Wednesday, June 14, 2006

Erotic Mathematics: Lessons in Perception

Eros ex Math 4
Digital image by Peter Miller ©2004
I was recently sent a gallery of erotic mathematical renderings by a friend with a remarkable nose for the obscure. They are certainly evocative. It goes to show how a little art training goes a long way in the pursuit of the harder sciences.

Naturally this got me thinking of on one of my favorite topics. How do we create high impact experiences without spending lots of money?

Realism: The obvious solution?
Suppose for a moment that I wanted to create a highly sensual environment in a game. The obvious solution is to drench the scenery in photorealistic voluptuous figures complete with taut pink nipples or pleasantly rippling pectorals. By getting hundreds of thousands of little details 100% correct, by replicating reality in our game, we can evoke the same emotions as if the player had experienced the situation for real. This train of thought drives much of the passion behind the quest for hyper realistic virtual reality.

Does the brain need all this stimuli in order to reach the equivalent level of arousal? Human perception is distinctly not photographic in nature. We see blurs where camera capture crisp detail. Our brains filter out extraneous shapes and details in the presence of faces or sudden distractions. Much of the history of the visual arts and almost all of the history of stage magic has been spent cataloging and hacking into our brains imperfect, quirky and highly biased shortcuts for sensing of the physical world.

Gorillas in our Midst
There is a famous study about a group of research participants that were asked to watch a tape of people passing a ball back and forth. The participants were asked to count the number of passes and if they got the right number they would get a prize. In the middle of the video, a person in an ape costume walks out into the middle of the room, pauses and then walks out of the room. Later when the participants were asked if they had seen anything unusual, a large fraction claimed to have not seen a thing. They were so focused on the task of watching the ball being passed back and forth that their brains had simply erased the ape from their senses.

If this had been a virtual room with virtual people passing virtual balls, would it have been cost effective for the developer to render the virtual ape?

Photorealism is a naïve strategy for rendering evocative experiences. We throw up our hands and say “I don’t know what causes people to tick, so I’m going to throw it all in and hope something sticks.” This is sometimes effective, but oh so expensive. Throw in a few untested skin shaders and a cutting edge facial animation system and you've created a classic high volatility risk cocktail. Even worse, sometimes by focusing on everything, you miss the few details that the human brain cues into strongly. The result is the uncanny valley where we create zombie-like monstrosities that do more harm to the experience than good.

Show only those elements that trigger responses
The smart way to create a highly sensual environment is to create only the subtle triggers that trick our primitive brain into reacting viscerally. What if instead of rendering those lovely photorealistic nipples, we instead took the path of the mathematician artist above. With a few soft curves and the appropriate color palette, a skilled developer could generate a virtual pornucopia of erotic mathematical landscapes. Mathematica fetishists aside, I suspect the results would be surprisingly successful and far less expensive than motion capturing hundreds of professional actors. After all, what is more erotic? The half glimpsed form in the flickering firelight or the full on frontal nudity of a Playboy / Playgirl photo shoot? Certainly, the viewer’s mileage will vary depending on their end goals, but for most casual situations, the former is quite effective.

Visual stimuli are a highly effective, but also admittedly expensive tool for rewarding players of your game. Always remember that your beautiful creations are passed through that quirky biological sensor known as the human brain that carefully filters out a larger percentage of what it receives. Pick visuals that matter and are pertinent to the task at hand, not merely ones that are ‘realistic.’

