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I have three invitations to write things:

1) Michael Tobis invited me to write an article about the Azimuth Project on Planet 3.0.

2) Jinqiao Duan of IPAM invited me to write an article on the Mathematics of Planet Earth blog:

We encourage personal commentary on any topic associated with MPE2013. A contribution can be a report on a meeting, a pointer to important research results or educational material, a website recommendation, a short essay on a key issue, a book review, a news item, or any other material that might be of interest to a broad audience. A contribution can be as short as a couple of paragraphs and may include a photo or illustration or even an audio or video clip. We recommend no more than about 1,000 words of text. In case you are a newcomer to the blogosphere, here is a link to a helpful web site: http://www.maa.org/pubs/FOCUSfeb-mar12_blogroll.html.

We anticipate a daily blog during the entire year 2013. You may choose your date(s) and topic(s) to blog about your favorite event(s). We understand that last-minute changes are part of the action.

Please send your post in an e-mail message to blog@mpe2013.org with an indication of preferred date and category.

3) Bruce Torrence invited me to write a short article on mathematics and the environment in Math Horizons, a magazine for math majors put out by the Mathematical Association of America.

All these seem like worthy causes. I wonder if anyone here would like to help me write one of these? Your reward would be: being an official coauthor. In other words, your name would appear on the article.

I have some ideas for what these articles could be like, but if you helped me write one you'd get some say about that. Needless to say, I want something that would have maximum impact while still being fairly easy to write - and in particular, not very technical.

For example, in the *Math Horizons* article I'd like math majors to realize how serious global warming is, but also get some idea of what people who know math can do about it.

## Comments

I would be interested in helping out with an MPE blog article.

What are your thoughts regarding this one?

`I would be interested in helping out with an MPE blog article. What are your thoughts regarding this one?`

I figure some mixture of scaring the shit out of mathematicians and providing them with some good ideas for things to do is the best way to get some to start working on useful things.

As for the first part, it seems that everyone should know, and not everyone does know, how we've knocked the planet off kilter by rapidly boosting the CO

_{2}concentration to levels not seen for millions of years. Not everyone knows the probable effects of a 4 °C temperature increase. Not everyone knows how rapidly we'd need to take action to prevent this. Etc.The second part is the harder part:

what should mathematicians do?Without a good answer to this second part, the first part just gets people depressed.Of course, one can imagine very different sorts of articles, but this, done right, could be the most helpful.

`I figure some mixture of scaring the shit out of mathematicians and providing them with some good ideas for things to do is the best way to get some to start working on useful things. As for the first part, it seems that everyone should know, and not everyone does know, how we've knocked the planet off kilter by rapidly boosting the CO<sub>2</sub> concentration to levels not seen for millions of years. Not everyone knows the probable effects of a 4 °C temperature increase. Not everyone knows how rapidly we'd need to take action to prevent this. Etc. The second part is the harder part: _what should mathematicians do?_ Without a good answer to this second part, the first part just gets people depressed. Of course, one can imagine very different sorts of articles, but this, done right, could be the most helpful.`

But if you have a different sort of idea, go ahead and say what it is!

`But if you have a different sort of idea, go ahead and say what it is!`

That is a good structure. I'm up for it. I will start meditating on it, and let's exchange further thoughts as they arise. Thanks -- Dave

`That is a good structure. I'm up for it. I will start meditating on it, and let's exchange further thoughts as they arise. Thanks -- Dave`

I'm potentially interested in helping out (either informally or formally) with (3), but that's partly because I'm interested in having math majors aware that the mathematics ending at about 1900 -- which is overwhelmingly what an undergraduate math degree covers -- is only one view on things, particularly with respect to some of the environmental modelling being done; so this may not necessarily be what you'd like to see the focus on. It's also the case that probably for at least a month I won't have "long session" internet access (ie, I'd be in a position to go away and write sections of stuff based on comments and repost the next day, but probably not having real-time IRC discussions.)

Should you think this would still fit with both the intended timescale and the topics you'd like to see covered, let me know and I'll start to think about the kind of things I'd mention so we can get a sense of whether we're thinking about the same sort of things.

`I'm potentially interested in helping out (either informally or formally) with (3), but that's partly because I'm interested in having math majors aware that the mathematics ending at about 1900 -- which is overwhelmingly what an undergraduate math degree covers -- is only one view on things, particularly with respect to some of the environmental modelling being done; so this may not necessarily be what you'd like to see the focus on. It's also the case that probably for at least a month I won't have "long session" internet access (ie, I'd be in a position to go away and write sections of stuff based on comments and repost the next day, but probably not having real-time IRC discussions.) Should you think this would still fit with both the intended timescale and the topics you'd like to see covered, let me know and I'll start to think about the kind of things I'd mention so we can get a sense of whether we're thinking about the same sort of things.`

Oh-oh - two coauthors named David T! It's gonna get confusing.

Seriously, this is great. D. Tanzer has sent me some emails about item 2, the MPE blog article. I've asked his permission for me to copy those emails to this forum, since I think it's sort of fun to let everyone listen in, and chime in now and then - especially since he's raising some big issues, like the role of the social sciences in tackling environmental problems, and what math might do to help that.

D. Tweed wrote:

I love the idea of letting math majors get a taste of (and maybe for) post-1900's math, and seeing how it can help us with big real-world problems. I saw a bunch of post-1900's math as a major, but most of it was of the sort that doesn't really help much with environmental issues: algebraic topology, mathematical logic, functional analysis and the like. (Well, the last one can be useful for PDE.)

Take a look at the articles on _Math Horizons to get a feel for their length and level. The articles tend to be short, so we have to avoid the desire to mull over big issues. I think that a single concrete example of how some interesting math helps solves a practical problem, explained in a clear and non-technical way, preferably with some pictures, would be great.

