
What Is Spacetime, Really? - champillini
http://blog.stephenwolfram.com/2015/12/what-is-spacetime-really/
======
codeulike
_In the beginning was a graph, more like diamond than graphite. Every node in
this graph was tetravalent: connected by four edges to four other nodes. By a
count of edges, the shortest path from any node back to itself was a loop six
edges long. Every node belonged to twenty-four such loops, as well as forty-
eight loops eight edges long, and four hundred eighty that were ten edges
long. The edges had no length or shape, the nodes no position; the graph
consisted only of the fact that some nodes were connected to others. This
pattern of connections, repeated endlessly, was all there was._

Intro to Schild's Ladder by Greg Egan. He was obviously thinking along similar
lines.

~~~
wlievens
Loved that book. Despite the cardboard characters :-)

Please tell me that last act made your think of Cellular Automata too!

------
j2kun
If the answer is "there is such a program that reproduces the universe," then
I have already found one such program that does it. Here it is: interleave the
simulation of individual steps of every Turing machine in lexicographic order.
That is, if the Turing machines are enumerated T_1, T_2, T_3, ... you do the
following:

    
    
        i = 1
        while True:
            j = 1
            while j <= i:
               simulate step j of Turing machine T_i
               j += 1
            i += 1
    

If there is some program, it will be in the list.

This is the pitfall you get into when you only care about finding extremely
short programs and don't think about efficiency. Similar pitfalls are in the
philosophy of artificial intelligence. You get no useful information or theory
or model if you ignore computational complexity.

~~~
Pharaoh2
Does this set of all turing machines contain the given turing machine? If yes,
then it would seem that you can never simulate even a single iteration of the
inner loop. If no, then you are not actually simulating all the programs are
you?

This goes a little beyond NP hard complexity, I believe.

~~~
j2kun
This set of Turing machines is the set of _all_ Turing machines. But you
misunderstand, I am only simulating a single step (constant time) of a finite
number of Turing machines in any given iteration of the inner loop.

It goes _arbitrarily far_ beyond NP hard complexity, which is my point.
Wolfram ignores complexity entirely, and that means this algorithm is fair
game.

~~~
Pharaoh2
1\. Why are the number of turing machines finite.

2\. But to simulate a single step of the turing machine, you will have to
simulate this turing machine too, so what you will end up doing is recursively
simulating the first step of this machine to infinity.

3\. Why do you assume all the programs in the world are turing computable.

~~~
drdeca
1: they aren't. They don't need to be, and they cannot be.

Simulate the first step of the first machine, then the first step of the
second machine, then the second step of the first machine, then the first step
of the third machine, then the second of the second, then the third of the
first, then the first of the fourth, and so on. Every step of every
program/machine is eventually reached.

For the same reason that the pairs of integers can be put into bijection with
the integers.

2) that is not a problem. The first step of that is not to run a step of a
program it simulates. The "simulating a single step of a given machine" is not
a single step. It is many steps. As such, there is no such recursive problem
like you describe. Simulating a single step of a machine always finishes,
regardless of what that step "represents". Even if the step being simulated is
part of some simulator machine, simulating it is still done in the same way,
and doesn't take longer.

3) Any programs for any computer we have can be simulated by a Turing machine.
They are quite general.

You might claim that some physical process is not computable, but that has not
been demonstrated for any physical process (well, except for maybe
consciousness, but that is contentious), and most ideas of how physics works
are computable, so there would be a significant burden of proof.

So, it seems like any program we can run can be simulated by a Turing machine.

