How to never wake up and go to work - using the power of maths!
Created | Updated Jan 28, 2002
Here's a simple tip for people not wanting to wake up in the morning:
1) Set your alarm clock to go off an hour before you need to wake up.
2) When you wake up at that time, set it to go off in 30 minutes time.
3) When you wake up in 30 minutes time, set it to go off in 15 minutes time.
4) When you wake up in 15 minutes time, set it to go off in 7 minutes 30 seconds time (if you have an alarm clock which is that accurate).
5) When you wake up in 7 minutes 30 seconds time, set it to go off in 3 minutes 15 seconds time.
6) Keep halving the extra time that you sleep - for ever.
Although in theory you will never wake up, this is, of course, IMPOSSIBLE!
Assumptions:
1) It takes a negligible amount of time to set the alarm, thus you are never awake for more than an infinitely small time.
2) Time is infinitely divisible. (Is it? - it APPEARS to be!)
A great tip for any pan-dimensional beings out there - for the rest of us, just food for thought...
Additional:
This 'paradox' highlights some problems with the rather vague view of infinity many people take. It is theoretically possible to sleep in forever using the above technique (a blatant copy of the tortoise and hair paradox), and yet never be late for work, because you never sleep past the time you were supposed to wake up. So how can you sleep for an infinite amount of time, and yet it takes NO time at all? The reason is, there are two types of infinity. I like to thing of them as 'small infinity' and 'big infinity' (ooh, sophisticated man). The big kind of infinity is the one that allows you to keep adding one to get a bigger number. If you keep on counting up, you can go on forever, and there is no limit to a number. The small kind of infinity has a ceiling. It allows you to keep incrementing a number by smaller and smaller chunks, without the number ever exceeding a certain limit. And yet the number can grow in size for ever! The trouble with the sleeping in technique is, the longer you want to sleep in, the shorter the periods are between the alarms going off, so you won't get much rest!
Some questions arise from this thinking. Is time infinitely divisible? It can't go along in discrete steps can it? It must be continuous! This entry probably highlights my lack of knowledge in current philosophical and scientific thinking, but hey, it's good to start a discussion off, and someone has to worry about these things late at night! More to come...
1) Set your alarm clock to go off an hour before you need to wake up.
2) When you wake up at that time, set it to go off in 30 minutes time.
3) When you wake up in 30 minutes time, set it to go off in 15 minutes time.
4) When you wake up in 15 minutes time, set it to go off in 7 minutes 30 seconds time (if you have an alarm clock which is that accurate).
5) When you wake up in 7 minutes 30 seconds time, set it to go off in 3 minutes 15 seconds time.
6) Keep halving the extra time that you sleep - for ever.
Although in theory you will never wake up, this is, of course, IMPOSSIBLE!
Assumptions:
1) It takes a negligible amount of time to set the alarm, thus you are never awake for more than an infinitely small time.
2) Time is infinitely divisible. (Is it? - it APPEARS to be!)
A great tip for any pan-dimensional beings out there - for the rest of us, just food for thought...
Additional:
This 'paradox' highlights some problems with the rather vague view of infinity many people take. It is theoretically possible to sleep in forever using the above technique (a blatant copy of the tortoise and hair paradox), and yet never be late for work, because you never sleep past the time you were supposed to wake up. So how can you sleep for an infinite amount of time, and yet it takes NO time at all? The reason is, there are two types of infinity. I like to thing of them as 'small infinity' and 'big infinity' (ooh, sophisticated man). The big kind of infinity is the one that allows you to keep adding one to get a bigger number. If you keep on counting up, you can go on forever, and there is no limit to a number. The small kind of infinity has a ceiling. It allows you to keep incrementing a number by smaller and smaller chunks, without the number ever exceeding a certain limit. And yet the number can grow in size for ever! The trouble with the sleeping in technique is, the longer you want to sleep in, the shorter the periods are between the alarms going off, so you won't get much rest!
Some questions arise from this thinking. Is time infinitely divisible? It can't go along in discrete steps can it? It must be continuous! This entry probably highlights my lack of knowledge in current philosophical and scientific thinking, but hey, it's good to start a discussion off, and someone has to worry about these things late at night! More to come...
