The Grand Central Academy is on winter break right now. Here's my drawing as I left it for the holidays:
One of the most important things I've learned this semester is how closely you can compress the range of values in the light areas when modeling. Jargon translation! What that means is two different shades of graphite in a light area can be barely different, almost the same way up close, but when you step back a bit, the two shades will look different enough to show a plane break. And by "barely different" I mean "three more dots of graphite". This is useful in practice because it it allows you to anticipate that, though you need to make this next plane darker than the one before, you'll only need a few dots of graphite to accomplish this. The end result will help keep the drawing bright, looking like a white cast, even while shading to show form. I'm still not great at this, and often get critiques that my cast looks "muddy" or "gray," but hey -- I've got it in theory.
While one of my teachers was explaining this to me, I immediately thought of how this relates to Weber's studies of the just-noticeable difference (called the jnd by psychologists) in the 19th century. The just-noticeable difference is the difference in the intensity of a stimulus needed to be able to distinguish it from another stimulus. Weber studied this in terms of weights: how much heavier must something be so that you can say it's heavier than something else? The interesting point (and one that Gustav Fechner later added to in a quantitative way) is that as the objects get heavier, you need more of a difference in weights to say that one is heavier -- you can tell which of two oranges is heavier when they differ by an ounce, but not which of two bags of oranges is heavier when they differ by an ounce. So the relationship between the stimulus (the actual weights) and the perception (how heavy you feel they are) is logarithmic. This idea applies to many kinds of perception.
In vision, our perception of brightness varies logarithmically with the actual intensity of the light (the number of photons per second coming off that source toward our eyes). I'm not sure whether the application of this fact to drawing in graphite is entirely valid, but it does mean that on the object we're drawing we perceive the drop-off of light into dark (as it turns into shadow) as happening very quickly, even if the change in the number of photons emitted is linear. Therefore a linear drop-off from light into shadow (in terms of number of photons reaching the eye) will appear to be bright for longer and suddenly dark. So it's interesting to think about whether we're re-creating this psychological effect in cast drawing by making the changes in the light areas very small, keeping areas lighter for longer, and then quickly making them darker as it turns into the shadow.
Phew. Enough science for you?