I've been holding off on this for a couple of days but I can't contain myself any longer. Did anyone else see the recent news item that January 24th is the "most depressing day" of the year? If not, you can read it on MSNBC and on the BBC. If you do a Google search for "most depressing day" you'll find hundreds of pages that mention the article, many belonging to reputable news sites. In short, the articles report that Cliff Arnalls, whom the BBC identifies as a part-time tutor at Cardiff University in Wales and MSNBC identifies as a doctor who "specializes in seasonal disorders" at the University of Cardiff, (and Sheffield Today calls Arnalls a "leading psychologist") has devised an equation to measure the most depressing day. All well and good except… according to the BBC the equation is:

1/8W+(D-d) 3/8*TQ M*NA

where (I'm cutting-and-pasting the BBC explanation),

W is weather, D is debt - minus the money (d) due on January's pay day - and T is the time since Christmas.

Q is the period since the failure to quit a bad habit, M stands for general motivational levels and NA is the need to take action and do something about it.

MSNBC doesn't have the numbers and gives the equation as:

[W+(D-d)]*TQ M*NA

Let's look at the latter, simpler, equation and not concern ourselves with why one version has numbers and the other doesn't.

Does anybody with more than a sixth grade education see a problem with the equation? Better yet, how many mistakes can you find? Let's see!

The first problem is, uh, this is not an equation. There are some variables and arithmetic, but there's no equal sign. There's also two parts to the formula: [W+(D-d)]*TQ and M*NA, but no stated relationship between those parts. Are you supposed to add, subtract, multiply or divide them somehow, or are they totally separate entities. The variable we are meant to solve, T, is in mixed up with the rest of the variables. Mathematically we should be looking at something like

T = (X – W)/[(D - d)*Q]

To get an actual equation I've added a mystery variable, X, ignored the odd M*NA, and rearranged the other variables.

This is a nice algebraic equation. It's got a little subtraction action going on, some division and some multiplication. It does have two unknowns, X and T, and should only have one, T, for which we are trying to solve, but X is the least of our worries and I don't want to get bogged down in details.

W is weather. This is what first caught my attention. What does this mean? Is there a way to characterize weather by one number? Is it temperature? Precipitation? I don't remember seeing a variable like this in any of the meteorology classes I took or taught. This is a completely nonsensical variable.

D is debt. It is not clear if this
refers to operating expense debt (like credit card balance, utility bills, auto
loans etc) or also includes capital debt (like home mortgage and home
improvement loans). I assume it is the
former because the latter number is going to be really big if you've got a
mortgage. Your mortgage might be
$100,000 or much more. That number is
severak orders of magnitude greater than the other variables in the equation
(unless the mysterious X factor is of the same size) that T will always be much
less than one. If Tis much less than
one, the most depressing day of the year is a few minutes after midnight on
December 26^{th}.

d seems to be your January paycheck, but it could be the amount of money you owe on your January pay day. (D – d) will work as both variables are in the same currency. But, what is that currency? The guy is in Wales so I assume the currency is in pounds sterling. If you're trying to use this equation in the U.S. you'll have to first convert dollars to pounds (or euros to pounds, or yen to pounds, etc).

One interesting thing to note is that if your paycheck is greater than your debt then your answer is going to be negative (assuming X is greater than W), meaning your most depressing day is <em>before</em> Christmas!

The definition of Q is worded awkwardly, but I take it to mean the time, in days, since you broke your last New Year's resolution.

Multiply Q by (D-d) and you'll get something with units day-pounds sterling. This is excellent information as it tells us what the units for X and W must be! T is in days, if the denominator is day-pounds, the numerator must be days-squared-pounds sterling. I can't think of any weather measurements that have currency in their units, but I'm not a part-time tutor at Cardiff University!

That takes care of the nitty-gritty, what about the somewhat bigger picture? The date that a New Year's resolution is broken, personal debt, and salary vary from person to person. For example, I haven't broken any resolutions, from the equation I will be undepressed for an infinitely long period of time! In addition, weather and currency obviously depend on location. The weather factor for Cardiff is different than that for New York or Los Angeles. Since all these variables depend so highly on an individuals habits, financial situation, and location, how can one date for the most depressing day of the year be calculated?

Here's what's depressing, though. I've looked at dozens of news sites and blogs the past couple of days to see how others have reacted to this nonsense. A few have taken it with the seriousness it deserves, but the vast majority of places I looked at take the item as gospel. It is sad that no editor or journalist at any ofthe news sites had neither the rudimentary math competence or critical thinking ability, to see that this equation is a bunch of crap. A sports column in the Birmingham Post treats the drivel as accepted fact, citing "statisticians and life-style gurus" as if people have actually done research on the topic. Wait 'til January 24th of next year when your local TV news will report "today is the most depressing day of the year" and the concept becomes accepted as truth. A place like Health Talk refers to the equation as a "complex mathematical formula". Complex? Since when is sixth grade math complex?

Luckily, there's Hugo Rifkind at The Herald in Glasgow, who pointed out how silly the concept is. However, Rifkind is the only other dissenter that I've been able to track down.

Unfortunately, this man's "equation" didn't work for me. The most depressing day of the year for me was actually January 22nd, the day I first read about the "equation to calculate the most depressing day of the year." I was extremely depressed because this equation made me realize that stupidity has now become the majority. When I went home and saw this topic on the news, I was even more depressed. Why is this national news? I think someone needs to be tutored in Mathematics, and his name is Cliff.

Posted by: Landyman | 01 February 2005 at 01:14 PM