Truly ideal, to my mind, would be a short discussion of some really important serious seemingly intractable environmental problem - something related to global warming, for example - followed by an example of how mathematical methods can help deal with it.

That's fine. I write lots of papers without actually

talkingto my coauthors. We clearly need to discuss things a bit before we get started, but I'm quite happy doing it here, on the Forum.`Oh-oh - two coauthors named David T! It's gonna get confusing. <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt = ""/> Seriously, this is great. D. Tanzer has sent me some emails about item 2, the MPE blog article. I've asked his permission for me to copy those emails to this forum, since I think it's sort of fun to let everyone listen in, and chime in now and then - especially since he's raising some big issues, like the role of the social sciences in tackling environmental problems, and what math might do to help that. D. Tweed wrote: > I’m potentially interested in helping out (either informally or formally) with (3), but that’s partly because I’m interested in having math majors aware that the mathematics ending at about 1900 – which is overwhelmingly what an undergraduate math degree covers – is only one view on things, particularly with respect to some of the environmental modelling being done; so this may not necessarily be what you’d like to see the focus on. I love the idea of letting math majors get a taste of (and maybe for) post-1900's math, and seeing how it can help us with big real-world problems. I saw a bunch of post-1900's math as a major, but most of it was of the sort that doesn't really help much with environmental issues: algebraic topology, mathematical logic, functional analysis and the like. (Well, the last one can be useful for PDE.) Take a look at the articles on _[Math Horizons](http://www.maa.org/mathhorizons/) to get a feel for their length and level. The articles tend to be short, so we have to avoid the desire to mull over big issues. I think that a single concrete example of how some interesting math helps solves a practical problem, explained in a clear and non-technical way, preferably with some pictures, would be great. Truly ideal, to my mind, would be a short discussion of some really important serious seemingly intractable environmental problem - something related to global warming, for example - followed by an example of how mathematical methods can help deal with it. > It’s also the case that probably for at least a month I won’t have “long session” internet access (i.e., I’d be in a position to go away and write sections of stuff based on comments and repost the next day, but probably not having real-time IRC discussions). That's fine. I write lots of papers without actually _talking_ to my coauthors. We clearly need to discuss things a bit before we get started, but I'm quite happy doing it here, on the Forum.`

Yes, I had a look at the "free articles"; assuming they're representative of the general standard (3 pages, etc) it looks enough to fit a "high-level overview of one brief idea" in. It'd be interesting to hear your ideas for suitable topics.

From my point of view, the post-1900 math was really a comment about how (at least from the point of view of a UK maths degree) most of the stuff you cover is obviously foundational, but it also gives an impression that "doing" maths is only involved the sort of things that were being done to that date. The differential equations course, for example, was a lot about various techniques for solving special differential equations, a little bit on existence proofs and unerlying algebraic structures, a little mention of non-linear systems but without really getting too involved, a tiny bit on methods of numerically solving DEs. I came away with the feeling that DEs was quite a "taxonomic subject" without very much behind it. One of the areas of interesting research these days is -- apparently, I'm not in that field -- finding symmetries/conserved quantities of differential equations and then coming up with numerical solution schemes which preserve those quantities (often the most naive numerical schemes don't preseve them). So it might be possible within the space limits to talk about how weather and climate have solving differential equations as a key issue, how accurately solving the equations is important, and then schematically give a rough example of the kind of way that being a bit more careful thinking about conserved quantities improves the accuracy. On the one hand it's starting with a common topic, linking it to the environment, and pointing out how both "deep about patterns" and computational issues are both used in getting better results, and best of all it should give the impressions that it's still a field where new stuff needs to be done. (Two downsides: 1. those kind of DEs are probably more heavily used in weather models than in climate and 2. this is just an area where I've skimmmed some papers rather than actually done anything in it -- mayber it'd be better to try for an area where at least one of us has extensive experience.)

I've got a couple of other vague thoughts, but I think hearing your ideas would be most helpful next.

(This goes by the technical name of multi-symplectic numerical solution of pde's)

`Yes, I had a look at the "free articles"; assuming they're representative of the general standard (3 pages, etc) it looks enough to fit a "high-level overview of one brief idea" in. It'd be interesting to hear your ideas for suitable topics. From my point of view, the post-1900 math was really a comment about how (at least from the point of view of a UK maths degree) most of the stuff you cover is obviously foundational, but it also gives an impression that "doing" maths is only involved the sort of things that were being done to that date. The differential equations course, for example, was a lot about various techniques for solving special differential equations, a little bit on existence proofs and unerlying algebraic structures, a little mention of non-linear systems but without really getting too involved, a tiny bit on methods of numerically solving DEs. I came away with the feeling that DEs was quite a "taxonomic subject" without very much behind it. One of the areas of interesting research these days is -- apparently, I'm not in that field -- finding symmetries/conserved quantities of differential equations and then coming up with numerical solution schemes which preserve those quantities (often the most naive numerical schemes don't preseve them). So it might be possible within the space limits to talk about how weather and climate have solving differential equations as a key issue, how accurately solving the equations is important, and then schematically give a rough example of the kind of way that being a bit more careful thinking about conserved quantities improves the accuracy. On the one hand it's starting with a common topic, linking it to the environment, and pointing out how both "deep about patterns" and computational issues are both used in getting better results, and best of all it should give the impressions that it's still a field where new stuff needs to be done. (Two downsides: 1. those kind of DEs are probably more heavily used in weather models than in climate and 2. this is just an area where I've skimmmed some papers rather than actually done anything in it -- mayber it'd be better to try for an area where at least one of us has extensive experience.) I've got a couple of other vague thoughts, but I think hearing your ideas would be most helpful next. (This goes by the technical name of multi-symplectic numerical solution of pde's)`

I know about the idea of "symplectic integrators", which must be closely related to what you're talking about. But I don't know if they're used in climate modeling or weather prediction. We could quickly find that out.

