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Memorizing reference positions

Posted By: Timothy Chow
Date: Saturday, 16 February 2013, at 3:00 a.m.

Buried in another thread, CMC asked how many reference positions was it "humanly possible" to memorize. I thought that this was an interesting enough question that I'm starting a fresh thread.

The verified world record for memorizing digits of pi is 67,890 digits. The digits of pi have no pattern to them so that puts a lower bound on how much straight random data is humanly memorizable. Let me very roughly equate memorizing a backgammon reference position with memorizing 20 random digits. That means that it should be "humanly possible" to memorize at least 3,400 reference positions.

However, backgammon positions aren't random data, so it's much easier to remember them than to remember digits of pi. Kim Peek, the "original Rain Man," could allegedly recall the contents of 12,000 books with 98% accuracy. If we say that a book is equivalent to 50 reference positions then that's about half a million reference positions. However, you could rightly object that books and reference positions are too different from each other for this to be a fair comparison. I'm also not sure how rigorously people tested Peek's memory, so the 98% figure may be an exaggeration.

A better comparison than either of the above may come from Scrabble. There are 267,751 words in SOWPODS. My impression is that nobody has this set of words perfectly memorized; however, I believe that top players can reliably memorize upwards of 100,000 words. (Maybe I'll email Nack to see if he can comment.) I'm not sure how many words correspond to a reference position; maybe 5 words? Then that would be 20,000 reference positions. This is a lot less than my Kim Peek estimate of half a million, but Peek was an exceptional individual.

Bottom line is that I'd guess that the limit is somewhere between 10,000 and 50,000 reference positions. It's hard to give a better estimate until someone actually tries to do it.

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