Hacker News new | ask | show | jobs
by antonvs 28 days ago
Among the uppercase letters, "S" is the only one that's not either based on a single primary ellipse, or combined with straight lines that provide structural constraints. The entire glyph is governed by continuously changing curvature with no stabilizing axis or primitive shape to enforce proportions.

This results in a more complex and less obvious mathematical definition.

Also, a naively symmetrical "S" tends not to look good, probably because of these same issues, so needs further adjustment to match our visual expectations. This complicates the definition further.
2 comments
noufalibrahim 28 days ago
If you do lettering by hand, S has a bit of reputation. It's hard to get right. Small mistakes stand out even to an untrained eye. However, once you do get it (subjectively) right, it's an extremely beautiful letter. This is even more true in hands like cancellaresca corsiva (the so called "italic font") where the letters are somewhat smooth flowing rather than built with rigid lines. More interestingly, because of all these parameters, you can play a lot with the letter especially if you want to do it as a drop cap or ornament it. As an example, making the lower bowl bigger as the the above comment invites gives the letter some personality.

This is all fine. What fascinates me with Knuth's work is how he applies mathematical rigour to concepts like these which are generally considered "artistic" and subjective. It underlines how mathematical ideas of symmetry etc. play a role in making the world we live in beautiful.

link
whatshisface 28 days ago
As Knuth points out, applying math to art is applying artistic sense to a continuum of forms all at once.
link
noufalibrahim 28 days ago
That's a nice quote.

I remember seeing an animated documentary as a child called "Donald in Mathmagic Land" which ends with a quote attributed to Galileo.

> Mathematics is the language with which God has written the universe

link
jll29 28 days ago
+1 for "S has a bit of reputation"
link
beambot 28 days ago
How does 's' compare to other languages' letters - e.g. arabic or chinese - in terms of difficulty?
link