Yet more proof that maths can be funny, this time from the comments left on a Slashdot article - Or just more reasons for a couple of friends to ridicule my sense of humour? You decide…
Why did the mathematician have complex numbers on his telephone?
So he could call all his imaginary friends.
And because physics is just bastard child of maths and the real world here are a couple more jokes for the those who like me believe that maths/science is not without it’s funny bits.
Whenever I’ve gotten a speeding ticket, I’ve thought about arguing with the Judge that the cop was lying on the ticket. He noted both where I was and how fast I was going, and since he can only measure one of those things, he’s clearly lying about the other.
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There’s an old joke about a guy who got a ticket for running a red light. He argued in court that the Doppler Shift made the light appear green. The judge agreed with him that the original ticked was no good, and then fined him… for speeding.
What makes the last joke so good is someone else then did the math to work out what speed you’d have to travel at for this claim to be true. Have a quick guess how fast you’d have to be going for a red light to look green due to the Doppler Effect. Here’s the answer:*
Lambda(red) = 620nm
Lambda(green) = 520nm
f = c / L
f(red) = 4.84*10^14Hz
f(green) = 5.77*10^14HzAssuming that he observed the light over a distance of 50m, there are this many waves of light in the red spectrum:
50 / (620*10^-9) = 8.0645*10^7
In order to “greenshift” that, he needs to cause this many waves to incident his retina:
50 / 520*10^-9) = 9.615*10^7
So he needs to travel at a speed such that he only views 8.0645/9.615 oscillations he otherwise would if he were stationary.
The redshift formula is:
f(final) = f(emit) + f(emit) * v/c
So:
f(final) = 5.77*10^14Hz
f(emit) = 4.84*10^14Hz
c = 3*10^8m/sv = c * ( ( f(f) - f(e) ) / f(e) )
= 3*10^8*((5.77*10^14 - 4.84*10^14)/4.84*10^14)
= 5.76*10^7m/s= 207,520,611 km/h
In English that’s a speed of about 128,947,329 mph or about 1/5 of the speed of light - Which would have to be worth more than a few points on your licence.
*I’ll admit that I haven’t done the calculation for myself, but if it were wrong someone on Slashdot would have pointed it out - It’s that kind of place.