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Miguel (working on TENNISmind...)
(from Valencia, Spain)
My latest game: Big*Bang, a simple abstract about the first minutes of the Universe
My best-rated game: Tetrarchia, about the tetrarchy that saved Rome
Physics Laws as Game Rules
When I design games, I am always driven by a theme. In fact, when anything catches my interest (book, movie, visit, discussion...), I find myself thinking about what game could be created out of it! Of course, most of the time the idea doesn't go very far, but there are exceptions. My first two games, BASKETmind and Tetrarchia, came out of my two main hobbies, sports and history — and I have science as a third "hobby" (as I'm a nuclear physicist), so...
I have written a recent article for the Game & Puzzle Design journal with the title "Physics Laws as Game Rules" (PDF sample), and this diary will be some kind of summary. As a gamer/designer and physicist, I have always wondered about an apparent contradiction. On one hand, physicists look for simple patterns within complex environments, trying to derive from them laws that are few and simple. On the other hand, game designers try to abstract the events they want to recreate into few and simple rules. Logically, one should expect a lot of board games about physics since the abstraction work has already been done by nature in the form of laws that could be taken almost directly as rules for board games.
So why are (good) board games about physics so rare? How should one proceed in order to make a game from physics laws? Big*Bang was born from my attempt to answer these questions. And if you want to understand the title of this diary, you'll have to keep reading!
Simple Laws But Complex World
The laws that govern a given interaction between two bodies may be simple, but when several kinds of interaction combine, or more than two bodies fall within the interaction range, the interplay between these simple individual "recipes" becomes wonderfully complex.
Take Newton's law of gravitation, for example. A body of mass M attracts other bodies at a distance d inducing an acceleration proportional to M/d^2. This is very simple. Double the mass, double the acceleration; double the distance, quarter the acceleration. However, add other massive bodies, let them all move, and soon things become convoluted. Of course, since the forces are simple and have analytical form, even the most complex trajectories can be calculated using a computer, and thus be implemented in video games — but board games cannot benefit from this assistance.
A good example of a game that tried to use this simple law is Triplanetary. However, even by making it simpler (ignoring the mass dependence and discretizing the distance dependence to either 1 or "infinity"), tracking the movement of the spaceship units required the fiddly use of markers on a laminated map (left):
Even the most simple laws lead to a complex ensemble full of details, and the simulation of all those details should be left to video games. When dealing with those simple laws, board games must make an additional abstraction effort. The challenge for the designer is first pointing out the most characteristic law, then finding a rule that at the same time is simple and intuitive and that lets players feel as if the game pieces actually obey that law. Two good examples are Gauss (center) or Momentum (right). Even if they use plastic pieces and one simple rule, in Gauss players evoke their memories of science classroom with red and blue metal magnets clashing together and spreading away, and in Momentum they feel like they're manipulating a multiple Newton's cradle.
In the end, designing a game (that is fun to play) from a physics law — that translates into a simple rule and leads to gameplay evoking the physics — seems possible!
Gaming the Big Bang
I was looking for a physics case that was fascinating and simple...then I thought about the formation of our universe. No doubt there are simpler cases! However, if one makes the abstraction effort I mentioned above, it can be easily described in broad outline. The main stages of the process are sketched below (from 1 to 6). At some point, a huge explosion we have named "Big Bang" liberated all the energy in our universe, which from then on expanded and saw its temperature decrease to the present 3 K (-270ºC).
The energy from this explosion materialized into equal amounts of matter and antimatter, which then annihilated each other into energy again, following a deadly cycle which could be broken only by a tiny excess of matter. The origin of this slight excess, which is responsible for the matter that we see today and of which we are made, is not fully understood yet. After the first second, the surviving matter had taken the form of protons and neutrons (stage 1). Those two particles began to combine and in the very first minutes formed the lightest nuclei*, mostly Hydrogen and Helium (stage 2), but could go no further.
