What the thermometer and tuning fork really have in common in this example is a person (or something) looking at a clock and then recording T_n and e_n. So the example already is a slightly more complex thermostrainometer. It’s interesting how much we take accurate measurements of time for granted; in the good old days astronomers had to invent precise definitions and mechanisms for measuring time in order to correlate the motions of the heavenly bodies with pseudo-periodic observations.
We don’t actually write down (t_0, e_0) and (t_2,T_2), we write down (clock-step_x, e_x), etc. Even if we’re using an atomic clock we’re really just counting the number of times a sine wave generator has cycled since we started it and not some nebulous substance called “time”.
What the thermometer and tuning fork really have in common in this example is a person (or something) looking at a clock and then recording T_n and e_n. So the example already is a slightly more complex thermostrainometer. It’s interesting how much we take accurate measurements of time for granted; in the good old days astronomers had to invent precise definitions and mechanisms for measuring time in order to correlate the motions of the heavenly bodies with pseudo-periodic observations.
We don’t actually write down (t_0, e_0) and (t_2,T_2), we write down (clock-step_x, e_x), etc. Even if we’re using an atomic clock we’re really just counting the number of times a sine wave generator has cycled since we started it and not some nebulous substance called “time”.