
A primer on causal emergence - okket
http://www.erikphoel.com/blog/a-primer-on-causal-emergence
======
raymondh
I really enjoy seeing thought-provoking posts like this on Hacker News.

The practical insight is that complex systems have some level of scale where
causality experiments yield the most fruit, and that this effect is
measurable.

The most interesting parts are the two justifications for why this may be
true. (1) "the determinism can increase and the degeneracy can decrease at the
higher scale (the causal relationships can be stronger)" (2) "Higher-scale
relationships can have more information because they are performing error-
correction."

------
shadowmint
> Measuring causal emergence is like you're looking at the causal structure of
> a system with a camera (the theory) and as you focus the camera (look at
> different scales) the causal structure snaps into focus. Notably, it doesn’t
> have to be “in focus" at the lowest possible scale, the microscale.

Talk about abstract metaphors that have no meaning.

The core of this argument seems to be:

1) Given a fixed state of a system, you can modify it by apply certain
operators on the system.

2) You can model the 'causal structure' by observing changes as you randomly
apply operators.

3) High level systems at a macro scale have a greater information density than
the sum of their parts.

Ie. In a nutshell, you can have high level (ie. real world) systems that
display behaviour that is not just hard to predict from changes to low level
systems... but actually _impossible_ to predict from them.

Which is to say, basically asserting that you cannot predict the behaviour of
macro systems from microscale systems; eg. you cannot predict the behaviour of
a molecule based on its quantum state / make up (clearly false) and you cannot
predict the behaviour of say, a person deciding what to have to for lunch
based on their quantum state/

...but not that you can't because it's hard.

You can't because its _not possible_.

Am I misunderstanding?

I think that sounds completely crack pot to me.

~~~
TheOtherHobbes
It's not crack pot at all.

Given an understanding of quantum chemistry and the periodic table, would a
reductionist approach be able to predict Hacker News?

You certainly can predict the behaviour - or at least a statistical envelope
for the behaviour - of a single molecule.

But once you get beyond a certain scale, information starts being processed
and abstracted in the _relationships_ that emerge between larger assemblies.

Naive reductionism has no tools for modelling that information or predicting
how it might appear or develop.

~~~
shadowmint
> abstracted in the relationships that emerge between larger assemblies.

Yes, but that's the point.

Obviously it's hard to make predictions a macro level _purely_ from studying
it at a super micro level and without looking at parts of the interactions it
might even be impossible; but that's not what's being asserted here.

What's being asserted here, is, in scott aaronson's words:

> In their new work, Hoel and others claim to make the amazing discovery that
> scientific reductionism is false—or, more precisely, that there can exist
> “causal information” in macroscopic systems, information relevant for
> predicting the systems’ future behavior, that’s not reducible to causal
> information about the systems’ microscopic building blocks.

Think about that for a second.

You're saying, there's a kind a of 'meta information' in complex systems, that
_cannot be reduced_ into information about its constituent parts or how they
interact.

For example, 'what you might pick for lunch' _cannot_ be represented as a
information about your blood, body, atoms, stomach.

It's a stupid assertion; if you assert that a system of any complexity cannot
be predicted by the behavior of its constituent parts, you're basically saying
that 'nothing makes sense'. It's patently false. It's just a flip off to
people building probabilistic models like, oh hey, don't bother, that doesn't
work.

It's just not true.

What's mathematically _interesting_ is how they've devised the paper.

If you _can_ show, mathematically, that you have more information for
predicting future state from considering a macro state than all micro states,
that's a pretty interesting result; but it's also exactly the point scott
demolishes in his blog post.

...and the rebuttal?

> Doing a series of A/B tests to capture the effects of the macroscale states
> doesn’t correspond to doing a series of A/B tests to capture the effects of
> microscale states. A randomized trial at the macroscale of medical
> treatments to see their effect on tumors won’t correspond to an underlying
> set of microscale randomized trials, because many different microstates make
> up the macrostates.

Which is where we started; ie. the assertion that the behaviour of microscale
effects doesn't reflect macro scale effects.

...but we know that it does. We don't invent new drugs by going off and
randomly trying crap; we model the molecules and predict the macro scale
effects they'll have.

What he's asserting here is quite literally, demonstrably false.

