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Okay, I won’t even pretend that I understand what the medial axis is, nor will I pretend that I know much about Computational Geometry. But if you’ve got a math presentation that involves South Park in one way or another I just have to check it out – and so do you.
First let me credit Ernie’s 3D Pancakes where I found out about Mesecina – computational geometry you can see. Check out the long demo talking about the medial axis and this crazy program called Mesecina which can even be downloaded, though so far you can only get the development version but apparently a release version with documentation will be available soon.
I might download it once the exams are over in case I have some time for crazy mathperiments.
Lately there have been a number of posts discussing the state of contemporary elementary maths teaching. While I certainly agree that Reform Math is bound to be a complete failure I’m not sure back to basics is the best alternative. One thing I’ve certainly despised about school is the endless hours we’ve spent wasted on practising long division. Of course I can still do long division but I highly doubt that it made me a better mathematician. Talking of old school algorithms my father was taught to take square roots using paper and pencil. Years ago I learned that algorithm on a whim and used it to calculate square roots mentally to keep me busy on my way to work.
Anyway, the point of this post is that while looking for pencil and paper algorithms for taking square roots (as I have since forgotten how to do this) I came across a paper entitled: Let’s Abolish Pencil-and-Paper Arithmetic which makes a point that mental arithmetic should be taught rather than pencil and paper methods and that there’s nothing wrong with using calculators.
Talking of people who dislike the use of calculators reminds me of a substitute teacher we once had for A-level maths who seemed almost violently opposed to calculators but loved slide rules so much that he wasted parts of a lesson to show us what they were and how to use them (as our generation had been so unfortunate to grow up without them). I mean, seriously, both calculators and slide rules are tools to facilitate computation so grow up and embrace the enemy.
Besides calculators are so old fashioned already. The new way to corrupt our youth are computer algebra systems. One of my first year computing lecturers might have been right as he said that at some point in the future these systems would become as commonplace as calculators nowadays and it could mean that the necessity to practice taking derivatives, etc. would vanish. I doubt it will happen soon but he’s got a point. Let’s face it, so far I’ve used Maple, Matlab and GAP and I have no intention to forgo their use in the future. Often when working on something or playing with a particular problem one may want to check a number of cases or just collect some data to get a feeling for what is happening. In such cases where one looks for patterns in the answers the actual computations are rather unimportant and it is only sensible to automate this task.
Then again, don’t take anything I say too seriously. After all I’m the kind of guy who’d favour getting rid of a number of compulsory mathematical methods courses and introduce at least one decent set theory and mathematical logic course in the standard undergraduate curriculum (and I would place it in the first year).
Check out this site which tells you everything you ever wanted to know about whichever number you enter (as long as it’s less than 10′000). Sounds like a pretty fun idea.
It also reminded me of the book The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip, by Keith Devlin. It’s a highly enjoyable book that tries to explain how humans acquired the ability to do higher maths (ie. things like Abstract Algebra, Analysis, etc. rather than numeracy which has been more thoroughly researched).
Naturally, the common people don’t want war, but after all, it is the leaders of a country who determine the policy, and it is always a simple matter to drag the people along, whether it is a democracy, or a facist dictatorship, or a parliament, or a communist dictatorship. Voice or no voice, the people can always be brought to the bidding of the leaders. This is easy. All you have to do is tell them they are being attacked, and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same in every country.
- Hermann Goering
I just read The Ecstasy of Influence which discusses plagiarism, copyright and intellectual property in general. What’s really great about this article though is that most of it is plagiarised (except that all the sources are listed at the end). One of the arguments presented in the article is that all art is influenced and as such plagiarism has always been a part of it. Granted I simplified the argument a bit, the text is much better written.
It’s rather long but I thought it was well worth my time. You can read it here.
I think so too.
Edit: After this post the result became
Hard to believe that it could be possible to take maths too far but sometimes just sometimes one has to wonder.
Take for example The social norm of leaving the toilet seat down: A game theoretic analysis in which Hammad Siddiqi analysis the toilet seat problem (just because some couple argue over it doesn’t make it scientifically interesting). In the introduction he says
The issue of whether the toilet seat should be left up or down after use seemingly generates a lot of passion among the parties concerned, however, scientific inquiries into the matter are almost non-existent.
Yeah, I wonder why.
But it gave me something to blog about.
Mildly amusing, too.
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