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Fun with Maths – Proving Douglas Adams

Aaron Abrams is director of implementations here at Nortridge. Not only is his knowledge of how NLS works immeasurable, he’s also a whiz at math. When he’s not helping Nortridge clients, he’s writing fun blog posts that marry his love of math with his love of Star Wars, quirky books, and various bits of unknown history.

First a word about the title. Is it “math” or “maths?” In America, it is “math” singular, but in the UK, they say “maths” plural. I use “maths” today for two reasons: 1) I’m writing about a comment made by the British author Douglas Adams in his book The Hitchhiker’s Guide to the Galaxy, and 2) “maths” makes more sense. Both “math” and “maths” are a shortened form of the word “mathematics.” So, it should be plural, right?

Now, to the point. If you have never read Hitchhikers, I highly recommend it. Those of you who have read it will recall a section about a small creature called a Babble Fish. Somehow, this small fish, if placed in a person’s ear, telepathically translates any language. Adams then goes on to reference tongue-in-cheek how the very existence of this creature resolves profound philosophical questions about the nature of existence, the specifics of which I will not get into here. After using the existence of the Babble Fish to prove this philosophical issue, “Man” exclaims, “’That was easy,’ and then goes on to prove that black is white and gets killed at the next zebra crossing.” In the UK, a zebra crossing is a crosswalk with alternating black and white lines. All of this is, of course, intended to be humorous in a very “English” way. But I cannot leave it at that. I am going to prove that black is white, mathematically.

To begin with, in order to mathematically prove that black is white, I need a mathematical definition of black and a mathematical definition of white. The RGB color model on my computer conveniently provides this. All colors are defined on a range of 0 to 255 by their intensity in the three primary colors of red, green, and blue. Black is the absence of all colors and so is defined by the numeric array (0, 0, 0). If all three colors are applied at the same time in full intensity, we get white, so it is defined as (255, 255, 255). So, all I have to do in order to prove that black is white is to prove that 0 = 255.

Here goes the proof:

0 x 0 = 0, and

0 x 255 = 0,


0 x 0 = 0 x 255

And so…

(0 x 0)/ 0 = (0 x 255)/0 **


0 = 255

QED (It is proven)

Black = White.

Watch out for those crosswalks.

** Okay, I cheated. Division by zero is not allowed. But this is the precise reason why division by zero is not mathematically allowed. What I really proved here is WHY we cannot divide by zero. If division by zero were valid, then “black = white” would be true, and so if we can divide by zero, then we can prove anything, and there is no objective truth. It is probably not surprising that Adams was a script writer for Doctor Who and had much experience with writing about warped perceptions of time, space, and reality.
The moral boys and girls:
Don’t divide by zero. Don’t do it!
And the speed of light… it’s not just a good idea. It’s the law.

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