Kirsh, D. (2010). Thinking With External Representations. AI & SOCIETY, 25(4), 441–454. doi:10.1007/s00146-010-0272-8 https://www.filepicker.io/api/file/mDUqbFjZTRG2bMTN2PtY
1. Introduction
2. Materiality And Its Consequences
3. Shareable And Identifiable Objects Of Thought
4. Rearrangement
5. Physical Persistence And Independence
6. Reformulation and Explicitness
7. Natural Encoding
8. Using Multiple Representations
9. Construction And Tools
10. Conclusion
2010:
Attempting a straight through read of this paper instead of a scholarly skimming for comparision, now that I have had practice skimming and summarizing a few papers.
"seven ways external representations enhance cognitive power: they..."
The work is broken into 10 sections.
"...changing the terrain of cognition can do more than change [computational] cost..."
The focus "of this work, [is] to ways we interact with representations to alter the cognitive terrain..."
Point of interest: consequences?
Interactive cognition enhances:
efficiency
"because it regularly leads to fewer errors or to greater speed."
effectiveness
"because it regularly helps subjects to compute more deeply, more precisely, and often more broadly."
"...involving visual and motor cortex."
interactive changes concern:
Define structure, symbols, location, and then reference as shown and manipulated.
"...a persistent element that can be measured and reliably identified and re-identified."
"...use them as things to think with."
Distinguish between memory and perception, do not ignore the medium- specific nature of encoding. (nor the act thereof)
Rearrangement makes "it easier to perceive semantically relevant relations."
Example:
"take lemmas that are non-local in inference space" and move them near what they were discovered from.
lemma: A subsidiary proposition assumed to be valid and used to demonstrate a principal proposition.
Abbreviations, definitions, and symbols are ways to represent clusters.
Computer space complexity vs real world lost of persistance upon changes. Which leads into section five...
Interesting claim:
"Tools can be deployed" on physical representations.
Scale model functions:
Restatement
explicite vs approximent
Covered so far: persistence, reordering, reformulation, and simulation
Next: "How external processes may increase the breadth of cognition."
Because sometimes "the natural representation of the content only exists outside." (or takes years of refine to perfectly internalize)
Music example again... but then "there are times when notation does reveal 'more'."
Making correlations between multiple representations because of their individual strengths can be benifical.
Power of Construction: "the summation of persistence, rearrangement, and reformulation."
"by constructing a structure, we prove that its parts are mutually consistent"
"For any reasoning problem of complexity n , how do we know there is not some person, somewhere, who can solve it in their head, or could, if trained long enough? To be sure, this says little about the average person."
Therefore: tools. ("cost structure" over "biological inability")
"we often mark, annotate and create representations; we rearrange them, build on them, recast them; we compare them, and perform sundry other manipulations"
The article argues "that much of thinking centers on interacting with external representations, and that sometimes these interactions are irreducible to processes that can be simulated, created, and controlled in the head."
"push further, compute more efficiently, and create forms that allow us to share thought."
New recipes, furniture building, and such examples; what about the effect of not wanting to screw up? (section 1)
The conclusion wraps the article up well.
Interestingly, I found it easiest to read the article from using two different pdf viewers. The text was clearer, all of the pictures rendered, and the pages flowed together in a free javascript based web-browser viewer. In the open source, stand alone, lightweight pdf viewer; I could more easily assess the layout of sections and construct focus patterns. It also allowed larger text jumps. (Can more readily distinguish examples and segues from statements and therefore more quickly extract the information I am after for summarizing.)