Analogy – ”partial similarity between two things that are compared”

Source analog – target analog

An analogy might be superficial or deep, where deep analogies share similar relations as well as similar features (Thagard calls them ‘interesting’)

The Dennett (1991) example:
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 strings.

A. Suppose the letter-string abc were changed to abd; how would you change the letter-string ijk in “the same way”?

Possible solutions:
1. What happened was that the rightmost letter was replaced by a d, hence: ijk ->ijd
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’, hence:
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: fluid concepts.”

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”, “neighbourhood”, …

The Architecture; Cognition and Perception

The architecture is neither connectionist (i.e., neural network), nor symbolic.

Points:
-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 computer.

-> 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.