Vectors are Not 1-Forms

So, I recently moved in to a new research area.  It's new to my advisor, too.  Actually, generally speaking, it's pretty new period, first appearing some ten years ago or less.  Anyway, this new field deals fairly heavily with Maxwell's Equations in curved spacetime, so to understand it we are needing to review differential geometry and general relativity, two fields which are not in the normal purview of my advisor's expertise.  I was asked to prepare a chalk-talk that would introduce the key concepts of differential geometry to them, and another talk to segue in to Maxwells Equations in curved spacetime.

Not like I'm an expert on differential geometry, but I've studied it some privately and as an undergraduate.

While studying for this, it dawned on me suddenly, like the storm clouds that pile higher and higher until the first bolt of lightning strikes the ground, that vectors and 1-forms are different.

Every thing I have ever read in physics equates them.  Or not really.  Everything I have ever read in physics doesn't even demonstrate that it understands why those two should occupy different semantic domains.

What the heck am I even talking about?

Happy Nice Guy Schadenfreude Day!

The title is actually all I wanted to say :P

Kingkiller Chronicles Speculation: Why Can't Kvothe Do Magic?

There's a certain type of book series that offers the reader the chance to be a detective; the entire world of the series is a mystery whose origins lie shrouded in a mist of narrative, yet enough light pierces that veil to allow the attentive reader to glimpse the nature of things.

The Kingkiller Chronicles is just such a series, perhaps the best such series.  It is written by a very talented writer, and it is already finished; every twist in the plot is already written in a manuscript, and Rothfuss is largely just fixing diction at this point (which is still taking him agonizingly long).  Further, the future of the series is already known; we know the end of the story, where Kvothe becomes the humble innkeeper of Nevarre and the world is torn apart by demon spiders, and we know that the rest of the story is going to explain how all of this happened.

So, as I have done in the past, I would like to take a moment to wildly speculate about the series.

There are, of course, SPOILERS.  Please do not read this until you have read the first two books, and thoroughly.  Try to piece things together for yourself, or you're missing half the fun of the series.

Dreams of Smoking

I still have dreams of smoking cigarettes.

It's been maybe five years since I quit.  I was 20 or so then, and I'm 25 now, so maybe five years.  Cold turkey; went to bed having smoked a whole pack that day, woke up and haven't touched 'em since.  It was during finals week, my first semester at my Alma Mater.  It was really stressful and I have never hated anything more in my entire life.

Of course, I haven't "entirely" quit smoking.  I still smoke a pipe, sometimes, when I'm in certain moods.  Some friends of mine smoke cigars and I've joined them more than a few times.

But I have not touched a cigarette since.  Except in my dreams.

When I first quit and was furious with withdrawal it was understandable.  And those stopped after a while, too.  But I guess they didn't quit entirely, either.  I would still wake up and recall the feel of smooth smoke trickle down my throat and fill up my lungs with the calm and succor, remember the feel of the cigarette between my fingers, the fluid motion of tapping out the ash.

Today, just now, randomly, I remembered several dreams I've had in the past month or so about smoking.  Usually, I was waiting somewhere, and there'd be a cigarette in my hand.  I'd smoke, then feel guilty about it since I've quit.  But, I'd console myself, it's just one, and no one's around to watch, and I'm not going to do it again after this.  A one-time lapse is allowable.

So I would.

That was my thinking in my dreams.  It's not much different than my thinking in the waking world.  Thankfully I haven't actually relapsed, and thankfully my conscious mind apparently misses cigarettes much, much less than my dream-self.

Funnily enough, in my dream, I would remember the other times in dreams that I'd also smoked a cigarette under similar conditions, and think, "See, we can do it now and it's not going to take over your life; it's fine; it's our thing."

I don't know if I'll always have these dreams.  I'd prefer not to.  At the least I should stop trying to recount them while awake, as just remembering the smoking-sensation of my dreams with my full mind makes me really long for them again in reality.

Anyway, I don't know what any of that means, or if dreams ever do mean anything, but it was on my mind and it's my blog, so I shared it.

What was Skynet Thinking?

A lot of people have a wonky understanding of time travel, based mostly on Back to the Future.  There probably isn't any such thing as time travel, so in that sense I guess anything you believe about time travel is true.  But the common view, that someone going back to the past from the future is able to alter events in the past from how they already happened, doesn't even make sense.

When we think of traveling to the past, we always think of this in terms of us, now, going to the past, and not in terms of someone else from the future coming to the present, so we we tend to think that we can change it.  Really, any "change" you make was already made, by you, before you left, and could have been recorded by historians if they had bothered to write about it.

It's an almost understandable mistake, due to our perspective.

But what the heck was Skynet thinking?

The Cosmic Order

Sometimes, it's comforting to know that, at the end of the day, there are a few basic principles which govern all interactions in the universe, and that they are always the same principles; the ones you've known your whole life.

No, I'm not talking about physics.  Nor about math.  I'm talking about principles much, much deeper, much more cosmically valid that those silly math and physics.  I'm talking about Murphy's Laws.

Today, I had these foundational constraints of existence verified in a particularly potent manner.

The Uncertainty Principle and Energy Non-Conservation and Why Your Textbook is Wrong

I read this all the time, in physics books and articles and on the internet: Apparent violation of conservation of energy is possible at the quantum scale for very short periods of time due to the Heisenberg uncertainty relation:
∆E∆t ≥h/2π
In that equation, ∆E is the "uncertainty" in the energy and ∆t the "uncertainty" in the time, meaning the accuracy to which we are able to measure these values.  The h in the equation is Planck's constant (which I didn't write as h-bar because I didn't want to encode LaTeX for one equation).  The two are inversely proportional, so as one goes up, the other must go down, so for short times, you can get enough "free" energy to send a particle through an energy barrier.

This is wrong.  Wrong, wrong, wrong.