Good Games for Sleep: Find the Perfect Solution

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Anton Alice
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Does anyone know a game, that is good for sleep? I have quite a signifcant problem with sleeping, and I would like to try out that, if there is something around. should not be too aggressive. Something that can be played on a laptop, while lying in bed.
I tried Dirt Rally. Well, even if I sit straight, completely awake, and try hard... I can not keep the damn car on track.
 
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I find that trying to solve mathematical problems while lying in a comfy bed in a peaceful, dark room, puts me to sleep.
A favourite of mine is the set of equivalent conditions for a metric space to be compact. There are several equivalent conditions:
1- Cauchy sequences converge
2- every sequence contains a convergent subsequence
3- space is complete and bounded
4- every open cover has a finite subcover

These may not all be exactly right. Part of the project is to work out for each one what the correct statement of the condition is.
The task is to prove that 1 implies 2, 2 implies 3, 3 implies 4 and 4 implies 1. If I get stuck, I try reordering them.
I have never gotten past completing one or two steps before waking up and finding it is the next morning.

I think one reason it works is that, like successful meditation (which I am no good at), it pushes all the busy, whirling, anxiety-provoking thoughts about one's life out of the mind.
 
isnt it that 4 is the most general? 3 only works on ℝn

But yeah,I found that effectively thinking about problems during the day, not only of mathematical kind, but something that is really on-topic, like a new invention for injured violinists, or new method for measuring eye vision is not only satisfactory, but also makes the mind tired, in a healthy manner.EDIT:

Oh sorry for my bad english. "x implies y" means y is needed to induce x.

Maybe this is why most mathematicians I have seen are very healthy physically. Because they sleep good, because their minds are occupied with things, which are neutral, or unpersonal.
 
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