
When does a physical system compute? - yiransheng
http://arxiv.org/abs/1309.7979
======
j2kun
I don't see what this paper is contributing other than the assertion that a
physical system needs to functorially agree with the mathematical model that
represents it. And that if that model is Turing complete, or represents some
useful subset of computational functionality, then the physical system
"computes." The fact that a sitting rock does nothing but sit is a perfectly
fine, albeit severely limited, computational system (it even satisfies their
definition of a computing physical system!). All of this just seems...obvious.

It looks like their definitions are so general that they don't answer their
own questions, which by their main motivations (section XI) are fundamentally
problems of construction and scale. It's not enough that there exists a theory
that proves your physical system computes, you have to know the representation
explicitly and be able to scale the system arbitrarily. [Edit:] The problem
being that this doesn't show up in their actual definitions.

Maybe I'm reading it too shallowly, though. Can someone who's more well-versed
in the background of this paper explain it better? It also doesn't help my
confidence that they seem to completely ignore the rest of computer science
(mentioning Turing machines only as an aside, and as part of a false assertion
about (quantum) Turing machines being the only universal logical systems).

~~~
danbruc
_The fact that a sitting rock does nothing but sit is a perfectly fine, albeit
severely limited, computational system (it even satisfies their definition of
a computing physical system!)._

It does not fit their definition because the whole point of the paper is that
a physical system is not computing anything unless an entity is using the
system to compute something by encoding the problem into the state of the
system and later decoding the answer from the state of the system.

~~~
j2kun
I'd like to compute the identity function. Let me denote by 1 the presence of
a rock, and 0 the absence of a rock. I'll set up the problem (the input) by
placing a rock appropriately, and after ten seconds, I'll check to see the if
a rock is present. If so, the output is 1, otherwise it is 0.

This is a theory, a valid interpretation, highly reliable, scales well, and it
commutes. Why isn't it a computation by their definition?

~~~
danbruc
Now it is a computation because you are the computing entity that encoded a
problem into the system and later decoded the answer. They paper essentially
establishes the distinction of a system just evolving under the laws of
physics and using this evolution to compute something by assigning an
interpretation to the state of the system. I could use the same stone to
compute something different, for example the boring trajectory of a stone
placed on a surface in a gravitational field, but without specifying what you
are computing the stone is not computing anything.

~~~
j2kun
This seems more philosophical than scientific. How can you use such a
distinction to do anything new and useful?

------
wfn
Two somewhat-related-pointers for people who decide that they're curious about
these things:

* a light and nice read: [https://www.frc.ri.cmu.edu/~hpm/project.archive/general.arti...](https://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1998/SimConEx.98.html) (an oft-cited article)

* the madness of Max Tegmark: [http://arxiv.org/abs/grqc/9704009](http://arxiv.org/abs/grqc/9704009) , [http://arxiv.org/abs/0704.0646](http://arxiv.org/abs/0704.0646) (cliff's notes: "The [...] postulate in this theory is that all structures that exist mathematically exist also physically, by which we mean that in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically ``real'' world." Which means: take [http://xkcd.com/505/](http://xkcd.com/505/) , and abstract it enough times so that you decide that the rocks themselves _are not needed anymore_.)

-> if anyone has any comments about the MUH, would be interested to hear them. My head is kinda-still-aching from the last time I tried to decide how seriously I should take his ideas.

~~~
picomancer
Wow. This is epic. I totally had this exact idea a few years ago -- that every
mathematically possible universe physically exists, with some probability
distribution. I was thinking maybe the probability of finding yourself in a
given universe is related to the length of the computer program that runs that
universe. And also, of course, to the probability of intelligent life evolving
in that universe (a formalization of the anthropic principle).

It's always neat when you discover you've independently invented an idea
proposed by someone famous :)

Although, to be fair to Tegmark, he goes further than I ever did: "The
predictions of the theory take the form of probability distributions for the
outcome of experiments, which makes it testable." This is a natural
consequence of the form of the theory, but I didn't really think in that
direction -- but now that Tegmark's pointed it out, it seems like an obvious
direction in hindsight.

~~~
wfn
I totally know what you mean!

I've been recommending this book left and right around these parts, but can't
hurt to say it again: you should probably read "Permutation City."[1] As far
as literature, character development and style goes, there is nothing much to
it. As far as (hard-ish) scifi goes, it's a big deal. In a way, what MT calls
MUH Egan calls "dust theory" (roughly). It's a very interesting exploration of
the whole idea, and it involves cellular automata, etc etc.

There's also a short story of his, "Wang's Carpets" (which you can read
online[2]) - it was later incorporated (as a chapter) into his book
"Diaspora"[3] (which is _also_ a great read that I've thoroughly enjoyed.)

