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Gunnar_Zarncke comments on December 2014 Bragging Thread - Less Wrong Discussion
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Let me tell you the 'story' behind the number I memorized:
286718338524635465625 (actually 21 digits which I got by something like 12345^5)
What is the pattern or story?
I grouped it as follows (the grouping is no fixed step, it happens as the 'story' unfolds):
286 718 3385 246 354 65 625
286 is an old intel CPU
7 is the lucky number of a friend (which incidentally has lots of old PCs possibly with 286s even)
7+1 is 8 (which is my lucky number thus connecting us, his birthday is also very close to mine)
33 is a double which stands out and 8 is the sum of the neighboring 3 and 5.
246 35 are +2 stepped interleaved runs. The last 4 is between 3 and 5.
65 was my hourly rate.
625 is 5^4 a quite memorable number and just adds a 2 between the 65 before (thus backward connecting it).
In this case there is not much story but the patterns are memorable enough even without a real story,
Note that the memorability of the last few digits is a direct consequence of the way you constructed the number (yes, it's 12345^5). The last 4 digits of n^5 when n ends in 5 are always among {0625,1875,3125,4375,6875,8125,9375}. If the digit before the 5 is even you always get one of {0625,3125,5625,8125}. At the very least, the final 3 digits are always a multiple of 125 and you probably recognize all of those.
Still, even a completely random number typically has lots of little patterns in it to help this kind of memorizing. For instance, I just generated a random 20-digit number: 66474746605022249923. The first things that occur to me, looking through it in order:
(I also noticed in passing that 60502 is reminiscent of 6502, the processor in the first few computers I used. Lovely instruction set. Having some overlap between the features one notices is useful because it makes it easier to remember what order things come in.)
I tried the obvious experiment: after writing the above, could I look away from it and reproduce my 20-digit number? Why yes, I could; and still could a couple of minutes later. I think I'd find things like reversing the digits quite painful, though.
Yes. Using x^y as a random number is bound to show patterns of this kind. I know enough number theory to recognize this. But it does alter the result only very slightly.
And yes. Your 'story' has the same basic structure as mine. I would have told it somewhat different but I think you got my approach. Note that it doesn't scale though. The major system beats it in that. But for small sequences of passwords it works nicely.
You made up this stories in a minute? Wow, fast system 1
There is not that much to make up. For me numbers (digit sequences) are somewhat like words. And building a story from words is mostly easy - compare to this xkcd. Compare this:
286 718 3385 246 354 65 625
cpu my-friend symmetric-hill stairs broken-stairs earning 5-squares.
The latter is not exactly how I read the digits but close enough to get an impression I hope. Constructing a story for the latter is easier than for the 'meaningless' digits themselves.
I guess it must be the same or rather much deeper for many mathematicians, esp. the number-theory ones. It was said about Ramanujan that every positive integer was one his personal friends.
Finally I mastered the skill) The trick was to put effort and make you sys2 to come up with a stories and then decode them into numbers again. I don't have deep mathematical and programming understanding like most of people here, so I had to use word almost time after time, for example "727" is almost Boeing 737