
A Brief Explanation of Greg Egan’s Dust Theory - 43t344efsg
https://cephalopods.blog/2020/08/14/a-brief-explanation-of-egans-dust-theory/
======
sxp
This article doesn't actually _explain_ Dust Theory to someone who hasn't read
the book. I haven't found a good standalone explanation of the theory that
explains it in a compact manner so my recommendation to people is to read the
book.

Permutation City is among my top 5 favorite books because I found Dust Theory
so mind blowingly amazing from a philosophical standpoint. I haven't seen it
discussed elsewhere outside the lesswrong.com forums (which are famous for
creating Roko's Basilisk). It's only $3 on Amazon so it's worth picking up if
you're a fan of hard sci-fi that gets into the philosophy of uploading:
[https://www.amazon.com/Permutation-City-Greg-Egan-
ebook/dp/B...](https://www.amazon.com/Permutation-City-Greg-Egan-
ebook/dp/B00FDWCPV2)

Dust Theory also provides an interesting option for people who want to achieve
True Immortality. That is, immortality that can survive the heat death of the
universe without violating the First or Second Laws of Thermodynamics. It also
provides a hard sci-fi version of the concept of Subliming from Iain Banks'
Culture novels where a civilization leaves this universe once they become
sufficiently advanced. (Sublimation in the Culture books is similar to
Ascension in the Stargate universe or Transcendence in Babylon 5.)

~~~
3pt14159
Almost a decade ago I independently invented the same idea. Discussion was
here:

[https://news.ycombinator.com/item?id=2727750](https://news.ycombinator.com/item?id=2727750)

It's a pretty simple theory, which I ultimately reject even to this day. If it
were true, however, the expanse of existence is truly terrifying.

This theory leads to any possible existence existing, short of maybe self-
contradiction[0]. Well, so if that is true, then there exists a relation of
beings where one of the beings is both powerful and has motives that are
purely antithetical to the others. Think "I Have No Mouth, and I Must Scream"
kinda bad, only armed with Knuth's up notation and applied to pain and
suffering. A hell that's truly beyond comprehension.

If this theory is correct, then all beings eventually find themselves in this
hell. Note that this isn't argumentum ad consequentiam. I'm not saying that
since this is such a horrific outcome that it's clearly false. I'm saying that
_if_ it is true, it is a horror beyond all horrors.

Though I suppose there is always a chance that a being that found themself in
such a situation could always randomly pop out into some other, better
existence by sheer chance.

Thinking about it is useful, but ultimately there are too many degrees of
freedom to come to any practical conclusions.

[0] An existence arising that stops the existence of the vast randomness
leading to all existences, for example.

~~~
jbotz
> This theory leads to any possible existence existing, [...]

This statement maybe superficially correct, but I interpret it differently.
Every _possible_ existence may exist, but not every _imaginable_ existence.
For something to exist in this manner, it has to be possible to generate it in
a logically consistent manner from some initial conditions and simple rules,
and while that allows for a "terrifying expanse of existences" we can't say
which imagninable existences can actually be thus generated, any more than you
can look at a random jumble of dots and say whether those could have been
generated by one of Wolfram's one-dimensional automata without generating all
possible patterns from those automata and seeing if one matches.

The fact that you can imagine a hell beyond all horrors is not proof that any
world-generating automaton would ever generate it... even in an infinite
Universe it may not actually be a "possible existence".

Infinity != Everything.

~~~
Reelin
> Infinity != Everything

More precisely, infinite sets come in different sizes. For example, there are
provably more real numbers than natural numbers even though both sets are
infinitely large.
([https://en.wikipedia.org/wiki/Aleph_number](https://en.wikipedia.org/wiki/Aleph_number))

~~~
a1369209993
I think their point is more along the lines of "there are infinitely many
(real or rational) numbers between zero and one, but none of them are equal to
two".

------
canjobear
Very interesting to think about. Here's my interpretation of the argument:
Suppose you have some system X whose dynamics are those of conscious agents in
a world. For example, maybe X is the real world. Suppose that the agents in X
really experience consciousness. Now suppose we apply some one-to-one function
f to X, yielding Y = f(X). Then Y contains all the same information as X. So
who's to say that the agents in X have consciousness but the agents in Y
don't? Now by an inverse argument, suppose you randomly encounter some blob of
random dust, Z. Then you can always come up with a one-to-one function g
mapping Z to X, X = g(Z). So apparently the dust Z already contained all the
conscious agents in the universe. Conclusion: The conscious experiences of all
agents are present in all sufficiently complex blobs of random dust and all
sufficiently complex networks of mathematical relations.

