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I'm back

I got back from Montreal last morning and now I'm mostly over jet lag.

I spent a lot of time over the last three weeks thinking about old favorite subjects of mine: quantum gravity (thanks to the conference in Zurich) and higher gauge theory (thanks to talking with my former student Derek Wise in Erlangen).

The two-week-long conference reaffirmed my belief that people working on quantum gravity are stuck. Many of those people are good friends of mine, so it was nice to see them again, but I'm very glad I quit working on that subject. If I had any regrets, they've been eliminated. I guess that's good.

On the other hand, talking to Derek, we had a really good idea on how to see general relativity as a higher gauge theory, and I couldn't resist helping him write a paper on this. The idea took one minute to have, so I wanted to write the paper in a 'blitzkrieg' style, finishing it off in one week, but it's not working that way. I'm sort of regretting this, because I want to focus on environmental issues. However, it's a very nice idea, and Derek keeps making it nicer. Since gravity is his main area of research, it's easy to forgive him!

One of my goals now is to write some This Week's Finds on Milankovitch cycles, glacial cycles, stochastic resonance and bistability. I guess I should start with an easy summary article, and then a more detailed one on Milankovitch cycles, and then... well, I've discovered that it's bad to plan these things out too carefully, because then they feel like 'work' and I resist doing them! I've already put this off for way too long, perhaps for that reason.

Comments

  • 1.

    The "stochastic resonance" part has a big advantage, as other simple dynamical systems with or without noise: It is easy to visualize and I think that climate people haven't squeezed all out of these models that could be of use. If you would like to publish a paper in the subject, to get known, this is one possible line of attack.

    On the other hand I don't think that there is any need of a bad conscience over thinking about general relativity. I'm very curious about this GR as higher gauge theory.

    People in numerical general relativity use spectral methods, too, for example, so I may think about GR in the future, too.

    Comment Source:The "stochastic resonance" part has a big advantage, as other simple dynamical systems with or without noise: It is easy to visualize and I think that climate people haven't squeezed all out of these models that could be of use. If you would like to publish a paper in the subject, to get known, this is one possible line of attack. On the other hand I don't think that there is any need of a bad conscience over thinking about general relativity. I'm very curious about this GR as higher gauge theory. People in numerical general relativity use [[spectral methods]], too, for example, so I may think about GR in the future, too.
  • 2.

    Do you have ideas on stochastic resonance that could be new? I need to start publishing papers on environmental/climate/energy issues, and I think it would be fun to write one with you.

    Lisa suggested that I try to write a review article on Milankovitch cycles and the like for Surveys in Geophysics. I might be able to do this after learning more and writing it up in This Week's Finds. It might seem unlikely that they'd want to publish an article from me (since I'm not a geophysicist), but I got an email from the editor asking me to write a history of the Earth's geophysics after I published The Earth - For Physicists in Physics World back in 2009. So, I might also try something like that.

    Comment Source:Do you have ideas on stochastic resonance that could be new? I need to start publishing papers on environmental/climate/energy issues, and I think it would be fun to write one with you. Lisa suggested that I try to write a review article on Milankovitch cycles and the like for _Surveys in Geophysics_. I might be able to do this after learning more and writing it up in _This Week's Finds_. It might seem unlikely that they'd want to publish an article from me (since I'm not a geophysicist), but I got an email from the editor asking me to write a history of the Earth's geophysics after I published [The Earth - For Physicists](http://math.ucr.edu/home/baez/earth.html) in _Physics World_ back in 2009. So, I might also try something like that.
  • 3.

    You could of course vary the potential, the noise and other inputs of the simplest model of stochastic resonance and see what you get, but that does not seem to be particularly interesting. But I wonder if it would be possible to determine the probability of observed time series given a parametric model. This is essentially a parametric estimation for a class of stochastic differential equations. It would result in some quantitative results, instead of simply illustrating that stochastic resonance is an interesting model in a qualitative way.

    Quite a simple thing to do, but I haven't found anyone who has done this. Not even for the famous hockey stick. Some people have claimed that they reproduced the hockey stick with an AR(1) process, but that does not mean anything at all. If you run enough simulations, sooner or later you'll get a path that resembles anything, this is a trivial implication of the theory :-) The important question would be about confidence intervals for parametric estimations.

    I also have a textbook on my desk about turbulence from the viewpoint of dynamical systems, this is about approximating fluid flow described by Navier-Stokes equations with a low dimensional system of ODE. I don't know if this could be of interest in climate science, but from what I have seen people in climate science have published very very simple models and considerations only.

    Comment Source:You could of course vary the potential, the noise and other inputs of the simplest model of stochastic resonance and see what you get, but that does not seem to be particularly interesting. But I wonder if it would be possible to determine the probability of observed time series given a parametric model. This is essentially a parametric estimation for a class of stochastic differential equations. It would result in some quantitative results, instead of simply illustrating that stochastic resonance is an interesting model in a qualitative way. Quite a simple thing to do, but I haven't found anyone who has done this. Not even for the famous hockey stick. Some people have claimed that they reproduced the hockey stick with an AR(1) process, but that does not mean anything at all. If you run enough simulations, sooner or later you'll get a path that resembles anything, this is a trivial implication of the theory :-) The important question would be about confidence intervals for parametric estimations. I also have a textbook on my desk about turbulence from the viewpoint of dynamical systems, this is about approximating fluid flow described by Navier-Stokes equations with a low dimensional system of ODE. I don't know if this could be of interest in climate science, but from what I have seen people in climate science have published very very simple models and considerations only.
  • 4.

