I’ve always had a keen preference for most things mathematical. In school, my favourite subjects were always Math, Algebra, Physics, Chemistry, Calculus, and Geo-Trig. I had a high proficiency for it and, not surprisingly, that was why I liked them so much. I kept being shocked and thne thrilled at how much overlap there was and how many interdependencies there were between the different studies, and how it all moved like a well oiled machine.

That’s not to say I found all Mathematics enjoyable. Perhaps surprisingly, given my current field of work, Logic was a subject I struggled with. Oh, I was fine with the symbols and equations, but as soon as the curriculum started mixing in the ambiguities of the English language, my comphrehension level lowered quite drastically. I have no problems with spelling or grammar (I just get lazy sometimes), and will even correct people almost to the point of them threatening physical violence. I have no problems rattling off coherent thoughts in essay form, but as soon as you try to adhere it to a logical argument, for some reason, my brain turns to cabbage. Oh, I can fake it very well, but I generally only do so for comical effect.

The higher levels of Linear Algebra also give me palpitations. I struggled all through my last Linear Algebra class in university. I understood the basics. I grasped the concept of matrices in their basic form and the equations they represented. But at a certain point, which I still haven’t been able to locate, a disconnect grew between the matrix manipulations we were performing and the underlying equations we were trying to solve. Jiggery-pokery with pivot columns turned into hocus-pocus and I suffered through the rest of the class just hoping to make good educated guesses.

The last subject I had trouble with was Statistics and Probability. I saw, and in most respects still do, Statistics as no less a pseudo-science or voodoo than Astrology, Alchemy, or Phrenology. I’m guessing a career in Quantum Mechanics is not waiting for me. I’d include Intelligent Design in that list of outlaw sciences, but it’s not even a pseudo-science, it’s a religion (but that’s for another time).

Statistics seems to be one of those sciences that is specifically designed to be counter-intuitive, and any similarities to common sense is purely by chance (no pun intended).

Which brings me to my point. I just saw the movie 21 last night and, needless to say given its subject, it involves some math-related exposition. One such example near the beginning of the movie is when Kevin Spacey’s character, Professor Micky Rosa, proposes a problem he calls the “game show problem” (more commonly known as the Monty Hall Problem or possibly also the Three Prisoners Problem), which basically goes as follows:

A contestant is presented with three doors and is asked to choose one. One of the doors hides a reward, while the other two do not. The host knows what lies behind each door. Upon making his/her choice, the contestant is shown what’s hidden behind one of the doors not chosen (the prize door will never be revealed). The host then gives the contestant the option to switch his/her choice to the only remaining unrevealed door. The question is: Is it in the contestant’s best interest to switch the choice?

Spoiler: Common sense tells us no, it doesn’t matter. It’s a 50/50 shot.

Mathematicians, however, would tell you that it does matter. In fact, they would tell you that you should always switch your choice. They would tell you you have a 66% chance to win the prize.

Huh?

This is also the conclusion reached in the movie as well. Being a fairly well-known problem, and one that flies in the face of common-sense, countless explanations are offered with varying attempts at explaining it simply, none of which seemed to give me any satisfaction. Though I’ll admit, the second table in the Aids to Understanding section of the Wikipedia article explain it quite well. The trick of the original problem is that the host knows where the prize lies, and at times his hand is forced depending on the original choice of the contestant.

I’m anything but an expert on probability and statistical analysis, but here’s how I arrived at a solution that makes sense to me. My first reaction, being a programmer, was to build a simple program that tooks a couple of inputs (numbers of choices, i.e. 3, and number of iterations, i.e. 10 times, 100 times, 1000 times, etc…), define an array to act as doors, use a random number generator to shuffle the position of the car and to make the contestant’s decision, reveal empty doors (as per the stated host’s behavious), and then tally the number of times the contestant wins by switching his choice.

Rather than think it all out into an algorithm ahead of time, i just took to the keyboard and started writing code, adjusting for the rules of the game as I went along. After a few minutes, it came abundantly clear to me why the mathematicians were correct. In a roundabout way, my program essentially aimed to disprove that always switching your choice is more beneficial.

