4 Comments »Posted on Tuesday 24 February 2009 at 8:51 am by Jacob Aron
In Getting It Wrong, Mathematics

It’s Pancake Day, or Shrove Tuesday for the Christians amongst us. Yesterday the Daily Mail published a story that began:

“With Shrove Tuesday tomorrow it was perhaps inevitable that an eager scientist would apply their skills to creating the perfect pancake.”

I’m tempted to re-word this:

“With Shrove Tuesday tomorrow it was perhaps inevitable that the Daily Mail would run some nonsense about a formula for the perfect pancake.”

Yes, we’ve got another one. Today’s formula faker is Dr Ruth Fairclough, who “worked out the food formula because her two daughters loved eating pancakes so much.” It appears that in between culinary calculations, she is part of the Statistical Cybermetrics Research Group at the University of Wolverhampton, who specialise in downloading and analysing large amounts of data from the internet. With that in mind, on to the formula:

100 – [10L - 7F + C(k - C) + T(m - T)]/(S – E)

Ooh, that’s big and scientific looking. Check out all those variables! What do they mean? Here’s the run down:

  • L: the number of lumps in the batter
  • C: the consistency of the batter
  • F: the “flipping score”
  • k: the ideal consistency
  • T: the temperature of the pan
  • m: the ideal temperate of the pan
  • S: length of time the batter sits before cooking
  • E: the length of time the cooked pancake sits before being eaten
  • The closer the result to 100, the better the pancake is

Phew. Everyone still with me? If you don’t mind, I’m going to skip over my usual complaints of meaningless variables (how do you measure “flipping score”?) and incompatible units, because frankly I’m bored of repeating myself.

As it stands, this formula is unusable. The “ideal” figures, k and m, are both constants, which means that they are the same each time – as you would expect, because if something is ideal then it shouldn’t change! An example of a constant in a real scientific formula is the “c” in the famous E = mc2. Here, c stands for the speed of light, which even Google knows is around 300 million metres per second. We’ve no idea what k and m are in the pancake formula however, so there is no way of evaluating it.

Even if you could, the construction of the formula contradicts itself. Take the term C(k-C), which obviously has something to do with consistency (no pun intended). It’s one of many terms in the formula that is being taken away from 100, and since we want our result to be as close to 100 as possible, we should probably try and make C(k-C) as small as we can.

Using a mathematical technique known as differentiation, it is easy to work out there is no minimum value for C(k-C), but there is a maximum – when C = k/2. Not much use there, but if we assume that C has to take positive values (after all, what does negative consistency mean?) then C(k-C) is at a minimum when C = 0 or C = k. In these cases, C(k-C) will be zero.

Hang on a second. That means that the formula is telling us that in order to get a perfect pancake, with should either strive for the ideal but unknown consistency k, or alternatively, the worst consistency possible (i.e., zero). That doesn’t sound too tasty. The maths is identical for the T(m – T) term, so a pan cooled to 0 °C will mean you are well on the way to perfection.

So, we’ve got our batter with its terrible consistency, and have just taken the pan out of the freezer. How long should we let the batter sit before starting? The worst thing we could do is leave the batter out for a fraction of a second longer than it takes us to start eating the pancake.

This is because as S and E become closer together, the S – E term will approach zero, causing the equation to balloon to infinity. Sit your batter for 10 seconds and your pancake for 9.999999999 seconds, and you’ll have a pretty awful snack on your hands. Conversely, let that pancake have 10.000000001 seconds rest before you tuck in, and you’re approaching culinary heaven because the minus sign is reversed.

Like most of its ilk, this formula is full of holes that are clear to any mathematician. Apologies if I’ve gone off on a slightly technical rant, but I really cannot stand these “formula for” stories, but what concerns me is that Fairclough actually teaches maths at Wolverhampton, or at least did in 2007 – she’s listed as the module leader for a variety of statistical units. If I were in her class, I’d be pretty worried.


  1. 4 Comments

  2. “This is because as S and E become closer together, the S – E term will approach zero, causing the equation to balloon to infinity. Sit your batter for 10 seconds and your pancake for 9.999999999 seconds, and you’ll have a pretty awful snack on your hands. Conversely, let that pancake have 10.000000001 seconds rest before you tuck in, and you’re approaching culinary heaven because the minus sign is reversed.”

    I don’t think this is quite right (why I’m nitpicking about your excellent dissection of this nonsense I have no idea…) -infinity is just as bad as + infinity, since we’re trying to get the score as close to 100 as possible. Having S and e close together is bad whichever is the bigger. What you want to do is have maximise the absolute value of (S-e). So either leave the batter to stand for a month before you cook it, or leave the pancakes for a few millenia after you’ve taken them out of the pan.

    By John Faben on Tuesday 24 February, 2009 at 12:41 pm

  3. Who employs this woman? (Oh, sorry, University of Wolverhampton).
    I think you could have ‘negative consistency’ though. If optimum consistency is zero then you could have ‘too thick’ or ‘too thin’ as positive or negative values. I’d guess this is what she was thinking – let’s minimise the C(k-C) term, because then the dimensions don’t matter, since C(k-c) = 0 when C = k = 0. Same for T. This avoids your two minima at this point. But she hasn’t taken into account the other terms – if the ‘lumps’ term is greater than the ‘flip’ term (e.g. same number of lumps as flips) then you will need a negative term to compensate – so now you get two minima again, implying either C or T has to be suboptimal. On your assumptions, or on mine, it is still bollocks. Why am I wasting my time on this? Because I love maths and I love pancakes (sprinkle of sugar and lemon juice = TASTY). Ruth plainly has contempt for maths, for pancakes and for maths-minded children, since I haven’t done anything here I couldn’t do when I was twelve. It must be pretty easy to get a Senior Lectureship at Wolverhampton. I think the Press Office at Wolverhampton have contempt for us all, though. And I shudder to think what it means for the standard of their courses.

    By Aspergers Mild and Bitter on Tuesday 24 February, 2009 at 8:02 pm

  4. John: You are correct. If we are trying to get close to 100, then +infinity is just as bad. Even so, the length of time you leave batter/pancake seems to have no relation to reality, according to the formula!

    Aspergers: I don’t know, setting the optimum consistency as zero feels like cheating to me. After all, if k = 0 then why even include it? Go for -C2 and be done with it!

    As an aside, I’ve just finished eating a lemon and sugar pancake. It was pretty yummy. I think that proves my equation.

    By Jacob Aron on Wednesday 25 February, 2009 at 1:54 am

  5. Brilliant! I know it has taken me a while to catch up with the entry but I reckon it’s one of the best!

    By Colin Stuart on Thursday 16 April, 2009 at 9:36 pm

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