Water with bacteria and liquid helium have the same Hamiltonian, AND the same constituent particles. If I give you a box and say "in this box there are 10^30 protons, 10^30 neutrons and 10^30 electrons," you do not have enough information to tell me how the system behaves, but from a purely reductionist stand-point, you should.
I'll admit that I am not a PhD particle physicist, but what you describe as reductionism is not what I believe to be true. If we ignore quantum physics, and describe what's happening on an entirely classical level, then we can reduce the behavior of a physical system down to its most fundamental particles and the laws which govern the interactions between those basic particles. You can predict how a system will behave by knowing about the position and the velocity of every particle in the system; you do not have to keep separate track of an organizational system as a separate property, because the organization of a physical system can be deduced from the other two properties.
If reductionism, to you, means that by simply knowing the number of electrons, protons, and neutrons which exist in the universe, you should be able to know how the entire universe behaves, then I agree: reductionism is false.
With that in mind, can you give an example of top-down causality actually occurring in the universe? A situation where the behavior of low-level particles interacting cannot predict the behavior of systems entirely composed of those low-level particles, but instead where the high-level organization causes the interaction between the low-level particles to be different?
That's what I think reductionism is: you cannot have higher-level laws contradict lower-level laws; that when you run the experiment to see which set of laws wins out, the lower-level laws will be correct every single time. Is this something you disagree with?
I don't think you understand what spontaneous symmetry breaking is
I probably don't. I was going based off of an AP Physics course in highschool. My understanding is basically this: if you dropped a ball perfectly onto the top of a mexican hat, symmetry would demand that all of the possible paths the ball could take are equally valid. But in the end, the ball only chooses one path, and which path it chose could not have been predicted from the base-level laws. A quick look at wikipedia confirms that this idea at least has something to do with symmetry breaking, since one of the subsections for "Spontaneous Symmetry Breaking" is called "A pedagogical example: the Mexican hat potential", and so I cannot be entirely off.
In classical physics, the ball actually takes one path, and this path cannot be predicted in advance. But in QM, the ball takes all of the paths, and different you's (different slices of the wavefunction which evolved from the specific neuron pattern you call you), combined, see every possible path the ball could have taken, and so across the wavefunction symmetry isn't broken.
Since you're a particle physicist and you disagree with this outlook, I'm sure there's something wrong with it, though.
In these systems, to describe low energy structures in such theories (most theories) the details of the microphysics literally do not matter.
Is this similar to saying that when you are modeling how an airplane flies, you don't need to model each particular nitrogen atom, oxygen atom, carbon atom, etc in the air, but can instead use a model which just talks about "air pressure", and your model will still be accurate? I agree with you; modeling every single particle when you're trying to decide how to fly your airplane is unnecessary and you can get the job done with a more incomplete model. But that does not mean that a model which did model every single atom in the air would be incorrect; it just does not have a large enough effect on the airplane to be noticeable. Indeed, I can see why computational physicists would use higher level models to their advantage, when such high level models still get the right answer.
But reductionism simply says that there is no situation where a high level model could get a more accurate answer than a low level model. The low level model is what is actually happening. Newtonian mechanics is good enough to shoot a piece of artillery at a bunker a mile away, but if you wanted to know with 100% accuracy where the shell was going to land, you would have to go further down than this. The more your model breaks macroscopic behavior down into the interactions between its base components, the closer your model resembles the way reality actually works.
Do you disagree?
So I think perhaps we are talking past each other. In particular, my definition of reductionism is that we can understand and model complex behavior by breaking a problem in to its constituent components and studying them in isolation. i.e. if you understand the micro-hamiltonian and the fundamental particles well, you understand everything. The idea of 'emergence' as physicists understand it (and as Laughlin was using it), is that there are aggregate behaviors that cannot be understood from looking at the individual constituents in isolation.
A weaker...
(At this point, I fear that I must recurse into a subsequence; but if all goes as planned, it really will be short.)
I once lent Xiaoguang "Mike" Li my copy of "Probability Theory: The Logic of Science". Mike Li read some of it, and then came back and said:
Then Mike said, "No, wait, let me explain that—" and I said, "No, I know exactly what you mean." It's a convention in fantasy literature that the older a vampire gets, the more powerful they become.
I'd enjoyed math proofs before I encountered Jaynes. But E.T. Jaynes was the first time I picked up a sense of formidability from mathematical arguments. Maybe because Jaynes was lining up "paradoxes" that had been used to object to Bayesianism, and then blasting them to pieces with overwhelming firepower—power being used to overcome others. Or maybe the sense of formidability came from Jaynes not treating his math as a game of aesthetics; Jaynes cared about probability theory, it was bound up with other considerations that mattered, to him and to me too.
