Saw several different people pointing out a math-realted idea from a NYT story about The Interview. One example out of the many is a blog article here:
with follow up on twitter here:
It all leaves me a bit uncomfortable. Here’s are some reasons why:
(1) What is the message being conveyed?
If the message is something other than “ha ha, the reporter couldn’t do some fairly basic math” the message is lost on me.
I say “fairly basic” because analogous problems appear as early as elementary school – and certainly before algebra. After seeing some of the posts about the NYT article yesterday, I looked through some of the MOEMS books and found two similar problems in the first few pages of exams. For example:
(A) At a special sale, all pens are sold at one price and all pencils at another price. If 3 pens and 2 pencils are sold for 47 cents, while 2 pens and 3 pencils are sold for 38 cents, what is the cost of a set of one pen and one pencil, in cents?
(B) Admission to a local movie theater is $3 for each child and $7 for each adult. A group of 12 people pay $64 admission. How many children are in this group?
These questions are from the set of exams for kids in 3rd through 5th grade. Aside from having smaller numbers, they more or less exactly the same as the question answered in the blog article above.
Since kids can understand the problem as well as the criticism, I worry about what they will think about the criticism if they themselves can’t solve the problem.
To me the it has the familiar ring of what Jordan Ellenberg calls “algebraic intimidation” in How Not to be Wrong. In the section “Evanescent Increments and Unnecessary Perplexities” there is this passage (page 43 of my copy). The topic in discussion is a common proof of why 0.99999…. = 1:
“These arguments are often enough to win people over. But let’s be honest: they lack something. They didn’t really address the anxious uncertainty induced by the claim 0.9999… = 1; instead, they represent a kind of algebraic intimidation. “You believe that 1/3 is 0.3 repeating – don’t you? Don’t you?”
I see a pretty similar thing going on here: you believe these two equations – don’t you? Don’t you?
Which is an easy transition to the next point
(2) What about the uncertainty
Oh, there’s lots of uncertainty in this problem and the equations in the blog article ignore all of it. Put yourself in the position of a NYT editor (or fact checker). Which would you prefer:
(a) The claims in the article: “Sony did not say how much of that total represented $6 digital rentals versus $15 sales. The studio said there were about two million transactions over all.”
(b) The math from the blog: “According to our analysis of the information provided by Sony, there were 1,666,666 $6 rentals and 333,333 $15 sales.”
[post publication edit. Dan Meyer contacted me on twitter and expressed concern about part (b) above. He thought that the quotation marks made it appear that part (b) is a direct quote from somewhere else. I did not notice the potential for that confusion when I wrote this post and certainly didn’t intend for there to be any confusion on that point. To be clear, part (b) is a hypothetical submission to the editor / fact checker designed to report the solution to the math problem that led to the various posts.]
Some commentators have pointed out the error of ignoring the uncertainty in the numbers. Here’s a good graph, for example:
But there are other problems too. For example – How do you know Sony’s numbers are correct? How do you know that all of the sales and rentals took place at $15 and $6 and not some other price(s)?
Blindly relying on the math to get to answers can and has lead to all sorts of problems in the business world. A great starting point for understanding some of the problems in finance is Roger Lowenstein’s book about the rise and fall of the hedge fund Long Term Capital Management, When Genius Failed. Bethany McLean’s book about the 2008 financial crisis – All the Devils are Here – is another good one. Or, if you think these books won’t interest you, just follow Nassim Taleb on twitter to learn daily that blindly relying on equations to solve problems that arise in business can lead you to answers that turn out to be drastically wrong.
Finally . . . .
(3) Is this a good example of why you should learn algebra?
For me – no. As I said above, pretty similar problems on elementary school math contests. No algebra is necessary to solve them.
I also do not think that many people would find the question of trying to back into Sony’s rental and sales numbers to be all that interesting. I’d be curious if anyone has ever tried to do a similar calculation for any other movie ever.
Some of the math that comes into play behind the scenes in When Genius Failed and All the Devils are Here may actually be a good example. An excellent starting point is Zvi Bodie’s paper:
If you think the math behind $15 million in movie sales would interest kids, just think about the math behind trillions and trillions of dollars in derivatives!! (to be clear: snark)
So, the whole shaming of the NYT for this bit of math leaves me uncomfortable. I think the implicit message it sends about the “we know math” crowd vs the “you don’t know math” crowd is terrible. I also think that the calculation is much more subtle than is being let on and ignoring those subtleties is something that’s caused lots of problems in the business world over time. Thinking that these sorts of problems can be solved by simply plugging into formulas is thinking that is mistaken. Finally, even ignoring the first two points, I do not see the problem itself as that compelling, and especially not compelling as a reason to learn algebra.