Thursday, May 21, 2009

More Really Is Different

I've mentioned before, many times in fact, on here about the issue regarding reductionism and "The Theory of Everything". I argued that a large fraction of practicing physicists, especially those in condensed matter physics, do not buy into this idea of a theory of everything, simply based on emergent phenomena that we observe in condensed matter physics.

The main "poster child" for such argument is Phil Anderson's "More Is Different" paper published quite a while back. Now comes a paper that strengthen Anderson's assertion that More Really Is Different.

Gu et al.[1] published a paper in which, using the 2D Ising model that simulates a cellular automata of magnetic spins.

Abstract: In 1972, P.W. Anderson suggested that ‘More is Different’, meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a ‘theory of everything’ governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.

A News and Views in Nature[2] this week article reviewing this paper explains it a little bit clearer for those of us not familiar with these 2D computation and the intricacies of cellular automata.

In their study, Gu et al. mapped the dynamics of a certain CA into the lowest-energy (ground) states of Ising models. In this framework, Figure 1 can now be interpreted as a snapshot of a two-dimensional spatial lattice of spins. They grouped spins into blocks that encode the logic operations needed to produce universal computation in the corresponding CA. They then defined the 'prosperity', p, of two-state systems as "the probability that a randomly chosen cell at a random time step is live" (live meaning state 1).

Using the computational properties of the CA, Gu and colleagues were able to show that p is undecidable for infinite, periodic Ising systems. They argued that, as a consequence, many macroscopic properties of an Ising system, including the system's magnetization and degeneracy (number of independent configurations) at zero temperature, depend on p and hence are also undecidable. Because Ising models have been used to describe not only magnetic materials but also neural activity, protein folding and bird flocking, the consequences of Gu and colleagues' results transcend both computer science and physics.


Nice stuff! This would be another compelling argument against reductionism and the fallacy of the "Theory of Everything".

Zz.

[1] M. Gu et al., Physica D: Nonlinear Phenomena, v.238, p.835 (2009). Also see the arXiv version here.
[2] P.M. Binder Nature v.459, p.332 (2009).

19 comments:

Kobra said...

Wonderful! It always struck me as bizarre that there were people who saw parallels or similarities in the equations and theories used to describe natural phenomena and immediately pursued the red herring of one giant unified equation that governs it all.

Not just bizarre, but foolhardy and reckless. If such a thing were true, we would eventually find it without rampant confirmation bias getting in the way.

Matt said...

Please tell me why you continue to propagate this common straw man that people looking for a unified theory believe it will provide insight into the behavior of macroscopic systems like the weather or cellular automata. That's simply not what people looking for a unified theory are seeking.

Steven Weinberg has actually been one of the clearest spokespeople for the actual claims of unified-theory searchers. The point is not to find a reductionism of phenomena or behavior, in which the behavior of macroscopic systems is reducible to the behavior of their microscopic constituents. What unified-theory seekers are trying to understand is the reductionism of the rules or laws that govern models.

Every system or model begins by laying out the basic ingredients (not necessarily fundamental ingredients, just effective ingredients) and the rules or laws that govern them. For example, for a fluid of molecules, those ingredients are the molecules and the chemical interactions between them.

Put together the ingredients and the laws, and you hope to predict phenomena and the behavior of the system. And it is true, as Anderson et al argue, that you don't need to obtain the model from any more fundamental model in order to make these predictions. The model stands on its own for purposes of studying behavior and making predictions.

But the natural question is then to ask, Why this model? And, more importantly, Why those rules and not, say, some other set of rules? There is no explanation within a model itself for where the rules of that models come from. In order to explain where those rules and laws come from, you need to go to a more fundamental model, with a more fundamental set of laws.

This reductionism of the rules or laws is what Weinberg and other people looking for a unified theory seek. The hope is that there exists some fundamental theory of nature---some fundamental set of laws---that cannot be derived from anything else, and from which the laws of all other systems are inevitable.

Nobody claims that the Standard Model will ever be a useful way to predict the weather. Indeed, Weinberg himself is a big advocate of the notion of "effective field theories," in which we only concern ourselves with effective ingredients and rules and not the underlying, fundamental constituents of which they are made.

But effective field theories, like all other models, have rules and laws, and the only way to find out where those rules come from is to obtain them from a more fundamental set of rules. The effective model itself cannot tell you where its own rules come from. That's the point.

So, please, do not continue to spread this straw man about reductionists. And please inform and educate your many readers of the difference! This bitter sniping between the condensed matter community and the high energy community has already gone on way too long.

JC said...

