london tube
"london tube"

What are the utilities of an analogy and what are its limits? Are analogies simply the Emperor's new clothes which blind us from the truth, or are they a kernel of language able to capture the full picture?

In studies regarding functional fixedness, task completion is dependent on breaking from fixed points(fourth wall), to simply see an object for more than what it is. However, all analogies are not equal: in studies related to functional fixedness, when an analogy contains narrative, fixedness is not overcome*.

“From a bit to a few hundred megabytes, from a microsecond to a half an hour of computing confronts us with completely baffling ratio of 10^9”, Djikstra EWD1036. In an essay by Djikstra titled, On the Cruelty of Teaching Computer Science, he advocates for the kindness of teaching students how to overcome the inability to face radical novelty. Djisktra was critical of visualization and the use of computers in writing programs.


Thinking beyond limits of structural framework, I recently tried to find a general solution to a puzzler question about inhomogenous ropes. The question is as follows: if two equal lengths of rope, which burn unevenely(inhomogenous), for a total of 60 minutes, then how can a length of 15 minutes be measured. I tried to use the exponential sum over n-inhomogenous groups equal to 60, a cdf, and encountered fungible numbers, none of which really answer the question.

  • Here is a logic puzzler: To prove that an Ace is always even, what additional information is needed?

Translated into a narrative example: how you would determine underage drinking in Montreal? Knowing someone over N_years drinks soda adds no additional information to the problem. To detect the age of cheaters, the only additional evidence required is to check those underage. Intuitively, enforcement of this rule, never relies on checking that the drinks of older people are also soda.

However, this is the sort of additional evidence (in the abstract domain) which is most often provided.

  • So I briefly outlined the utility of a functinoal analogy(not narrative) to get something done.
  • The issue of complexity and scale complicates matters; Djikstra advocates for the purity of reason.
  • Sometime frameworks/structure are incapable of encapsulating the problem, such as inhomogeonous ropes.
  • Finally, a logical proof is translated into a narrative, and is easily determined.

… I believe the ability to emotionally relax is critical part which make any of these components work.

*While the narrative domain does not overcome functional fixedness, its use helps with problems relating to abstract logic, as in the card-example.


human reasoning - Some ideas on writing: - [Knuth - Mathematical Writing](/files/knuth_mathematical_writing.pdf) - [Vonnegegut - How to Write With Style]( and [The Shape of Stories]( - [Orwell - Politics and the English Language](