Another topic that leaps to mind is this. In both climate modeling and weather prediction, people commonly discretize space (e.g. the atmosphere) with some sort of grid, but then they need to make assumptions about what happens on "subgrid scales". Information at short distance scales, which isn't modelled, winds up affecting information at longer distance scales, which is. This is a difficult and important problem, and I think there's a lot of math here.

But as you note, it might be good to talk about an issue where at least one of us has extensive experience.

If you had to write about something

youknew a lot about, which was mathematically interesting and also relevant to "planet Earth", what would you pick?Here's something I don't know a

lotabout, but that I want to learn about, which seems mathematically interesting and potentiallyveryimportant. It's the task of taking time series data and looking for signs that a system is approaching a "tipping point".I know how to write the initial section of a paper on this, where we list a few potential tipping elements in the biosphere and convince our young readers that it's really important to keep an eye on these.

Then comes the math. For that, I'd start here:

International Journal of Chaos and Bifurcation(2010).Abstract: There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term auto-correlation coefﬁcient ARC in a sliding window of the time series: this stability coefﬁcient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7 C in 50 years. A second gives an excellent prediction for the end of ’greenhouse’ Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Paciﬁc sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models.Some quotes:

Nature461(2009), 53-59.Abstract:Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.`I know about the idea of ["symplectic integrators"](http://en.wikipedia.org/wiki/Symplectic_integrator), which must be closely related to what you're talking about. But I don't know if they're used in climate modeling or weather prediction. We could quickly find that out. Another topic that leaps to mind is this. In both climate modeling and weather prediction, people commonly discretize space (e.g. the atmosphere) with some sort of grid, but then they need to make assumptions about [what happens on "subgrid scales"](http://www.scholarpedia.org/article/Turbulence:_Subgrid-Scale_Modeling). Information at short distance scales, which isn't modelled, winds up affecting information at longer distance scales, which is. This is a difficult and important problem, and I think there's a lot of math here. But as you note, it might be good to talk about an issue where at least one of us has extensive experience. If you had to write about something _you_ knew a lot about, which was mathematically interesting and also relevant to "planet Earth", what would you pick? Here's something I don't know a _lot_ about, but that I want to learn about, which seems mathematically interesting and potentially _very_ important. It's the task of taking time series data and looking for signs that a system is approaching a "tipping point". I know how to write the initial section of a paper on this, where we list a few [[Tipping point|potential tipping elements in the biosphere]] and convince our young readers that it's really important to keep an eye on these. Then comes the math. For that, I'd start here: * J. Thompson and J. Sieber, [Predicting climate tipping points as a noisy bifurcation: a review](http://www.ucl.ac.uk/~ucess21/00%20Thompson2010%20off%20JS%20web.pdf), _International Journal of Chaos and Bifurcation_ (2010). **Abstract**: There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term auto-correlation coefﬁcient ARC in a sliding window of the time series: this stability coefﬁcient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7 C in 50 years. A second gives an excellent prediction for the end of ’greenhouse’ Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Paciﬁc sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models. * Peter Ashwin, Sebastian Wieczorek and Renato Vitolo, [Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system](http://arxiv.org/abs/1103.0169). Some quotes: > In the last few years, the idea of “tipping points” has caught the imagination in climate science with the possibility, also indicated by both palaeoclimate data and global climate models, that the climate system may abruptly “tip” from one regime to another in a comparatively short time. > This recent interest in tipping points is related to a long-standing question in climate science: to understand whether climate fluctuations and transitions between different “states” are due to external causes (such as variations in the insolation or orbital parameters of the Earth) or to internal mechanisms (such as oceanic and atmospheric feedbacks acting on different timescales). A famous example is [[Milankovitch cycles|Milankovich theory]], according to which these transitions are forced by an external cause, namely the periodic variations in the Earth’s orbital parameters. Remarkably, the evidence in favour of Milankovich theory still remains controversial. > Hasselmann was one of the first to tackle this question through simple climate models obtained as stochastically perturbed dynamical systems. He argued that the climate system can be conceptually divided into a fast component (the “weather”, essentially corresponding to the evolution of the atmosphere) and a slow component (the “climate”, that is the ocean, cryosphere, land vegetation, etc.). The “weather” would act as an essentially random forcing exciting the response of the slow “climate”. In this way, short-time scale phenomena, modelled as stochastic perturbations, can be thought of as driving long-term climate variations. This is what we refer to as noise-induced tipping. > Sutera studies noise-induced tipping in a simple global energy balance model previously derived by Fraedrich. Sutera’s results indicate a characteristic time of 105yr for the the random transitions between the “warm” and the “cold” climate states, which matches well with the observed average value. One shortcoming is that this analysis leaves open the question as to the periodicity of such transitions indicated by the power spectral analysis. There is a considerable literature on noise-induced escape from attractors in stochastic models. These have successfully been used for modelling changes in climate phenomena, although authors do not always use the word “tipping” and other aspects have been examined. For example, Kondepudi et al consider the combined effect of noise and parameter changes on the related problem of “attractor selection” in a noisy system. > More recently, bifurcation-driven tipping points or dynamic bifurcations have been suggested as an important mechanism by which sudden changes in the behaviour of a system may come about. * Marten Scheffer, Jordi Bascompte, William A. Brock, Victor Brovkin, Stephen R. Carpenter, Vasilis Dakos, Hermann Held, Egbert H. van Nes, Max Rietkerk and George Sugihara, [Early-warning signals for critical transitions](http://deepeco.ucsd.edu/~george/publications/09_critical_transitions.pdf), _[Nature](http://www.nature.com/nature/journal/v461/n7260/full/nature08227.html)_ **461** (2009), 53-59. **Abstract:** Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.`

Linked from "symplectic integrators" is geometric integrator which is apparently another name for this approach. It talks about the more sophisticated view that the aim is numerical methods which preserve various geometrical invariants of the solution, some of which happen to be invariants with well-known physical interpretation such as energy, angular momentum, etc. I did skim through a grant proposal a while ago that mentioned weather (with a big picture of the damage the famous UK storms, but I don't recall how much of that is borne out in the details and which can't currently refind the page.) On the one hand this is the kind of thing that could be made "intuitively understandable" with some diagrams and without a virtually any actual equations, on the other hand I grow more nervous as I realize how little I understand of the details so I might make some silly mistake when giving an overview. I'll have a quick dig and see if I can find anything about these that talks in details about climate (or at least weather) modelling.