One issue with this argument that hasn't been brought up yet is Kolmogorov
complexity. Must random blobs of dust Z will be algorithmically random, not
containing any real structure. In that case, the complexity of the function g
that decodes Z into X will have to be huge. Essentially, the decoding function
g itself will have to contain all the information that eventually ends up in
X. So the information about conscious agents isn't really in the dust Z, it's
in the decoder g.

~~~
ajconway
If you believe in mathematical realism than the fact that there surely exists
a mapping between a random set of data and a simulation with conscious agents
in it, that should be enough.

~~~
chr1
It's not enough if the mapping function does not use the information from the
random set. For instance it is easy to construct a mapping from ordered digits
of pi to ordered letters of your comment, but all of the information of your
comment will be in the mapping.

~~~
ajconway
I believe the argument goes like this: assume that conscious agents can be
simulated (that is, consciousness is computable). What is computation? If
sudden wind arranges leaves on the ground into a pattern that looks like “2 +
2 = 4”, was there a computation? We would usually answer “no”, as computation,
like many other things, requires causal connection. But Greg Egan states that
“there is nothing more to causality than the correlations between states”.

Now, a deterministic simulation can be represented as a series of states
recorded on a medium. Then you, an observer, can rewind and inspect what’s
going on there, similar to reading a book or watching a movie. But the
inhabitants of the simulation couldn’t care less about you observing their
states. They already “exist”. In that case, why do we need the states of the
simulation be recorded on the “film” in the order that makes sense for an
outside observer? Surely a random arrangement would not affect the
“simulation”. The same goes for the encoding.

Now, if the arrangement doesn’t matter, and the encoding doesn’t matter, why
there needs to be a specific physical medium at all? Surely somewhere in the
Universe you can find arrangements of “dust” that “encode” the same states (in
no particular order).

~~~
chr1
What does “encode” mean here? If it is supposed to contain the whole state in
one chunk, the space of possible deterministic algorithms is too huge compared
to the amount of dust, so it can't contain that. If it is supposed to find
small chunks and rearrange them, it will not be using any information from the
dust, and with same success encoder could use just any set of 0s and 1s. To
circumvent finiteness of dust One could use digits of an irrational number or
simple counting, but that is a very strange definition of existence. By that
logic every possible history is just a number, so everything exists. The
Important question is how to construct these numbers, find them in the sea of
other meaningless numbers.

I think Stephen Wolfram's idea of computational irreducibility is very useful
here. It says that most computations (even very simple systems like some of
cellular automata) cannot be replaced by other computations, and even to
verify that a number represents result of a computation, one have to carry out
that same computation. So the part of the book where states of the simulation
are computed out of order is simply wrong, the latter state of the simulation
could not have been computed without computing the intermediate states, and
all the methods of computing that state were equivalent to the person living
through that interval of time.

~~~
ajconway
You are still talking about mapping the simulation to a representation that
will make sense to you.

The episode that I found fascinating to think about is when a simulated
character reflects on his existence: “And if the computations behind all this
had been performed over millennia, by people flicking abacus beads, would he
have felt exactly the same? It was outrageous to admit it-but the answer had
to be yes.”

It looks like the physical medium and the representation do not matter to the
simulation, as long as computation occurs. Then the question is, what is
computation. If you believe that all digits of Pi exist, then every possible
computation should also exist.

We don’t usually believe that. It seems that information in our universe
cannot exist without some physical medium.

The out of order computation was added to the story to make it more dramatic,
the author states.

~~~
chr1
>You are still talking about mapping the simulation to a representation that
will make sense to you.

I am talking about mapping that will make sense to anybody at all, be that
inside or outside the simulation. If such mapping cannot be constructed, then
how can we state that information about these computations exists in dust?

The part about abacus is very good, but it is also very different from dust
theory, since with abacus there is a process of computation, states are
obtained one from another sequentially, and the positions of abacus beads are
not random. In the case of dust the information about the simulation is
clearly not contained in the dust, so it's unclear how dust can cause the
simulation to exist.

> It seems that information in our universe cannot exist without some physical
> medium

isn't that simply due to the definition of the word exist?

------
KerrickStaley
Here is an explanation of Dust Theory from Wikipedia:

"[Dust theory states that] there is no difference, even in principle, between
physics and mathematics, and that all mathematically possible structures
exist, among them our physics and therefore our spacetime...The dust theory
implies that all possible universes exist and are equally real, emerging
spontaneously from their own mathematical self-consistency."

