Re: The semi-magic number 7? Not for lists.

Subject: Re: The semi-magic number 7? Not for lists.
From: Ben Kovitz <apteryx -at- CHISP -dot- NET>
Date: Thu, 6 May 1999 09:45:49 -0600

Geoff Hart wrote:

> The bottom line is that Miller's research focused on short-term
> memory (e.g., remembering phone numbers), not information
> presented permanently on the printed page. Although Miller's
> general observation is broadly applicable (i.e., shorter lists are
> easier to handle than longer lists, all else being equal), his
> specific observation is not broadly applicable, and certainly
> not to lists. Moreover, even if it were, there would be
> countless factors more important than the number of list
> items: how well written or how complex each item is, whether
> mnemonic aids were included with each item, whether the
> reader's context is stressful or relaxed, and on and on.
>
> I haven't provided the citation for Miller's article because it's
> not light reading and I wouldn't lightly recommend it to
> anyone else; I've managed to make it through once through
> sheer cussedness, and one day I'm going to sit down and
> write an English summary for my own use that I can
> understand with less effort. It's not that he's writing about
> anything really difficult to understand, just that he's writing it
> so badly.

Interesting that you say this. My understanding is that Miller's
article is often mentioned as exceptionally clear and congenial
writing--almost light reading, yet conveying some very deep
insights and without sacrificing content. I happen to agree with
the majority opinion: it seems to me a pretty simple,
straightforward article--actually, the written version of a
lecture, I think. (Someone please correct me if I have any of
this wrong.)

However, I've observed something many times now about this
article: many people "know" what the article is about before they
read it, and what they "know" is wrong. That is, people expect
the article's main idea to be, "People can't understand groups
containing more than 7 +/- 2 items." Consequently they're
baffled when they read the article, because that's not what it
says. It never seems to come to the point or spell out this
proposition clearly--because that's not its point.

When they finish the article, they had no idea what it was about,
but they nevertheless think, "Ok, this was empirical evidence
that people can't understand lists with more than nine items.
Now that I've read the article, I am In The Know, and from this
day forward, I shall break up all lists with ten or more items
into hierarchies, because Science hath decreed it so."

In fact, the first two thirds of the article is not about
short-term memory, but about the accuracy with which people can
estimate quantities that vary along a single dimension that they
can perceive with their senses, such as the loudness of a sound
or the degree of salinity of water (you sense the latter with
your tongue). He wants to know the amount of information in
these judgements: that is, how many distinctions we can make.
For a lot of these things, people could only accurately
distinguish something like seven levels, give or take quite a lot
depending on the stimulus. If you asked them to estimate which
of 15 levels something was, they'd tend to mess up.

Miller then points out that in practical life, we distinguish far
more levels than that all the time. So we must have some kind of
clever ways of defeating this limitation. For example, musicians
defeat it all the time, because they can tell you which of the 88
keys on the piano someone just played.

The final third of the article is about short-term memory.
Miller starts by asking how much information we can hold in our
short-term memories at once--that is, how many *bits*. This is
exactly like asking how much RAM your computer has: the amount of
RAM sets an upper limit on, say, how large a spreadsheet it can
keep in memory at once.

So Miller describes an experiment that "demonstrates" that we can
hold maybe about nine or ten bits of information in our minds at
once. The experiment consists of reading a string of 1s and 0s
to people and asking them to recite them back. That is
essentially the same thing as typing data into a computer
(without storing it to disk) and asking the computer to show it
to you again. Most people lose track somewhere around ten bits.
That's 2^10 distinctions, or 1024 distinct strings of binary
digits that people could hold in their short-term memories at
once (only one at a time, of course).

But then Miller shows that actually, bits is the wrong measure.
You can increase the amount of information that you can hold in
your short-term memory by using decimal digits instead of
binary digits. If you can remember a string of nine decimal
digits, that's 10^9 distinctions, or 1,000,000,000 distinct
strings of decimal digits. The proper measure of short-term
memory, he says, is *items* (or "chunks"), not bits.

And finally, Miller observes that in fact we defeat the limit of
7 +/- 2 chunks all the time, and that understanding how we do so
would be a worthy thing to find out. Coalescing sequences of
small chunks into larger chunks is one method: people can be
trained to recite strings of around *forty* binary digits by
learning to translate little groups of, say, four bits into a
single hexadecimal digit and holding just the latter in their
short-term memory.

Overcoming the 7 +/- 2 limit is in fact commonplace and of
tremendous importance in daily life. Imagine if we couldn't
understand sentences of more than seven words. Yet we do so all
the time. A note in a melody is a chunk, but we have no
difficulty following melodies that contain more than seven notes.
A telephone book is a huge list, but we don't use it by holding
its entire contents in our short-term memories at once. And on
and on and on.

*That* is the point of the article: that we have *ways of
overcoming these limits on how much information we can take in at
once*, and that doing so is commonplace and of tremendous
importance in explaining how humans are able to do the many
spectacular things that they can do.

Anyone who thinks that people can't handle more than 7 +/- 2
chunks of information in a single "list" simply isn't paying
attention. And anyone who reads Miller's article thinking that
that's what it says is probably going to be pretty confused.


Here's the citation, by the way:

George A. Miller. "The Magical Number Seven Plus or Minus Two:
Some Limitations on Our Capacity for Processing Information."
_Psychological Review_ 63 (1956), pp. 81-97. Reprinted in _The
Psychology of Communication: Seven Essays_, New York: Basic
Books; and _Psychological Review_ 101, no. 2 (1994), pp. 343-352.

I recommend that all tech writers read it, just so they won't be
bullied and bamboozled by the Learnèd Ignorant.

Lastly, for folks looking for some kind of rejoinder to the myth
that people can't understand lists of than 7 +/- 2 elements, ask
them if the Old Testament would have been vastly more
comprehensible if there were Nine Commandments instead of Ten.

--
Ben Kovitz <apteryx -at- chisp -dot- net>
Author, _Practical Software Requirements: A Manual of Content & Style_
http://www.amazon.com/exec/obidos/ASIN/1884777597
http://www.manning.com/Kovitz


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