* An atom's nucleus is formed by a combination of protons (charge +1) and neutrons (charge 0), each element having a characteristic number of protons. The atom consists of its nucleus surrounded by a cloud of electrons (charge -1). The number of electrons in the cloud equals the number of protons in the nucleus, so that the atom is neutral.
The universe underwent a long and quiet period until electrons were slow enough for them to be captured by those light nuclei, forming the first atoms (stage 3). Then gravity took the lead, and the neutral atoms began to condense into clouds, which further condensed into stars (stage 4). Inside stars, Hydrogen fused again into Helium, and thanks to the strong gravitational fields three Helium nuclei could fuse into Carbon, going beyond the limit reached at the end of stage 2. From Carbon, fusion kept going until the formation of Iron, which can no longer sustain fusion reactions, then stars collapsed under their own gravity and exploded (stage 5).
The extreme violence of these explosions, known as "supernovae", created the environment needed to build up heavier nuclei on top of Iron and up to Uranium, then dispersed them into space. And then back to stage 4: Atoms condensed into clouds and new stars, but now those clouds contained most of the elements, and around these second generation stars there could be rocky planets on which life could develop (stage 6).
This complex process, spanning 14 billion years, can nevertheless be sketched in the six main stages above. What kind of game can be designed out of this? The space and time scales are too vast, the stages too diverse, the interactions governing them too different. I chose to focus on parts of the overall process. Until stage 4, there were only a few well-identified pieces, but a goal for the players had to be found.
A Race to Carbon?
Carbon has a relatively light nucleus, with six protons and six neutrons in its most abundant form, Carbon-12 (C12). If I wanted to design a game about the formation of Carbon, then protons and neutrons should be the natural game pieces. Those pieces appeared at stage 1, formed Hydrogen and Helium at stage 2, then waited until stage 4 to continue forming heavier systems. We can better understand why with the diagram on the right, in which we see all the nuclei that exist up to Carbon-12.
For each combination, the number of protons (red, top line) gives the element name (from 1 to 6: Hydrogen, Helium, Lithium, Beryllium, Boron and Carbon), and the number of neutrons (blue, bottom line) defines its mass number (protons plus neutrons). For example, Lithium-8 has three protons and five neutrons.
Only some combinations are allowed, and just a few are stable (white cells). The rest are unstable because the equilibrium of "pieces" is too unbalanced, and after a given time they will undergo radioactive decay in search of balance by transforming a proton into a neutron (pink cells on the upper left) or a neutron into a proton (cyan cells on the lower right)*. The color shades correspond to the varying decay times — the darker they are, the shorter they are, with times ranging from millions of years to tenths of a second.
* This relatively simple type of decay, in which a neutron becomes a proton or vice-versa, is known as "beta decay". There are other types of radioactive decay (alpha, gamma, fission...), but they are not relevant for the case considered here.
At the end of stage 2, free neutrons had disappeared and most of the pieces were in the form of the most stable H1 and He4. The reason why the process stalled is displayed by the forbidden symbols in the diagram: none of their binary combinations (He2, Li5, Be8) are allowed. Due to this quirk of physics, Hydrogen and Helium had to wait a billion years until gravity could play a significant role inside stars, enabling the ignition of more complex reactions and, in particular, the one that fuses three He4 directly into one C12.
For the game, I could then use red and blue pieces on a hexagonal grid, and let the players fuse them into stacks following the patterns above. These were some potential game issues:
• Several combinations are unstable, so in addition to the fuse action there should be a decay action in which a proton/neutron in the pink/cyan stacks was replaced by a neutron/proton. It could be a random mechanism (as the real decay) using dice, or a voluntary choice of the players.
• Players should use the diagram above as an aid in their race to Carbon. They could fuse stacks to increase their size, then choose to follow the stable (white) diagonal or either of the two colored regions, then return to the diagonal via decays.
• Players would not be "red" and "blue"; they would need (and share) all the pieces.
