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Vi Hart Weekly, June 5th

This week’s weekly Vi Hart news includes the following topics that have been in my brain this week, gathered here for your Vi Hart news consumption experience: music/improv/earworms, VR stuff, Caitlyn Jenner, and this week’s book reviews.

1. Music Section: improvisation and earworms

This section is first so that you can hit play on this embedded sound file if you want accompaniment for the rest of your consumption experience.

The above is an improvisation on my piano that happened. I did record it and put it on the internet.

I also watched/listened to this amazing video at least 20 times. I could not get it out of my head, so I did a weird improvised “let’s play” on the section most stuck in my head, which I also posted but then deleted a few days later because it’s not very good for anything but curing that particular stuck-in-head disease.

I’d do better to describe it to you: I play the theme in a lot of ways: cliche ways, weird ways, same notes but in the context of different keys and/or different chords, and in the end go on to destroy context entirely and get all atonal on it for a while.

That is how things often get stuck in my head, and definitely how they get stuck in my head when it’s in a really bothersome way. They transform, combine with other songs or pieces, and in the end become unrecognizable as the original. An aspect of it might repeat in a maddening way, but everything around it changes and changes.

That, at least, is what I experience that is closest to the cliche of the annoying earworm. But more often the music in my head is beautiful to listen to, and plays through larger sections or skips around different parts, rather than looping. A familiar and beloved string quartet can play through my head unaltered. Or my own compositions, in which I know the purpose and order of every note.

But sometimes I’ll have something stuck in my head and have trouble placing it, and maybe it will end up that it is my own unwritten composition, or after a while I’ll recognize it as an orchestration of something else, or maybe I never figure it out. I’d say a large percentage of music that gets stuck in my head is music that I have never heard in real life, whether it be a cover version or variation of something “real”, or something completely invented. Music that I know is my own unwritten composition can play again and again in a way that is quite maddening until I finally write or record or otherwise make the thing “real” and get it out.

Sometimes I find I have more than one thing stuck in my head at the same time, but they’re not overlapping or synching, they’re just sort of running in parallel but completely separately (which wouldn’t work in real life). Or I find that the piece is stuck in my brain but it’s not playing so much as just in my brain all at once, or some combination of the above.

I mention this because also this week, I read Mike Rugnetta’s Reasonably Sound intermission post in which he talks about how he just found out that some people only get songs stuck in their head as short repeating loops, while he only gets songs stuck in his head in their complete form, and only instrumental work. I had never heard of that before. This has me interested in the different ways music gets stuck in people’s heads, and so I thought I’d add mine the list.

It’s also weird to listen to myself improvise, and I’d like to record myself more often and see if it gets less weird. I feel like I should know what I’m thinking and where I’m going, that it should be even easier to follow my own thoughts when I’m not also busy playing, but it’s hard to think those thoughts without actually using the piano and my hands as an extension of the brain. I understand my improvised self much less than I understand my composed pieces.

2. Virtual Reality Research News

Yep, still doing VR.

We just passed the one year anniVRsary of our “hello world” post on eleVR (and almost 1 year since my own post about it on this site).

One year doesn’t seem like a lot of time, but we’ve had the luxury of being able to focus all our time doing research, rather than having to create a product and do business and marketing stuff, so we’ve been able to cover a huge amount of ground. I can’t believe how much VR content we’ve created, and how much research content we’ve shared on our blog in just the past year. There’s a lot there.

This week in eleVR:

-I set up (still under construction, it is the future we’re talking about after all)

-Emily’s been posting a series of articles on editing VR video

-Emily and Andrea are doing some stereo video experiments and I don’t really understand what’s going on but I think there’s codecs involved? Also they did an awesome interview and they are awesome.

-Elijah is working on a post about the work he’s doing with 3d models and capturing panoramas in Maya and I want to reaaaad itttt

-I sent a million emails because apparently that is who I have become.

3. This Week’s Trending Topics Opinion Column: Thoughts on the Caitlyn Jenner media experience and Gender and Identity and Stuff

A month or so ago it seems, I was having a scotch with some colleagues in a sports bar. On the 20 television screens of this sports bar appeared the face of someone I had never heard of before, doing an interview.

There’s a lot of terrible soul-sucking media ridiculousness that I wish were not in my brain. I wish I were not wasting brain space knowing who Lady GaGa is dating or what Snookie’s hair looks like. But I am glad that, thanks in part to the media machine that infects us all with the cultural consciousness of who has been judged to look awesome on magazine covers, I know who Caitlyn Jenner is.

