iNTELLIGENCE

IQ solution to: The infinity machine - a gedanken experiment

It is obvious that the addition of 60 + 30 + 15 + 7.5 + ... converges to the value of 120. The addition of all elements up to infinity in fact leads to 120. But if you did an infinite number of switches, every time the lamp is on, it has to be switched off immediately. On the other hand, every time the lamp is off, it has to be switched on immediately!

Therefore, at 120 seconds the lamp is either on and off, or neither on or off?!

But let's take a bit of maths into it:

If “0” means the lamp is off and “1” the lamp is on, we can calculate the sum of the switching operations:

(+1 for switch on, -1 for switch off)

+ 1 - 1 + 1 - 1 + 1 - 1 ....

After 120 seconds, there is no result; instead this infinite sequence oscillates between two values (0 and 1). That means were are able to determine the status of the lamp for every time point before 120 seconds, but not for 120 seconds (or later). This is simply because an infinite sequence does not have a last term.

In other words: It is true that the lamp has to be on or off after 120 seconds, but we are not able to find out which is the case!

Gimme more intelligence!