• The quirk of physics leading to the triple fusion of He4 into C12 should be a key ingredient. Players could fuse two stacks along empty straight lines, or three adjacent stacks, and of course the result should be a valid known nucleus.
The components and mechanisms seemed clear, the aim of the players not so much. If the winner was the first player forming Carbon-12 and both players shared the same pieces, then the game could stall with players not wanting to do the next-to-last move. No player would want to fuse two He4 nuclei, enabling the opponent to add the third one.
I could instead award points for the formation of each element as an incentive for both players to contribute to the race, but this would require a detailed balance analysis to determine the optimal number of points per element, or I could make the game a cooperative one in which the players solve a puzzle and try to maximize the formation of Carbon stacks...
In any event, the diagram above was too convoluted to make an effective player aid. Even nuclear physicists would need to constantly refer back to the aid to check what can or cannot be done, and I was looking for a game, not homework! Further, the unstable combinations have decay times ranging from tenths of a second to millions of years (Be10), so I should establish a hierarchy. Moreover, from a practical point of view, moving stacks of up to twelve pieces and replacing pieces inside them would be cumbersome.
Even if the initial idea was good, the game boundaries clear, and the number of pieces small, this "Race to Carbon" was far from the simplicity and elegance of Gauss or Momentum. If I wanted to design the Big Bang for effect, I had to escape this frame.
A Race to Helium?
Returning to the timeline sketched above, using protons and neutrons as the game pieces was the best part of the previous idea, and the complexity of the nuclear chart up to Carbon-12 was the worst. So I kept the good idea, but limited it to stages 1 and 2 to create a race to build Helium-4, one of the most stable bricks in the universe and the precursor of Carbon.
The orange (lower left) region of the diagram above shows how simple the nuclear chart becomes; it contains only two game pieces and four composite stacks, with only one of them (H3) unstable. The player aid becomes trivial even for non-scientists: no more than two protons or neutrons per stack, and not only two of them alone. Players should fuse pieces up to He4, and the decay option would be open only for the neutron and H3, with a straightforward hierarchy (H3 decays more slowly).
This was conceptually closer to Gauss or Momentum, with stacks of at most four pieces. However, forming He4 would be relatively easy, so the aim of the game could not be being the first one to do so. Players could instead aim to make the most He4, sharing the red and blue pieces and keeping track of how many they created — but this could again lead to deadlocks as players would be disinclined to create H2 nuclei near existing ones since the opponent could fuse them into a He4 nucleus.
Player vs. Antiplayer!
I had found an appropriate framework for the game, but lacked a mechanism that generated competition and a clear aim for the players, mostly due to the fact that they shared the red and blue pieces. So what about incorporating other ingredients from the physical scenario as game pieces?
Hidden between the Big Bang and stage 1 on the timeline above, there was a huge production of matter and antimatter in almost equal quantities, followed by a huge annihilation of both into light. The matter we see around us today comes from a tiny, still mysterious excess that survived. If I started the game before stage 1, then I could incorporate such ingredients as "antipieces".
Antiparticles have the same properties as their corresponding particles but the opposite charge. For example, antielectrons are positive and antiprotons negative, but those two particles can combine to form an anti-Hydrogen atom, with properties similar to a standard Hydrogen atom, or an antineutron plus an antiproton can form an anti-Hydrogen-2 nucleus.
The diagram on the right shows the mirrored antimatter images of the nuclear chart up to Helium-4. Again, the nuclei shown in the upper right region are classified by the protons (red, top arrow) and neutrons (blue, right arrow), while their antimatter counterparts shown in the bottom left region are classified by their antiprotons (black, bottom arrow) and antineutrons (grey, left arrow).
This solved the problem of sharing the pieces as one player would use red and blue pieces, while their opponent — the "antiplayer" — would use the black and grey ones. Each player now had a clear aim: Build the most He4*, and there was no longer a need to keep track of exact particle counts throughout the game since both He4 were now different.
* Antiparticles are usually noted with a bar on top, but I use the same symbol for both here, for simplicity.