For selfish reasons as well as general desire for social progress, I really wish this and other recent examples of trans visibility in media had all happened so much sooner, that I had been exposed to all this when I was young. I really did not understand the whole transgender thing when I was a teenager, and besides that I might have been a better and more thoughtful person, it also would have helped me understand myself better.

I really could not, when I was younger, understand why people made a big deal of gender at all. Why would anyone ever feel the need to point out that they were “A Man,” or “A Woman?” I thought it silly and attention-seeking when anyone would call attention to their gender in any way. Profile names of the form [thing I like]+[gendered identifier] caused an instant dislike to well up in me. I assumed that gender mattered as little to other people as it did to me, and thus if they made a fuss about, for example, being misgendered, it was a purely dramatic show made in bad faith.

This made quite a puzzle out of the fact that apparently some people considered their gender to be so strongly a part of their identity that, if it just so happened that they had been assigned the wrong gender at birth, they’d go through the trouble to transition. I believed that humans are social animals who tend to take the path of least resistance both physically and culturally, so if someone does something that’s very difficult, there had to be a good reason for it. Being trans sounded like a lot of effort to me, hard to justify if gender doesn’t really matter after all.

And it was too long, not until I was in college, that any actual trans voices made it across my radar, and I realized this was not just a theoretical curiosity from far away, but something people actually do. Real people go through all this trouble, and for what, gender?

The only conclusion that fit the facts was that indeed, gender is a thing. Maybe it’s culturally created, or maybe it’s biological, or maybe it’s something else, but it’s definitely real. And if it’s real when trans folk do it, maybe it’s even real when cis folk do it.

In understanding that gender identity is a real thing, I also understood that I don’t have it. I don’t identify as nonbinary either, I simply don’t identify. I have all the privilege of being fine with keeping the default I was born with, as well as the privilege that when people use the “wrong” pronoun when they email me or write an article regarding my work, I don’t feel misgendered (although I might feel tired of sexist assumptions).

My condescending teenager attitude came from a false belief that other people are basically like me. I didn’t care, therefore others don’t really care, therefore if they act like they care then it’s just an act for attention, or drama, or because they’re bored, because I know that if I were acting like that, it could only be for those reasons.

The same fallacy made me think that since I thought beer tasted terrible (before I lived in Belgium and learned what beer is), everyone thinks beer tastes terrible, therefore if they say they like it they’re just pretending to be cool, just like I’d be doing. And if I have a bias that I pretend to be politically correct about, everyone secretly agrees with me but is also just pretending to be politically correct, and why can’t we just all admit, as a culture, the truth about these people and their beer?

It turns out people are truly different from each other, and thankfully not every human secretly harbors the same inner feelings, same tastes, same resentments, same biases, as my idiot teenage self.

I managed to finally realize that when someone says “I am a Woman,” they actually mean something by it, in a way I never will. I wish I grew up knowing any of this were a thing, I probably would have been better to others as well as to myself.

So the transgender community taught me a lot, and I am thankful for this, and I’m glad not just for Caitlyn Jenner and the trans community but also for teenagers like who I was, and anyone else trapped in the uncaring meat of their head who is finally being forced to imagine that maybe the world is truly different from the stupid spiteful place they imagined in their own image.

4. This Week’s Book Reviews: Dissanayake and Wittgenstein

Homo Aestheticus, by Ellen Dissanayake

Dissanayake argues that art evolved as a useful human activity in and of itself, rather than being fundamentally useless, or an accidental side-effect of other human abilities such as language.

If this book had been written well and in confident tone, most academics would know this book and Dissanayake’s name. Just 20 years ago when it came out, Dissanayake’s ideas were completely new, and she encountered a lot of hostile push-back. Now, the idea that art-making might have evolved as a specific adaptive behavior seems like an obvious one, hardly worth making a fuss about.

The result is that, from a modern perspective, much of the book is self-justifying and defensive. Her ideas were revolutionary, but not well formed or well argued, and in her rush to shove in piles of examples and evidence from other fields to try to legitimize her work, she frequently contradicts herself or seems out of her depth. There’s occasional bits of great stuff in there, but almost the entire book is spent simply justifying that it’s worthwhile to write about the topic in the first place, making it a frustrating read for anyone who is already on board with the idea that it is worthwhile to think about art from an evolutionary perspective.