> _Although, to be fair to Tegmark, he goes further than I ever did: "The
> predictions of the theory take the form of probability distributions for the
> outcome of experiments, which makes it testable."_

I wonder, though, if this is not a bit of a stretch. I certainly understand
what he (and you) mean by probability distributions, but it seems to be there
because he _really wants_ to be able to call it a "scientific theory," which
requires it to be falsifiable (<=> testable.) But, yeah, it's pretty neat!

> _I was thinking maybe the probability of finding yourself in a given
> universe is related to the length of the computer program that runs that
> universe._

 _Now_ , can some of those programs run a (say, finite-tape-version-of) Turing
machine[4] (can some of them not run it)? Does this have any implications (re:
/ in relation to the halting problem, for example)? I don't have the faintest
idea. Tegmark has a thing to say about mathematically incomplete (in the Godel
sense) universes, but again, I'm not sure how much of it is just him having
fun. ;) (which is the best way of having fun, as far as I'm concerned.)

...anyway. Good stuff! Let's try and not go insane within our heads with these
things. Then again, some insanity is always a _good thing_ , imo.

 _edit_ P.S. there's also [http://plato.stanford.edu/entries/computation-
physicalsystem...](http://plato.stanford.edu/entries/computation-
physicalsystems/)

 _editedit_ P.P.S. if you haven't, maybe also read the (very) short story of
Borges, "The Library of Babel."[5] It's basically an articulation of the idea
that a "description" of a universe _is_ that universe. And a "description" can
very well be thought of as a program. And if you imagine a multidimensional
"computational-symbol-space," a "path" to that program/description (first
choose this symbol/predicate, then that one..) _is_ that program (and, by
extension, "kinda-is" that particular universe.) These ideas are not new in
themselves in the very least. e.g. I'm still yet to try and honestly delve
into Kant's "Critique of Pure Reason," which actually addresses some of that
stuff (in its own very particular vocabulary and context.) Also, lots of stuff
to read from the theoretical CS side of things. And mathematics (Yoneda lemma
in category theory, and other things which I like to pretend to understand!)

[1]:
[http://en.wikipedia.org/wiki/Permutation_City](http://en.wikipedia.org/wiki/Permutation_City)

[2]:
[http://bookre.org/reader?file=222997](http://bookre.org/reader?file=222997)

[3]:
[http://en.wikipedia.org/wiki/Diaspora_(novel)](http://en.wikipedia.org/wiki/Diaspora_\(novel\))

[4]: a good read (and/or rehash) on this:
[http://plato.stanford.edu/entries/turing-
machine/](http://plato.stanford.edu/entries/turing-machine/)

[5]:
[http://jubal.westnet.com/hyperdiscordia/library_of_babel.htm...](http://jubal.westnet.com/hyperdiscordia/library_of_babel.html)

------
kremlin
This is a question I've wondered myself. I once read a bit about someone using
live crabs to perform computations -- a group of crabs behaves
deterministically (enough) to make a series of logic gates that can be used
for (very slow) computations. Since reading that, this has been a question on
my mind.

(source) [http://www.gizmag.com/crab-computer-
kobe/22145/](http://www.gizmag.com/crab-computer-kobe/22145/)

~~~
kremlin
For me, the next natural question is this:

if a brain can be simulated by any turing-complete system with enough memory,
and a bunch of crabs can comprise a turing-complete system...can a bunch of
crabs arranged properly into trillions of logic gates produce consciousness?

~~~
Geee
Yes, they can. And they actually do, in a sense. There was recently a thread
on HN about lots of ants behaving as a one intelligent entity although a
single ant is very dumb:
[https://news.ycombinator.com/item?id=7658551](https://news.ycombinator.com/item?id=7658551)

The discussion 'evolved' into evolution (of systems). It's strange that this
paper discusses computation also as evolution, but I'm not sure if they mean
the same thing. I also suggested that human brain computes (or thinks) by
'simulating' evolution. In this case, your individual brain cells would be
like those bunch of crabs, just doing their business and producing thoughts as
a whole.

~~~
tree_of_item
You seem pretty confident about that; how could you possibly know if a
collection of crabs produces "consciousness"? That's not even the same sort of
thing as ants dropping pheromones, which is trivial to model on a computer.

~~~
mnemonicsloth
You seem pretty confident that _you_ are conscious, but I've seen no
conclusive evidence. How can a person possibly know if a collection of brain
cells produces "consciousness"? What brain cells do is definitely not the same
sort of thing as the inner life of my experience.

