tag:blogger.com,1999:blog-5439168179960787195.post8803974643279601860..comments2024-03-28T17:13:01.117+10:00Comments on Condensed concepts: Illustrating emergence with an example from geometryRoss H. McKenziehttp://www.blogger.com/profile/09950455939572097456noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-5439168179960787195.post-60085551523986021752009-06-09T09:52:33.590+10:002009-06-09T09:52:33.590+10:00I think it's a great analogy, but I'm not ...I think it's a great analogy, but I'm not clear how far to take it comparing it to the complexity that emerges in regular physics.<br /><br />Adding higher dimensions isn't *quite* the same thing as adding more particles, is it? I mean, yes you need more parameters to define your state, but in one case you're changing the laws of physics, while in the other you're uncovering unexpected (typically many-body) phenomena that are based on the same simple (haha) rules, and hence discover another new large scale law/theory/phenomena.<br /><br />I really like your comment, Ben, about predicting emergent phenomena. Nice!Joelhttps://www.blogger.com/profile/00837076025978911665noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-10094202739685246652009-06-01T20:01:36.334+10:002009-06-01T20:01:36.334+10:00This is a very germane example, and a tantalizing ...This is a very germane example, and a tantalizing hint of the power of exterior algebras in many-body physics.Seth Olsenhttps://www.blogger.com/profile/09304457461800104790noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-74387731956165068022009-05-31T22:35:56.963+10:002009-05-31T22:35:56.963+10:00"However, a priori these segments can be assembled..."However, a priori these segments can be assembled into many different structures with dimensionality one, two, or three. A cube is just one of many possibilities."<br /><br />So what criteria are used to select the cube over these other possibilities? Is it just a case of a thing that we like emerging from a crowd of things that we don't like as much? <br /><br />This relates to the following basic question I have about emergence in CMP.<br /><br />The same microscopic Hamiltonian gives rise to a large number of qualitatively different macroscopic phases (depending on fine tuning of its parameters). So part of the problem in predicting emergent phenomena is just that there are many candidates, most of which might never occur in accessible nature. But my understanding is that this is not the interesting part of the problem. Rather, that the majority of these possibilities will be dull and the interest is in a small minority of special cases. These are the cases (like superfluidity) that really call for new concepts. (I guess 'dull' is defined as everything that we can understand well enough WITHOUT new concepts.)<br /><br />Is this a shared view? Or do we just like superfluidity because we observe it and just like cubes because cubes are the kind of thing that we like?Unknownhttps://www.blogger.com/profile/05410107734176990734noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-45882817185046917762009-05-27T21:06:13.204+10:002009-05-27T21:06:13.204+10:00Thanks, Ben. I agree I overstated the case. I hope...Thanks, Ben. I agree I overstated the case. I hope others will post comments to clarify my thinking.Ross H. McKenziehttps://www.blogger.com/profile/09950455939572097456noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-5987443232165991632009-05-26T17:12:13.629+10:002009-05-26T17:12:13.629+10:00There are some very nice points about this example...There are some very nice points about this example. But I also think it's important to stress something. Emergent properties are, as you say, very hard to predict. But they are not impossible to predict. <br /><br />You say that "it is not clear that a cube can be predicted in a flat world where a cube has not been seen before." But, we live in a 3d world (a least so far as low energy processes are concerned). And we have predicted hypercubes and studied geometry in many higher dimensions.<br /><br />A more important example is Bose-Einstein condensation, which was predicted long before superfluid He was observed.<br /><br />I would argue that, perhaps, the most important problem in theoretical physics today is to learn how to predict new emergent phenomena. Further, I would argue that, perhaps, the most important problem in experimental physics is to learn how to achieve new emergent phenomena in a controlled way rather than waiting for serendipitous discoveries. I would strongly recommend Fleming and Ratner's discussion [Phys. Today 61, 28 (2008)] of this.Ben Powellhttps://www.blogger.com/profile/04312113344388752854noreply@blogger.com