Of course it’s worthwhile to think about art from an evolutionary perspective! Or at least, such an idea seems obvious to me over 20 years after her book came out, thanks to her work. Who would have guessed that so much would change in only 20 years?

If I didn’t have to read it for this week’s office book club meeting, I would not have read past the first chapter, but I’m glad I forced my way through because there’s some interesting tidbits and perspectives in there. The greatest interest comes from knowing the history and context in which this book was written, and seeing how many of the ideas in it got picked up and made known by others in clearer more convincing work. It’s valuable to look at badly-formed self-contradictory thoughts that live in the process of trying to say a new thing. I will share some of what I think are the best ideas here, to save you the suffering of ever having to read Homo Aestheticus yourself.

“Making Special” is this great concept that Dissanayake uses to describe the human behavior of… making things special. Adornment of houses or bodies or objects, the special movements of dance or music, personalization of things, affected speech, all this artistic activity makes important objects special, or important activities or rituals special, with the evolutionary advantage that a community will pay attention to those important things, do them more willingly, increase cultural identity and community cohesion through their specialness, etc.

I love “make special.” I feel like the concept was just waiting for the right label, and “making special” is perfect. It’s a very simple phrase that aptly describes a wide range of artistic behavior. It has already found its way into my personal vocabulary, and I can see it sticking around our office lingo for a while.

(“WHAT DID YOU DO TO MY WALL?” “Um… I ‘made it special’?”)

Dissanayake’s perspective on artistic behavior is focused on the history and cross-cultural existence of non-Western art, looking at art’s functions in human communities as we evolved, all but ignoring the Western art culture of the past couple hundred years (negligible in terms of human evolution). There is almost no mention of things like individuality and self-expression. Curiously, for a book taking an evolutionary perspective, there is very little discussion of art-like behavior in animals, beyond some discussion of the bowerbird (which is probably what led to it being the canonical example today).

She puts out the idea that art may be a misapplied instinct to do stuff, that people do art when they’re not sure what else to do. Having an instinct to do something in all cases is better than an instinct to do nothing when it seems convenient. It may be therapeutic and keep us in the habit of doing things that feel worthwhile, even when there’s no directly useful action we can take in response to a situation.

One of the things of particular interest that she mentions, in her surveys of different cultures and making special, is that all cultures (or at least many) have an idea of an alternate reality, a special world more or less real than this one. I need to do more research on this, look into just how universal it really is and think about the implications for VR.

The great philosopher Iris Murdoch says that art, by showing us things in different ways, makes the original thing more real, helps us understand it better. That by contrast through an art version (or a “made special” version), we can better see what the thing is in the first place. I like how Dissanayake’s thoughts connect to Murdoch’s, and how making things special might in fact make them more of what they were in the first place, at least to our understanding.

The most remarkable things Dissanayake argues, to me, is that art evolved as its own thing, separate from language. Art does not come from the same place as language or symbols, it is its own alien thing that we might layer language onto, but that doesn’t fundamentally have anything to do with language or symbols or communication. We may, she argues, even destroy the thing that is the art, when we try to use language to understand it.

I realized that it has been an assumption in my brain that art, especially music, is a linguistic, symbolic, communicative thing. This is the lens through which I’ve seen it, and whether Dissanayake is right or not is less important than realizing that this assumption has been limiting my thoughts. I don’t think she argues particularly convincingly for her conjecture, but I do know that imagining her perspective when I think about art will make me a better thinker.

Remarks on Colour, by Ludwig Wittgenstein, edited by G.E.M. Anscombe

This I read as part of my ongoing research on VR and philosophy. In contrast to the above painfully long book, Remarks on Color might be less revolutionary, but it’s much more fun.

Short and pithy in classic Wittgenstein style, but on a more accessible concrete topic than usual. Written near the end of his life and edited posthumously for publication by Anscombe. She included his later more concise version, as well as the longer earlier version, which provides some interesting insight into Wittgenstein’s thought process, and which I think contains some of the most interesting material.

The thoughts themselves are outdated by science, but the thought process is not. We know a lot about how color vision works now, which makes a lot of philosophy on color obsolete. The way of thinking is still interesting, the logic that gets to these conclusions that we know now have nothing to do with reality, as well as the good questions that now have good answers (such as why we can perceive yellowish-red but not reddish-green).

