FORMAL EDGE / SUPERTASK MACHINE 04
Can midnight arrive before the switching settles?
Accelerate the lamp until infinitely many idealized switch-times fit before midnight. The spectacle is the mismatch between a converging clock and a non-converging state sequence.
No quiz. Touch the machine and watch what happens.
PLAY FIRST / THE LAST SWITCH
Make infinitely many switches fit before midnight.
Each press cuts the remaining time in half and flips the lamp. The switching times race toward an ordinary endpoint while the lamp keeps alternating.
Watch two things separate: the clock can converge even when the ON/OFF sequence never settles.
SUPERTASK / THOMSON LAMP
Midnight keeps getting closer.
MIDNIGHT → 0
Cut the remaining time in half. Flip the lamp. Repeat.
What you just saw
The idea arrives after the spectacle.
The times1/2, 3/4, 7/8, … can crowd toward one finite moment.
The statesON, OFF, ON, OFF, … do not approach one final value in the same way.
The pressure point“All scheduled events occur before midnight” does not by itself tell you what the lamp must be doing at midnight.
Independent educational interpretation inspired by Agustín Rayo’s work and course materials. Public wording, visuals, and interactions are original to The Mercurial World; no collaboration, review, sponsorship, endorsement, or approval is implied.