Tetherd Cow Ahead

Calloo callay, oh frabjous day! Or perhaps ‘Callow callay’ might be a more appropriate salute in this particular case, for next week sees the release of Julian Doyle’s Chemical Wedding, a film starring the wonderful Simon Callow, that has some misguided university types using ‘the world’s biggest super-conductive (sic) computer’ to resurrect the spirit of the redoubtable (if arguably substantially unhinged) Aleister Crowley to possess the body of a classical history professor.

Of course it all goes horribly wrong (as things necessarily must if one attempts to strike up a rapport with the self-proclaimed greatest Satanist of our time) when the reborn Crowley embarks on an effort to call up the Power of the Abyss to unite the Biblical Beast of Revelations with the Whore of Babylon in the Ultimate Satanic Rite – The Chemical Wedding. A showdown between the forces of magic and technology, and other jolly antics, thence ensue.

Oh how I look forward to this film! No-one can do this kind of high camp techno-occultism with anywhere near as much panache as the British, and when the director is the guy who edited Brazil and the writer is the lead singer of Iron Maiden how can it possibly fail to be worth the price of the ticket?!

___________________________________________________________________________

Props to Sean for the heads-up!

…and RaJ – how can I possibly have failed to miss the Number of the Post? And I call myself a Reverend. I’m definitely losing my touch.

___________________________________________________________________________

Whilst browsing over at Modern Mechanix just now, I found the pic above captioned thus:

Dancing Robot performs a merry jig by remote control. Patrick Rizzo who built it in his spare time, claims the $100,000 creature is the first of its type.

Oh great, that’s all we need – a robot crossed with a ventriloquist doll. That dances.

The correct answer to The Monty Hall Problem is: Yes, you should definitely change your choice when Monty gives you the opportunity. You will improve your odds of walking away with the car from your initial 33.3% to an impressive 66.6%.

Those of you who said that your chances remain the same as they were to start with, or improve to an even 50/50, are in error. I know, it seems bizarre on the face of it: if you change your mind, your chances of winning the car are not just better, but substantially better. But how can that possibly be?

I think the best way to approach the Monty Hall Problem is like this:

First of all, remember that Monty knows what’s behind every door. This is critical.

When you make your initial random choice from Doors A,B & C, there is a 2-in-3 chance that you will pick a goat. That is, two times out of every three your first random choice would give you a goat. Are we agreed on that point? Good. Therefore, on those two times out of every three, after Monty knows your choice, he will have no option but to open the door where the other goat is (presuming, of course, that he doesn’t want to show you the door with the car). Logically, therefore, Monty Hall allows you to know two thirds of the time where the car is† (that is, behind the door you didn’t choose). So you should always change your choice when he gives you the opportunity to do so.

It’s infuriatingly counter-intuitive. When I was first presented with the Monty Hall Problem I was convinced the choice was a mere 1/2 and therefore it made no difference if I changed or not. But the maths don’t lie. If the Word of the Cow isn’t good enough for you, go to the maths department at the University of California & San Diego and conduct yourself some practical trials. If you always change your choice when given the opportunity you will walk away with the car more often than not. You can also see the accumulated trials of everyone who has done the experiment before you: it’s inarguable – the best strategy is to swap doors when Monty gives you the choice!

Why do we have such difficulty with the Monty Hall Problem? I think the answer is twofold – firstly our brains are not naturally great at interpreting statistics, and secondly, The Monty Hall Problem is not strictly a problem of maths.

Statistically we can all see quite clearly that the chance of choosing the car initially is 1-in-3. We then tend to think that by being shown an ‘irrelevant’ door and given two remaining options there is an equal chance that either may hide the prize. This is in fact true; in a strict statistical sense, taken in isolation, the prize may indeed be behind either remaining door. But Monty (unwittingly, we must suppose) is not giving you that kind of choice. He is instead giving you the opportunity to change your mind about your first choice which is an entirely different thing altogether. And that opportunity is informed by the fact that Monty knows something about what’s behind the doors that you don’t.

In other words, a purely statistical experiment is muddied up by the fact that the experimenter knows something about the outcome and stirs that into the experiment, irrevocably removing the random element.

Or, put another way, if Monty doesn’t know what’s behind each of the doors (or, alternately, if you don’t tell Monty which door you’ve initially chosen) then the Monty Hall Show plays out exactly as your intuition might suggest. (Of course, if Monty doesn’t know what’s behind the doors, in all possibility he may reveal the car when he opens a (necessarily) random door to show you what’s behind it, immediately increasing your odds of walking away with the prize to 100%).

The Monty Hall Problem is a good reminder of how easily it is for the human brain to be lead astray, and why our intuitive grasp of things is not a reliable indicator of the way they really are…

___________________________________________________________________________

†Of course, on the one-in-three times you choose the car on your first go, Monty can show you either of two doors with a goat, in which case your chance of getting the car if you swap doors is merely 50/50. But that’s only for one out of every three times you randomly choose correctly on the first pick!

Correction courtesy of din.

___________________________________________________________________________

A couple of days back I was reading an article about statistical method in experiments in primate behaviour and the writer mentioned The Monty Hall Problem as a possible source of unintentional introduced error or experimenter bias.

Now The Monty Hall Problem is a fascinating mathematical conundrum, and since I know those kinds of things are always of interest to Cow Readers, I thought those of you who are not familiar with this puzzle might like to exercise your mental muscles on it.

The Monty Hall Problem goes like this:

You are on a game show with your host Monty Hall who is offering you the chance to walk away with the Car of Your Dreams. He shows you three doors, A, B & C.

“The Car of Your Dreams is behind one of these doors,” he says, “The other two doors each conceal a goat. As your Games Master, only I know which door conceals which object. Now, please choose a door to claim your prize!’

You choose your door. You tell Monty “I have chosen Door B!”

“Well done!” he says. “I knew you were a contestant of superior ability! But before we open your door, I’m going to open one of the other doors and show you what’s behind it.” He opens Door C to reveal a goat. “Now that you’ve seen what’s behind Door C,” he says, “I’m going to give you a special opportunity to stick with your chosen door, Door B, or change your choice to the other remaining door, Door A. I’ll give you ten seconds to have a think about it!”

Here’s the question: To win the car, is there any advantage in changing your mind and swapping from your initial choice of Door B to Door A?

Answers on my desk by end of class.

According to this this report from that pinnacle of reputable British journalism The Sun, a stunted, pointy-hat-wearing gnome is haunting a small South American town.

“Teenager Jose Alvarez – who filmed the gnome – yesterday told national newspaper El Tribuno that they caught the creature while larking about in their hometown of General Guemes, Argentina.

“One of my friends was so scared after seeing that thing that we had to take him to the hospital.””

The video footage is creepy in a ‘Blair Witch’ yeah-and-pull-the-other-one kinda way, but the real question must be: Hands up who’s seen Polanski and his midget sidekick lately?

(I really wish this had happened in the Emerald Isles. It would have given me the unparalleled opportunity to use the headline ‘Gnome Man is in Ireland’)

One of the intriguing things about coming to live in a different country city is learning to converse in the manner of the locals. Now, English is a language of which I have a fairly good grasp but every now and then down here in Melbourne I hear or see something that completely floors me, such as the newspaper banner above. It was on display as I walked through Flinders St. Station in the city centre.

My brain made a sort of popping noise as I passed on down the stairs trying to make sense of it. Some kind of setback for the fastfood industry…? A cocaine racket financed by a pastry magnate…? A contest to win the Great Australian Meal with lungpower…?

I had to get a local to explain it to me.