~~~
knughit
Chaotic functions of continuous real variables are not computable. Computable
physics assumes a discrete lattice, which the universe is not proven to be.

~~~
Natanael_L
Can't find any proof of that claim. So far it seems more likely that all
physical systems are computable. Although you may need infinite time to
achieve perfect accuracy when computing them in a simulation, but
matematically that's still computable.

Computability makes no assumption on the geometry, only on the rules the
system follows.

------
4ad
> OK, so one can derive Special Relativity from simple models based on
> networks. What about General Relativity—which, after all, is what we’re
> celebrating today? Here the news is very good too: subject to various
> assumptions, I managed in the late 1990s to derive Einstein’s Equations from
> the dynamics of networks.

What a crackpot. He links to his own book, which is a non-mathematical, non-
technical book.

There is no mathematics in the linked material, so it's impossible to see
whether he is correct, in fact it's impossible to see what he means at all!

Nobody has seen this mythical derivation he did in the 90s.

Amazing how someone brilliant who used to do real science fell into
crackpottery like this.

------
yk
I think Stephen Wolfram fell in the trap, that any continuous dynamical system
can be approximated by a discrete one. His position is a bit like claiming the
fundamental theory of the universe is Brainfuck. Proof: I can encode general
relativity and quantum field theory in Brainfuck, at least to a arbitrary good
approximation. The initial conditions are then just the program to simulate GR
and QFT plus the initial conditions in more conventional physics. Thus the
fundamental theory of the universe is Brainfuck. ( At least if Turing machines
are the most powerful model of computation that can be implemented in our
universe.)

~~~
hcarvalhoalves
Why would it be a "trap"? The uncertainty principle hints that something
discrete may lie at the bottom. It's clear it's deliberate, not something you
fall into due to naiveness.

Also, Wolfram isn't the only one in this line of thinking, and this is a topic
that rears it's head time and time again in the history of physics.

~~~
euyyn
> The uncertainty principle hints that something discrete may lie at the
> bottom.

Not necessarily. The uncertainty principle is a direct consequence of some
quantities being "the Fourier transform" of each other. You can't play a pure
tone unless it extends infinitely in time, and vice versa: You can't play an
infinitesimally short sound unless you ring all frequencies. That's all.

And actually, if something discrete lies at the bottom of spacetime, the
uncertainty principle implies that there's a maximum energy and a maximum
momentum. For the same reason that there's a Nyquist frequency when sampling.
So, if anything, our intuition that there aren't such maxima makes the
uncertainty principle hint that there's nothing discrete underneath.

~~~
yetihehe
There IS known max energy, it's called Planck scale
([https://en.wikipedia.org/wiki/Planck_scale](https://en.wikipedia.org/wiki/Planck_scale)).

~~~
euyyn
The only "max" about that is in the name Max Planck :)

------
peter303
If he finds a network that is consistent with what we have observed so far,
then predicts something new, and we find it, then it will be significant.

------
chengiz
If all you have is cellular automata, everything starts looking like a
network.

~~~
iofj
Same can be said about string theory. In fact, there's an (in)famous book
about exactly that statement :

[http://www.amazon.com/Not-Even-Wrong-Failure-Physical-
ebook/...](http://www.amazon.com/Not-Even-Wrong-Failure-Physical-
ebook/dp/B00JLMMEQQ)

(Word of warning: do not indicate to your promotor that you're interested in
this book's subject, or even have read it, unless you're damn sure where he
stands on the subject, unless you want get a very effective demonstration that
physics might be value-free, professors definitely aren't)

------
openasocket
Maybe a physicist could help me out: the idea here of treating space as a
simple discrete network, and particles just being emergent behavior sounds
very interesting. But doesn't this violate Bell's Theorem, that no local
hidden variables could completely explain quantum mechanics?

~~~
philipov
I am not a physicist, but Wolfram covers this.

"Because there’s a theorem (Bell’s Theorem) that says that unless there’s
instantaneous non-local propagation of information, no such “hidden variables”
model can reproduce the quantum mechanical results that are observed
experimentally."

Wolfram's continues by saying he is allowing instantaneous non-local
propogation because network nodes have no coordinates; coordinates (and
dimensions themselves) arise as a result of how nodes are connected.

"And even though the network may mostly correspond on a large scale to 3D
space, it’s perfectly possible for there to be 'threads' that join what would
otherwise be quite separated regions."

He has changed the definition of locality.

