This year I have been trying to draw more. I haven't been very consistent, and as a result I haven't actually improved at all even though that was my original goal. One of the obstacles to drawing for me is something that comes up in my life quite often, which is that I spend too much time trying to think about what would be the "optimal" way to learn a task, or the "optimal" way to go about doing it. As a result I've spent a lot of time this year also thinking about drawing instead of actually drawing. However, this morning I had a thought that might be useful to people other than myself so I thought I'd record it.

Something I have been kind of worrying about is the prospect of drawing a lot without improving. To this end I waste a lot of time trying to look at other people's drawing improvements. For example, there are a ton of examples on Youtube. There are also lots of drawing classes that advertise student results, so you can see how much improvement there was before and after. If you do this exercise, you will find that there is extreme variation in improvement, but the average (if you try to avoid selection bias) seems to be quite low.

For example, one popular free drawing course is drawabox.com, which is infamous for basically making people draw a ton of boxes and cylinders (I think 250 of each). Reading people's experiences with this kind of suggests some of the obstacles to improving. For example, I have read claims that this challenge is excessive because people have spent a year on this and got demotivated. When you think about this, it's patently ridiculous. Even if you try very hard, it probably does not take more than five minutes to draw a box, so the time it would take to complete the challenge should be like 1250 minutes, or something like 21 hours. If you draw for an hour a day, that would be less than a month. But it doesn't take five minutes to draw a box because you get quicker as you practice. If you draw five boxes a day (which really doesn't sound terribly onerous) you would finish in a bit under two months. So the first obstacle to improvement seems to be not drawing. This makes sense to me since I spend a lot of time engaged in not drawing and I'm not improving.

However, the group of people I found a bit disturbing were the people who finished the challenge and seemed to still be bad. On the discord you can find a channel only open to people who have verified their completion of the course by submitting their assignments for each section, but a lot of drawings posted in there seem to still have issues with things the course is supposed to correct. Namely, they look flat. Since the point of the course is to learn how to construct drawings out of primitive 3d forms, it would appear that people who still have this issue have basically learned nothing, and the improvement they had was mostly just due to getting better at controlling a pen or stylus.

Once you start looking, there are lots of places where people share their improvement journeys (maybe because these days everybody wants to be a content creator) and as long as you look for people who aren't successful and going viral for their extreme improvement, there's a ton of examples of people who seem to be drawing consistently and not improving. This is kind of alarming to me because I suppose I am anxious about the future and unwilling to do things without "guaranteed" results¹. What might account for this difference?

You have to think

Some clues might come from looking at people who did improve and trying to understand the difference between what they did and what our sample of non-improvers did. There are two Youtube channels that I think are pretty good examples because they actually had quite noticeable and quick improvement during the period that the channels have been active, and also they have good introspection into what made their process work. The first is Can I Learn to Draw? and the second is 10,000hrs. When we combine these sources with our negative examples, I think that's kind of the missing piece to understanding why some people improve and others don't.

One of the main things that I've noticed is that they tend to have a critical eye towards the specific skill they are trying to practice at a given time. For example, in old videos on the Can I Learn to Draw? channel from when he was just starting (six months) you'll notice that sometimes he would draw the same subject five or six times, even when the exercise was to produce a simplified mannequin that doesn't look that much like a real person even if you do it perfectly. It seems that by doing this kind of repetition you would be trying to train a mental skill rather than trying to draw a picture a certain way. On the other hand, as he points out, some of the people posting drawings for critique on the website for the course he was taking seem to be trying to speed through the content by only completing copies of the instructor's examples, which would seem like they aren't really trying to integrate the underlying way of thinking and seeing that you need to produce the drawing that the exercise demands.

I have noticed that some drawing tutorials propose a construction method for the head, say, and that a lot of people who do not improve at drawing like to repeat these exercises endlessly, making a bunch of portraits that don't really look like the subject. I think what is probably failing here is that they are in some sense mechanically following a series of prescribed steps and never developing the correct idea of what a head looks like and what the underlying structures being simplified by the sphere (for example) actually are. As a result, repeated practice is mostly just practice in drawing lines in a certain order rather than practice in representing a subject as a drawing.

