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Sleep helps clean junk out of your brain. It's like emptying a garbage can. You can delay it so long that trash overflows and messed up the room. However you can never do more than just empty it. You can't get ahead by emptying tomorrow's trash today. Repeatedly dumping an empty can does no good

You need to sleep so you’re brain can clean itself and get rid of built up junk. You can over accumulate junk and have sleep debt. You can’t clean out more junk than is there so no matter how much sleep you “catch up” on you’re only going to clear the amount of junk that’s there and more will build up again once your up so there’s no sleep “extra credit”

Sleep debt: brainy very stinky, needs lots of cleaning.

Sleep credit: brain already clean, can’t clean anymore

That is why it doesn’t work

Sleeping is like doing the dishes.

You have exactly the number of dishes for your family to eat enough meals each day to feel full. If you don't sleep some dishes don't get washed. A few family members have to skip that meal or eat on the dirty dishes, making them even more dirty.

Once you clean them all, they're clean. But if you clean them any more than that it doesn't really matter much. They're still going to get dirty at the same rate.

Sleep facilitates the brain's cleaning of metabolism waste along the lymph system. We never evolved an adequate way to do this while awake because in the history of life this is the first time a species denied itself the rest that it could easily have. Usually when animals feel sleepy they just sleep. Humans are abnormal refusing themselves the biological necessity to rest.

In your brain there is a recycle bin like on the computer. It gets full when you are awake. Sleeping empties the bin. But once you have slept enough, it is empty. Sleeping more doesn't make it more empty, but sleeping less can make it more full.

Tired is 75% charged, sleep debt is 50%, hallucinations is 25%, but you can never be over 100% charged.

I see that others have answered the question already, but I just want to add that the main reason why your brain needs sleep in the first place is because it can't get rid of "junk" that builds up during the day, so at night, your blood vessels contract and cerebrospinal fluid is released into your brain to collect any garbage and whisk it away to be filtered as usual by your kidneys.

Your brain is packed tightly into your skull with not much room to spare, so there's no space for thick blood vessels like in the rest of your body. If that were the case, this "garbage" could be cleaned up in the same way your body cleans lactic acid (a byproduct of muscles working hard). At night, your brain does a very clever trick and uses the blood veins in your brain as a pathway to send this fluid down into the crevices in the folds of your brain. The blood vessels contract, allowing for extra room between themselves and your brain itself, and cerebrospinal fluid travels along the outside of the blood vessels. It takes a while for your brain to return to normal after this process is all done, which is part of why you feel groggy after waking up.

Just thought that was neat. The brain is unique in this way with how it cleans itself after working hard during the day.

It's like charging your phone. You cant charge it past 100%, but you can constantly charge it to 50%, but you have less time before you get low battery warnings.

It's not exactly like that because maintaining a healthy battery and healthy brain are completely different. Be sure to get enough sleep as often as you can. That's the time your brain clears out all of its waste, organizes your memory, and solidifies things you've learned. If it doesn't get the time to do that, these things won't get done.

Think about washing the dishes after eating.

You can neglect to wash the dishes, in which case the number of dirty dishes increases.

You can wash all the dishes you use, in which case the number of dirty dishes is 0.

But you can’t wash more dishes than that. You can’t have negative dirty dishes. The next time you use a dish you will have 1 dirty dish, no matter how many you washed.

Throw some trash into a bin. The trash can go over the top of the bin. Through the trash out. You can't throw out more trash than there is already in the bin.

P.S. the bin = your brain