The Art of Snaring Dragons

This page is part of a web-site devoted to the study of qualitative thinking, with an emphasis on those problems, quite formidable and challenging, called Dragons which can be solved without having to write anything down or perform a calculation. See Dragons for an introduction to Dragons with a physics emphasis, Mostly dragons have answers like yes/no, more/the same/less, left/right, top/bottom, up/down. But also there is a category of such problems called by the philosopher of mathematics Lakatos, Monsters, wherein the problem is to debug what looks like a counter-example to a known solution to a problem. But if you learn that YOUR solution to a Dragon is false -- the canonical wrong answer -- and become convinced that this is indeed so -- then to you this first solution IS a Monster, that has to be debugged.


The Dragon for detailed scrutiny is The Milk Bottle Problem  Milko


 How Do People Solve Milko ?

The Dragon Milko contains not just a question in qualitative physics, but a measure of suggestion and counter-suggestion.

Such as the observation that the w.b.p. (would-be-physicist) who predicted no change took his milk in cartons.

Back in 1974/5 I posed Milko (aka The Milk Bottle Problem) to various students and others, to find there were just a few styles of attacks on this Dragon. The participants were asked to voice their thinking -- "Loud Thinking" -- and I only intervened to progress the discussion -- not to lead it. ( The "Loud Thinking" interview approach.) Unfortunately these interviews were not taped -- but written transcripts were made. All these attempted "solutions" could be categorised by a principal problem solving idea, or heuristic.

For Milko I observed just five different heuristics in use -- these heuristics I called
Click on the links to see how to apply each of these heuristics to solve Milko with confidence. These solutions, motivated by these five heuristics are presented in the downloadable technical memo,

Harvey A. Cohen,  The Art of Snaring Dragons   M.I.T.   Artificial  Intelligence Laboratory Memo Number 338, May 1975. Download as PDF   

These heuristics are collections of problem solving ideas -- centred on a core heuristic.
There is arguable evidence, that not only have 5-year old children been observed to apply the Heuristic called Process, and also ByPass but so has a horse -- see
Strategic Problem Solving: ByPass Heuristic
But just what, in greater detail, is going on during the development of intelligence ? In Heuristics and the Growth of Intelligence it is shown how children elaborate the heuristic that they apply to estimations of quantity and number. It is proposed that the (core) heuristics possessed by children (and probably some animals) is elaborated during the education and training of physicists.

The author continues to collect Dragons, and the sagas of forays upon those frabjous beasties by physicists, both professional and tyros (=beginners), as well as like beasties in advanced fluid dynamics and stability, tackled expertly by dragon flies and bees, and far less expertly by human aeronautical engineers. I'm contactable by Email at
after making the obvious substitutions.