Month: December 2013

I’ll return to the previous topic once I get around to implementing the 3D game I described in my last post. Meanwhile, let’s circle back to something in two dimensions.

About eight years ago I heard a talk by the founder of a leading electronic whiteboard company. He said that when they first founded the company, soon after the birth of the Web, their intended market was executive briefings.

However, they kept getting calls from teachers, wanting to use the product in classrooms. At first they ignored these calls as an annoyance. But the calls kept coming — more and more over time.

It turned out that something new was happening: Because of the Web, pedagogical content was freely available on-line. Teachers wanted to project those Web pages and build lectures around them. Electronic whiteboards where the perfect way to do this.

Eventually the company got the message. It shifted most of its focus to the K-12 educational market, and soon became enormously successful.

Fast forward a decade or so. An eighth grade math teacher I know told me that there are electronic whiteboards in his school, but teachers don’t really use them. Now that all the kids have tablets, teachers are building lessons around the ability to write on a tablet and have everybody see the result on a large monitor in the front of the classroom.

The advantage of this is that it can be participatory. With the right software, any student in the class can jump in and contribute from their seat, using the tablet they are holding. Once the advantages of active, distributed and cooperative learning kick in, it is difficult for an old fashioned electronic whiteboard to compete.

User interfaces, like any organism, evolve over time, adapting to an ever changing ecosystem. What was once a cutting edge technology can all too soon become an anachronism.

To me the take-away lesson is this: Technology changes, but people do not. We can always be counted on to embrace whichever tools will best allow us to communicate with each other.

I don’t know about you, but for me the results of yesterday’s experiment in “seeing a cube like a Flatlander” were discouraging.

After all, you and I have something in common: We are very familiar with three dimensional objects like cubes. All of us can understand what is going on when we see a cube rotating, and some people can even mentally rotate a cube entirely in their mind, without needing to look at a cube.

Yet when I look at the representations of a rotated cube that I made in yesterday’s post, I experience a disconnect. Intellectually I know that the rotations are correct, because I can trace the path of each of the cube’s eight corners as it travels to its new position.

But looking at this visual representation does not give me the automatic intuition that I get from viewing the usual perspective view of a rotating cube. My spatial intuition does not quite survive the change in visual representation — even though the new representation is indeed spatial and geometric.

The conclusion I reach from this (since I am an optimist by nature) is the following: In order to use a technique like this to gain an intuition about four dimensions, we would first need to train ourselves to develop a spatial intuition for nested “outer/inner” as a stand-in for “front/back”.

One way to do this would be to develop a game that portrays a 3D cube using “outer/inner” to represent depth, and then challenge the player to solve a progression of puzzles that require rotating that cube. Eventually the player’s existing spatial intuition about cubes and 3D rotation would transfer over to this new representation.

And then we would be ready to try to tackle the 4D hypercube. To do this, we would start with a true 3D cube, and add “outer/inner” as a graphical stand-in for a fourth dimension.

I’m not saying this multi-stage plan would work. I’m just saying that it seems like a reasonable thing to try. I’d love to get the opinions of others on this.

Continuing our discussion from yesterday, if I were a Flatland creature trying to understand a cube, it’s not good enough merely to look at it. I need to do things with it.

Before going on, it is important to clarify something: In this discussion I sometimes use color. The color itself is not important. Color just provides a way to label things, to make the pictures easier to talk about. The only thing that is really important is the geometry: Where things are. That’s where all of the insight will come from.

Our Flatland creature, after staring at her picture of the 2 × 2 × 2 cube, decides she would like to rotate it and see what happens. Being a rather clever Flatlandian, she knows that a cube can be rotated in at least three different ways: (1) about its Left/Right dimension; (2) about its Up/Down dimension, and (3) about its Front/Back dimension.

To make it easier to see what happens when the cube rotates, we’re going to add a little more color for labeling. Specifically, we will make the colors of the four “bottom” cubes more vivid:

Now let’s see what happens when our Flatland friend rotates this cube 90^o in each of the three ways:

about horizontal axis		about vertical axis		about front/back axis

What does the result tell us, if anything, about what rotation in three dimensions might seem like to a Flatland creature? More tomorrow.

One of the problems in describing things in four dimensions is that they are hard to see. If I used the classic view, where Z and W are both in perspective, it would probably just be confusing.

So let’s ask ourselves: If we lived in a 2D Flatland, and we wanted to do puzzles on a 2 × 2 × 2 cube, how would we visualize the cube?

