Part 3 The Kitchen Formula Calculator v4 & The Logical Structure Of A Recipe

Recipes As Argument Form, The Well-Formed Formula

Baker’s Percentages use weight of flour in a formula as reference point, the “formula basis”. All other ingredients are expressed as a percentage of the weight of flour. In a very real sense, Baker’s Percentages constitute the logic of all bread formula. Strictly speaking, ingredient Baker’s Percentages *are* the formula because they determine ingredient weights.* The Unabaker's Master Formula Calculator* can calculate Baker’s Percentages working in reverse if they are not given, but not giving them doesn’t mean the logic of the formula has disappeared, It only means the formula was not well-formed. If a formula were an argument, then its Baker’s Percentages are (along with the Total Dough Weight, and the ingredients list) its assumptions. Those assumptions function as premises, and the ingredient weights derived therefrom are conclusions. Ingredient weights flow from those assumptions. This is the well-formed formula. Ingredient weights are the logical consequences of Baker’s Percentages, though contingent upon additional assumptions as mentioned. Baker’s use logic to write formulae, though I doubt that many of them think of it quite like this. Numbers are really just a specific type of logical symbol. If they occur in one set of proportions, we get one type of bread, or in other proportion, another type. I might awake one morning feeling like making an argument for Pain au Levain, or perhaps having got out of bed on the other foot, I argued Rugbrød instead. It’s so hard to know which or why, but The Unabaker can be very argumentative like that.

Seeing a recipe as argument form, a set of premisses, that lead to a conclusion helps also to understand the essentials of a formula. We need only assume an ingredient list, the desired yield, and ratios of all ingredients compared to some formula basis. When these are specified, we can deduce practical stuff like how much of each ingredient is needed to produce the assumed yield, but that practical information is a consequence of the assumptions made, and will change when any of the assumptions change. On the other hand, the unchanging logic of a formula are its ingredient ratios. We can make more or less of the product, i.e. change the Total Dough Weight assumption, but doing so changes the quantities of ingredients required, but the logic, i.e. the ratios do not change. The ratios are the same whether we make a handful of it or a hand bagful, until we specify otherwise. What happens if we do that? What happens is we have written a new formula. As soon as Baker’s Percentages change (or we change the ingredients list), we have rewritten the formula. You might argue that this is not logic at all, it’s just simple Mathematics, but in fact, all of Mathematics reduces to logic. In this sense, the Baker’s Percentages, and the ingredients list are truly the essence of the formula, but to make those two things draw a conclusion (in this case, calculate ingredient weights) we need to provide some idea of scale, i.e. how much to make, which is called Total Formula Weight, or for bread craters, Total Dough Weight. To make practical sense of our argument we must assume (i.e. stipulate) a total yield, always expressed as formula weight. We can quibble about whether that makes Total Yield essential or not, but I think most people like to eat an oatmeal cookie, not just design abstract argument forms for “cookieness”. Unabaker loves a smartly crafted argument, but loves eating cookie more.

The argument, if put into words, is as follows.

*Given a dough of specified total weight,*

*and a set of ingredients necessary to make the dough,*

*and each ingredient having been assigned a Baker’s Percentage value, then*

*the weights of the individual ingredients can be determined, the total of which will equal the specified total dough weight.*

Based on a set of assumptions that include Total Dough Weight, an ingredient list, and the stipulated ratios of those ingredients (aka Baker’s Percentages), the weights of those ingredients required to equal the Total Dough Weight can be known. Assume a dough weighs 1000 grams, that the list of ingredients includes flour, water, salt and levain, and we specify a Baker’s Percent value for each, we can deduce all ingredient weights, and know that the total of those weights will equal the Total Dough Weight.

So how does any or all of this relate to kitchen formulae? Let’s see.

