Still on the subject of MaDi's question: Blind contour drawing is, or should be, an exercise of intense concentration, better done in a Zen-like state. There is a passage from the Mahabharata that goes something like this:
Drona was testing his students one day. He placed a bird on a tree and asked each one to take aim with his bow. Then he asked: ”What do you see?”. The first one said “I see the bird. I see the tree. I see the clouds behind the tree. I see the arrow. I see my hand”. Drona was vexed by this and did not allow him to shoot. He repeated this with the others, with the same results. Finally Arjuna took aim. Again, Drona asked the question:
-What do you see?
-I see a bird
-Describe the bird!
-I cannot.
- Why not?
-I can only see its eye.
-Release the arrow!-ordered Drona. Arjuna did so and the arrow pierced the bird’s eye.
While doing a blind contour drawing, never allow yourself to see too much. The point you are drawing is enough.
41 comments:
Of course, you still have to see a little further than the point itself, to keep moving in the right direction.
For the mathematicians in the audience:
More exactly, see infinitesimally further, i.e., see not the point but the tangent vector at that point.
That is the shortest object that contains both position and direction, and you should allow for no more in this exercise.
Again, these are meta-thoughts on the matter, not to be had while doing it.
I meant the affine tangent vector, of course.
Note: the purists will object to me on several accounts (this is my pre-emptive strike):
1-I have used a version of the Mahabharata excerpt more similar to the one in Peter Brookes play than to the original.
2-I have used an example from Hinduism after mentioning Zen.
My answer to 1) is that I find this version cleaner, more compelling, and (gasp!) better for the present aim than the original. No offence intended to the religious or historical Nazis (oops, purists) among you.:)
My answer to 2) is that hunting season is open for complaining bores, so…duck! :))
:)
Thank you, omwo!
omwo,
what you are proposing is not an exercise on drawing but an interpolation exercise.
you stated it correctly except when speaking for the mathematicians :)
for the human eye sees far beyond C1 curves. take MaDi's thumb in her 2nd drawing. she got it right up to the 2nd or 3rd derivative!
here's an exercise for you:
draw your hand again, seeing nothing but the point and the affine tangent vector.
and again, this time taking also in account the acceleration vector.
what's the difference?
:)
Dear mathematician in the room :)
I was merely being metaphorical, but I should know better than to be less than exact around mathematicians. I should have said "the theoretical physicists in the room" and waved my hands around for a bit ;)
But ok, I'll play the game at least for a round or two :)
Ok, first let me try to be exact...let's reformulate the whole thing.
I don't want my metaphor to deal with second or third derivatives, not even with the first, really. Notice I never mentioned velocity but merely a tangent (you could take the unit tangent) because I wanted to avoid a specific parametrization of the curve. Why? Because you should draw really slowly, meaning the perfect blind contour drawing is the lmit of this procedure when velocity tends to zero. If you look at this as a finite interpolation method can you really see the difference if the step is small enough? I don't know how far you can go in being sure that the human eye can "see C^3 curves" but I am sure that neither MaDi nor perhaps michelangelo would draw the hand correctly up to arbitrary precision - how do you know how correct it is if only she saw the model, btw?? Now that is some hand waving :))
In fact the human eye is allways jumping around and focusing in small areas at each jump. That is hardly continuous, much less smooth, so you can hardly be too demanding on these metaphors!
Let's try it in a whole different way then.
The following will do quite nicely, I think:
When you are drawing point p, do not see beyond a disc of radius epsilon around p, where epsilon should be small enough that the intersection of the contour passing through p with the disc is conected, and there are no other contours within the disc.
The point is that this should prevent you from seeing and identifying complex forms such as fingers.
