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I get the math, but the reasoning feels unjustified: why should we assume our brains work that way?Well, the math doesn't change if we make other assumptions. The relative amount of time that passes us by is less in our 30s and 50s than in our 1s and 10s.
Routine by itself ain't the answer as kids also have routines (school is whole big routine, as is living day-in/out with your parents, going to lessons, playing with friends, etc.), but their days don't "pass unnoticed", and a year of e.g. middle school seems to last forever when you are young.
>It would make sense if we remembered the same amount of stuff every year, but reality is, you have fewer memories of the past.
The concept I described is not related to memories per se, but to new experiences -- which is subtly different (and not totally unlike your explanation).
You know what a party is, and it's not that exciting the nth time you go to one, because you've seen 50 other parties in your lifetime, whereas the first times you went to parties (or had your first drink, or visited another country etc) were more impressive. That's regardless of if you actually remember all or any particular of those 50 other parties in any great detail -- it's enough that you remember the experience of having been to parties many times already.
Now, the problem with merely saying "routine makes every day the same and days just pass unnoticed" is that it's a limited version of the above. What it lacks is seeing that even if you added random stuff to your days, you'd still have seen and done most important stuff in the past. You can't re-drink your first drink, learn about pop music and films for the first time, re-give your first kiss, go to your first party etc. You'll have to get even more random (and add stuff that is either too crazy or has less impact and importance) to beat those experiences later on.