Look Who it Was Random video

Donald Knuth - Mathematical formula for letter shapes (53/97)

2,242 views · Published 2 February 2016 · 5:42 · Indexed 6 November 2026

Channel: Web of Stories - Life Stories of Remarkable People · 2016 · Science & Technology

Watch on YouTube

To listen to more of Donald Knuth’s stories, go to the playlist: https://www.youtube.com/playlist?list=PLVV0r6CmEsFzeNLngr1JqyQki3wdoGrCn

Donald Knuth (b. 1938), American computing pioneer, is known for his greatly influential multi-volume work, 'The Art of Computer Programming', his novel 'Surreal Numbers', his invention of TeX and METAFONT electronic publishing tools and his quirky sense of humour. [Listener: Dikran Karagueuzian; date recorded: 2006]

TRANSCRIPT: I decided to go to Stanford instead and… and there… at that time, Stanford had a really great artificial intelligence laboratory up in the mountains presided by… presided over by John McCarthy. He welcomed me to come up there and do everything… anything I wanted and it was a great place to work for the year that I spent.  But we didn't have very good equipment compared to what they had at Xerox. We had TV cameras that I could use, but if it changed the lighting in the room just a little bit, the letters would change drastically from thin to thick or vice versa.  So there was no way to get consistency from one day to the next.
 
I should mention that my publishers had sent me beautifully printed copies of previous editions of my book. Beautiful… what I mean by beautifully printed is, the way the books are actually produced… are kind of interesting. With monotype, they set in lead and they print one copy, and then they take that one great copy and photograph it and print offset off of the… the film that they’d taken.  And that was getting great results.  But they had saved the original copy that came off of the lead, so they sent me 50 pages of the real, you know, absolutely definitive versions of what had been used to do the previous edition of my book. So I took these to the… to our TV cameras at the AI lab, but I couldn't get any consistency at all. So I didn't know what to do about this. I was talking to Jill and she said… well, she could make some good slides, she could photograph these pages and we could make 35mm slides and they would be sharp, and we could see what we could do with that instead of working with a TV image. So, we tried that and then I got my home projector, and I projected the 35mm slide from the end of the corridor on to a wall and so that it would be large enough, and I could trace on a piece of paper what the letter forms were. But the images were very fuzzy. When enlarged that much that… you know, we didn't have any way to magnify things now, like film scanners or anything – that didn't exist. Certainly we had no such equipment.
 
So I'm sitting there looking at these, but trying to trace the letters and figure out what are the shapes and suddenly it occurred to me, you know, these letters were actually designed by a human being who had something in mind.  And if I could only psyche out what that person had in mind, I could figure… I could write mathematical formulas that would match that person's intentions. This was a weird dream, but anyway, this was what – I was naïve and I thought this would be fine – and as I had said, when I was in high school, I played a lot with graphs and the relationship between shapes and mathematical formulas that make those shapes. So as I'm sitting there with my pencil and paper trying to trace the outlines off of these blurry slides being projected on the wall, you know, I noticed a lot of regularities. For example, I noticed that the letter n was exactly twice the width of the letter i, and the letter m was exactly three times the width of the letter i.  And okay, great, you know, there was consistency that… there, that if you have a word like minimum, all of those vertical strokes are coming at exactly the same spacing. Also the u was the… was, you know, the same width as the n. So it occurred to me then that if I could figure out, you know, what all these principles were that the… that the type designer had done, it wouldn't be too much of a problem to capture that in mathematics.

Okay, so instead of using… so then my whole focus shifted so that I wasn't going to just copy the output of a previous design, I was going to try to discover the intelligence behind it, and program the intelligence into the computer, so that you could tell a computer, draw a letter m, and it would draw a letter m.  And I… but I could say, now make it a little bolder, now make it a little taller, a little narrower, and it would adapt everything correctly. Now this was a weird concept to type designers. Type designers always, you know, approached it with a completely visual approach and no mathematics, probably thank goodness, because they came up with beautiful design, but at any rate, I naïvely thought that this was going to be easy.  And, of course, my whole, my goal, it was to have Volume Two ready for the printer after my sabbatical year. I had one year to write these programs and to capture the letter forms and figure out how to typeset them.

More from this channel