About two...
There is no jump, because "I don't know" is the maximum entropy distribution. The maximum entropy distribution is the distribution over probabilities which creates the maximum information-theoretic entropy, while obeying the observed parameters of the system. This works because entropy is just the expected value of the information gained from measuring a system. You want the maximum entropy distribution because anything else is literally pulling information out of thin air. If you pick a lower entropy distribution when you can construct a higher entropy one consistent with the data, then you're expecting less information to be given on a measurement, as if you already knew something about it.
The maximum entropy hypothesis on any yes/no question is a 50/50 chance. At those odds, cryonics are great!
However, they probably have information which adjusts their probability down. An actual "I don't know" would be the result of a coinflip, whereas anything under than a 50% probability of cryonics working is based on information which makes you think it's unlikely. So they have beliefs about it.
I don't think entropy quite works that way. For notational convenience, let Q(p) denote the entropy of p. Then just because Q(p) > Q(q), does not mean that q is strictly more informative than p. In other words, it is not the case that there is some total ordering on distributions, such that for any p,q with Q(p) > Q(q), I can get from p to q with Q(p)-Q(q) bits of information. The closest statement you can make would be in terms of KL divergence, but it is important to note that both KL(p||q) and KL(q||p) are positive, so KL is providing a distance, ...
Sorry if this seems incomplete - thought I'd fire this off as a discussion post now and hope to return to it with a more well-rounded post later.
Less Wrongers are used to thinking of uncertainty as best represented as a probability - or perhaps as a log odds ratio, stretching from minus infinity to infinity. But when I argue with people about for example cryonics, it appears most people consider that some possibilities simply don't appear on this scale at all: that we should not sign up for cryonics because no belief about its chances of working can be justified. Rejecting this category seems to me one of the key foundational ideas of this community, but as far as I know the only article specifically discussing it is "I don't know", which doesn't make a devastatingly strong case. What other writing discusses this idea?
I think there are two key arguments against this. First, you have to make a decision anyway, and the "no belief" uncertainty doesn't help with that. Second, "no belief" is treated as disconnected from the probability line; so at some point evidence causes a discontinuous jump from "no belief" to some level of confidence. This discontinuity seems very unnatural. How can evidence add up to a discontinuous jump - what happened to all the evidence before the jump?