On The Mathematics of Bran Muffins

A truism that I hear repeated frequently that cooking is an art, while baking is more of a science which requires accuracy and following recipes to the letter. I don't think that is necessarily true, I certainly improvise changes to baking recipes frequently and usually with good results. But I think there is an underlying element of truth, which is that with cooking you can generally imagine what will result from a change, whereas with baking it can be much more difficult for us amateurs to predict.

That got me thinking about just how many variations there might be for something as simple as bran muffins. Let's start with a bran muffin recipe I've used before with good success and try to calculate how many ways they could be made. Obviously there are actually effectively infinitely many variations - you could add just one more molecule of baking soda. My goal is to get a rough count of distinguishable variations that a sensitive human could tell apart.

To get started, here are the ingredients:

• 1.5 c. wheat bran
• 0.5 c. yogurt
• 1.5 c. milk (preferably whole milk)
• 1 egg
• 4 T. blackstrap molasses
• 1/4 c. brown sugar
• 1 c. all purpose flour
• 1 t. baking powder
• 1/2 t. baking soda
• 1/2 t. salt

Let's take the amount of wheat bran as a given, and then we can adjust the ratios of all the other ingredients to it. For the yogurt, milk, molasses, sugar and flour let's assume we could use 25% less, 12% less, the same amount, 12% more, or 25% more. Already that is 5^5 = 3125 combinations.  For the egg, let's say we could use 0, 1, 2, or 3, so that is a factor of 4. For the baking powder and baking soda let's assume 4 variations of each, and the salt is assumed to be equal to the baking soda, that's 16 more options.

Of course that is assuming a fixed set of ingredients. We could use cereal bran flakes or oat bran, whole, part skim or fat-free yogurt or sour cream, and the same for the milk, or soy milk, any of a dozen kinds of brown sugar, maybe 4 kinds of molasses and maybe 4 distinguishable kinds of white flour, not to mention that you could whole wheat, or spelt, or teff.. We could use honey or agave nectar or half a dozen other sweeteners. We could add some applesauce for additional moisture. That is 147546 more combinations, not even considering that we could add fruit or nuts or seeds.

Then let's figure that there could be at least 3 levels of how thoroughly we mix the batter, 3 of how big the muffins are (which affects the surface area to interior ratio), 4 types of pans, 6 oven temperatures, and 4 variations of how deeply brown we cook them to, for 784 more options.

That gives us a grand total of 23,135,212,800,000 ways to make a basic bran muffin! 23 trillion ways. And I believe those are legitimate differences, meaning that a reasonably sensitive taster could tell any two of them apart in a head-to-head comparison, and tell you which of the two they thought was better. And if anything, this is probably an underestimate given how conservative some of the assumptions above are.

So what conclusions can we draw from this? I guess one is that there is real value in a recipe. Someone has been willing to put a stake in the ground and say "this is the best bran muffin out of 23 trillion options!" And on the flip side, there is value in experimenting, as there is real reason to believe you can improve your baked goods. Since you clearly can't explore that number of variations, the best way to experiment is hold all other variables constant and change just one thing, like the milk or the type of flour over a few batches, and keep track of which one you like best. Of course that would miss any second-order effects like preferring whole milk with bread flour but skim milk if you used pastry flour. That is just the chance us muffin scientists will have to take!