~~~
Totient
Scott Aaronson argues that, based on what we know about quantum mechanics,
Wolfram's "long-range thread" cannot reproduce special relativity and Bell
inequality violations:

www.scottaaronson.com/papers/nks.ps

~~~
smaddox
It seems to me that Aaronson's argument can be easily bypassed by adding non-
local hidden variables in the form of a loosely connected network that
essentially injects pseudo-randomness into the approximately flat Minkowski
spacetime network. Note that Bell's inequality does not rule out non-local
hidden variables as a viable explanation of quantum mechanics.

------
tux1968
Things like this always leave me feeling stupid. How is one supposed to wrap
their mind around the idea of space emerging from an underlying "network"?

What exactly is being networked; what is the "stuff" of the network? He
describes the network in terms of connections, which in my mind requires a
topology, or space within which to exist; yet space does not apparently exist
at this level. If there is no space, then what separates the nodes in the
network? If no space separates the nodes, what defines the distinct
connections between them?

Yes, i'm completely lost.

~~~
codeulike
What is matter made of? The answer, whatever it is, cannot be matter. From
what fundamental thing does 'space' arise? The answer, whatever it is, cannot
be anything that would exist in a 'space' as such. And so we creep towards the
idea that at a low enough level, everything is just information.

~~~
dragonwriter
> What is matter made of? The answer, whatever it is, cannot be matter.

Sure it could (in principle) be; its matter all the way down, and there is no
lower-level thing of which matter is made. (Though, actually, I think the
standard answer to "what is matter made of" under current way of interpreting
things would be "energy", but then you could repeat the exercise with "energy"
in place of "matter" and its the same issue, _mutatis mutandis_.)

~~~
brianberns
Greenness disintegrates: [https://goo.gl/2X4288](https://goo.gl/2X4288)

------
Artistry121
This is a very well done piece. I love how many links and additional paths it
leads to in thinking.

It's a constant challenge for scientists to realize that nearly _everything_
we know is an approximation or only true in certain circumstances. It also
takes an amazing amount of humility to work knowing that you may be proving
yourself, your heroes and all many people have worked for wrong.

Thank you Mr Wolfram for your thoughts.

------
peatfreak
> I mostly just assumed Einstein’s whole mathematical setup of Special and
> General Relativity—and got on with my work in quantum field theory,
> cosmology, etc. on that basis.

I like the way he nonchalantly throws that "etc" in there, as though to
indicate that working in these areas is no big deal, really.

------
amelius
Same topic, different approach: [1]

[1]
[https://www.youtube.com/watch?v=W2XdhzCORbo](https://www.youtube.com/watch?v=W2XdhzCORbo)

~~~
grkvlt
FYI - "The first lecture in a series given by Dr Peter Rowlands of the
University of Liverpool on the Foundations of Physical Law. Further lectures
will be uploaded after they have been given."

~~~
amelius
Actually, there are more lectures available already.

------
drdeca
I'm having trouble finding any other references to a notion of a dimension of
a graph which is based on howthe number of vertices which can be reached
through a path of a given length increases with the length.

I'm finding things like, a dimension of a graph as the minimum dimension of
euclidean space where the vertices can be placed and have each edge have
length 1, and another thing which seems closer which is based on a metric from
the graph, but that is based on the idea of a metric basis, which I don't
think is equivalent (in it, a subgraph can have a higher dimension than the
graph it is a subgraph of, which I don't think is the case in the version
mentioned in this blog post. And one example I'm p sure has finite dimension
in the blog post version, but infinite dimension in the other thing, so, I'm p
sure they are different things).

Does anyone have any non wolfram references for the notion of the dimension of
a graph as is explained in the post linked?

~~~
chr1
His definition of the dimension is quite similar to the definition of the
dimension of a fractal.

His definition also works better than euclidean dimension, e.g. for a grid on
cylinder euclidean dimension will be 3 and his definition will give 2. I think
a modification of the definition above to allow minimum dimension of non-
euclidean space will be same as Wolframs definition for the cases when
dimension of the graph is not fractional number.

------
memracom
Let's see, everything is just nodes and connections.

Category theory says everything is just objects and morphisms.

Brown's Laws of Form starts with "drawing a distinction".

Could this last be the starting point? Is it consistent with either the
network or with Category Theory?

Lots to think about...

------
interpol_p
The thing that bugs me about his theory is that it just assumes the existence
of time. That patterns within the network are replaced according to certain
rules. And it seems that this replacement rule corresponds to time at the high
level.

His low level model seems to require propagation / evolution without being
able to model it. Whatever enacts the replacement rule is an external force
that acts upon his network, and so falls outside his definition of the
universe.

I guess it's a limitation of the cellular automata model. You have to assume
that something outside of the system "steps" the simulation forward.

------
mrwilliamchang
Here's my attempt at a summary. Wolfram speculates that the universe is a
network of nodes and connections. This network changes over time by simple
substitution rules. Specific patterns in the network give rise to effects that
on the larger scale that we experience as the physical world. He has shown
that if you model the universe this way, you can neatly derive special
relativity and general relativity. He is also doing a brute-force search
through networks to look for one that exhibits properties like our universe.

I'm curious if I got it wrong.

------
amelius
What I wonder is: how does the fact that we live in a 3D (spatial) world come
out of this model? Or is that also part of the a-priori model?

------
javajosh
All of our theories are single-threaded in the sense that the reader begins at
the beginning of the paper and reads it through to the end. Theoretical
physics at this level has always seemed to me a kind of weird mirror of this
fundamental constraint on the 1-D nature of theories themselves.

