Dyson says he doesn''t want his legacy to be defined by climate change, but his dissension from the orthodoxy of global warming is significant because of his stature and his devotion to the integrity of science. Dyson has said he believes that the truths of science are so profoundly concealed that the only thing we can really be sure of is that much of what we expect to happen won't come to pass. In "Infinite in All Directions," he writes that nature's laws "make the universe as interesting as possible." This also happens to be a fine description of Dyson's own relationship to science. In the words of Avishai Margalit, a philosopher at the Institute for Advanced Study, "He's a consistent reminder of another possibility." When Dyson joins the public conversation about climate change by expressing concern about the "enormous gaps in our knowledge, the sparseness of our observations and the superficiality of our theories," these reservations come from a place of experience. Whatever else he is, Dyson is the good scientist; he asks the hard questions. He could also be a lonely prophet. Or, as he acknowledges, he could be dead wrong.
Let's say, hypothetically speaking, you met someone who told you they had two children, and one of them is a girl. What are the odds that person has a boy and a girl?
You often hear the complaint that people don't understand math. In this instance, however, an equally valid way of explaining what's going on is that mathematicians don't understand people.
The mention of assumptions and word games introduces an important caveat. We can't expect to reach the same conclusions unless we all play by the same rules and understand the problem in the same way. A number of commentators - going back to the first wave of controversy in the early 1990s - have pointed out that certain assumptions are crucial to the analysis of the Monty Hall puzzle. In particular, it's important that Monty Hall must always open one door and offer the option of switching, and the door opened can never be the one initially chosen by the contestant, nor can it be the winning door.