I think this does a pretty good job of summarizing the concept: the universe
is simulatable, but there is nothing doing the simulation; it just exists as a
pure mathematical object. All other possible universes that are simulatable
(i.e. follow some mathematical model) are equally as real as ours.

~~~
pbhjpbhj
Not familiar with the concept, but how does it square with Godels
Incompleteness theory, is any mathematical universe even possible?

~~~
a1369209993
The closest GIT gets to being relevant is that some mathematical universes
exist (or 'exist') that cannot be proven to exist. Alternatively - since
Godel's Incompleteness Theorm is the same thing thing as the Halting Problem -
some simulations that can't be proven valid (ie that each step of the
simulation halts) are nonetheless valid.

------
aaron-santos
The article really ought to close the loop by tying it back to the final 10%
of the book. The big point in the book is that you can craft arbitrary
surjections and have an infinite set of justifications for your subjective
experience. A physical substrate is just as good as a
computational/mathematical substrate. In this sense you can bootstrap your
simulated existence into the immortal world of forms.

~~~
croissants
The part I don't understand about this, which is the same as the part I don't
understand about dust theory, is that it seems to ignore the distinction
between an abstract representation of an object and the object itself.

By the logic of dust theory, I can walk into a bank and say "give me the
money, or else I'll throw this handful of sand into the air, and it might
encode a universe where you're tortured for a billion years!"

~~~
aaron-santos
You're right. To which the teller can reply, "I've crafted an encoding where
you are tortured for billions of years."

The idea is more about swapping out the substrate of your current subjective
experience than creating a new encoding of your current universe. The book has
the convient liberty of actually jumping between simulations/encodings to
illustrate this, but it's ancillary to the main idea.

------
yourkin
Greg Egan is definitely in the list of authors with the most radically hard
science fiction ideas, even more extravagant than those I found in Alfred
Bester books.

Speaking of the Dust Theory, this looks very close to concept as Max Tegmark's
Mathematical universe hypothesis:
[https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...](https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis)

Tegmark's book goes over it in a very readable way:
[https://www.amazon.de/Our-Mathematical-Universe-Ultimate-
Rea...](https://www.amazon.de/Our-Mathematical-Universe-Ultimate-
Reality/dp/0241954630)

------
maxs
Greg Egan is my favorite author. My favorite book of his is Diaspora.

If you loved Permutation City you may also love Diaspora. The first chapter of
Diaspora is brilliant, if you try reading it, and find that you enjoy it, you
will then like the whole book.

~~~
_jal
Thumbs up for Diaspora, that's probably my favorite of his.

If anyone wants to sample him first, if you like the short stories on his
website, you'll almost certainly like his books.

[https://www.gregegan.net/BIBLIOGRAPHY/Online.html](https://www.gregegan.net/BIBLIOGRAPHY/Online.html)

------
throwaway_pdp09
Looking at other stuff ISTM this is generated by one of them newfangled GPT3
things or whatever:

"Nonetheless, It is because of my faith in science and its processes that I
have always been of the opinion that the state pension, though grisly from a
naive “one-worlder” perspective is actually a remarkably humane, efficient and
(dare I say) generous social program."

([https://cephalopods.blog/](https://cephalopods.blog/))

and if you look at the home link
[https://cephalopods.blog/about/](https://cephalopods.blog/about/) anyone else
think that looks like a generated face?

~~~
codethief
> and if you look at the home link
> [https://cephalopods.blog/about/](https://cephalopods.blog/about/) anyone
> else think that looks like a generated face?

More importantly, it's a new face every time you reload the page.

~~~
throwaway_pdp09
So it is! Well spotted. I think you've proven it.

~~~
codethief
Not sure I'd consider this a proof. Maybe it's just some weird dude :)

------
codethief
He lost me right in the second paragraph:

> Because computation is sort of subjective, just a set of relations that can
> be usefully interpreted as representing a function, this seems to imply that
> the function you identify with can be interpreted as being simulated by any
> sufficiently complex set of relations.

Can anyone explain? I'm already struggling with the premise: Why should
computation be subjective in the first place?

~~~
vladTheInhaler
If I understand correctly, it's not that the computation itself is subjective,
but that the interpretation of the results is. Like how things are represented
in lambda calculus - is this _really_ an integer, or is it just a blob of
function applications that has an interpretation _consistent_ with being an
integer? That part is subjective. Edit: to be more explicit, the parallel is
"is that _really_ a mind, or is it just a blob of molecules that has an
interpretation _consistent_ with being a mind?"