Take care

Gallery of erotic mathematics

A description of “"Gorillas in our midst: sustained inattentional blindness for dynamic events" (Perception, vol 28, p 1059),

An alternative view on richness of perception


  1. it might be a bit of a tangent, but this heavily ties into a friendly argument i often find myself engaged in.
    "What makes a game realistic?"
    i often hear others refer to realism in games as the effect/attempt to mirror the world in which we live. however, i really feel quite different about the subject. i'm much more in tune with the concepts in this topic regarding the important details that our brains pick up on. these, to me, are what create realism.
    the conveyance of light,life, emotion.
    if an interactive experience can truly capture such elements, then it becomes realistic to me - regardless of how photo-like the visuals are. as you stated, the more photo-like games tend to really dive into the uncanny valley and force me away from enjoying or becoming immersed in their world space.
    take what i consider to be the most realistic game to date, The Legend of Zelda: The Wind Waker, as an example. this is a game that uses the most cell-animated visuals i can think of, yet is so alive, immersive, and "real" that it is a joy just to wander, explore, and interact with the world. the depiction of light, time, weather, life, et al are all crafted masterfully. but none of them are conveyed in a complex manner by any means. simple use of colors, subtle motions, shadows, etc. all very very downplayed as individual elements in the game, yet they all work in tandem to create a true alternate reality.

    sorry if my lack of erotica bounced the subject too far off track.

    if so, then maybe i can redeem myself:

    a bead of sweat rolls across the curve of her inner thigh...


  2. Oh Danc... Why in the love of Pete would you want to do this sort of thing. Don't you know most of us read your blog from work. Now we're gonna get in big trouble.

    Ya big jerk.


  3. Hopefully this isn't considered 'not safe for work'. One of the things I found fascinating about the pieces is that I completely blushed when I first saw them. Yet upon closer examination, there really isn't anything explicit at all. Yet the simple shapes and colors trigger the response.

    Hence the essay.

    Erotica is admittedly an unlikely topic for most games and doesn't quite turn my crank like a good turnbased strategy game. The basic lesson about tailoring content to fit the biases of human perception is a much more broadly applicable topic.

    take care

  4. quite the fascinating article - just wanted to say i recently discovered the blog and i love it. i happened to read your bio a moment ago and caught this piece:
    "I got my first job while in college working on a shooter called Tyrian at a little company called Epic Megagames."

    TYRIAN!!! Oh my god that was one of my first favorites ever. I loved it so much; it beat all the other top-view shooters i discovered.

    glad to know you were part of it :D

  5. Danc: It's Peter Miller here - I'm terribly sorry but somehow I seem to have trashed the email you sent me this morning. I'm preparing to leave on an overseas trip and I obviously was a bit too vigorous with the digital broom. Please write to me again so I can stick you in my whitelist and avoid it happening again.

    Now, as to your query, yes, by all means you may use the Eros images in your essay. I would be most pleased.

    Your post is very interesting and raises all kinds of questions. I think you have hit a very important point by asking 'how much of an experience happens in the outside world, and how much inside our heads'? Personally, for my tastes, this single reason is why most computer games fail for me. You are so correct in asking whether the pursuit of realism is a valuable pastime for game designers. I would assert that it is something that might be desirable, but not necessary for a great game. Spending your render cycles on making things appear more realistic is just an easy way of making a show of advancement in technique. But just as in the movie business, clever special effects and heightened realism are completely useless if you don't have a good emotional basis for using them.

    We could have a long discussion about this, but I am frantic getting ready to go, so perhaps when I'm back in a few weeks.

    In the meantime, I'm glad my Eros series has caused some interest, and particularly glad to find someone whose first question wasn't the banal 'but how did you make them...?



  6. This ties in tangentially with my desire for an impressionistic virtual world. Surely it can't be that hard? :)

  7. Just to give a clear (to me at least) case for something Dan talks about.

    If you've ever seen some of the latest facial motion capture in games, you'll see that no matter how far we've come (and fair enough its pretty far) we still cant quite capture the essence of a human face enough for our minds to see it as another human. There is just something subtle missing.

    So counterpoint that with the animation in GTA3 etc. If you play these games, from a technical standpoint, you'll see that the characters are blocky, relatively low poly by todays standards and are generally not what you'd call leading edge mocap.

    Now to my mind, the latter case serves as an indicator on how much gesture plays an important part in us connecting with other beings. I think that we go too far in our quest for realism in a graphical sense and have much less of a notion of form in the motion sense.

