It’s Friday again, the 25th of September.  There are only three more shopping months until Newtonmas.

Yes, I know that it isn’t strictly accurate to celebrate Newton’s birth on “Christmas”, because Newton was born on December 25th according to the Julian calendar.  The Gregorian calendar had been invented already; England just hadn’t adopted it (partly because it was a Catholic invention).

But Newton’s birthday was a lot closer to December 25th than Jeshua bin Josephus’s was.  According to what I’ve read and heard from scholars who specialize in such things, the Nazarene was born sometime in the summer.  Oh, and also, there was no census requiring men to return to their towns of birth ever promulgated by Caesar Augustus, not according to any single official record of any kind.  The author of that gospel just threw that in to provide an excuse to have Jesus born in Bethlehem, so that his birth could comply with certain messianic prophecies.

Yes, the so-called fulfillment of prophecies that is used as “evidence” that Jesus was the messiah was added after the fact, by people who never knew Jesus, writing decades (or longer) after his death.  This shouldn’t surprise anyone, really.  Religions in general don’t tend to be very coherent and consistent; they just sort of happen by a kind of memetic evolution, and they are made of various hodgepodges of prior myths and folklore and post-hoc shoe-horning into supposed prophecies.  They bear no hallmarks of having actually been created and/or delivered by supernatural entities of any kind, let alone omniscient ones.

I certainly don’t think any deity is responsible for the fact that today is Friday, so I will not be thanking one, whether God or Brahma or Amaterasu or Quetzalcoatl or Odin or Jupiter* or Whatever.  Also, I am scheduled to work tomorrow, so this is not the end of my work week, anyway.

I’m relatively pleased to inform you that I’ve been reading a decent book for the past few days (not continuously, ha ha).  It’s called Vector, and it’s about (oddly enough) vectors‒the mathematical entities that have magnitude and direction, among other things.

It follows the lives and insights and advances of people like Hamilton, who brought us quaternions (which are very cool) among other vector insights, and various other people who developed the mathematics and science of vectors (we will be getting to tensors and so on before long).

Currently I’m in the midst of the discussion of Maxwell and his astounding development of the principles of electrodynamics, including his recognitions that electricity and magnetism would, if oscillating, produce a self-propagating wave that would travel at precisely the “speed of light”, by which he deduced that light is in fact an electromagnetic wave.  (This accomplishment is one of the most impressive in the history of science, and it is a tragic injustice that Maxwell’s name is not as well-known as those of Newton and Darwin and Einstein and Schrodinger and so on.)

Indeed, the very invariance of the speed of light as revealed by Maxwell’s equations was one of the things that led Einstein to postulate that the speed of light is an absolute constant in all reference frames, leading to Special Relativity (and eventually, even more impressively, to General Relativity, which will make use of and extend the vectors and tensors and matrices to which we’re gradually being introduced).

It’s very exciting.  Honest, it is.

And, of course, there’s the very cool fact that quaternions ended up being useful for describing the curious properties of particle “spin”, including the fact that, for spin ½ particles (which are “fermions”), if you want to rotate it and get back to the state in which you started, you have to rotate 720 degrees, not 360.

If this seems counterintuitive, just think about a Mobius** strip.  Are you thinking about it?  Good.  That should distract you nicely from trying to grasp the nature of fermion spin.

Kidding!  It helps to show you how the notion is not something deeply bizarre or seemingly nonphysical.  With a simple Mobius strip, going around 360 degrees will land you on the opposite side*** of the paper from the place where you started; you need another full trip around 360 degrees to return to where you began.

I’ve occasionally thought that it would be fun to set up an art gallery or other kind of museum with a single “circular” corridor that crosses over itself (by going up or down a level gradually) and that requires visitors to go around twice to get back to the entrance.  It wouldn’t really be difficult to pull off, and it would be much better (I think) than the Guggenheim layout.  Unfortunately, I don’t have the resources to commission such a gallery, so I’ll leave that as an exercise for the reader.

Don’t let me down.

Okay, well, that’ll about do it for today.  I should be writing a post tomorrow, so if that’s something that pleases you, then you can safely and reasonably anticipate being pleased, exclusis improvisis.  In the meantime, I hope you have a good day.

*Though the planet Jupiter deserves some thanks for helping make life on Earth more possible and stable by sweeping up a lot of the stray space debris that might otherwise have slammed much more often, or much more persistently, into Earth.  But, being a planet, Jupiter doesn’t require thanks or praise to do what it does.  It just requires physics.

**He shows up in the book, too.

***Though the Mobius strip has only one side, really.  And a Klein bottle has a continuous, single surface encompassing its inner and outer aspects (i.e., the inside and outside are the same), and crosses through itself without breaking that surface.  At least, it does that in 4 spatial dimensions.  Our three dimensional Klein bottle models are shadows, if you will, of a true Klein bottle, much as a drawing of a Mobius strip is just a shadow of such a strip.