From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Tue Jun 03 2003 - 14:29:54 MDT
Robin Hanson wrote:
> Eliezer S. Yudkowsky wrote:
>
>>>> ... You can go forward from the discovery of new evidence; I'm not
>>>> sure it makes sense to selectively eliminate evidence you were born
>>>> with and ask what your "priors" were before that. ...
>>>
>>> ... Perhaps you were born a much smarter baby that the rest of us,
>>> but most babies have no idea what their name is, how many humans have
>>> lived before them, how it is that a universe coughs up a mind, or
>>> even that they are in fact a mind that a universe coughed up.
>>
>> I was born with the evidence. I hadn't yet processed that evidence,
>> but at birth, I was human. There was never a point at which I started
>> doing anthropic calculations knowing I was a sentient being, but not
>> that I was human.
>
> But that is the situation with pretty much all the evidence we ever get
> or ever could get. The universe knew it when we were born, but we did
> not know it. If you're going to refuse to consider your priors over
> possibilities that the universe had rejected when you were born, you'll
> have to refuse to consider pretty much all possibilities other than the
> actual state of the universe.
It's not just that the universe knew it, it's that the evidence was
actually embodied in the shape of my mind at birth - that this was a human
mind and not a posthuman one. For there to be priors, evidence, and
posterior, there must actually be a mind that holds the prior, an
encounter with the evidence, and then updating to the posterior. In this
case, you're trying to extrapolate back from before the prior...
Actually, this argument is now disintegrating because I'm trying to phrase
it in a language that I have learned is wrong. Let me try again.
Let's say that we have a doctor, a patient who may or may not have cancer,
and a mammogram. Before the doctor sees the mammogram, we can calibrate
the doctor's pointer state directly by figuring the frequency of that
pointer state next to patients with the environmental fact of cancer.
After the doctor sees the mammogram, we can, if we like, recalibrate the
doctor's pointer state directly by figuring the frequency of that pointer
state next to patients with the environmental fact of cancer. If the
doctor knows the correct probabilities throughout, the relation between
the doctor's calculated probabilities will obey Bayes' Theorem, just as
the actual correlation between the pointer states and the environment
obeys the naturalistic version of Bayes' Theorem.
In other words, we have the interesting fact that the calibration of
pointer states, as it changes over time, obeys Bayes' Theorem with respect
to environmental correlations borne by incoming evidence. This is why
Bayes' Theorem works. Or to put it another way, this is a naturalistic
description of the fact that Bayes' Theorem works.
It looks to me like you're trying to extrapolate back my pointer state to
a prior that I never actually had, that is poorly defined (what is the set
of observers?), and where many of the members of the so-called "reference
class" may not yet exist, or may not exist at all, or may exist or not
exist depending on present-day choices. Why should I extrapolate back to
this prior I never had, to this non-naturalistic object, especially if it
is ill-defined? Why not calibrate the pointer state directly?
Each time you recalibrate the pointer state from scratch, you should
arrive at an answer consistent with applying Bayes' Theorem to past actual
pointer states - otherwise you haven't been a good rationalist, and the
Fairy of Doubt won't bring you any new evidence for Newtonmas. But this
doesn't mean you can extrapolate back before there were any pointer
states, by subtracting evidence that already calibrated your pointer state
at the moment you booted up, to get a "pre-boot-up" pointer state. Not
surprisingly, such "What were your priors before you were born?" questions
are often ill-defined, and so they often give ill-defined answers. Asking
whether pointer state recalibrations obey Bayes' Theorem when they are
extrapolated backward in time to before my birth strikes me as an
unnaturalistic thing to do. Should I really give a hoot whether I was a
good Bayesian before I actually existed? Yes, if you give a
*well-defined* reference class of "pointer states that don't point to
anything yet", you will get the Self-Indication Assumption on that
reference class, followed by the Doomsday Argument to whatever your
pointer state actually says. But so what?
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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