# Arranging Books on a Shelf

My wife recently did some major rearranging of the books in our library. We have a large number of books, and we needed to downsize and make it easier to find what we are looking for. She asked for my advice about arranging books on a shelf. This brought to my mind a column in Astronomy magazine in January of 2013. In Bob Berman’s “Strange Universe” column, he often presents some interesting facts, and we have referred to his articles previously. In that particular column, he wrote about what random events or “chance” can or cannot accomplish.

The connection with library books goes like this. If you have 4 books on a shelf, how many ways can you arrange them? The answer is “4 factorial,” which is 4 x 3 x 2. Multiply it out, and you find that there are 24 possible ways. However, what if you have 10 books to arrange? That would be 10 factorial, which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2. Multiply those numbers, and you will find there are 3,628,800 different ways to arrange 10 books on a shelf. We have way more than 10 books in our library, and I am not going to compute how many possible arrangements there are. Neither my calculator nor my brain could handle it.

When my wife asked for advice on arranging books on a shelf, she didn’t realize what a difficult question she was asking me. However, I had no problem giving a suggestion because I have enough intelligence to know what books should go together by topic. But if you were to put 10 books on a shelf at random, the chance that they would all be in alphabetical order would be about one in 3.6 million. Try it blindfolded and see how long it takes for you to get it right.

Why am I talking about arranging books on a shelf? What’s the point? There are many more than 10 options when it comes to designing any part of the complex universe in which we live. What are the chances that they all came together without any intelligent direction? The possibility would be far lower than for all of the books in our library to be in alphabetical order, or even in topical order, if we just randomly put them on the shelves. The question then becomes: “Can anyone believe that this universe, our solar system, planet Earth, life, consciousness, and intelligence all happened by chance?” My library disproves that theory.