I don’t possess any personal animus towards Mr. Ray. I, quite honestly, feel sorry for him. The man is obviously deluded, and I believe that he needs to be shown the error of his ideas, for his own good. Being the laughing stock of the Internet is not a particularly optimal position.

lanfranc(10:48:15) :This proof is also predicated upon that fact that (-1)(1)=-1, which shall call “axiom 2″. I doubt that even Gene Ray will dispute this.You may be a little too optimistic there.

This is obviously vastly different from figure 1, therefore, (-1)(-1)≠+1. Q.E.D.AHA! But are they different when you look at them from the perspective of a Cubic Earth with 4 simultaneous corner days in 1 rotation of Earth?! Bet you hadn’t thought of that, you Evil Singularity Oneist!

Linus(14:00:31) :But, but -1 added to zero/counted one time is obviously -1! AAAAAARGH!

You’re right, I hadn’t thought of that! I’ve been defeated!

Human(05:51:29) :“However, he makes one claim that is easily demonstrated to be true or false, which is that (-1)2=+1”

“However, if we assume that (-1)(-1)=-1, as Mr. Ray suggests”“therefore, (-1)(-1)≠+1. Q.E.D”

Um, you slipped a gear on purpose, right?

Linus(22:51:51) :I suppose that did sound rather odd…

David(07:43:03) :http://www.wolframalpha.com/input/?i=(-1)2

(-1)^2 DOES = +1

well, not +1, that’s math-gramatically incorrect in some ways, but (-1)^2 = 1

and, before you ask, i stalked you through a link from RationalWiki’s time cube talk page >.>