I don't get it, why can't a theory of everything include both the laws governing the universe at a microscopic level and lay the foundation for the myriad emergent behaviours that appear in the universe at a macroscopic level?

Emergent behaviour will always appear to obey laws independent of the basic rules of a system. If it didn't then then everything from relativity and quantum mechanics to economics and evolution would fall under the umbrella of physics.

ZapperZ said...

Er.. hello? Did we miss the name "THEORY OF EVERYTHING" in the label given to such a thing? There is a fallacy that is attached to that name in which the knowledge of the basic interactions is sufficient to derive ALL other interactions and phenomena. If not, why give it a misleading name of "EVERYTHING"?

And *I* am not the only one who is perpetuating this "straw man". The fact that Anderson's article was published in Science, and Lauglin's two PNAS papers published recently, and his recent book, clearly indicates that this isn't a straw man. I don't see you rebutting any of these papers.

Furthermore, one can see that what I've adopted is clearly the clear stand of each camp. For example, this article clearly is consistent with what I've written here.

http://www.newvisions.ucsb.edu/visions/emergent_nature/index.html

In fact, one only needs to look at Weinberg's book "Facing Up - Science and Its Cultural Adversaries", where he addressed his disagreement with Phil Anderson, NOT based on what you wrote, but based on the central argument of reductionism and his belief that it IS the "theory of everything", that emergent phenomena are nothing more than added complexity.

But either way, even if we adopt your view, it doesn't look good for people who are doing such a thing that we call "reductionism". If they truly agree that such microscopic understanding doesn't really do anything about our ability to arrive at such emergent phenomena, then how in the world do they have the GALL to dare call something a "theory of EVERYTHING"? How presumptuous can one get? It's like the US Baseball League calling their championships "The World Series"!

Zz.

Matt said...

I wasn't around when people gave names to everything. I disagree with the name "theory of everything" as much as you do, much as I'm sure we both disagree with the popular use of "the God particle" to describe the Higgs boson, for example.

The terminology is bad, and perhaps some of the people seeking a unified theory are misguided when they use it, but the fact I expressed earlier still stands, semantics to the contrary.

In order to obtain the starting rules of a given model, you need to look to a more fundamental model. There's a causal arrow of the rules themselves.

There may not exist a unified theory out there, but it is already true that when you play the game of asking where the starting rules (not the resulting emergent behavior) of a given model come from and iterate repeatedly, you end up either with the Standard Model or general relativity, or else in the awkward, unresolved space between the two. If a unified theory exists, one of its goals would be to explain where the rules of the Standard Model come from, and also where the rules of GR come from, and how these two theories fit together consistently.

You'd probably never use the unified theory to do a GR calculation, or a QED calculation. It might even be calculationally impossible to do so, just as you'd never use GR or QED to explain the static cling of freshly-done laundry in your house. But that's not the point. And I'm happy that lots of people are studying the behavior of all kinds of models--I don't think everybody should be looking for a unified theory. But there's still a significant philosophical reason to look for one, and that reason still exists, whatever the semantics imply.

You don't need to know the unified theory to go from a model with starting rules to the resulting emergent behavior, and anyone who says differently is obviously mistaken. But the foolishness of humans does not imply that the basic idea is wrong: You do need to look for a more fundamental model when you want to know where those starting rules come from. And the mysterious path down that causal chain of rules is what drives many of us in our search for a unified theory of nature.

ZapperZ said...

But is this YOUR opinion, or what is truly accepted by those on BOTH sides of the argument. I find that it is the latter.

Both Weinberg and Anderson (and Laughlin) have been arguing this for years, and none of them are using YOUR version of it. Both camps are arguing it based on what I had described.

So I am not propagating a straw man by any means, which is what I'm arguing against based on your original comment. That is what I am countering. You have not shown how what you are arguing is the position that either camp in this debate are adopting. Even Weinberg does not adopt such a stand or we wouldn't be having a continuing debate on it, as evident in the paper that I cited.

Zz.

Matt said...

So I suppose the lesson here is that Weinberg is wrong. Imagine that! :)

It is certainly wrong-headed to trivialize the work of those who study emergent behavior. There exist plenty of phenomena exhibited by macroscopic systems whose existences cannot be predicted directly from an underlying, microscopic theory. On that we fully agree.

While I clearly do not agree with Weinberg's apparent claim that emergence is just the trivial addition of complexity, there is one argument that he makes that is sensible.