------
westoncb
I read Scott Aaranson's initial criticism of Hoel's causal emergence paper
(which is pretty funny because of things unrelated causal emergence really: "
_Higher-level causation exists (but I wish it didn’t)_ ":
[http://www.scottaaronson.com/blog/?p=3294](http://www.scottaaronson.com/blog/?p=3294))

I've skimmed the linked article, and will in all likelihood go back to it—but
I wonder about some stuff from the conclusion:

> _It also provides some insight about the structure of science itself, and
> why it’s hierarchical (biology above chemistry, chemistry above physics).
> This might be because scientists naturally gravitate to where the
> information about causal structure is greatest, which is where they are
> rewarded in terms of information for their experiments the most, and this
> won 't always be the ultimate microscale._

I don't see how more information existing at higher levels would explain the
hierarchical structure of the sciences: saying there's more information at the
higher levels is the reason would imply that e.g. we found biology to be more
valuable than physics, whereas the actual situation seems to be that we value
these levels equally. Maybe that's just a phrasing issues. In any case, it
seems simpler that we organize the sciences hierarchically because the human
brain organizes information that way.

I also don't see how there being _more_ information at certain levels is
necessarily useful: isn't the quality of the information as important or more
important than the quantity? But I guess if the it's specifically 'causal'
information, there's an implication (at least for the sciences) of ideal
quality...

~~~
kalu
I think you are looking at it in a linear way. But maybe the relationship
between scale and causal information is nonlinear. Causal information might
oscillate as the scale increases. So that physics, chemistry, and bioligy are
concentrated around scales that are associated with peaks in causal
information.

------
nabla9
>What’s causal emergence? It’s when the higher scale of a system has more
information associated with its causal structure than the underlying lower
scale.

I don't understand why the writer invents new (grand) terms to discuss
phenomena that is already widely studied.

Information as a function of scale in a system is well known phenomenon in
physics and complex systems theory. Systems different in microscopic scale can
behave similarly in macroscopic scale. Renormalization group formalizes this
emergent principle of universality. Multiscale information theory is
generalization of it.

[https://en.wikipedia.org/wiki/Renormalization_group](https://en.wikipedia.org/wiki/Renormalization_group)

[https://arxiv.org/abs/1409.4708](https://arxiv.org/abs/1409.4708)

------
maxhodges0
I think you need an additional primer on the topic of: why I should care about
"casual emergence". What's the point? How can it be put to use? Started
reading your article but couldn't get into it. Is it just a pointless
philosophical notion?

~~~
mannykannot
I think the third paragraph suggests the point is that it is allegedly a
measure for whether a purely reductionist approach is a useful way to explain
a given thing or phenomenon. For example, while I have no doubt that the
history of life on earth could, in principle, be explained in terms of
physics, I find that a Darwinian theory of evolution is a more useful way of
looking at it.

Aaronson's argument seems to be that the resulting measure is an unsurprising
outcome. I am not sure whether that _proves_ it is irrelevant, but I think the
onus is on its proponents to show that this measure goes beyond being
trivially true, and is actually useful.

In the conclusion of the article, Hoel seems to be making a stronger claim:
"The theory does imply that universal reductionism is false when it comes to
thinking about causation, and that sometimes higher scales really do have more
causal influence (or information) than whatever underlies them." There seems
to be a hint of the motte-and-bailey strategy here, with Hoel defending the
narrower claim but expecting us to accept the broader one.

I have not figured out how this measure is actually calculated without having
a reductionist measure of the system's information content, so I wonder if it
has been created to be used as a pawn in some philosophical argument, perhaps
such as the nature of consciousness.

------
cousin_it
> _Maybe, as the physicist Yakir Aharonov has advocated, our universe has not
> only a special, low-entropy initial state at the Big Bang, but also a
> “postselected final state,” toward which the outcomes of quantum
> measurements get mysteriously "pulled"—an effect that might show up in
> experiments as ever-so-slight deviations from the Born rule._

Me, me! I know a kind of postselection effect that can be explained on a
napkin (though nobody knows if it's actually true). As a bonus, it can affect
not just the Born probabilities, but the probabilities of anything you choose,
even things that already happened. Here's how it works.