~~~
goldenkey
The Model vs The Map

~~~
davidivadavid
Syntax vs semantics?

------
tomrod
Interesting article!

As linked in the article, Egan posted some FAQ/counterarguments for issues
raised here:
[https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html](https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html)

~~~
croissants
Nice, IMO this (short) FAQ has a lot more useful info than the featured
article. His claim at the end that creating intelligent life through evolution
is deeply immoral confuses me, though -- by all accounts, _we_ arose through
that process, and relatively few people seem bothered by it.

~~~
codeulike
He means that deliberately setting up a synthetic evolution process to
generate intelligent life would be immoral.

His short story Crystal Nights deals with this. Its a corker of a story.

[https://www.gregegan.net/MISC/CRYSTAL/Crystal.html](https://www.gregegan.net/MISC/CRYSTAL/Crystal.html)

 _“What created the only example of consciousness we know of?” Daniel asked.

“Evolution.”

“Exactly. But I don’t want to wait three billion years, so I need to make the
selection process a great deal more refined, and the sources of variation more
targeted.”

Julie digested this. “You want to try to evolve true AI? Conscious, human-
level AI?”

“Yes.” Daniel saw her mouth tightening, saw her struggling to measure her
words before speaking.

“With respect,” she said, “I don’t think you’ve thought that through.”

“On the contrary,” Daniel assured her. “I’ve been planning this for twenty
years.”

“Evolution,” she said, “is about failure and death. Do you have any idea how
many sentient creatures lived and died along the way to Homo sapiens? How much
suffering was involved?”_

------
mdoms
Greg Egan is truly one of the most creative minds on the planet. He has a book
called Dichronaughts that's set in a universe with 2 space and 2 time-like
dimensions. It's very hard to get your head around but the result is a
universe with a hyperbolic geometry where movement on one axis implies
changing your shape entirely.

------
finm
This reminds me of David Chalmers' 'Does a Rock Implement Every Finite-State
Automaton'?
[http://consc.net/papers/rock.html](http://consc.net/papers/rock.html)

------
j-pb
I don't know the original theory, but this explanation is brief to the point
where it's nonsensical.

~~~
boxed
Might be because the entire thing is nonsense. Entropy shoots a hole in the
entire thing as far as I can tell. The problem is that the information can
never be retrieved, so if it exists or not is really pointless.

~~~
xwdv
If you _are_ the information though then you have retrieved it.

~~~
boxed
Not really. Brains don't exist and cannot exist without a medium to work in.
It's the old idea that we have souls that are independent from our bodies and
underlying reality. This is nonsense.

------
hgibbs
Well yes, you could construe any physical object as having conciousness by
having a sufficiently detailed/complex schema that assigns 'meanings' to each
of its states.

But we all agree a rock is not conscious, so this definition doesn't pass the
common sense test.

One mistake is then claiming that this usage of the word conciousness can be
substituted for the commonplace usage in all situations. E.g. why don't we
feel the same ethical obligation to a potentially conscious rock that we do to
animals, humans and, arguably, seemingly intelligent entities?

For a nice exposition of this one can read chapter 2 of Gary Drescher's book
'good and real'.

------
domenicd
A while ago I wrote up my own take, inspired largely by Permutation City but
also by Tegmark's mathematical universe hypothesis:
[https://blog.domenic.me/mathematical-
consciousness/](https://blog.domenic.me/mathematical-consciousness/)

To me this line of thinking is very attractive. As someone who has been a
mathematical Platonist forever, this gives a very satisfying answer to big
questions like "why is there something instead of nothing" and "why is our
universe so perfectly described by mathematics".

~~~
GeekyBear
> Permutation City

I haven't read that book since the early 90's but it dealt with ideas that
have really stuck in my mind.