To be clear, we are talking about very smart Flatland people here, who know perfectly well what a cube is. The understand it has six faces, twelve edges and eight corners. They just have trouble visualizing it, since the world they grew up with — and therefore all their intuitions — is two dimensional.

If I were such a 2D individual, and I ran out of places to put that pesky third dimension — the one that doesn’t fit in my world — I might try nesting things one inside the other.

If you take that approach, then an intrepid Flatlander might visual a cube by doing something like this:

Our Flatland friend has found a way to position all eight subcubes of the 2 × 2 × 2 cube, by nesting one thing inside another.

In the above picture, a Back cube is represented by a pink inner square and a Front cube is represented by a blue outer square.

Maybe we three dimensional folks can use a similar trick to allow us to think about 2 × 2 × 2 × 2 hypercube puzzles. More tomorrow.

In my periodic quest to understand what four dimensions are like, this week I decided to reduce it down to the simplest four dimensional world I can think of.

My basic reasoning was like this: If you want to understand what two dimensions are like, this simplest thing you can make is a 2 × 2 arrangement of squares. In this tiny world, you can travel between top and bottom, and you can also travel between left and right. The world you can explore this way is kind of boring, since it has only four rooms to visit, corresponding to the four corners of a square:

Top Left Top Right             Bottom Left Bottom Right

The equivalent in three dimensions is a 2 × 2 × 2 cube. Now you can also travel between front and back. This world is a little more interesting, since it has eight rooms to visit, corresponding to the eight corners of a cube.

So I’ve been looking at what happens when you extend this idea to just one more dimension. Now you have a 2 × 2 × 2 × 2 hypercube. You can travel back and forth in any of four dimensions, which means you can visit sixteen different rooms.

I started posing little puzzles to solve in this tiny world, and some of those puzzles have turned out to be surprisingly interesting. More on that tomorrow.

Apologies to Mark Twain for borrowing, for the title of today’s post, only the first two thirds of his Disraeli quote.

On the other hand, perhaps, for today’s topic, it is apt to play fast and loose with Mr. Clemens’ historical “quote”, since as far as anyone can tell, Disraeli never actually said “Lies, damned lies and statistics.” We are pretty sure, however, that the phrase was indeed penned in 1891 by Eliza Gutch, the suggestrix of the Folklore Society, in Notes and Queries, writing under her usual pseudonym St. Swithin (Mrs. Gutch having been born on St. Swithin’s day).

But I digress.

BG Porter made the observation yesterday that “Fargo” is an example of a fictional movie purporting to be fact. I would argue that “Fargo” falls into roughly the same exempt category as “Being John Malkovich”, since the Coen brothers are not actually trying to rewrite history.

Rather, they are playing an aesthetic game, starting off their absurdist black comedy by linking it stylistically to Truman Capote’s “In Cold Blood” and similar modern works of Grand Guinol vérité. The important thing here is that the audience is in on the game. It becomes very clear as the film progresses that what we are watching is more Ionesco (or perhaps Jarry) than Capote.

In any case, the transgression of a film like “Hollywoodland” or “JFK” is not that it toys with history, but that it uses a veneer of sincerity to toy with our memory of a very well known historical figure.

Imagine, for example, a film about Nelson Mandela that invents a past for him in Vaudeville. Something like that could only work if it telegraphed that it is not history. For example, a rethinking of “Singing in the Rain”.

In our film, the character of young Nelson could take the Gene Kelly role, but the whole thing would really only work if he were teamed with the character of a youthful Tenzin Gyatso in the Donald O’Connor part. I, for one, would pay good money to see some high spirited young actor as the future 14th Dalai Lama singing “Make ’em Laugh”.

It goes without saying that the Debbie Reynolds part would feature a young Maggie Thatcher (Carey Mulligan would be excellent in the role, presuming she can sing).

So you see, we are now safely out of the realm of “rewriting history”. A claim that, alas, cannot be made by films like “Hollywoodland” and “JFK”.

A few months back I finally got around to seeing “Hollywoodland”, a sort of biopic from 2006 about George Reeves, who starred in the Superman TV show in the 1950s. Ben Affleck is excellent in the lead role, and the movie is quite stylish and entertaining.

However, even a cursory investigation reveals that some of the most important points of the film are simply made up — they make for good movie making, but they never actually happened. The net effect is that we are given a fictional version of George Reeves, which is presented as fact.

Is it really ok for a movie to do something like this? To me, it all comes down to the implied contract with the audience. In a film like “Being John Malkovich”, writer Charlie Kaufman never expects us to believe that we are seeing the actual John Malkovich.

