That was much more impressive than I thought it would be given the title. The presentation gives a very nice demonstration of how the gears do calculations.

The mechanism seemed overly complex to me; e.g. to multiply by 5/19ths, why not just use two cogs, one with 5 teeth the other with 19 (or some multiple thereof)?

Lego gears only come in specific sizes (and therefore are limited to certain ratios).