In last line there should be
therefore p(city has less than 2992 buses | bus has number 1546) = 0.5
avturchin
Karma: 4,336
For example, If I use self-sampling to estimate the number of seconds in the year, I will get a correct answer of around several tens of millions. But using word generator will never output a word longer than 100 letters.
I didn’t understand your idea here:
It’s not more wrong for a person whose parents specifically tried to give birth at this date than for a person who just happened to be born at this time without any planning. And even in this extreme situation your mistake is limited by two orders of magnitude. There is no such guarantee in DA.
Gott started this type of confusion than he claimed that Berlin wall will stay 14 more years and it actually did exactly that. A better claim would be “first tens of hours with some given credence”
It was discussed above in comments – see buses example. In short, I actually care about periods, and 50 per cent is for “between 15 and 30” hours and other 50 per cent is for “above 30 hours”.
Using oneself as a random sample is a very rough way to get an idea about what order of magnitude some variable is. If you determine that the day duration is 2 hours, it is still useful information as you know almost for sure now that it is not 1 millisecond or 10 years. (And if I perform 10 experiments like this, one on average will be an order of magnitude off). We can also adjust the experiment by taking into account that people are sleeping at night, so they read LW only during the day, evening, or early morning. So times above 12 or below 2 are more likely.
You are right that the point of the experiments here is not to learn the real time of the day, but to prove that I can treat myself as a random sample in general and after that use this idea in domains where I do not have any information.
I think the basis to treat myself as a random sample is the following:
I am (or better to say my properties are) randomly selected from the LW-readers population.
There is some bias in that selection but I assume that it is not large and I still can get the order of magnitude right even if I do not calculate the exact bias.
The sample size is sufficient if I want to learn the order of magnitude of some variable or if the difference between two hypotheses is sufficiently large. (If I take only one ball from a vase with 1000 balls, of which only one is green and 999 red, or from an alternative vase with 999 green and one red, I can identify the vase with high credence.)
In Gotts’ approach, the bus distribution statistic between different cities is irrelevant. The number of buses N for this city is already fixed. When you draw the bus number n, you just randomly selected from N. In that case, probability is n/N, and if we look for 0.5 probability, we get 0.5 = 1546/N which gives us N = 2992 with 0.5 probability. Laplace came to similar result using much more complex calculations of summing all possible probability distribution.
Agree that in some situations I have to take into account non-randomness of my sampling. While date of birth seems random and irrelevant, the distance to equator is strongly biased by distribution of the cities with universities which on Earth are shifted North.
Also agree that solving DA can be solution to DA: moreover, I looked at Google Scholar and found that the interest to DA is already declining.
Don’t agree. You chose word length generator as you know that typical length of words is 1-10. Thus not random.
I didn’t rejected any results – it works in any test I have imagined, and I also didn’t include several experiments which have the same results, e.g the total number of the days in a year based on my birthday (got around 500) and total number of letters in english alphabet (got around 40).
Note that alphabet letter count is not cyclical as well as my distance to equator.
Do not understand this:
Even if your parents specifically timed your conception to give you birth on the first of January, therefore putting you in a very specific “reference class”, you won’t be extremely mistaken about these numbers following your methodology.
If I were born 1 of January, I would get years duration 2 days which is very wrong.
‘double’ follows either from Gott’s equation or from Laplace’s rule.
I think you right that 1546 has the biggest probability compared to other probabilities for any other exact number, that is something like 1:1546. But it doesn’t means that it is likely, as it is still very small number.
In Doomsday argument we are interested in comparing not exact dates but periods, as in that case we get significant probabilities for each period and comparing them has meaning.
In my view, a proper use here is to compare two hypothesis: there are 2000 buses and 20 000 buses. Finding that the actual number is 1546 is an update in the direction of smaller number of buses.
Experimental testing: can I treat myself as a random sample?
I can also use functional identity theory, where I care about the next steps of agents functionally similar to my current thought-line in logical time.
