Tuesday, 24 February 2009

The Perfect Pancake

Ok, so I'm probably not the first, and I'm sure I won't be the last, to deconstruct this utterly ridiculous formula, but I mean, seriously... which utterly ridiculous formula you may ask? There are, of course at least two a week in the Metro. Well, for now let's do this one. Dr. Ruth Fairclough who is a "maths expert" and teaches at Wolverhampton University has come up with the following formula for the perfect pancake:

Dr Ruth, who teaches at Wolverhampton University found that
100 - [10L - 7F + C(k - C) + T(m - T)]/(S - E) created the tastiest snack.

In the complex formula L represents the number of lumps in the batter and C equals its consistency.
The letter F stands for the flipping score, k is the ideal consistency and T is the temperature of the pan.
Ideal temp of pan is represented by m, S is the length of time the batter stands before cooking and E is the length of time the cooked pancake sits before being eaten.

The closer to 100 the result is - the better the pancake.
Now we all know how this bit goes. I decide to vary the inputs and see how utterly ridiculous the formula becomes. First let's start with the units. So far as I can tell we have units of "lumps + consistency^2 + Temperature^2)/time". It's a long time since I did any dimensional analysis, but I don't think this is a dimensionless parameter.

Second, let's see what happens if we increase S. In fact, let's increase S a lot, let's leave the batter to stand for, say, 2 million years before we cook it. Then (assuming that the units make some sort of sense) it doesn't matter how bad we get our consistency, or how many lumps we have, it's going to be damn-near perfect. (Anything divided by 2 million years is pretty small).

Now let's see what happens if we let S and e be really close together. Say we let the pancake batter stand for a minute before we cook it, and then eat the pancakes a minute after we have cooked them. Well then, unfortunately, our (S-e) term goes rapidly towards infinity, and it doesn't matter how perfect our consistency was, or how hot the pan - the pancakes are going to be terrible.

We'll skip over the question of what "flipping score" is supposed to mean, and resist the urge to make the obvious play on words...

Finally let's consider those consistency and temperature terms. They are, remember: C(k - C) and T(m - T) where C and T are actual temperature and consistency and k and m are ideal temperature and consistency (why the strange choice of letters I have no idea. Now, depending on the value of (10L-7F), we are either trying to maximise or minimise these terms. If we are maximising them, a little calculus shows that we want to choose C = k/2 and T= m/2. So then we don't actually want to set the pan to the ideal temperature, we want half of the ideal temperature.

But we're probably minimising them (that seems to make more sense.. although why that should affect anything to do with this formula I have no idea). Then we want to choose either T to be one of 0 and m and C to be one of k and M (of course, as these functions are continuous, T arbitarily close to zero will give arbitrarily close to the minimum value. So the optimal temperature for cooking pancakes is either the ideal temperature or zero. And the optimal consistency is either the ideal consistency or zero... remind me again what ideal meant?

Of course, there's no reason why that term we subtract from 100 should be positive. If you're damn good at flipping pancakes, (F is very high) then you might be wanting to minimise those temperature and consistency terms, in order to stop the whole lot being 'too negative'.

Of course, this is all nonsense. I haven't even gone into how one is supposed to give a numerical value to 'consistency' and 'lumps', or the fact that we're not even told what units we're measuring temperature in. It's poppycock, and balderdash. No wonder people think scientists waste all their time doing pointless things when some idiots are willing to put their name to a formula like this. It doesn't help anyone, it's completely uneducational, and it just adds to the idea that maths is something complicated and useless.

I don't know who Ruth Fairclough teaches at the University of Wolverhampton, but I bet she doesn't let them get away with sloppiness on this level in their coursework.

Addendum: Just noticed this excellent post, which makes much the same points as I did, but has a much prettier layout...

1 comment:

paulsc said...

I found your blog when I was searching Google to try and discover what qualifications Dr Ruth actually has (not easy, the only vaguely relevant reference I have found is here http://www.wlv.ac.uk/default.aspx?page=8823). The search was part of my preparation to blog about the stupid formula but you have done such a good job that I will just link to yours.