Consider both the audience, and the materials available.
Most premodern cookbooks were written by professional cooks, for professional cooks. So they often didn’t feel the need to walk their peers through every step- as there were many things that they would expect any other cook to already know. Each cook learned their art through working with more established chefs- and in theory should not need to be told how to judge if a food is ready to eat, or the exact right amount of seasonings. Contrast this with today’s recipes, which are most commonly professional or amateur cooks writing for amateur cooks, and so they assume only basic knowledge. Although when the pros write for other pros today, they can be extremely specific, due to what I’ll talk about next.
Second, both the cooking supplies and the foods could be very inconsistent. If you’ve ever seen a painting of raw foods from bygone eras- they often looked very different. (Such as Giovanni Stanchi’s 17th century watermelons, which barely look edible compared to today’s bright pink seedless melons). Modern food production is very standardized and relatively consistent, so we can have precise recipes that work out, because generally cooks know how big certain products will be and what flavors and the potency they will have. But if one cook is writing for another cook in another place, working with potentially very different products, telling them to use three carrots in a dish can be somewhat unpredictable- maybe they are bigger or smaller or of a different tasting variety that has long since stopped being widely available- so the idea is that if the recipe has carrots, the cook should use his good judgment to determine the appropriate amount for however many servings he will make.
Third, modern cooks, both amateur and professional, have the advantage of consistent heating elements. The gas stove was a 19th century invention, so anyone before that was largely limited to putting their pots and pans over fires/hot coals, or into an oven- and for all of those it was difficult to maintain a consistent temperature. So there’d be no sense in writing “fry the onions for three minutes” or to “bake the cake for 35 minutes”. Any cook worth his salt should know what fried onions or a baked cake should look like- so a lot of recipes sound more like “cook until done” without explicitly saying what that means.
Anyway, much like Medieval cookbooks I’ve been a bit vague so far, so here’s a more concrete example of how this works. This is a recipe for “Gallina Dorada” (Gilded Hen) from Nuevo Arte de Cocina (1746) by Juan Altamiras, a Spanish friar and cook. (obviously this is from after the medieval period, but it is a recipe that was old then, and I think still reflects the cookbook writing mindset leading to OP's question).
“Take a well-fattened hen, cut off its feet, wing tips and neck, clean it well and boil it in your stewpot for meat. When it is tender, fasten it on the spit. Now wrap a little lump of cured ham fat in paper, spear it on the point of the spit, set fire to the paper and hold the spit upright so the melted fat drips down all over the hen. Crack open four eggs, beat their yolks, paint them on your hot hen and, as it roasts, add sugar and cinnamon, or just cinnamon. You may serve the broth first as a soup spiced with cinnamon and take it to table before your gilded hen. This is a good dish for capons or other birds too.”
The recipe doesn’t tell you how big a hen you need, how long exactly to boil or to roast it, how much lard, sugar or cinnamon to use. But yet, it still largely makes sense. The amounts of those other ingredients depends on how big a hen you have (or if you use another bird entirely), or how much you like the taste of cinnamon sugar on chicken (spoiler alert, my SO did not like it at all when I made this). Similarly, there’s no time given, but… it’s a chicken. Boil it until it is cooked, then take it out- with the inference to be made that you don’t need to roast it for very long, just long enough for the egg, lard, cinnamon sugar glaze to set. Depending on your fire, that time could vary, but hey, you can serve some nice chicken broth to your guests while you work on that.
How many online recipes have you glanced over, knowing that you'll probably never make them? How many times have you sighed and swiped or scrolled down, down, down, down past the story of the blogger's great-aunt's best friend's sun-dappled terra-cotta kitchen floor? Cookbooks, as scholars have long recognized, are a literary genre of their own.
That doesn't mean that medieval cookbooks were exclusively in the "read for fun" category. In medieval/early modern German lit, we'd call them a subset of Sachliteratur--mostly instruction books/books about practical subjects. But what kind of practical use, and how, definitely differed. And medieval reader-users were not just looking for directions from their cookbooks.
One important use of cookbooks was actually medicinal. Medieval medicine was based around the idea of keeping a balance of the four humors in the body, a balance that needed to be maintained and fixed including through the ingredients and preparation of food. So cookbooks as diverse as Ibn Sayyar al-Warraq's from 10C Baghdad and Anna Weckerin's in 16C Colmar (which enjoyed massive popularity in print) stress very heavily the possibilities of some of their recipes to help cure the sick. (And also, in Weckerin's case, "[Here is the section] about fish, but these don't help sick people and are of little use.")
Another use, particularly in medieval Christian Europe, was to show cooks ways to change up meat dishes for Lent, like the 14C Italian cookbook that suggests substituting ground-up almonds for the meat in a lasagna recipe.