Once the Standard Model and GR are known to be part of the high energy laws that govern our universe, could a cool collection of electrons and protons not behave like hydrogen atoms? Could a very large ball of gravitationally-bound hydrogen atoms not behave like a star? Could such a universe, governed at the fundamental level by the Standard Model, not exhibit things like superconductivity and superfluidity?

In other words, does the fact that the universe is governed by certain microscopic laws make all the known macroscopic phenomena inevitable, even if no direct calculation from the microscopic theory could be tractably done to prove it?

If we could create a second universe from scratch, imposing on it only the rules of Standard Model and GR, would that universe, likewise, exhibit phenomena like superconductivity? Would balls of hydrogen in that universe likewise burn like the stars of our own universe? Etc.?

(The fact that the universe is governed by the Standard Model and GR do not, obviously, make the existence of human beings inevitable, of course, nor the existence of a specific planet Earth located 93 million miles from a yellow star the sun. There are some things in the universe, like the byproducts of biological evolution, that are simply historical accidents.)

The very fact that emergent phenomena of macroscopic models, like superconductivity and various phenomena associated with phase transitions, are, indeed, independent of any microscopic theory is what prevents us from figuring out the microscopic theory from the macroscopic model. You can't start with a macroscopic model and necessarily figure out a unique microscopic theory.

The existence of superconductivity does not make the Standard Model inevitable in the same way that the Standard Model makes superconductivity inevitable. One could imagine many possible universes that exhibit superconductivity that are not fundamentally governed by the Standard Model. The question is whether the reverse is true. If we created a second universe governed by the Standard Model, could it avoid having superconductivity in it, just like our universe does?

In any event, I personally think that the antagonism between the high-energy and condensed-matter communities is highly misguided. Maybe some healthy competition is always a good thing, but I've actually witnessed professors visibly scoff at the work of others. That can't be good. Science is driven by people's various passions. Why do people get upset at the idea that some people's passions take them in one direction, while other people's passions take them in another direction?

ZapperZ said...

But do you think your opinion here is shared by the majority of physicist in elementary particles? I don't think so.

As someone who interacts with high energy physicists every single day, I can tell you that they share Weinberg's point of view. In fact, talk to many postdocs in such a field and they'll look at you funny when you talk to them about emergent phenomena.

BTW, the "division" between Condensed matter physicists and elementary particles/high energy physics certainly came to a head during the congressional hearings on the fate of the SSC. Weinberg, I believed, admitted as much that the testimony of Anderson against the SSC was as damning and damaging to the SSC's fate as the cost overruns.

So this is certainly not simply a matter of having a 'straw man' to play with, but a serious division of philosophy.

Zz.

Matt said...

Right. But you know that there's ill will on both sides, right? There's Murray Gell-Mann calling solid-state physics "squalid-state physics," but there's also the whole parade of low-energy physics professors I've met who tell their students that high energy physics and string theory are "ruining science" and that it's all baloney. There's been a real poisoning of impressionable young minds.

And the SSC brought out the worst in this rivalry. You are probably aware of just how damaging the collapse of the SSC project has been to high energy physics, which lost two decades as a result. A whole generation of high energy physicists grew up in a data-impoverished environment. It is unsurprising that when the stakes are so high, people are going to say and write awful things, and animosity will fester for years after.

Can't we agree that these people are all wrong, and that there's plenty of physics out there for all of us? I don't really care what people say--the quest for a unified theory, at least as I've been careful to define the term, is a perfectly reasonable research goal, as is the quest to understand emergence.

I would have appreciated it if you'd been a bit more careful not to paint all of high energy physics and the quest for a unified theory with one large brushstroke.

You can rightfully complain about certain attitudes among segments of the high energy community, but it would be great if you could just add a note pointing out that the failures of these human beings does not imply that their work is a fool's errand, as I've heard many in condensed matter say out loud. There are quite a few good people in high energy who don't hold such negative attitudes, and to lump them and their larger work in with the nay-sayers seems unethical.

That's all I'm saying.

ZapperZ said...

But you are wrong as well in painting this as merely a straw man, and accusing me of perpetuating such a thing. Both of them are wrong. It is NOT a straw man, certainly not on both sides of the camp, and I am not perpetuating it, because it IS an issue that continues to be debated.

There are always exception to the case, but it is undeniable that the MAJORITY of people on each side of the camp hold on to each of those opinions. And for that, I am not paining each field with wide brush strokes, because it is an accurate reflection of the philosophy of each group.

Zz.

Matt said...

A straw man is defined as a modified version of an opponent's argument---generally, a weaker version---that is set up and defeated instead of the opponent's actual argument.

