Re: Miller: Magical Number 7 +/- 2

From: Harnad, Stevan (
Date: Thu Nov 16 1995 - 12:05:39 GMT

ws> From: "Smith, Wendy" <>
ws> When we categorise, do we start off with an (?infinite) number of
ws> categories containing 1 item each, and build them up into larger but
ws> fewer categories? Or do we start off with one category and break it
ws> down into smaller but more categories? Or do we do both? Or is it
ws> effectively the same thing?

You are asking an empirical question (i.e., it has to be answered by
experimental analysis and modeling), but a guess would be that there's
some of of the "top-down" kind of categorisation, where all things are
lumped together in one big pile and then sorted into smaller sub-piles
when/as needed (as dictated by the consequences of NOT sorting them, or
sorting them the wrong way). There are also biologically prepared
categories (like the colors) that already come pre-sorted for us, with
inborn feature-detectors tha filter inputs into their proper categories.

The rest is a question about specifics. Some things one can venture to
doubt, though:

(1) It's not "bottom-up" [this is a nonstandard use of "bottom-up," just
for this special case]: It's not everything in a unique category, and
then we combine them into bigger superordinate categories. There are
both psychophysical problems with such an idea:

(a) As Miller shows, we don't really have absolute categories that are
1 jnd wide: the jnd is just a relative judgment; the maximum number of
categories in a single dimension is probably 7 +/- 2.

(b) If we DID have an infinite rote memory, like Luria's S or Borges's
Funes, then what we would have would not be an infinity of categories
with one member in each, we'd have no categories at all, because each
experience, each input, would be infinitely unique, and would never
recur or repeat (it couldn't recur, because the time, at the very least,
would be different every time). Remember that categorisation is
generalisation, invariance selection, and reduction. There is a
trade-off between faithfully preserving the details of any case, and
being able to generalise so as to sort it into a category, which, after
all, is a KIND of case.

So, no infinity of unique categories. But it may well be that with the
categories we do have -- whether the biologically repared ones or the
learned ones -- the our future categorisation experience (as dictated by
te consequences of sorting one way or another) can go both up and down:
We can combine categories we already have into bigger and
coarser-grained superordinate ones, or we can subdivide them into smaller
and finer-grained subordinate ones. Or we can even cut across the
uo/down hierarchy sometimes...

ws> Also, Miller says ".... did not demonstrate that people can judge only one
ws> attribute at a time. .... people are less accurate if they must
ws> judge more than one attribute simultaneously."
ws> So, when we need to judge several attributes, perhaps for different
ws> purposes, does it make better survival sense to judge several
ws> attributes in the same category, and perhaps sacrifice accuracy?
ws> Or form categories according to context, and use the context to cue
ws> which attribute to use? Or do both?

You need to think of a specific task. I don't think there is a general
answer to this. And it also depends on whether the judgment is relative
(dsicrimination) or absolute (categorisation). In general, the world
(whether the physical/biological world of food, water, mates, etc., or
the social world of loyalties, fashions, conventions, etc.) that
dictates when we are "right" or "wrong" in how we react to things.

Context is a separate, special issue. We'll be discussing it more. For
now, what do you mean by context?

ws> (This is my third year project; am I questioning along the right lines?)

Yes you are!

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