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.
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 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.
The universe that is described by an infinite string of zeroes differs from the universe that is described by the empty string in what manner?