Jazz improvisation following chord changes or modes: although the actual music is always different, always moving, from a harmonic standpoint and at an abstract enough level, it’s always the same succession of chords/modes
Mix of pan-fried vegetables: although each vegetable is cut into slightly different size chunks and mixed with all the other, almost any spoonful will include the same distribution of vegetables and vegetable cuts.
Research: although the topics change all the time, I expect to be doing broadly the same thing for every month (reading, writing my ideas, talking about them with people, looking for flaws, arguing,...)
Bonus exercise:
Jazz improvisation following chord changes or modes: parts are the chords/modes, part-states are what’s actually played, probability-mass-flow is the chorus frequency (the inverse of the “period”, the number of chords/modes per chorus). Then we literally have freq=1#chords=O(1#chords)
Mix of pan-fried vegetables: Parts are the pieces of vegetable cuts, part-states are the shapes and quantities of each vegetable, and probability-mass-flows is the distribution of vegetables in a spoonful. Increasing the number of parts (adding more pieces of vegetable) has a different effect depending on what is added:
If things are added in proportion with the original distribution, then it stays the same
Otherwise, it is moved (by adding only carrots for example)
Research: Parts are the hours of research, part-states are the generic tasks these can be allocated into, and the probability-mass-flows is the distribution over how many hours are allocated in each tasks. If the number of tasks increases the distribution flattens in its extends its support. And if the number of hours increases… well it depends on where the new hours are allocated.
Jazz improvisation following chord changes or modes: although the actual music is always different, always moving, from a harmonic standpoint and at an abstract enough level, it’s always the same succession of chords/modes
Mix of pan-fried vegetables: although each vegetable is cut into slightly different size chunks and mixed with all the other, almost any spoonful will include the same distribution of vegetables and vegetable cuts.
Research: although the topics change all the time, I expect to be doing broadly the same thing for every month (reading, writing my ideas, talking about them with people, looking for flaws, arguing,...)
Bonus exercise:
Jazz improvisation following chord changes or modes: parts are the chords/modes, part-states are what’s actually played, probability-mass-flow is the chorus frequency (the inverse of the “period”, the number of chords/modes per chorus). Then we literally have freq=1#chords=O(1#chords)
Mix of pan-fried vegetables: Parts are the pieces of vegetable cuts, part-states are the shapes and quantities of each vegetable, and probability-mass-flows is the distribution of vegetables in a spoonful. Increasing the number of parts (adding more pieces of vegetable) has a different effect depending on what is added:
If things are added in proportion with the original distribution, then it stays the same
Otherwise, it is moved (by adding only carrots for example)
Research: Parts are the hours of research, part-states are the generic tasks these can be allocated into, and the probability-mass-flows is the distribution over how many hours are allocated in each tasks. If the number of tasks increases the distribution flattens in its extends its support. And if the number of hours increases… well it depends on where the new hours are allocated.