Or: If you want to go the whole way, You could say that the perfect blind contour drawing is the limit of this process when epsilon goes to zero. But you can get a good drawing for any finite epsilon verifying the conditions stated :)
Anyway, there are many exercises in drawing that are interpolation exercises though this is hardly the case. In some exercises, you take points at the proper locations and then put lines through them, that you later refine. Now, *that* is interpolation. I have to propose one of those, by the way :)
Anyway, these are just funny remarks on the thing, of course. The exercise is about feeling the curve, connecting the movement of the hand to the movement of the eye, and doing it by watching as small an area as possible at any time. The rest is just me being unable to keep from conceptualizing even while talking of an anti-conceptual method of drawing :)
That is why I said "never think such things while doing it"
Oh, btw, I forgot to respond to your solicitation!
Actually my demonstration drawings where "fast contour drawings" ( because I didn't have the time to do proper ones )so I already *felt* the difference. Can you *see* it? :)
Exercise for you: Do the exercise I proposed, first as slow as possible, then faster. Then tell me how easy or hard it is to even know "where" your eye "is" at each instant. Then you tell me if you think it is useful to stress the metaphor so far or if you felt you were "seeing up to C^infinity"...:)
If you still think so then feel free to bring in the whole arsenal of parametric curve theory, Frenet and all. You should provide the statement, of course :)
PS: Just for you I will soon make a post that will include a totally unreasonable metaphor envolving category theory! the horror ! :))
I would say that there are at least fake C1 curves. Whatever that means...
God!
Who is this mathematician in the audience?
Derivatives, primitives, parametric curves theory,...
I just want to learn to draw...
Dear MaDi,
you cannot learn to draw without knowing at least Lie theory in abstract differentiable manifolds.
....
....
(just kidding :))
Dear omwo,
take it easy!
Every undergraduate sees the difference between a continuous non-differentiable curve and a differentiable one. It looks reasonable to me to suppose that after some training the experienced eyes would see the difference between a C1 and a C2.
Anyway, interpolation is a very good way of learning. The brain uses it a lot! And also in mathematics and martial arts. It's easier to dissect a line or a movement or a logical argument and study small portions of it before you get the hole picture.
Now "speed contour drawings" are a different thing. And they're good exercises to feel the volume of an object, not to feel the curves. I'll try a couple of them!
Cheers.
MaDi,
There is no such thing as "just" learn to draw! :)
That is like saying:
*just* learn to live
or
*just* learn to die
or
*just* learn to fly
The Gods of drawing will not be pleased :)
They demand that sacrifices be burned at the temple. Hecatombs for Apollo, Dionisus and aphrodite at the very least! ;)
Oh, I would like to *just* learn to fly ;)
Omwo,
Are you also the mathematician?
You are a little bit more schizophrenic than I thought.
MaDi, we are all mathematicians
:-) :-) :-)
Hi mathematician :)
the thing is, it is somewhat "imoral" to let a vague metaphor go beyond C1, I think :)))))
About interpolaion, you are right. I agree completely, whether in drawing, mathematics or martial arts. In this exercise, precisely because the eye is allways jumping, you do interpolate blindly between the spots you actually focus on. But you do not act with such an attitude when you draw, and the metaphor should induce the right attitude above all.
Again, because of those jumps and that unconscious interpolation, the fact that the curve you actually draw on the papaer could be modeled in some way as being C1 or C2 or even C^inf (all this by streches of course) is of little consequence, because the curve you draw will only correspond to the curve you see in a much vaguer way, that, in some sense, is not even C0!
My whole point is: the curve actually drawn on paper is the least important thing. You can do this exercise even without paper ( I'll talk about it later )
Finally, I disagree completely with your last statement. Fast blind contour drawings are still done in a totally local fashion. They are not about volume at all, but about line and flow of line. It is still like caressing the surface with your eye and feeling that motion on your hand, only it's now a fast caress, like you would do to feel the general curve of a girl's back and not, say, the details of the lumps between her ribs...
I think you are thinking either of something called "gesture drawing", or of "mass drawing". If I talk of all of that I'll end up writing a drawing book right here, and I am not *that* arrogant ;). Check Nikolaides, for instance, he describes all that...
