Hi and welcome to Ask Doctor Math, the warm cozy corner of the Internet where anyone with a math question can pull up a virtual seat, grab a mug of hot virtual cocoa, and sit by the glowing virtual fire of knowledge as I attempt to answer questions mathematical. I created this blog as a forum for people young and old to clear up some lingering misconceptions, bring fuzzy notions a little more into focus, and, with luck, add a few more tools to the toolbox of ideas they use to make sense of the world. I may not be that kind of doctor, but I'd like you to think of me that way anyway--the friendly old small-town physician you can come to with anything, from questions about birth control or that rash on your back to home remedies for a colicky baby or a toothache; hell, I'll even help birth a foal, if that's what you need. (Note: the preceding was just an extended metaphor.) I hope to be your guide on a journey of mathematical discovery. So please, come on in and make yourself at home. Take off your virtual shoes if you like, or don't, it's up to you.
To kick things off, I thought I'd reply to a question that seems to be on a lot of people's minds these days regarding the alleged difference between the "mathematical world" and the so-called "real world."
Dear Doctor Math,
A guy on TV keeps telling me that "We all use math every day." Is that really true? Give several dozen examples.
Dr. Math (you)
Before even beginning to scratch at the surface of that question, I think we should talk a little about what we mean by "math" exactly. For a lot of people I've talked to, "math" is basically synonymous with "numbers." So, in that sense, yes, we probably do all encounter math every day, telling time, riding on a bus, dialing a phone, etc. If we didn't have numbers, we'd be forced to use little pictures of things, so it's convenient to have a shorthand. But a lot of that could only be superficially described as mathematical.
Perhaps a little more tangible application of math is in quantitative reasoning--the kind of thing we're forced to do a lot in our capitalistic society ("How much is 30% off $80?", "How do I split a $32 dinner bill 3 ways?", "Which is a better value, a 2'x3' rug for $25 or a 4'x6' rug for $60?", "How long will it take me to go 90 miles if I average 55 miles per hour?", "How many fluid ounces are in 2.5 liters?", etc.). The main tools we generally use here are fractions, percents, ratios, and basic arithmetic--addition, subtraction, multiplication (and its evil stepchild division). A lot of the time we just ballpark it, though, and our powers of guesstimation are more or less adequate to get us through a typical day. When it's really important that we get something right, we outsource the job to a computer, cell phone, calculator, or cash register. So in that sense, I'd say we use math, but we could probably all stand to be a little better at it. At any rate, there's not much genuine thinking involved.
Probably what the writers of Numb3rs had in mind, though, is the notion (championed by high school math teachers everywhere), that even when we're not explicitly dealing with numbers (or numb3rs), we frequently use our powers of analytical reasoning in a way that could be broadly be considered mathematical. Our toolkit here includes such things as deductive logic ("Just because I said that dress doesn't make you look fat doesn't mean you don't.", "Every girl knows someone who likes everyone else more than her."), elementary hypothesis testing ("My doctor said the test is 90% accurate; how concerned should I be?", "I guess there could be an innocent explanation for why that guy would be running down the street carrying a TV at 2am." ), and management of risk ("What does it mean that my birth control method is 99.9% safe?", "The weather forecast calls for a 30% chance of rain; should I bring an umbrella or not?"). I would also include in this category some basic optimization problems, like "How do I fit all these boxes in the car?", "Is this couch too big to fit through my hallway?", or "Should I park here or look for a better spot?". Again, these questions don't really tap our quantitative skills so much as our rational/logical thinking skills. A lot of it is intuitive, but a lot can be trained by thinking our way through other rational/logical problems. At its core, that's what math is really all about--practice for the kind of problem-solving that's required of us to navigate a sometimes complex and baffling world.
And like it or not, we are being subjected to persuasion of an increasingly mathematical bent. News reports like clockwork regularly tell us what activities or foods might be correlated with cancer or aging. As we move into political crunch-time, we are barraged almost daily by statistical arguments about the state of the nation and who might be to blame for what, as well as the frequent polling results with their "margins of error" and what this means for the so-called "electoral math." The present crisis on Wall Street has, among other things, shown the hazard in trusting all of our quantitative risk-management to a few experts, whom we treat like the high priests who are the only ones allowed into the holy sanctuary. If we're afraid to take responsibility for our role in distinguishing mathematical argument from fallacy, we will only get more and more manipulated by those to whom we yield that authority.
In other words, we may not use math every day, but it sure as hell uses us.