Lab · How news spreads消息怎么传开练习 · 消息怎么传开
When does news of spare seats reach Arts?选修课还有名额的消息，什么时候传得到文学院？
The same 40 students. One Engineering student mentions that an elective still has seats. Each day that news can pass along a recorded conversation, with the chance you set, and it does not expire. If everyone in Engineering has heard, it is easy to tell the faculty office that the whole campus knows. Arts still never hears it when nobody talked across the two faculties. That missing conversation is a bridge: one recorded talk between Arts and Engineering, the only way the news can cross.还是这 40 名学生。工程学院的一名学生说，选修课还有名额。每一天，这句话可以沿一次已记下的谈话传出去，机会由你来定，而且消息不会过期。工程学院如果人人都听到了，就容易跟教务处说“全校都知道了”。可是两个学院之间没人说过话时，文学院谁也听不到。缺的那一次谈话就是桥：文学院和工程学院之间记下的一次谈话，消息只能沿着它跨过去。
Why it matters.为什么要紧。 The news moves only along recorded talks. Diffusion here just means that day-by-day passing. If no talk crosses the faculties, Arts never hears about the seats, however easily the news passes inside Engineering. The blank between the two clouds is not what stops it. A missing talk is.消息只沿已记下的谈话走。这里的扩散，就是这种一天一天往下传。如果没有谈话跨过学院，文学院永远不知道还有名额，哪怕消息在工程学院内部传得再容易。挡住它的不是两团之间的空白，而是缺了的那一次谈话。
Try this试一试 Set Arts–Engineering talks to zero and watch the Arts squares. Then raise those talks, and leave the chance of passing along a talk where it is. Does Arts hear about the seats?把跨学院的谈话设为零，看文学院的方块。再把那些谈话调高，沿谈话传递的机会先别动。文学院听得到还有名额吗？
How to read the chart怎么读这张图
If you read this wrong要是读错了
If the faculty office sees that Engineering has all heard, and then stops putting up posters, Arts students never learn there are seats left. The news can reach every Engineering student it can reach and still stop where no talk crosses to Arts.如果教务处看见工程学院人人都听到了，就不再贴海报，文学院的同学就永远不知道还有名额。消息可以传到它到得了的每一个工程学院学生，然后停在没有通向文学院的谈话那里。
What this picture is enough for这张图够说明什么
Enough to see that a missing Arts–Engineering talk stops the news, not only a low chance of passing it along.看得出：挡住消息的，不只是传递机会低，还有文学院和工程学院之间缺了的那一次谈话。
Not enough for a real plan to tell students about the seats. You still need the talks that were actually recorded, and a way to separate “heard it from a friend” from “would have seen the poster anyway.”还不够拿来安排怎么通知选课。你仍需要实际记下的谈话，也需要把“从朋友那里听到”和“反正会看见海报”分开。
The equation, and where it stops式子、假设和边界
The talks are drawn the same way as on the previous page: every possible pair is an independent yes-or-no, a Bernoulli draw. The news then spreads like a rumor that does not fade. One Engineering student starts with it. Each day, everyone who has heard can pass it to a friend they talked to, with probability β, independently. Nobody forgets it, and nobody hears it except along a talk. In the epidemic textbook this is a susceptible–infected process. Here the “infection” is having heard about the seats.谈话的画法和上一页一样：每一对人都独立地回答有没有说过话，也就是一次伯努利抽取。然后消息像一条不会淡掉的传闻往下传。工程学院的一名学生最先知道。每一天，已经听到的人可以按概率 β，独立地传给上个月聊过的朋友。没有人会忘掉，也没有人能不靠谈话就听到。教材里这叫易感—感染过程。在这里，“感染”就是听到了还有名额。
The news cannot leave the group of students connected to the person who said it first. That group is the component. If the chance of an Arts–Engineering talk is zero, every draw has no bridge, so Arts never hears. A small chance can still draw zero talks by luck. For one draw, the coin flips that carry the news are fixed, so raising β can reach more students without redrawing who talked. Changing a talk probability does redraw the talks.消息离不开和最先说出来的人连在一起的那一组学生。这一组叫连通分量。跨学院谈话的机会如果是零，每一次抽取都没有桥，文学院就听不到。机会很小的时候，仍可能碰巧一次都没有。同一次抽取里，传不传的那些硬币是固定的，所以把 β 调高可以让更多人听到，而不必重画谁和谁说过话。改谈话的概率，则会重画谈话。
Easy to get wrong.容易踩的坑。 A faculty that has all heard is not evidence the other faculty is about to hear. The news can reach everyone it can reach and still stop at a missing bridge. Another mistake is to read the gap between the two clouds as the barrier. That gap is just the layout. The barrier is the list of talks. A third is to treat one draw as the typical spread. The next draw can cross on a different bridge.一个学院人人都听到了，并不能说明另一个学院马上也会听到。消息可以传到所有到得了的人，然后停在缺了的那座桥上。另一个错，是把两团人之间的空隙当成障碍。那个空隙只是排版。障碍是谈话清单。第三个错，是把一次抽取当成通常会怎样传。下一次抽取可能从另一座桥跨过去。