The idea of observer’s stability is fundamental for our understanding of reality (and also constantly supported by our experience) – any physical experiment assumes that the observer (or experimenter) remains the same during the experiment.
The same is valid for life extension research. It requires decades, and many, including Brian Johnson, say that AI will solve aging and therefore human research in aging is not relevant. However, most of aging research is about collecting data about very slow processes. The more longitudinal data we collect, the easier it will be for AI to “take up the torch.”
The problem with the subjective choice view is that I can’t become Britney Spears. :) If I continue to sit at the table, I will find myself there every next moment even if I try to become someone else. So mapping into the next moments is an objective fact.
Moreover, even a single moment of experience is a mapping between two states of the brain, A and B. For example, moment A is before I see a rose, and moment B is after I see it and say: “A rose!” The experience of a red rose happens after A but before B.
The rainbow of qualia theory is objective but it assumes the existence of a hypothetical instrument: a qualiascope. A qualiascope is a mind which can connect to other minds and compare their experiences. This works the same way as my mind can compare qualia of colors and sounds without being any of them. Whether a qualiascope is physically possible is not obvious, as its observations may disturb the original qualia.
I think there is more to consider. For example, we can imagine a “qualia rainbow” theory of identity. I don’t necessarily endorse it, but it illustrates why understanding qualia is important for identity.
Imagine that infinitely many different qualia of “reds” could denote one real red. Each person, when born, is randomly initialized with a unique set of qualia for all colors and other sensations. This set can be called a “rainbow of qualia,” and continuous computing in the brain maintains it throughout a person’s life. A copy of me with a different set of qualia, though behaviorally indistinguishable, is not me. Only future mind states with the same set of qualia as mine are truly me, even if my memories were replaced with those of a rat.
Anthropic Trilemma is masterpiece.
Generally, I agree with what you said above—there is no (with some caveats—see below) soul-like identity, and we should use informational identity instead. Informational identity is objective, measurable sameness of memory and allows existence of many copies. It can be used to survive the end of the universe. I just care about the existence of a copy of me in another universe.
The main caveat is that the no-soul view ignores the existence of qualia. Qualia and the nature of consciousness are not solved yet, and we can’t claim that the identity problem is solved without first solving qualia and consciousness.
The theory of quantum immortality depends on the theory of identity which—as you correctly pointed out—is difficult.
There are two objective facts about identity:
I will be in my next observer-moment in the next moment of time. There is an objective process which makes mind states follow one another.
I can recognize myself as me or not.
In your thought experiment, these two properties are deliberately made to contradict each other.
A simple answer here is that you should not anticipate becoming a pig because a pig can’t think about personal identity. Anticipation assumes comparison between expectation and reality. A pig can’t perform such an operation. But this is not a satisfactory model.
It can be solved if we assume that we have two types of identity—informational (me or not me) and continuous. This seems paradoxical. But if we then assume that continuous identity passes through all possible minds eventually, then any pig will eventually become me again in some multiverse timelines, and I can calculate a share of my future copies which have a memory of being a pig.
This thought experiment can be done without any supertechnology, just using dreaming as an example: what if some of my copies will have a dream that they are pigs, and others have a dream about being themselves. The idea of anticipation produces error in that case, as in one way it assumes the existence of a mind capable of comparison, but in another way it assumes natural consequences of mind states.
In short, a correct identity theory allows one to compute correct probabilities of future observations in the situation of many different copies. See also my post The Quantum Mars Teleporter: An Empirical Test Of Personal Identity Theories.
There is a way to escape this by using the universal doomsday argument. In it, we try not to predict the exact future of the Earth, but the typical life expectancy of Earth-like civilizations, that is, the proportion of long civilizations to short ones.
If we define a long civilization as one which has 1000 times more observers, the fact that we find ourselves early means that short civilizations are at least 1000 times more numerous.
In short, it is SSA, but applied to a large set of civilizations.