Thomson's Lamp (To infinity and beyond)

Written by Adi Cox

20th October 2015_____________________________________________________________________

The lamp is switched on and then it is switched off. First it is switched on for 1 minute and then off for half a minute. Then on for a quater of a minute and off for one eighth of a minute and so on. After 2 minutes is the lamp on or off?

So if we say that time s is the geometric series:

s = ar^0 + ar^1 + ar^2 + ar^3 + ... + ar^n

Then the summation where n=0 and goes to n=infinityis the summation of 2^-n (where 0 2 = 1-(1/2)^n -> 1 = -2^-n -> 2^-n = -1 -> -nln(2) = ln(-1) -> n = -ln(-1)/ln(2)

Using Euler's identity:

e^i(pi) = -1 so ln(-1) = (pi)i

and

e^i((pi)/2) = i so ln(i) = ((pi)/2)i

therefore:

n = -ln(-1)/ln(2) = -((pi)i)/ln(2) = -3.141592654i/0.6931471806

n = -4.532360142i_____________________________________________________________________

From infinity n becomes an imaginary number.

I would suggest that Thompson's lamp is neither off nor on as it is in the process of breaking when time is at two minutes. So I would say that at two minutes the lamp has reached maximum disorder with regards to entropy. I would say that after two minutes Thompson's lamp is more off than on.