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Here's a list of projects I want to finish off. I've been thinking about a lot of new stuff for the last year and a half, but I have to go back and teach at U.C. Riverside in September, so it's time to stop starting things and start finishing things.

This is a mix of Azimuth-related stuff and unrelated stuff.

This weekend I checked the galley proofs for the book

*Infinite-Dimensional Representations of 2-Groups*, which I wrote with Derek Wise and two other guys. Derek still needs to check it before we give the publisher the okay to publish it. We've been working on this since 2007, so it'll be great to get that done.Today I finished off the paper Teleparallel gravity and higher gauge theory, also written with Derek. Again, Derek needs to check it before we put it on the arXiv and submit it for publication.

I want to finish the paper A Noether theorem for Markov processes, based on a blog post written with Brendan Fong. Right now this only applies to Markov processes with bounded transition rates - that needs to be fixed, since these don't include the examples coming from stochastic Petri nets.

I want to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire. This is 'recreational mathematics' as far as I'm concerned, which makes me feel a bit guilty, but we got invited to write about it for the

*AMS Notices*, and it's lots of fun too, so I want to do it.I want to write a long paper on stochastic Petri nets with Jacob Biamonte, based on the network theory blog posts. This will take at least a couple of months, mixed in with other activities. I'll be happy if it's done when I leave Singapore.

I can imagine other papers, e.g. on quantropy, but this should be enough to keep me busy! I also have some blogging to do:

I want to publicize Allan Erskine's simple online climate models, starting with a blog post.

I want to edit and publish Tim Van Beek's blog post on [[Blog - fluid flows and infinite-dimensional manifolds|fluid flows and infinite-dimensional manifolds]].

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]].

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper.

Blogging makes a fun break from 'real' writing, so I'll go back and forth between these two activities!

I'm writing this list mainly to put my thoughts in order, but I hope I'll feel a burst of pleasure each time I post a comment here saying I've finished another job!

Source Text:

`hoidle`

## Comments

Sorry, but I'll get more done if I keep saying what I've done:

Last night I wrote a blog article on Elsevier dropping its support for the Research Works Act. That was pretty exciting.

This morning I found that the Research Works Act is dead, so I blogged about that, and what we should next. That was even more exciting! But if I'd known this would happen so soon, I would have skipped the previous blog article.

Today I got word from Derek that our book was okay, and told the publisher that. So that item is off the list. Yay!

I pestered Derek asking him if he thinks our teleparallel gravity paper is done.

I decided to avoid distracting issues of analysis in the Noether's theorem paper with Brendan Fong. By restricting to finite state spaces, as we did in the blog entry, everything will become very easy. One alternative is to consider countable state spaces and unbounded Hamiltonians... but this makes it more tiresome to say what it means for an operator to commute with the Hamiltonian. An even more strenuous alternative is to consider arbitrary measure spaces and unbounded Hamiltonians. But this paper is supposed to be short and sweet. So, I've started rewriting it to work with finite state spaces.

`Sorry, but I'll get more done if I keep saying what I've done: 1. Last night I wrote a blog article on [Elsevier dropping its support for the Research Works Act](http://johncarlosbaez.wordpress.com/2012/02/27/elsevier-gives-up-on-research-work-act/). That was pretty exciting. 1. This morning I found that [the Research Works Act is dead](http://johncarlosbaez.wordpress.com/2012/02/28/research-work-act-dead-what-next/), so I blogged about that, and what we should next. That was even more exciting! But if I'd known this would happen so soon, I would have skipped the previous blog article. 1. Today I got word from Derek that our [book](http://math.ucr.edu/home/baez/2rep.pdf) was okay, and told the publisher that. So that item is off the list. Yay! 1. I pestered Derek asking him if he thinks our [teleparallel gravity paper](http://math.ucr.edu/home/baez/teleparallel.pdf) is done. 1. I decided to avoid distracting issues of analysis in the [Noether's theorem paper](http://math.ucr.edu/home/baez/noether.pdf) with Brendan Fong. By restricting to finite state spaces, as we did in the blog entry, everything will become very easy. One alternative is to consider countable state spaces and unbounded Hamiltonians... but this makes it more tiresome to say what it means for an operator to commute with the Hamiltonian. An even more strenuous alternative is to consider arbitrary measure spaces and unbounded Hamiltonians. But this paper is supposed to be short and sweet. So, I've started rewriting it to work with finite state spaces.`

Oh, it is going to be a full book in print?

