The Forbidden Truth About What Is Billiards Revealed By An Old Pro > 자유게시판

EABAonline. English Amateur Billiards Association. 1⁄16 inches (52 mm) in diameter, the latter being the same size as the balls used in snooker and English billiards. Snooker cue ball and other balls are normally 4.5mm smaller than the pool balls. Like the regular pool, it uses 15 balls and a cue ball. Like history, ecology is (mostly) not "just one damned thing after another." But it’s hard not to think of it that way, and to teach our students not to think of it that way. 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. In fact, what is billiards there’s a lot happening. Births and deaths are happening instantly and continuously. That does not mean nothing’s happening! A prey individual was born, which caused prey abundance to increase by one, which caused… No. What that increase in prey abundance did was slightly change the expected time until the next birth or death event, by increasing prey abundance and (in any reasonable model) feeding back to slightly change the per-capita probabilities per unit time of giving birth and dying.

Now, you could try to drill down even further, down to the underlying physiological (or whatever) causes of individual births and deaths, and the underlying mechanisms linking per-capita birth and death probabilities to species’ abundances. And you know he might even rush over without putting all his clothes on, as smitten as he is with the ladies-who-can't-cook down the street. Before the game begins, the shake bottle is placed neck down (inverted) on the center of the pool table. Pocketing the 1 ball scores 1 point.Pocketing the 2 ball scores 2 points.Caroming the cue ball off both object balls scores 1 point.- check Caroming the cue ball off one or both object balls and then into the bottle knocking it onto its side scores 5 points.- check Caroming the cue ball off one or both object balls and then into the bottle knocking onto its base results in an automatic win. 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. The event saw players qualify by virtue of winning other events in the season, with 16 champions competing. Eventually, your purpose and satisfaction is not going to come from the winning of games, but from moving closer and closer to perfect control.

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. The lighting in your rec room is going to have a significant impact on the look of your felt, no matter what color you choose. You’ll probably have to replace it more often than is normal for an indoor pool table. For instance, you can have a sequence of causal events in which the magnitude of the effect is nonlinearly related to the magnitude of the cause. What’s the next domino to fall in the sequence? "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. 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.

For concreteness, let’s say it’s a limit cycle in the Rosenzweig-MacArthur model. 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. Predators convert consumed prey into new predators, and they die. Why do the predators and prey cycle? You’ve got some prey that reproduce and die, and some of those deaths are due to predators. 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. 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. Another prey birth? No. A prey death? In the real world one could in principle write down, in temporal order of occurrence, all the individual birth and death events in both species. No. A predator birth or death? 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.