Because the results of the game are either you win the prize or you don’t, I found it easier to think of the problem in terms of its complement. Going with the assumption that we are always going to switch our answer, the only times we’ll lose is when we initially chose the door with the prize. So because the chance of choosing the door with the prize is 1/3, the chance of winning is 1 – (1/3) or 2/3.

Now maybe that’s the wrong way to think about it, but like I said, probability’s never been my strong suit.

I wonder if any studies have been done regarding Deal or No Deal…

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Well, I had one of those moments two weeks ago while watching the programme Corner Gas on CTV HD. I was watching the episode entitled “Coming Distractions” when it came to the setting shot the show used to transition to the scene in the theatre. Lo and behold, that’s the very same theatre I frequent a couple times a week, which is less than a ten minute walk from home.

Maybe I shouldn’t be so surprised when that happens, considering they mainly film in a town not an hour’s drive away from the city, but I don’t care. It’s still pretty cool, nonetheless.

Maybe it’s because it’s shown nationally during prime time and has huge ratings. It’s not the same as Puttnam’s Prairie Emporium, which never left the studio AFAIK. And as cool as they are, local cable access channels don’t count either.

As for movies, I had it a few times watching Just Friends, but less so during The Messengers and not at all during Decoy.

—

My apologies to Miss Judy Garland.

This morning, however, was a little different. As soon as I turned through the side entrance doorway, I spotted all the tables on the right hand side of the dining area had been converted into one incredibly long table, and was completely surrounding by people sitting and having a meeting. At first, I had to step back and see if there was a notice on the door, but there was not. Seems kinda odd to hold a meeting there during peak coffee break hours.

But it kinda reminded me of all that stereotypical imagery of Medieval banquets involving long tables occupied by royalty and nobility. You know the kind.

Anyway, it got me thinking. Usually, when you see those banquets scenes portrayed, the people are often only seated along one side of the table(s), with the tables positioned in one long row, semi-circle, or an open-sided square configuration. Portrayals always seem to imply this is for a courtyard of sorts or for entertainers to perform jokes, stunts, or music (e.g. the first series of Blackadder).

My question is, after having looked through the Medieval cuisine article on Wikipedia, I’m a bit curious how often or infrequently (if it even ever happened at all). Obviously, I’m mainly just talking about the aristocracy and rolalty, not the layity.

How often did they have meals in such grandiose fashion, and did they always just sit on one side or was that an invention of screen and television, so you could see the actors.

The reason I ask is because I wonder if that one side of the table always gets worn down more than the other. And if so, do they rotate the position of the tables in between banquets to save on supplies?

But I think I just wore out the poor thing. Mom and I both bought the exact same player, at the exact same time, at the exact same place, and hers still works great, but has never been used to the extent that mine has. Plus hers is situated in a basement which is a cooler environment all year round, while mine is above ground in a cramped bedroom that is always several degrees warmer than anywhere else.

The symptoms it first exhibited were longer load times, stuttered playback, and all round a generally noisier box than normal. At first I was able to workaround it by sometimes tilting the box slightly in one direction or another, but then I had to move it out of my cabinet altogether (thinking it might not be getting proper airflow and overheating), to me finally having to remove the outer case. Then lastly, a couple of days ago I went to go play a move after having not used the player for a few days, and it just wouldn’t play. It would keep spinning up and spinning up, desperately trying to read the disc, making all kinds of racket in the process, always worrying me that it was scratching my discs.

Finally, I got fed up and starting scouring the Web for a decent player from a reputable company that I could buy in town at a decent price and make region free. The one I ended up getting was a Philips DVP5960 from *ewwww* The Source. I don’t know what it is about RadioShack/TheSource and easily hackable DVD players, but that’s also where I bought my Daewoo oh so many years ago.

So far it does everything I could want it to do. The upscaling only works through HDMI, which I have on my TV, but don’t have a cable for (but that wasn’t really a driving factor for me anyway). It also has a USB port (apparently only USB 1) for playing video files of an external drive, but I don’t know if I’ll ever even use that.

Go nuts.