Maths-Whizz Blog

The excellent Steven Strogatz, writing a series of online-only articles about maths for the New York Times, has just posted his latest piece. It’s about that hairy beast of mathematics - division!

Taking a broad and accessible view of the problems of fractional quantities and how much we struggle with them, Strogatz weaves in the Daniel Day Lewis film My Left Foot and the awesome mind-bendingly-bad maths of a customer service rep.

The customer “V” is querying an error in which he was charged 0.002 dollars per kilobyte of web use, rather than the correct 0.002 cents:

V: “Do you recognize that there’s a difference between one dollar and one cent?”
A: “Definitely.”
V: “Do you recognize there’s a difference between half a dollar and half a cent?”
A: “Definitely.”
V: “Then, do you therefore recognize there’s a difference between .002 dollars and .002 cents?”
A: “No.”
V: “No?”
A: “I mean there’s … there’s no .002 dollars.”

As Strogatz points out, and as the God of Whizz knows all too well, fractional maths concepts are often deeply unnatural for a brain that seems naturally to prefer wholeness, roundness, solidity.

When our internal concept of a mathematical value only goes so far in describing something, we stop and shrug our shoulders.

A few moments later Andrea says, “Obviously a dollar is 1.00, right? So what would .002 dollars look like? I’ve never heard of .002 dollars… It’s just not a full cent.”

The challenge of converting between dollars and cents is only part of the problem for Andrea. The real barrier is her inability to envision a portion of either.

This difficulty conceptualising fractional quantities and how they interact was shown in the first episode of the Channel 4 doc The Kids Don’t Count, in which we saw how children and adults struggle with dividing one fractional quantity by another.

I recommend you read the article in full (plus any others in his online series). Strogatz concludes by noting that irrational numbers - weird numbers that cannot be expressed as a ratio (or fraction) of any whole numbers - are far more common than those lovely rational numbers that we know, love, and think the world is made up of, like 1, 5, 3/4, and 0.333…

If that doesn’t pique your interest, you clearly need to spend more time with the God of Whizz!