Anthropics makes sense with shorter people

by KatjaGrace4 min read11th Apr 201118 comments


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Reproduced from Meteuphoric by request.

Often people think that various forms of anthropic reasoning require you to change your beliefs in ways other than conditionalizing on evidence. This is false, at least in the cases I know of. I shall talk about Frank Arntzenius' paper Some Problems for Conditionalization and Reflection [gated] because it explains the issue well, though I believe his current views agree with mine.

He presents five thought experiments: Two Roads to Shangri La, The Prisoner, John Collins's Prisoner, Sleeping Beauty and Duplication. In each of them, it seems the (arguably) correct answer violates van Fraassen's reflection principle, which basically says that if you expect to believe something in the future without having been e.g. hit over the head between now and then, you should believe it now. For instance the thirder position in Sleeping Beauty seems to violate this principle because before the experiment Beauty believes there is a fifty percent chance of heads, and that when she wakes up she will think there is a thirty three percent chance. Arntzenius argued that these seemingly correct answers really are the correct ones, and claimed that they violate the reflection principle because credences can evolve in two ways other than by conditionalization.

First he said credences can shift, for instance through time. I know that tomorrow I will have a higher credence in it being Monday than I do today, and yet it would not be rational for me to increase my credence in it being Monday now on this basis. They can also 'spread out'. For instance if you know you are in Fairfax today, and that tomorrow a perfect replica of your brain experiencing Fairfax will be made and placed in a vat in Canberra, tomorrow your credence will go from being concentrated in Fairfax to being spread between there and Canberra. This is despite no damage having been done to your own brain. As Arntzenius pointed out, such an evolution of credence looks like quite the opposite of conditionalization, since conditionalization consists of striking out possibilities that your information excludes - it never opens up new possibilities.

I agree that beliefs should evolve in these two ways. However they are both really conditionalization, just obscured. They make sense as conditionalization when you think of them as carried out by different momentary agents, based on the information they infer from their connections to other momentary agents with certain beliefs (e.g. an immediately past self).

Normal cases can be considered this way quite easily. Knowing that you are the momentary agent that followed a few seconds after an agent who knew a certain set of facts about the objective world, and who is (you assume) completely trustworthy, means you can simply update the same prior with those same facts and come to the same conclusion. That is, you don't really have to do anything. You can treat a stream of moments as a single agent. This is what we usually do.

However sometimes being connected in a certain way to another agent does not make everything that is true for them true for you. Most obviously, if they are a past self and know it is 12 o clock, your connection via being their one second later self means you should exclude worlds where you are not at time 12:00:01. You have still learned from your known relationship to that agent and conditionalized, but you have not learned that what is true of them is true of you, because it isn't. This is the first way Arntzenius mentioned that credences seem to evolve through time not by by conditionalization.

The second way occurs when one person-moment is at location X, and another person moment has a certain connection to the person at X, but there is more than one possible connection of that sort. For instance when two later people both remember being an earlier person because the earlier person was replicated in some futuristic fashion. Then while the earlier person moment could condition on their exact location, the later one must condition on being in one of several locations connected that way to the earlier person's location, so their credence spreads over more possibilities than that of the earlier self. If you call one of these later momentary agents the same person as the earlier one, and say they are conditionalizing, it seems they are doing it wrong. But considered as three different momentary people learning from their connections they are just conditionalizing as usual.

What exactly the later momentary people should believe is a matter of debate, but I think that can be framed entirely as a question of what their state spaces and priors look like.

Momentary humans almost always pass lots of information from one to the next, chronologically along chains of memory through non-duplicated people, knowing their approximate distance from one another. So most of the time they can treat themselves as single units who just have to update on any information coming from outside, as I explained. But conditionalization is not specific to these particular biological constructions; and when it is applied to information gained through other connections between agents, the resulting time series of beliefs within one human will end up looking different to that in a chain with no unusual extra connections.

This view also suggests that having cognitive defects, such as memory loss, should not excuse anyone from having credences, as for instance Arntzenius argued it should in his paper Reflections on Sleeping Beauty: "in the face of forced irrational changes in one's degrees of belief one might do best simply to jettison them altogether". There is nothing special about credences derived from beliefs of a past agent you identify with. They are just another source of information. If the connection to other momentary agents is different to usual, for instance through forced memory loss, update on it as usual.



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I know that tomorrow I will have a higher credence in it being Monday than I do today, and yet it would not be rational for me to increase my credence in it being Monday now on this basis.

It seems like if you cash out the concept of "it being Monday" in terms of timeless facts about the block universe, that there is no change in belief only time. Your strength in belief in the referent of the quotation "it is Monday" changes only because the referent itself changes.