~~~
hyperion2010
That is not necessarily true. Just because you can serialize a set of ideas
does not mean that they can be interpreted or understood in their serialized
form alone. You almost always require a parser that has some structure which
will convert the serialized ideas into something with significantly higher
dimensionality where it can actually be understood and operated on.

Just because I can write down a function (using only a single dimension) that
operates on 10 dimensional data doesn't somehow imply that the data is
suddenly one dimensional.

~~~
javajosh
Your understanding of the non-serialized form is itself serialized, in the
sense that something in your mind is stepping the simulation. You might not
perceive it, but intellectually I'm sure you know that's what's happening
(unless you subscribe to some non-physical description of the mind).

~~~
hyperion2010
I would say that the physical processes that underlie our mental
representations of concepts are fundamentally not serialized (part of why it
is often so hard to put thoughts into words). They are non local in the sense
that many different actors can operate on the data at the same time to create
or modify some higher dimensional state and are not necessarily contingent on
prior state in the way parsing is.

You can't really parse a paper by reading every paragraph at the same time.
Even if you could do it physically, some ordering would have to be applied to
interpret subsequent parts based on statements in earlier parts.
Representations in the brain have no such inherent limitation on ordering.

~~~
javajosh
Whether or not the brain is "really" parallel, with a fast enough computer you
can simulate parallelism. So our "understanding" is either one-dimensional, or
isomorphic to a one-dimensional process.

~~~
nitrogen
How many variables are part of this simulation? Are those not dimensions?

~~~
javajosh
You can impose a one-dimensional ordering on a finite state of any size.
Drawing a parabola, for instance, yields a 2-D figure. But the process that
draws it (on a computer) is 1-D:

    
    
        Start at the origin
        Move right X
        Move up X*X
        Make a dot
        If X = Screen.Width Stop
        X=X+1
        Repeat
    

There you go: a 2-D thing from a discrete sequence of 1-D steps. I hope you
can see that it generalizes to N-D things.

~~~
hyperion2010
I think the question here, which has been raised in other parts of the
comments here, is what the complexity of the operation to
serialize/deserialize is and how one might think about translating between
computational complexity and dimensionality.

~~~
javajosh
My contention is that _all things are understood one step at a time_ , and I
believe this is influencing theoretical physics in a way that the
theoreticians themselves are not fully aware of. Especially Wolfram's theory.

------
hguant
It's interesting to see that, while philosophy has been sitting in the post-
Hume doldrums for the last hundred years, physics has gone all the way around
and started tackling metaphysics again!

------
justifier

        I’ve come to suspect it may actually have led us on a
        century-long detour in understanding the true nature 
        of space and time
    

come to suspect? knowing theories are incomplete is science, seek questions
stead answers

detour? hardly, science is directed by utility and the systems inherent in the
theoretical coupling that formed relativity have shown to be extremely useful
and any inevitable addendum, appendage, or usurper will need to prove itself
more useful

we need to ask the questions that will reveal those use cases untouched by the
contemporary thought

    
    
        now we have to wonder how long it will be 
        before we actually know the final theory
    

i see, and foresee, an existence where every new finality conjures new
questions

