Infinite Flashy Bulby Thingy

Snotzenfartz

Suppose you have a lamp that turns on then after 1/2 a second turns off. A 1/4 of a second later turns on again then a 1/8, 1/16 and so on. By the time a whole second has passed it will have flashed on and off infinitely many times.

Now, when it gets to 2 seconds, will it be on or off?

inb4 off because the bulb has blown. :pac:

Snotzenfartz

It would be on, i just worked it out.

Michael Collins

It will never get to 2 seconds!

Snotzenfartz

Snotzenfartz wrote: »

It would be on, i just worked it out.

Or maybe off. Probably one or the other.

Snotzenfartz

Michael Collins wrote: »

It will never get to 2 seconds!

Sure it will. Past the one second mark the number of switches, n, will become imaginary.

[latex]n = -log(1-t) / log2[/latex]

Michael Collins

Michael Collins wrote: »

It will never get to 2 seconds!

It reminds me of the old "If a frog hops across a pond (on lilypads, presumably!) and its first jump from the edge brings it to the centre, and each proceeding jump is half of the length of the previous one, will it ever reach the other side?" The trick in the OP, where one second is turned into two, is tantamount to asking can the frog then cross twice the distance of the pond, but asking this after it has already taken its first jump. If it only reaches half way (i.e., the full width of the original pond) in the limit, then it won't ever reach the new width (i.e., double the original width). (At least, I think that's fairly equivalent!)

Michael Collins

Snotzenfartz wrote: »

Sure it will. Past the one second mark the number of switches, n, will become imaginary.

[latex]n = -log(1-t) / log2[/latex]

Interesting formula -- does it not come with a resistricted domain for allowed values of "t"? Your question comes down to asking if n is even or odd, lamp on or off, after 2 seconds. But since even and odd are only (usually*) defined for the integers, your question has no answer since to approach 1 second, the number of terms must approach infinity (which is not an integer).

*You can define them for functions too, and perhaps other structures - for complex numbers, for example, you could restrict to the Gaussian integers: z=a+ib, where a and b are both real integers, which is even if both a and b are even, and odd if a and b are odd.

Snotzenfartz

Yeah, it's all matter of definitions and an exercise in imagination. What would it mean to say that the number of flashes goes "beyond infinity" as the one second mark passes and how do we class that amount as odd or even?

It's just a bit of fun to stretch the mind.

im invisible

http://en.wikipedia.org/wiki/Planck_time

bnt

It will be both on and off. Call it Schrödinger's Lamp ...

Snotzenfartz

It will break through the infinity barrier and enter a trans-infinite state in which it is neither on or off, or on and off but something altogether different. A state of being a right angle to normal reality.

Splagmata

Don't you go all Borges on me!

im invisible

is it being powered by AC or DC?

c-note

It will be onff

ray giraffe

The bulb might blow after too many switches?!

Reminds me of a problem that only engineers can solve.

"A line of boys & a line of girls stand against opposite walls in a dance hall, each boy facing a corresponding girl. Each walk towards a centreline, making it half way, and stop there. After 10 seconds, they walk half that distance again. Another ten, another half, and so on. How long will it take for the two to meet?"

A Mathematician would say "Impossible! They'll never meet, the series lasts to infinity!"
A Physicist would say "They will meet when Time is Infinity"
An Engineer will say "Well, in 'bout a minute or less, they'll get close 'nuff for all practical purposes....."