Moreover, a law of physics provided a new ingredient that lead to lots of player interaction: annihilation. The original idea was based on a "quiet" construction of nuclei, but with these new pieces, players could now not only build their own nuclei in parallel, but also annihilate the opponent's! I could even make it more interesting by forcing the players to choose between these two options, leading to an interesting dilemma similar to that found in the game TZAAR: "Shall I make myself stronger or my opponent weaker?"
A Big (*) Bang!
I had finally found a suitable frame for the game (synthesis of Helium), its pieces (protons, neutrons and their antiparticles), mechanisms of play (fusion, annihilation and decay), and some ideas for its goal (such as building the most Helium). I had also introduced player interaction through matter/antimatter annihilation. However, unlike most games that involve capture, such annihilations resulted in the removal of both players' pieces, which had a somewhat self-defeating feel to it and didn't let players strengthen their own pieces or position. But since annihilation transforms each matter/antimatter pair into light, I could instead use this mechanism as a new aim: Produce the most light.
This allowed two paths to victory: a pacifist path that involved building the most Helium, and a bellicose path that involved annihilating matter/antimatter pairs into light. If each player concentrated on one path, however, the game would not be very fun or strategic and would lead to draws. This could be addressed by introducing a scale with which to compare the relative magnitude of each victory condition, but this would complicate matters and make the game confusing for players. Instead, I chose a third condition.
There is another victory condition that was easy for players to understand and that respected the laws of physics. The formation of Helium was followed by the formation of stars, and those were powered by the fusion of Hydrogen. At the endgame, after particles had disappeared through annihilation and others had fused into stacks, the board would look like clusters of nuclei. If we identified the clusters of each player as their stars, an interesting victory condition would be to form the star with the most Hydrogen fuel. Players should therefore fuse particles into Hydrogen, then Helium, and produce light by annihilating pairs, but at the same time keep some Hydrogen "alive" in some of the clusters that appear towards the end. This made the number of victory conditions odd, so ties would be unlikely.
What about the decay of unstable combinations? With respect to the Carbon-12 game idea, I was left with only two of them: each player's neutron and H3. To add more interaction, I could let players force the decay of the opponent's unstable stacks in order to disturb their plans. Since decay here means replacing a neutron with a proton, this option would be available only when protons would start leaving the board through annihilation. Therefore, the players themselves would regulate the decay "clock" (the timing and impact of decays) depending on how much annihilation they chose, making no two games play the same.
The turn sequence would be:
1. Either fuse a pair of your stacks or annihilate a pair stack/antistack.
2. Force a decay, if possible.
As with Gauss or Momentum, the game was abstract in the sense that it focused on simple concepts that evoke laws governing real processes, so was best played on a regular grid. However, it still had a strong theme, which might be lost on players if the board was a sterile grid. I opted for an evocative background image depicting the Cosmic Microwave Background of stage 3 in the timeline above. This image has been obtained with increasing resolution by the satellites COBE (1992), WMAP (2003) and Planck (2013):
The intermediate resolution of WMAP was a good compromise (left). It represents the oldest light in our universe, with darker (slightly cooler) areas corresponding to the concentration of matter due to fluctuations that gravity amplified to form the first galaxies. For the game grid, I chose an ellipsoidal hexagonal one to match the shape of the image. (For a detailed discussion on the shape and size of the grid, see here.) This left space in the corners of the board for simple player aids and the three victory conditions (see the prototype on the right).
I chose an unusual name — Big*Bang — with an asterisk that evokes the first explosion and the subsequent annihilation, and that sets the game apart from the whole series of games using "Big Bang" in their names. The rulebooks (in English, Spanish and French) are available for download at the game page on the nestorgames website. As usual with Néstor, the production of the game has been a very smooth and constructive process! And also as usual, the result is a very compact, light and beautiful edition:
The Link with Physics Laws
I started the diary with a discussion about gaming physics in general. With all the different compromises I have met in order to keep Big*Bang interesting as a game, has the link with physics been lost?