However sometimes being connected in a certain way to another agent does not make everything that is true for them true for you.

The words "current time" refer to different facts when used by agent at different times. It's better to see different agents as asking different questions (even if using the same words), this way they won't disagree with each other and will be able to refine understanding of the facts which either of them contemplates. A future agent could point out that the past agent wasn't entirely correct, for example, and the past "current time" was actually 12:02 and not 12:03.

This is similar to the problem of making sense of subjective/objective aspects of value. The best method, as far as I know, is to consider different agents as pursuing different ideas, but with the ideas themselves (the laws of developing them) arbitrarily representable, that is objective.

For anyone feeling bewildered by antrophics, I highly recommend Katja's Honours Thesis:

"Anthropic Reasoning in the Great Filter" (Katja Grace, 2010)

It's the best discussion of anthropics I've ever read.

This is the first solution to Sleeping Beauty problem I've seen that seems to just simply make sense. Upvoted.

Katja didn't give a complete solution to the Sleeping Beauty problem here. She just advocated identifying an epistemic agent as the observer-moment doing the reasoning at that time. But, for example, both SIA (which advises a thirder position) and SSA (which advises a halfer position) can be phrased in terms of observer-moments.

Upvoted, but I would love to see the points made here expanded on separately. Would probably improve my comprehension.

This seems like a lot to digest. A lot of these discussions about anthropics just leave me feeling very confused. I'll just say that when I saw the title my initial thought was that it was talking about people who were short in stature.

when I saw the title my initial thought was that it was talking about people who were short in stature.


Did you ever figure out what the intended meaning was?

No. I tentatively think that it might mean that it makes sense with beings with shorter histories?

I'm fairly convinced that it means "Anthropics makes sense with one person for each moment - each person being very short (as measured by their time of existence)."

Thanks for the clarification. Although I wonder if one can make a serious sort of anthropic argument about size. one shouldn't expect to find to be a member of a large species since that means that there's less room for lots of observers of that type. So we should expect to be large enough to be able to discuss anthropic reasoning but not much larger.

People who only exist for a short period of time. Once I read the actual article, I thought the title was a clever pun, but I can see how it could be confusing.

The Anthropic Principle

References and Resources

[...] how to reason when you suspect that your evidence is biased by “observation selection effects”—that is, evidence that has been filtered by the precondition that there be some suitably positioned observer to “have” the evidence. This conundrum—sometimes alluded to as “the anthropic principle,” “self-locating belief,” or “indexical information”—turns out to be a surprisingly perplexing and intellectually stimulating challenge, one abounding with important implications for many areas in science and philosophy.

There are the philosophical thought experiments and paradoxes: the Doomsday Argument; Sleeping Beauty; the Presumptuous Philosopher; Adam & Eve; the Absent-Minded Driver; the Shooting Room.

And there are the applications in contemporary science: cosmology (“How many universes are there?”, “Why does the universe appear fine-tuned for life?”); evolutionary theory (“How improbable was the evolution of intelligent life on our planet?”); the problem of time’s arrow (“Can it be given a thermodynamic explanation?”); quantum physics (“How can the many-worlds theory be tested?”); game-theory problems with imperfect recall (“How to model them?”); even traffic analysis (“Why is the ‘next lane’ faster?”).

In physics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe that the fact that the Universe's fundamental constants are within the narrow range thought to allow life is not remarkable.

The Strong Anthropic principle as explained by Barrow and Tipler (see Variants) states that this is all the case because conscious life, in some sense, needed to exist. Critics argue in favor of a Weak Anthropic principle, which states that the universe's fine tuning amounts to selection bias; in an infinite universe, some worlds might evolve conscious life. Douglas Adams used the metaphor of a living puddle examining its own shape, since, to those living creatures, the universe may appear to fit them perfectly (in fact, they simply fit the universe perfectly).

UDASSA is a philosophical "theory of everything" (TOE). It provides a framework to understand the universe and our place within it. Basically it can be summed up very simply as: Universal Distribution (UD) plus ASSA (absolute self selection assumption).

To make progress in cosmology we really need to understand the fundamental issue of how to compare different theories and work out the posterior credences of different models in the light of what we know and observe.

I don't really know a lot about anthropics, but once I read through this article with a sufficient level of focus, it made sense. I had not heard of the Shangri-La problem before...I have read about the Sleeping Beauty problem. I don't know any of the others: what is Duplication or John Collins' Prisoner?

[-][anonymous]10y 0

Ungated copy of Arntzenius' "Some Problems for Conditionalization and Reflection" here