Monthly Archives: June 2014

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!

elevr.com

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.

Screen Shot 2014-06-24 at 11.03.43 AM
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)
Split-quaternions
Split-octonions
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.