So if you are not constructing a straw man here, please do tell me *who* is arguing that a unified theory is going to be able to allow us to directly predict and calculate the weather, human behavior, and high-T superconductivity? Who believes that you can predict the existence of human behavior by studying a single brain cell alone? That appears to be your straw man. And a lot of people upset with the high-energy community promote this straw man.

What is *not* a straw man is the claim that many in the high energy community have a negative or condescending attitude toward the work of people in condensed matter. Perhaps they think condensed matter represents a less lofty set of pursuits. That's not a straw man. Some people in high energy really are that disrespectful. But which of them believes in what I write in my previous paragraph?

Just because a lot of people promote a straw man doesn't mean it's not a straw man. And even if lots of people are promoting it doesn't mean we should, too. (I would like to see a poll somewhere confirming your view that these opinions are held by a "majority." Are you speaking anecdotally here?)

Look at politics today: A very large chunk of people today really believe that if you are against torture, then you don't believe that the terrorists are bad people. Or religion: A majority of the fervently religious argue that without belief in a deity, the universe is totally lawless and arbitrary. That's the mother of all straw men.

A lot of people in a lot of arguments push straw men. The fact that a particular straw man is invoked by a lot of people doesn't make it less a straw man. And none of us should be adding to it.

Matt said...

But by all means, if you do really believe that the majority of your friends in high energy think this way, then please ask them the following simple question:

"Would a unified theory that resolves our questions about quarks, the Higgs, gravity, the origin of the universe, etc., tell us anything at all, or allow us to predict anything at all, about the weather, human behavior, materials science, high-temperature superconductivity, or other emergent phenomena?"

What do you think they'd say?

ZapperZ said...

They would say, in principle, YES. That's the whole philosophy behind reductionism. And yes, I've asked this already.

The fact that we can't prove this one way or the other is the very reason why this is still being debated. It is like the EPR paradox before Bell came out with his inequality to test for such hidden variable. We can't construct a large enough many-body interaction to compute and come up with these emergent phenomena, so both camps can't argue their cases based on solid evidence. All they can point to are indications of which way things will roll.

This is why the paper that I cited is so crucial, because it is giving clear evidence towards the side of emergent phenomena as not being derivable, even in principle, from the microscopic understanding of the interactions!

Zz.

Matt said...

I'd like to know the name of any physicist who honestly believes that knowing more about quarks would have any value whatsoever for understanding biology or other such emergent phenomena. I simply don't believe that any serious physicist honestly believes that. I don't believe Weinberg really thinks that, and I'd be happy if you could find me a quotation that refutes me.

And that's really what we're talking about. It's a patently unserious claim, and it's unserious to ascribe it to other physicists.

Yes, in principle, if I have a big and powerful enough computer and I plug in the Standard Model, I could get the behavior of some simple systems, but everyone knows that the problem gets exponentially complicated as you consider bigger systems so that the task becomes practically impossible.

Can it be done "in principle" though? If it could never, ever be done in practice, who cares? A lot of things are possible in principle. But if they are impossible in practice, who cares?

ZapperZ said...

Read Phil Anderson's review of Weinberg's "Facing Up..." book in Physics Today, July 2002, pg. 56. And I quote:

"In one of the essays in Facing Up, written for a Newton tricentenary event, he celebrates the standard model (and its possible successors) in physics as embodying the Newtonian ideal of discovering the UNIVERSAL LAWS that apply ALWAYS AND EVERYWHERE. Here he sees the proress of science since Newton's time as extending unification to more and more of the world around us, until, at present, we can seque into scientific explanations of ALL OF THE FACTS OF NATURE."

"Thus, I don't accept the opinion expressed by Weinberg in another essay "Night Thoughts of a Quantum Physicist" that there are "no freestanding principles of ... biology or economics." My view is closer to E.O. Wilson's consilience than to Weinberg's reductionism".

I can also point to the several papers by Laughlin who continue to assault such principles. Again, if these differences of opinion are nothing more than superficial imagination of a small group of people, no one would make such effort into writing lengthy articles about them, and certainly not by prominent and respected physicists.

I also find it odd that you require that I show evidence for how what I understand is being the accepted norm, where as you have shown to similar evidence. Can you show me where and how many in high energy and condensed matter that actually agree with your assertion? Can you show publications that are consistent with what you have stated? It appears that the burden of showing and supporting such arguments have been asked only upon me, while you've gotten away without showing any sources as a valid gauge of the group of physicists that you claim to represent.

Zz.

Matt said...

The reason for all the controversy between the high-energy and low-energy camps stems fundamentally from a battle over resources and over young recruits. There is therefore a strong incentive to create straw men to discredit the other camp.