The discretization issue is interesting, although I don't know enough about it to know if there's a well accepeted 1 or 2 big concepts that could be put into a very high-level form.

Part of the difficulty is that a lot of the things I know a great deal about are rather niche areas that I think are important but which aren't commonly agreed to be; I think the goals of the artilce would be better served with something more mainstream. I know a bit about the background to the kind of stuff Nathan Urban is doing, trying to fit a model to some observed data using Bayesian modelling. That seems to be reasonably well viewed as mainstream.

The tipping/point bifurcation area seems promising. I know a certain amount about "ad hoc" analysis of time series using statistics, but virtually nothing (yet) about analysing time series analytically when you've got a physically motivated model. I'll try to look through some of those papers.

`Linked from ["symplectic integrators"](http://en.wikipedia.org/wiki/Symplectic_integrator) is [geometric integrator](http://en.wikipedia.org/wiki/Geometric_integrator) which is apparently another name for this approach. It talks about the more sophisticated view that the aim is numerical methods which preserve various geometrical invariants of the solution, some of which happen to be invariants with well-known physical interpretation such as energy, angular momentum, etc. I did skim through a grant proposal a while ago that mentioned weather (with a big picture of the damage the famous UK storms, but I don't recall how much of that is borne out in the details and which can't currently refind the page.) On the one hand this is the kind of thing that could be made "intuitively understandable" with some diagrams and without a virtually any actual equations, on the other hand I grow more nervous as I realize how little I understand of the details so I might make some silly mistake when giving an overview. I'll have a quick dig and see if I can find anything about these that talks in details about climate (or at least weather) modelling. The discretization issue is interesting, although I don't know enough about it to know if there's a well accepeted 1 or 2 big concepts that could be put into a very high-level form. Part of the difficulty is that a lot of the things I know a great deal about are rather niche areas that I think are important but which aren't commonly agreed to be; I think the goals of the artilce would be better served with something more mainstream. I know a bit about the background to the kind of stuff Nathan Urban is doing, trying to fit a model to some observed data using Bayesian modelling. That seems to be reasonably well viewed as mainstream. The tipping/point bifurcation area seems promising. I know a certain amount about "ad hoc" analysis of time series using statistics, but virtually nothing (yet) about analysing time series analytically when you've got a physically motivated model. I'll try to look through some of those papers.`

I haven't read the whole comment, but

This is a kind of typo, because actually the jargon is that information at short distance scalesisbeingmodelled, it has to be modeled because it is not resolved (yes the same word model is used differently when speaking about a weather model as a whole, which is rather about the resolved information). The problem is that these subgrid models are not as accurate as the basic equations would be (well, a "more basic equation") but these basic equations need quantities which are too variable for the chosen grid size. Therefore, because resolving these quantities is computationally expensive, one has to model them.I would say it's often loosely reminiscent of the integrating out of heavy degrees of freedom in hep, except that it usually works better there ;-)

[EDIT: if you like to discuss these subgrid issues further in another thread I'd be happy to join as far as I'm able to]

`I haven't read the whole comment, but > but then they need to make assumptions about what happens on “subgrid scales”. Information at short distance scales, which isn’t modelled, winds up affecting information at longer distance scales, which is. **This is a kind of typo**, because actually the jargon is that information at short distance scales **is** being *modelled*, it has to be modeled because it is not resolved (yes the same word model is used differently when speaking about a weather model as a whole, which is rather about the resolved information). The problem is that these subgrid models are not as accurate as the basic equations would be (well, a "more basic equation") but these basic equations need quantities which are too variable for the chosen grid size. Therefore, because resolving these quantities is computationally expensive, one has to model them. I would say it's often loosely reminiscent of the integrating out of heavy degrees of freedom in hep, except that it usually works better there ;-) [EDIT: if you like to discuss these subgrid issues further in another thread I'd be happy to join as far as I'm able to]`

Okay: what I meant by "not being modelled" is that they're not being

resolved. Thanks!Steve Easterbrook pointed out another use of language that's a bit special to the weather and climate modelling community: they seem to distinguish between

dynamics, which is the explicit rule for updating the quantities that have been resolved, andphysics, which goes into choosing a model for the quantities that haven't. Or something like that.Perhaps all this proves that I shouldn't write an article about this stuff, because even if I learn enough to know what I'm talking about I won't say it in a way that real experts would.

`Okay: what I meant by "not being modelled" is that they're not being **resolved**. Thanks! Steve Easterbrook pointed out another use of language that's a bit special to the weather and climate modelling community: they seem to distinguish between **dynamics**, which is the explicit rule for updating the quantities that have been resolved, and **physics**, which goes into choosing a model for the quantities that haven't. Or something like that. Perhaps all this proves that I shouldn't write an article about this stuff, because even if I learn enough to know what I'm talking about I won't say it in a way that real experts would.`

David Tweed wrote:

Maybe we should talk about that, then. An especially nice feature of this is that I've already interviewed Nathan about his work, and he's available for questions.

