Yesterday I introduced you to the idea of words as numbers. There are many ways to create a map between words and numbers. For example, we could assign them the number that represents their position in the dictionary. That would make words that start with “A” have smaller numbers while words that start with “Z” would have the largest numbers.
There are also ways to treat the words themselves as numbers. We can interpret the letters the same way we do digits. Each letter has an assigned numeric value, and then a string of letters—just like string of digits—forms a number. The scheme I showed you yesterday allows us to treat (only!) single words as numbers.
Now let’s extend this so that entire sentences—or even entire books—become numbers!
Today I’d like to introduce you to a concept I picked up from mathematician Rudy Rucker in his 1987 book, Mind Tools (The Five Levels of Mathematical Reality). I’ll warn you now that there is some math ahead (but no math homework—unless you want to). It won’t get any more complicated than multiplication and addition, but we will be dealing with some extremely large numbers (so large they are more ideas than numbers).
The end result is that we’re going to tie together the written word with numbers. I’m going to show you how every word, every sentence, every book, magazine and blog article can be reduced to a single (very large) number. That we can do this provides a foundation we can use to discover some amazing things about mathematical reality.
It may sound dry or intimidating, but stick with it! You just might find it worthwhile.