Friday, April 2, 2010

For fear of negative numbers

Neil deGrasse Tyson is a funny, funny man. Which is an odd way to praise an astrophysicist. I am sure the profession prides itself as highly scientific, rigorous, quantitative, dealing with the truly big questions, and so on. Tyson does all those things too, as Director of the Hayden Planetarium in New York City. He also does more than a room-full of astrophysicists combined to make this branch of science accessible to your regular Joe. He does so with a passion that is contagious, an energy that is infectious and a sense of humor that is nerd heaven.

As I was saying, Neil deGrasse Tyson is a funny, funny man.

Death by Black Hole is an old collection of Tyson's many essays on science, people of science and all things scientific. Much of the book is memorable, and I would heartily recommend it to any casual reader interested in science, who wants to be entertained while being educated at the same time. To me, it is the kind of writing that makes popular science worth the while at all. Some while back, when I tried to list out the best writers of popular science, Tyson made my list purely by the dint of this book.

One of the most memorable essays in the book is one where Tyson talks about the unspoken, irrational fear most Americans seem to have of numbers. There are many ways this shows up - the fear of the number 13 (no airplane seats with that number, no hotels with that floor); the fear of decimals; the inability to truly comprehend large numbers etc.

[I highly recommend reading the entire article, offered here on the Hayden Planetarium website. It might be the best 7.5 minutes you spend today.]

I read Death by Black Hole maybe three years ago, but this particular essay has stuck with me. Why? Because I keep running into irrational displays of these fears every so often. Take for instance the biggest of all these fears - the fear of negative numbers. For some reason, the average American - I say 'American' more due to familiarity, not due to a firm knowledge that this is somehow a US-centric pandemic - seems unable to imagine that there is a living, thriving world under the placid surface of water level called zero. They seem unable to think that it might be possible, even pleasurable, to dip their toes into the sub-zero range. In fact, they seem positively fearful of entering that nether world at all.

Conducting job interviews for my company, I have the dubious opportunity to meet this curious fear regularly. Just the other day, I was taking a candidate through a case interview. Seemed like a sharp enough young man: very well put together, confident like only youth can be. He is doing well enough, as these things go, and confident starts going on cocky. Which is fine too. Hey, good for him.

Then, we come across a little glitch. The question that he faces now is the equivalent of: 'So it appears that we make $150, by spending $180. What is our profit in this case?'


Followed by some more silence.

A hand through perfectly coiffeured hair.

A wrinkled brow.

Is it truly possible? Is this all it takes to throw the best of our youth off their kilter? A little 2-3 puzzle?

Our protagonist stumbles through the next few minutes. Later, we are trying to draw a graph. As it happens, the line on the graph needs to dip into negative territory for a little while before re-emerging into the 'real world'.

You guessed it. Our John Edwards look-alike can 'see' all the parts of the graph in the positive territory. But everything under-water? Forget about it.

Negative numbers are a concept. A concept that can only be understood in theory, in the abstract. For a generation of students taught in purely tangible terms, it isn't an easy concept to wrap their head around. When your local school taught you numbers by showing you three red balls and five blue balls add up to eight ball, it sounds like good touch-and-fell pedagogy. But mathematics is, in many ways, a science in the abstract. It is a language. To really understand it, you need to leave the world of wooden balls, and enter one in which you start with three red balls, and then take away five red balls. Theory trumps experimentation.

So the next time I am talking about education models, and someone tells me 'But their teaching is so theoretical' with a wrinkle of their nose, I am going to ask them - Say you have 150 apples and I take away 180 apples from you, what are you left with?


  1. Guess the distinctintly old school Indian way of teaching Maths as an abstract subject entirely disconnected from physical reality had its merits.

    Btw, did you try asking the apple question to Nishtha? I am curious what she would say.


  2. Unable to give you a heart. so have a reply to push up your post. ........................................