Re: George Miller [Magical Number 7 +/-2] Part 4

From: Stevan Harnad (
Date: Mon Mar 16 1998 - 14:18:08 GMT

On Mon, 2 Mar 1998, Elizabeth Cole wrote:

> Part Four: Subitizing
> Miller starts off by talking about an experiment by
> Kaufmann, Lord, Reese and Volkmann, in which a number of
> dots, from one to over 200, were flashed on a screen for only
> one fifth of a second. The participants' job was to say how
> many dots they had seen on the screen. The results of this
> showed that for patterns containing 5 or 6 dots the
> participants were ALWAYS correct. The name given to this was
> the ability to "subitize" and was how the participants could
> recognise virtually without fault patterns containing up to
> SEVEN dots. However, as above seven the participants couldn't
> recognise immediatly the number of dots, they had to
> "estimate".

In Latin and in Italian, "subito" means "suddenly," or "all at once."
People can judge the "numerosity" of a small number of objects; that is,
they can tell all at once how many there are, without having to count
them one by one. But once the number of objects gets higher than the
Miller limit, mistakes happen and the ability to subitise breaks down.

> Miller then questions if this is the same process as when
> "unidimensional judgements" are limited to seven catagories.
> However, he concludes that there is a difference, as there
> are several ways of processing the number of something (for
> example the number of dots) "there are about 20 or 30
> distinguishable catagories of numerousness". Therefore there
> is a difference in the amount of information recieved from
> one-dimensional and two-dimensional displays.

This is probably partly because any collection of objects you look at
is at least two dimensional (except for objects arranged along a line).
Our informational capacity may be higher there not only because of the
extra dimension, but also because there are many "special" patterns we
recognise in 2 dimensions: We immediately know that objects arranged in
a symmetrical hexagon would have six corners. If we see two hexagons, we
know there are twelve corners, and so on. All those special cases may
help us subitise the number of objects when they happened to be arranged
in a way that resembles any of these special ones.

Increasing your informational capacity this way would also be an example
of recoding into bigger chunks.

> Miller then goes on to question if in a two dimensional
> display, the relevent dimensions of numerousness are area and
> density (which obviously wouldn't both be in a unidimensional
> display). Therefore this would then lead to a
> difference, depending on the dimension of the display, to how
> information about the number of something is processed.
> However, the number of items also has a bearing on how the
> information is processed. Miller adds

Probably both dimensionality and recoding have something to do with why
we can subitise more numerosities than just 7.

> > "When the subject can subitize, area and density may not
> > be the significant variables, but when the subject must
> > estimate perhaps they are significant"
> Therefore, at least in the case of a two-dimensional pattern
> of dots, there is a difference between the way in which
> groups of below seven items are processed to estimating the
> number of items if it is greater than seven. This is due to
> other factors, such as the area and density of the display,
> which affects the number of items guessed by the participant.
> I hope I haven't confused you too much (although I think I'm
> still a bit confused by it - but I tried my best!!).

No, the possible role of adding dimensions or of recoding is fairly
clear. If you're using shape information, you use more dimensions than
if you just subitise quantity. (And let's not forget that when we go
past the subitising limit, we can still see and remember how many things
there were by using one of our most powerful learned codes in which to
code their quantity: counting using numbers!

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