> From: Taylor, Karl <krt196@soton.ac.uk>
>
> I guess the short form of this is: although something is taken to be
> modular (e.g. vision) is it still assumed to use the same mechanisms
> that were proposed generally (i.e. computation, analog -> the hybrid
> model)?
Yes. All three possibilities -- symbolic processing, analog processing,
and neural net processing -- could have a role in general models
of the mind, or in modular models of parts of it. The critical point is
that modules, if they are indeed modules, hence functionally independent
of everything else going on in the mind, can be explained on their own
terms, without reference to the rest. Explaining many independent parts
of the mind would be easier than explaining all of it.
But the jury is still out about what -- besides the sense and motor
modalities (seeing, hearing, touch, movement) -- is independent and
modular in the mind.
> I think I understand the two different approaches to cognition that
> were described earlier in the course: the computationist (symbol
> manipulation) vs. the imagist (image manipulation).
But don't forget neural nets too...
> Whilst reading chapter 4 of Green et al. it seemed like the same ideas
> were coming up again with new names and without any mention of the
> old. Are these really the same things or do they just look the same?
>
> There is a section under Object Permanence called something like
> "Invariants and Transformations" which introduces the idea of
> prototypes (or templates) as a visual mechanism, and how these might be
> matched to seen objects through some processes of transformation.
>
> At the beginning of the course there was a description of an experiment
> investigating recognition of 2-D projections of 3-D objects. The
> suggestion was that the time taken to recognise an object was
> proportional to how much one image was rotated from another. This was
> evidence for the validity of the mental images theory.
>
> Are these two ideas must be the same? Doesn't the imagist concept of
> cognition involve this same use of templates and transformation
> described for vision?
Yes they are. And bravo for realising it. (Don't forget that each
chapter is by a different author. They do sometimes say the same thing
with a slightly different terminology.)
> The chapter also introduced the idea of coded descriptions (i.e.
> verbal, parametric). These sound like they use symbols. So aren't these
> like algorithms?
Yes they are; right again.
> I thought, if invariants vs. transformations is the same as symbols vs.
> images then wouldn't a "solution" be the hybrid approach, like before?
> i.e. that we use descriptions in reference to some descriptions
> ultimately ground in images.
I knew there would be some confusion there, and it's not your fault.
For some reason the author of this chapter doesn't seem to realise that
invariants and transformations are flip sides of the same coin: An
invariant is always an invariant under a transformation. What is
"invariant" is what stays the same under the transformation.
For example, the length of a line (but not its position) is invariant
when we rotate it, Rotation is a transformation.
The problem of object constancy is about how we can "recover" one and
the same object under many transformations: left/right, up/down,
near/far, rotation, etc. The brain uses these invariant to see an object
as being the same object despite all the changes that its "shadow"
undergoes.
So there is no "invariants VERSUS transformations": invariance is always
invariance under a transformation.
The difference between a symbolic representation of an object and an
analog "image" of it is that the shape of the symbols is arbitrary
whereas the shape of the image is not. The image preserves some of the
shape of the object, the symbol does not.
But remember that anything can be SIMULATED as closely as we like
using symbols and rules: Consider mental rotation. The easiest
and most sensible way to implement a capacity to see an object
as the same under all rotations is to do an analog rotation on an analog
of the object. (Note that this rotation is done unconsciously for you by
your brain.)
An alternative way to do it is to turn the 2-D shadow on your retina
into a grid of pixels (0's and 1's) and compute which 2-D shapes
come from the same 3-D object using a numerical approximation
to solid and affine (perspective) geometry.
To summarise: There is no invariance VS transformations; they are
mutually dependent. And this (non)distinction is not like symbols vs.
images. What is like symbols vs. images concerns whether you represent
something using algorithms operating on symbols (e.g., numerals)
or you represent it as transformations on sensory shadows and
what can be recovered from them.
> p117 of Green says:
> "...the representation can be envisaged as a generalisation of the
> "form" [the same as a mental image?] plus parameter means of encoding
> global shape [the description, right? A string of
> symbols?]...recognition does not involve extracting the invariant
> information over exemplars but extracting the parameters of the form
> [huh?]...."
>
> Is this the same as I imagined the hybrid theory would be?
Not exactly. Examplars are actual shadows on your sense-organs; one
approach is to try to recover the object from the small local
invariants in those shadows... Another approach is to look for global
invariants in the form as a whole.
The first approach applies only to parts of an object; the second
applies to the whole object. The example given is of the fine scale
structure of the leaves on the tree (local) and the overall shape of
the tree.
The author of Chapter 4 tries to distinguish global parameter
representations from prototype or template matching. To match a sensory
shadow to a template, several templates are applied to it, and the one
with the best fit is used. In global form representation of, say, a
blimp, the blimp would not be represented as an average over all blimps
see, but as a parametrised shape, represented by its length and
its circumference. This sort of representation is symbolic.
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