For whatever reason, the sense I get of Jaynes is one of terrifying swift perfection—something that would arrive at the correct answer by the shortest possible route, tearing all surrounding mistakes to shreds in the same motion. Of course, when you write a book, you get a chance to show only your best side. But still.
It spoke well of Mike Li that he was able to sense the aura of formidability surrounding Jaynes. It's a general rule, I've observed, that you can't discriminate between levels too far above your own. E.g., someone once earnestly told me that I was really bright, and "ought to go to college". Maybe anything more than around one standard deviation above you starts to blur together, though that's just a cool-sounding wild guess.
So, having heard Mike Li compare Jaynes to a thousand-year-old vampire, one question immediately popped into my mind:
"Do you get the same sense off me?" I asked.
Mike shook his head. "Sorry," he said, sounding somewhat awkward, "it's just that Jaynes is..."
"No, I know," I said. I hadn't thought I'd reached Jaynes's level. I'd only been curious about how I came across to other people.
I aspire to Jaynes's level. I aspire to become as much the master of Artificial Intelligence / reflectivity, as Jaynes was master of Bayesian probability theory. I can even plead that the art I'm trying to master is more difficult than Jaynes's, making a mockery of deference. Even so, and embarrassingly, there is no art of which I am as much the master now, as Jaynes was of probability theory.
This is not, necessarily, to place myself beneath Jaynes as a person—to say that Jaynes had a magical aura of destiny, and I don't.
Rather I recognize in Jaynes a level of expertise, of sheer formidability, which I have not yet achieved. I can argue forcefully in my chosen subject, but that is not the same as writing out the equations and saying: DONE.
For so long as I have not yet achieved that level, I must acknowledge the possibility that I can never achieve it, that my native talent is not sufficient. When Marcello Herreshoff had known me for long enough, I asked him if he knew of anyone who struck him as substantially more natively intelligent than myself. Marcello thought for a moment and said "John Conway—I met him at a summer math camp." Darn, I thought, he thought of someone, and worse, it's some ultra-famous old guy I can't grab. I inquired how Marcello had arrived at the judgment. Marcello said, "He just struck me as having a tremendous amount of mental horsepower," and started to explain a math problem he'd had a chance to work on with Conway.
Not what I wanted to hear.
Perhaps, relative to Marcello's experience of Conway and his experience of me, I haven't had a chance to show off on any subject that I've mastered as thoroughly as Conway had mastered his many fields of mathematics.
Or it might be that Conway's brain is specialized off in a different direction from mine, and that I could never approach Conway's level on math, yet Conway wouldn't do so well on AI research.
Or...
...or I'm strictly dumber than Conway, dominated by him along all dimensions. Maybe, if I could find a young proto-Conway and tell them the basics, they would blaze right past me, solve the problems that have weighed on me for years, and zip off to places I can't follow.
Is it damaging to my ego to confess that last possibility? Yes. It would be futile to deny that.
Have I really accepted that awful possibility, or am I only pretending to myself to have accepted it? Here I will say: "No, I think I have accepted it." Why do I dare give myself so much credit? Because I've invested specific effort into that awful possibility. I am blogging here for many reasons, but a major one is the vision of some younger mind reading these words and zipping off past me. It might happen, it might not.
Or sadder: Maybe I just wasted too much time on setting up the resources to support me, instead of studying math full-time through my whole youth; or I wasted too much youth on non-mathy ideas. And this choice, my past, is irrevocable. I'll hit a brick wall at 40, and there won't be anything left but to pass on the resources to another mind with the potential I wasted, still young enough to learn. So to save them time, I should leave a trail to my successes, and post warning signs on my mistakes.
Such specific efforts predicated on an ego-damaging possibility—that's the only kind of humility that seems real enough for me to dare credit myself. Or giving up my precious theories, when I realized that they didn't meet the standard Jaynes had shown me—that was hard, and it was real. Modest demeanors are cheap. Humble admissions of doubt are cheap. I've known too many people who, presented with a counterargument, say "I am but a fallible mortal, of course I could be wrong" and then go on to do exactly what they planned to do previously.
You'll note that I don't try to modestly say anything like, "Well, I may not be as brilliant as Jaynes or Conway, but that doesn't mean I can't do important things in my chosen field."
Because I do know... that's not how it works.