Drawing¶
658 words on Uni
Drawing things is hard. Particularly if – like me – you are neither talented nor trained. This is tough luck which is even tougher if you frequently find yourself wanting to draw or illustrate things and your attempts at doing so fail miserably more often than not. And as soon as the things you want to draw go beyond fairly simple geometric shapes, I find that a computer doesn’t help too much either: To get the pretty shapes into the computer you either have to draw them to begin or you have to battle the complicated world of graphics programs to make them display what you have in mind, potentially in a very long row of tiny steps.
So for many things it seems to be reasonable to stay in the world of hand-drawn things if you want to keep the effort minimal. In fact, even for very small editions it may be much simpler and quicker to just draw something six times than to make some graphics program display what you want before you can smugly hit the ‘6’ button while in the print sheet’s Copies field.
And that’s exactly what I did earlier this year when making an announcement for my boss’ current ‘kids’ seminar. It’s an interesting seminar (on the geometry of surfaces) which lends itself to many interesting little pictures. So I had an idea for the pictures I wanted rather quickly. And due to having seen and drawn those many times before, I managed to draw them reasonably well after a few tries. Because we only needed a handful of those notices to put up around the department, I figured it’d be much quicker to just draw them into each announcement printout by hand rather than starting to struggle with graphics programs.
At the end of the seminar the students should be able to give a meaningful explanation of these drawings.
Is it just me who finds getting such drawings into a computer hard? I find using my graphics tablet usually doesn’t give as good results as drawing with a proper pen does – particularly since the switch to Mac OS X, in which the pen movements don’t seem to result in equally smooth curves as they did before. Sure I could manually draw, scan and vectorise (potrace is great if you don’t mind its interface and the strange file formats) or try to fiddle with basepoints and tangents manually. But both of those procedures seem sub-optimal and very time-consuming.
In addition, when people actually learn to draw they seem to learn how to tell which lines are important for drawing an object and which aren’t. While I have a pretty good idea how to draw some mathematical objects, the characteristics of which I know well, I find it very difficult to see the important bits of everyday objects. Trying to draw them, usually results in a mess of lines.
Finally, let me mention the quality of drawings in mathematics. People like using drawings. For simple diagrams or for depicting geometric objects and concepts. That can be very helpful and they are frequently used on the blackboard during talks. But computer-written texts the graphics seem to be less frequent and of poorer quality. I assume that the reason for this is that making good looking graphics on a computer is both very hard and time consuming (or damn-near impossible if you are trying to do it using Xfig…
An ultra honourable mention in this area should go to Allen Hatcher whose texts, particularly the book on Algebraic Topology which, in a very cool way is still available online but at the same time can be bought for a very reasonable price as a proper book . He made the effort to have a number of drawings in there. And made sure that each of them looks just right - with everything looking smooth and well-proportioned. This must have been a tremendous effort!
