Archimedes' Bathtub: The Art and Logic of Breakthrough Thinking

by David Perkins, Ph.D.

The author suggests that “breakthrough thinking” isnot really a different type of thinking.  There’s no unique mental mechanism that kicks in.  Rather, there are types of problems which require some different mental approaches because they are “unreasonable”, they cannot be solved solely by the application of reason.  He deems these “ Klondike problems” because of the similarities they share with the problems faced by gold prospectors in the Klondike gold rush:

Wilderness of possibilities – a large solution space

Clueless plateau – with few clues

Narrow canyons – that tend to trap the search process in a solutionless area

Oases of false promise – where the measure of promise is high, but that do not contain a solution.

The structure of these problems creates a distinctive problem solving experience involving a long search, little apparent progress, a precipating event, and a “cognitive snap.” 

Examples of real life Klondike problems and their solutions include, as suggested by the title, Archimedes’ search for a way to measure the gold in the king’s crown, Gutenberg’s invention of the printing press, the search for a method of heavier-than-air flight, Darwin’s (and Wallace’s) development of the theory of survival of the fittest.

Throughout the book, the author uses “insight problems” and research done with them to develop points and to give the reader a chance to practice “ Klondike thinking.”  These are puzzles with an “either you get it or you don’t” quality.  The problem solver flails around with little apparent progress until a moment of insight produces a “cognitive snap” as the solution becomes clear.  Here are two examples of this type of problem:

Dots:  place three rows of three dots, aligned vertically and horizontally on a piece of paper.  Connect the three dots with no more than four straight lines.

The Mask:  There’s a man at home with a mask.  There’s a man coming home.  What’s going on here?  Perhaps it will help to know that the man with the mask is not a thief, that the man coming home does not live there, and that the man with the mask is not going to hurt the other man.

If you immediately saw the answer to these problems (or remember your first experience with them), then you know the “cognitive snap” feeling.  If you didn’t experience this, it might help, at least for the second problem, to know that I picked it partially because I write this on the way back from a baseball tournament.  The  book offers many more such problems.

The strategies for addressing Kondike problems include:

Roving:  Systematic or random coverage of the solution space.  This can include analytical thinking to reduce the solution space by noting redundancies, eliminating large areas of unlikely possibilities, etc., as well as “brainstorming”, systematic trials of all possibilities (e.g., some modern approaches to drug development), and the intentional introduction of random elements in the search.

Detecting subtle clues:  Sometimes, what appears to be a clueless plain may actually contain small, subtle, but important clues that will reveal themselves to either careful observation, superior knowledge, or both.  Think of Sherlock Holmes.

Reframing:  Challenge assumptions.  Remove search restraints not dictated by the problem.

Decentering:  When a seeming area of promise has not yielded a solution, move away from it in some fashion to search elsewhere in the solution space.

Are all “ Klondike problems” scientific?  Not at all.  The author uses and example of a middle-age career changer.  He has a large solution space of possible career changes (roving), without clear direction (detecting), may become trapped in a small area (reframing, say from a new job to improving some other underlying problem), and may become fixated on an attractive possibility that does not yield a solution (decentering).  Klondike problems” can also occur in the worlds of art, business, sports and games (chess), and many other areas.

Other factors affecting the ability to do Klondike thinking include:

·        Inert knowledge – knowledge that is not readily brought to bear on problems. 

·        Pattern-priming (immersing onself in the problem) prepares the solution-seeker to see clues to the solution where others would not.   Would Archimedes have even noticed the water overflowing from his tub had he not been simultaneously immersed in the search for a method for measuring the volume of an irregular object?

Evolution as a Form of Breakthrough “Thinking”

Chapter 13 is an interesting analysis of the process of evolution as an approach to Klondike problems.  Dr. Perkins, treating evolution as a strictly natural phenomenon with no supernatural component (no designer behind the design), shows how it approaches Kondike problems such as that of flight.

Evolution addresses the wilderness, canyon, and oases aspects of Klondike problem by overwhelming them:  ultimately, all variations are tried, and those with any degree of viability can then vary further to develop radically different creatures.  In the case of flight, feathers evolved as a form of insulation, with longer ones providing better insulation.  Eventually, variations of structure and feathering produced creatures that were slightly more likely to survive because of longer “hops” that were partially glides.  From this to the existence of the first true birds was a rapid development in the time frame of evolution.

Dr. Perkins notes, however, that discontinuous solution spaces cannot be explored by the evolutionary model.  In other words, if there is, for example, a possible set of creature we might call “Superbirds” that could exist and function, but no pathway of even marginally viable forms connects current creatures to that set of forms, then evolution can never develop such creatures.  Unless, of course, humans should do so and that result be attributed to the evolutionary development of human intelligence and imagination.

Memes are a form of evolutionary development in human thought and society.  First proposed by Richard Dawkins in The Selfish Gene, and developed by Daniel Dennett in Consciousness Explained, “meme” stands for “mental gene”, a unit of thought that thrives in the ecology of human culture and communication.  Memes can be ideas (democracy), industrial practices (smelting iron), medical procedures (bleeding), or wise sayings or proverbs.  Today, I would suggest that the blogosphere is a key development area for memes.  As I write this, various political bloggers are using “mullahcracy” or “mullarchy” (rhymes with “malarkey”) to denote the current government of Iran .  It would seem the “fitter” of these two memes will survive.  In fact, come to think of it, “blogging” itself is a meme.

Why We’re Stuck with Breakthrough Thinking (Chapt. 15)

Basically, the universe does not appear to be structured as a sequence of neatly reasonable problems.  To the extent reasonable problems exist, they are readily solved, leaving only the unreasonable ones for us to struggle with.  And, those very solutions develop patterns of practice that limit our awareness of other possibilities (canyons) even as we refine and perfect those practices.  Thus, any change in conditions puts us into a Klondike problem.

See also:

Wicked Problems