Memory in Immortals

We'd like to live forever. However, our heads are only so big, and they can only fit so many memories. It's a good bet that by the age of 50 we're already forgetting things at least as fast as we learn them.

If we live forever but only have finite memory, how much can we remember? Are we doomed to forget everything? Suppose we could choose the strategy for what to remember, rather than just having the past evaporate on us outside of our control. Here are a couple strategies.

Cut in Two

The strategy here is, every 2n years, forget half of what you remember from 2n+1 years ago up to 2n years ago.

For example, at year 1 you forget half of what you remember from 2 years ago to 1 year ago (year -1 to 0), then at year 2 you forget half of what you remember from 4 years ago to 2 years ago (years -2 to 0), and also half of what you remember from 2 to 1 years ago (years 0 through 1). At year 3 you forget half of years 1..2, and at year 4 you forget half of -4..0, half of 0..2, and half of 2..3.

This gives you an equal amount of stuff remembered from 2n+1 years to 2n years ago, for all n. That means the memory required increases to infinity, but at a logarithmic rate. That might be acceptable, it might not. It means really old things aren't going to be really small, since a billion-year-old needs 30x more memory than a 1-year old. Even so, what you remember is predominantly recent stuff.

Cut in Three

The strategy here is, every 2n years, forget 2/3 of what you remember from 2n+1 to 2n years ago. This is like the cut-in-two strategy, but it leaves you with (2/3)n memory for 2n+1 to 2n years ago as you have for the last year. This converges to 3 times the memory that you have for last year, total, plus this year is equal to last year, so 4 times one year worth of memories total. It's finite. Really old things can be just as small and nimble as nearly new things.

Special case for Childhood

There are some definitive times and events that you'd like to not be forgotten. That's allowed, even if the goal is to have finite memory total. The trick is to have some portion of memory set aside for these formative events. For example, you could do the cut-in-three strategy from current backwards, but also from birth forward. This doubles total memory, but it guarantees that some fixed set of memories from birth aren't forgotten.

Special case for distant past

The cut-in-three strategy ends up giving increasingly small amounts of memory allowed for the distant past. To get around having meaningless summaries for each, and eventually single letters or single bits, beyond some point in the past have a fixed chunk of memory dedicated to the distant past. Since it's finite size it doesn't interfere with you having finite memory. It's up to you how and when you edit it. Most likely it would be organized by subject rather than by time.

Cleaning the attic

Cleaning your attic is really the identical problem to this. What do you keep, what do you throw out, and how do you organize it so you spend as little time cleaning the attic as possible? These strategies suggest putting things in boxes and labeling boxes by year. Which year it is and what strategy you're following tells which boxes you need to consolidate and how many you need left over after consolidation. For really old stuff you'd have some fixed number of boxes that are by subject rather than by year.

Concretely, using the cut-in-three strategy, you'd have 9 boxes for the current year, 9 for the year before, 6 total for years 2..4 ago, 4 total for years 4..8 ago, 3 total for years 8..16 ago, 2 total for years 16..32, and 4 for everything before that. Each box would be labeled with the year it represented, so most years you could ignore most boxes. 37 boxes total. You could neglect to clean the attic at all for the first 4 years (giving you 36 boxes), but after that you'd have to purge stuff yearly to keep with the program.

Bob Predicts the Future

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