And between the stuff about color, there’s some fascinating stuff about language, content, and philosophy itself. Some standalone favs:

II-11. In philosophy we must always ask: “How must we look at this problem in order for it to become solvable?”

III-301. That I can be someone’s friend rests on the fact that he has the same possibilities as I myself have, or similar ones.

I-15. In every serious philosophical question uncertainty extends to the very roots of the problem. We must always be prepared to learn something totally new.

Wittgenstein is so much fun. “Remarks on Colour” did not introduced any big new concepts that will stick with me and change my thinking, possibly because Wittgenstein’s ideas have had such a huge influence on modern philosophy and he’s referenced all over the place (at least in the areas of philosophy I tend to study), but his words are brain candy snacks nom.

Ok, that’s what’s up in my brain this week, or at least all I have time to write about. See you next time.



Above is a gif of an interactive model of hyperbolic space tiled with 12 Days Dodecahedra. It’s part music video, part mathematical model, and all holiday cheer (or absolutely terrifying, depending on who you ask).

At this point it seems obvious to me that one must tile hyperbolic space with right angle dodecahedra that have pictures of gifts from a holiday song that blink on and off in time to a 12-tone rendition of the music, and that it should be accompanied by a holiday craft so you can make your own dodecaration (hyperbolic space not included).


Equally obvious is that it should be in virtual reality. The interactive page is webVR-enabled, so if you’ve got a webVR browser and a compatible headset you can navigate through the hyperbolic space and see the interesting stereo effects. It’s cool in a regular browser, and it’s REALLY cool in VR. It’s like hyperbolic space is what VR was made for.

There’s also a video version if you like. The comments are interesting. Most people associate dissonance with horror films, and most people aren’t familiar with the strange curvature of hyperbolic space, so I guess I understand why it’s frightening to some people, despite the ridiculous graphics. Looks normal to me…

The song and craft page are both public domain (CC0), so feel free to do whatever you like with them! You can download the original Illustrator file, pdf, or jpg.

The interactive code stuff comes from a massive collaboration with Henry Segerman, Andrea Hawksley, Mike Stay, Marc ten Bosch, and draws from code by many others. The whole open-source mess is on github.

For more 12 days math fun, see the Gauss Christmath Special:

and for a better understanding of 12-tone music, see Twelve Tones:

In theory I’d like to talk more about this whole project, but I’ve got more twelve tone carols to make!

edit: here’s one!

edit2: here’s another!

Also another interactive holiday thing, “child.


Parable of the Polygons

Screen Shot 2014-12-08 at 2.54.02 AMParable of the Polygons is a “playable post” on how harmless choices can make a harmful world.

Nicky Case and I started working on this dynamic explanation of Schelling’s segregation simulator months ago. Little did we know that matters of systemic bias would be even more topical now.

It’s changed a lot as we struggled to make the unusual format work and the ideas come through. I mean, if there’s two subjects that get a really defensive and hateful reaction, it’s mathematics and social justice, so we figured we’d do them both at once.

The simplest design choices took weeks of trying different things. We hope this design, with small rhetorical examples integrated into the text and larger simulations breaking up sections, with cute little shapes and very explicitly stated rules/goals, with graphical double-sliders and changing percentages integrated into text, will seem as obvious to you as it does to us in retrospect. Also we put it in the public domain (creative commons zero).

So give it a read, or maybe a play!

edit: now available in spanish!

A Case Study in Musical Memory and Past Lives

Piano yeah

[I just made this giant tech post on the eleVR blog about audio for VR film, which got me in the mood for a post with actual audio included in it. Sorry for neglecting you, regular blog!]

This is a story about two piano pieces.

Memory is weird. Things change fast and I change fast and sometimes I come across some evidence that I was a person in the past, evidence stronger than words or pictures because it’s in the language I know best.

I might come across a bit of music that I composed, or that past-me composed, and say, like an outsider to myself: “huh, I guess I’m a person. I bet I have feelings and stuff, inside me.”

Here’s a recording I made, trying to remember a piece I’d written and immediately forgotten about three years earlier.

The above recording was created in a literal act of self-preservation. I was out at dinner and found that the above piano piece was in my head. It played inconspicuously for a bit, and then I noticed it was there, and at first I didn’t recognize it as something I myself had written.

Written years ago, in another life, before I had any hope of success and was planning to starve to death as a composer, trying and failing for years to get into a graduate school and unable to come up with any livable plan for myself. I wrote it in under an hour, a throwaway doodle I hadn’t thought of it since.

