(no subject)
Dec. 4th, 2004 04:38 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslLast night I introduced myself to my upstairs neighbour at 12:15AM, to friendlyly ask him to turn his music down (especially the bass).
I like thinking about acoustics, especially when I want to insulate myself from noise.
So I've been thinking about noise cancellation. The idea is that you copy the incoming noise (possible, since the signal can travel faster than sound) and reproduce out of phase by half a wavelength (or to be moe precise, in phase but with the amplitude inverted). So you're putting more energy in. But by the principle of energy conservation, either the sound gets louder in some places or the waves will all get turned to heat.
Btw (1), I have an excuse to leave my laptop on: saving gas! When I close my laptop, it stops emitting light outside, so all of its energy expenditure becomes heat. Since everything is regulated by a thermostat, my laptop saves a house radiator from getting warmer (though gas energy is probably cheaper).
Btw (2), I've once used a similar thought to prove that
amplitude is additive, energy is conserved in a closed system, energy is a function of amplitude |= energy is proportional to amplitude^2
(the argument was about a light interference pattern)
though perhaps I should refrain from using "|=" until I have a formal proof, or at least formal models for this stuff.
My physics professors were impressed with my "proof", but I just thought (and still think) that this should be normal science. Unfortunately, such a logical approach is missing from science education (and probably research too). Taking my physics classes as an example:
* premises are almost never explicit
* the structure of arguments is informal (even *more* informal than in mathematics classes)
This lack of formality doesn't bother them, and in fact in most cases.
But Feynman tells the story of the S-shaped sprinkler, where people had to resort to experiment in order to resolve the question. But it's the sort of question that should be decided by theory.
Even though there might be fluid effects that are not covered by the theory, the question was meant as a brainteaser: I believe Feynman was asking about the "ideal" sprinkler.
I like thinking about acoustics, especially when I want to insulate myself from noise.
So I've been thinking about noise cancellation. The idea is that you copy the incoming noise (possible, since the signal can travel faster than sound) and reproduce out of phase by half a wavelength (or to be moe precise, in phase but with the amplitude inverted). So you're putting more energy in. But by the principle of energy conservation, either the sound gets louder in some places or the waves will all get turned to heat.
Btw (1), I have an excuse to leave my laptop on: saving gas! When I close my laptop, it stops emitting light outside, so all of its energy expenditure becomes heat. Since everything is regulated by a thermostat, my laptop saves a house radiator from getting warmer (though gas energy is probably cheaper).
Btw (2), I've once used a similar thought to prove that
amplitude is additive, energy is conserved in a closed system, energy is a function of amplitude |= energy is proportional to amplitude^2
(the argument was about a light interference pattern)
though perhaps I should refrain from using "|=" until I have a formal proof, or at least formal models for this stuff.
My physics professors were impressed with my "proof", but I just thought (and still think) that this should be normal science. Unfortunately, such a logical approach is missing from science education (and probably research too). Taking my physics classes as an example:
* premises are almost never explicit
* the structure of arguments is informal (even *more* informal than in mathematics classes)
This lack of formality doesn't bother them, and in fact in most cases.
But Feynman tells the story of the S-shaped sprinkler, where people had to resort to experiment in order to resolve the question. But it's the sort of question that should be decided by theory.
Even though there might be fluid effects that are not covered by the theory, the question was meant as a brainteaser: I believe Feynman was asking about the "ideal" sprinkler.
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(no subject)
Date: 2004-12-04 10:42 am (UTC)(no subject)
Date: 2004-12-05 02:11 pm (UTC)This experiment is hardly the kind of experiment that would exhibit the existence of new phenomena. Do you agree that *some* experiments are not worth doing?
Also the number of theories that are at work in given phenomena make problems interesting.
I agree here. I find it interesting to see how different theories and explanations can interact coherently.
Btw, this argument reminds me of the debate about the Monty Hall problem... some mathematicians were so blinded by their intuition (that the probability should be 1/3 regardless of whether she switches), that they could only revise their beliefs when faced with experimental results (probabilistic simulations). It makes me wonder why they didn't try to convince them with a formal set-theoretical proof. Mathematics, afterall, has such a "logical framework", that I keep referring to.
My dream is to see a physicist showing a computer proof: "See, if you accept conservation of energy, blah-blah-blah and etc; you *MUST* accept this theorem" and no-one could argue.