`<blockquote> <p> Today I got word from Derek that our book was okay, and told the publisher that. So that item is off the list. Yay! </p> </blockquote> Oh, it is going to be a full book in print?`

Yes,

Infinite-dimensional Representations of 2-Groupswill be published as a slim book in a series called Memoirs of the American Mathematical Society. It's more like an article than a book, but it was too long for any journal to publish as a single article, and we didn't want to chop it into pieces.It's annoyingly technical, but it involves a curious mix of 2-category theory and nice old-fashioned ideas from analysis developed by Mackey, Varadarajan and Dixmier: fields of Hilbert spaces (which are sort of like bundles with Hilbert spaces as fiber) and standard Borel spaces (which turn out to be a very nice class of measure spaces). I can imagine you liking that stuff (though not our book).

I also had to learn much more than I ever knew or even thought wanted to know about the classification of locally compact abelian groups. It's a rather charming subject though not sexy by modern standards. You can't completely classify them, but there's a nice structure theory.

`Yes, _Infinite-dimensional Representations of 2-Groups_ will be published as a slim book in a series called Memoirs of the American Mathematical Society. It's more like an article than a book, but it was too long for any journal to publish as a single article, and we didn't want to chop it into pieces. It's annoyingly technical, but it involves a curious mix of 2-category theory and nice old-fashioned ideas from analysis developed by Mackey, Varadarajan and Dixmier: fields of Hilbert spaces (which are sort of like bundles with Hilbert spaces as fiber) and standard Borel spaces (which turn out to be a very nice class of measure spaces). I can imagine you liking that stuff (though not our book). I also had to learn much more than I ever knew or even thought wanted to know about the classification of locally compact abelian groups. It's a rather charming subject though not sexy by modern standards. You can't completely classify them, but there's a nice structure theory.`

Yesterday and today:

I wrote another blog article on the journals problem, called The Education of a Scientist. It features a cartoon that everyone should watch and show their friends!

I may have finished my paper with Brendan Fong, A Noether theorem for Markov processes. I'd be interested in comments, especially from Tim van Beek and Martin Gisser, who might enjoy the analysis used in the Conclusions. It's sort of weird to end the paper with a conjecture as we do - especially since the conjecture is probably not very hard! But on the one hand I don't feel like proving it right now, and on the other I think someone should.

`Yesterday and today: 1. I wrote another blog article on the journals problem, called [The Education of a Scientist](http://johncarlosbaez.wordpress.com/2012/02/29/8410/). It features a cartoon that everyone should watch and show their friends! 1. I may have finished my paper with Brendan Fong, [A Noether theorem for Markov processes](http://math.ucr.edu/home/baez/noether.pdf). I'd be interested in comments, especially from Tim van Beek and Martin Gisser, who might enjoy the analysis used in the Conclusions. It's sort of weird to end the paper with a conjecture as we do - especially since the conjecture is probably not very hard! But on the one hand I don't feel like proving it right now, and on the other I think someone should.`

So here is a revised and pleasantly shorter to-do list:

I want to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire. This is 'recreational mathematics' as far as I'm concerned, which makes me feel a bit guilty, but we got invited to write about it for the

AMS Notices, and it's lots of fun too, so I want to do it.I want to write a long paper on stochastic Petri nets with Jacob Biamonte, based on the network theory blog posts. This will take at least a couple of months, mixed in with other activities. I'll be happy if it's done when I leave Singapore.

I can imagine other papers, e.g. on quantropy, but this should be enough to keep me busy! I also have some blogging to do:

I published Tim Van Beek's blog post on fluid flows and infinite-dimensional manifolds.

I want to write and publish a post on the master equation for monatomic/diatomic gases for the network theory series.

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], again for the network theory series.

I want to publicize Allan Erskine's simple online climate models, starting with a blog post - perhaps a This Week's Finds.

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper.

I want to write another article about Burgers' equation and diffeomorphism groups, or get Tim to do it.