I didn’t know if I’d ever made a recording of it. I’ve made hundreds of quick recordings of quick compositions, but even more go unrecorded, and sometimes I get something stuck in my head that I know I’ve never saved anywhere, and I wonder if that is the last time it will ever enter a human brain, and I will forget it and it will be dead.

Yet this one came back, for no apparent reason, during dinner at a place I’d been before, eating my usual. The shape of things was somehow right, and having been there before was part of that shape. And the topic of dinner discussion was not unusual, but also fit into the other shapes in just the right way that when you put them together they had the same shape as the song, somehow. The same outline. Just filled with different stuff.

I tried to grab what little bit of my past self I could.

And then, after recording the above, I found that I did have a recording of the piece from years earlier.

Later I’d feel stupid and inadequate at my awful recreation of a much better original, but the first thing I felt was wonder and joy. I was listening, as if for the first time, to something that had literally been made just for me by someone who knows just what I like, someone who exactly speaks my language. Someone good, really good. I was glimpsing into the mind of someone who is like me, but better.

When the inversion came in, something I’d completely forgotten in my inferior recreation, I laughed out loud. How clever of past-me. And what self-control, what perfect editing, to plow right through the inversion the first time though and go back to that awesome inverted cadence, just a taste before later coming back to it and spending the amount of time I expected the first time, as if I were inverting not just the melody but the form. And I wish I myself could play piano so artfully!

I, current me, know the piece, can reconstruct past-me’s thought process and feel as if I’m the composer, in the same way I can play Brahms and feel I know the piece, understand the necessary place of every note, feel I am Brahms for a moment. I feel equally a stranger, and equally close, to my own mind and many others. I don’t listen to Beethoven, I become him. I’ve been possessed by Schoenberg, I’ve been the brief reincarnation of Bach. Sometimes I even feel I am myself.

I’ve sacrificed something, by not starving to death as a crazy artist. I absolutely do not miss being the person who wrote and recorded that “doodle”, yet, listening to my past self, I can’t help but feel I’ve lost something. I don’t know if I really have.

Here’s where the plot thickens.

All the above happened about a year ago, and I’d thought it would be interesting to write up a blog post but got distracted by whatever. Too many things. So, seeing as it’s been so long, I thought it would be interesting to try recording the piece again, with only a year’s gap this time, and see how it came out.

My first attempt came out like this:

Now, savvy listener, you’ve probably noticed a certain discrepancy earlier than I did. After recording that much of it, I got stuck, and it took me a bit to figure it out.

I knew it was supposed to go into the inversion that I’d forgotten last time. I remembered it being good and clever. Yet I could not figure out what came next! The melody is so simple, and the inversion just didn’t make sense. I didn’t recognize it. I thought I must have been really extra clever, if I’d actually come up with something good. Maybe in the left hand? Still doesn’t seem familiar!

I poked the keys with a frown, until eventually I realized I was playing the wrong piece.

It’s interesting that somehow the melodic information and form information are stored separately enough in my brain that I could accidentally mix and match.

But this incorrect piece was not chosen arbitrarily. I’d written both pieces the same day, perhaps in the same hour, and the two are supposed to be together. They capture the same feeling, though they say different things about it.

Two pieces, written and forgotten together, and also originally recorded together:

Sometimes I feel a pull towards seriously doing music again. I am a much better composer than mathemusician.

Economics wins though: there’s millions of musicians working hard all day every day for years, while almost no one puts that kind of work into making youtube videos about math. The game I’m playing now isn’t easy, but there’s not much competition.

And music is terrifying. You can hear in the above piece how fragile it is, could accidentally tear apart with the slightest touch, a thorn through a dragonfly’s wing. It is my past self telling me to stay away. She’s lovely, but I wouldn’t want to be her.

No real music allowed! Stick with bagels and snails and laser bats and tiny throwaway doodles.

Memory is terrifying too. The only thing that has any real power over me is my own brain.

Music eats you up. It’s easy to get stuck in a piece. I made another attempt and my mind wandered and I got stuck

Research shows that contrary to our perception, the more we recall a memory the more inaccurate it becomes. It changes, warps. We feel as if the more we rehearse it the clearer it becomes, and while it may seem clearer, it’s further from the original. The most accurate memories are the ones that pop up out of nowhere after years without thinking of them.

