Tom Caylor writes:
> I disagree.  How can the worm apply a probability distribution over 
> things that he knows nothing of, such as trees, people, and evolution?  

The same way that we can reason about things we know nothing of, such
as blinkers, puffer trains, glider guns and other objects in Conway's
Life universe.  It is all a matter of pure logic.  In our case we
need computers to help us think clearly, but all of these objects are
implicit in mathematics and logic.  Trees, people and evolution are
equally implicit in their existence.  Mathematical/logical reasoning
will allow the worm to conceive of our universe, as well as all others.

> Using the Wormopic Principle, when the worm proclaims that, "The 
> universe is just complex enough to produce and sustain such a worm as 
> I, and the inside of an apple," how can he be meaning anything (in his 
> own mind, mind you, since explanatory power refers to being able to 
> explain the universe to him) that even remotely resembles our universe? 

It is as I explained: the worm can conceive of all universes that might
include him and the apple, because they are all part of the multiverse.
And then the judgement about which universe is more complex may not come
out in the way you expect.  As I explained before, there is a sense in
which our universe may actually be simpler than one which consists of
just an apple and worm.

>   (As an aside, as much as we know about our universe, we totally cannot 
> rule out the possibility that a worm that understands "sufficient 
> mathematics" actually exists in our universe!)  Instead, even if he 
> developed the in-apple technology to explore quantum mechanics and DNA, 
> he might come up with a quantum theory similar to ours (but who knows 
> the probability of that?!!), but he would likely come up with a very 
> weird theory of how his DNA was formed, having nothing to do with how 
> it actually was formed (according to our theories).

We are assuming (or at least I am) a hypothetical worm who is very smart
indeed, one who is able to come up with all possible mathematical/logical/
computational systems and identify which ones are consistent with his
experiences.  Among those will be ones that have DNA and QM and all
the other aspects of our physics (or, whatever turns out to be the true
physics of our universe).

Now, maybe there are mathematical systems that have worms
indistinguishable from him but without DNA, without QM, perhaps without
cells.  We might imagine a sort of cartoon of a worm and think that
such a simple sketch would be able to do everything the worm does,
without all the baggage of our universe.

Yet on further thought it is clear that this cartoon worm is not logically
possible.  How does he think, how does his digestion operate, what are
the details about how he is able to move?  We will have to equip this worm
with organs, muscles, all the other biological components.  And then, how
do they work?  Why must he eat a certain amount, what about water and air?
By the time you explain all that in full detail, you will need something
with the complexity of our own biological systems.  I suspect you will
need the complexity of DNA.  And then, how does DNA work?  Won't that lead
to atoms?  Atoms are unstable without QM, so we need something like that.
And then, what are the atoms made of, and the sub-atomic particles?

We don't know the answer to that last step yet, but presumably we will
find a way to get down to pure mathematics.  I suspect that a worm will
find his way there as well.

The cartoon worm is a fantasy.  A worm who delves deeply enough will need
real physics, not just a gloss which skips over the hard details.

And, to reiterate, if in fact there is a mathematical description of a
worm in an apple which is much simpler than our universe, and still is
consistent with the worm's experiences, then he is right to assume that is
where he lives.  Most worms will in fact live in such universes, and not
in ones like ours, if this turns out to be true (which I rather doubt).

> You make a good point about the complexity of living things.  If you 
> ask biologists and other non-physics scientists about the Theories of 
> Everything, a lot of them would say that we're a long way from it.  
> Roger Trigg, University of Warwick, in his book, Rationality and 
> Science: Can Science Explain Everything?, makes this point.  Also, for 
> instance, the premier biologist Carl Woese, in his recent article, A 
> New Biology For A New Century, calls for biologists to get out of their 
> myopic pursuit of genetically breaking things down into the smallest 
> biological quantum, and to step back and look at the big picture, 
> saying that there are whole levels of complexity that we will totally 
> miss if we don't, resulting in being totally disabled in being able to 
> explain everything in biology (to our satisfaction).

I don't see the relevance.  Scientists of all stripes may find it useful
to work at higher or lower levels of abstraction.  That doesn't change
the fact that it must all be grounded somewhere.

> I should make another point, that it seems very likely that the worm 
> has no way of developing the in-apple technology to find out about 
> quantum mechanics or DNA.  This emphasizes the fact that we, with our 
> quantum theories, M-theories, and loop gravity etc. could be just as 
> far away from explaining the universe as the worm is.

It is true that we have created our physical theories based largely on
experimentation with devices that could hardly be constructed by a worm in
an apple.  Yet I think most physicists would agree that there is no real
alternative for describing even the ordinary, everyday universe based
on simpler theories.  As I described in the worm case, to really have a
theory of biology we need cells; and to have a theory of cells we need
atoms and molecules; and to have a theory of atoms and molecules we need
subatomic particles; and we still need a theory of subatomic particles.

Even though historically it did not work this way, in principle I
believe that our common observations of the world are enough to deduce
the laws of physics.  At least, I am not aware of any alternative physics
which would work and explain the commonplace world in great detail and
precision, even if we leave out radioactivity and observations with
microscope and telescope.

So contrary to Quentin's point about Plato's allegory of the cave, I
believe that even people in that situation, if they were intelligent
enough, would be able to deduce the nature of the universe they were

Hal Finney

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