Saturation, Distillation, Improvisation: A Story About Procedural Knowledge And Cookies

Most propositional knowledge (knowledge of facts) is pretty easy to come by (at least in principle).  There is only one capital of Venezuela, and if you wish to learn the capital of Venezuela, Wikipedia will cooperatively inform you that it is Caracas.  For propositional knowledge that Wikipedia knoweth not, there is the scientific method.  Procedural knowledge - the knowledge of how to do something - is a different animal entirely.  This is true not only with regard to the question of whether Wikipedia will be helpful, but also in the brain architecture at work: anterograde amnesiacs can often pick up new procedural skills while remaining unable to learn new propositional information.

One complication in learning new procedures is that there are usually dozens, if not hundreds, of ways to do something.  Little details - the sorts of things that sink into the subconscious with practice but are crucial to know for a beginner - are frequently omitted in casual descriptions.  Often, it can be very difficult to break into a new procedurally-oriented field of knowledge because so much background information is required.  While there may be acknowledged masters of the procedure, it is rarely the case that their methods are ideal for every situation and potential user, because the success of a procedure depends on a vast array of circumstantial factors.

I propose below a general strategy for acquiring new procedural knowledge.  First, saturate by getting a diverse set of instructions from different sources.  Then, distill by identifying what all or most of them have in common.  Finally, improvise within the remaining search space to find something that works reliably for you and your circumstances.

The strategy is not fully general: I expect it would only work properly for procedures that are widely attempted and shared; that you can afford to try multiple times; that have at least partially independent steps so you can mix and match; and that are in fields you have at least a passing familiarity with.  The sort of procedural knowledge that I seek with the most regularity is how to make new kinds of food, so I will illustrate my strategy with a description of how I used it to learn to make meringues.  If you find cookies a dreadfully boring subject of discourse, you may not wish to read the rest of this post.

I. Saturation

The first step is to collect procedural instructions for the object of your search from many different people, saturating your field of search with a variety of recommendations.  A Google search did it in my case; for more esoteric knowledge, it might be necessary to look harder.  Half a dozen of the more popular sets of instructions tends to be plenty for recipes, but the ideal number could easily be higher for procedures with a wider variance of detail or an unusually high number of people who have no clue what they are talking about.  Here are four recipes for meringues that I referred to and one recipe for meringue pie topping that also informed my learning.  I also got one recipe from a friend.

All of the recipes purported to teach me to do the same thing: turn some eggwhites and sugar (and varying other ingredients) into puffy little cookies.  They varied in such details as: ingredient ratios, type of sugar, other ingredients called for besides eggwhites and sugar, oven temperature, what to line the cookie sheet with, and mentions of other factors such as having a clean mixing bowl or humid weather.

II. Distillation

The second step is to extract what all of the procedures have in common, and decide which non-ubiquitous steps to include.  In this case, I first had to multiply all the recipes to make them call for the same number of eggwhites (since those are very difficult to halve or otherwise adjust, I chose them instead of sugar as my starting point).  All five of the recipes (after this revision) called for four eggwhites; all of the recipes call for either caster/superfine sugar or unspecified sugar1; all of them call for vanilla; all of them instruct me to beat the eggwhites to peaks first and then add the sugar and beat it in.  Four of them call for salt.  Four of them call for cream of tartar.  Most of them call for components like candy and nuts, but since I know that meringues come in a wide variety of flavors (by, for example, reading these recipes) I treat these all as optional.  Proposed oven temperatures/baking times are (200/1.5 hours), (250/30 minutes), (300/25 minutes), and (325/15 minutes).  They vary in whether the cookies are to be baked on a greased cookie sheet, a greased and floured cookie sheet, on baking parchment, on paper towels, or on tinfoil.

A good place to start is to go with the majority: I decided to include both salt and cream of tartar.  Next, I eliminated the impractical: I could not find superfine sugar at the store and I don't own a food processor, so I went with granulated sugar.  As for the rest of the instructions, it was a free-for-all.  No two recipes agreed about the cookie sheet arrangement; the two of them that mentioned "cracking" disagreed on whether it was a desireable outcome; and worst, none of them explained why every time I tried to make these cookies, they refused to foam up and form peaks2.  Time for the last step.

III. Improvisation

A close reading of the more verbose recipes turns up urgent cautions about not letting any grease into the batter, be it a smear from a prior cooking adventure left on the mixing bowl, a bit of yolk, or - in one recipe - the oils that are naturally on skin.  This last, it turned out, was the key: I was separating eggs by hand, and was not very neat about it.  I switched to a technique recommended by a friend involving spoons, and presto, I could get the meringue batter to hold peaks...

