An important thing to realize is that people working on anthropics are trying to come up with a precise inferential methodology. They’re not trying to draw conclusions about the state of the world, they’re trying to draw conclusions about how one should draw conclusions about the state of the world. Think of it as akin to Bayesianism. If someone read an introduction to Bayesian epistemology, and said “This is just a mess of tautologies (Bayes’ theorem) and thought experiments (Dutch book arguments) that pays no rent in anticipated experience. Why should I care?”, how would you respond? Presumably you’d tell them that they should care because understanding the Bayesian methodology helps people make sounder inferences about the world, even if it doesn’t predict specific experiences. Understanding anthropics does the same thing (except perhaps not as ubiquitously).
So the point of understanding anthropics is not so much to directly predict experiences but to appreciate how exactly one should update on certain pieces of evidence. It’s like understanding any other selection effect—in order to properly interpret the significance of pieces of evidence you collect, you need to have a proper understanding of the tools you use to collect them. To use Eddington’s much-cited example, if your net can’t catch fish smaller than six inches, then the fact that you haven’t caught any such fish doesn’t tell you anything about the state of the lake you’re fishing. Understanding the limitations of your data-gathering mechanism prevents you from making bad updates. And if the particular limitation you’re considering is the fact that observations can only be made in regimes accessible to observers, then you’re engaged in anthropic reasoning.
Paul Dirac came up with a pretty revisionary cosmological theory based on several apparent “large number coincidences”—important large (and some small) numbers in physics that all seem to be approximate integer powers of the Hubble age of the universe. He argued that it is implausible that we just happen to find ourselves at a time when these simple relationships hold, so they must be law-like. Based on this he concluded that certain physical constants aren’t really constant; they change as the universe ages. R. H. Dicke showed (or purported to show) that at least some of these coincidences can be explained when one realizes that observers can only exist during a certain temporal window in the universe’s existence, and that the timing of this window is related to a number of other physical constants (since it depends on facts about the formation and destruction of stars, etc.). If it’s true that observers can only exist in an environment where these large number relationships hold, then it’s a mistake to update our beliefs about natural laws based on these relationships. So that’s an example of how understanding the anthropic selection effect might save us (and not just us, but also superhumans like Dirac) from bad updates.
So much for anthropics in general, but what about the esoteric particulars—SSA, SIA and all that. Well, here’s the basic thought: Dirac’s initial (non-anthropic) move to his new cosmological theory was motivated by the belief that it is extraordinarily unlikely that the large number coincidences are purely due to chance, that we just happen to be around at a time when they hold. This kind of argument has a venerable history in physics (and other sciences, I’m sure) -- if your theory classifies your observed evidence as highly atypical, that’s a significant strike against the theory. Anthropic reasoning like Dicke’s adds a wrinkle—our theory is allowed to classify evidence as atypical, as long as it is not atypical for observers. In other words, even if the theory says phenomenon X occurs very rarely in our universe, an observation of phenomenon X doesn’t count against it, as long as the theory also says (based on good reason, not ad hoc stipulation) that observers can only exist in those few parts of the universe where phenomenon X occurs. Atypicality is allowed as long as it is correlated with the presence of observers.
But only that much atypicality is allowed. If your theory posits significant atypicality that goes beyond what selection effects can explain, then you’re in trouble. This is the insight that SSA, SIA, etc seek to precisify. They are basically attempts to update the Diracian “no atypicality” strategy to allow for the kind of atypicality that anthropic reasoning explains, but no more atypicality than that. Perhaps they are misguided attempts for various reasons, but the search for a mathematical codification of the “no atypicality” move is important, I think, because the move gets used imprecisely all the time anyway (without explicit evocation, most of the time) and it gets used without regard for important observation selection effects.
In other words, even if the theory says phenomenon X occurs very rarely in our universe, an observation of phenomenon X doesn’t count against it[...]Atypicality is allowed as long as it is correlated with the presence of observers.
I read this as: Rather than judging our theory based on p(X), judge it based on p(X) | exists(observers). Am I interpreting you right?
It’s a bit more complicated than that, I think. We’re usually dealing with a situation where p(X occurs somewhere | T) -- where T is the theory—is high. However, the probability of X occurring in a particular human-scale space-time region (or wave-function branch or global time-slice or universe or...) given T is very low. This is what I mean by X being rare. An example might be life-supporting planets or (in a multiversal context) fundamental constants apparently fine-tuned for life.
So the naïve view might be that an observation of X disconfirms the theory, based on the Copernican assumption that there is nothing very special about our place in the universe, whereas the theory seems to suggest that our place is special—it’s one of those rare places where we can see X.
But this disconfirmation only works if you assume that the space-time regions (or branches or universes or...) inhabited by observers are uncorrelated with those in which X occurs. If our theory tells us that those regions are highly correlated—if p(X occurs in region Y | T & observers exist in region Y) >> p(X occurs in region Y | T) -- then our observation of X doesn’t run afoul of the Copernican assumption, or at least a reasonably modified version of the Copernican assumption which allows for specialness only in so far as that specialness is required for the existence of observers.
