Analogy – ”partial
similarity between two things that are compared”
Source analog – target
An analogy might be superficial
or deep, where deep analogies share similar relations as well as similar
features (Thagard calls them ‘interesting’)
The juvenile sea squirt wanders through the sea searching for a suitable
rock or hunk of coral to cling to and make its home for life. For this
task, it has a rudimentary nervous system. When it finds its spot and
takes root, it doesn’t need its brain anymore, so it eats it! (It’s
rather like getting tenure.)
To understand the analogy,
one must understand what the mappings are: the professor and the sea squirt,
finding a rock and getting tenure, and so on.
The Copycat Project
What I really want to talk
about is The Copycat Project by Douglas Hofstadter
and Melanie Mitchell.
Copycat is a computer program
designed to be able to discover insightful analogies, and to do so in
a psychologically realistic way. It operates in a micro world of short
A. Suppose the letter-string
abc were changed to abd; how would you change the letter-string ijk in
“the same way”?
1. What happened was that the rightmost letter was replaced by a d, hence:
2. The whole string was replaced by abd, hence ijk -> abd
3. All c’s were changed to d’s, hence ijk -> ijk
4. The rightmost letter was replaced by its alphabetic successor: ijk
-> ijl. This is what most people answer, and it is the answer Copycat
gives on 980 out of 1000 runs.
B. Suppose the letter-string
aabc were changed to aabd; how would you change the letter-string ijkk
in “the same way”?
As in the first problem, most
people see the change as “the rightmost letter was replaced by its
alphabetic successor”. But should that give you
1. ijkk ? ijkl ? This seems to ignore the doubled ‘a’ and
the doubled ‘k’.
2. Should we therefore change both k’s (as they form a unit)? ijkk
--.> ijll? Now the concept of a letter has “slipped”, suddenly,
we are comparing a group of letters to a letter. But we are still ignoring
the ‘aa’. ‘aa’ and ‘kk’ plays similar
roles, don’t they? > So, what is the counterpart of the ‘c’?
If the leftmost object ‘aa’ corresponds to the rightmost object
‘kk’, then surely ‘c’ corresponds to ‘i’.
Therefore, we could simply take the successor of the ‘i’,
3. ijkk ? jjkk. But since we have mapped ‘aa’ to ‘kk’
AND ‘c’ to ‘i’, it seems natural to read ‘ijkk’
in reverse. This reverses the alphabetical flow in the string. The conceptual
role of successorship in aabc is now being played by that of predecessorship
in ijkk. Hence, we get ijkk -> hjkk.
So, two concepts have “slipped”
during this investigation: a ‘letter’ turned into a ‘group
of letters’, and ‘successorship’ turned into ‘predecessorship’,
and this gave us a deeper analogy, one that “feels better”
(maybe because of the symmetry?).
Copycat ->The Real World
Now Hofstadter and Mitchell
make a bold claim: “… the Copycat Project is not about simulating
analogy-making per se, but about simulating the very crux of human cognition:
The fluidity they are talking
about is the “slipping” we observed; under pressure, concepts
slip into “related” concepts. Concepts such as ‘predecessorship’
and ‘successorship’ are intended to be idealised versions
of any non-identity relationship in a real-world domain, such as “parent
of”, “neighbour of”, “friend of”, “employed
by”, “close to”, and so on.
The group (e.g., abc) plays
the role of any conceptual chunk based on such a relationship: “family”,
The Architecture; Cognition and Perception
The architecture is neither
connectionist (i.e., neural network), nor symbolic.
-Complexity theory the “opposite” of chaos-theory: Complex.
Th.: Order emerges from chaos.
In parallel processing, there
is an inherit “randomness” (chaos); you don’t know when
the next signal is coming in from another processor.
This randomness needs to be
implemented in a system (added to a system) that is to run on a serial
-> Likened to the massive
parallelism of the brain (reentrant pathways).
It is quite likely that a good
theory of “consciousness” not only can accommodate this randomness,
but also actually rely on it to work (Edelman &
Tononi, 2000). -> Copycat relies on the randomness.