Why is it you can’t convert a TrueType font to PostScript or the other way around?

This is one of those outrageous assertions you find very frequently in the intarwebs: “You just can convert this TTF font to PostScript” or the same thing backwards. Someone with technical knowledge explains why it is not possible to obtain a remotely decent result and then another pundit repeats the same stupid assertion.

The technical reality of it all is this: PostScript fonts use quadratic equations to describe shapes (“splines”), while TrueType fonts use cubic equations to describe splines. Furthermore, hinting is very different. PostScript fonts use generalized hinting subroutines that need an external hinter to produce properly shaped output at the required sizes (is there still people old enough to remember and have used Adobe Type Manager anywhere that are not professional typographers or typesetters?). On the other hand, TrueType hints are full blown self shape-modifying programs, the font modifies itself at the given output sizes and the external hinter influence on final output is minimal if any — I’m not touching subpixel rendering here, just in case someone engages keyboard before brain in the, very unlikely, comments.

A brief analogy: A PostScript font is like an Arabian racehorse. Beautiful and very fast but to win it requires a jockey who can read the animal’s quirks and needs to take it first in a race. A TrueType font is like a Formula 1 race car. The car is a fully computerized machine where the pilot’s role is to keep it on the road and make sure it doesn’t splat onto a wall or chrash with another car while trying to go as fast as possible. The computers and the technical team take care of the rest remotely.

To convert a PostScript font to a TrueType font just by using Fontforge, FontLab, etc., or the other way around, is like taking an Arabian racehorse, putting it in a meat grinder and expect to obtain a Formula 1 race car in the other end. QED.