    Hmm. I have no particular need or desire to publish in journals of climate science. It could be that a journal of probability and statistics is the best place to write about parameter estimation for stochastic resonance, and it could be that a journal of fluid mechanics is the best place to write about approximating Navier-Stokes by low-dimensional PDE.

    I would, however, like to work on a subject where I (or someone I know, like you ) have a spark of insight and the main job is filling in the details. Which can, of course, be a lot of work.

    I don't yet have a spark of insight regarding Milankovich cycles and glacial cycles, but I feel that kind of excited curiosity that tends to precede such a spark...

    Comment Source:Hmm. I have no particular need or desire to publish in journals of _climate science_. It could be that a journal of probability and statistics is the best place to write about parameter estimation for stochastic resonance, and it could be that a journal of fluid mechanics is the best place to write about approximating Navier-Stokes by low-dimensional PDE. I would, however, like to work on a subject where I (or someone I know, like you <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt = ""/>) have a spark of insight and the main job is filling in the details. Which can, of course, be a lot of work. I don't yet have a spark of insight regarding Milankovich cycles and glacial cycles, but I feel that kind of excited curiosity that tends to precede such a spark...
  • 5.

    Well, that was just some brainstorming about stuff that I may get into. But I'm quite sure that it would be a lot of fun to write a paper with you, probably about something else, then. Whenever you need someone to program a simulation, numerical approximation or visualization of anything...

    Comment Source:Well, that was just some brainstorming about stuff that I may get into. But I'm quite sure that it would be a lot of fun to write a paper with you, probably about something else, then. Whenever you need someone to program a simulation, numerical approximation or visualization of anything...
  • 6.
    edited July 2011

    Okay, let's do something. I could get excited about those 2 things you mentioned if you or I came up with a clever idea about them. I just don't feel I have a clever idea about those particular things yet... so right now, they make me feel stupid instead of excited.

    I really really really want to know why the Earth's climate has been fluctuating so erratically over the last million years or so. I'll start reading more about this, and writing about it, and coming up with questions, and we'll probably think of something fun to do.

    It could require us to do parameter estimation for stochastic resonance!

    Comment Source:Okay, let's do something. I could get excited about those 2 things you mentioned if you or I came up with a clever idea about them. I just don't feel I have a clever idea about those particular things yet... so right now, they make me feel stupid instead of excited. I really really really want to know why the Earth's climate has been fluctuating so erratically over the last million years or so. I'll start reading more about this, and writing about it, and coming up with questions, and we'll probably think of something fun to do. It could require us to do parameter estimation for stochastic resonance!
  • 7.
    edited July 2011

    Sounds great! The estimation thingy is just one thing I would like to do, because it seems to be the obvious thing to do when you have time series in one hand and SDE models in the other hand. I wrote a short introduction about this topic almost a year ago: Parametric estimation for stochastic differential equations.

    Comment Source:Sounds great! The estimation thingy is just one thing I would like to do, because it seems to be the obvious thing to do when you have time series in one hand and SDE models in the other hand. I wrote a short introduction about this topic almost a year ago: [[Parametric estimation for stochastic differential equations]].
  • 8.

    I may have mentioned it before, but if you're thinking of writing a review article on the Milankovitch cycles, you might want to read Michel Crucifix's review article on the subject, either for inspiration or ideas for what hasn't been covered in previous reviews.

    Comment Source:I may have mentioned it before, but if you're thinking of writing a review article on the Milankovitch cycles, you might want to read Michel Crucifix's <a href="http://www.astr.ucl.ac.be/users/crucifix/2010_Springer_Encyclopeadia_Crucifix.pdf">review article</a> on the subject, either for inspiration or ideas for what <em>hasn't</em> been covered in previous reviews.
  • 9.
    edited July 2011

    Hi, thanks for stopping by!

    I've got that paper by Michel Crucifix on my hard drive. I'm sure we have linked it on the Wiki, too.

    But: Has the "I have reproduced the hockey stick with an AR(1) process" been addressed already? It would be understandable if climate scientists ignore such claims, but it is something that we could do over here for starters.

    Comment Source:Hi, thanks for stopping by! I've got that paper by Michel Crucifix on my hard drive. I'm sure we have linked it on the Wiki, too. But: Has the "I have reproduced the hockey stick with an AR(1) process" been addressed already? It would be understandable if climate scientists ignore such claims, but it is something that we could do over here for starters.
  • 10.

    Over the years there have been about a bazillion statistical analyses on the web, from both "sides", of Holocene paleotemperature reconstructions as well as the instrumental temperature record. Personally I'm bored to death by them, and feel that there are plenty of more useful things that could be done here. I don't even think the hockey stick is that relevant to the "debate". But feel free to pursue your own interests.

    Comment Source:Over the years there have been about a bazillion statistical analyses on the web, from both "sides", of Holocene paleotemperature reconstructions as well as the instrumental temperature record. Personally I'm bored to death by them, and feel that there are plenty of more useful things that could be done here. I don't even think the hockey stick is that relevant to the "debate". But feel free to pursue your own interests.
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