The Untold Secret To Mastering What Is Billiards In Just Seven Days > 자유게시판

But ecology is mostly not like billiards, or falling dominoes, or Rube Goldberg machines. Rube Goldberg machines are sequences of causal events. Falling dominoes are sequences of causal events. There are no sequences of events here. The event saw players qualify by virtue of winning other events in the season, with 16 champions competing. For serious players or those who intend to spend a lot of time playing for fun, green or blue are the best bets. When all reds are pocketed, players attempt to pocket the other balls in numerical order. Your cue strikes the cue ball, causing it to roll into another ball, causing that ball to roll into the corner pocket. Billiards is a reference name given to a bunch of three games; pocket billiards, snooker carom billiards. The billiards scene in Vietnam has recently flourished at both amateur and professional levels. However, it is possible to find sets for amateur use that are numbered with their point value on them. But my point would still hold. They are, but that’s not my point here.

Here are a few ideas to give you some inspiration for your dream billiards room. Billiards is all about sequences of causal events. 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. You cannot think about equilibria in terms of sequences of causal events, it’s like trying to think about smells in terms of their colors, or bricks in terms of their love of Mozart. 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.

When humans think about causality, they find it natural to think in terms of sequences of events. 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. 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. Simultaneity, not sequences. Feedbacks, not one-way traffic. Now I can hear some of you saying, ok, that’s true of the math we use to describe the world, but it’s not literally true of the real world. That would have certainly added to its growing and wider popularity, even amongst the "lower classes." Over time, the game migrated around the continent and into the wider world. 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.

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. 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. 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. 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.

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