 One of the first sequences of puzzles you encounter in the Witness, gets you to understand the principle of segregation. You solve a sequence of increasingly complex puzzles, all of which teach you to separate black and white tiles. You add this knowledge to your conceptual lexicon, and proceed to another area, one which has puzzles that revolve around symmetry, having to trace and navigate two lines simultaneously. A third area in the desert adds another rule, the idea of reflection, as you try to observe panels at the right angle, so that the sun reveals its solution. These puzzles all exhibit the conventions of so-called good puzzle design. There is a core mechanic, implicit learning, a steady escalation of complexity, and even reprisals that are subverted. For example, this area's mechanic asks you to map a panel to a tree outside of it, with the apple designating the solution. You travel through a sequence of these, each with a twist, until you reach the final tree, and there is no apple at all. It's a subversion, but the solution requires we break the assumption we have held thus far. A broken branch reveals its location, and the reward? More puzzles. The brilliance of Jonathan Blow's design, though, is that he takes this conceptual language and maps it onto a theme. What do segregation, symmetry, and reflection say about us? A hidden audiologue for segregation reveals it represents the divide between the subjective and objective ways of acquiring truth. Beauty is tied to a Nicholas de Cousa quote, where he talks about the parody between the heavens and the earth, and the temple of reflections has a glyph that shows a ritualistic process by which the adherents mediated between their realm and the gods. All these puzzles are tied to an overarching theme of the game, that being the pursuit of truth and beauty, and the divide between the subjective and the objective. We now know of secret glyphs that reveal videos by scientists and artists, all of whom speak to different ways to acquire truth, none of which are universally true. This is doubly fascinating, because Blow's design philosophy for puzzles is exploratory in nature. It is itself a process of finding the truth. The themes of the game reflect the very process by which it was made, which in turn exemplified the search for truth at the heart of puzzles. As should be clear through the rhetorics of the witness, there is no one process to acquire truth, and similarly, there is no one type or way to make a puzzle. They can be strictly mechanical puzzles with no reference to theme, or can be conjured for a specific purpose. They can have one solution, or like in the games of Zachtronics, be systems that have multiple solutions to them, engendering creativity. We can also make puzzles that are meant to be immersive and embedded. Also, we can have dynamic and non-authored puzzles, whether it be the emergent possibility space created by the random blocks of Tetris, or the abstract decision tree we navigate as we are engrossed in a game of chess, turning the mind of another into a puzzle of its own. This hasn't stopped people from trying to formalize what puzzles are. In her GDC top, Solving Puzzle Design, Jolie Menzel borrows Jesse Shell's definition of a puzzle and asserts that a puzzle is a game with a dominant solution that takes us through an emotional journey from uncertainty to competence. Designers like Chris Crawford emphasize how puzzles are static, unchanging, and have no opponents, whereas a game is dynamic and shifts according to user interactivity. Like any good Wittgensteinian critic, though, attempts like these to formalize may be useful, but they always end up being reductive, excluding things we would otherwise call puzzles. Also, attempts by game designers to formalize what puzzles are neglects how puzzles far predate video games, computers are just the latest interface that has hosted them. To understand what a puzzle can be, we need to understand why it is we solve them to begin with. In his book, The Puzzle Instinct, Marcel de Nacey surveys the history of puzzles in our species and how they have expressed themselves. For one, puzzles have been used as ciphers to mediate understanding between the heavens and the earth, whether it be through Runes divination or the Ai Qing. Puzzles have also inspired mathematicians to conjure new theories, and thinkers like Euler have conceptualized puzzles to solve mathematical conundrums, like the Konigsberg bridge problem. Also, mathematical treatises and books have all been framed as puzzles, turning a science into an art, aestheticizing a mode of inquiry. Speaking of which, puzzles have also inspired literary works like Lewis Carroll's Alice in Wonderland, creating a fiction out of a puzzle's many paradoxes. And puzzles have also become a part of our daily rituals, whether it be through crosswords, sudoku, or detective fiction. Puzzles have been used for religious, artistic, and scientific purposes, all modes of inquiry into the question of what it means to be human. So puzzles reveal the truth, but they can also reveal the absurdity of such a claim. Riddles show us how limited our languages and visual illusions reveal the fallibility of our senses. The famous Liar's Paradox, this sentence is a lie, is an unresolvable paradox that speaks to mathematical concepts like Girdle's incompleteness theorem. Puzzles help us seek the truth, but also destabilize our apprehension off it. They are intrinsically paradoxical. Denesi provides a fascinating survey, but also suggests that puzzles have the value