Wednesday, April 19, 2023

Having Trouble Sleeping: Time for Math

Some people count sheep. I do squares of two digit numbers.  It is easier than it sounds.  Any two digit number can be factored to a power of ten plus the last digit.  58 is (50 + 8).  Binomial theorem makes that 50x50 +2x50x8 + 8x8.  Each of those is easy to do in your head 2500 + 800 + 64.  Line them up in columns and add 2500 + 864 equals 3364.  Now you do it.  54 squared.

Multiplying dissimilar two digit numbers is easier than you might think if at least of them is composite it is easier.  If both are prime you will need to do it in your head like on paper.  But if at least one is composite or better both are composite even easier.

See if you can factor one of the two digit numbers to something with a 5.  Ideally both have a 5 as a factor.  15 x 35 becomes 3x5 x 5 x 7.  5x5 is 25 which is special.  3x7 is 21.  Any number x25 is number x 100/4.  2100/4 you can do in your head: 2100/2 is 1050.  Divide by 2 again and you have 525.  If you have only one 5 in your factors, fine.  45 x 21 is 5x9 x 7x3.  9x7 is 63.  3x63 you can do in your head.  189.  189x5 is 1890/2 or 210.

Good.  I am almost tired.

1 comment:

  1. That's exactly the wrong thing to do. You want to avoid mental stimulation as much as possible.

    For a good nights sleep start in the morning. Within the first hour or two of waking go outside without sunglasses for at least 10 minutes without sunglasses. Being in a car driving doesn't work. What you're doing is triggering some retinal ganglion cells that help synchronize your circadian rhythm. This will set you up for melatonin release later in the day.

    Adenosine buildup is the thing that makes you feel sleepy. Caffeine binds to the same receptors as adenosine, and blocks its effects. Caffeine has a 5 hour half life. So don't drink any caffeine for the first hour or so of the day (this helps prevent the early afternoon "crash" and stop drinking caffeine 10 hours before bedtime.

    The whole "don't get blue light in your eyes at night" thing is probably overrated, but it's a good idea to start detaching yourself from the world and settling down an hour or two before bed. Having a going to bed ritual that starts an hour before you put your head on the pillow, something like "check the house, start the dishwasher, take a hot shower..." and doing those 9 nights out of 10 help embed the circadian rhythm more firmly.

    Diet can help too--eating at roughly the same time every day.

    And for those nights when the mind just won't let go, look into "mindful meditation". It's not the eastern religious practice, it's more breath work and training yourself to let intrusive thoughts go--which works both for focus, and for not thinking about things and going to sleep.