You write: "Again, if these differences of opinion are nothing more than superficial imagination of a small group of people, no one would make such effort into writing lengthy articles about them, and certainly not by prominent and respected physicists."

So, yes, there is a strong incentive for people, even respected people, to make such efforts.

And I think Anderson mischaracterizes Weinberg in his review. As usual, it comes down to language. Anderson wants to show that Weinberg believes ridiculous things, straw men, and so he twists the meaning of Weinberg's language, perhaps unintentionally.

For example, consider Weinberg's use of the phrase "universal." He doesn't mean that you can derive everything in practice from the Standard Model, and certainly not by hand. What he means is that there is no system in the universe, at least at energies below 1TeV, where the laws of the Standard Model are explicitly violated. There are no systems where quarks are unconfined, where there are objects that are not QCD-color neutral. There are no massive objects that do not gravitate. Etc.

In what systems in the universe do gravity and the Standard Model not apply? Where do they not apply? They apply everywhere, at least to all systems at energies lower than 1TeV, where the Standard Model is believed to break down. The goal of finding a unified theory would be a theory with universal validity.

There may be *additional*, nontrivial behaviors that are not apparent at the level of the microscopic laws, but those microscopic laws don't stop being true. But since those emergent behaviors are not practically obtainable from the micro-theory, we need people studying those emergent phenomena directly. That's why condensed matter is so important.

And when Weinberg uses the phrase "no freestanding principles," he doesn't mean that emergent principles are obvious and analytically derivable from a micro-theory. Heck, Weinberg of all people knows full well that confinement can't be derived analytically from QCD.

Weinberg only means that those principles are inevitable given the micro-theory. And that's true. As I said, if you created a second universe governed at high energies by the Standard Model, you'd get the same kinds of phenomena that we have now. Electrons and quarks left to themselves at low energies would always settle into atoms, very large blobs of atoms would always form stars, metals at very low temperatures would superconduct, etc. That's probably what Weinberg means when he says that emergent principles are not "free standing."

What's true is that macro-systems with different micro-theories can exhibit identical emergent behaviors. In that sense, they are "free standing." But that's not the meaning Weinberg is using. Indeed, Weinberg helped create the field of effective field theory, which is based precisely on the idea that the behaviors of a low-energy theory are independent of its high-energy completion, and indeed that such a low-energy theory can have many possible high-energy completions.

Again, it comes down to language, and to turf battles. People have a strong incentive to mischaracterize what the other side thinks. It's the same thing in politics. Every good American wants the country to be as good as it can be, and yet you have huge numbers of people in each party alleging that the other party is not really patriotic. There are very strong incentives to build up straw men and misinterpret language to discredit the other side. Unfortunately, science is not free from politics.

I just wish that people like you and me can avoid playing into this game. All physicists, whichever camp they belong to, are doing good work. When Weinberg or Anderson mischaracerizes the language of the other side, its hurts everybody.

Matt said...

There's a point that needs to be added here. In the paper you cite, Gu et al consider a system of infinitely many spins. That's all well and good, except for the fact that no such system could ever actually exist in Nature. They address this very point in their conclusion. All mutually-communicating physical systems in Nature are actually finite, a limitation enforced by special relativity. (Which, by the way, is also universal and never violated, in the sense that signals containing information never, ever exceed the local vacuum speed of light.)

Is it possible that, in a certain limit, a system's behavior becomes totally, exactly decoupled from a micro-theory? Possibly. But no such systems actually exist, because all such limits are mathematical idealizations. They're approximations. Even Newtonian physics is complete and independent if you take the limit in which the atomic size goes to zero. But atoms are not zero-size!

Since the limits are, however, very good approximations, it is true that no human calculation could ever derive the macro-phenomenon from the micro-phenomenon. But I'm afraid the micro is still more fundamental than the macro as far as Nature herself is concerned. Why this fact scares or upsets anybody is beyond me.

ZapperZ said...

It looks like we are going to have to agree to disagree. I do not read the same interpretation of what Weinberg said, and neither did Anderson, Laughlin, Pines, and a whole lot of other physicists. You still haven't shown any indication that what you have adopted and interpreted is shared by many (majority?) of people.

And as for the infinite spins, please read the News and Views article that I cited. This issue was addressed in the case of finite spins configuration.

Zz.

hellas said...

For Matt: here's a reductionist (a plant biologist!) at work:

Anthony R. Cashmore 2010 "The Lucretian swerve: the biological basis of human behavior and the criminal justice system" PNAS 107(10): 4499-4504 (March 09, 2010).