Furthermore, the basic concept of Bayesian modelling is the kind of simple general abstract thing that young mathematicians like. And furthermore, this particular concept is one that most young mathematicians don't learn! Not if they're in math departments like mine, anyway.

`David Tweed wrote: > I know a bit about the background to the kind of stuff Nathan Urban is doing, trying to fit a model to some observed data using Bayesian modelling. That seems to be reasonably well viewed as mainstream. Maybe we should talk about that, then. An especially nice feature of this is that I've already interviewed Nathan about his work, and he's available for questions. Furthermore, the basic concept of Bayesian modelling is the kind of simple general abstract thing that young mathematicians like. And furthermore, this particular concept is one that most young mathematicians don't learn! Not if they're in math departments like mine, anyway.`

Maybe you can bring some outsider insights, and then in the end the ideas only need to be translated to the existent jargon :)

`> Perhaps all this proves that I shouldn’t write an article about this stuff, because even if I learn enough to know what I’m talking about I won’t say it in a way that real experts would. Maybe you can bring some outsider insights, and then in the end the ideas only need to be translated to the existent jargon :)`

Hi John,

have you already got any information about word-lengths, illustrations issues, house style, etc that you could let me know about (either here or by email), or shall I try and contact them directly to find out this stuff? (The way I'm inclined to approach this is via partly trying to work with a budget from the start even as we're investigating what ideas to cover to try to keep a rough track of the "amount of stuff that we can cover in a way that remains comprehensible" rather than initially work unconstrained and then be faced with cutting bits out without also making it much harder to follow. Possibly you might have a different approach you'd like to use?)

`Hi John, have you already got any information about word-lengths, illustrations issues, house style, etc that you could let me know about (either here or by email), or shall I try and contact them directly to find out this stuff? (The way I'm inclined to approach this is via partly trying to work with a budget from the start even as we're investigating what ideas to cover to try to keep a rough track of the "amount of stuff that we can cover in a way that remains comprehensible" rather than initially work unconstrained and then be faced with cutting bits out without also making it much harder to follow. Possibly you might have a different approach you'd like to use?)`

John wrote:

I don't think that there is much math in there today, but that its rather a collection of heuristics, after glancing through

But since none of us has any working knowledge of this, I happily agree that this is not my primary choice of a topic either :-)

David Tweed wrote:

Do you already have a storyline for this topic that makes it interesting?

John wrote:

That would actually be my first choice, since we already wrote a little bit about it over here, in the context of stochastic resonance (the bistable system is the simplest example of a system with a tipping point).

It also has a great story line:

1) Start with the picture of an ice planet (from "The Empire Strikes Back" or any sci fi show - I know we probably cannot use original pictures, but I think you get the point). Point out that Earth may have looked like that once.

2) Explain that such drastic changes have happened in the past, may happen again.

3) Trying to understand models that show this behaviour is essentially 20th/ 21rst century mathematics, that is: very much modern.

4) Talk a little bit about random walks, stochastic differential equations, dynamical systems with random elements,

5) Maybe point out a simple example of the Feynman-Kac formula, the heat equation in two dimensions.

6) A lot of simple questions about such models are open, but results from mathematicians are necessary to check computer models.

A remark to 5: I remember how I was enthusiastic about the fact that one can solve a partial differential equation like the heat equation by simulating a random walk and taking averages, because that means that the physical intuition behind the derivation of the heat equation has actually a mathematical equivalent. I even gave a talk in the math department about this :-)

I think that the story with how Earth maybe once was an ice planet is a perfect introduction for an article which gets readers interested to go beyond the first paragraph.

I'll try to find the time to read the references that John cited and come back after that.

`John wrote: <blockquote> <p> In both climate modeling and weather prediction, people commonly discretize space (e.g. the atmosphere) with some sort of grid, but then they need to make assumptions about what happens on “subgrid scales”. Information at short distance scales, which isn’t modelled, winds up affecting information at longer distance scales, which is. This is a difficult and important problem, and I think there’s a lot of math here. </p> </blockquote> I don't think that there is much math in there today, but that its rather a collection of heuristics, after glancing through * David J. Stensrud: "Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models" But since none of us has any working knowledge of this, I happily agree that this is not my primary choice of a topic either :-) David Tweed wrote: <blockquote> <p> I know a bit about the background to the kind of stuff Nathan Urban is doing, trying to fit a model to some observed data using Bayesian modelling. That seems to be reasonably well viewed as mainstream. </p> </blockquote> Do you already have a storyline for this topic that makes it interesting? John wrote: <blockquote> <p> Here’s something I don’t know a lot about, but that I want to learn about, which seems mathematically interesting and potentially very important. It’s the task of taking time series data and looking for signs that a system is approaching a “tipping point”. </p> </blockquote> That would actually be my first choice, since we already wrote a little bit about it over here, in the context of stochastic resonance (the bistable system is the simplest example of a system with a tipping point). It also has a great story line: 1) Start with the picture of an ice planet (from "The Empire Strikes Back" or any sci fi show - I know we probably cannot use original pictures, but I think you get the point). Point out that Earth may have looked like that once. 2) Explain that such drastic changes have happened in the past, may happen again. 3) Trying to understand models that show this behaviour is essentially 20th/ 21rst century mathematics, that is: very much modern. 4) Talk a little bit about random walks, stochastic differential equations, dynamical systems with random elements, 5) Maybe point out a simple example of the Feynman-Kac formula, the heat equation in two dimensions. 6) A lot of simple questions about such models are open, but results from mathematicians are necessary to check computer models. A remark to 5: I remember how I was enthusiastic about the fact that one can solve a partial differential equation like the heat equation by simulating a random walk and taking averages, because that means that the physical intuition behind the derivation of the heat equation has actually a mathematical equivalent. I even gave a talk in the math department about this :-) I think that the story with how Earth maybe once was an ice planet is a perfect introduction for an article which gets readers interested to go beyond the first paragraph. I'll try to find the time to read the references that John cited and come back after that.`

Hi Tim, glad to hear from you. I had a long answer that the browser has just eaten... Quite how the world ended up with such a braindead way of implementing functionality on the internet I've no idea. I''ll try to retype in a day or so when I've got time, but the key point is that Math Horizons looks to take 3-4 page, 3 columns per page articles which have a really quite small amount of explicit formulae. So it's going to be important not to try to stuff too many things/details in there.

