New aggday: square root

[dreeves]

Desiderata

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1. Stick sqrt in the list of aggday functions
2. Unsnooze https://github.com/beeminder/beeminder/issues/3212

Interesting use case:

For me it's about writing, though I'm sure it can work for other subjects as well! I want to try to build this writing habit: write everyday. But also the more the better. The first daily step is the hardest, so that's the one I want to favor most. On the other hand, I still want to reward every further step, though with smaller return. A "did I write today" (or, write xxx words) goal is perfect for the first step. But it doesn't encourage to continue once the goal is achieved. On the other hand, a "write more" goal is good to motivate to sustain effort. The issue is that the reward is too strong, which allows (for some goals) to bypass the "everyday" part. If I put my daily goal to 100, and on a great a day I write 1000, a little leeway is good to balance less productive days. But 10 days off is too much: then the habit is broken. I considered autoratchet but it seems crude and arbitrary, and falls back to the 1st issue: if I know I autoratchet everything more than 3 days, I will be unmotivated to continue working after 300 words. That's why I was thinking about the square root. It seems like the most elegant solution:

• rewards to start everyday
• on a great day where I write 10x the daily goal, I get 3x daily leeway, that seems kind of right
• still, every further step is rewarded (with no limit)

In beeminder's custom goals, that would be like the counterpart of triangle: triangle is great for "do less" goals (punish with increasing force). This could be an equivalent "reward with decreasing force" for "do more" goals.

Specifically this would be the square root of the daily sum. Probably called sqrt.

Cognata

• https://github.com/beeminder/beeminder/issues/3212
• https://secure.helpscout.net/conversation/1927631452/124800/ (support thread with Eino Gourdin re: "square root of the daily sum")
• 427293e

Verbata: aggday proposals, sqrt,