~~~
justifier
i wish i knew what was so unsettling about the above opinion

i'm interested in discussion

~~~
Pyxl101
I haven't voted on your comment, but here's what stands out to me: (1) It's
not written in good style. People who care about how their ideas are received
by others take the time to write properly, including capitalization and
punctuation.

(2) It reads like a middlebrow dismissal. It's critical but doesn't add much
of substance on its own through the criticism. Wolfram certainly realizes that
he hasn't proven his case, that current science is indeed incredibly useful,
and that the current path will only be a "detour" if network- or automata-
based models are proven correct in the end. That's why he says he "suspects"
it "may" have led us to a detour. He certainly understands that the theory
needs to be developed further. Put simply, Wolfram would probably agree with
your overall sentiment, so the remarks are not insightful, but they're
presented as if they'd likely be at odds with his position.

(3) Beyond style, the diction is unclear, such as the choice of the word "use-
case". It's unclear to me what you're referring to. It's unusual to refer to
physics as "use-cases". If that's intended as an analogy, then for me it
doesn't connect or succeed.

(4) The ideas themselves are not clear. "... reveal those use-cases untouched
by contemporary thought"; "an existence where every new finality conjures new
questions". It's not clear what you're trying to convey with those phrases.
You probably could say what you're trying to say in a simpler, more direct,
and less critical way way. You might benefit from this advice:
[http://paulgraham.com/talk.html](http://paulgraham.com/talk.html)

> Here's a simple trick for getting more people to read what you write: write
> in spoken language. Something comes over most people when they start
> writing. They write in a different language than they'd use if they were
> talking to a friend. The sentence structure and even the words are
> different. [...] But perhaps worst of all [mistakes], complex sentences and
> fancy words give you, the writer, the false impression that you're saying
> more than you actually are.

If I was to try to rephrase what you've said in simple language, then I end up
with something like: "The ideas need to work to be useful. We need to think up
new ideas. I think we'll always have more questions to answer", which isn't
that interesting. With the current phrasing it reads like a middlebrow
dismissal.

~~~
justifier
i appreciate the thought out response.. i'll try to address your points

1) sorry, it's the way i write

2) solid response:

    
    
       It's critical but doesn't add much of 
       substance on its own through the criticism. 
    

what you said there mirrors my immediate reaction to the linked piece by
wolfram, and in all fairness i felt it myself of my comment and intended to
reply with a more directed response to the piece but found it difficult to
find anything to riff off of

    
    
        So then the question arises: could one of these simple
        programs in the computational universe actually be the
        program for our physical universe?
    

this seems to be the base line on which his potential final theory is
predicated, but this just reads as a rewrite of the infinite monkey theorem

if the universe is programmable, then surely within the bounds of every
possible permutation of computation therein must lie a representation of the
universe..?

3) 'use case' and 'science as directed utility' seemed explicitly to go hand
in hand

4) "... reveal those use-cases untouched by contemporary thought"

one such important use case that showed the inherent utility of relativity was
understanding retrograde motion(o), this was the sort of use case i was
referring to one where the contemporary thought was unable to reach insight

"an existence where every new finality conjures new questions"

here i'd agree i erred on poetics to allow for some self discovery, what i
hoped to express was that every 'final theory', as wolfram puts it or finality
as i put it, i think will introduce more questions mocking the title of final

relativity is sussed out and people, as wolfram attested, assume it to be
true, but then later find it only reveals, seemingly by conjuring, questions
they were unaware of

even einstein, the one person who stood to gain the most by espousing that his
theory was 'the final theory', knew relativity to be wanting

it is my impression that i do write 'in spoken language'

when was the last time you heard a capital letter? or 'proper' punctuation?

these are the words i would use to talk to you about this topic

the diction may seem off because i avoid negative constructions:no, not,
never, none,etc; with hopes that the a subsequent generation will have the
patience to write out even negating prefixes: un-,i-,a-,etc;

i find removing negative constructions is a means of making discussion more
inviting and less authoritative

next time someone asks if you've seen some new media, instead of saying 'no'
see what reaction something like 'i've yet to have seen it' will afford

if a sentence comes easily as "which isn't that interesting" i will take
whatever time necessary to rewrite in order to write out the negative

reading your rewrite:

    
    
        The ideas need to work to be useful. 
        We need to think up new ideas. 
        I think we'll always have more questions to answer
    

could placehold as a rewrite of wolfram's piece

i'll express it as your rewrite on one side of a colon and applicable sections
from wolframs piece on the other, ctrl-f confirmation encouraged

