The Kitchen Formula Calculator v3

Part 2  The Kitchen Formula Calculator v4 & The Logical Structure Of A Recipe

The Essential Elements Of A Formula

What is a recipe? There’s more to a recipe than meets the eye. There’s an unseen mathematical framework for any recipe. A basic understanding of "recipe" imagines that if you write down what you do when you make Pork Green Chile, that you’ll have a list of all the ingredients required, how much of each, and a given methodology for what to do with the stuff. If you do this, you’ve written a recipe. That’s the common sense understanding of “recipe”, which is true enough, but not enough. This understanding has limited practical ramifications. If you have a way to analyze the Pork Green Chile recipe to determine what are the ratios of each ingredient to the whole, you can understand it more clearly. You can also analyze any other recipe by entering it in The Kitchen Formula Calculator. Obviously, it’s useful to keep a record of recipes from great Chefs, and other reliable sources. The calculator is a way to organize, and store these things. Determining ingredient ratios is a very easy calculation, but cooks don’t do such stuff, and few understand the word “recipe” in these terms. Ratios exist, but they aren’t specified. For the most part cook’s don’t even think about it. They know about ingredient balance, and understand the concept of ratios of course, but not what can be done with the actual ratios if calculated. That’s why The Unabaker devised a Reverse Engineering calculator as part of The Kitchen Formula Calculator.

These ratios are what The Unabaker calls “Cook’s Percentages”, and to be precise, the answer to the question is: a recipe is its mathematical structure, viz. the ingredient ratios expressed as percentages of the whole. A recipe is its Cook’s Percentages. Just as Baker’s Percentages are the mathematical framework for bread formulae, Cook’s Percentages is a concept used in The Kitchen Formula Calculator to provide for all recipes that are not bread the same sort of mathematical logic that Baker's Percentages provides for bread formulae. By this definition, given a list of ingredients, and a Cook’s % value stipulated for each, and a Total Formula yield, defines as total weight, you’ve written a recipe. Ingredient weights for a cook's recipe are, exactly as for a bread maker's formula, merely derivative data, determined by comparing an ingredient's stipulated Cook’s % to the total weight of the formula. It’s a simple equation. 

Ingredient weight = Total Formula Weight x Ingredient Cook’s Percentage

Methodological notes are obviously a practical necessity, but when we talk about a recipe, it’s really talk about a “formula”. Methodological notes are words. Formulae are written in symbols. The cook’s recipe consists of the ratios of an array of stipulated ingredients to the whole. The formula consists of the Cook’s Percentage of each ingredient added together to equal the Total Formula Cook’s Percentage (which is always 100%). If a stipulated Total Formula Weight is given, then the formula can be applied to derive all the individual ingredient weights. 

Methodology simply informs the cook about mixing and handling. Often the “methodology” isn’t necessary to express. All of my old Pastry Shop recipes are simply lists of ingredients, the corresponding quantities specified, and a stated yield. “Yield” in a very casual sense means how many portions it makes. This is how my Pastry Shop formulae expressed the concept of yield. The Cheesecake formula makes seven 10” cakes. Experience, and repetition, teaches the aspiring pastry cook what to do with this basic data.

As a mathematical fact, any change to any of the ingredient ratios, by which I mean the ingredient’s Cook’s % value, produces a completely new recipe. The change may seem slight, but all of the other ingredient ratios update to reflect a change made to the single ingredient. The same thing does not occur if any one of the ingredient quantities is changed. No other ingredient quantities change. Only the recipe yield changes. On the other hand, a singular edit to any ingredient Cook’s % value changes all the other ingredient Cook’s % values. Why does it do so? Because unlike a bread formula that uses the weight of total flour as the formula basis, and the Total Formula Baker's Percentage will always add up to more than 100%, the cook's recipe has no such singular ingredient. The formula basis of a cook's recipe is the Total Formula Weight, and therefore the Total Formula Cook’s Percentages must add up to 100%, never more, never less. “Cook’s Percentage” is defined as an ingredient’s percentage of the whole. The whole is 100%. It’s clear that the ratios of ingredients in a recipe, i.e. their Cook’s Percentages are the formula. Any change to an ingredient ratio in the Pork Green Chile recipe, no matter how slight, amounts to a new formula for Pork Green Chile. You have written a new recipe. 

