Posts in "Curios"
I think I have absorbed more abstract mathematics over the course of today than during my entire undergraduate degree. In need of some compelling formal arguments to round out my latest paper, I've been trawling the web trying to answer the big questions of life ("Does the set of equivalence classes of first-order sentences form a complete boolean lattice? Is logical consequence over this set a well-founded partial order?") while maintaining my sanity. The later was helped immensely when I stumbled upon what has officially become (despite not understanding a lick of it) my favourite branch of mathematics: Pointless Topology.
Yes, Pointless Topology.
Literally, the study of topology without points. Oh sure, they could call it "point-free topology" or some-such, but I like to think that the topologists are making a little in-joke about the reputation of their profession, which is often (as in, even by other mathematicians) treated to adjectives such as "ugly", "pathological" and "useless".
If only other academic pursuits were named so honestly.
Thought Experiments - What if...
I doubt many people think that probability can be the slightest bit interesting, but check out this little gem from the folks at Grand Illusions: the Monty Hall Problem.
The problem goes like this: you are a contestant on a game show and
are playing for the grand prize. You have to choose one of three doors.
Behind one door is a brand new car. Behind the other two doors is a
goat.
Having made your choice, the host proceeds to play up the suspense. Instead of showing what's behind the door you selected, he decides to open a different door which, of course, reveals a goat. He then offers you "one last chance" to change your mind. The audience and enthusiastic people watching at home shout you advice, and you are left doubting and re-doubting and creating great TV drama.
So the question is, what should you do? Given that the host will always reveal a goat from behind one of the remaining doors (otherwise where's the suspense?), should you change your mind or stick with your original choice? Does it even matter?
Think about it before reading on...
Most people's initial response is something along the lines of "How can it make any difference? There is equal probability that it car is behind either door - the odds are 50/50.". My reaction was something along those lines. Given that many professional mathematicians and even the great Cecil Adams have also responded this way, I dont feel too bad about it...
Long year ahead
According to a bulletin from the International Earth Rotation and Reference Systems Service, we are due for a Leap Second at the end of the year. This will help keep our atomic-clock-driven Coordinated Universal Time in line with "solar time". Just like there aren't exactly 365 days in a solar year, there aren't exactly 86400 seconds in a solar day. Unfortunately we cant predict when leap seconds will be needed due to the irregularity of the Earth's rotation, and must rely instead on emergency leap-second bulletins from the good folks mentioned above.
The extra second will be added to the UTC time signal at the end of December 31st, so it will go 23:59:59, 23:59:60, 00:00:00. Hence, those in Greenwich will have an extra second to count down as they ring in the new year. For we Melbournians on Australian Eastern Daylight Time (UTC+11, including the daylight savings hour), we should put our clocks back 1 second at 11:00:00 on January 1, 2006. Failure to do so will result in chaos of millenium-bug proportions!
While surfing the official Metlink Melbourne website for information on what to do with a defective ticket, I stumbled across a few interesting bits of info that made me think "Huh! I didnt know that!". So, I'm starting a new series in my blog to document these helpful little facts.
- It is possible to buy metcards online with your credit card.
- You are required by law to validate your metcard every time you travel, even if it's already valid.
- Weekly and Monthly metcards allow you to travel in all zones on the weekend, regardless of the zones on the card.
To be fair, Sazz has been telling me about the last one for months now but I have never been able to confirm it. Now, to feed my online shopping addiction with a few Monthly metcards...