Tangle Toy and the dice-loading problem

The Tangle Toy is one of those marvellous things which excites the eye, hands and brain! (I saw one in Denmark being sold by a Dutchman - I wish I'd bought it!)

It is extolled by Peter Wolfenden (at 'pack of wolves'), who also presents the dice-loading problem.

I investigated this about 15 years ago, using a. a lot of kids who threw a lot of carefully constructed dies b. a model which basically said the probabilities were proportional to the k-th power of the base size - so if k=2, then a base with area 2x would have FOUR times the chance of 'winning' (being base-down) compared with a base of area x. (A refinement used the angle-subtended at the centre of gravity instead of base-size as the key parameter)
Our conclusions were 1. The best-fit value of k was extremely high (I think it was 10.9 or something like that) 2. Different materials behaved VERY differently - wood was different from paper etc etcThere was an article in the Mathematical Gazette which tried a 'theoretical' approach
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Explanation given at http://www.wolfendens.com/dice_load.html


My dice loading problem
Given a rigid but slightly elastic homogeneous polyhedral mass in Euclidean 3-space (ie a chunk of material with flat sides, like a die for example), determine from the geometry of the object what the probability is of it coming to rest (when dropped towards a hard surface under the pull of gravity from a "reasonable" height (at least several times its diameter) with "random" orientation and angular momentum) on each of its sides.

There's a bit of an issue with defining precisely what rigidity, reasonable height, and random orientation & angular momentum all mean. Also with the physics of perfectly sharp corners and edges. But my intuition says that the mechanical system of this polyhedral mass rolling around on a hard surface produces behavior which is so sensitively dependent on initial conditions that we could define almost any sort of continuous distribution on almost any small (but sufficiently energetic) subset of possible initial "die positions" in almost any approximately reasonable physics and still get the same set of probabilities.

My intuition also says it shouldn't be necessary to go through the pain and expense of actually performing any simulations to generate this set of weights. I have a really neat idea for treating this as a stochastic problem, but I'm stuck on scale invariance - I don't think it should matter if I've got a chunk of material a centimeter on a side or a meter on a side. But for any given distribution on initial conditions, it seems to matter a great deal.

http://www.wolfendens.com/grid_project.html

"Chance of one in a billion"

How often do you hear 'Gee-whiz' statements such as "The chance of this happening was less than one in a billion"?

For example, Planetscience News has just sent me the following:


"CALLING ALL ROCK HUNTERS!

Steve Irwin, Crocodile Hunter, is old news. Rock hunting is the new craze to sweep the nation in 2004. But we're not just talking about any old rocks though; we''re talking rocks of meteoric proportion!

The Open University is asking the public to check in their gardens for unexplained objects, which they suspect could be meteorites. More than 30 are believed to fall in the UK each year. Last week, a great grandmother was lucky to escape serious injury when a suspected meteorite hit her arm as she was hanging out the washing! The chance of this happening is one in a billion."

Well, that's impressive!

But what (if anything) could it possibly mean? (And how did they do the calculation?)

Does it mean that everytime anybody hangs out the washing, the chance of them getting hit by a meteorite is one in a billion? Well if so, that probably means several hits per day, given that the world population is six billion and we all hang out the washing well - at least several times per day!

Or is one in a billion the chance of being hit on the arm?

Or is it just statistical hype - the 'fallacy of the big lie', that if we say anything large enough, then somebody will believe us.

I THINK WE SHOULD BE TOLD !!

Munch's 'Madonna' and 'Scream'

Why is Munch's 'Scream' so much better known than his delectable 'Madonna'?

And why is so little heard of either until they are stolen?

.

"Tragic Week" in Barcelona

In Spain, the "Tragic Week" began on Monday 26 July 1909 when the union, Solidarad Obrero, which was led by a committee of anarchists and socialists, called a general strike against the call-up of the mainly working class army reservists for the colonial war in Morocco.[17] By Tuesday, workers were in control of Barcelona.



The Tragic Week must be understood as an anti-imperialist uprising situated within a long tradition of anarchist anti-imperialism in Spain. The "refusal of the Catalonian reservists to serve in the war against the Rif mountaineers of Morocco," "one of the most significant" events of modern times,[19] reflected the common perception that the war was fought purely in the interests of the Riff mine-owners,[20] and that conscription was "a deliberate act of class warfare and exploitation from the centre." [21]

eBay, Amazon etc

Try these links:

• My eBay listings
• My wife's Amazon listings

Gaudi etc.

Just reading a book on Gaudi - preparing for a visit to ECSITE in Barcelona next November. It's The Essential Gaudi" by Jordi Bonet
.
and focuses especially on the relationships between geometry and architecture, which is something that interests me (The subtitle is "The geometric modulation of the Church of the Sagrada Familia". 'Modulor' is of course a concept beloved by Le Corbusier.)

I was struck by the diagrams - they include some of Gaudi's originals as well as others created by the author.

It made passing reference to Albert Schweitzer, who visited Gaudi. Schweitzer used to be a hero of mine (extolled to me along with Gandhi by my marvellous junior school teacher, Miss Elsie Salmond of Underhill School, Barnet - Schweitzer later slipped in my hagiography, although Gandhi and Salmond did not).

Other links:

• gaudiclub.com
• Schweitzer
• Gandhi
• Miss Salmond
.

• My schools (Underhill/QEGS/Kingston High School/Accra Academy)
• Geometry and Architecture, Corbusier etc.
• Sagrada Familia
• Barcelona
• ScienceTourist
• Gaudi and Bonet