(Hope this doesn't sound wrong. I believe the "trimming hangnails" is an important and often overlooked job.)

Perhaps it would make sense to reverse time from bottom to top. Right now it reflects the standard flow of time, forward, like on a watch. But in reality, our time is only running out.

When you have a timeline going from top to bottom, it feels like it will keep going further, but if you reverse it, you see what's left — without illusion.

for example, i have spent 35 years thinking about the events which took place at age 8, but i have only spent 8 years thinking about the events of age 35.

I guess the "natural" base to use to get the "right" number of increments is a pointless exercise, since it ultimately bottoms out in the question of "why is a regular year as long as it is?", but if we assume a base of 2, I'm currently in my 6th log year, and hope to die comfortably into my 7th. Actuarial odds are >80% in my favor.

Extending the music analogy, we could call those powers of two "octaves", and divide it into twelve exponentially-spaced steps (i.e. 2^(years/12)).

The break even is about 75 steps (i.e. six octaves and three steps), which is about 76 years, since 2^(75/12) = 76.1.