There’s parts of music that are like that. How a performance of a piece went. How its supposed to be played. How it felt to play it, the energy in the room, the quality of the instrument. The non-compositional details are the ones that fade and change like normal memory. But the thing itself, unlike memory, truly exists. A piece of music is a real thing. It is the part that does not change or fade no matter how often you assert its existence.

There’s other similar pieces I wrote just a week before the originals of the ones above, and I kept up with them, remembered them through the years, playing them now and then. Those I recall perfectly and accurately. Unlike memories, the music that suddenly pops up after years is the one that has lost something.

The two original piano doodles above were written the day before I started working on “Doodling in Math Class: Snakes and Graphs,” which was released just a few days later, and was the first of my videos to go viral. It’s no wonder I dropped those pieces entirely from my consciousness for three years. The gulf between who I was that day and who I was the next cannot be reconciled.

If I wrote this piece now, maybe instead of getting distracted and stuck, lengthening, same-ifying, I would immediately become bored of perfect crystal forms and crush it swiftly:

I have so many tools now.

You might have noticed the key keeps changing. The memory I had of the original piece was purely musical, no mechanical muscle memory, no visual where-my-hands-go memory, and I don’t have perfect pitch. And so the original, in g minor, was recreated in a minor a year ago, but for the above version it wanted to feel bumpier to the fingers, and without remembering what the previous keys were, b minor felt right.

B major, on the other hand, would have been the correct original key for the other piece, which I recreated in D major while intending to recreate the other piece that had been in g and a.

Now I am tired of writing this post. Thus ends the story of two insignificant pieces.

[All music in this post is free to download and distribute under a creative commons noncommercial share-alike license.]

Transcendental Darts

So I made that video about different kinds of infinity, and then had to go deeper into explaining Cantor’s diagonal proof that one infinity really can be bigger than another, and then of course needed to answer some frequently asked questions about infinite digits going to the left in a reverse-cantor, and now I’m on to further explaining how the infinity of all the rationals is 0% of all real numbers.

I forget which other video I even mentioned the dart thing in, but yeah, the original script had so many tangents on so many topics that I edited out a potential infinity of spinoff videos, and every time I work on one of those it breeds more… we’ll see what happens next.

Carpool Lane Songs

These are some of the songs I invariably sing when in the carpool lane. Sometimes I fantasize about properly making an entire album of carpool lane songs and then touring the country as a carpool lane rock star, but for today I decided to settle for making rough recordings of a few.

The first, the original carpool lane song:

It’s easy to make up lyrics to the above song indefinitely, but sometimes I want to mix it up.


Oh, you know that I like diamonds,
but you don’t have to buy me a ring, no no,
just take me in the carpool lane,
and I’ll have everything.

And I don’t need a fancy car, no no,
just as long as it’s built for two, so you,
can take me in the carpool lane,
that’s what I want to do.

Yeah, I just want to have a simple life
Without any traffic or this honking and hubbub and lanes closed slow rolling rubber necking braking

No I don’t need a fancy vacation,
no, I’m happy to travel nearby, so I
can take you in the carpool lane,
and you can take me in the carpool lane,
yeah, we’ll both be in the carpool lane,
and baby, that’s all I need.

Just before entering the carpool lane, I like to burst into the chorus of this one, which someday I’d like to record properly with a full band behind it:


Life’s too short for the slow lane,
so let’s take the fast lane.
It’s better when we’re together,
You don’t have to be alone.

I know you like your independence,
Wanna control the situation,
But you’re just lettin’ all the other people in your way,
so baby get inside my car.

’cause I know just where to go,
I know just where to go,
Come on, sugar baby, don’t you see
those magical letters H-O-V

I wanna HOV it baby, with you.

I’m goin’ faster than you’re used to,
but just relax and let me drive you.
Baby you know I’m gonna keep you safe
So don’t be scared.

Don’t gotta worry ’bout the others,
It’s more fun when we’re together.
You know I want a high occupancy vehicle,
so baby get inside my car.

’cause I know just where to go,
yeah, I know just where to go, oh, oh,
Come on, sugar baby, don’t you see
those magical letters H-O-V

I wanna HOV it baby.

We’re gonna fly down the highway
we’re goin’ faster, than the rest are
and we’ll arrive at the same time
we’ll be together, when we get there.
Oh, oh, oh, oh…

Maybe someday I’ll share some of my Loading Bar songs.

Edit: Ok fine, here’s a sneak peak!