of being paradoxical, elegant, non-obvious, and meaningful. They facilitate divergent thinking, a flash of insight that elevates us to a new realm of understanding. But in doing so, they reveal new aesthetic properties of our thoughts. For example, this puzzle, called the 9.4 puzzle, requires you draw four straight lines through all dots without leaving the paper. You start by trying out all permutations, but you suddenly have a flash of insight and realize you need to break free of the implied box to solve the puzzle. This puzzle has a meaning. The meaning is, thinking outside the box. It's a puzzle about what a puzzle is. Puzzles are, in some sense, a flash of insight facilitated by thinking outside the box. At a talk entitled Impuzzlement, delivered by Jonathan Blow, Mark Ten Bosch, and Drogen, the three discuss what they think the values of a puzzle ought to be. Blow starts by asserting that he thinks that there is no distinction between the mechanics of a game and its dynamics and aesthetics. The meaning is intrinsic. In the fourth world of Braid, the mechanic is that your physical movement through space is tied to time. This is explored in fascinating ways. One puzzle requiring you to jump on an enemy that is moving backwards through time. However, Blow ties this to the level's theme in characteristic fashion. The level is called time and place. It tells the story of how a physical space is tied to a temporal memory. The theme is about how space and time are interconnected, just like the mechanic. In World 3, certain objects are immune to rewind, and so Blow explores the idea of how certain memories can never be forgotten. Next, Drogen talks about the importance of non-verbal communication, something quite evident in his game Starseed Pilgrim, a puzzler where you have to figure out all the rules for yourself. This is a heuristic that is pervasive in puzzle design. For example, the game Steven's Sausage Roll is a grid-based Sokoban puzzle game where you have to cook both sides of his sausage on designated grills to complete levels. The game teaches you the mechanics by constraining the possibility space. Later in the game, when you have to learn how to skewer a sausage, the game does this implicitly. It constrains the possibility space so that you have to push against a tree, showing you how to skewer using a solid background object. It then guides you through a linear path with one exit, showing you how to detach from it as well. The rest of the level uses two other devices, playgrounds and skill tests, to get you to demonstrate your skills using play. One of the most famous moments in the puzzle game portal illustrates this well. Level 10 requires you to use a portal on a lower level to propel yourself across a gap. To get the players to this insight, though, the designers had to constrain the possibility space. The idea was embedded in the player's head, and the designers had to map what skills the player had at different points. This requires the use of what some designers call a puzzle dependency chart, a way to explicitly map what a player needs to know to solve a puzzle. Mark Tenbush spoke next, and he is creating a puzzle game called Megakure that explores the question, what if there are four spatial dimensions? This is his contribution about the value of puzzles. Ask hypotheticals and explore the implications through design. Most puzzle games start with a what if. The braid is, what if I could manipulate time? Fez is, what if I was a 2D being in a 3D universe and could shift between planes? In fact, each of these games was inspired by a book, braided by Einstein's dreams and Fez by the story Flatline, showing how speculative fiction and science are important parts of generating ideas. Even artists can inspire puzzle ideas in conceptual language, much like how the bizarre spatial geometry of MC Escher's work has inspired games like Echochrome, Monument Valley, and the upcoming game Manifold Garden, all of which play with our spatial reasoning skills in different ways. In any case, what's fascinating here is that each of these speakers makes games in alignment with their purported values for what a puzzle should be, whether it be thematic, nonverbal or speculative, although they do all agree with each other as well. In another talk that just blow and Tenbush gave, called Truth in Puzzle Design, they set out a list of values in puzzle design. Richness, completeness, surprise, lightest contrivance, boundaries, compatibility, orthogonality, generosity, and emergence amongst them, suggesting puzzles are oriented towards a higher calling, truth. They think puzzles are consistent systems, like mathematical constructs, that map onto hypotheticals in any number of universes. The trick is to explore all the implications of a system, like a mathematical superstructure. One example they give on how to explore this is a puzzle in Portal 2, where you have to realize that if you collapse the light bridge you are on onto a lower plane by using a portal, you can drop safely and traverse the space. They also emphasize simplifying the space enough so that emergence can arise. Blow did this with the witness, when he cut out lines that weren't straight, it actually enhanced the possibility space. Again, both think we are discovering things the universe has already conjured, listening to the emergent patterns of puzzles as they reveal themselves. Puzzles are abound in the design of puzzles, which generates lists for what constitutes good and bad puzzle design. Blow says puzzles don't necessarily have to be