So while it seems quite harsh, it seems like one of the obstacles to improvement is just simply not thinking about what you're doing. A simple example that this phenomenon is definitely possible is just by noticing most children, even if they draw a lot, often draw from their imaginations. Since there is no ground truth for what a better drawing would look like if this is all you do, most children don't get much better at drawing if this is the bulk of their practice. I am speaking from experience, but again if you look at art improvement journeys that don't have a lot of improvement this is often something you notice - a lot of repetition doing the same incorrect thing over and over.

You can't observe thinking

What got me mulling over this topic this morning was reading Kimon Nicolaides's The Natural Way to Draw. The two fundamental exercises that he begins the book with are blind contour drawing and gesture. The most important aspect of the exercises is that they are not intended to produce finished drawings or good drawings, although students may occasionally surprise themselves nevertheless. They are worth trying to explain here in an abbreviated form.

In blind contour drawing, the student does not look at the pencil and paper. Instead, the student fixes her gaze on the subject, and attempts to find the sensation that her pencil is in fact touching the object. Then, she moves her gaze around the contour of the object, allowing the pencil to follow. Throughout, the student is to maintain the conviction that she is in contact with the subject. Sometimes, the contour will turn inwards and to continue the drawing requires a repositioning of the pencil - the student is allowed to look at the paper to do so, but once the pencil finds its new starting point, she has to once again convince herself that the pencil's position is on the contour of the physical object and continue to trace it out. (It should be noted that contours and outlines are not the same thing.)

If you try this by drawing your off hand, the illusion is relatively easy to produce. We have access to the direct sensory perception of our other hand since we can not only look at it but also sense its position in 3d space as well as whatever haptic sensation it might have. What I realized doing this is that the exercise is about producing a certain mental process. In particular, it's about inducing a mental representation of the object being drawn as a whole form via its contours. Crucially, this representation of the object cannot be drawn, since it is quite literally all in your head, and exists in a format that is not compatible with a 2d drawing surface. The representation in your head of the subject (in this case the hand) is not a picture at all. When you draw, you need to be able to fix this representation in your head so that you know what you're trying to draw, but even though it's essential to your ability to draw it is not the drawing itself. Therefore, the result of a blind contour drawing is a byproduct of a mental process. The point of the exercise is to get you to do something in your head. There is no visibility from outside whether a student is actually "seeing" correctly because there is no way to look inside other people's heads and experience their imagined sensations. As a result, the blind contour drawing exists as a teaching tool, because in order to produce one, you need to somehow find a way to make that mental operation. The drawing is a cue for the mental operation.

Gesture drawing is often boiled down to timed figure drawings. During a timed figure drawing you can just about do anything. Many teachers have their idea of what gesture is. Nicolaides's instructions seem almost frustratingly vague compared to something concrete like "draw the torso as two simple masses", "draw a stick figure with dynamic pencil marks", etc. The point, Nicolaides claims, is to "feel" within yourself the action of what the subject is doing. Even an inert object you need to understand as "doing" something. If the subject is a live model, the student must be able to feel in their own body the pose being taken. There are no particular instructions on line quality. As a result, the gestures he reproduces from his students as guides barely look like pictures. They are an attempt to grasp the whole subject at once. In particular, he remarks that it is not necessary that even the artist is able to interpret what the gesture depicts once the subject is not available. This is a very important remark, because it points towards the realization I had, which is that the drawing is not the point! The point is to engage in some kind of mental operation that cannot be directly taught because there's no way for the instructor to show the student how to think.

Like the previous exercise I realized that this exercise again exists because it is training some sort of mental faculty required for drawing, and the actual picture it produces is almost entirely beside the point. The gesture drawing is a record of the artist's mental operation of again constructing some kind of tactile representation of the subject. It is not necessarily that doing a gesture is about making a 3d model in your head, but that the artist develops some parsimonious representation of the object which can then be depicted through the normal mechanical means of line, form, value, etc.

Math bears some similarity to drawing and vice versa

This train of thought made me realize that actually these exercises bear a lot of commonalities with mathematics, of all things. Earlier this year I read David Bessis' Mathematica. One of the principal ideas in this book is that the manipulation of algebraic expressions is not really what professional mathematicians are doing. In reality the mental operations they make are much more intuitive and have a kind of quasi-physical reality or tactility to them. However, because these mental operations are impossible to perfectly communicate to others, mathematical notation serves as a way to unify people's perceptions and clarify whatever mathematical object is at hand. In addition, the rules of logic that govern the manipulation of mathematical notation serve as a way to check the correctness of those mental representations.

