Transitions between two ways of thinking can be complicated. For example, there are things you need to do when trying to introduce people to reasoning in four dimensions that would be unnecessary if you were talking to people who were already comfortable with four dimensional reasoning.
In that sense, the discussion about “how to enable people to think in four dimensions” reminds me of other discussions I’ve had recently about transitions. For example, this question about the (possible) transition to a world in which cars drive themselves.
The general reasoning here, which seems plausible to me, is that as computers become ever more powerful, computer driven cars will eventually become so much safer than human driven cars that the huge death toll caused by driver accidents will come to seem socially unacceptable, and eventually illegal — kind of like what has been happening with smoking in the workplace.
But the transition between a world with only human drivers and a world with only robot drivers is rather complicated. During this transition, robot drivers will need to correctly model and react to what those crazy human drivers are doing. And this can be far more difficult to compute than simply making rational decisions in a world that has only rationally acting robot cars.
Analogously, I suspect that even if we do manage to figure out how to transition people to reasoning in four dimensions, a lot of that effort will consist of relating everything back to the three dimensional reasoning people already understand (even if that isn’t the best way to think in four dimensions). I don’t really see any way out of this — we’re probably just going to have to do this the hard way.
How did you learn to reason in 4 dimensions?
BTW, “Tesseract Pong” would be a cool name for your game. And it reminds me of Madeleine L’Engle’s “A Wrinkle in Time”, which I loved as a kid.
I’m confident that people will learn to reason in 4 dimensions, if there is indeed any reason for them to do so! Although… is there?
Sharon: I still love “A Wrinkle in Time!” And when I was a kid I definitely wanted to know how to tesser. 🙂 I think I’m still learning to reason in 4 dimensions.
Pastries: Three dimensions is so much richer than two in so many ways — from design to architecture to organization to all of our appreciation of the forms in nature (including our own). I very much suspect we would find four dimensions as much richer than three as we find three dimensions richer than two — and that we would find concommitant practical uses for all that richness — if only we could roam about it freely in our minds.
This helped me to understand just a bit better the challenge/process of visualizing a tesseract. Good stuff.
http://youtu.be/lwL_zi9JNkE
Is it true, then, that understanding FIVE dimensions would lead to even richer experiences? Isn’t it possible that our appreciation of physical space has a threshold at which it becomes useful and interesting, and simply increasing the amount of dimensions that we perceive (or, more accurately, attempt to intuit) leads to rapidly diminishing returns?
I’m sure understanding five dimensions would lead to even richer experiences, because it’s a far richer space than four dimensions (let alone a mere three). But I strongly suspect that an intuitive navigation of N+1 dimensions requires first mastering N dimensions and it’s not even clear yet how well people can learn to intuitively navigate a four dimensional space.