Cheers :)
I'm not...
"But I don't want to go among mad people,' MaDi remarked.
'Oh, you can't help that,' said the Cat: 'we're all mad here. I'm mad. You're mad.'
'How do you know I'm mad?' said MaDi.
'You must be,' said the Cat, 'or you wouldn't have come here.'
-"MaDi in Wonderland", Lewis Carroll
I know I am mad.
But I am NOT a mathematician, only a scientist. And this is pretty much already.
:)
Why did u get into a network of math blogs? Poetry and drawing r only disguises...
Why do people insist on specialization? Why do I have to say "I am this"? Hey man, you are not your job!
This blog is not a disguise for anything. It is what it is. It started as a way for me to reflect openly on drawing of a specific kind, namely, the drawings I've been doing in buses, etc. Very fast drawings, that require you to look in a certain way. But I will not be a slave to my own momentary intention. I will write on what I want, when I want.
I know some maths, I know some physics. I know some biology. I'll write about that if I want. Will the site become a "disguise" for those things? I do Karate, I did some skydiving. I'll write about that if I want. ALL of it at the same time if I want. I like sex. I'll write about sex if I want. I like to run. I'll write about running if I want. Hey, I already mentioned the patents thing here, is the site a disguise for politics?
I did not join a network for math blogs, but I didn't join a network for art blogs either. I don't care for networks. You can't do anything these days without having to "belong". Well, I don't need to belong. I don't want to belong.
I'm just doing my own thing, my friend. Anything wrong with that? Hey, it's free, read it if you enjoy it :)
When you think about a subject, all the other things that you think about come and join in. You cannot help but make connections. That is the only network I care about. I write a blog, first of all, for myself. I register here my reflections for further use. Or for the trash bin. Whatever. I'm not writing for mathematicians, I am writing for anyone who cares to read. But I will not restrict myself to the taste of the majority. Anyone means everyone. Including those who actually enjoy to mathematize a bit, although that is far from my aim. Believe it or not, my main aim is still drawing, in a very non-analytical way in fact.
Anyway, I am sorry if the maths talk bored you, but I can't do anything about that. You can allways start a new topic of conversation if you want. Go ahead :)
"A human being should be able to change a diaper, plan an invasion, butcher a hog, design a building, write a sonnet, set a bone, comfort the dying, take orders, give orders, solve equations, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects."
Robert Henlein
Furthermore, when I asked "how is drawing like a martial art? How is drawing like making love?" I wasn't being cute or rethorical.
Some activities have a natural ability to be maps for greater things.
Awa would say that archery could be more than just the art of destroying paper targets by throwing stuff at them. Well, drawing can be more than just making pretty pictures. If you want, if you absolutely need a theme for this blog, that is it. I have mentioned it many times already, though I am still preparing the background to speak the first word on it.
It's hot here.
Bye, bye...
In bed
With the beloved woman
The mathematician performs his art
Dear mathematician
why not join poetry network
mathematics mere disguise
Have no time now
All this *mathematics*
is consuming me
:)
Leave the bed
the beloved woman
strangles the muse
:)
The beloved woman and the muse went on
dancing through the night
I can't say no to a lady, or two.
Two?
'There once was an old man of Lyme
Who married three wives at a time
When asked "Why a third?"
He replied, "One's absurd!
And bigamy, Sir, is a crime." '
;)
:D
Então, macha!
Afinal entendes esta língua estranha? Por vezes, seria melhor não entender...
senhor omwo... senhor omwo...
publique lá um post'zinho que os seus leitores assíduos já têm saudades...
;)
Para muito breve, está prometido :)
até breve:)
Faltam os desenhos do Samurai! O OMWO fala, fala...mas já não desenha??
equilibrio precisa-se!!! :)))
a tua ideia de MUITO breve não condiz com a de muita gente, omwo
MaDi,
é Agosto, tudo se move um pouco mais lentamente :)
Não... percebi... :)
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