Introducing eleVR

Short version: earlier this year it became clear to me that virtual reality is now the near future of everything, so I found the best people (Andrea Hawksley and Emily Eifler) and we started a project called eleVR, where we do stuff like create an open source web video player compatible with the Oculus, produce the first VR vlog (for, not about, virtual reality), and figure out how to film and produce stereo spherical video, sharing our findings on our blog the entire way.

I'm pretending to work very very hard

Long version: I’m somewhat involved with the game dev community, and at the beginning of the year I started to encounter game after game being developed for the Oculus rift. VR gaming in the Oculus was clunky, low-res, and unconvincing to me, but I did come away certain that VR was the future, not because the Oculus headset itself was all that impressive, but because of the passion of the many developers putting so much time into creating content for it.

It’s games that sell gaming platforms, and VR was getting the games. All those kickstarter backers were fully invested, making new sorts of experiences that the gaming genre desperately needs. VR hardware will get better, and better, and suddenly I looked at the limited little rectangle of my videos and saw something soon to be archaic, an arbitrary shape chosen by technological convenience rather than anything fundamentally meaningful to the human experience, and I saw VR as the platform for video, for social media, for the entire internet.

I’m not going to wait around until my medium is dead, then jump onto other people’s platforms after they’ve already made the rules. I decided to get in right away and create a VR video culture that is open, diverse, and in the hands of individual creators, just as the Oculus got its start as an open platform in the hands of independent game developers. I saw two possible futures: one where people sit around detached from the world all day every day, absorbed in vacuous AAA games and websites designed to addict you with algorithmic perfection, and then the other future, where virtual reality is developed and controlled by real people, the ultimate personal tool for communication and self-expression. In this second future, sure the addictive AAA experiences exist, but it is not only huge corporations that have control over the virtual world.

That was what I was thinking about before Facebook bought Oculus. Now that the creators of the rift no longer have ultimate control over how open it stays, I’m all the more determined to do what I can to make the virtual world be our world, created and experienced by anyone who wants. Hence the creative commons videos, tech posts, and open source video player.

eleVR is a project of the Communications Design Group, a research group supported by SAP, which means I get to spend lots of time having fun researching how to do VR video and sharing it all on eleVR in addition to making my usual videos. It’s pretty awesome having a job that lets you work on so many different things and then give it all away for free, unlike all the VR-related startups and kickstarters that have to worry about making money and having an actual product if they want to be able to do stuff, so I’m really lucky I can do this.

And the questions that come up in VR video research are surprisingly in line with some of my favourite things in math. In VR video, we have to deal with spherical projections, vector fields (see my post on the hairy ball theorem), and quaternions, and just wait until we get to the spherical audio stuff… so much fun!

Proof some infinities are bigger than other infinities

A followup to How Many Kinds of Infinity Are There? that contains Cantor’s Diagonal Argument and The Fault in our Stars references.

Also see Numberphile’s video about the proof with James Grime, and Minute Physics‘ short and sweet version.

Nothing ever gets done if you wait for ideal circumstances. In the first infinity video, I had 20 minutes of time in our very professional sound booth before my office mate needed to use the booth and mic. When it comes to great audio, it’s hard to beat couch-cushion-fort-under-a-desk, so that is an example of ideal circumstances.

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Sometimes there’s no time for building professional pillow forts because you have to record in a big echoey room in time to make your flight and then edit audio on a plane with your arms all crunched up like a t-rex to use the keyboard of your laptop that’s half-shut because the person in front of you had the audacity to lean their seat back. Not quite ideal, but still good enough for getting things done, and not exactly an uncommon occurrence.

There is a third video on infinities half-scripted, so we’ll see how that goes.

How many kinds of infinity are there?

Types of infinite numbers and some things they apply to:

Cardinals (set theory, applies to sizes of ordinals, sizes of Hilbert Spaces)
Ordinals (set theory, used to create ordinal spaces, and in ordinal analysis. Noncommutative.)
Beth Numbers (like Cardinals, or not, depending on continuum hypothesis stuff)
Hyperreals (includes infinitesimals, good for analysis, computational geometry)
Superreals (maximal hyperreals, similar to surreals)
Supernaturals (prime factorization matters, used in field theory)
Surreals (Best and most beautiful thing ever, maximal number system, combinatorial game theory)
Surcomplex (surreal version of complex numbers)
Infinity of Calculus (takes things to limits)
Infinity of Projective Geometry (1/0=infinity, positive infinity equals negative infinity)
Infinite Hilbert Space (can be any Cardinal number of dimensions)
Real Line (an infinite line made up of all real numbers)
Long Line (longer than the real line, in topology)
Absolute infinity (self-contradictory, not really a thing)

