Brain acceleration?

So last night I was doing a LOT of Algebra homework. Started around 9PM and finished around 4AM. Don't get me wrong, I'm not dumb (4.0 GPA), but I was super lazy while doing this, actually going on Facebook and chatting on WhatsApp several times throughout the night. I was in no mood for doing my homework at all. Around 3AM I was getting really tired and I was yawning frequently. All of a sudden I started doing my work faster than I thought possible. I was doing all these problems like nothing, with my mental math calculating things really, really fast. I finally finished around 4AM and went to bed. I woke up today and wondered about this. Maybe the desire of sleep forces my brain to tap into more resources to finish my work sooner....? Hmm, just a thought.

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I've had that before. When I get tired like that, I enter a lucid thinking state. I write, talk and game better. After the fact, I get into a dead tired state where I just suck at everything. Usually the sleep I get after one of these episodes is especially deep and relaxing and it's accompanied by a easily remembered dream. I don't know what causes it, but it happens frequently after consecutive episodes of slight sleep deprivation.
 
Maybe when you got tired, you got calmer and put more focus on math and less on facebook and whatsapp.

Just for add, I read somewhere that some guys on shooting competitions try to sleep less on the day before the competitions. The lack of rest, somehow, increase their accuracy.
 

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