The Importance of Cook’s Percentages

Cook’s Percentage is a concept The Unabaker formulated, named, and implemented in *The Kitchen Formula Calculator*, but did not invent. Ingredient ratios exist for every recipe, but may not be thought about by most cooks. Just as Baker’s Percentages are the logic of a bread crafter’s formula, Cook’s Percentages are the ingredient ratios that form the mathematical framework of a cook’s recipe. All of cooking, not just bread making, involves the careful combination of ingredients in ratios, one to another, but for most savory cooking recipes, these are more flexible or suggestive than for baking. Because of the looser tolerances cooking allows, more exact recipes have generally not been deemed necessary. Leeway is built in to a degree determined by Chef. Volume measurements are common because there is leeway. And, since any recipe other than for bread baking and most of pastry shop production is an interactive process from beginning to end, the product can be tinkered with as much as deemed necessary during that process. In-process adjustments are common place. In fact, if you aren’t tasting the stuff, and refining it as you’re cooking, you’re not a very good cook. Imagine Chef swings by your station, and asks how the Coq au Vin is going, and you told him “dunno Chef, but i’ll give it a check since you’ve inquired”. I can tell you this is never the correct answer. Nevertheless, despite the day to day need to veer from the written source, there are advantages to having the mathematical structure for reference. Cook’s Percentages are similar to Baker’s Percentages, but with important differences.

The most significant differences between bread making, much of Bake Shop production, and food preparation in the Kitchen are the degrees of precision required, and quite crucially, the inability to make adjustments once the baking process has begun. You cannot adjust the product once it’s in the oven. Getting it right requires careful measuring, and formulation finesse, plus proper mixing, and portioning methodology. Once it’s in oven, you’re going to get what you get. This is why understanding what are called “process phenomena” in baking is important. You don't get a Mulligan. Baker’s have Baker’s Percentages clearly spelled out in the formula. Measurement, mixing and other processes are followed as precisely as possible, whereas cooks don’t normally consider ingredient ratios as law, and the relevant mixing and cooking processes provide a fairly handsome degree of leeway.

With the advent of *The Kitchen Formula Calculator*, The Unabaker adds a technique for evaluating kitchen recipes according to the logical structure of a formula. Why do we need this if leeway is the kitchen way? Because there are daily changes to kitchen production demand that cause problems, are error prone to resolve, and obscure inherent data that otherwise can be useful. Such stuff as calculating formula yield to match business flow, or the numbers of guests you’ve invited to your house for dinner, as well as, recalculating the ingredient quantities that attend to the changed yield, the cost of ingredients, recipe cost, plate cost, and menu cost, as well as, vital operational stuff like an operation’s Food Cost Of Goods Sold are all vastly easier to compute, and to control. These cost associated aspects of designing a recipe are layers added on by such folk as controllers, general managers, owners, investors, and even home cooks that have to budget food expense. It's a fact of life. Eventually, Chefs have to do costings, and costings always involve ingredient conversions from volume to weight measures. If you start with formulae written in weight measures, the subsequent tasks are all that much easier.

Another point of differentiation involves the concept of recipe or formula “yield”. In popular kitchen recipe writing mode, and even in some commercial operations, the number of *portions* a recipe can make is the same as recipe *yield*. The logic of the formula isn’t apparent, because ingredient ratios are not considered fundamental in the same sense as in bread crafting. A standard recipe found in most popular sources is comprised by a list of ingredients, quantities for each, and the numbers of portions to be expected. This is easy for beginners, but not very educational, nor helpful when comes time to change the number of portions required; a feature of cooking that’s always just around the corner. Correctly understood, just as for a bread formula, a recipe’s yield is identical to its Total Formula Weight, not portions possible. This is because the number of portions derived from the recipe is completely relative to intended use, and varies Chef to Chef.

In spite of such colloquial habit, all food preparations revolve around time tested combinations, the ratios of all ingredients used, one to the other, whether or not these ratios are fully apparent to the cook, and whether or not they are inviolable. If given a recipe, i can easily figure out the ratios of ingredients one to the other, and to the whole, and then expressing these ratios isn’t my imagination. It’s simply calculation. Posting the ratios as an integral part of the formula, and using these to determine ingredient weights is advantageous. Simply because the ratios are meant to be guidelines which good cooks follow, but from which they’re often obliged by taste tests in process to have small changes made to does not mean the ratios are unimportant. Importance is a practical matter, and subjective in any event, but the fact is a recipe can be more readily evaluated, and analyzed according to the ratios of its ingredients which The Unabaker has dubbed “Cook’s Percentages”. In most savory cooking operations, the ratios have hitherto not been specified, but this doesn't mean they aren’t there. Ratios are the logical, mathematical underpinnings of any recipe, whether bread, pastry or kitchen. Bread baker’s simply make these quite clear, and for good reasons to be illumined later. With the advent of *The Kitchen Formula Calculator* these are made clear for all other cookery methods.

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