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Title is misleading. This isn't learning exponentially. Anybody who has used a spaced repetition app (like Anki) knows that you generally learn around the same

Title is misleading. This isn't learning exponentially. Anybody who has used a spaced repetition app (like Anki) knows that you generally learn around the same number of words every day. You're not going to be learning 10 words in a day and then one week later, learn 1000 words in a day. This article talks about how the reps needed to learn one piece of information, reduces exponentially over time. You might need 1 rep per day at the beginning, but only 1 rep per 100 days after a month. This basically means that if you have a lifespan of 100 years, spaced repetition means you only need around 10-20 reps to remember each piece of knowledge for the rest of your life. But learning N items will still take 10*N reps. It scales linearly. A far cry from exponential

Denzel 4y ago
The rate of repetitions scales sublinearly with respect to time. Consider a uniform repetition approach that repeats each item once per day. The rate of our uniform repetition system scales linearly with respect to time. If one item takes 1 second to review, then I will lose 1 second per day. Therefore, N items causes me to lose N seconds per day. Even in the case where I don’t add items to my list, I lose N seconds per day. In contrast, as you stated, the amount of time we lose per item per day reduces exponentially with spaced repetition, however. If we don’t add any items to our list, the review time asymptotically approaches 0 seconds/day. Unrelated to all of this, I agree the title may be a touch embellished. :)
p-christ 4y ago
Think about it in terms of how many days of knowledge each rep gets you. The first rep gets you 1 extra day of knowledge. The next rep gets you 2 extra days. The next one gets you 5 extra days. So each rep is getting you more and more knowledge even though the time required to execute the rep remains the same. This is exponential growth. If you only have 1 card then for most days you won't have any reviews to do so it doesn't work. But if you add cards regularly then over the long-run every day you'll be getting more and more "extra days of knowledge" by doing the same amount of reviews each day.
- woojoo666 4y ago
  My main point is that when people think about "learning", they think about learning new pieces of information. Reps only reinforce old pieces, they don't teach anything new. Retaining knowledge is part of learning, sure, and I saw your article about "learning is remembering" which was a good read. And I support your initiative, spaced repetition is an amazing tool. But I'd still say "learn exponentially" implies more than just retention. I'd personally love a system that lets me pick up exponentially more new knowledge per day, though I'm not sure if that's possible
- dekleinewolf 4y ago
  It's not giving you more knowledge though. It's giving you the exact same amount of knowledge - you're just retaining it longer.
  - p-christ 4y ago
    If you've forgotten something then you don't have that knowledge anymore. So remembering things for longer means you are effectively gaining knowledge. It's like someone giving you $10 and then trying to argue that they haven't actually given you $10 because just a few minutes ago you had a $10 bill in your pocket but you spent it on something else.

Denzel 4y ago

The rate of repetitions scales sublinearly with respect to time. Consider a uniform repetition approach that repeats each item once per day. The rate of our uniform repetition system scales linearly with respect to time. If one item takes 1 second to review, then I will lose 1 second per day. Therefore, N items causes me to lose N seconds per day. Even in the case where I don’t add items to my list, I lose N seconds per day. In contrast, as you stated, the amount of time we lose per item per day reduces exponentially with spaced repetition, however. If we don’t add any items to our list, the review time asymptotically approaches 0 seconds/day. Unrelated to all of this, I agree the title may be a touch embellished. :)

p-christ 4y ago

Think about it in terms of how many days of knowledge each rep gets you. The first rep gets you 1 extra day of knowledge. The next rep gets you 2 extra days. The next one gets you 5 extra days. So each rep is getting you more and more knowledge even though the time required to execute the rep remains the same. This is exponential growth. If you only have 1 card then for most days you won't have any reviews to do so it doesn't work. But if you add cards regularly then over the long-run every day you'll be getting more and more "extra days of knowledge" by doing the same amount of reviews each day.

woojoo666 4y ago
My main point is that when people think about "learning", they think about learning new pieces of information. Reps only reinforce old pieces, they don't teach anything new. Retaining knowledge is part of learning, sure, and I saw your article about "learning is remembering" which was a good read. And I support your initiative, spaced repetition is an amazing tool. But I'd still say "learn exponentially" implies more than just retention. I'd personally love a system that lets me pick up exponentially more new knowledge per day, though I'm not sure if that's possible
dekleinewolf 4y ago
It's not giving you more knowledge though. It's giving you the exact same amount of knowledge - you're just retaining it longer.
- p-christ 4y ago
  If you've forgotten something then you don't have that knowledge anymore. So remembering things for longer means you are effectively gaining knowledge. It's like someone giving you $10 and then trying to argue that they haven't actually given you $10 because just a few minutes ago you had a $10 bill in your pocket but you spent it on something else.