`Hi Tim, glad to hear from you. I had a long answer that the browser has just eaten... Quite how the world ended up with such a braindead way of implementing functionality on the internet I've no idea. I''ll try to retype in a day or so when I've got time, but the key point is that Math Horizons looks to take 3-4 page, 3 columns per page articles which have a really quite small amount of explicit formulae. So it's going to be important not to try to stuff too many things/details in there.`

David Tweed wrote:

As for word lengths, they said this was somewhat flexible, but we should aim for the "3-4 page, 3 columns per page" size you mention. This is very short, so the key thing is to invent a simple story that will be exciting to students majoring in math, and resist all digressions or elaborations. And as you note, there should be very few formulae! It's not a math paper, it's a news story with the delicious feature that it only needs to be enjoyed by people who don't run away screaming if there's an equation or two.

As for ‘'house style', I suspect that if the paper is written in LaTeX and fairly simple they will deal with that. I'll ask at some point.

As for illustrations, they said they can do high-quality graphics and they really like that! So, we should try to make somehting nice. To be rather rude, something like this will not be good enough - we should try for something visually beautiful.

I'm completely in sympathy with Tim van Beek's suggestions - most of them, anyway. But if I'm writing this with you (David Tweed, that is), it should be about a subject

youlike.`David Tweed wrote: > have you already got any information about word-lengths, illustrations issues, house style, etc that you could let me know about (either here or by email), or shall I try and contact them directly to find out this stuff? As for word lengths, they said this was somewhat flexible, but we should aim for the "3-4 page, 3 columns per page" size you mention. This is very short, so the key thing is to invent a simple story that will be exciting to students majoring in math, and resist all digressions or elaborations. And as you note, there should be very few formulae! It's not a math paper, it's a news story with the delicious feature that it only needs to be enjoyed by people who don't run away screaming if there's an equation or two. As for ‘'house style', I suspect that if the paper is written in LaTeX and fairly simple they will deal with that. I'll ask at some point. As for illustrations, they said they can do high-quality graphics and they really like that! So, we should try to make somehting nice. To be rather rude, something like [this](http://www.azimuthproject.org/azimuth/files/stochres_weaknoise.jpg) will not be good enough - we should try for something visually beautiful. I'm completely in sympathy with Tim van Beek's suggestions - most of them, anyway. But if I'm writing this with you (David Tweed, that is), it should be about a subject _you_ like.`

Tim: if you want to help me write a blog article for the Mathematics of Planet Earth blog, we could probably write something about bistability or Snowball Earth, even if I write another article for them with David Tanzer. I doubt they have too many people wanting to write blog articles - and capable of writing good ones.

And this article could probably, perhaps after some further polishing, be officially published in a journal or magazine somewhere. In case that's what you want.

`Tim: if you want to help me write a blog article for the Mathematics of Planet Earth blog, we could probably write something about bistability or Snowball Earth, even if I write another article for them with David Tanzer. I doubt they have too many people wanting to write blog articles - and capable of writing good ones. And this article could probably, perhaps after some further polishing, be officially published in a journal or magazine somewhere. In case that's what you want.`

David wrote:

Ok, so maybe my suggestion is a little bit oversized, but I'll just wait to see what you have in mind.

John wrote:

No problem :-). I'd be happy to help you and David with your article even without being included as a co-author, but I'm not a graphical type, so don't expect any beautiful graphics from me. I always have to force myself to create any graphics at all for any concept or presentation I write for my bread-and-butter job (software project lead and lead developer, so those who know what that entails know that there are a lot of concepts and presentations involved).

Ok, we could prepare two, one with David as a lead author and one from myself. Coming back to Azimuth after an almost year long hiatus, I find that I'm still interested in the same stuff, that is: computational fluid dynamics starting with the Burgers equation (which will maybe make me pick up the "Fluid flows and infinite dimensional manifolds" series) and Time series analysis. Which leads us to...

Some time ago I collected some references for nonlinear time series analysis on the Time series analysis, including the Kantz and Schreiber book that is referenced by Thompson and J. Sieber. A blog article for the Mathematics of Planet Earth blog should probably explain the basic ideas of Thompson, Sieber and the other papers you cited, right? Some "original" work for Azimuth could consist in trying to apply these techniques to model output like the bistable system from stochastic resonance. While stochastic resonance is also cited in the Thompson and Sieber paper, there is no citation of work where such a model system was used as a time series generator.