Non-infinite kinds of numbers:

P-adic (alternative to real numbers)

Natural numbers (1, 2, 3…)
Integers (…-3, -2, -1, 0, 1, 2…)
Rationals (1, 1/2, 2/1, 2/3, 3/2, 3/4, 4/3…)
Algebraic (sqrt 2, golden ratio, anything you can get with algebra)
Transcendental (real numbers you can’t get using any finite amount of algebra, like pi and e)
Reals (all possible infinite sequences of digits 0.123456789101112131415…, includes all of the above)
Imaginary (reals times i, where i^2=-1)
Complex (one part real, one part “imaginary,” a consistent, commutative, associative, 2-dimensional number system)
Dual numbers (instead of imagining a number where i^2=-1, make up a number where ε^2=0 and use that)
Quaternions (make up numbers that square to -1, but are different from each other. i^2=j^2=k^2=ijk=-1. 4d, noncommutative.)
Octonions (make up even more numbers, 8d, noncommutative and nonassociative.)
Split-complex (imagine if i^2=+1, but i isn’t 1)
Bicomplex number, or tessarine
Hypercomplex (category that describes/includes all complexy number systems that extend the reals)

Also see combinatorial game theory, which extends the surreal numbers to get numberlike but not-quite-number values such as “star.” Star gets confused with zero, in a mathematical definition of confusion, but it is not actually zero.

You can also write real numbers in other bases, including negative bases, irrational bases, and even complex bases.

Every Thing

A snail on a viola scroll experiences mellow depression:

Song up on Soundcloud.

This is the third in a series of “Crazy Snail” videos, after a quick snail video throwing some footage together, and then what was supposed to be a quick video throwing more footage together but accidentally turned into something more.

I had the concept for this one not long after I finished Crazy Snail 2, and recorded a mock-up of the beginning of the song. I got stuck at the point that I needed a violin, and figured I’d get one eventually, so it sat. For a year.

I’m finally moving out of my snail-infested apartment, so I figured now was the time. I had the bright idea that an electric violin would let me record without worrying about both making and recording noise in my thin-walled apartment. Maybe I could actually record something without my upstairs neighbor turning up his music to unbearable levels in noise-revenge!

I hunted outside for a snail and found one hidden in the leaves within minutes. Filming snail footage takes patience and improvisation and snail knowledge. You can drip water on a sleeping snail to convince it that it might be a good time to check out what’s up in the world, but besides that, one cannot coerce a snail into doing much of anything. All you can do is follow it along and take advantage of the individual snail’s personality.

And snails do have personalities. If there’s one thing I’ve learned from my years of snail filming experience, it’s that snails are individuals. They behave in different, and recognisable, ways. I would have thought they’d be rather algorithmic, so this surprised me.

Luckily this snail was nothing like the snail the song’s about, and took to the viola scroll quite happily. The way it arched and swayed while I was playing! The way it happily curled up to sleep when I was done, right at the top! How it perched on a tuning peg and regarded its spiral companion… I wonder if the scroll triggered familiarity in its snail mind?

I knew I had some great footage. Now time to produce the song!

It turned out the cheap electric violin I got for this makes more extra noise than any amount of neighbors and leafblowers ever could, but it was too late to turn back now, so I went ahead and used my trusty old viola. Heavy, loud, and has survived past video abuse (see What Is Up With Noises). Had to change up the composition a lot, from high tiny delicate life to dark and low and slow, and of course as soon as I start recording, my neighbor turns up the beats.

Ah well, so much for production quality. You can hear the distant pulse of pumping bass in a bunch of my videos, and hopefully this will be the last, what with the new place and all. In the end, with the many tracks overlaid with echo it evens out to a low distant thunder that I kind of like, which makes me wish that I had bothered a little more with production quality in other aspects. Oh well.

And none of those things are the things people care or ask about after watching the video. They want to know about EMOTIONS. Well! I’d meant to capture an infinite curled-up moment of a particular feeling, including the odd self-aware beauty of feeling that feeling. That stuff is in a snail video because the snail is the perfect metaphor, literally curling up in its delicate spiral shell, an ugly distasteful thing portrayed in all its first-person beauty.