This is a bit abstract, but perhaps an example from linear algebra might help (although my discussion here will not be enlightening for those who don't know linear algebra). Bessis describes thinking of maps between linear spaces which may have different dimensions as being like tubes between barrels which might be bigger or smaller. Personally I tend to think of this kind of thing like a physical motion: linear maps that have large null spaces I imagine snapping shut a cube into a flat plane, for example. The point is that these things are not "correct" - it is obviously not the case that this is how linear maps work in dimensions higher than three, or that have null spaces of dimension one or higher. But the mental representation helps "chunk" a bunch of related concepts together that I don't have to verify individually when I am trying to think through a problem with lots of moving parts.

The important conclusion here is that the mathematically correct written version that comes out of this mental process is the map and not the territory. Mathematicians work in their heads through a series of mental manipulations on "virtual" objects that may not even be particularly accurate representations of the actual mathematical topic at hand. In order to check and correct the results of their thinking, the rules of logic allow them to transfer their intuition into a written form that can also be communicated to others. But the actual activity that led to the result is not observable directly by others. In other words, the paper or solution that results from mathematical cognition is merely a map describing what was done rather than what was actually done.

I actually think most math majors will recognize that they have had discussions about problems that exist in this kind of vague handwavey manner. It's because with other people sometimes you can directly gesture at some sort of physical intuition. Because this intuition is about the real world around us, this physical intuition can be transferred across people. Greater levels of abstraction are harder to communicate because we may lack common metaphors. I think this explains the difficulty I had with abstract algebra compared to real analysis, and also that I tend to find it easier to prove statements that seem "morally true" and very difficult to disprove statements that seem "morally true". Our sense of whether a mathematical statement is "morally true" is a reflection of our understanding of math based on the chunked representations we habitually reach for when doing math.

One reason some people are good and bad at math therefore might be that some people have good or bad internal representations of mathematical concepts. I suspect that this is what's going on when people draw a lot without improving: they lack the correct mental habits, but since all they can rely on are looking at other people's drawings (or of course, photos and the real world), it is not at all immediately obvious to them that this underlying ability to see is what's really their problem. Following the mechanical procedures of drawing learned from books and tutorials does not guarantee that they will get better. Some people spend a year drawing for ten hours a day and improve explosively even without a very explicit and reasoned plan of study. By drawing a lot they get exposure to the task and build mental shortcuts that let them draw better. But just like there is wide variance in mathematical ability for students who finish the same number of years of compulsory math classes, there is wide variance in drawing ability even when controlling for hours spent in the activity because it is not guaranteed that just drawing a lot will let you build the right intuitions and habits.

Some practical areas where I sense this may be a problem for me include proportion and value. I find that when I am patient, I can draw portraits where the likeness is fairly good. However, this involves a lot of measurements and proportion checking. When I am lazy here, the likeness often suffers a lot. However, it is also the case that there are many people who can, without any guidelines, immediately throw down a likeness. I suspect that what's happening is that they already have some mental representation of the portrait that allows them to immediately see if the marks they put down is correct or not. A simple obvious example is that I tend to get things wrong on the horizontal plane. Clearly what I should do, then, is make more vertical guides/plumb lines and check that things that are supposed to line up top to bottom do, so that they don't go drifting off to the left or right. This is a mental habit I currently lack, and so it's something that I should try to actively practice until I develop an intuitive sense for placement and a habit of measurement integrated into my looking at subjects.

Similarly, I am lazy when it comes to value and trying to shade my portraits generally doesn't work. This is probably a failure of my mind in representing my subjects' value structure parsimoniously, as well as an expression of my general laziness and short attention span. Like the previous issue, it's something that I could probably fix if I deliberately practiced it. These two points, I hope, illustrate my theory that drawing is about finding good mental representations of the subject (including imaginary ones) as well as the mark-making process, and that drawing exercises are only useful insofar as they produce the correct mental changes, rather than producing plausible-looking images.

Anyways, these are just some ideas I had this morning. I think that the main obstacle to my drawing progress is still just not drawing enough, but I feel like the basic insight here that the skill is mostly something that can't be directly transmitted due to the fact that it's a mental process is important since it has bears on how you should think about the objective of practice. You want to make better decisions, not necessarily better pictures. In that sense it could probably be applicable to skill development more generally, since expertise often consists of the ability to make use of resources better than novices, rather than an entirely different stock of resources.