With purposes like those, exact amounts are sort of beside the point--it's a different type of instruction being sought and offered. In general, though, the lack of precise quantities and time frames reflects modern cooking practices, just not modern cook books. Look at any 5-star recipe on allrecipes.com, and the comments/reviews will say "This is the GREATEST RECIPE! All I had to do was halve the amount of flour, add 10 minutes more of steeping the duck breast in the mixture of spices, oh and I added saffron and honey to that mixture, and...seriously, THE BEST food I have ever had."
And people were generally not working from nothing--these cookbooks aren't a matter of someone getting into a new cuisine entirely. Massimo Montanari remarks that many medieval cookbooks were aimed at experts; not necessarily professionals, but people who do know the basic methods and ingredients available to them. The cookbook did not exist in a vacuum. It united with the cook's personal experiences and in-person instruction/experimentation to create what we would consider a "full" recipe.
And then, of course, there were the fancy, even illuminated cookbooks that served exactly the function of our blogs and bookmarks today: a marker of aspiration and social status. I am [want to be] the sophisticated, open-minded person capable of cooking and enjoying all these foods. No mind that the only way I will ever actually eat them is if I pay someone else to make it. [whether a servant or a restaurant chef].
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While you're waiting, you might be interested in these threads:
Were medieval chefs highly prized by monarchs? Did they have a chef's guild or anything similar where they hid their recipes? by /u/picklepeep
Why are historical cookbooks so crap? by /u/snackburros
It should be noted that the practice of providing exact instructions and measurements dates can be traced back to a particular school, the Boston School of Cooking, which was the product of a greater social movement which aimed to codify and elevate traditional women's work into "domestic science."
You might complain about the lack of amounts, instructions, and times on ancient and medieval recipes - people like Fannie Farmer, born 1857, had the same complaints. A chef at the Boston School of Cooking, she authored a cookbook in 1896, The Boston Cooking-school Cook Book, which provided not just a standardized system of measures - she was known as "the mother of level measurements" for her insistence that measuring-cups be levelled - but also a distinct approach that emphasizes the chemical and physical aspects of food. This cookbook vastly outsold its initial printing, and was still in print at of 1990, over 100 years after its initial publishing.
Many social developments of the 1800s and early 1900s changed the way Westerners see food, cooking, and the traditional roles of women which led to this more standardized and scientifically-minded approach to cookbookery. The industrial explosion in cities changed how most people worked and live, leading to the development of what we today call the "separate spheres" ideology. Men belonged to the public sphere, working outside of the home and subjecting themselves to strenuous physical or intellectual work for which he would be paid a salary. Meanwhile, women belonged to the private sphere, and was responsible for creating a peaceful, beautiful, and morally ideal place for a man to escape the pressures of the outside world and in which to raise healthy, morally upright children.
Developments in the physical sciences were also a major influence. Newly developed preservatives, colorants, flavoring agents, and fillers were added to foods, which were more and more processed in industrial settings, calling into question the purity and health of these new foods, and rightly so, because a lack of oversight and regulations combined with the drive to maximize profit meant many foods contained wonderful additives like arsenic for color. (Worth reading more about people like Harvey Wiley, who fought for the Pure Food and Drug Act) Meanwhile, to address the pressure from women's advocacy groups to widen the scope of the "private sphere" and allow women to participate in public life, we see the creation of the new science of "home economics," a field of science which aimed to perfect and standardize tasks like cleaning, child-rearing, and cooking using scientific knowledge and methods. Ellen Richards, the first woman ever admitted into MIT, was a pioneer in this field, which emphasizes the importance of what might have once been dismissed as women's work (without challenging women's assumed role as homemakers).
Fannie Farmer, too, worked in this field, making domestic work into a trade or field of knowledge taught in schools, rather than something passed through word of mouth from mother to daughter. Farmer's approach might be attributed to how late she arrived to the art of cooking - she was one of four daughters and cooked rarely as a child. She probably would have become a schoolteacher, but after an illness (probably polio) left her permanently weakened and with a limp, she instead turned to working as a helper in a family friend's house, and began to learn to cook at the age of twenty-eight, enrolling in the Boston School in 1887. There, she learned to cook not with the cups, bowls, and spoons available in her mother's kitchen, as so many did before her, but with the standardized measuring cups newly available at the school. Her aim with her cookbook was to create recipes that could be recreated by anyone, anywhere, at any level of knowledge. Her approach was massively popular, and she later went on to run the school, and even later founded her own school, Miss Farmer’s School of Cookery, which unlike other cooking schools (like the Boston School) aimed specifically to train housewives, rather than professional cooks or servants.
I hope this helps provide some context for your question by reframing it - rather than asking why ancient or medieval recipes were so vague, we might wonder why they evolved into the exact measurements and times we have today, and when this change happened.
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