📜 Sloppiness and Emergent Theories in Physics, Biology, and Beyond
Mark K. Transtrum, Benjamin Machta, Kevin Brown, Bryan C. Daniels, Christopher R. Myers, James P. Sethna
(Submitted on 30 Jan 2015)
🔗 https://arxiv.org/pdf/1501.07668
📌 ABSTRACT
Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. We show how the manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.
Mark K. Transtrum, Benjamin Machta, Kevin Brown, Bryan C. Daniels, Christopher R. Myers, James P. Sethna
(Submitted on 30 Jan 2015)
🔗 https://arxiv.org/pdf/1501.07668
📌 ABSTRACT
Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. We show how the manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.
🔹 Roughly speaking, an #ergodic system is one that mixes well. You get the same result whether you #average its values over #time or over #space.
🔗 https://www.johndcook.com/blog/tag/ergodic-theory/
🎯 In the late 1800s, the physicist Ludwig Boltzmann needed a word to express the idea that if you took an isolated system at constant energy and let it run, any one trajectory, continued long enough, would be representative of the system as a whole. Being a highly-educated nineteenth century German-speaker, Boltzmann knew far too much ancient Greek, so he called this the “ergodic property”, from ergon “energy, work” and hodos “way, path.” The name stuck.
🔗 footnote on page 479: http://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/
🔗 https://www.johndcook.com/blog/tag/ergodic-theory/
🎯 In the late 1800s, the physicist Ludwig Boltzmann needed a word to express the idea that if you took an isolated system at constant energy and let it run, any one trajectory, continued long enough, would be representative of the system as a whole. Being a highly-educated nineteenth century German-speaker, Boltzmann knew far too much ancient Greek, so he called this the “ergodic property”, from ergon “energy, work” and hodos “way, path.” The name stuck.
🔗 footnote on page 479: http://www.stat.cmu.edu/~cshalizi/ADAfaEPoV/
📄 The Fate of Ernst Ising and the Fate of his Model
Thomas Ising, Reinhard Folk, Ralph Kenna, Bertrand Berche, Yurij Holovatch
🔗 https://arxiv.org/pdf/1706.01764
📌 ABSTRACT
On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.
Thomas Ising, Reinhard Folk, Ralph Kenna, Bertrand Berche, Yurij Holovatch
🔗 https://arxiv.org/pdf/1706.01764
📌 ABSTRACT
On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures ( http://www.icmp.lviv.ua/ising/ ) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.
📄 How and why does statistical mechanics work?
Navinder Singh (2011)
🔗 https://arxiv.org/pdf/1103.4003
📌 ABSTRACT
As the noscript says we want to answer the question; how and why does statistical mechanics work? As we know from the most used prenoscription of Gibbs we calculate the phase space averages of dynamical quantities and we find that these phase averages agree very well with experiments. Clearly actual experiments are not done on a hypothetical ensemble they are done on the actual system in the laboratory and these experiments take a finite amount of time. Thus it is usually argued that actual measurements are time averages and they are equal to phase averages due to ergodicity. Aim of the present review is to show that ergodicity is not relevant for equilibrium statistical mechanics (with Tolman and Landau). We will see that the solution of the problem is in the very peculiar nature of the macroscopic observables and with the very large number of the degrees of freedom involved in macroscopic systems as first pointed out by Khinchin. Similar arguments are used by Landau based upon the approximate property of "Statistical Independence". We review these ideas in detail and in some cases present a critique. We review the role of chaos (classical and quantum) where it is important and where it is not important. We criticise the ideas of E. T. Jaynes who says that the ergodic problem is conceptual one and is related to the very concept of ensemble itself which is a by-product of frequency theory of probability, and the ergodic problem becomes irrelevant when the probabilities of various micro-states are interpreted with Laplace-Bernoulli theory of Probability (Bayesian viewpoint). In the end we critically review various quantum approaches (quantum-statistical typicality approaches) to the foundations of statistical mechanics.
