Hello from London! I’m traveling around Europe for a few weeks, but I wanted to start posting as I read Innumeracy just to get the discussion started. First off, congratulations on deciding to read a book that will undoubtedly open your eyes to some pretty cool math.
I also wanted to let you know that even though this isn’t a “technical math” book, per se, there will be certain paragraphs and passages that contain mathematical explanations. I think that many of them warrant a good honest attempt at understanding, which may require you to read them more than once (reading math is a bit different than reading prose). However, I don’t want you to get frustrated if you’re unable to understand a certain paragraph or passage. Just move on, and maybe post a question up here so that I can address it. At the very least, underline or a make a note of something you want to understand better so that we can talk about it when we meet up at the end of August.
The point is this: Don’t lose the forest for the trees. Try to appreciate the overall message of the book, and to really understand some of the cool examples that Paulos gives. If you don’t understand them all, no worries.
Now, reading this book always reminds me that I want to incorporate more “number sense” into my math classes. I mean, just think about some of the statements that Paulos makes and how insane they really are! For example “The size of the universe is, to be a little generous, a sphere about 40 billion light years in diameter” (p. 20) Sure, the words all make sense, but what does that even mean? 40 billion light years is the distance that a beam of light would travel in 40 billion years. Given that light can travel 5,865,696,000,000 miles in one year, that number times 40,000,000,000 would be the diameter of our galaxy, in miles. This blows my mind.
If there’s one “mathy” section that I would encourage you to really try to understand, it’s the section entitled “The Multiplication Principle and Mozart’s Waltzes” (p. 22), especially its analogue to probability on p. 27. It’s actually quite simple: take the following example. If there’s 50% chance of rain tomorrow (Sunday) and a 50% chance of rain on Monday, then the chance that it rains on both Sunday and Monday is 50% x 50%, or .50 x .50 = .25. In other words, there’s a 25% chance that it will rain on Sunday and Monday.
Pretty simple, huh? The one thing to be careful of is this: Being the astute meteorologist that you are, you might argue that “Hey, those two events aren’t independent because they actually affect one another. If it rains on Sunday, that means it’s actually more likely to rain on Monday too, so the chances of that happening would be bigger than 50%.” You might actually be right, or maybe if it rains on Sunday then it’s less likely to rain on Monday (because the rain cloud will have already passed over us). In either case, the point is that the two events are not completely independent. Indeed, we can only multiply the probabilities (like we did in the previous paragraph) when we’re talking about independent events. But a lot of times if it’s not too crazy to do so, we will simplify our life a bit and just pretend that two events are independent, even if that might not be completely true.
Of course, one of my favorite examples from the first chapter is the one I used to entice you to read this book in the first place at the community meeting — the probability that you just inhaled a molecule of air that Julius Cesar exhaled in his dying breath. If you don’t get it, post your question (even if it’s just, “I don’t get it!”) here and we can talk about it. Because it really is worth getting. It’s a beautiful example of how basic probability can yield the most surprising results, dispelling the awful myth that math is boring and predictable.
