The politics of math

I’m writing a computer graphics software package that I definitely want other people to use. And today I made an unusual decision in its design.

You see, there is one place where all of the standard packages ask users to specify an angle in degrees, so that a full circle is 360o around. This seems reasonable enough on the face of it. After all, it’s the way most people think about a circle.

But in fact, when people do actual math in computer graphics, they always work in radians, so that a full circle is 2π around (just like they teach you in math class). Hence my dilemma.

Should I go with the same “friendly to most people” standard that the other packages use (degrees), or should I be consistent with the way computer graphics is actually done by people who do computer graphics (radians)?

Eventually, I decided that this is really a political question: When I invite people to use my package, what tribe am I asking them to align themselves with? Because there really are multiple tribes here.

There are the people who say “I just want to call a software package that does stuff for me, and I really don’t care to know how it works.” Then there are people who say “I am using this package as a starting point for what will be my own experiments and mathematical innovations in computer graphics.”

Since I teach computer graphics, I realized that I’m really designing this for that second tribe — my tribe. I want people to poke around inside my code, see how I am doing things, maybe come up with their own way of doing it better. I am making this software available not merely to provide a convenience but to invite a dialog.

In the end I am choosing radians. Which means that I am chosing sides, aligning myself with those people who really want to dive deep and learn all about computer graphics.

Because math, like everything else, is political.

Boom boom

Today I started thinking about what I might be doing at the age of one hundred. I have every intention of still being around then, teaching, doing research, and generally having a great time, although I cheerfully acknowledge that certain aspects of the situation are beyond my control, like getting hit by a bus before those self-driving vehicles take over.

Fortunately for me, I will arrive at that august age after a wave of baby boomers have already gotten there. And I am firmly convinced that such a huge group of self-interested Americans will contain enough extremely well connected, resource-rich and ingenious people to make a difference. These folks are not only going to want to avoid death, they are going to want to continue to enjoy life.

People used to say that thirty was the new twenty. Then they said that forty was the new thirty. Already people are saying that fifty is the new thirty. Not too long from now, I suspect they will be saying that eighty is the new forty. Relentless advances in medicine, food science, computation, miniaturization, wearables and technology in general are going to have a cumulative effect.

The concept of “life-style prosthetics” will become common. Assisted walking, muscle control, memory and navigation will be taken for granted. Technologies to improve eyesight and hearing, then eventually smell, taste and proprioception, will become first stylish and then eventually invisible.

Eventually we won’t even think about these prosthetic enhancements, any more than we now think about how our modern shoe-coddled feet can no longer walk barefoot across a hot desert.

It might be fun to think about what prosthetics that will help 100 year olds live vibrant and enjoyable lives might look like in a few decades or so. It might also be fun to eventually enjoy that experience first-hand.

If I can just manage to avoid getting hit by that bus.

Holmes for the holidays

Since before the start of Thanksgiving I have been steadily hunting down a pernicious bug in my software. Finally, only this evening, I found it and fixed it. My sense of triumph and relief is probably all out of proportion to the situation, but there it is.

Usually it doesn’t take so long to find a bug. After a little poking and prodding, most bugs pretty much announce their cause loud and clear. But this one was different.

This one lasted for days, threatening to grow into my very own great white whale. Its origin was elusive, its symptoms inexplicable. Try as I might to lay a trap for it, to grab it by its metaphorical throat, things would mysteriously shift, and I would be left holding air.

Of course we must try to resist the tendency to anthropomorphize inanimate things, to imbue our own software bugs with some sort of crafty sentience. But I suspect that’s the way the human mind is wired.

In the end I fixed it by using the tried and true method so elegantly expressed by Sherlock Holmes himself: “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

Star turns

Kurt Russell Crowe in “Escape from L.A. Confidential”

Jennifer Jason Lee Marvin in “Last Exit to Black Rock”

Ru Paul Newman in “Cool Hand Lucy”

Ashley Judd Nelson in “Divine Secrets of the Ya-Ya Breakfast Club”

Meg Ryan Gosling in “Addicted to Crazy Stupid Love”

Robert Patrick Stewart in “Terminator, the Next Generation”

Olivia Newton John Corbett in “My Big Fat Grease Wedding”

Wallace Shawn Astin in “My dinner with Frodo”

Only human

Nearly every guy I know over 40 has back problems. This is not surprising. After all, the evolution of our primate ancestors to adapt to bipedal travel happened over an extremely small time scale, as these things go. You and I and all of civilization have happened along only quite recently.

In fact, the entire history of human civilization is just a tiny blip in evolutionary time. So it should not be surprising that the adaption of our spinal cords for upright posture is still very much a work in progress.

I think we have a similar problem with our human Theory of Mind. By far our biggest power-up as a species is our ability to model each others’ thoughts and emotions, and thereby, with the help of natural language, to use those mental models to form kinship groups that let us cooperate in ways that greatly increase the survival fitness of our species.

But this evolution too is a work in progress. When the exponential growth of civilization started to really take off — a mere five thousand or so years ago — our species was still in the process of gradually evolving its biological capacity for Theory of Mind.

To it’s not surprising that people have so much difficulty understanding each other. It’s not that there is anything wrong with us. It’s just that we are us. The brain of each human acts as an imperfectly evolved instrument for creating, and then acting on, a mental model what is going in the brains of other humans.

