/sci/ - Science & Math

Yes

>>4300939

It's neither. You will have collapsed the lamp wavefunction and activated the Schrödinger cat paradox of inanimate objects. Also, Heisenberg.

>seriously, GTFO.

>>4300946

on

>>4300960
off

>>4300974
on

Clever way of phrasing the question, but what you're really asking is if infinity is and even or odd number. But infinity isn't a number, so the question doesn't make sense.

>>4300939
>it is easy to see that all these infinitely many time intervals add up to exactly two minutes.
No, it approaches and converges at two minutes. Very different.

You would break the universe if this occurred in reality. It would never end.

>>4300982

>No, it approaches and converges at two minutes. Very different.
>Cannot into calculus

Summing the series will give you exactly 2 minutes.

>>4300987
>doesn't know what 'converges' means
>thinks this scenario can be applied to a system with a transitory present in which time is always an independent variable

>>4300995

>thinks a convergent series doesn't have a sum

Seriously are you really that retarded.

>>4300987
Wrong. You cannot acuratly sum the series because it approaches, but does not reach, zero. Therefore no matter how far you take the serious the sum will get infinitely close to two but never actually be two.

>>4300939
It's off because the switch broke after 100,000 switching events, and likely because the lamp's circuits aren't meant to deal with high frequency switching.

>>4301003
Ehm.. series, not serious :P

>>4301007
this fag here again.
>>4300939
also,
The time it takes for a light bulb to turn off is much larger than about 99% of all of the switching events in the two minutes. The lightbulb is therefore, "on" much longer than 2 minutes.

>>4301002
You, sir, are the definition of an idiot. Did you even read what I stated? Did I ever imply that? Do you know what 'convergence' or 'tends to' means?

>>4301017
Assuming you could get to two minutes te light would have simply be on for the majority of the two minutes but not more than two minutes.

>>4301016

>>it is easy to see that all these infinitely many time intervals add up to exactly two minutes.
>No

The sum of the series that models the amount of seconds that pass while the lamp is being switched on and off is exactly equal to 2. What you are arguing is basically that I cannot walk one foot forward because there are infinitely many points in between me and where I'm going.

i bet its off

>>4301030
That is not at all what is being argued. When your walking you don't half the distance you move everything you take a step because you would never actually reach your destination. Walking is fairly constant, flipping the switch and then waiting the amount of time you waited last time divided by 2 causes the amount of time you wait to get infinitely small.

>>4301050

>That is not at all what is being argued. When your walking you don't half the distance you move everything you take a step because you would never actually reach your destination.

This is just plain fucking wrong. You DO do that. Each time you cut the distance in half, the time it takes to traverse that distance is also cut in half. Zeno's paradox is completely resolved by integral calculus. Your way of thinking is outdated and fucking retarded.

>>4301030
No, I am arguing that a system in which such a scenario occurs is physically impossible (and incompatible) as time is independent of the switching.

What you are doing is essentially this:
<div class="math">1=1+0+0+0+0+\cdots</div>
<div class="math">=0+1+0+0+0+\cdots</div>
<div class="math">=0+0+1+0+0+\cdots</div>
<div class="math">=0+0+0+1+0+\cdots</div>
<div class="math">=0+0+0+0+1+\cdots</div>
<div class="math">\vdots</div>
<div class="math">=0+0+0+0+0+\cdots</div>
<div class="math">=0</div>

>>4300939
Maybe.

>>4301070
>A group of boys are lined up on one wall of a dance hall, and an equal number of girls are lined up on the opposite wall. Both groups are instructed to advance toward each other by one quarter the distance separating them every ten seconds. When do they meet at the center of the dance hall? A mathematician says they will never actually meet because the series is infinite. A physicist says they will meet when time equals infinity. An engineer says that within one minute they will be close enough for all practical purposes.
>engineer detected

>>4301070
The time it takes for that step is cut in half, not the time it takes to walk a foot from a set start point to a set end point.

>>4301073

You're sort of close but still wrong.

The answer is undefined, but not for the reason you said. Whether or not the lamp is on can be modeled by Grandi's series:
<div class="math"> 1-1+1-1+1... </div>
This series does not converge as it approaches infinity, so whether or not the lamp is on or off is indeterminate.

>>4301088

That's not even a relevant analogy. That's a different type of series.

>>4301092
>implying that doesn't converge at 1/2

>>4301092
That's a great way to tackle this mathematically.

Physically, however...

>>4301103

http://en.wikipedia.org/wiki/Summation_of_Grandi%27s_series#Stability_and_linearity

http://en.wikipedia.org/wiki/Grandi%27s_series#Heuristics

The series is divergent. The only way to prove that the sum is 1/2 is by performing manipulations on it that are only valid for convergent series. This is circular reasoning, and you can use it to prove several other sums for the same series, presenting a paradox.

>>4301115

Since the experiment in question is only possible as a mathematical thought experiment, I don't think physical reality has much bearing on the problem.