It's not my primary objective since I don't crave for my name to be printed on high-gloss paper or to expand my publication list on my CV :-)

`David wrote: <blockquote> <p> So it’s going to be important not to try to stuff too many things/details in there. </p> </blockquote> Ok, so maybe my suggestion is a little bit oversized, but I'll just wait to see what you have in mind. John wrote: <blockquote> <p> To be rather rude, something like this will not be good enough - we should try for something visually beautiful. </p> </blockquote> No problem :-). I'd be happy to help you and David with your article even without being included as a co-author, but I'm not a graphical type, so don't expect any beautiful graphics from me. I always have to force myself to create any graphics at all for any concept or presentation I write for my bread-and-butter job (software project lead and lead developer, so those who know what that entails know that there are a lot of concepts and presentations involved). <blockquote> <p> Tim: if you want to help me write a blog article for the Mathematics of Planet Earth blog, we could probably write something about bistability or Snowball Earth, even if I write another article for them with David Tanzer. </p> </blockquote> Ok, we could prepare two, one with David as a lead author and one from myself. Coming back to Azimuth after an almost year long hiatus, I find that I'm still interested in the same stuff, that is: computational fluid dynamics starting with the Burgers equation (which will maybe make me pick up the "Fluid flows and infinite dimensional manifolds" series) and [[Time series analysis]]. Which leads us to... <blockquote> <p> It’s the task of taking time series data and looking for signs that a system is approaching a “tipping point”. </p> </blockquote> Some time ago I collected some references for nonlinear time series analysis on the [[Time series analysis]], including the Kantz and Schreiber book that is referenced by Thompson and J. Sieber. A blog article for the Mathematics of Planet Earth blog should probably explain the basic ideas of Thompson, Sieber and the other papers you cited, right? Some "original" work for Azimuth could consist in trying to apply these techniques to model output like the bistable system from [[stochastic resonance]]. While [[stochastic resonance]] is also cited in the Thompson and Sieber paper, there is no citation of work where such a model system was used as a time series generator. <blockquote> <p> And this article could probably, perhaps after some further polishing, be officially published in a journal or magazine somewhere. In case that’s what you want. </p> </blockquote> It's not my primary objective since I don't crave for my name to be printed on high-gloss paper or to expand my publication list on my CV :-)`

I may be able to help with pictures. I mostly use R for graphs and Inkscape (SVG format) for diagrams.

`I may be able to help with pictures. I mostly use R for graphs and Inkscape (SVG format) for diagrams.`

Hi Graham et al., I also might be able to help with pictures; I also use Inkscape. Maybe we can even work on some together.

I drew a lot of the pictures for the network theory series, and can send anyone the SVG source files or modify them to make new ones, as needed (just email me if you want the zip file: jacob.biamonte@qubit.org).

If we need anything fancy, I also hired a part time artist who is likely much more serious about this stuff than either of us! It's better when using her to have really specific things in mind.

`Hi Graham et al., I also might be able to help with pictures; I also use Inkscape. Maybe we can even work on some together. I drew a lot of the pictures for the network theory series, and can send anyone the SVG source files or modify them to make new ones, as needed (just email me if you want the zip file: jacob.biamonte@qubit.org). If we need anything fancy, I also hired a part time artist who is likely much more serious about this stuff than either of us! It's better when using her to have really specific things in mind.`

Thanks, everyone! I guess I'll start by:

Trying to decide - mainly with David Tweed since he wanted to be a coauthor - what we will write about for

Math Horizons. We should decide on something soon, and we need to finish this article by August.Trying - mainly with David Tanzer since he wanted to be a coauthor - what we will write about for the MPE blog. I'd like to decide this soon, too! The ultimate deadline is late in 2013, I guess, but sooner seems better to me.

Once we know what we're writing, we can start thinking about pictures and other ways people can help out. We can also start thinking about more blog articles.

Let me talk only about the article with David Tweed in this thread, since I've got another thread going with David Tanzer.

The articles I can easily imagine writing are:

Something about tipping points and bistability in the Earth's climate system, stochastic resonance, etc.. This would be easy to write based on existing Azimuth Blog articles, and easy is good. Left to my own devices I could write a draft of this in a day. Then the trick would be getting nice pictures.

Something about detecting incipient tipping points in time series data. I don't know enough about this, so this would require reading and thinking, but it would be something I want to do.

Something about Bayesian estimation of parameters. The interview with Nathan Urban gives a nice example application to climate change, but that interview didn't give a sufficiently detailed explanation of the basic ideas, starting with Bayes' Rule.

Something else.

What do you like best, David Tweed?

`Thanks, everyone! I guess I'll start by: 1. Trying to decide - mainly with David Tweed since he wanted to be a coauthor - what we will write about for _Math Horizons_. We should decide on something soon, and we need to finish this article by August. 2. Trying - mainly with David Tanzer since he wanted to be a coauthor - what we will write about for the MPE blog. I'd like to decide this soon, too! The ultimate deadline is late in 2013, I guess, but sooner seems better to me. Once we know what we're writing, we can start thinking about pictures and other ways people can help out. We can also start thinking about more blog articles. Let me talk only about the article with David Tweed in this thread, since I've got another thread going with David Tanzer. The articles I can easily imagine writing are: 1. Something about tipping points and bistability in the Earth's climate system, stochastic resonance, etc.. This would be easy to write based on existing Azimuth Blog articles, and easy is good. Left to my own devices I could write a draft of this in a day. Then the trick would be getting nice pictures. 1. Something about detecting incipient tipping points in time series data. I don't know enough about this, so this would require reading and thinking, but it would be something I want to do. 1. Something about Bayesian estimation of parameters. The interview with Nathan Urban gives a nice example application to climate change, but that interview didn't give a sufficiently detailed explanation of the basic ideas, starting with Bayes' Rule. 1. Something else. What do you like best, David Tweed?`

For the above cited three links it doesn't look as if a high graphical standard is needed, although planet 3.0 looks as being more aware with respect to graphical issues. However if you want to publish elsewhere then one should keep in mind that it may be the case that aggregators/journals etc. may have other needs. In particular some magazines etc. have a graphical language which is with respect to the whole magazine. I.e. regardless how fancy your images may look they may want to alter them and your layout too.

In particular the terrible

this- graph may be just fine and cool in some alternative fanzine.I could also try to help you with the graphics, but as I currently try to find a work opportunity through freelancing, I may end up asking money for this work.

