mtbdesignworks

A friend of mine recently sent me this quote from J.C.R. Licklider (an important figure in computer science) from around 1969, talking about one of the first display of 3D on a screen:

Sutherland’s demonstration […], is a step that takes us into a new world. It does so […] because the laws of this new world are the laws the modeler programs into it. The effects that can be created are thus constrained by limitations of the programmer’s imagination rather than by the way things actually are on this mainly Euclidian-Newtonian earth.

The laws of the model’s nature have to be logically and mathematically consistent with one another, but not with physics.

I like how clear it was to him even at the time. I especially like the following, because it is something I realized myself:

It will be intellectually at least as exciting to perceive and explore a synthetic 4-D world as to perceive and explore a merely actual, merely 3-D moon.

The concept of space is so fundamental to us. We built the concept of a dimension in order to explain the physical world, but the concept is strangely naturally not bound by it, in the sense that dimensions are not simply limited to 3. Width, depth, height; just add one more number! Even more surprisingly, we can take everything we know about our 3D world and extend it to 4D. This new world has something deeply interesting about it. It is very similar to ours in many ways, but all its differences stem from changing one single number in the mathematical representation we have of physical space itself.

So in a sense we can think about logically and mathematically consistent worlds as the new frontier for human exploration, which we have discovered a new way to extend. It’s fun to think of games and interactive simulations as sort of spaceships that allow people to explore a different part of our universe.

When I started working on Miegakure I only had vague ideas of how it would play or even look like on screen! I just set up the rules, and followed where they lead me…

More next time.

I am fascinated by the parallel between the player’s experience and the scientific process. By playing with a system we get a feel for the rules that govern it. We build up this data on what is possible in this system, and our brains look for patterns in that data to summarize it. By throwing balls, dropping apples, and looking at the moon for a while, humankind was able to formulate the theory of gravity. Formulating a mathematical theory is just another step in a process of finding patterns.

In the above except from the No Ordinary Genius documentary Richard Feynman talks about how research in physics is similar to watching some gods play a chess game without knowing the rules and only being able to see parts of the board. You may learn from careful observation about how the bishop doesn’t change color, or how it may only move along a diagonal. Or you may witness castling and you didn’t expect it.

In old games a lot of gameplay elements where left to be discovered by playing, and not explained verbally using tutorial text. And nowadays there is a resurgence of games that do this, the most extreme example that comes to mind being Starseed Pilgrim which gives almost no hints about many of its mechanics.

Feynman talks about how sometimes in physics there are these unifications and the theories become simpler. They can seem more complicated (possibly because they explain more) but they are actually simpler. Then he says that it doesn’t happen in Chess and that the rules seem to get more complicated. I think this is not true for all rules.

If you only ever saw a queen moving diagonally and suddenly it moved a square horizontally to the left, and maybe later on you saw it moving three squares horizontally to the right, you may think that queens move diagonally, except horizontally three square to the right, and one square to the left, but over time you might realize that they can move any number of squares horizontally and everything becomes simpler again.

However, I assume Feynman is referring to rules like castling or promotion of a pawn to a queen that feel like rules added on top of the previous rules, and can never be unified. Aesthetically these types of rules often feel less beautiful to me. I consider a game that can be “unified” a sign of a beautiful game. It is beautiful from a pure game-design aesthetic sense but in addition the moments when the brain connects these distinct elements into a single whole are magical.

Miegakure brings these concepts from science and games together very tightly because it is as much a game as it is a realization of a mathematical concept. Miegakure is built such that it is simple at first but if you look deeper you can build a better model of what is happening. For example you can play almost the entire game just using the large cubes (actually Tesseracts), but you may gradually learn that your position within each cube does matter. And so your model might expand from thinking you see these thick slices of objects, to knowing you see along an infinitely thin slice and that suddenly explains why things change based on your position (etc…) and your model becomes simpler again.

And there is a beautiful example involving certain blocks being longer along the fourth dimension but because of spoilers I can’t really talk about it in details. But basically, players can build a working ruleset of what is happening, and that allows them to solve puzzles, but that ruleset is very simple. Even people that understand the math well seem to sometimes still use the approximate ruleset because it works so well. I know I do. I love the idea that you could explain the simple rules to someone and they would be able to play, or you could make a game that would be just about these rules, but they are in fact part of a larger, more mysterious whole.

I am reminded of the gameplay layering that happens in good Zelda games: a crack on the wall might not mean much to the player at first, but once the bombs are acquired the whole game world is seen from a new light. In Miegakure the secrets are more intrinsic, and when someone comes to truly understand the unifying rule it is a beautiful thing to see.

People often ask me: will this game make me understand the fourth dimension?

The thing about this question is that there are multiple ways of understanding something, so we have to define which way we mean.

I think about Miegakure as a toy ball. I mean that in the sense that by playing with a toy ball as a kid you intuitively learn about how gravity works. You can adjust the throwing angle and force and see the different paths the ball takes. You learn about parabolas without even knowing the word for them.

This is very different from knowing the second-order differential equations of motion under the force of gravity. Clearly you don’t need to understand them to know how to throw a ball.

In the same way, Miegakure doesn’t explain anything explicitly about the fourth dimension, it just lets you be inside of a 4D world. If someone wants to learn the mathematical theory, however, it can be built upon stronger instincts.

I have watched tons of people play Miegakure and I see people fall along a spectrum between two types: intuitive and reasoned.

The intuitive types try something, fail and try something different. They often don’t understand how they are able to solve the puzzles or know exactly what they are doing and why. But they gradually build an intuition for the patterns they encounter.

The reasoned types, on the other hand, when put in situation they do not understand, stop and think: what is this system I am interacting with? They formulate theories and test them. They move a little bit, think, press a button and examine the results. Some people go back to previously solved levels in order to test theories. They quickly build a model of how the rules of the game work and it is this model that allows them to solve puzzle effectively.

This is not to say that any type is better. I have seen very smart people in both categories. I have seen someone play for 4 hours, beat almost the whole game, all on intuition. At the end I asked: so can you explain to me what happens when you press the “rotate” button? Their first answer was no, but as they started thinking about it they had an epiphany: oh! I see this is how it works!

I can tell a lot about the way someone thinks from the way they play Miegakure. I am reminded of David Sirlin’s great GDC 2012 microtalk [Blog Post] [GDC vault link]. It is about the difference between conscious thought and unconscious thought, and contains this quote from Capcom’s Seth Killian :

I can learn more about someone by watching them play 10 seconds of Street Fighter than 10 hours of an RPG