Shawn Hargreaves Blog
It makes sense that our brains have evolved to be better at calculus than probability. This is a survival trait: calculus is necessary any time you want to kill a rabbit with a sling, but you can get by with only crude estimates of probability (see tiger, run: no need to bother computing the exact probability it will try to eat you :-)
What makes less sense to me is why our brains are so much better at doing math and physics in 2D than 3D.
Sure, 2D is simpler because there are fewer numbers involved, but this is more than just reducing vectors from three to two components. There is something fundamentally mind-warpingly hard about trying to visualize 3D math, where in 2D we would just sketch the problem on the back of an envelope, or construct an imaginary sketch in our mind.
Reality is 3D, or at least does a good job of appearing that way, theoretical physics notwithstanding. So how come my brain can easily remember, compare, and reason about many complex 2D scenarios, yet struggles with even simple 3D? Wouldn't it have been more useful if we had evolved a better ability to process the world the way it truly is?
It seems to me that this quirk of our mental geometry processing explains the everlasting popularity of 2D games. If you stop to think about it, the idea of flattening realistic physics onto a 2D plane is somewhat ridiculous! As babies, we learned the rules of inertia, friction, and gravity, but we have only ever experienced these things in a 3D universe. Yet when we pick up the controls of a 2D platformer, we instantly recognize when physics is working as it should, thinking "yeah, that jump felt nice and realistic", without even noticing an entire axis has been removed!
Brains are weird.
I would say it's because of the medium we play on: the flat screen.
If we had holographic technology, where the game objects actually appeared around the player in a 3-dimensional space, we'd be much better at it in-game.
I think it's a problem of conditioning from early age. Many maths problems and ideas are illustrated in 2D at school and it becomes almost a second nature to deal with 2D.
I would argue that it's not brains but the "brain training" we've had that is the problem.
Yes, we tend to sketch things in 2D but maybe that's because paper is 2D. We even represent 3D by projecting it in 2D - so our mental image of 3D is kind of 2D projection of 3D. I wonder what would happen if we had a 3D sketching method and were well versed in that from early age.
Also, IMO, most problems with programming 3D (in games I guess) come from the fact we are trying to mentally visualise things - we shouldn't. Letting go of that concrete image and dealing with the problem in more abstract and analytical manner - like linear (or geometric) algebra for example, almost always proves to be more robust.
One theory to explain our 2D preference is that we have evolved on what is essentially a 2D plane. When our ancestors hunted, they really only needed to think in 2D - how far away is that deer and what direction is it going. Its height above the ground didnt really matter. So the high level thinking, the big questions, all took place in 2D. Granted, 3D does come into it a bit when you get closer to the deer and want to hit it with a club.
If we were an underwater species, or lived in outer space, then we'd have had to live and hunt in much "truer" 3D, and then we'd think in 3D without any problem.
I can't remember where I read this, I think it was Richard Dawkins.
More likely the issue is that we're viewing 3d in 2D space. I would more than guess that has 3d gets more and more real with real 3d displays that this will go away. People have no problem processing this stuff in reality such as baseball etc specifically because it is real and not fake 3d on a 2d surface.
2d on 2d makes sense to us, 3d on 2d doesn't.
Fascinating question, and a lot of good answers!
Here's another possibility: we've evolved to naturally project 3D problems into 2D models. Need to find your way home to the cave? Refer to your mental 2D map. Need to hit a mammoth with a spear? Consider the vertical plane joining you and the mammoth.
Most simple problems can be broken-down this way, and ones that can't may well tend to be computationally unfeasible or of a type our sense organs can't fully capture anyway (ie problems with concave shapes so that our vision of the problem is occluded)
Obviously our brains aren't as strict and formalized as this, but I would expect they'd be aggressive in excluding less important spatial information wherever possible, leaving us ill-experienced and ill-equipped in dealing with three axes all at once.
While 2D games don't match up to reality, they do match up to our mental models of it.
Wouldn't some of this be down to the difference between the calculation you are consciously thinking through (the 2d maths) and the sub conscious knowledge of spacial relativity (the 3d world we live in).
Let me support this theory. A child aged 4 can throw a ball to their parents, yet they would be unable to mathematically calculate this information using their conscious mind; regardless if it was a 2D or 3D set of space.
I think your point about estimation is the key; we have evolved to find the near enough is probably good enough when it comes to the calculations in our 3d environment and that doesn't translate well to a calculated answer on a piece of paper.
~Sebastian
I agree with the first poster. the medium (a flat screen) is the issue. You (the game developer) are doing your darndest to simulate 3D space but it is a simulation and our brains are (slightly) rejecting the concept.
bring on the holo-screens!
[A little off]
There IS a 3d Sketching method that kids like to use a lot. Its Called LEGO =)
This kind of toys can be used to sketch things in 3d...
I think maybe because we work on a 2D plane. From an early age its glyphs on a flat plane (reading), screens are 2D, Windows/Mac/Linux is 2D.
Although, that said we do react stronger to 3D. The Vista switcher and Linux Compiz are good examples of this. I cant cite or anything, but neurons actively die if you dont use them (if you dont use it you loose it). So as babies we probably can conceptualize 3D space.
So as Rodrigo said: Lego FTW =). Dont mess around with crummy 2D games with your kids, get them thinking in 4 dimensions (time) - maybe some 4D game such as Cogs.
The obvious answer is that the mind gravitates towards simplicity, and 3D is fundamentally more difficult than 2D. I can't even begin to imagine how 4D might look, 3D is big and complex, but I can totally own 2D.
It could also be partly a product of our generation. We all grew up sinking countless hours into those 2D games, which often even attempted to be 3D with parallax backgrounds. We're all so used to it that it Just Makes Sense. Perhaps with the increasing amount new 3D televisions and movies, kids will start to visualise problems in 3D much more easily than we ever did.
I can empathise Shawn, anything other than the simplest 3D maths inevitably makes me feel like a complete dullard!
Personally I think it's down to a several different things:
- There are always more factors to consider - 3 'basic' planes instead of 1; extra vector components. This has 2 knock-on effects:
- There are many more combinations of interacting factors to consider.
- We run out of 'working memory' much more quickly! Human brains can only deal with quite a limited number of simultaneous considerations.
- Things like matrices and quaternions which help with 3D maths are much more abstract than basic trig stuff (which is pretty much all the maths that's required for 2d).
- The diagram issue: As other people have mentioned, the difficulty in sketching out clear 3d diagrams on 2d paper makes it that much harder to keep track of everything.
"where in 2D we would just sketch the problem on the back of an envelope"
This part is great! At the time of writing this I have at least three empty envelopes lying on my table with sketches of some 2D logic I've been trying to visualize >_<
Quote from Shawn's post:> There is something fundamentally mind-warpingly hard about trying to visualize 3D math,
Here's a perspective on a difference in visualizing the math between 2d & 3d.
The math that gets complicated is often rotations. In 2d there is only ever one rotation axis that you have to worry about. No matter what, all rotations occur about the Z axis.. period. Rotationally speaking, 2d is really only 1d.
In the same sense though (rotationally speaking), 3d is really infinity[d] as an object can rotate about an infinite number of different axis at the same time. Sure, all the rotations that occur at the same time can be summed up into one axis and one angle, but even that summed axis has an infinite range of value possibilities. But not 2d, it's always (0, 0, 1), and that's one reason 2d is easier to mentally keep up with.
Although we live in a 3d world we only perceive it through our 2d vision, it only seems 3d because we see it through stereoscopy giving us depth perception