~~~
croissants
The main detail I remember from that book is that credit card companies would
track whoever you dined with at a restaurant and then serve you ads featuring
computer-generated people who resembled those people to manipulate you into
trust. Pretty ahead of its time for 1994!

~~~
GeekyBear
At the time, using computational chemistry to simulate an entire living,
evolving life form was just a mind blowing idea.

------
idlewords
There's a philosophical literature on this, which is also known as the
"dancing with pixies" argument.

See: [https://www.consciousentities.com/2009/07/dancing-
pixies/](https://www.consciousentities.com/2009/07/dancing-pixies/)

And:
[http://www.doc.gold.ac.uk/~mas02mb/Selected%20Papers/2009%20...](http://www.doc.gold.ac.uk/~mas02mb/Selected%20Papers/2009%20Cognitive%20Computing.pdf)

------
MiroF
> This is sort of like the Boltzmann brain idea but even worse because it
> applies to any set of relations. According to Egan’s argument all possible
> experiences that can be computed by any sufficiently complex set of
> relations are in fact computed by them.

This idea seems identical to the Boltzmann brain hypothesis and I don't
understand how this paragraph differentiates it at all.

~~~
ardy42
>> This is sort of like the Boltzmann brain idea but even worse because it
applies to any set of relations. According to Egan’s argument all possible
experiences that can be computed by any sufficiently complex set of relations
are in fact computed by them.

> This idea seems identical to the Boltzmann brain hypothesis and I don't
> understand how this paragraph differentiates it at all.

I don't claim to totally understand this, but my impression is "Dust Theory"
implies that the mind is more frequently simulated than in "Boltzmann brain"
theory. IIRC, the latter imagines a literally brain being formed briefly out
of matter.

~~~
MiroF
> IIRC, the latter imagines a literally brain being formed briefly out of
> matter.

I see. FWIW I think that is a very narrow reading of the Boltzmann brain
hypothesis and while it may have been true to when it was first presented, I
think the general "brain as abstract relations that can be simulated by
physical systems" Boltzmann brain is what most contemporary cosmologists are
talking about.

------
scarmig
I've not read the book, but I'm trying to digest this. For someone who has a
good grasp of Dust Theory, if you answer from its perspective...

1) Does believing that consciousness is simulateable commit you to thinking of
consciousness as a purely mathematical object, apart from any physical process
it might model?

2) If the universe were just an infinite space filled with dust in a wild zoo
of different configurations, does my consciousness exist in it so long you can
find a dust configuration that admits a mathematical representation that's
isomorphic to the one representing my "real" consciousness?

3) How does complexity fit into this? If the entirety of the universe were a
single static point particle, would consciousness still fall out of it? It
seems as if it could, if you had a sufficiently complicated encoding scheme.

~~~
namanyayg
1\. Yes, what physical processes? It's just signals.

2\. I can postulate that to be true, but unless I have hard proof I cannot say
it to be true. If that isomorphic consciousness finds _itself_ to have a
subjective experience... Then it knows that dust theory exist, no one else
does.

3\. I do not understand this question

------
xwdv
I think I can somewhat grasp what is being explained but maybe not really.

As a thought experiment, if you had a screen of fixed resolution that
displayed random color pixels, given an infinite amount of time, you could
watch an entire specific movie (along with every other image), perhaps in
random order, but from the movie's perspective if it were conscious it would
not be aware of whatever order it's playing in, it would just perceive itself
to be going forward I guess. The movie itself is like a function that displays
an image as a function of time.

So I guess they're saying consciousness in Dust Theory could be like that?
What we perceive as a conscious moment is a brief output of random noise for a
random timestamp?

------
dvt
The problem with these kinds of theories (eternal recurrence, random quantum
state fluctuations, simulation):

\- There are plenty of things that aren't computable that our universe seems
to do just fine (entropy being one)

\- The universe seems to be intelligible, especially w.r.t. its causal chain
-- if we only _happen_ to be conscious in these very specific instants (where
we have intelligibility, causality, etc.), the question is _why_?

At the end of the day, you end up with some kind of Maxwell's demon type of
situation where there's all this trickery that needs to happen to support a
theory where we're in a simulation or Boltzmann brains.

------
garmaine
> If you think experience is simulatable, you buy computational or
> “patternist” theories of identity, there are some very strange implications
> that are not commonly brought up.

Maybe the sentence isn't worded correctly, but these are two entirely
different claims. It's relatively simple and straightforward to argue that
one's experience is simulatable, but that identity lies in the instance of the
simulation itself, so a copy of a simulation would be a different being. That
two machines running the same computational process represent the _same_
entity is a separate, unverifiable claim.

------
mcguire
" _That is, for any random set of relations with enough complexity to
represent a human mind, Egan claims, there exists an exotic encoding scheme
that can interpret this set of relations as representing any arbitrary
function, including the function that you would call “I”._ "

"There exists an X" is significantly different as a statement from "This X"
(or "All X", for that matter).

Since I assume that solipsism is a fallicy, I don't find this philosophical
position all that useful.