But how long to cook them, at what temperature, and sitting on what?  There, it was necessary to experiment (fortunately, after having narrowed the search space somewhat).  This stage depended as much on my personal taste, the local weather, and the behavior of my oven as on the accuracy of the original recipes; it seems that my oven runs hot, so I need to bake them at 250 degrees or cooler and babysit them after the first ten minutes, or they will burn.  Additionally, parchment paper and tinfoil3 wound up burning the bottoms of the cookies before the tops were even dry; paper towels worked.


1Caster and superfine sugar are the same thing, and you can make a reasonable facsimile using a food processor.  When the type of sugar is not specified in a recipe, it means to use granulated white sugar; other kinds are named (e.g. light or dark brown sugar, turbinado sugar, confectioner's sugar, etc.).  This is one of the examples of a situation where background knowledge of the field comes in handy.

2Not that this stopped me from baking the batter anyway.  It just turned into round, flat cookies instead of puffy, light ones.

3I didn't get around to trying greased nor greased and floured bare cookie sheets - I prioritized these tests last because they involve more dishes to wash.

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More generally, it's easier to learn to accurately recognize successful performance of a professional skill than to achieve it yourself. At the very least, you can always taste the cookie, or check whether the program works, or read the prose, and judge how good it is. So, the process naturally starts with training a critic, by observing the successful work by others.

A critic, being a creature of human general intelligence, is able to compare more or less successful performance even at the meager levels of skill, to tell with at least some measure of correctness what choices you need to make at your own level.

This allows to guide you on the steady progression from inaptitude to expertise, every step of the way, a kind of reinforcement learning with the critic rewarding or punishing, with ever finer granularity and contextual generality in its critique.

The worst cooking I have ever had came from a person who seems to lack any sort of ability to criticize food. It's not that she didn't have the skill to be a good cook. She simply could not tell when her cooking was bad. Being a good critic is certainly not sufficient, but it is necessary.

This post raises an aspect of a topic that I've considered, and seems potentially relevant to rationality--how to formalize and train the art of learning, particularly in knowledge/skills that don't reduce simply to the kind of propositional knowledge you can look up on Wikipedia. There's a lot of knowledge out there that could be useful to a rationalist, and at least until Eliezer's secret-knowledge weirdtopia gets implemented we might as well look for ways to climb onto the giants' shoulders. After all, rationality ought to be good for something other than becoming more rational.

Unfortunately, most extant discussions of learning I've seen are written around the perspective of a teacher assuming default passivity from students, and usually are somewhat lacking in empiricism.

how to formalize and train the art of learning

I agree that this is a really interesting question. A couple of half-baked thoughts:

  1. Alicorn's formulation here is basically a search algorithm. The first two stages (Saturation and Distillation) are ways of using existing information to find decent initial values; the final stage (Experimentation) is the stepping algorithm. Thinking about it this way, it's immediately obvious that there's a lot more that could go into this last part: how to carve up the search space, how to decide which direction to step, whether to accept a step, etc. all of which have been explored extensively in other contexts. (Note: I'm not suggesting that this makes the problem trivial, or we should just think about this in terms of existing search algorithm paradigms; merely that thinking about things in this way could provide useful insights.)

  2. One interesting facet of this sort of problem is that the precise mode of "failure" of a particular experiment can give information about where to step next. At a very basic level, you have things like burning, which, as most people will realize, suggest cooking at a lower temperature or for less time. At a higher level, you have things like the failure to form peaks, which, unless you can get more information from elsewhere, or you have a good understanding of food chemistry, you probably won't have much of an idea how to fix.

IMO, it has to involve -- amongst other things! -- personal practice of the sort I describe in the following.

If you want to avoid falling into mental 'traps' (not to make assumptions, not to fall victim to biases, etc), then you have to be able to spot when you are about to, or just have, commited one.

You need a highly-refined "bullshit detector". And it is crucial that you can use it automatically. When you're in the midst of thinking about something you can't just sit back and consciously reason about your own thinking in order to spot every mistake. You have to be really good at automatically spotting them.

If it needs to be automatic then it has to come from practice. So I say get as much practice as you can: anywhere and anyhow.

Always have it as a consicous priority to want to avoid falling into any mental traps. Always consider how what you're thinking could possibly be wrong. The same for anything you hear anyone else say. And in particular, for anything that you read. I always have a pencil with me when I'm reading things and whenever I think I've found someone falling into some sort of mental trap I try to note the details of it.

(This is about having a pretty constant critical attitude but it doesn't mean being a jerk who has a negative outlook on life, or who needlessly attack others' views in public, or who shows off by pointing out mistakes, etc.)

Over time, you'll build up a more substantial toolkit, and those capabilities will become more automatic.

Curiously, this is pretty much what I normally do when learning new procedures, but being aware of those S.D.I. steps in a more explicit manner seems to be useful in terms of having a less hesitant, "what the heck should I do next?" attitude when about to do something.

I liked it. Very good procedure to learn new procedures.

