Predominantly Erroneous (Exohedron nonsense blog)

The kind of coworker who, due to it being laundry day for him, is actually dressed better than usual.

 

I really wish I didn't have such awful reactions to alcohol. I don't get drunk, or even tipsy or relaxed; I go straight from drinking to headache without any of the desirable effects of alcohol.

 

Finally back to the paper! Had a long break since the last time since I accidentally closed the tab with the paper in it and thus lost momentum.

Section 6.4: Factorizability and Cohomology
Another reminder that for pure states we get actual factorizability, but for mixed states we don't.

Section 6.4.1: Factorizabilia (I really like this title)
Factorization of a bipartite state is equivalent to factorizability of the expectation of observables of the state.
In the pure state case, this is usually detected via partial traces.
Support factorizability: support equivalent to a product state. Extends to the mixed state case via computation of ranks.
For pure states support factorizability implies factorizability, but not so in the mixed states.
I'm pretty sure that the explanation of the counterexample is wrong. I mean, it's a counterexample, I think, but the constraint in the "factorizable iff" statement doesn't make any sense.
Separable: convex lin comb of factorizable states. Generalization of entangled to mixed states.
The example for non-separability just doesn't make sense at all. It's linear in the relevant parameter, which means that it's not a state most of the time. Also the paper claims that it's a "Werner state", but it's not.

Section 6.4.2: Pure States
Oh, the Schmidt rank is the rank of the partial trace. Okay. Things that would have been nice to know before starting this paper.
I guess it would be way too much effort for papers to give lists of prereqs. And if this is in fact written for physicists and quantum information theorists in particular, I guess it makes sense that they would be familiar with this things already.
Some nice proofs that the cohomology detects factorizability. Okay, I like that.
I keep forgetting how the functional calculus works. The presentation here is a lot better than "oh we just pull out the positive-frequency bits".

Section 6.4.3: Mixed States
Yay obstructions!
And as always examples. Let's see if these make more sense.
Separable states that have nonvanishing cohomology. Bad. Cohomology detecting classical communication?

And that's it for section 6.4. I'll try to not take so many breaks next time.

#MathPaperLiveBlog

 

Starting to realize that my jokes about "what I have accomplished" maybe should be a little less self-deprecating, at least when they're parts of presentations at work.

 

Urban Dictionary's sole entry on "Scarlet Number" is surprisingly boring.

 

The kind of metaphysics that considers holes to be at least as ontologically real as anything else.

 

This is the second computer that I've managed to damage the down button to the point where it's unreliable. But I never would have expected that an unreliable 4 button would be so awful.

 

We like to think that we are masters of our reality, but every once in a while the gods reach down and say "No, bad humans. That's not knowledge for humans, that's knowledge for gods. We left you plenty of human knowledge in your dish, go learn that."
Eventually if we are persistent enough we might be given a nibble of god knowledge, often to our regret.
Also "don't stick your mind in there, for the last time. You'll get stuck again."

 

Akagami no Shirayuki-Hime is really...something. In the beginning it makes itself out to be a romance between a prince and a peasant girl, and they fall in love and are going to get married despite opposition from various nobles etc etc. And there's going to be drama and love triangles and maybe some intrigue or jealousy. It's feudal romance, right?
Except...there isn't. For the most part, everyone is super well-adjusted and everybody, everybody is thinking about duty to the kingdom first. I mean, sure, there's an arc where she has to prove that she's worthy to marry the prince, but after that they basically get engaged and then don't see each other for like half a year because he's running the kingdom and she's training to become a research pharmacist. And they're drawn back together when she helps solve a medical crisis that requires government intervention, but then they separate again with a smile and without a doubt that somewhere down the line they'll get married.
The closest thing there is to actual romance drama is one of the prince's sworn knights, who doesn't marry the woman who he loves and who loves him because of said duty. Even the prince gave him a bit of side-eye for that.

Anyway, I'm super not complaining because this story is so warm fuzzies, but it definitely wasn't what I was expecting.

 

Back when I was thinking about actually putting stuff on my tumblr, I had a plan for dealing with anon hate: periodically, I would give all of the anon hate a collective grade based on creativity and effectiveness without publishing any of it. Given that it's anon hate, I wouldn't expect that grade to be very good, and so I would have the slight pleasure of telling people who want me to be upset that they need to do better. By giving a single grade to the entire pack, I would avoid giving any particular anon message real attention and thus avoid giving the anon noticeable validation; this system doesn't even guarantee that I would read any of it; grades can be assigned heuristically or frivolously.

Of course, now tumblr is going down the crapper, slowly, and also I realize now that I probably wouldn't have ever posted anything that would inspire anon hate, unless a really angry ultrafinitist happened to find me somehow.

I was kind of looking forward to it.

