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In this game the object is to pocket the 9 ball after the cue ball first makes contact with the lowest-numbered ball on the table. While no-one can tell you which style is right for you, the best option is to go with something that fits the aesthetic you’re creating for your pub, game room or bar. Most people find that the bright, vibrant colors tend to strain their eyes, while the darkest colors make the balls and pockets harder to see. Cooler colors might foster more in-depth, reflective dialogues. It did have balls, of some sort, but the devices that were used to strike the balls were called "maces." We could assume that these older tools might have resembled a "mallet" (again, like a "croquet club"), much more than they did a modern "cue stick." According to some, the earliest manifestations of the game did utilize six pockets, but the number of balls used, and the rest of the physical make-up of the game can get rather archaic. And that’s why you might have felt that one of the two types of balls was smaller than the other. Purely for the sake of simplicity (because it doesn’t affect my argument at all), let’s say it’s a closed, deterministic, well-mixed system with no population structure or evolution or anything like that, so we can describe the dynamics with just two coupled equations, one for prey dynamics and one for predator dynamics.

No. A predator birth or death? Another prey birth? No. A prey death? At every instant in time, prey are being born, and prey are dying, and those two rates are precisely equal in magnitude but opposite in sign. And at every instant in time, predators are being born and predators are dying, and those two rates are precisely equal in magnitude but opposite in sign. And again for the sake of simplicity, let’s say it’s a constant environment and there’s no particular time at which organisms reproduce or die (e.g., there’s no "mating season"), so reproduction and mortality are always happening, albeit at per-capita and total rates that may vary over time as prey and predator abundances vary. For instance, let’s say the system is at equilibrium, meaning that predator and prey abundances aren’t changing over time. Or, let’s say the predators and prey exhibit cyclic dynamics. For concreteness, let’s say it’s a limit cycle in the Rosenzweig-MacArthur model.

Since most of us are not using a light meter for exact lighting measurements, let’s just take this to mean a comfortably bright lighting level for the human eye in indoor environments, and the brightness should be consistent across the entire table. Births and deaths are happening instantly and continuously. In fact, what is billiards there’s a lot happening. That does not mean nothing’s happening! There was a revival in the 1890s, but from then on, croquet was always a minority sport, with national individual participation amounting to a few thousand players. A discipline of carom billiards, players aim to recreate a portion of 76 pre-set shots of varying difficulty against an opponent. Competitive trick shot events, inspired by artistic billiards, began in the 1970s. Coordinated by world champion Paul Gerni with the World Trick Shot Artists Association, events were first held until 2000, when the World Pool-Billiard Association created the WPA World Artistic Pool Championship. Shall we go play billiards, then, friends? This is a case where it’s sooo tempting to think in terms of sequences of events; I know because my undergrad students do it every year. It’s just a bit of ecology I know well. I think it also makes it hard for professionals to do ecology.

"The prey go up, which causes the predators to go up, which causes the prey to crash, which causes the predators to crash." In lecture, even I’ve been known to slip and fall back on talking this way, and when I do the students’ eyes light up because it "clicks" with them, they feel like they "get" it, they find it natural to think that way. That is, SEMs mesh with and reinforce our natural tendency to think about causality in terms of colliding billiard balls. You cannot think about this dynamical system in terms of sequences of causal events. But you’re never going to find something that lets you redescribe predator-prey dynamics in terms of sequences of events, each causing the next. Giddy up, because in this article, we are going to discuss everything regarding the size of cue ball and other balls. 3: And to clarify further, no, I’m not trying to argue against the notion that population dynamics are ultimately a matter of individual organisms giving birth, dying, and moving around. The example is predator-prey dynamics.