------
visarga
> In fact, even if you imagine a static set of relations that do not evolve in
> time there still exists encoding schemes that can interpret this set of
> relations as any arbitrary function, so in some sense the set of
> mathematical objects that represent “you” and “me” and all possible minds
> can be said to exist in these timeless relations.

The argument fails because "you" and "me" are processes, embodied agents while
the interpretations of data are "virtual".

------
nkingsy
Just finished Diaspora. It made me feel rather stupid, as the analogies it
weaves throughout (as way to dumb it down I suppose) were sort of like reading
the cliff notes. Okay 6 dimensions, ok 12 sure. And this one is 5 dimensions
but they’re all sort of visible or something. But really it’s infinite
dimensions and all that science proofing I skimmed was wrong. Great.

I did love the artificial mind part in the beginning. Is this book a deeper
dive on that?

~~~
askvictor
All of Egan's books make me feel stupid, but in the best possible way :) I
always feel I'm getting half the picture but would need a PhD in whatever
speciality he's focussing on in this book to get the whole thing, yet
thoroughly enjoy every book all the same.

Permutation City is something of a different take on the artificial mind to
Diaspora. Schild's Ladder deals also has the artificial mind theme, perhaps a
bit closer to Diaspora, but with it's own take again.

------
guscost
All formal systems are incomplete or inconsistent. There is zero evidence that
the universe is either.

~~~
drdeca
There is a difference between a mathematical object and a formal system.
Surely you would not call a differential equation with a given initial
condition describing a simple harmonic oscillator along with an initial
condition “inconsistent”. Would you call it incomplete? Doing so would seem
rather odd seeing as there is exactly one solution (given the initial
condition). And the sense of “incomplete” that the incompleteness theorems are
about doesn’t apply to this. I don’t just mean that it isn’t true of it. I
mean that it is not an applicable idea. It is like asking what the
northernmost point of the color blue is.

People should be careful when trying to apply Gödel’s incompleteness theorems
to philosophical questions, as people often do so without really understanding
what they say, and, importantly, what they do not say.

Something that may help is to familiarize oneself with Gödel’s _completeness_
theorem.

~~~
guscost
> Surely you would not call a differential equation with a given initial
> condition describing a simple harmonic oscillator along with an initial
> condition “inconsistent”.

No, certainly not.

> Would you call it incomplete?

Yes, absolutely. There is no such thing as a harmonic oscillator that exactly
follows an equation like that. Show me one. Either the formal system has
nothing to do with the real world, or it is an incomplete approximation of it.
All other known physical theories are the same way.

Can even a part of the universe be described completely by _any_ (incomplete)
formal system? Is it even meaningful to talk about a “part” of the universe in
this sense? Well, there’s exactly zero evidence either way. That’s what I’m
implying when I say “the universe may not be incomplete.”

~~~
drdeca
> Either the formal system has nothing to do with the real world, or it is an
> incomplete approximation of it.

Ok, but this is a totally separate meaning of “incomplete” than what the
incompleteness theorems are talking about.

So, if that is what you meant by “incomplete” in your original comment, you
should know that your comment looked like it was appealing to Gödel’s
incompleteness theorems, which do not deal with that sense of “completeness”.

~~~
guscost
Added some clarification - Yes, the incompleteness theorems only concern the
behavior of mathematical/formal systems themselves. But to me it seems
perfectly reasonable that correspondingly, there may be features of the
universe ("true statements") that cannot be modeled ("proven") by any given
physical theory ("formal system"). I cannot prove this, but nobody can prove
the opposite belief, either.

------
josh_fyi
I'd like to see more of this. Egan's work got more mathematical and harder to
understand as the years went by.

Not that I'd want him to dumb it down, but explanations are appreciated.

------
layoutIfNeeded
[https://xkcd.com/505/](https://xkcd.com/505/)

------
saeranv
Dust theory is cool, but I really, really wish someone could simplify and
explain the world of Egan's Dichronauts to me.

------
geuis
I’ll take this one. Can someone provide some background as to exactly what is
being discussed here?

~~~
db48x
A major plot point and thematic element from a novel by Greg Egan called
Permutation City.

~~~
Flow
Would you consider this to be a spoiler for the book? I've not read my copy
yet.

~~~
db48x
You probably won't understand this brief "explanation" until after you read
the book. It's brief largely because it assumes that you know at least the
events in the book, even if you couldn't follow the definitions and other
exposition.

------
sfink
tl;dr - I am possible, therefore I am.

