This entry explains the meaning of life, the universe, and everything as only Douglas Adams can (straight from the horse's mouth, in fact!), and also teaches you how to use some of those funny looking symbols on your digital calculators. Here is where to begin:
Fans of the Hitchhiker's Guide to the Galaxy will know that the answer to the question about life, the universe, and everything is forty two. But what is the question?
In the story, Arthur and Ford discover (inconclusively) that the question is "What is six times nine," which is 54. Arthur explains upon hearing this that he always felt there was some fundamental flaw in the universe.
Some very smart readers of the original story took this joke a little too far, and inferred that they would have to bend the conventional definitions of math in order to understand Adams's meaning. In the case of the Question, these very smart people discovered that if they counted using thirteen single-digits instead of the ten that we're used to (explained below), then suddenly 6 x 9 does in fact equal 42. How brilliant!
This is a very intelligent and insightful thing to do and is exactly the sort of thing that Douglas Adams WOULD have intended (just read Dirk Gently's Holistic Detective Agency if you wonder where that thought is grounded). Now here is the important thing:
They are completely wrong about it. Douglas Adams announced in a television interview that he did not intend this joke. "I don't," he explains in the special features of the BBC series DVD, "Make jokes in base thirteen." Adams chose 42 because it was the funniest number. And how right he was.
This rumour is everywhere. It's all over the internet and often scrawled in the margins of library copies of the original book. So sorry to all those brilliant mathematicians who adore Adams and look a little too deeply into his meaning, but there it is in the documentary as plain as it ever will be, and we'll just have to accept it and move on.
Now - what IS base thirteen? What the heck does that MEAN? Well, it's easy.
If you know what binary is, then base thirteen is to thirteen symols as binary is to two symols. If that explanation is still unclear, then please read on.
Count the number of fingers you have. Unless you've suffered a tragic accident, a perfectly acceptable birth defect, or have polydactly (lucky you!), then the answer is 10. You have 10 fingers.
Your ten fingers are the reason that our number system goes to nine and starts over. If humankind had one less finger, then we would go to 8 and then start over, and 10 would actually be 9, 100 would actually be 81, and 1000 would actually be 729. We would be counting in base nine.
Now what if you had thirteen fingers instead of ten? Well then we would all have been counting all along with thirteen different one-digit symbols (0,1,2,3,4,5,6,7,8,9,A,B, and C) and THEN we would start over. So the number 10 would actually be the number 13, and so on, and so forth, and six times nine would equal forty two.
In case you're still having trouble, below are the numbers from one to thirty in base thirteen. Note than in base ten, which is what we are accustomed to counting in, there are 39 numbers listed below, not 30.
Base thirteen is not used for anything in our world, except that now and then physicicists will use to it to try to explain the universe as thirteen dimensions - but then again they also use base seven or base twenty or base WHATEVER just as often. Physicists are smart and amazing people. Base thirteen, for the sake of simplicity, is not really used for anything except trying to make 6 x 9 = 42.
But there ARE alternatives to base ten that are used very often. There are other entries in the Hitchhiker's Guide to explain some of these systems and their uses in the real world.