But that brain is still, as far as we know, the best goddamned instrument for doing such a thing. So while we bemoan (understandably) the tragedies of war, terror, irrational prejudice and unreasoned hatred, perhaps we can take a moment to remember that this is the best human brain we’re going to get, and that even in its imperfectly evolved form that brain is still pretty amazing.

Sure, we are often totally screwing up this whole civilization thing. But then again, we are only human.

Flight done right

A year and a half ago, at the 2014 SIGGRAPH Conference in Vancouver, I first tried out Birdly, a kind of virtual reality experience in which you put on a VR headset and get strapped into a contraption that looks vaguely like a bird. When you flap your arms, you find yourself “flying” around San Francisco, like a bird soaring through the air.

Today I was thinking about this experience because our current “Future Reality” research at NYU involves using Tactonic Technology floor mats as a kind of magic flying carpet that lets you fly around in virtual worlds merely by shifting your weight — much as I imagined doing as a little kid, when I first learned about magic carpets, and wondered why I couldn’t have one.

This in turn made me think about the flying dreams that I still have from time to time, and which are always completely delightful. In my flying dreams, I am often soaring around cityscapes, swooping gracefully between buildings and generally having a grand old time.

And in all those dreams, I have never once hit anything. Whenever my flying self gets near to a building, I merely veer to the side, or cleanly soar up over it. In the moment, this seems ilke the most natural experience in the world.

In contrast, the first time I tried Birdly I kept crashing into buildings. That just didn’t seem right to me, since I know quite well that I can do better, from all the extensive flight time I have put in while in slumberland.

I guess that’s one of my motivations in wanting to use the Tactonic floor mats to allow us to soar through the air in our VR research at NYU. Why should my magical flying self ever need to crash into a building? It’s one of those situations where I know it can be done better, because I’ve seen it done better.

Even if I was sound asleep at the time. 🙂

In another 50 years

In a recent post I remarked that I had been thinking about historical events every 50 years. Some students at Trinity college had observed that Alice’s Adventures in Wonderland was published exactly 150 years ago, and that Einstein’s theory of general relativity was first presented 100 years ago.

So I got to wondering what might have happened 50 years ago which similarly challenged our notions of time and space. I concluded that it was “Moore’s Law” — the prediction 50 years ago by Gordon Moore that the cost of computation will continue to decrease exponentially with time. This remarkable and prophetic statement has held true for the last half century, leading to profound and astonishing changes in our world.

But then the other day somebody asked me what might be happening right now — in the year 2015 — that people will one day look back upon as the next step in this legacy. Will it be virtual reality, neural implants, or something else that is so radical and paradigm changing that we are as yet unable to even recognize it?

I am open to suggestions.

Body relative

In our Future Reality research at NYU, we’ve been trying all sorts of things. One set of experiments has involved embodied conversations between people whereby we create the illusion that participants vary greatly in scale.

For example, in one experiment I found myself shrunk down to about 6 inches tall. I seemed to be standing on a table, so that the room around me seemed vast and cavernous, the walls and ceiling impossibly far away.

People who were of “normal” size appeared as huge, giant creatures who loomed against the sky, peering down at me as from a great height. The effect was quite compelling.

One question that comes up when you create such experiences is what, exactly, should the subjective experience be for each participant. After some experimentation, we came to an interesting conclusion.

If you find yourself virtually transformed into a six inch tall version of yourself standing on a table, then the most effective subjective experience does not create the impression that you have shrunk down in size. Rather, it creates the impression that the world itself has blown up to vast dimensions, and that you have not changed at all.

For example, the audio in the room will feel the most natural if it seems to be a vast chamber, hundreds of feet across. When the “normal” sized people speak, you should hear booming and echoing voices, as though the sound is traveling across a great distance, and bouncing off the walls of a giant space.

In effect, you are experiencing a different physics. From your perspective, sound still travels at 1100 feet per second. But because the entire world has become impossibly large, the time it takes for that sound to travel from one end of the room to that other is creating a noticable echo.

Meanwhile, the “normal” sized people should hear your voice as tinny and lacking bass, because you are a tiny being whose body contains no large resonant cavities. You will still sound normal to yourself, but to them you will sound like a small creature.

The take-away lesson is this: As we try to transform ourselves to travel through virtual worlds, our subjective experience will always be body relative. If we become tiny or huge in these alternate worlds, the most natural interface will be one that seems to keep us the same, while changing the entire universe around us.

My day

I spent most of the day finishing up a 3D modeling software package that I started implementing a few days ago. Today was the day I added support for textures of various kinds.

To test everything out, I created a little “rogue’s gallery” of objects. Over the course of the day I kept going back to these objects, to make sure they still looked like they should. So I spent much of the day watching these shapes swirling around on my computer screen.

I didn’t realize how embedded this collection of shapes was in my mind until this evening, when I went to see some experimental theater. At the very beginning of the play, the performers handed out paper and markers, and asked us to draw an image that represented our day.

I ended up sketching the collection of animated objects that I’d been staring at for hours. Which is when I realized how much this particular collection of shapes had seeped into my brain.

So here, for your amusement, is my day — not a mere sketch on paper, but the computer graphic original, in all of its hopelessly nerdy glory:

In case you were wondering, the complete text on the bagel-like thing on the lower right says “This is not a bagel.” It is, I suppose, a sort of New Yorker’s version of Magritte.