Morning has broken!

Does anyone out there know a good, reasonably priced morning repair service or person?  I really don’t have the money or time to go pick out and buy a new morning.

Ha ha.

Sorry.  I know that’s quite a stupid joke.  Still, it should give you some idea just how tired I am.

I should have been able to get a decent sleep last night, but I did not.  That shouldn’t be anything new to me, but some days the effects of the insomnia seem to pile up far more than on some other days.  And today is one of those “pile up” days, it seems.

Thus, I intend to make this a relatively short blog post today if I can.  To that end, I’m setting my “target” number of words to be 701 instead of the usual 800*.  701 has the added advantage of being a prime number, which always makes things at least a little bit better from my point of view.

It’s funny how, as numbers get bigger, there seem to be fewer primes (they fall off as something like the natural log of the number range at which you’re looking, if memory serves).  And yet, there are an infinite number of them‒the same “countable infinity” as the natural numbers, “aleph nought”:

Also, we have the twin primes conjecture‒which apparently most mathematicians think is correct‒that there are an infinite number of primes that are with 2 of each other.

It has apparently been proven that there are an infinite number of primes separated by no more than about 500 or some such (it’s probably a lower separation now, but I haven’t looked into it in a while).  That may not seem like much of an accomplishment, but remember, we’re talking infinity here.  No matter how big the numbers get** you will never stop finding new sets of prime numbers that are no more than about 500 apart.

That’s not particularly useful to anyone but number theorists, I suppose, but it seems very interesting to me.

Incidentally, 701 is not part of a pair of twin primes, since 703 is not prime (it has four factors) and 699 is obviously divisible by 3.  And of course there is only one even prime (the number 2) because all other even numbers are divisible by 2.

Sorry, I know many people find these things boring, but I’m a fan of prime numbers.  In any case I’m trying not to be so negative in my blog posts, since I think it bothers a lot of people and may even be contagious at times.

It certainly doesn’t appear to do me any more good than does being a voice crying out in the wilderness, so to speak.  And despite the excellent biblical reference***, voices crying out in the wilderness usually are not heard or received by anyone or anything that can even understand them, let alone offer them any help.

I guess I can still talk about “imaginary” and complex numbers, because they just involve the square roots of negatives, but are not necessarily negative themselves****.  As long as I avoid multiplying them together, I should be able to steer relatively clear of negativity.

Ha ha, again.

I’m trying to try to avoid making other people miserable by expressing my own dark thoughts, so instead it seems I will make others miserable with my bad jokes.  You’re welcome.

Thinking about complex numbers makes me start feeling like I want to learn more about quaternions and spinors and so on, which seem truly fascinating, but about which I have only highly superficial knowledge.

It would be nice to learn more about them.  I probably will not, knowing me and my fatigued and distractible mind, but at least I can maybe be on the lookout for Numberphile videos about related subjects.  There’s at least one YouTube channel with a series on spinors.  Unfortunately, PBS Infinite Series stopped making new videos some time ago, but at least PBS Spacetime is still going strong, as are all of Brady Haran’s excellent channels.

And now, I’m over 701 (in the first draft), and so I’m done (for today at least).  I hope you all have a good day, and that your subsequent good days scale as the number of days, not as any logarithm thereof.

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*I almost always go over my target, but at least it gives me a noteworthy place to decide it’s “time to wrap this up”.

**And there are described numbers so large that if you could memorize every digit of them, the information would be so concentrated as to turn your head into a black hole.

***It’s from the book of Isaiah.  John the Baptist supposedly quoted it and referred to himself as that voice, but then again, a lot of the writers of the “New Testament” shoehorned in references to supposed prophecy in the “Old Testament” to make the whole thing seem more sexy-cool (I guess).

****I just have to try to keep to the right upper quadrant of the complex plane.