The idea is a variation on anthropic reasoning, originally due to Bostrom
([http://www.anthropic-
principle.com/preprints/cau/paradoxes.h...](http://www.anthropic-
principle.com/preprints/cau/paradoxes.html)) If there's a completely fair
quantum coin, and many people over many generations decide to have kids iff
the coin comes up heads, then the coin might appear biased to us for anthropic
reasons (more people in the heads-world than in the tails-world). You can
influence all sorts of things this way, like Bostrom's example of Adam and Eve
deciding to have kids iff a wounded deer passes by their cave to provide them
with food. (That's if anthropic probabilities work in a certain intuitive way.
If they work in the other intuitive way, you get other troubling paradoxes in
the same vein. All imaginable options lead to weirdness AFAIK.)

A few years back I spent a long time on such problems, and came up with a
simple experiment about "spooky mental powers" that doesn't even involve
creating new observers. It's completely non-anthropic and could be reproduced
in a lab now, but the person inside the experiment will be deeply troubled.
Here's how it goes:

You're part of a ten-day experiment. Every night you get an injection that
makes you forget what day it is. Every day you must pick between two
envelopes, a red one and a blue one. One envelope contains $1000, the other
contains nothing. At the end of the experiment, you go home with all the money
you've made over the ten days. The kicker is how the envelopes get filled. On
the first day, the experimenters flip a coin to choose whether the red or the
blue one will contain $1000. On every subsequent day, they put the money in
the envelope that you didn't pick on the first day.

So here's the troubling thing. Imagine you're the kind of person who always
picks the red envelope on principle. Just by having that preference, while
you're inside the experiment, you're forcing the red envelope in front of you
to be empty with high probability! Since your mental states over different
days are indistinguishable to you, you can choose any randomized strategy of
picking the envelope, and see the result of that strategy as if it already
happened. In effect, you're sitting in a room with two envelopes, whose
contents _right now_ depend not just on what you'll choose _right now_ , but
on what randomized strategy you'll use to choose _right now_. If that's not
freaky, I don't know what is.

Going back to Aaronson's original point, the world as it looks to us might
easily contain postselection and other weird things. Reducing everything to
microstates is a valid way to look at the universe, but you aren't a
microstate. You are an observer, a big complicated pattern that exists in many
copies throughout the microstate, and the decisions of some copies might
affect the probabilities observed by other copies at other times. The effects
of such weirdness are small in practice, but unavoidable if you want a correct
probabilistic theory of everything you observe (or a theory of decision-making
for programs that can be copied, which is how I arrived at the problem).

~~~
omginternets
>Since your mental states over different days are indistinguishable to you,
you can choose any randomized strategy of picking the envelope, and see the
result of that strategy as if it already happened. In effect, you're sitting
in a room with two envelopes, whose contents right now depend not just on what
you'll choose right now, but on what randomized strategy you'll use to choose
right now.

You lost me, and I'm not sure where... could you elaborate?

~~~
cousin_it
Imagine two people going through this experiment, Alice and Bob.

When Alice wakes up, she decides to pick red, because she always picks red
which is her favorite color. Lo and behold, the red envelope is empty with
>90% probability (because if Alice picked it on the first day, it will be
empty on the next 9, and Alice doesn't know which day it is).

When Bob wakes up, he decides to flip a coin, because that's how he always
makes decisions. The coin tells him to pick red. Lo and behold, the red
envelope is full with 50% probability. _Even though Alice and Bob chose the
same color._

Nerdy explanation: if you maximize expected utility in the Von Neumann and
Morgenstern sense, you can prove a theorem saying there's always an optimal
strategy that's deterministic. You shouldn't need randomization, even if the
world is random. In my experiment, the classical assumptions don't apply
(specifically the axiom of independence), so the theorem becomes false and you
need randomization to get the best result. The point of the experiment is
showing that the axiom of independence isn't reasonable when you have copies,
so vNM utility maximization needs to be modified. (For cases like this one,
the right fix is modeling utility maximization as a single player game with
imperfect information, chance moves, and behavioral strategies.) Bostrom's
anthropic problems also show the same weirdness, but my contribution is making
a non-anthropic scenario with fixed number of observers that still shows the
weirdness.