hard, good, or fun, so long as they are interesting. He also stresses the importance of exploratory design, and not assuming the solution before you craft a puzzle. Some argue puzzles should be a linear progression, allowing the deliberate management of a player's experience, whereas others suggest nonlinear design enables player agency. Jolie Menzel says puzzles need to be rational, show the goal, and have clear information and feedback. She also gives tips on how to modulate difficulty in puzzles, by altering things like the steps it takes to solve. Another recent dichotomy in the value of puzzles is the dichotomy between puzzles and problems, whether puzzles should have one solution or multiple. In Bob Bates' book on game design, he argues that having multiple solutions to a puzzle cheapens it, is very hard to design for, and undermines the meaning you can communicate. It stands to reason that you can't control how a player experiences a game if they can conjure their own solution. However, if the games made by Zaktronics, Infinifactory, and SpaceSchem amongst them are anything to go by, multiple solution problems are in fact becoming more popular. They allow for more creative freedom, and are also more replayable. When asked how to create puzzles with multiple solutions, Zakt states that you do so naturally by creating a system. This is perhaps why his puzzles are abstract simplifications of real-world problems, whether engineering or programming, which allows him to naturally encode multiple solutions. Other studios, like the team who made Zelda Breath of the Wild, deliberately generate puzzles and scenarios that have multiple solutions to them to ensure that there is a creative possibility space. They also made sure to connect everything in the world, something Zaktronics games also employ. In any case, to ZAK, this type of design is more natural and comes easier. However, it is also true that the experience for multiple solution problems does vary. The takeaway again, though, is much like puzzles themselves. There is no one way to design them, which requires we be flexible whenever we assert an intrinsic set of values for the creation of puzzles. Aside from his skepticism about problems, Bob Bates' work on puzzle design is an absolutely essential read. He created a taxonomy of all types of puzzles he could find, including divergent puzzles, building puzzles, information puzzles, codes, but also logical forms. He then gives a list of bad practices that might seem obvious, but are often ignored. Don't create binary yes-no puzzles. Don't create hunt-the-pixel puzzles. Don't presume information outside the game when solving them. And don't create a massive logical or spatial incoherence between puzzles, something old adventure games did to needless effect. Another interesting point he makes is that functionally, all puzzles are fundamentally alignment problems, an order of operations problem, in either space or time. Tetris is an alignment puzzle in space, you have to clear entire lines, whereas a game like the Talus Principle requires you to do a sequence of actions in a specific order. In terms of positive values for puzzles, he states we should have a clear goal. The puzzle should be about how to do something, not what to do. And they should also be fair, embedded in the environment and thematic, overlapping with the insights of other designers. Again I stress though, heuristics for good puzzle design are just that, guidelines that aren't necessarily what is true or false, right or wrong. Those suggest you should never work backwards when designing a puzzle, but that is exactly what RV Takari did when he created his game Bubba Is You. Bubba Is You takes the idea of subverting rules to a deeper level. In the game, you can change the rules of the playspace by manipulating blocks that encode simple logic. For example, one level has what seems like an impassable lava stream, so instead of trying to cross it, you can shift a block to change the properties of the lava to make it pushable. Another level requires you to change a rule that is out of reach, so you use a sequence of rocks to dislodge the existing rule, allowing you to progress. The layers of depth the designer pushes the idea to are astonishing, creating a cascading array of rules you have to manage to solve puzzles. The idea of examining this idea in an exploratory way may seem daunting, but that is exactly what the designer initially did. He tried simple combinations of rules and conjured up fascinating sequences, however, he then reverse engineered levels to fit these novel phenomena, leveraging forward thinking but also backwards-oriented design. The possibility space here was perhaps too dense to just keep accumulating procedures, so going against Blo's philosophy and working backwards from a solution is what worked here instead. The game gets ridiculously complex by the end. It has meta levels that are built by using blocks called level, which allows you to change the properties of the level itself at the menu screen. You can even win the menu screen by creating a Bubba and a flag. The puzzles now become about managing rules at multiple resolutions, as you coordinate a hierarchy of rules in embedded worlds. In contrast to his previous subversion of Blo's philosophy, this aligns with the value of exploring the richest possibility space, of taking an idea and expanding it as far as you can take it. This always requires periodic conceptual leaps to sustain though. Braid starts with rewinding time, but then objects immune to time are