The huge matter-antimatter clash occurred in the first fractions of a second after the Big Bang, and only later did Helium start forming, while in the game both processes occur simultaneously. Furthermore, our universe seems to consist mostly of matter only, while the game has equal amounts of matter and antimatter.
So is the game totally science fiction? Maybe not. We assume that only one of matter or antimatter could survive the initial annihilation, and since we live in a matter world, we assume that only matter did. But what if the rapid expansion that followed the Big Bang pushed antimatter-dominated regions far enough away from matter-dominated ones?
In that case, annihilation would have halted due to the physical separation of both populations, and the universe would also contain antimatter galaxies. However, since the chemistry of antimatter is identical, those galaxies would look exactly like matter ones. Our only chance to spot them would be their collision with a matter galaxy, through the gigantic annihilation flash that would follow. In fact space missions are searching for the characteristic signals of such a clash, or for antinuclei produced in "antistars", but no evidence has been found yet. Leaving this hypothetical matter-antimatter coexistence aside, what about the other physics laws?
The spirit of the primordial nucleosynthesis is captured reasonably well. The first fusion step is H2, the only stack of height 2. By forming H2, players shield against annihilation by the more abundant individual pieces while threatening the formation of the opponent's H2 nearby, and prepare the way to Helium. (On the right you can see a He4 stack surrounded by a neutron, an antiproton and two antineutrons.) Depending on the annihilation rate chosen, neutrons start disappearing sooner or later, adding angst to the race since you may end up with proton-dominated regions that, without neutrons, will be doomed fusion-wise. However, the third victory condition I introduced gives sense to these Hydrogen areas, too, since they represent the future: a first generation of stars that will generate the ingredients of life, followed by the next generations that will live long enough to witness it.
These simplifications allow only the spirit to be captured, but this was the intended goal. Some add-ons could make the physics more explicit, but once a critical balance between complexity, playability, and theme has been met, adding rules should be avoided. One can still propose variants, though, e.g., electric repulsion could be incorporated by allowing the fusion of stacks with protons only if they are adjacent, or the formation of Carbon-12 could be introduced as an automatic victory condition if a player succeeds in linking three Helium-4 stacks.
Big*Bang is by no means an exact simulation of any part of the Big Bang process. However, at the end of the game, players will have followed the key stages that shaped the first minutes of our universe, the physical laws that guided them, and — from the final board position — even imagine the next steps that followed.
This diary started with a question: Why are (good) board games about physics so rare? Closely mimicking physical laws is not enough to make a good game; this is where mere simulations differ from games. For example, even though the pieces in Triplanetary give the impression of moving as real spaceships would, the result is somewhat fiddly in its implementation. Gauss and Momentum, on the other hand, are examples in which the simulation and the game work well; these games evoke souvenirs from a science classroom when played.
The design of Big*Bang illustrates well the process that takes us from the physics to the game. The physics case was too vast, letting us explore the parts of it that exhibit "simple patterns", the possible pieces and rules that would translate them, and the games that they would make. Sometimes the physical process itself is not well-suited for an interesting game, sometimes clear rules lack a competitive and fun dimension. I reached a dead end first with a game about the "Race to Carbon", then another one with a "Race to Helium".
In the end, it was the introduction of antimatter that solved the playability issues — quite unexpectedly, to be honest — to make Big*Bang work well as a game. In this sense, the game design process mimics the scientific method: trying things that mostly lead to dead ends but that sometimes lead to a happy end. Answering our original question, maybe dead ends are more common in games about physics because the laws are what they are. We cannot tweak them beyond reality as we may do with rules from other themes, and sometimes the laws do not lend themselves to make a game work, however they are implemented.
Maybe good games about physics are rare because the laws of physics are not made for interesting gameplay, but for making our world work!
P.S.: You may want to check my other designer diaries, about BASKETmind and Tetrarchia. These three first games complete the trilogy of my hobbies: sports, history and science!