Heh. To me it was just a classic illustration of "mathematics thinking": problems are never "hard" or "easy", they are either "interesting" or "not interesting"...
These are my thoughts immediately upon seeing the problem. (1) The theoretical physicist in me is treating it as a reverse wheatstone bridge (applying a known potential differance to both points and integrating the resistance over the current path elements). (2) The computational physicist in me is considering the problem in a similiar manner, except reiteratively analysing the current flow according to the resistance of each path element (effectively the same thing but less accurate), which is not as mathematically accurate, but you are going to lose any precision beneath machine epsilon, anyway. (3) But the experimental physicist in me is looking for my soldering iron and multimeter, as we speak. I do consider myself to be an experimental physicist, btw. It's more fun. The motto of this story is that mathematicians shouldn't set puzzles for physicists. We'll just ignore the interesting maths in order to find a workable solution that makes mathematician pull their hair out and say "you can't do that." We've had plenty of experience
( ... )
Greens functions! Thankyou very much. I'd almost successfully forgotten that part of my life (which accompanied the worst exam I've ever encountered at university). Admittedly it was only four questions of sixteen or so consecutive parts. Biut who could calculate the Green's function of a typewriter in a filing cabinet [blatant exaggeration warning]. And who would want to? I think people got marks for successfully writing their name. It's the first time I've seen the lecturer cry at an exam when he realised that it might have been considered a "tad difficult" and "unexpected" by his students. I'll be over here in a ball in the corner if anyone needs me. PS: Gold, and 10^-2 is Silver (EIA standard anyway). PPS:
Oh, they fill me with teh fear, too! That and Gramm-Schmidt orthogonalisation! Well, Gramm-Schmidt is not actually that painful. At Uni they were the kinds of things where examiners took great pleasure in claiming they were testing your knowledge of the Universe when they were actually testing
Can I remember integral tables I could look up were I not in an exam
Can I not drop a minus sign or a factor of two, on something I could feed through Mathematica, were I not in an exam
I guess it's very good training for obscure jobs in Whitehall (where my Uni seemd to excel), where pedantry and a memory optimised for long tables of facts are probably your way to advancement
( ... )
This happened at a party we went to on the weekend. (Not the truck part, just the puzzle part.) In this case, it was a rather nice little "eighth grader extra credit" puzzle:
Suppose five pumpkins are weighed two at a time in all possible ways. The weights in pounds are recorded as 16, 18, 19, 20, 21, 22, 23, 24, 26 and 27. How much does each individual pumpkin weigh? (No fractions, please.)
The xkcd "hard logic puzzle" is fun (though I can't find it, atm). I think really is a brilliant example of maths in action: It took me 24hrs (on and off) to get it, but once I had worked out a coherent notation and definitions, it only took an hour!
(I've not worked out if my solution is the same as the one which is posted on the net (the answer is, but I'm not sure about the method)).
Have you read Recreational Mathematics by, um, someone famous? It's good fun. Gardner, I think (but I could be confusing him with Gerald): lots of brilliant thought experiments in his stuff, amongst the sillier things. He's annoying as a commentator though (whatever his name is!), a touch too much of "The Brights" in him.
The way I would approach it is to start with a small square, and then mathematically build it up there in oder to develop it into an infinite series, then integrate.
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I mean, blackholes may be very strange and dramatic, but they're also a long way away, and not doing any harm: why not just leave them be!?
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And it's interesting to see what the universe gets when it suffers a "divide by 0" error.
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These are my thoughts immediately upon seeing the problem.
(1) The theoretical physicist in me is treating it as a reverse wheatstone bridge (applying a known potential differance to both points and integrating the resistance over the current path elements).
(2) The computational physicist in me is considering the problem in a similiar manner, except reiteratively analysing the current flow according to the resistance of each path element (effectively the same thing but less accurate), which is not as mathematically accurate, but you are going to lose any precision beneath machine epsilon, anyway.
(3) But the experimental physicist in me is looking for my soldering iron and multimeter, as we speak. I do consider myself to be an experimental physicist, btw. It's more fun.
The motto of this story is that mathematicians shouldn't set puzzles for physicists. We'll just ignore the interesting maths in order to find a workable solution that makes mathematician pull their hair out and say "you can't do that." We've had plenty of experience ( ... )
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I spent about a week on this very problem, some time in 2005 ish, :). I think google started it.
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Greens functions!
Thankyou very much. I'd almost successfully forgotten that part of my life (which accompanied the worst exam I've ever encountered at university). Admittedly it was only four questions of sixteen or so consecutive parts. Biut who could calculate the Green's function of a typewriter in a filing cabinet [blatant exaggeration warning]. And who would want to? I think people got marks for successfully writing their name. It's the first time I've seen the lecturer cry at an exam when he realised that it might have been considered a "tad difficult" and "unexpected" by his students.
I'll be over here in a ball in the corner if anyone needs me.
PS: Gold, and 10^-2 is Silver (EIA standard anyway).
PPS:
Reply
- Can I remember integral tables I could look up were I not in an exam
- Can I not drop a minus sign or a factor of two, on something I could feed through Mathematica, were I not in an exam
I guess it's very good training for obscure jobs in Whitehall (where my Uni seemd to excel), where pedantry and a memory optimised for long tables of facts are probably your way to advancement ( ... )Reply
Suppose five pumpkins are weighed two at a time in all possible ways. The weights in pounds are recorded as 16, 18, 19, 20, 21, 22, 23, 24, 26 and 27. How much does each individual pumpkin weigh? (No fractions, please.)
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(I've not worked out if my solution is the same as the one which is posted on the net (the answer is, but I'm not sure about the method)).
Have you read Recreational Mathematics by, um, someone famous? It's good fun. Gardner, I think (but I could be confusing him with Gerald): lots of brilliant thought experiments in his stuff, amongst the sillier things. He's annoying as a commentator though (whatever his name is!), a touch too much of "The Brights" in him.
Reply
The way I would approach it is to start with a small square, and then mathematically build it up there in oder to develop it into an infinite series, then integrate.
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