introduced, a mechanic where space is time, and then the ability to create doppelgangers is presented, all of which are there to escalate the conceptual space. Steven's Sausage Roll starts with simple grid-based movement, but then you can attach to objects or release your skewer. English Country Tune also starts as a Sokoban style puzzle game, but then eventually requires you to use an editor to build the puzzle levels that will eventually allow you to solve them, turning you from puzzle solver to puzzle creator. The witness may start on panels, but you then realize there are puzzles that refer to and incorporate the outside world, and then puzzles that break free of the constraints of the panels themselves. In his GDC talk, Hearts and Minds, Frank Lance argues that games make thought visible to itself. They are an art form that reveal the inner workings of our mind. As designers, we have to think about thinking, not just ours, but those of our players. A puzzle, in some sense, is an even purer form of this, one that strips away any extraneous details and is fixated solely on walking us towards enlightenment. In some sense, puzzles are the art of thought itself, thought instrumentalized towards insight. Like we examined earlier, puzzles contain their own contradictions, they are as much an exploration of truth as they are a deconstruction of it. This is why many puzzle games seem to build into their narratives a subversive rhetoric. Famously, Portal is a game that seems benign on the surface, you are participating in a series of tests, an art to be rewarded with cake at Obstacle's end. Of course, as GLaDOS's steady deterioration makes quite apparent, not everything is as it seems. You have to break free of the linear path presented to you, and emancipate yourself from her tyrannical control, and perhaps the designers as well. GLaDOS is as accurate a portrayal of a designer in the fiction of a game as there might ever be, she is editing our experiences as a designer does. Portal appreciates its own puzzleness and builds a fiction around it. GLaDOS communicate their own meanings, it's up to us to appreciate this and reflect it in the game's fiction. Presented with a conundrum, humans seem incapable of placating their curiosity, and we see this in the communities that build around games. The Dark Souls lore community are obsessed with the game's world, and stop at nothing to piece together every little detail they can scrounge. This is a community-wide effort to uncover some truth, but it is ultimately a truth conjured by other humans. What's fascinating with games is that we can meet the gods of these new universes, and can be somewhat assured that there must be some purpose. In the game Fez, there was a practically unsolvable puzzle called the Black Monolith that had a community of puzzle solvers obsess over it. Some believe the solution was somehow related to a strange poem about the creation of the universe, which could be deciphered through some careful translations of a mysterious tome found elsewhere. Some thought it might have to do with a clue elsewhere in the game they might have missed. I'll spare you the details, but what ended up happening is the community brute-forced the solution. However, they ended up with a solution to a question they did not know. The meaning of a puzzle is not in the solution. It seems to be in how we go about solving the question that is posed to us. Puzzles emerged at roughly the same time mysticism emerged, but they were also fueled by revolutions in scientific and mathematical thought. In some sense, puzzles are a reification of our thoughts. They are an aesthetic manifestation of something that would otherwise remain intangible. Jonathan Blow might have caught wind of this when he designed the witness. You solve puzzles throughout the island, moving up a chain of abstraction that sees you assemble a language of terrifying complexity. You activate beams after solving sequences of them, all of which point to a destination, the top of a mountain. Enlightenment beckons, you think to yourself. These puzzles are guiding me towards my own apotheosis. The mountain and its mysteries lead you to a cage, a cage which seems positively divine, except it takes you right back to where you started. The puzzles were a false prophet, they led you astray. There was no truth to be found, only a reminder of the fallibility of obsessing over puzzles themselves. However, what if the truth you were seeking was right in front of you all along? The witness strives for conciliance. It wants to bridge the divide between the arts and the sciences, between the rational and the emotional, the materialistic and the ascetic. Fortunately, this seems to be what puzzles are inherently about, the very search for truth. The thesis of Dinesi's book is that puzzles cannot be subject to any singular definition, they resist being solved by their very nature. They are autological, the word puzzle describes itself. The real world has calculus to peer into its mysteries, and the digital world has programming to make manifest our will. But puzzles are the domain of human thought itself. They reveal the mysteries that lie within, but also out there in the universe. This is a paradox, but paradoxes, like puzzles themselves, reveal the limits of human reason. T.S. Eliot said that true knowledge starts with comprehending the forces that make us us, about understanding ourselves. A puzzle is a looking glass through which to view ourselves, and what we see is an instinct to solve the very thing through which it is seen.