This sort of incremental tweaking of ingredients is a natural part of what happens after a recipe is written. The cook carefully prepares the mise en place for the recipe, then tests the recipe by cooking it up. This is called a “cook test”. One makes notes of any changes to ingredients, time, and temperatures made during the test. After which, the cook updates the recipe by revising the affected variables in the calculator table. If the Chef is satisfied, the updated recipe is entered into the Kitchen Guide.

The actual ingredients list, and the quantities of ingredients used to make Pork Green Chile are flexible, reflecting a cook’s style, preferences, local tradition, or whim. If you change ingredient quantities, but retain the ratios of each to the other, you’ve not changed the recipe, you’ve simply changed the yield. To change a recipe, you have to change the ratios of ingredients, or change the list of ingredients, or both. Ratios are the mathematical superstructure of a recipe. Ratios are recipe logic.

I will write more extensively about Cook's Percentages compared to Baker's Percentages in a subsequent installment, but first some detail about the structure and  logic of bread formulae.

The essential elements of a bread formula include the ingredients list, and the Baker’s Percentages specified for each ingredient. However, to calculate ingredient weights, we must specify a Total Dough Weight (TDW). Total Dough Weight is what bread makers mean by “yield”. The numbers of portions a recipe can make is not the same as yield because portion sizes change one cook to the next, one shop’s need to another. Yield is strictly understood as Total Dough Weight, TDW. Consequently, professional bakers understand what is a recipe as follows.

A formula is not more than a list of ingredients, the baker's percentage specified for each, and a desired yield, expressed as the Total Dough Weight. 

Ingredient weights depend upon what Baker’s Percentage the Chef has specified for each. This is how bread formulae are written.

How are the ingredient weights calculated, and why is TDW an essential in bread formulae, but not considered so in kitchen formulae? First of all, to calculate ingredient weights, the Total Dough Weight must be given, and the reason it must be given is why it’s essential. All ingredients in a formula are compared to the amount of flour in the formula to calculate their weights. All ingredients except the flour ingredients. We cannot derive weight of flour ingredients used by comparing it to itself. Instead, weight of flour required is derived by referencing the Total Dough Weight divided by the total value of the formula Baker’s percentages which always add up to more than 100%.

Note also that the flow of the formula calculation is from the specified ingredient Baker’s % to the ingredient weight. Weight is derivative data, it is not the same as the formula, and therefore it is fundamentally not an essential element of a formula. It is practically significant of course, but as weights of ingredients change according to whatever Total Dough Weight is specified, it’s conditionally relevant only. The crucial stuff are the Baker’s Percentages. Baker’s Percentages are the formula. These do not change unless we desire to change the formula. If we change the Total Dough Weight we haven’t changed the formula, we’ve only changed its yield. A formula is quite simply a list of ingredients, specified ratios of those ingredients, and a yield desired. In bread craft, flour is the basis for specifying ratios. In the kitchen, we shall soon see that specifying ratios is quite different. Nevertheless the ratios are the fundaments of the kitchen formula just as for a bread baker’s formula. 

The stipulation of a recipe's Total Formula Weight  ( or Total Dough Weight) makes “proving” the formula quite easy. If the total weight of all ingredients equals the stipulated Total Formula Weight, then the formula is true. Conditions may change, but a formula does not change unless the ratios change. You might be inclined to think the recipe for your favorite cookie is the collection of words and numbers used to spell it out, but as has been noted, there’s an underlying logic to cook's recipes (which include almost all of Pastry Shop formulae), the ratios of each ingredient to the whole that these numbers represent. If the logic is made clear, then it’s easy to see that these ratios are the formula, and to understand that the volume or weight yield of the formula is a conditional specification that can change. Nevertheless, simply by changing the formula yield the only thing that changes is the weights of all ingredients needed to match the newly specified yield. The ingredient ratios remain constant no matter the yield specified. Thus, ratios drive the formula; they are the formula, whereas ingredient quantities are (when a formula is well-formed) always derivative values. For professional bread baker’s, to specify the ratio is to stipulate a Baker's Percentage for each ingredient. In the kitchen, recipes are never written like this because the idea of ratios, though important, are never spelled out. It doesn't mean they aren't there, it's just a matter of how different kitchen cooking methodology, and crucially, the adjustability of a recipe during the cooking process is from the bread baker's world. More about this in a future installment.

