Introduction to Dragons - Formidable Problems in Qualitative Physics

Dragons in Qualitative Physics and Mathematics
Dragons are formidable problems. challenging, and yet solvable using little or even no algebra or calculus. A collection of Dragons, focussing on mechanics, was published long ago, in the out-of-print collection:

Harvey A. Cohen, A Dragon Hunter’s Box

where the Dragons were magnificently illustrated by Ms Jeni Rawson, who wrote out the text by hand, and embellished, sometimes with adapted borrowing from classic illustrative artists such as Doré.

The Dragon Hunter's Box included material interpretting Dragon Hunting -- forays at Dragons -- in terms of ideas developed by Thomas Kuhn and Imre Lakatos to explain the evolution of physics and mathematics. An important analysis of Dragons in relation to Piagetian Conservation puzzles and to Marvin Minsky's Frames theory of knowledge was published as Harvey A. Cohen, The Art of Snaring Dragons, MIT Artificial Intelligence Laboratory Memo 338, (1975) downloadable as PDF (in a new window)

which was the first, and defining paper, in the field of qualitative physics (as a domain of study within cognition and instruction).

One Dragon from the original compilation is YoYo, or strictly speaking, YOYO in the Upper Case, and yoyo in the lower case:

YOYO
yoyo

Which way does the YoYo go ? Left or right? In both cases?

Do you need help? Even if you don't, try moving the mouse over the frabjous, beasties, ZsaZsa, TseTse, and Garbo web versions of the creatures of the Dragon Hunter's Box. But whose suggestions should one listen to, or are they both right or both wrong ?

To repeat, The Dragon Hunter's Box is out of print. This site is intended to provide a web version of The Box. Animated versions of various Dragons together with hints and tales of Dragon snaring will be posted here in the coming months.

In sum -- the Dragons in The Box and on this site are accompanied with playful suggestions, sometimes very helpful, sometimes highly misleading, all calculated to direct the would-be Dragon Slayer to the weapons of his/her arsenal. But please note: wooden stakes are NOT suitable -- these are Dragons and Not Vampires!

ZsaZsa says -- Darlings --
In both cases the cord is pulled to the right. In UPPER CASE cord is drawn off the top of the YoYo to compensate, and so YOYO rolls right. In lower case, the yoyo rolls to the right to compensate for the end of the cord going in that direction

The "Hint" page for YoYo from A Dragon Hunter's Box can be viewed by Clicking Here or in PDF by clicking on the token

A sentient being has to have a capability at qualitative physics and mathematics in order to interact with the world about us. The development of our knowledge of the world tends to go by stages, where at each stage a simpler scheme is replaced by a more sophisticated. This is also true with regard to the development of Science, as stressed by Thomas Kuhn, and the development of mathematical theory as discovered by Imre Lakatos. Children's ability to use quantity and number likewise undergoes an amazing transformation at about the age of five, as evidenced by the following:

Note that the top diagram, with one egg in each cup, is what the child initially views. Then in front of the child the eggs are removed the cup, and spread out as shown in the lower diagram.
In this game for children, invented by the Swiss psychologist Piaget, a simple question is asked, to which both the younger and older children give a confident answer. This is an instance of a mathematical Dragon. Just what is going in children's head both before and after this stage is reached is discussed in Heuristic Growth and Intellectual Development.

Links to the Dragons now on-line are included in the subset of Dragons::

	The Milko Bottle Problem aka the dragon Milko
	The Ilya Revel
	Inducia Capillaria I a Lakatosian Monster
	Inducia Capillaria II a Mercuric Lakatosian Monster
	The Coin Problem
	The Flying Omnibus: How and Why Aeroplanes Fly
	The BumbleBee Paradox: Why It Can't Fly But Does
	The Satellite Paradox: Negative Mass in Low Earth Orbit
	Executive Toy -- A Challenge in Metacognition
	Cyber -- a 3D Perceptual Dragon
	Ayelet's Challenge -- a mathematical puzzle
	The Ant on the Box Problem - a new mathematical Dragon
	Sir Arthur Eddington's Cricket Puzzle -- For Cricket Fans only

Just what is a Dragon? And just how does one go about snaring Dragons ?
The answer is given is given on the web pages entitled

The Art of Snaring Dragons

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 as aboutdragonsATtpg.com.au {Replace the AT by @ in your mail program.}

$Colour phograph of the Lipson LEGO model of \"Belvedere\"$

There is an interesting correspondence between Dragons and the category of visual illusions -- the Impossible Figures -- that form the basis of Escher's famous lithographs.

The Escher lithographs stimulate. In Waterfall for instance, one traces the flow of water down, down, down, until the water flows into its starting location. Simply impossible.

Recently LEGO models based on the Escher Lithographs, Balcony, Belvedere, Waterfall, Ascending and Descending. and Relativity were produced by Andrew Lipson. Photographs taken of these models match the Escher lithographs on which they are based. Yet these are real constructible models of the impossible.
Note that the 2007 version of Internet Explorer (unlike earlier versions) does not support Java required to view Lipson's animations.
Or are Lipson's models Lakaosian Monsters, a special category of Dragon discussed on these web pages ?

And lastly, here is a mathematical riddle, called the Case of the Missing Dollar