Rather, we are being shown a deeply fictional version of the man. In a clever ironic twist, this make-believe John Malkovich is played by the real one. Because we are in on the joke, no implied contract has been violated.

But sometimes the contract is not so clear. Oliver Stone’s “JFK” manages to replace any plausible reality about the assassination of our 35th president with some sort of whacked out gay conspiracy.

Do the makers of a Hollywood film that purports to reveal truth have any obligation to actual truth? Or is this a case of caveat emptor? Maybe the audience is simply supposed to know, despite all signifiers to the contrary, that “It’s only a movie.”

To me, the real significance of a completely successful attempt by Hollywood to make an all-CG film that doesn’t seem like computer graphics is this:

Whenever we see some level of special effects in a movie, what we are seeing is the cutting edge of what can be computed in about an hour of compute-server time (more or less). Then, about a decade or so later, that level of computation shows up in computer games.

So it takes about ten years for some level of computer graphic realism to go from “that took about an hour” to “that took about 1/60 second”. The transition is not as difficult as you might think, because games, unlike movies, can take advantage of special purpose graphics hardware. Because the requirements of movies to be true to reality are relatively high, they can’t take advantage of the latest in special-purpose hardware acceleration. So compared with game graphics, movie graphics lose up a factor of 100 in efficiency (which they gain back in flexibility and generality of effects).

What all this means, in the larger picture, is that sometime in the next ten years your consumer-grade augmented reality glasses will be able to simulate visual reality more or less as well as the film “Gravity” does now. This means that you will be able to look around and see a transformed reality, if you like, which is indistinguishable from the real thing.

Except, maybe, for faces.

I heard a quote once that was attributed to Stephen Spielberg: “The best special effects are the ones you don’t know are there.” Part of the significance of Alfonso Cuarón’s “Gravity” is the extent to which you don’t think about what you are seeing as special effects.

This is in marked contrast to some other effects heavy films, such as “Sky Captain and the World of Tomorrow” or “Prometheus” where the extreme foregrounding of what were obviously CG special effects overwhelmed the film itself. There are, alas, plenty of similar examples.

Noel Coward once said of a musical he didn’t like (The 1962 London production of Lionel Bart’s “Blitz!”, if you must know): “I came out humming the sets.” This is about the most damning thing you can say about a musical. One could argue that the same principle applies to effects heavy feature films. If you leave the theatre only admiring the CG effects, it means somebody didn’t do their job right.

But why is any of this important? Why do we care so much whether Hollywood special effects can manage to transcend visual gimmickry to bring us something deeper?

This question brings us to Willis Ware, the great computer pioneer who passed away this last weekend at the age of 93. Here’s something he said in 1966 (quoted in last Sunday’s NY Times): ““The computer will touch men everywhere and in every way, almost on a minute-to-minute basis. Every man will communicate through a computer, whatever he does. It will change and reshape his life, modify his career and force him to accept a life of continuous change.”

Now suppose we combine Ware’s highly prescient prediction with what we can see, nearly fifty years later, on the big screen in a film like “Gravity”? To be continued…

I’ve been thinking for the last few weeks about the experience I had of seeing “Gravity”, in gorgeous stereo, on the big screen — an experience I highly recommend. From the point of view of computer graphic special effects, it’s a very important film, a landmark really.

Let us compare it with “Life of Pi”. A lot was made of the computer graphic tiger in “Life of Pi”. In some ways, that synthetic tiger was an important part of the marketing of the film. And yet, when I spoke to people involved in the production, I learned that the tiger was a mix. Some shots were CG and others were of a real tiger. Not that there’s anything wrong with that, but it’s a telling point.

In contrast, the marketing of “Gravity” doesn’t really emphasize just how much was computer graphics. Of course there was lots of computer graphics, but that’s a given these days for such films. In fact, as I learned from talking to people who worked on the production, it was a lot more than you might think.

In the shots with Sandra Bullock and George Cluny, absolutely everything on screen is computer simulated, except for their faces. Even the actors’ bodies are computer generated — clothing, torso, arms, legs, feet, hands, all of it. In those scenes, you are essentially seeing a computer animated film, with two actors’ faces composited in.

Once you are aware of this unpublicized aspect of the film, watching it becomes an even richer experience. You realize that you are witnessing pure artistry at work, a constructed “reality” as beautifully artificial in its way as any painting by Rembrandt or sculpture by Donatello.

So yes, as a benchmark for computer special effects “Gravity” is extremely important. But to me it is important for another, more compelling, reason — for what it has to tell us about our own future.

More tomorrow.