Now, with the advent of The Kitchen Formula Calculator, The Unabaker has formulated Cook’s Percentages which can be used to do the same thing for cook's as Baker's Percentages do for bread bakers. What yield may be required is a data point to be determined daily, depending upon anticipated sales volume (or personal consumption needs for home cooks). It is a precondition that will, as a consequence, effect ingredient weights, but the formula is still the formula until the ingredient Cook's Percentages, i.e. the ratios change. The fact of this is evident, but the practice of recipe writing for kitchen preparations has never made it so. As a result, there’s an on-going problem for upscaling or downscaling the yield required. This is the reason The Unabaker spent time developing the system of Cook’s Percentages. It solves the problem. 

If a professional well-formed formula is fundamentally only two things, a list of ingredients and their specified ratios (baker’s or cook’s percentages), by contrast, popular sources of recipes usually consist of three elements: the ingredients list, volume measures (or combinations of volume and weight measure) required for each, and the numbers of portions one might expect assuming basic skills. This of course confuses formula yield with the number of pieces of it one might be able to get. A commonplace recipe begins by telling the user how many portions it will make, then the appropriate ingredients, and their quantities follow. For amateurs, the preparation and the baking methodology is tantamount to being a fourth formulaic element, whereas in bakeshops, process methodology, if stated at all, is scant. You need to know how to make Buttercream or Brioche. In any case, it's not formulaic, it’s the stuff of years of training, and of learning by doing, and by observing various expert Chefs who may well have different methodologies. My handwritten Pastry Shop formula guide from 1979 is full of lists of ingredients and measurements, almost no methodology. I had to pay attention to my Chef, practice, practice, practice, and since they were paying me to do this stuff, I was expected to get it quick. Understanding process phenomena and methodological aspects of executing a recipe is not formulaic stuff, it is experiential. It has nothing to do with the formula itself, but everything to do with practice. 

One final note regards an interesting feature of bread formulae that sets it apart from all other types of recipes. Baker’s want to know about the expected dough feel, it's texture, and what sorts of bread can be expected from a particular dough formula. To understand that, they evaluate the amount of water in the formula. More or less of which changes the dough in ways beyond mere dough feel. Hydration is an important factor in other process phenomenon such as the organic acid profile that’s developed during fermentation, a primary determinant for the taste of bread, as well as, the specific micro-biome the dough nourishes. Bread maker’s refer to a dough’s Hydration Percentage. Hydration Percentage is the ratio of the weight of water compared to the weight of flour in the formula.  It can be calculated by dividing the weight of water by the weight of total flour. In a simple formula like for classic French bread (aka Pain Ordinaire), one needn’t calculate since it’s a stipulation the baker has written into the formula. You can see it at a glance. The Baker’s % of water is 65%. Understanding from experience what level of hydration is required for the various types of flour used, and the type of product the formula is designed to make, it’s organic acid profile, the specifics of the dough micro-biome desired to exhibit a unique organoleptic character is an advanced bit of bread crafting, and a way that the very best artisan bakers can design a “signature” loaf, much as a knowledgeable and skillful Barista can profile the “god shot”, making it distinctive from his pals and competitors. Hydration is an important metric, but it’s not a fundamental element of the formula, it’s an analytical evaluation, a way to understand what the formula will do. Knowing the hydration percentage of a dough is of tremendous practical value as it’s one of the chief things bakers tinker with when they’re developing a new bread formula, or refining an existing one. In bread craft, the ratios, aka Baker’s Percentages, are the fundamental, essential elements of the formula. In all other kitchen departments, using ratios to calculate ingredient quantities hasn’t been done before, therefore the notion that the underlying ratios are essential had not quite dawned, until now. The next installment in this series looks at recipes as an argument form.