WELCOME TO DOUG CLARK'S HOME PAGE.

My main interests are:

• Probability puzzles, paradoxes and problems.

• JavaScript.

This page was most recently edited on 11/11/2005.

On this page are summaries of and links to articles on The Sleeping Beauty Problem (1), The Shooting Room Paradox (2), Dr Stern's Nasty Problem (3), two types of Squircle (4, 5), a JavaScript Microbial Growth Rate Calculator (6) and a JavaScript Cyclic Cellular Automata Pattern Generator. (7).   Click here to email me.

(1) THE SLEEPING BEAUTY PROBLEM.

Beauty agrees to participate in an experiment.

On Sunday evening the researchers explain the experimental protocol to Beauty and later put her to sleep. On Monday morning they awaken her, interview her and then give her a potion, which puts her to sleep and erases all memory of the Monday morning awakening. Depending on the toss of a fair coin the experiment then follows one of two routes. If heads; she remains asleep until Wednesday when the experiment ends. If tails; she is woken on Tuesday morning, interviewed and then put to sleep. On Wednesday she is woken and the experiment ends.

In the three awakenings that may occur during the experiment the evidence available to Beauty is identical. On each occasion the researchers ask her, �What is your credence that the coin lands heads?�

Some say that Beauty should answer a half because the coin is unbiased while others argue that her answer should be a third because the coin lands heads in only one of the three possible awakenings.

See how Beauty solves her problem in my version: more  top

(2) THE SHOOTING ROOM PARADOX.

This has been described as a 'good, hard paradox' and 'a cogent line of reasoning alongside a spurious one, masquerading as horns of a dilemma.' Make up your own mind: more  top

(3) DR STERN'S NASTY PROBLEM.

This problem is from Gary Fuller's Probability Net website. For my solution and a link to Gary's interesting site click here: more  top

(4) HOUDINI'S SQUIRCLE.

'Houdini succeeded in escaping from the box which had been submerged in the Cuyahoga. While resting on the bank and doodling on a piece of bark with a pencil lying about he saw, to his amazement, that he had drawn a square circle.' Click here for the construction of a curve that is both the perimeter of a square and the circumference of a circle: more  top

(5) PETER PANHOLZER'S SQUIRCLE.

This family of shapes was given the name SQUIRCLE by Peter Panholzer. The page displays shapes that are intermediate between squares and circles. A browser equivalent to Internet Explorer 5+ is required to use this page: more  top

(6) MICROBIAL GROWTH RATE CALCULATOR.

If you are interested in growing batch cultures of bacteria in microtitre trays you might like to try this calculator out. A browser equivalent to Internet Explorer 5+ and Excel are required to use this page. Carefully read the help file before use: more  top

(7) JAVASCRIPT CYCLIC CELLULAR AUTOMATA PATTERN GENERATOR.

This page runs on 'Applet' free JavaScript: more  top