Combatting Sleeplessness With Mathematics

Randi wrote:

In my recent very long bout with pain and sleeplessness, I opted to work on mental mathematical calculations – simple four-by-four multiplications and extraction of square roots, as examples – and found the distraction rather effective.

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Good grief, I do much the same thing! One of my favorite exercises is to compute Pythagorean triples or pseudo-Pythagorean triples (in which one if the sides is irrational but its square is an integer). Further, I break numbers into their factors. I also square numbers and do computations around squares, and occasionally convert a number from one base to another. I also try to "check my work" by doing the same calculation with different techniques.

The starting point for many of these exercises is often the number showing on my digital clock.

I have an article (autographed!) by John Conway from some years ago in a New Scientist I think that says that he has screens that display on his computer that won't let him in his computer until he answers several of these type of mental math calculations

(yikes, Id never get any work done)

I guess I'm more of a visually oriented person. What works best for me is designing some sort of machine or apparatus that might help me in one of my hobbies. I never get very far into the process before falling asleep, but eventually I arrive at what I consider a fairly elegant solution.

I hop around the galaxy, or at least I wish I could.

T'ai Chi said:

I have an article (autographed!) by John Conway...

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Okay, it worked. I'm officially jealous.

hopfen said:

I guess I'm more of a visually oriented person. What works best for me is designing some sort of machine or apparatus that might help me in one of my hobbies. I never get very far into the process before falling asleep, but eventually I arrive at what I consider a fairly elegant solution.

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Sometimes I do this, too. One of my efforts went into the creation described in this thread, although the actual computations were things I had to do while wide awake.

In another elaborate exercise, I devised a complicated story problem, for which I then constructed a rather nice solution. I am hesitant to go into too much detail, because the idea could fairly easily be developed into a decent plot for a novel or a movie. The story is not so much a "whodunnit" as a "howdidit": a catastrophic event happens and the question is whether the catastrophe was the result of an unintended accident or an intentional wrongdoing. The problem is that no one could make such an event happen even if they tried, so it must be accidental; and yet, if it is next to impossible to cause such an event by deliberate design (due to several safety features designed specifically to avoid such catastrophes), shouldn't it be even more unlikely that the event was caused by accident??

Slimething said:

I hop around the galaxy, or at least I wish I could.

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This is something I've done as well. Some of the space journeys have been fairly short (e.g., trying to imagine how I would conduct an Earth-to-Moon tour that included a flyover of the Apollo 11 landing site) and others have been more "Star-Trekian" in nature, assuming that faster-than-light travel is possible.

Does counting sheep qualify as "mental mathematical calculations"?

JoeTheJuggler said:

Does counting sheep qualify as "mental mathematical calculations"?

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Yes it does, as long as you don't lose count, or even worse, count the same sheep twice

The Shank said:

Yes it does, as long as you don't lose count, or even worse, count the same sheep twice

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i bet you folk from derby often go to bed thinking of sheep

If I think of anything at all I can't go to sleep.

If I catch myself thinking, I lie on my back and imagine all my thoughts falling backwards out the back of my skull. When all the thoughts are gone there is nothing left to do but go to sleep.

Mostly, though, I just go straight off to sleep because there's no thinking going on anyway.


BJ

andyandy said:

i bet you folk from derby often go to bed thinking of sheep

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Nice

Like BillyJoe, I find the fastest way to get to sleep is to blank my mind totally.
Next thing I know, it's time to get up.

Lewis Carroll made math puzzles when he couldn't sleep and eventually published them as Pillow Problems.

I have my own running soap opera in my head. It's incredibly boring and I usually drop off right away.

Lewis Carroll had his own pillow book?

Soapy Sam said:

Like BillyJoe, I find the fastest way to get to sleep is to blank my mind totally.

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I just wonder why I keep nodding off during the day as well.

arthwollipot said:

Lewis Carroll had his own pillow book?

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You owe me $17.95 for that set-up.

andyandy said:

i bet you folk from derby often go to bed thinking of sheep

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Only the ones without sisters.

...in some parts it's billygoats...and stuff their sisters!