I figured I’d put together a simple (Arabic)number–(Roman)letter correspondence, try to internalise it and see how much it helps with remembering numbers.

Some principles seem worth trying to apply:

a) Use easy-to-remember mappings
b) Have a suitable vowel-consonant balance to maximise the chance of having pronounceable syllables
c) Avoid letters that will sometimes necessarily generate ambiguous sounds

Here’s one possible set of isomorphisms (setting 1 and 7 a counterintuitive way round, because I think an important part of memorisability is that the sequence 0-9 itself be faintly pronounceable):

0123456789
OLZEaSGIBq

(intending to always pronounced ‘z’ as in ‘zoo’, and ‘S’ as in ‘sea’, unless a familiar word crops up that I’m confident I’ll remember better, eg ‘lies’. ‘q’ will be a k sound. I’m slightly concerned that I and E might be too similar, but I think with fewer than four vowels you’ll get too many unpronounceable consonant strings, and no letter obviously lends itself to a U).

Can anyone suggest improvements? If not, I’m going to try to internalise this to the point where I mentally pronounce numbers as I read them.

0n3 342y w4y 0f pr4qt757n6 th75 72 t0 7nv3rt 7t, wr7t7n6 4 f3w 53nt3n535 w7th 42 m4ny num3r412 42 p0557813, 7n91ud7n6 ph0n3t7q tr4n214t70n2.

If you don't mind me asking, what is the point of doing this? To try and memorize numerical strings for some purpose? Cryptography?

It's pretty low personal cost, so the payoff doesn't have to be huge. I think there are a few gains:

a) Memorising telephone numbers and numeric passwords
b) Memorising numbers as a party trick
c) Memorising the output of one part of a calculation that you'll later have to draw on, when doing mental mathematics

I think c) potentially has very high value - my memory is worse than most people's, so it may apply more to me, but if I'm doing two operations with numbers I often find myself redoing calculations multiple times over, because as soon as I start thinking about other numbers, it's like someone saying numbers at you while you're counting - new numbers muddle the memory of older ones.

Are all the number combinations pronounceable? I think that could be a problem.

3.141592653
E.LaLSqZGSE

E - lal - skiz - guh - se?

How easy is it to remember how to turn the letters back mentally? Or do you write them down and then convert?

Are all the number combinations pronounceable?

In some sense yes, though you might have to stop in unusual places, but that’s a bit of a cheat. Some numbers will obviously be so garbled that it doesn’t help mnemonically – the idea is that it’s a big improvement on the absolute unpronounceability of Arabic numerals rather than a guaranteed pronounceable system. The latter I think would take significantly more effort to construct and, more importantly, to memorise, so that realistically no-one would ever bother doing it.

The pronunciation might be more frequently natural if I included U, but I chose not to initially a) because it doesn’t map too memorably (which numeral looks most like a ‘U’?), b) because vowels already often sound alike (eg the vowels in ‘begin’ sound similar or identical depending on your accent), and c) because ‘unpronounceable’ consonants can take an implicit vowel sound ‘ess’, ‘kew’ etc, whereas long strings of vowels blend into each other more naturally but IMO less memorably.

Could easily be persuaded that those reasons are insufficient or even wrong, though. As I wrote the third one I was already starting to doubt it…

What’s your instinct? Should U bump out one of the consonants (or other vowels)?

It occurred to me the current mapping isn’t that great for the first digits of pi, but I don’t think that’s a great litmus test.

How easy is it to remember how to turn the letters back mentally? Or do you write them down and then convert?

I think atm it’s fairly easy – if you forget the mapping, just visualise the letter and you can figure it out, and after you’ve done it a handful of times it should become second nature anyway. Even if you always have to infer them visually, you’ll probably spend less time on number memorisation than you will otherwise.

An alternative mapping that I originally thought of is convert each two digit sequence to the corresponding letter of the alphabet if possible (ie if <= 26), else convert the first digit only. From a superficial test on pi that worked very well, producing C.NOIZE for the first 10 digits, but it seems hard to imagine that would be better in expectation or as easy to internalise.

Arepo wrote:because ‘unpronounceable’ consonants can take an implicit vowel sound ‘ess’, ‘kew’ etc, whereas long strings of vowels blend into each other more naturally but IMO less memorably.

I think this is the case. Though the downside is then you have to remember that the implicit vowel is not a letter to be converted...

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Arepo wrote:It occurred to me the current mapping isn’t that great for the first digits of pi, but I don’t think that’s a great litmus test.

I think it is a good litmus test -- it's probably, by far, the most popular string of numbers to be memorized.

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Arepo wrote:From a superficial test on pi that worked very well, producing C.NOIZE for the first 10 digits, but it seems hard to imagine that would be better in expectation or as easy to internalise.

I feel like that's just a strange coincidence.

If I want to memorize the string "2235567890", for example, it maps to 22 3 5 5 6 7 9 9 0, or MDFFGHJJM, which is unpronouncable. (Note this conversion assumes 0 = A, 1 = B, 2 = C, etc.)

peterhurford wrote:I think this is the case. Though the downside is then you have to remember that the implicit vowel is not a letter to be converted...

Yeah. Maybe it's just worth experimenting.

I think it is a good litmus test -- it's probably, by far, the most popular string of numbers to be memorized.

But not for any good reason. If people specifically want to memorise umpteen digits of Pi, then there are better ways of doing it than this, but it's not a good use of anyone's time. See SMBC

I feel like that's just a strange coincidence.

So... not a good litmus test?

What's your instinct on the current setup, then? Your responses seem to pull in differing directions...

Arepo wrote:What's your instinct on the current setup, then? Your responses seem to pull in differing directions...

Sorry for not being clear. I'm skeptical about the added value. I think it will end up being pretty sensitive to how well things end up being pronounceable.