## Interview for the Creators Project

Did an interview for the Creators Project. I think it came out pretty well!

When did you first think of the idea for a 4D video game?

I had the idea for a hyper-dimensional game in college, maybe around 2005? When you program a 3D game, every object’s position is represented using three numbers (usually called x, y and z), but that concept easily generalizes. Why not four numbers or more? At the time, a big tech company’s programming interview question involved computing whether two 2D rectangles overlap. It turns out the code for this generalizes extremely easily to the 3D case of cubes and to any number of dimensions: you just have to change a single number, the dimension of the space. So the idea came from this as a joke almost, like “I could answer your programming question for any number of dimensions.” But it made me start to wonder, what would it an actual n-dimensional game be like?

The idea stayed in the back of my mind until around 2008, when I decided I wanted to make a game that would satisfy both my love of game design and tech, in particular computer graphics. I made a list of my most experimental game ideas, and a 4D game came at the top of the list, so I started to build some prototypes. The first few prototypes were not very good however, and I later realized the main reason was that even though the game was taking place in a 4D world it was not clear to me what the consequences of being able to move in 4D were. What could you do that you couldn’t do in 3D? [...]

Tell me about the programming tech behind the puzzles.

The game runs on its own custom 4D engine that I developed from scratch. Every position in the game is *actually* represented with four numbers. There are no tricks or hacks. We are building what a 4D world would be like, in many ways. This creates a space were puzzles happen naturally: they are just simple consequences of 4D space. More traditional puzzle games very carefully set up situations, and the behavior is limited to what the designer has intended (for example you need to input the right code to open the door, and the code is written down somewhere hidden). Because what we are building is so general, I might not know all the solutions to a particular puzzle… or I might discover a lot of puzzles by just setting up random situations and playing and seeing what happens. If something surprising and interesting happens, I will make it into its own puzzle.

## PAX East 2014 Report

PAX East went very well. We had four stations, and they were all filled for the whole duration of the show. I wish we could have had more for the people who waited in line; maybe next time we will get a larger booth. We also had the trailer looping on a large TV, and an explanation of "how to walk through walls using the fourth dimension" running underneath, on a smaller monitor (it will be the next trailer).

I noticed I don't learn much from playtesting the beginning of the game anymore. It is solid and people just get it eventually. I guess that means all there is left to do is finish the game!

I do still learn a lot from explaining the game to people. Every time I do it the explanation gets more concise, and different people need different explanations. This becomes useful later on when writing for the website, or to explain the game to press. But really sometimes I feel other people are better at explaining the game than I am, as I'm too close to it now. Thanks to Christopher Hart & Colin Hart for helping out at the booth!

## What is that shape at the end of the trailer?

The shape at the end of the trailer is called a 120-cell (or Polydodecahedron, or Hecatonicosachoron, which sounds cooler, but a bit too hard to pronounce). It is actually modified a bit, but first let me explain some basics.

You see, a 3D object has a 2D surface, whereas a 4D object has a 3D surface (an nD object has an (n-1)D surface). So while a dodecahedron has 12 faces which are pentagons, a 120-cell has 120 "faces" which are dodecahedra (called cells, since they are 3D).

The 120-cell is a Convex Regular Polychoron, the 4D analogs of the 3D Platonic Solids (Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron). All the faces of a 3D platonic solid are the same 2D regular polygon, while all the cells of a "4D platonic solid" are the same 3D platonic solid! It's basically building shapes out of the the most symmetrical elements each time.

Interestingly, there are infinitely many regular 2D polygons (just divide the circle equally into n sides: triangle, square, pentagon, etc...), 5 regular 3D convex polyhedra, 6 regular 4D convex polychora, but in 5D or more there are only 3 types! It appears that building shapes this way gets more and more complex until it is no longer possible, save for a few very generalizable cases (the hypercube, for example).

But what you see in the game is not quite a 120-cell, it is actually a 120-cell with a hole inside each cell. Vi Hart [Youtube Channel] came up with the idea to do this, inspired by drawings by Leonardo Da-Vinci.

In the drawings, a hole has been cut inside each 2D face, or rather only the edges are visible. In the game a hole has been cut inside each 3D cell (each cell is hollow), or rather only the faces are visible.

The way this is implemented in the game engine is using our 4D Mesh Structure (a 3D mesh is made out of triangles, a 4D mesh is made out of tetrahedra).

What you see is a 3D slice of a 4D object. While the 4D object is static, the 3D object you see transforms as the slice changes, similar to what you see in a moving slice produced by an MRI machine, but in one higher dimension (The image on the right is an MRI slicing though a banana flower).

The reason the number of faces changes is that depending on which slice you take, you might go though a different number of cells (each cell you slice will produce a face). If you slice the 4D object near its tip, you will get a small 3D object. If you slice the 4D object near the center, you will get a larger object. This is similar to slicing a 3D sphere with a 2D plane. Use the following sliders to slice through a dodecahedron, and its "Davinci'd" version. (Note that in the game we are rotating the 3D slice whereas here I am letting you move a 2D slice up and down, but the morphing effect is the same).

## Miegakure playable at PAX East

Miegakure will be playable at PAX East as part of the Indie Megabooth!

## Hands On: Miegakure

Miegakure is a 4-dimensional puzzle game. What this means is that I am going to struggle to convey exactly what playing it entails. That’s not to say that the game’s designer, Marc Ten Bosch, has made something alienating or overly intellectual. It’s a warm, funny, deeply intelligent game, which I was pleased to have the opportunity play on the periphery of this year’s GDC.

Jim Rossignol (Rock Paper Shotgun)

Here is a Hands On of Miegakure by Jim Rossignol (from Rock Paper Shotgun)

## Screenshot: The Old Windmill

Stumbled upon an old windmill standing by the edge of the lake. Its various gears rustle and screak as the breeze keeps it dutifully busy.

## Screenshot: A strange stone. (work in progress)

A strange stone lies between the hills of the meadow. Who could have carved it? And what is its true shape?

## The Moon

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.

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## Unified Rules and Intrinsic Secrets

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.

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