Welcome

I know a lot of people who are intelligent. They really are -- any way you look at it, they're sharp. If you get in an argument with them, they're very quick at picking up discrepancies and finding ingenious counter-arguments. They can navigate the maze of ideas with ease.

But they all gave up on mathematics at one time or another, and even a mention of the word mathematics is a cue for them to start heading for the exit.

Here is an example of this mathematics-phobia. People rarely make a statement about coke (the drink), then the same one about diet coke, then repeat the same thing for pepsi and dr. pepper. Unless they're comparing tastes, they usually just call them all soft drinks and talk about soft drinks in general. The terms soft drinks and soda are abstractions that everyone seems comfortable with.

When taken literally, the word "soft drink" doesn't make any sense. A smoothie is perhaps, literally, a soft drink. But everyone understands that the word is just a label and that when the word is mentioned, we don't try to imagine a hard drink that's been softened, we just know it's a label and we go straight to the thing that it refers to.

But when a number is called irrational, which simply means "not a ratio of two whole numbers", somehow this term becomes mind-numbing and an obstacle to understanding. Perhaps the cause is the great authority mathematics has -- after all, you can't argue with something that's been proven, and in mathematics everything is either proven, or so complicated that no one has proven it yet. So this sense of ultimate authority carries over to the mathematical jargon, which is ironic, because it's actually anything but. It's very human -- in fact, littered with expressions of astonishment at the newly found concepts. Consider such words as irrational (beyond reason!), transcendental (beyond the realm of the senses!), and imaginary. All of them were labels for concepts that were new at the time. If we were to come up with new names for these concepts now, we'd probably choose much more mundane words.

So maybe it's the great mathematical authority and intolerance to error that creates a stumbling block for most of us. Perhaps, and here is another likely reason -- it is the really inflexible rate at which things get taught in school -- students who are a little too fast get bored, the ones who are a little too slow get clobbered, and all are forced to remember as many answers as they need to pass the exam. The way they get even with mathematics is lose all interest in it and forget all about it the moment their grade doesn't depend on it.

But sooner or later, they get curious: what are all these mysterious terms, like complex and transcendental numbers, what's so natural about the natural logarithm anyway? And what is a logarithm? (it's the number of digits in a number). Popular books on mathematics and the nature of the universe will all mention famous, intriguing equations like e^iπ+1 = 0. These people look at these equations like they were Greek ornaments, and don't appreciate the conceptual beauty, even though they want to. This purpose of this blog is to allow them to do it.

My mission is to explain all the steps leading up to the equation above to a normal, intelligent, non-mathematical person in a way that they will understand. It won't be a "dash for the finish" -- there is no time restriction on this, no exam at the end. The scenery is beautiful along the way, and can be appreciated for what it is.

This blog should be read top-to-bottom. Since each post depends a little bit on the previous post, I'm backdating them to make them appear in the right order. If you are a fellow traveler, what I would appreciate most of all is letting me know if you get lost by leaving a comment. Once this blog is finished, I'll just leave it sitting here.

I will revise, reorder, and modify these posts in response to the suggestions I receive.