What you describes here is the Laplace sunrise problem: If sun rose 5000 times, what are the chances that it will rise tomorrow? Laplace solved the problem and got almost the same equation as Gott’s Doomsday Argument—and got 1 in 5002 chance of non-rise tomorrow—which gives around 50 per cent chances of non-rise in next 5000 days. But everyday his estimation could be updated on the data that the sun has risen again.
But he didn’t use anthropic reasoning, but instead did the sum of all possible hypothesis about sunrise probabilities consisted with the observation. Anyway, he may have some assumptions about how hypothesis are distributed.
He didn’t “solve” it, not in any meaningful sense of the term “solve”. He probably implicitly assumed a certain distribution and did the calculation for the next day only. To solve it would mean to gather all possible data about the reasons the sun might not rise, and define what “sun not rising” even means.
While sun-rise problem setup is somewhat crazy, the bus waiting problem is ubiquitous. For example, I am waiting for some process to terminate in my computer or file starting to download. The rule of thumb is that if it is not terminating in a few minutes, it will not terminate soon, and it is better to turn off the process.
Leslie in “The end of the world” suggested a version of DA which is independent of assumptions of probability distributions of events. He suggested that if we assume deterministic universe without world-branching, then any process has unknown to us but fixed duration T. For example, the time from previous bus arrival to the next bus arrival is Tb. It is not a variable, it has fixed value for today and for this bus, and Omega may know it. Say, it 15 minutes. It doesn’t depend on the way how arrivals of other buses are distributes, are they regular, normally distributed etc. It is only for this bus.
Now you arrive on the bus station. You only know two things: the time from last arrival and the fact that you came in a random moment relative to bus arrivals. In that case, you can estimate time until next bus’s arrival according to doomsday argument logic: it will be around the same time as from previous arrival.
What you describes here is the Laplace sunrise problem: If sun rose 5000 times, what are the chances that it will rise tomorrow? Laplace solved the problem and got almost the same equation as Gott’s Doomsday Argument—and got 1 in 5002 chance of non-rise tomorrow—which gives around 50 per cent chances of non-rise in next 5000 days. But everyday his estimation could be updated on the data that the sun has risen again.
But he didn’t use anthropic reasoning, but instead did the sum of all possible hypothesis about sunrise probabilities consisted with the observation. Anyway, he may have some assumptions about how hypothesis are distributed.
He didn’t “solve” it, not in any meaningful sense of the term “solve”. He probably implicitly assumed a certain distribution and did the calculation for the next day only. To solve it would mean to gather all possible data about the reasons the sun might not rise, and define what “sun not rising” even means.
While sun-rise problem setup is somewhat crazy, the bus waiting problem is ubiquitous. For example, I am waiting for some process to terminate in my computer or file starting to download. The rule of thumb is that if it is not terminating in a few minutes, it will not terminate soon, and it is better to turn off the process.
Leslie in “The end of the world” suggested a version of DA which is independent of assumptions of probability distributions of events. He suggested that if we assume deterministic universe without world-branching, then any process has unknown to us but fixed duration T. For example, the time from previous bus arrival to the next bus arrival is Tb. It is not a variable, it has fixed value for today and for this bus, and Omega may know it. Say, it 15 minutes. It doesn’t depend on the way how arrivals of other buses are distributes, are they regular, normally distributed etc. It is only for this bus.
Now you arrive on the bus station. You only know two things: the time from last arrival and the fact that you came in a random moment relative to bus arrivals. In that case, you can estimate time until next bus’s arrival according to doomsday argument logic: it will be around the same time as from previous arrival.