Beware of what I call Pascal's scams: movements or belief systems that ask you to hope for or worry about very improbable outcomes that could have very large positive or negative consequences. (The name comes of course from the infinite-reward Wager proposed by Pascal: these days the large-but-finite versions are far more pernicious). Naive expected value reasoning implies that they are worth the effort: if the odds are 1 in 1,000 that I could win $1 billion, and I am risk and time neutral, then I should expend up to nearly $1 million dollars worth of effort to gain this boon. The problems with these beliefs tend to be at least threefold, all stemming from the general uncertainty, i.e. the poor information or lack of information, from which we abstracted the low probability estimate in the first place: because in the messy real world the low probability estimate is almost always due to low or poor evidence rather than being a lottery with well-defined odds:
(1) there is usually no feasible way to distinguish between the very improbable (say, 1 in 1,000) and the extremely improbable (e.g., one in a billion). Poor evidence leads to what James Franklin calls "low-weight probabilities", which lack robustness to new evidence. When the evidence is poor, and thus robustness of probabilities is lacking, then it is likely that "a small amount of further evidence would substantially change the probability. " This new evidence is as likely to decrease the probability by a factor of X as increase it by a factor of X, and the poorer the original evidence, the greater X is. (Indeed, given the nature of human imagination and bias, it is more likely to decrease it, for reasons described below).
(2) the uncertainties about the diversity and magnitudes of possible consequences, not just their probabilities, are also likely to be extremely high. Indeed, due to the overall poor information, it's easy to overlook negative consequences and recognize only positive ones, or vice-versa. The very acts you take to make it into utopia or avoid dystopia could easily send you to dystopia or make the dystopia worse.
(3) The "unknown unknown" nature of the most uncertainty leads to unfalsifiablity: proponents of the proposition can't propose a clear experiment that would greatly lower the probability or magnitude of consequences of their proposition: or at least, such an experiment would be far too expensive to actually be run, or cannot be conducted until after the time which the believers have already decided that the long-odds bet is rational. So not only is there poor information in a Pascal scam, but in the more pernicious beliefs there is little ability to improve the information.
The biggest problem with these schemes is that, the closer to infinitesimal probability, and thus usually to infinitesimal quality or quantity of evidence, one gets, the closer to infinity the possible extreme-consequence schemes one can dream up, Once some enterprising memetic innovator dreams up a Pascal's scam, the probabilities or consequences of these possible futures can be greatly exaggerated yet still seem plausible. "Yes, but what if?" the carrier of such a mind-virus incessantly demands. Furthermore, since more than a few disasters are indeed low probability events (e.g. 9/11), the plausibility and importance of dealing with such risks seems to grow in importance after they occur -- the occurrence of one improbable disaster leads to paranoia about a large number of others, and similarly for fortuitous windfalls and hopes. Humanity can dream up a near-infinity of Pascal's scams, or spend a near-infinity of time fruitlessly worrying about them or hoping for them. There are however far better ways to spend one's time -- for example in thinking about what has actually happened in the real world, rather than the vast number of things that might happen in the future but quite probably won't, or will likely cause consequences very differently than you expect.
So how should we approach low probability hypotheses with potential high value (negative or positive) outcomes? Franklin et. al. suggest that "[t]he strongly quantitative style of education in statistics, valuable as it is, can lead to a neglect of the more qualitative, logical, legal and causal perspectives needed to understand data intelligently. That is especially so in extreme risk analysis, where there is a lack of large data sets to ground solidly quantitative conclusions, and correspondingly a need to supplement the data with outside information and with argument on individual data points."
On the above quoted points I agree with Franklin, and add a more blunt suggestion: stop throwing around long odds and dreaming of big consequences as if you are onto something profound. If you can't gather the information needed to reduce the uncertainties, and if you can't suggest experiments to make the hope or worry falsifiable, stop nightmaring or daydreaming already. Also, shut up and stop trying to convince the rest of us to join you in wasting our time hoping or worrying about these fantasies. Try spending more time learning about what has actually happened in the real world. That study, too, has its uncertainties, but they are up to infinitely smaller.