 

There's a reason that a lot of blockbuster movie fight-scenes go well to pop music, and it's because they share the same structure. I mean, the tonal dissonance is fun, but the rhythm and larger structures are often very similar, because that's kind of how human attentions go.
Firstly, the fact that fight scenes have rhythm. A lot of types of movie scenes depend on timing and pacing, and fight scenes are no different. And part of that is that fighters often fall into rhythms, based on their natural reflexes and trying to read their opponents and such, but part of it is that it is a movie, and movie watchers appreciate movements, both of actors and of camera, and cuts that fall on nice intervals, i.e. on a beat. Not necessarily regular, but fairly so. "Jarring" and "awkward" and "abrupt" apply just as well to movie scenes as they do to songs.
The other similarity is in structure. The verse-chorus-verse-chorus-bridge-chorus structure that a lot of pop music falls into is pretty deliberate, a structure meant to move between building and releasing tension in order to retain interest. And that's precisely what a lot of fight scenes do as well, building and releasing tension.
It's all choreographed. From a cinematic perspective, fighting is dancing, and people like to see dancers who can move with the music.

 

I gave a presentation at work a few weeks ago. I was going to make a bunch of jokes because a lot of the presentations in that office are kind of jokey, but in the end I only made like one or two because it turns out that I don't plan ahead enough and the only things that I can spur-of-the-moment remember to say tend to be either self-deprecating or "so you can probably guess how this story ends".
It might be for the best, however, given that one of the jokes I had planned was about how in contrast to the other presentations, my presentation was going to be "dead serious", at which point I would briefly put up a slide of Bellatrix Lestrange.

 

I was talking to a coworker who got a masters in math in the same field that I did my PhD in, and as usual when I start talking about math in real time I basically just start infodumping without real thought as to how much background might be needed to parse what I'm saying. Like, I think to myself "okay, he mentioned studying [large branch of mathematics], obviously he knows all of it".
So it was just like half an hour of "...you can make octonionic projective lines by simply adding a point at infinity, and it turns out that you can also almost make octonionic projective planes, but not anything higher because of the nonassociativity...", and while I know that he did some research into the octonions for his master's thesis, I was pulling from like three different branches of mathematics, some of which would definitely be considered PhD-level, so I have no clue how much he was able to follow.

 

I manage to eat ice cream regularly without getting brainfreeze, but smoothies? Whelp.

 

I must have been about 14 or 15 or so when I first came across Shoujo Kakumei Utena. Due to not knowing anything about it other than that the packaging was bright pink and there were swords involved, I ended up watching the movie before the series, and that probably shaped my general appreciation of it. I mean, sure, the series is full of deep meaning and complex, interwoven symbolism with deliberate, carefully-positioned and paced interactions and plot events over the course of the series, and in comparison the movie is a flashy jumble of references that don't tie together without the context of the series.
So of course the movie didn't make any sense when I first watched it.
But damn is it aesthetic. It knows that it doesn't have time for characterization or plot or any of that garbage, so it just goes all in on the symbols of the show. Swords, cars, architecture, roses, all of it swirled together operating on dream logic without any desire to say anything.
So even though as a narrative and a metanarrative the movie doesn't hold up to the show, I definitely like the movie better.

 

The problem with a lot of discussions of the determinism and freewill vis-a-vis physical theories is that they often equivocate between whether the mind is or is not part of the physical universe. On the one hand, being a physical system it must obey physical laws. On the other hand, the mind can only be viewed as an external, aphysical influence on the physical body and therefore only acts in contravention of physical law.

I mean, I'm the kind of asshole who thinks that we're all p-zombies, but to me this is pretty literally putting Descartes before the horse.


In other news, don't read Roger Penrose's stuff on consciousness. He's a good physicist; as a cognitive scientist/philosopher of the mind not so much.

 

I probably shouldn't be trying to power through Baba Is You like this, because I'm not actually great at the game, specifically the levels where you have to plan ahead. Which is like all of them. Not quite all of them; some of them you can just do something horrendous at the beginning and then noclip your way to the goal, but some of them require at least a few steps that have to occur in a certain order.

[EDIT] Speaking of, the extra level of the Ruins is one of the most awful things I have ever seen, and by awful I mean I love that you need to do that kind of nonsense and also that I never would have thought of it myself.

 

Welp, my G+ account is now dead. I should probably have backed up some of my posts or something. Hope nobody really wanted to reread my thoughts on the sociomusicological implications of Hatsune Miku. I might make a version of my Rubik's Klein's Quartic post here, though, now that I think about it.

 

In case anyone is wondering, the earliest (at least, with the lowest number) extant entry on AO3 is this, All You Had To Do Was Ask by Élizabeth (watersword), in the Dead Poet's Society (1989) fandom.
In particular, there doesn't appear to be a /1 or a /0.

 

It occurs to me that in magical worlds people are probably even more sensitive about other people playing with their hair. Just in case they happen to steal any.