At least some of the magic of 7 comes from the gods who, as we all know, live in the sky. Back in the day – the day of the Sumerians, Chaldaeans, etc – this is waaaay back in the day – 7 was the number of planets – mercury, venus mars, jupiter saturn, sun, and moon. This made 7 Very Sacred.
There’s an excellent PDF on this topic here:
“How magical is Miller’s famous Seven for HCI issues?”
Many people do employ conscious memory visualisation techniques to help memories “meaningless” data.
Unconsciously, I think we do this automatically when remembering digit strings and such, although I have no idea what mechanism is used - needless to say, it’s not very good (since there was never any evolutional advantage in being able to remember meaningless symbols).
I use a common technique called the “Major” system, which assigns a unique consonant sound to each digit, like so:
1 t, d
2 n
3 m
4 r
5 l
6 sh, j, (soft) g type sounds
7 k sounds
8 v, f sounds
9 b, p
0 s, z sounds
I did an aptitude test years ago, and was asked to remember longer and longer strings of digits. As they progressed, I was a bit surprised and didn’t perform too well, but then I was asked to repeat the number forwards and backwards, and by that point, I had decided to visualise each string of digits as if I was dialling them on a phone keypad as she called them out. Doing it that way, I had perfect ultra-short term recall up to 15 digits or so when she stopped the test.
So I guess the key is, most of us basically suck at this if we don’t use or devise a conscious aid for memorising the input somehow. This can be difficult when you’re trying to organise such a system when a live stream of data is coming at you, of course…
A fascinating read on these topics is “The Mind of a Mnemonist: A Little Book About a Vast Memory” by A. R. Luria, about a Russian mnemonicist called Shereshevsky who started out as a journalist, and when someone asked him why he wasn’t taking notes at a press conference, answered that he didn’t need to as he could remember everything the speaker had said, and immediately repeated the entire speech from memory when challenged on the point. This guy experienced a condition known as synesthaesia where the senses are apparently not mutually exclusive and could see and smell sounds, taste colours and so on.
The French composer Olivier Messaien (whose music is very bizarre, but interesting) also had this condition.
Anyway, it seems that having synesthaesia allowed Shereshevsky to easily associate seemingly meaningless incoming data with known concepts, turning for example an abstract sound into a wave, or a clothes line upon which his mother was having some washing. And we know that we’re very good at remembering visually meaningful events like this - that’s how all mnemonic memory techniques work.
Man this was a long comment. 
I meant to expand on that bit about the Major system.
When you encounter a number, say in this case, 5551212, you go through it, converting each digit to a consonant and construct words by filling in vowel sounds at will.
For example: 55 = “l l”, 512 = “l t n”, 12 = “t n”, which could be expressed as “Lolly latin tin”.
So one might imagine a hundreds of lollypops chanting in Latin, falling from a tin can.
The more ridiculous the image, the more exaggeration (hundreds…) the better such an image will stick in the mind. For longer strings, it’s better to have separate images for each association (perhaps “lolly light”, “light net”, “net noah” (in the book I learned the system from, 2 is represented as “noah”, for which you imagine an old man…)).
Then, you associate the starting point with the meaning of the number, say it’s your office phone number, then you imagine arriving at your office to find lollypops all over your desk.
Easy peasy. Well no, complex, but after a while, you don’t have to think about it so much.
Just like Albert once said;
never memorize things you can look up in books…
By the way, in Holland it isn’t common (anymore) to write phone numbers in chunks. We have one chunk (the area code) and then a chuck of 7 numbers. So, are we generally smarter? Do we have more brainspace?
I think the answer is a definite yes.
And how about the 10 commandments, is it impossible to live a sinless life, because we can only remember 5 to 9 of them? Think about it. If you take this post beyond it’s original point (which is in my opinion; keep it simple) it just doesn’t make sense, just like this comment.
Interesting about the phone numbers. It makes me think of when I give my number to someone else over the phone to write down; if I just blurt out all 7 digits, I usually get the “whoa, slow down there!” So I pause after the first 3 digits, then give the final 4, as do others when giving me their number. Is this because it’s natural to only retain 3-4 digits at a time, or because phone numbers are already grouped that way?
People do definitely tend to look for patterns, and remember better with those. Way back in high school they once had about 100 magnets each with one obscure word printed on it. People always arranged them into phrases - usually attempting to make them sound naughty, but more importantly, people remembered the phrases even if they made no sense. Much more so than the words on the lone magnets which didn’t make it into groups.
Patterns and groupings definitely have an effect. Maybe that explains why people can find a number in a phone book, where every listing looks the same, but can never find a feature under the Tools menu - because it’s the leftovers, a bunch of mutually unrelated features that just didn’t fit anywhere else.
A recent Scientific American article cited the 7+/- 2 rule and explained a little about the “chunking” workaround.
The Expert Mind:
http://www.sciam.com/print_version.cfm?articleID=00010347-101C-14C1-8F9E83414B7F4945
I agree that as it applies to software development we should try to minimize human memory requirements and when possible, design for better chunking.