?? todd mentions "splitting the difference" in connection with "fourier analysis"... ?? this idea of "splitting the difference" as sort of resolution of "twin paradox" in special relativity ..... ???? also "arrow of time paradox" in thermodynamics (??? ....) .... ???? forwards vs backwards transition probabilities .... ???? ..... ?? relationships ?? .....

??also talks about gaussian "carried to itself by fourier transform" .... ??? but mustn't this sort of self-duality (?? ...) be riding a higher level of self-duality ??? .....