I guess I'm not seeing the distinction between propositional and procedural knowledge. I get that people don't always realize what all the little steps they follow are (or their significance); but things like "Don't introduce any grease into the batter, or peaks will fail to form" are propositional knowledge, are they not?

(or from my own baking experience: It's very important to CUT the butter into scones, but a large percentage of recipes will fail to mention that.)

The phrase "non-propositional knowledge" brings to my mind things like Zen Buddhism...

(EDIT: If you're saying procedural knowledge is a subset of propositional knowledge, then I have no qualms...)

Procedural knowledge is often initially constructed out of propositional knowledge. But once procedural knowledge is had, it also incorporates things like body memory and pure automatic habit, which, when observed in oneself, are just as likely to be rationalized after the fact as they are to be antecedently planned for sound reasons. It's also easy to forget the initial propositions about a mastered procedure. I am likely to forget why I separate eggs with spoons at some point, until and unless I decide to go back to doing it by hand and get the corresponding poor results: I will just reach for the silverware drawer and set about separating eggs. (This is probably a bad example, since by mentioning in the post above my reasons for changing methods, I've cemented those reasons in my mind. However, I'm sure there are a dozen things I do automatically in the kitchen that have no cognitively occurrent relationship to the reasons I started doing them in the first place.)

Here's possibly a better example of procedural cooking knowledge: salt.

Indepdent of the perceived "salty" flavor, low levels of salt in food have the subjective effect of bringing out other flavors. Undersalted food will smell good, but taste mysteriously flat and bland. On the other hand, too much makes the dish taste actively salty, which is often not desired.

A cook with some degree of skill and practice will usually have an intuitive grasp of how much salt to put into a dish, depending on the size of the batch and the saltiness of other ingredients. This is a key skill for cooking, but nearly impossible to communicate propositionally, which is why when a novice cook asks me how much salt a dish needs I end up waving my hands around and saying "Uh, however much is enough!"

But once procedural knowledge is had, it also incorporates things like body memory and pure automatic habit, which, when observed in oneself, are just as likely to be rationalized after the fact as they are to be antecedently planned for sound reasons. It's also easy to forget the initial propositions about a mastered procedure.

I've also noticed this kind of thing in my martial arts training.

For instance, often times high level black belts will be incredibly successful at a particular technique but unable to explain the procedure they use (or at least, they'll be able to explain the basic procedure but not the specific detail that makes the difference). These details are often things the practitioner has learned unconsciously, and so are not propositional knowledge for them at all. Or they may be propositions taught long ago but forgotten (except in muscle memory).

The difference between a great practitioner and a great teacher is usually the ability to spot the difference that makes a difference.

Thanks, that makes your point much clearer.

Perhaps another example is learning to drive a stickshift; it seems no amount of talking will help someone find the sweet spot on the clutch any faster.

I think the clearer examples (of procedural knowledge) tend to be things like physical skills that we can learn to reliably perform, but without necessarily being able to articulate how it is that we perform them. In that sense it wouldn't be accurate to say it's simply a subset of propositional knowledge; it's more that the two may intersect to some extent, and the boundaries of each can move as we learn to articulate what it is that we're doing, or to think about what we're doing in propositional terms. (EDIT: or, as Alicorn suggests, forget the propositional reasons why we did things a particular way in the first place.)

The classic example of riding a bicycle comes to mind. No amount of propositional knowledge will allow you to use a bike successfully on the first go. Theory about gyroscopic effects of wheels and so forth all comes to nothing until you hop on and try (and fail, repeatedly) to ride the damn thing.

Conversely, most people never realise the propositional knowledge that in order to steer the bike left, you must turn the handle bars right (at least initially and at high speeds). But they do it unconsciously nonetheless.

I tend to view procedural knowledge as being infered from propositional knowledge. You have the map (propositional), draw the route (procedural) and then store/transmit essentially only the route without the map (the how without all of the justufucation, although some does leak in). Mentions to automatic habit etc. can essentially be considered caching that persists even after the propositional knowledge has been discarded.

I view Alicorn's method as essentially 1. gathering a lot of (procedural) routes to similar goals, 2. reverse-engineering propositional knowledge from them by using (mostly) voting and 3. adding extra knowledge through experimentation and the current circumstances. This arrives at a new procedure that reaches a goal in cookie-space that is satisfying to Alicorn's taste, constrained resources available to her, in short, an Alicorn-optimized procedure.

First, saturate by getting a diverse set of instructions from different sources. Then, distill by identifying what all or most of them have in common.

Distillation may be relatively simple for recipes, but in general it could be extremely difficult. Effectively having to come up with either a common language for all the ways of conceptualising the subject matter, or some sort of universal translation mechanism, which are notoriously difficult types of tasks.

Or perhaps not. Maybe you don't need a perfect means of distillation, just something rough but useful. It's hard to know just from recipes example.