An important thing to realize is that people working on anthropics are trying to come up with a precise inferential methodology. They’re not trying to draw conclusions about the state of the world, they’re trying to draw conclusions about how one should draw conclusions about the state of the world. Think of it as akin to Bayesianism. If someone read an introduction to Bayesian epistemology, and said “This is just a mess of tautologies (Bayes’ theorem) and thought experiments (Dutch book arguments) that pays no rent in anticipated experience. Why should I care?”, how would you respond? Presumably you’d tell them that they should care because understanding the Bayesian methodology helps people make sounder inferences about the world, even if it doesn’t predict specific experiences. Understanding anthropics does the same thing (except perhaps not as ubiquitously).
So the point of understanding anthropics is not so much to directly predict experiences but to appreciate how exactly one should update on certain pieces of evidence. It’s like understanding any other selection effect—in order to properly interpret the significance of pieces of evidence you collect, you need to have a proper understanding of the tools you use to collect them. To use Eddington’s much-cited example, if your net can’t catch fish smaller than six inches, then the fact that you haven’t caught any such fish doesn’t tell you anything about the state of the lake you’re fishing. Understanding the limitations of your data-gathering mechanism prevents you from making bad updates. And if the particular limitation you’re considering is the fact that observations can only be made in regimes accessible to observers, then you’re engaged in anthropic reasoning.
Paul Dirac came up with a pretty revisionary cosmological theory based on several apparent “large number coincidences”—important large (and some small) numbers in physics that all seem to be approximate integer powers of the Hubble age of the universe. He argued that it is implausible that we just happen to find ourselves at a time when these simple relationships hold, so they must be law-like. Based on this he concluded that certain physical constants aren’t really constant; they change as the universe ages. R. H. Dicke showed (or purported to show) that at least some of these coincidences can be explained when one realizes that observers can only exist during a certain temporal window in the universe’s existence, and that the timing of this window is related to a number of other physical constants (since it depends on facts about the formation and destruction of stars, etc.). If it’s true that observers can only exist in an environment where these large number relationships hold, then it’s a mistake to update our beliefs about natural laws based on these relationships. So that’s an example of how understanding the anthropic selection effect might save us (and not just us, but also superhumans like Dirac) from bad updates.
So much for anthropics in general, but what about the esoteric particulars—SSA, SIA and all that. Well, here’s the basic thought: Dirac’s initial (non-anthropic) move to his new cosmological theory was motivated by the belief that it is extraordinarily unlikely that the large number coincidences are purely due to chance, that we just happen to be around at a time when they hold. This kind of argument has a venerable history in physics (and other sciences, I’m sure) -- if your theory classifies your observed evidence as highly atypical, that’s a significant strike against the theory. Anthropic reasoning like Dicke’s adds a wrinkle—our theory is allowed to classify evidence as atypical, as long as it is not atypical for observers. In other words, even if the theory says phenomenon X occurs very rarely in our universe, an observation of phenomenon X doesn’t count against it, as long as the theory also says (based on good reason, not ad hoc stipulation) that observers can only exist in those few parts of the universe where phenomenon X occurs. Atypicality is allowed as long as it is correlated with the presence of observers.
But only that much atypicality is allowed. If your theory posits significant atypicality that goes beyond what selection effects can explain, then you’re in trouble. This is the insight that SSA, SIA, etc seek to precisify. They are basically attempts to update the Diracian “no atypicality” strategy to allow for the kind of atypicality that anthropic reasoning explains, but no more atypicality than that. Perhaps they are misguided attempts for various reasons, but the search for a mathematical codification of the “no atypicality” move is important, I think, because the move gets used imprecisely all the time anyway (without explicit evocation, most of the time) and it gets used without regard for important observation selection effects.
I read this as: Rather than judging our theory based on p(X), judge it based on p(X) | exists(observers). Am I interpreting you right?
It’s a bit more complicated than that, I think. We’re usually dealing with a situation where p(X occurs somewhere | T) -- where T is the theory—is high. However, the probability of X occurring in a particular human-scale space-time region (or wave-function branch or global time-slice or universe or...) given T is very low. This is what I mean by X being rare. An example might be life-supporting planets or (in a multiversal context) fundamental constants apparently fine-tuned for life.
So the naïve view might be that an observation of X disconfirms the theory, based on the Copernican assumption that there is nothing very special about our place in the universe, whereas the theory seems to suggest that our place is special—it’s one of those rare places where we can see X.
But this disconfirmation only works if you assume that the space-time regions (or branches or universes or...) inhabited by observers are uncorrelated with those in which X occurs. If our theory tells us that those regions are highly correlated—if p(X occurs in region Y | T & observers exist in region Y) >> p(X occurs in region Y | T) -- then our observation of X doesn’t run afoul of the Copernican assumption, or at least a reasonably modified version of the Copernican assumption which allows for specialness only in so far as that specialness is required for the existence of observers.