Explaining 4D rotation

March 19th, 2019

I am working on a technical paper that describes a technique I once came up with for rotating objects in four dimensions. And I want my explanation to be really clear.

I don’t just mean clear to mathematicians. I mean clear to anybody who might be interested in the question of how you might rotate things in four dimensions.

So I need to find a way to describe what I did that doesn’t just rely on lots of mathematical formulas. The description needs to make visual sense. But how do you create an explanation that is visually clear if the “visual” in this sense is four dimensional?

I’m probably going to need to figure out some really good analogies to lower dimensions — to something that can happen in just two or three dimensions. And I think that approach should work.

But isn’t it funny that this should be so difficult? Sometimes it’s harder to come up with a clear explanation of something you did than it was to do it in the first place.

Dream people

March 18th, 2019

I’ve been having some rather intense dreams lately, in which I imagine entire worlds filled with people. As I wander through a surreal office building, or carnival, or social gathering, I look at all of the people around me, and I wonder where they come from.

Clearly they came from my mind, but why the high level of detail? Do they each have individual personalities, back stories, goals and desires? Do they have persistence?

Sometimes I will have a recurring dream, in which I find myself back at a dream place that I have visited on previous nights. Are the people I meet there the same people as before, or are they merely a form of procedural texture, generated by my mind in that moment to flesh out a desired feeling of place and time?

It would be intriguing to think that there is a cast of characters waiting in the wings, poised to inhabit these dreams. Perhaps when I am not in slumberland they spend their down time hanging out in each others’ company.

They gossip and flirt and prepare for future performances. And the next time I see them, perhaps in a dream cafe or island, as I wander in silence through these shadowy crowds, I remain unaware of the rich world that has continued on its way while I have been absent and awake.

Captains Marvel

March 17th, 2019

I realize DC Comics can no longer publish the original Fawcett Comics Captain Marvel as Captain Marvel, because Marvel Comics now holds the trademark to the title “Captain Marvel”.

And so, alas, when Billy Batson says “Shazam!” he now turns into Shazam, not Captain Marvel. But wouldn’t it be cool if they bent the rule, just once?

Imagine if DC’s Captain Marvel teamed up with Marvel’s Captain Marvel. Together they could save the Universe in ways hithertofore undreamt of.

I think it would be marvelous.

Secret passageways and cabinets of wonder

March 16th, 2019

Every one of us inhabits two universes. There is the universe we share with everyone else, the one we refer to as “objective reality”.

Then there is that other universe, the one inside our own mind. This rather vast second universe is filled with its own miracles, its secret passageways and cabinets of wonder.

Somehow we each manage to negotiate this double reality. To most of the world we reveal only a small portion of our inner universe, one which fits within the limited framework of culturally acknowledged understanding.

But to those we are close to, the ones we truly trust, we reveal far more. A deep relationship between two people is a window into each others’ miracles, their secret passageways and cabinets of wonder.

The writing is on the wall

March 15th, 2019

Apple has finally started to let the rumors leak about its forthcoming AR glasses. The descriptions are vague, but they are clear enough.

The vision of AR is finally coming into focus. We can most likely expect a first product release in the first half of 2020 (a very apt choice of year).

For the first time, my colleagues who are not technologists, the ones who are artists and creators, are sitting up and taking note. Whenever Tim Apple (sorry, couldn’t resist) finally makes a move, it means something is coming down the pike that is actually relevant to consumers.

The writing is on the wall. But you will need those glasses to see it.


March 14th, 2019

There is something so gloriously nerdy about pi day. Today people at our lab greet each other by saying “happy pi day!” and always with a big goofy smile on their faces.

Mathematics is very pure. It isn’t swayed by politics, religion or tribal preferences. It does not care a fig about your age, gender preference or ethnicity.

Math is simply that which is true. Not “true because we said so” or “true because it’s on the news channel I like”, but literally, absolutely, stone cold provably true.

And not just in this Universe, but in any possible Universe.

So when we greet each other on the fourteenth of March with the words “happy pi day”, we are affirming for each other something deep and powerful. It may seem nerdy to everyone else, but we are acknowledging our mutual connection with absolute truth.

Even younger

March 13th, 2019

It’s always interesting to see where they take the X-Men franchise. So many and varied super-abilities, so many origin stories and complicated personal relationships to wander through and explore.

There are many levels to this exploration. The casting alone is a kind of meta-game. Who is going to play the twenty-something Patrick Stewart, or Hugh Jackman?

But one rule that seems fairly consistent is what I call the “even younger” principle. Every time they make an X-Men prequel, we get to see an even younger version of our favorite characters.

As I watched the trailer for the latest “wow look, they are so young in this one” prequel, I found myself wondering whether there is some age line that they will never cross. At what point do they need to stop?

By maybe they don’t need to stop. As long as audiences keep coming, they can continue to make ever earlier prequels.

What about the X-Men as toddlers? Perhaps one day we will see the ultimate prequel: X-Men: the Terrible Twos.

Millennial baby

March 12th, 2019

It is said that the millennial generation consists of those who were born between 1981 and 1996. Of course that is merely one definition, but it seems to be a popular one.

By that reckoning, the World Wide Web, which was born thirty years ago on this day — the twelfth of March, in the year 1989 — falls squarely in the middle of the millennial generation. It would be fair to say that the Web is a millennial baby.

But has it truly really reached maturity? Perhaps these first thirty years have merely been a stage of incubation.

The Web may only truly come alive when everyone is experiencing it all the time through their wearables, as an integral part of the physical world. What was it that Yeats said, exactly a century ago?

“And what rough beast, its hour come round at last,
Slouches towards Mountainview to be born?”


March 11th, 2019

When I think of classic films I tend to go fairly old-school. My thoughts run to Casablanca or The Third Man, or perhaps On the Waterfront.

Our lab recently decided to start a weekly movie night. We created a Slack channel where people could contribute suggestions for what to watch.

There were a number of interesting suggestions, but one in particular jumped out at me, mainly because of the wording:

the princess bride is classic

“Wait a minute,” I thought to myself, “that’s a good movie, but how is it classic?”

Except what I was actually doing was staring intently at the word “classic” and thinking to myself “I do not think that means what you think it means.”

And that’s when I realized he was right — it’s a classic.

Octopedic arias

March 10th, 2019

Today we did a solid day of rehearsals for the collective VR theater experience that we will be showing at the SIGGRAPH conference in July. It was exciting to see talented actors applying their wonderful stage smarts and improvisational wit to characters who will be seen on an entirely virtual stage.

The characters in this particular piece will look human (more or less), but for future productions that does not need to be the case. For example, using this sort of technology, it would be possible to put on a stage musical where every character is a different species.

But what would that be? Would it be akin toe July Taymor’s stage production of “The Lion King”? Or would it be more like the Disney film of the same name that it was based on?

Or would it be something else entirely? I for one would quite enjoy a love duet sung by an octopus and a tarantula (when they realize they have so many things in common). But I’m not sure exactly what to call the medium itself. Is it animation, puppetry, theater, immersive cinema, or something else entirely?