Navinder Singh (2011)
🔗 https://arxiv.org/pdf/1103.4003
📌 ABSTRACT
As the noscript says we want to answer the question; how and why does statistical mechanics work? As we know from the most used prenoscription of Gibbs we calculate the phase space averages of dynamical quantities and we find that these phase averages agree very well with experiments. Clearly actual experiments are not done on a hypothetical ensemble they are done on the actual system in the laboratory and these experiments take a finite amount of time. Thus it is usually argued that actual measurements are time averages and they are equal to phase averages due to ergodicity. Aim of the present review is to show that ergodicity is not relevant for equilibrium statistical mechanics (with Tolman and Landau). We will see that the solution of the problem is in the very peculiar nature of the macroscopic observables and with the very large number of the degrees of freedom involved in macroscopic systems as first pointed out by Khinchin. Similar arguments are used by Landau based upon the approximate property of "Statistical Independence". We review these ideas in detail and in some cases present a critique. We review the role of chaos (classical and quantum) where it is important and where it is not important. We criticise the ideas of E. T. Jaynes who says that the ergodic problem is conceptual one and is related to the very concept of ensemble itself which is a by-product of frequency theory of probability, and the ergodic problem becomes irrelevant when the probabilities of various micro-states are interpreted with Laplace-Bernoulli theory of Probability (Bayesian viewpoint). In the end we critically review various quantum approaches (quantum-statistical typicality approaches) to the foundations of statistical mechanics.
⭕️ Inspired by Laszlo Barabasi's award talk at CCS 2017 in Cancun, a small group of Twitter users have started discussing the idea to create "Complexity Literacy", a list of core ideas that should be taught/learned in Complexity / Complex Systems courses.
🔗 https://docs.google.com/forms/d/e/1FAIpQLSeWUfPNyjC1-_NeHfHWIl0IXwhnWntdTuwhKKLxgWHv-UmWjA/viewform
You can find a similar effort in Network Science here => http://tinyurl.com/networkliteracy.
This form is to initiate an initial brainstorming process by collecting various ideas from the Complex Systems community at large. Please identify yourself so we can contact you for further discussions in the future!
Hiroki Sayama (sayama@binghamton.edu)
🔗 https://docs.google.com/forms/d/e/1FAIpQLSeWUfPNyjC1-_NeHfHWIl0IXwhnWntdTuwhKKLxgWHv-UmWjA/viewform
You can find a similar effort in Network Science here => http://tinyurl.com/networkliteracy.
This form is to initiate an initial brainstorming process by collecting various ideas from the Complex Systems community at large. Please identify yourself so we can contact you for further discussions in the future!
Hiroki Sayama (sayama@binghamton.edu)
Google Docs
Complexity Literacy Brainstorming Form
Inspired by Laszlo Barabasi's award talk at CCS 2017 in Cancun, a small group of Twitter users have started discussing the idea to create "Complexity Literacy", a list of core ideas that should be taught/learned in Complexity / Complex Systems courses. You…
هفتهی آینده، هفتهی نوبل است. اعلام نام برندگان از روز دوشنبه و با جایزهی پزشکی شروع خواهد شد.
برندگان (یا برندهی) نوبل فیزیک، روز سهشنبه، و در زودترین زمان ساعت ۱۳:۱۵ به وقت تهران مشخص خواهند شد. معنای در زودترین زمان این است که تاخیر قابل قبول است. برای نمونه در سال ۲۰۱۳ که پیتر هیگز و فرانسیس انگلارت جایزه را بردند، آکادمی نوبل در حدود ۲ ساعت تاخیر داشت.
برندگان (یا برندهی) نوبل فیزیک، روز سهشنبه، و در زودترین زمان ساعت ۱۳:۱۵ به وقت تهران مشخص خواهند شد. معنای در زودترین زمان این است که تاخیر قابل قبول است. برای نمونه در سال ۲۰۱۳ که پیتر هیگز و فرانسیس انگلارت جایزه را بردند، آکادمی نوبل در حدود ۲ ساعت تاخیر داشت.