Re: George Miller [Magical Number 7 +/-2] Part 7

From: Stevan Harnad (
Date: Mon Mar 16 1998 - 15:31:53 GMT

On Mon, 2 Mar 1998, danielle still wrote:

> Miller's paper is his attempt to discuss his thoughts
> on the limitations of people's capacities for processing
> information. Miller thought that the variance was seven
> pieces of information for most people, however the number did
> vary slightly depending on the person. Miller stated that
> variation was plus or minus two pieces of information.

Don't confuse the number of alternatives or items with the number of
bits. The number of subdivisions of one dimension that we can identify
and the number of items we can remember is 7 +/1. That corresponds to
about 3 bits.

Information is also related to variance. The less a signal varies, the
less information it can encode. But don't confuse variance in the sense
of the informativeness of a signal (where more is better and less is
worse) with ERROR variance, or noise in the signal.

Here is the difference.

If I have to transmit signals over a wire by morse code, how many bits
do I need to convey the entire English alphabet?

There are 26 letters in all, but to make the bits come out even, let's pretend
there are 32 letters. so this means the following YES/NO questions.

I. First 16 or second 16?

II. First 8 or second 8?

That's 2 bits, and we already know that for 8 it's 3 more bits.

So for a 32-letter alphabet we would need a 5-bit channel. For 26
letters let's say it's 4.5 bits. So if the variance of the signal
was LESS than 4.5 bits, you could not code all the letters of the

That's GOOD variance, when it is correlated with the message you are
trying to send. Morse Code has enough variance. It is binary [meaning it
really only has two symbols, "short" and "long" or "dot" ("*")
and "dash" ("-")], but using that binary code, it can encode all 26
letters of the alphabet as a series of four symbols. ["A" is "*-"; "B" is
"-***"; "E" is "*" and the famous distress call, "S O S" is "*** --- ***"].

If you tried to encode all 26 letters as pairs of * and - you would not
have enough pairs: All you would have would be *, -, *-, -*, ** and --.
That's not enough variance to code 26 letters. You need 4.5 bits worth.

BAD variance would occur when you sent a -*** (B) and the first bit
dropped, so what was received was a *** (S). That's error variance or
noise. It does not covary systematically with the 26 letters but instead
distorts them randomly.

The idea is to maximise "good" variance (covariance with the signal)
and minimise "bad" variance (noise distorting the signal).

> Resulting in people's capacities varying from five to nine
> pieces of information. Miller was unable to make a judgement
> on the number seven, as he was not able to say why seven was
> the chosen number.

Be careful not to confuse the limits on the number of chunks or items
(5-9) and the limits on the number of bits (about 3). The chunk limit is
rigid, but the number of bits you code into a chunk is highly flexible.

> Firstly, it is thought that the span of absolute
> judgement imposes a limitation on our capacities. This
> limitation could be due to the fact that our learning is
> inhibited or that our nervous system is unable to receive all
> the information being presented to it. Or it could be that
> all the information is received yet only a certain amount is
> processed or only the parts relevant to the person is
> processed and the rest is disregarded.

The limits are probably passive (limited capacity) rather than active
(inhibition). But recoding into bigger chunks and/or selectively
attending to some dimensions and ignoring others is also active
and most of the deeper questions about cognition are related to HOW the
mind learns and uses categories. This is the capacity that distinguishes
us from Funes the Memorious, who just keeps replaying the unique
videotapes of every instant of his life and cannot select or ignore

> Following on from
> this is the limitations of immediate memory, it is shown that
> people are able to process more than one attribute
> simultaneously. However it means that they will be less
> accurate with the limitation of seven pieces of information
> being split between two stimulus's. Miller thought that by
> organising the information into their separate dimensions
> that they would be able to be put together to form a
> sequence. Therefore only taking one slot of information e.g.
> the sun comes out at night would be six separate pieces of
> information but if it was chunked together to form a sentence
> it would become one piece of information. This according to
> Miller streches the informational bottleneck allowing the
> capacity of information processing to grow.

Yes, recoding into bigger chunks is what it is all about. See the
earlier discussion of recoding. And notice how subitising numerosity
turns into the sequential coding of number using strings of symbols
called "numerals": 1, 2, 3, ...

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