Interesting, but would it matter if the model can learn the non-linearity?
But these guidelines for how to measure flour by volume are also important simply for historical reasons: lots of the most respected cookbooks measure by volume, not by weight.
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WEIGHING VERSUS MEASURING
For years, chefs, professional bakers, and cookbook authors alike have urged home cooks to become comfortable with a scale, but habits are hard to change. Your mother and grandmother probably didn’t use scales, and you may even have their measuring cups in your kitchen drawer. But using a scale will change the way you cook and bake for the better in many ways.
And the merits of weighing are not only about accuracy: weighing is also more convenient. Weighing is a much easier and cleaner way to measure peanut butter, molasses, or corn syrup, for example—you simply set the mixing bowl on the scale, tare the scale (set it to zero), and measure the ingredient into the bowl, rather than having to scrape it into and out of a measuring cup. And, of course, there is the additional bonus that more than one ingredient can be measured into that same bowl.
Precision matters more in baking than in savory cooking, which is why Sebastien and Matthew provided exact weights, for optimum results. You’ll see that most of these recipes have what may seem crazily specific weights: 519 grams of flour, for instance, or 234 grams of sugar. This is because we converted these recipes from the larger-scale recipes used by the bakery. (This is another benefit of using weights—all recipes can easily be halved, doubled, or tripled, and so on, and they will work.) Do not be intimidated by these specific amounts—when you use a scale, it’s easy to measure 234 grams. However, when converting those weights to volume, we often had to round them off (despite Sebastien and Matthew’s preference that we not). In a short time it should become readily clear why weighing is the preferable route.
We strongly recommend using digital scales, either a bigger one that weighs to the tenth of a gram, or a basic kitchen scale for larger quantities and a palm scale that weighs smaller quantities.
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For cakes, all other ingredients should be measured in multiples of the used egg parts.
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Likewise, eggs vary slightly in weight from one to another; measuring eggs by weight ensures great accuracy. “Large” eggs are 56 grams/2 ounces by definition, but they vary in weight by 10 or more grams, so calling for eggs by weight, as we do in these recipes, guarantees more consistent results. And weighing allows you to use any size egg you have access to, which is especially helpful if you use farm-raised eggs, which are often not graded by size.
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Where baking is done can override volumetric measuring, even with sound, consistent technique. I'm a professional bread baker working at altitude in a low humidity environment. One cup of flour for me will weigh less than a cup for someone in a high humidity area. Parents and grandparents passing down volumetric recipes in the past were unlikely to experience inconsistent baking/cooking outcomes because back in the day succeeding generations were apt to remain in the same geographic area.
But yes, I did not mean to endorse measuring by volume—only that you can avoid much of the problem if you follow proper measuring technique. As I noted in my post, I personally use weights when baking.
As for the historical justification for using volumetric recipes: you’re probably overthinking it if you’re connecting it to geography, and especially if you’re connecting it to altitude. More likely the reason would just be that volumetric measuring was easier and cheaper to reproduce until quite recently. Scales can be expensive, can break, etc. Cups are cheap and durable.
And altitude may be an issue, never had to consider that.
I think there are other factors that affects the amount of flour you should use, such as the ratio of water already in the flour.
If you use fresh flour directly from the mill, you may not need as much water in the dough.
I also imagine the method of grinding the flour may make a difference.