We can't tell we're in the all-zero universe by examining any finite number of bits.
What does it mean for the all-zero universe to be infinite, as opposed to not being infinite? Finite universes have a finite number of bits of information describing them (This doesn't actually negate the point that uncomputable utility functions exist, merely that utility functions that care whether they are in a mostly-empty vs perfectly empty universe are a weak example.
These preferences are required to be coherent with breaking things up into sums, so
Ultimately, I am advocating a logical-induction like treatment of this kind of
thing.
* Initial values are based on a kind of "prior" -- a distribution of money
across traders.
* Values are initially inconsistent (indeed, they're always somewhat
inconsistent), but, become more consistent over time as a result of traders
correcting inconsistencies. The traders who are better at this get more
money, while the chronically inconsistent traders lose money and eventually
don't have influence any more.
* Evidence of all sorts can come into the system, at any time. The system might
suddenly get information about the utility of some hypothetical example, or a
logical proposition about utility, whatever. It can be arbitrarily difficult
to connect this evidence to practical cases. However, the traders work to
reduce inconsistencies throughout the whole system, and therefore, evidence
gets propagated more or less as well as it can be.
2Abram Demski3y
What it means here is precisely that it is described by an infinite number of
bits -- specifically, an infinite number of zeros!
Granted, we could try to reorganize the way we describe the universe so that we
have a short code for that world, rather than an infinitely long one. This
becomes a fairly subtle issue. I will say a couple of things:
First, it seems to me like the reductionist may want to object to such a
reorganization. In the reductive view, it is important that there is a special
description of the universe, in which we have isolated the actual basic facts of
reality -- things resembling particle position and momentum, or what-have-you.
Second, I challenge you to propose a description language which (a) makes the
procrastination example computable, (b) maps all worlds onto a description, and
(c) does not create any invalid input tapes.
For example, I can make a modified universe-description in which the first bit
is '1' if the button ever gets pressed. The rest of the description remains as
before, placing a '1' at time-steps when the button is pressed (but offset by
one place, to allow for the extra initial bit). So seeing '0' right away tells
me I'm in the button-never-pressed world; it now has a 1-bit description, rather
than an infinite-bit description. HOWEVER, this description language includes a
description which does not correspond to any world, and is therefore invalid:
the string which starts with '1' but then contains only zeros forever.
This issue has a variety of potential replies/implications -- I'm not saying the
situation is clear. I didn't get into this kind of thing in the post because it
seems like there are just too many things to say about it, with no totally clear
path.
What does it mean for the all-zero universe to be infinite, as opposed to not being infinite? Finite universes have a finite number of bits of information describing them (This doesn't actually negate the point that uncomputable utility functions exist, merely that utility functions that care whether they are in a mostly-empty vs perfectly empty universe are a weak example.
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