`>As for illustrations, they said they can do high-quality graphics and they really like that! So, we should try to make somehting nice. To be rather rude, something like *this* will not be good enough - we should try for something visually beautiful. For the above cited three links it doesn't look as if a high graphical standard is needed, although planet 3.0 looks as being more aware with respect to graphical issues. However if you want to publish elsewhere then one should keep in mind that it may be the case that aggregators/journals etc. may have other needs. In particular some magazines etc. have a graphical language which is with respect to the whole magazine. I.e. regardless how fancy your images may look they may want to alter them and your layout too. In particular the terrible *this* - graph may be just fine and cool in some alternative fanzine. I could also try to help you with the graphics, but as I currently try to find a work opportunity through freelancing, I may end up asking money for this work.`

By the way some websites allow also for more intricate visualisations, so for these you would probably want to promote your interactive charts.

So eventually for the graphical part you would consider hiring an information architect, see e.g. the website of Gregor Aisch

`By the way some websites allow also for more intricate visualisations, so for these you would probably want to promote your interactive charts. So eventually for the graphical part you would consider hiring an information architect, see e.g. the website of <a href="http://driven-by-data.net/about/zeit-nuclear/#/0">Gregor Aisch</a>`

By the way for those who got interested in the US nuclear power plant map: unfortunately there is not link to the map. It looks as if the red bubble on the lower part of the image comes from the oyster creek station which was luckily

"...shut down for a refueling and maintenance outage prior to the storm and the reactor remains out of service.

during Sandy.

...where the last words in the citation read now as:

As NRC staff made clear, their goal was to listen to the petitioners, though the staff did explain why the NRC denied the petitioners’ request to keep Oyster Creek shut down following the storm.

`By the way for those who got interested in the US nuclear power plant map: unfortunately there is not link to the map. It looks as if the red bubble on the lower part of the image comes from the <a href="http://en.wikipedia.org/wiki/Oyster_Creek_Nuclear_Generating_Station">oyster creek station</a> which was luckily <a href="http://public-blog.nrc-gateway.gov/2012/10/30/nrc-keeps-eye-on-nuclear-plants-in-sandys-path-including-three-that-shut-down-during-the-storm/">"...shut down for a refueling and maintenance outage prior to the storm and the reactor remains out of service.</a> during Sandy. ...where the last words in the citation read now as: <a href="http://public-blog.nrc-gateway.gov/2013/01/">As NRC staff made clear, their goal was to listen to the petitioners, though the staff did explain why the NRC denied the petitioners’ request to keep Oyster Creek shut down following the storm.</a>`

I wrote:

Is anyone interested in helping me with this one? I think this is our big chance to write something about how the Azimuth Project has been going and where we want it to go. I could take the lead but it might be more fun with a coauthor!

`I wrote: > 1) Michael Tobis invited me to write an article about the Azimuth Project on [Planet 3.0](http://planet3.org/). Is anyone interested in helping me with this one? I think this is our big chance to write something about how the Azimuth Project has been going and where we want it to go. I could take the lead but it might be more fun with a coauthor!`

Is there a constraint about the topics? And about time/format?

In principle I would like to help, but perhaps I should finish my own blog articles on Azimuth first.

In fact, thanks to Azimuth (indirectly) I moved from physics to earth sciences (but, no, not to atmospheric and radiation sciences, in that case my blog articles were probably already finished ;) ). I graduated just before Azimuth came online.

`> 1) Michael Tobis invited me to write an article about the Azimuth Project on Planet 3.0. Is there a constraint about the topics? And about time/format? In principle I would like to help, but perhaps I should finish my own blog articles on Azimuth first. In fact, thanks to Azimuth (indirectly) I moved from physics to earth sciences (but, no, not to atmospheric and radiation sciences, in that case my blog articles were probably already finished ;) ). I graduated just before Azimuth came online.`

Frederik wrote:

It's supposed to be about the Azimuth Project. He's trying to give us a chance to get more people interested in the Azimuth Project. So, I imagine we should tell some story about what we've done, what we're like, and what we're trying to do. We could even talk about how it's hard to be exactly sure what we should do! But we should probably

mostlyact like we know what we're doing.The time is completely flexible, but naturally sooner is better, since the planet is going to hell.

The format... just an ordinary sort of blog article. If you look at articles on Planet 3.0 you may get a better idea of what they want. But it's pretty flexible, I think.

Well, that's great! That counts as a success of the Azimuth Project, I think.

You've been around for almost all of the project, I guess. It's interesting to think how people like David Tanzer, very active now, were not present for the initial phases of the project and don't know what that felt like.

(I don't know if there's anyone else

likeDavid Tanzer, but you know what I mean.)`Frederik wrote: > Is there a constraint about the topics? And about time/format? It's supposed to be about the Azimuth Project. He's trying to give us a chance to get more people interested in the Azimuth Project. So, I imagine we should tell some story about what we've done, what we're like, and what we're trying to do. We could even talk about how it's hard to be exactly sure what we should do! But we should probably _mostly_ act like we know what we're doing. > And about time/format? The time is completely flexible, but naturally sooner is better, since the planet is going to hell. The format... just an ordinary sort of blog article. If you look at articles on [Planet 3.0](http://planet3.org/) you may get a better idea of what they want. But it's pretty flexible, I think. > In fact, thanks to Azimuth (indirectly) I moved from physics to earth sciences... Well, that's great! That counts as a success of the Azimuth Project, I think. You've been around for almost all of the project, I guess. It's interesting to think how people like David Tanzer, very active now, were not present for the initial phases of the project and don't know what that felt like. (I don't know if there's anyone else _like_ David Tanzer, but you know what I mean.)`

Hi John,

I wrote something here but then I thought I might prefer to email you instead! Since I was not keen to own a post in a public forum. Hope that is ok.

`Hi John, I wrote something here but then I thought I might prefer to email you instead! Since I was not keen to own a post in a public forum. Hope that is ok.`