    Interesting discussion Dan. I'm not entirely sure I'd agree about how the erotic thing would work out. One anecdote I can recall though, is the "silhouette dancer" from the old amiga demo "five fingers". Basically very similar to the Bond films intro scenes or the recent ipod commercials. I think a moving silouette of a nice looking form (i.e a nice female body in my case) does a lot more than you would expect.

    It'd definitely be interesting to try.

  8. Definitely have to agree with the article and many of the comments made.

    Very few videogame companies can actually get the "realism" remotely correct. Aside from a company like Nintendo (Wind Waker is a great example) or Valve (Half Life 2), few game companies appear to even be interested in subtleties that actually add to the realism and instead vie for textures that end up looking distinctly out-of-place around well-rendered backgrounds filled with inorganic materials.

    This is especially true when looking at companies like Square-Enix and Tecmo. Final Fantasy games have this awful habit of creating faces that lack much diversity, as well as have some of the most unattractive facial and body movements in both their games and their movies. Advent Children is especially bad with this; there's incredible texture detail, but it's pretty painful to watch the people move and look (and act) like manaquins. And how about the Dead or Alive games? The girls look "good" but they all wear the same expressions and movements, as if you're watching a doll with big boobs. Everything other than the body shapes seem to actually change between the female characters.

    It's probably both a case of misattribution and laziness. Making these animations correct is extremely difficult, especially in a realistic setting. When a game or a medium is more of a cartoonic sense, setting these emotions is much easier just in the sense that expressions are exaggerated. Which is why a company like Pixar is able to produce such high-quality films compared to something like the Final Fantasy movies. You not only get the high texture quality, but you see the amount of work put into the animations, people can instantly recognize what a character feels, and in general it's more than gawking and something shiny but actually getting into it emotionally. But it takes a huge amount of resources (and some actual brains and creativity) to be able to accurately depict human emotions.

    Maybe developers should try this route and figure this out? Or how about they actually make a fun game and spend less time and money in general on graphics?

  9. Danc... you didn't happen to time this to follow the recent Sex in Video Games Conference, did you? :)

    I was on a panel there trying to get people to realize just how much of the game experience (especially an erotic game experience) goes on in the player's head.

    Two related tidbits:

    - I was recently watching that ASCII broadcast of the world cup, and noticed that if you just looked at the screen normally, it just looked like a bunch of ASCII characters, but if you squinted to the point where you had them barely open, you saw it as clearly as if it were on TV, with filled in details.

    - The more we learn about the human brain, especially the forebrain and the other "recent additions", the more it seems that the brains main function is inhibitory -- shutting out the 90-whatever percent of input that would be too much to deal with all at once... it's probably the only way humans ever got consciousness and language -- too much "real" input and we'd never be able to categorize and communicate it all.

    - Jeb Havens

  10. I caught bits and pieces of the Sex in Video Games Conference. It is a rather fascinating area of game design, quite aside the sex aspect to be quite honest. Many of the titles I've read about seem to be as much about expressing player emotions, relationship building, fantasy exploration and flirting as they are about doing the nasty. Each of those areas are great seeds for pushing game design out of the shooter ghetto where it currently schlumps (shmups?) about.

    The topic of what we actually percieve is a fun one that is directly tied to our jobs as 'tweakers of sensory perceptions.' As an artist, I'm always amazed at how much I can get away with and still evoke emotional responses in viewers. All artists cheat and tweak the viewers perception of reality. It is what we do. Once we sweep away the technocrat pride that drives the current manifest destiny 'quest for photorealism', game developers will realize that they are no different.

    take care

  11. So, the discussion about visual style is pretty interesting and all, but I'm wondering why you guys haven't discussed sound? From the games I remember, with crazy visual styles (like Katamari, or Darwinia) the sound matched really well. So, I think that's pretty important also.

  12. This is old now, so very few will probably ever read this comment, but I felt I had to point something out:

    The structure of the human body is encoded in a powerful fractal algorithm. It's called "DNA". So of course you're bound to run across simpler fractals that resemble human nakedness.

    Everything in the natural world runs on math. Even human bodies, naked or otherwise.