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,
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
in the downloadable technical memo,
- In Toto
- Divide and Conquer
- Formula Crank
- Columns (Two different Styles)
- Add Effects (and Subtract Effects)
Harvey A. Cohen, The Art of Snaring Dragons M.I.T. Artificial Intelligence Laboratory Memo Number 338,
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 --
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.