(when I say 'some sort of universal translation mechanism' what i mean is, something that applies to all the different sets of instructions for performing that task, not something that applies to any instructions for any possible task)

This may be another situation in which background knowledge is important. Let's take another example besides food; say I'm learning to play the piano. Trying out several different methods could trip me up if one relies on solfège, one relies on note letter names, two use staff notation (one starting the introductory lesson in treble clef and one in bass), and one does everything by showing pictures of a pianist's hands on the keyboard. It would be important to know how all of those ways of representing notes correspond to each other, so they can be interpreted in whatever way is most accessible. That, however, is propositional knowledge, much easier to come by.

I think transfer of mental models is often crucial for efficiently learning new procedural knowledge. Your skin oil problem is only a small example. Consider for example the task of adding up to numbers, the task of computer programming, or the task of designing a mechanical structure. Once you have been told about decimal places and carry, about memory and variables, about stress and strain and whatnot, reasoning about your problems suddenly becomes a whole lot easier and more successful.

Depending on the problem domain, supervised learning from an expert or the procedure in the post might be more appropriate.

I find it interesting that you chose cooking as your example, because this is exactly the technique I use when trying to learn how to cook something I've never done before.

This is more or less my technique as well. Sometimes I use a slightly different version:

  1. Saturation

  2. Fermentation: I form old ball theories explaining my new knowledge until I come upon one I like (completely unscientific)

  3. Test.

I'd say half of my cooking adventures turn out badly... but the other half are quite edible. My worst attempt, by far, has been sauerkraut. Anything that involves genuine fermentation is probably something that isn't going to be figured out so easily with half-baked search methods.

Little details - the sorts of things that sink into the subconscious with practice but are crucial to know for a beginner - are frequently omitted in casual descriptions. Often, it can be very difficult to break into a new procedurally-oriented field of knowledge because so much background information is required.

I've been quite interested in how you can extract this implicit information - and make it explicit so it can be taught.

People who already know how to do something tend to be no longer aware of all the little things they learned as they were developing that capability. They may never have been aware of picking up some of those things in the first place.

One possible strategy would be to pay close attention when you're teaching a newbie (like in a face-to-face class or tutorial). If they are having trouble or are getting stuck, consider what it is they're missing. When you're helping them out, is some part of what you're showing one of these things you take for granted and don't explicitly teach?

I also think the simple effort of explicitly paying attention to what you know and how you perform the task would help.

People who already know how to do something tend to be no longer aware of all the little things they learned as they were developing that capability.

On the other hand, people with lots of experience teaching newbies often have quite a detailed knowledge of the most common failure modes for beginners, and can be very useful for precisely this reason. As a second best, people who have only recently learned how to do things often remember their own learning experience sufficiently well to be useful (provided there aren't so many distinct failure modes that their individual experience is unlikely to be representative).

My advice for cooking is to choose a cookbook intended for beginners that includes a lot more information than just recipes (eg, the Joy of Cooking). This might generalize to other fields. The concept of a recipe is so clear that it's easy for a beginner to recognize a book doing something else; this may not be so easy in other fields, even if the beginner thinks to look--and people don't seem to look for cooking instruction beyond recipes.

This kind of knowledge is very easy, as it's cheap to experiment, there is little randomness, and it's easy to measure outcomes.

A more difficult case of procedural knowledge acquisition problem: seducing women.

Go try to figure out how to make great sourdough bread from information you read on the Internet. You'll find there's tons of information, written by people that know what they're doing and have had success doing it, but it's still damn hard to learn how to get it right yourself.

It's easy to experiment if you know what to change. Having a variety of recipes will suggest things to change--like time/temperature combinations. But I see a lot of variation in how well my eggs whip. It never occurred to me to worry about oil from my hands. (and I doubt that's my problem, but at least it's something new to try)

It's easy to experiment if you know what to change. Having a variety of recipes will suggest things to change--like time/temperature combinations.

And sometimes relevant parameters are nonobvious to a non-expert. Consider whipped cream, a task superficially similar to making meringues; oils clearly don't matter, since the substance you are whipping is itself roughly 40% fat. On the other hand, local ambient temperature matters a lot--the cream won't stiffen as well if it is warm, so using a chilled bowl can improve results.

Continuing the cooking theme, other subtle factors can be the acidity of various ingredients (important for chemical leavening), the ambient humidity, and even the local ambient microbial life--the flavor of sourdough breads, lambic beers, and certain cheeses are dramatically influenced by local microbes, to the extent that certain strains of yeast and bacteria share the names of the region that is known for their flavors, cf. Penicillium roqueforti, Brettanomyces bruxellensis, and Lactobacillus sanfranciscensis.

I think you have this backwards: cooking experiments are more expensive. Talking to people is free, ingredients aren't.