------
cessor
In cognitive sciences there is a dispute about the nature of cognition and
what scientific tools to apply. Some say cognition is computation, others say
its just behavior of a dynamic or connectionist system. A good sumary of
aspects can be found in Fresco, Nir, 2012 - The explanatory Role of
Computation in Cognitive Science, Minds & Machines, 22, 353-380.

The discussion is quite interesting, because computation is very hard to
define. Understanding what makes a system compute can yield useful insight for
understanding cognition.

~~~
nmac
I think people like Jerry Fodor define computation as the manipulation of
logical symbols by some algorithm. The idea is that you use a standard
functionalist analysis (see someone like Putnam 67) to analyze the inputs(X)
and outputs(Y) of a cognitive system. So you have (schematically) something
like: X->?->Y. Where the "?" defines the project of cognitive neuroscience
(i.e. figuring out the physical instantiation of the manipulation of
intercalated proteins & neurotransmitter). So, in this picture cognition is
not a "state" that needs to be defined a priori but a "black-box" process that
needs to be spelled out empirically. At bottom, stuff is continuous, not
discrete.

But too much ink gets spilled over this philosophical issue. It seems much
more fruitful to analyze the mind as a Turing machine (contentious) and apply
computational complexity theory to define limits on human computation based on
the hierarchy-- my two cents.

~~~
wfn
Re: Fodor, Folk Psychology, and the Language of Thought hypothesis, obligatory
link to Paul Churchland's retort :)

"Eliminative Materialism and the Propositional Attitudes":
[http://commonsenseatheism.com/wp-
content/uploads/2010/08/Chu...](http://commonsenseatheism.com/wp-
content/uploads/2010/08/Churchland-Eliminative-Materialism-and-Propositional-
Attitudes.pdf)

Basically, a critique of the approach of formalizing thought processes as
(first predicate, or multipredicate, or whatever kind of) logical computation
(of symbols.) It's a good read even if one thinks that the overall debate is
pretty fruitless.

~~~
cessor
Thanks, I'll give it a read! I don't have a definite stance on the topic but I
am aware that a lot of people are making a lot of points on this - indeed -
very philosophical topic. I often lean back and enjoy the discourse, it is
very good entertainment :) I am far away from pointing it out as fruitless but
I can definitely understand why many cog-sci folk would thinks so (often
depending on their background, really). I particularly liked what Tim van
Gelder wrote on dynamicism, although I don't agree with it and he appears to
have a poor view on the connectionist perspective.

~~~
wfn
Hmm, maybe it's high time I gave an honest re-read of
[http://plato.stanford.edu/entries/connectionism/](http://plato.stanford.edu/entries/connectionism/)
\- last time I glanced at it, it gave many sparks and inspiration to delve
deeper into things. And lots of good pointers. So I guess I can recommend
doing the same thing. :)

------
csense
I'm surprised the authors didn't cite the (in)famous "Do Dogs Know Calculus?"
article [1] when they ask whether a "dog catching a stick" is an example of
computation.

[1] PDF link:
[http://www.indiana.edu/~jkkteach/Q550](http://www.indiana.edu/~jkkteach/Q550)

~~~
j2kun
I was surprised to click on a "PDF link" and get the ugliest, most retina-
scalding HTML page I have ever seen.

~~~
jacquesm
You've been 'fuchsiarolled'. That really does hurt.

------
wyager
My question:

When does a physical system reach a "halting state"?

This question has led me to some confusion when considering the possible
isomorphism between physical systems and turing machines.

~~~
eurleif
The halting problem is solvable for a program which is known to use finite
memory. It's only unsolvable on a Turing machine because Turing machines have
infinite memory.

~~~
wyager
Right, but how do you define the halting state for a physical system? A stable
state? No free energy left? Is it arbitrary?

~~~
im3w1l
It is up to the person claiming that the system can be interpreted as a Turing
machine.

"If we view these parts of the beach as the tape, and all crabs being in a
state described by these rules as corresponds to halting, then this crab
population can be seen as a Turing machine!"

------
goldenkey
Furthermore, is time quantized? If it's not quantized, are universal changes
atomic? Or do they dopple? (At the speed of light?) This would mean that a
clock cycle of universal change takes (length of universe) / (speed of light)

I think that time being quantized, would beg the question, are universal
changes atomic locally, or globally?

Our perceptions are clearly operating on universal change, so our sense of
time is as well. These are quite deep questions.

------
thisjepisje
Can't we define the universe as the computing system, the state of the
universe at t=0 as the encoding of the problem into the computing system, and
the state of the universe now as the decoding step? As far as I understand it,
the framework presented doesn't explicitly permit the computing entity to be
inside the computation.

------
jxjdjr
I've thought this for a while now. The only reasonable definition of
computation is in relation to other systems. It's good to see this popping up
other places than inside my head :)