    
    
        ideas need to be useful: "provides the only successful way 
        we have of describing spacetime"
    
        we need to think up new ideas: "started on my long journey 
        to go beyond traditional mathematical equations and instead 
        use computation and programs as basic models in science"
    
        I think we'll always have more questions to answer: 
        "But what would such a program be like?..what’s the basic 
        “data structure” on which this program operates?.." and on and on
    

so yes, i agree, markedly uninteresting

(o)
[http://theory.uwinnipeg.ca/mod_tech/node60.html](http://theory.uwinnipeg.ca/mod_tech/node60.html)

.. an aside, can we talk to the fact that middlebrow seems the only brow held
in contempt, i feel low brow and high brow each have their accepted merits(i)
but i've yet to have seen something quantified as being middlebrow used in
promotion

i wonder what the says about adjudged middles

(i)
[http://nymag.com/nymag/culture/approvalmatrix/archive/](http://nymag.com/nymag/culture/approvalmatrix/archive/)

------
redthrowaway
I found this incredibly hard to read, due to Wolfram's constant need to self-
aggrandize. The entire tone of the piece is, "I discovered this, then I
discovered that". In reality, most of his "revelations" were discussed by
others long before he arrived on set.

~~~
grkvlt
Agreed. Benoit Mandelbrot was the same; "When I discovered Fractals, which are
a thing that I discovered, including the Mandelbrot Set, which is named after
me, because I discovered it..." Wth some people it means I just stop listening
to them, but I just ignore it here, since both Mandelbrot and Wolfram usually
have interesting and insightful things to say as well.

~~~
vixen99
Rather like Ms. Elk on the subject on the Brontosaurus

[https://www.youtube.com/watch?v=cAYDiPizDIs](https://www.youtube.com/watch?v=cAYDiPizDIs)

------
amoruso
If you want a second opinion, Cosma Shalizi reviews _A New Kind of Science_ by
Stephen Wolfram:

[http://bactra.org/reviews/wolfram/](http://bactra.org/reviews/wolfram/)

~~~
username223
Subtitle: "A Rare Blend of Monster Raving Egomania and Utter Batshit
Insanity."

This is a classic that everyone should read, utterly destroying a shameless
self-promoter gifted with some intelligence and a grasp of jargon.

------
maurits
It is a tragedy really, his ideas always seem to get lost in senseless
narcissism.

~~~
copperx
Dijkstra's ideas (not just his contributions to math) survived despite his
arrogance. The difference is that Wolfram's ideas are not testable.

~~~
AnimalMuppet
Dijkstra's ideas survive, but are (mostly) not used...

~~~
GFK_of_xmaspast
There's a whole lot of structured programming going on these days.

~~~
jerf
Indeed! I've got a blog post on deck that likens it to a fish in water; we all
use it so thoroughly nowadays we don't even notice it because an unstructured
programming language is almost inconceivable to us.

------
iandanforth
At the risk of humor, this cartoon exactly summarizes my reaction to this
post: [http://www.smbc-comics.com/index.php?id=3805](http://www.smbc-
comics.com/index.php?id=3805)

~~~
Xcelerate
I mean... I think deep down most (scientific) people think that's probably the
fundamental truth. The challenge is in reifying the notion.

Let there be math, and then the laws of physics fall out as trivial
tautologies.

------
zzalpha
Err... is Wolfram now taking credit for this idea, which began circulating
back in 2009?

[http://www.nature.com/news/the-quantum-source-of-space-
time-...](http://www.nature.com/news/the-quantum-source-of-space-time-1.18797)

Because I don't see his name in the citations...

~~~
zardo
I don't think that's the same idea, but he's got a chapter on the network
universe idea in his book that was publshed in 2002.

Original credit for a discrete nature of the universe belongs to Democritus.

~~~
zzalpha
_I don 't think that's the same idea_

Hmm, upon a second read I think you're right.

One of the key distinguishing factors is the aforementioned Nature article
actually cites hints of a real scientific theory based on established physics,
while Wolfram's self-aggrandizing ramblings haven't actually led to any real
discoveries... :)