`So here is a revised and pleasantly shorter to-do list: 1. I want to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. This is 'recreational mathematics' as far as I'm concerned, which makes me feel a bit guilty, but we got invited to write about it for the _AMS Notices_, and it's lots of fun too, so I want to do it. 1. I want to write a long paper on stochastic Petri nets with Jacob Biamonte, based on the [network theory](http://math.ucr.edu/home/baez/networks/) blog posts. This will take at least a couple of months, mixed in with other activities. I'll be happy if it's done when I leave Singapore. I can imagine other papers, e.g. on quantropy, but this should be enough to keep me busy! I also have some blogging to do: 1. I published Tim Van Beek's blog post on [fluid flows and infinite-dimensional manifolds](http://johncarlosbaez.wordpress.com/2012/03/12/fluid-flows-and-infinite-dimensional-manifolds/). 1. I want to write and publish a post on the master equation for monatomic/diatomic gases for the network theory series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], again for the network theory series. 1. I want to publicize Allan Erskine's [simple online climate models](http://www.math.ntnu.no/~stacey/Mathforge/Azimuth/comments.php?DiscussionID=892&Focus=6042#Comment_6042), starting with a blog post - perhaps a This Week's Finds. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. 1. I want to write another article about Burgers' equation and diffeomorphism groups, or get Tim to do it.`

I would reorder your blogging list as items 2-4 all sound more exciting than 1.

You've observed yourself that the simple model we implemented could use some work to make it interesting, and also I haven't noticed you blogging on other uninteresting subject matters (eg "The tawdriness of squares"). Perhaps we could incorporate some suggestions and revisit?

`I would reorder your blogging list as items 2-4 all sound more exciting than 1. You've observed yourself that the simple model we implemented could use some work to make it interesting, and also I haven't noticed you blogging on other uninteresting subject matters (eg "The tawdriness of squares"). Perhaps we could incorporate some suggestions and revisit?`

Allan wrote:

If you have the energy and desire to improve the software, I

certainlyhave the energy and desire to make the model more exciting. In fact I'll be more eager to blog about what we've got so far if the prospect of improvements is dangling before me like a tempting plum. And sad to say, I think we'llneedsomething more exciting before George Musser gets interested. I've been feeling bad about this...So: great! Let's talk about it on the 'simple climate models' thread, or something like that.

`Allan wrote: > Perhaps we could incorporate some suggestions and revisit? If you have the energy and desire to improve the software, I _certainly_ have the energy and desire to make the model more exciting. In fact I'll be more eager to blog about what we've got so far if the prospect of improvements is dangling before me like a tempting plum. And sad to say, I think we'll _need_ something more exciting before George Musser gets interested. I've been feeling bad about this... So: great! Let's talk about it on the 'simple climate models' thread, or something like that.`

Papers get a life of their own and don't

wantto be finished. At least that's my theory. It's happening now:Derek Wise is not satisfied with Teleparallel gravity and higher gauge theory in its current state. This was going to be a 2-part paper, and though we weren't easily able to finish the second part, there's a bunch of material in there. Derek has a plan for making the first (and now only) part better using some of that material. Luckily he's willing to do most of the work, but at some point I'll need to go back to it and polish what he's done, while simultaneously making sure I understand it!

I couldn't resist proving the conjecture at the end of A Noether theorem for Markov processes. I've spent the last 4 days doing that. It's almost done except for an annoying subtlety that most casual readers probably won't even notice! I still need to straighten that out. But I think I can do it.

So, I've almost proved that an observable commutes with time evolution in a Markov chain iff its mean and variance don't change with each time step. More precisely:

Theorem:Suppose $X$ is a $\sigma$-finite measure space and $U: L^1(X) \to L^1(X)$ is stochastic operator. Suppose $O$ is an observable - that is, an operator $O: L^1(X) \to L^1(X)$ given by multiplication by some function in $L^\infty(X)$. Then $[O,U] = 0$ if and only if for all probability distributions $\psi$ on $X$, $\langle O, U \psi \rangle = \langle O, \psi \rangle$ and $\langle O^2, U \psi \rangle = \langle O^2, \psi \rangle$.This in turn gives a similar theorem for continuous-time Markov processes. The proof was surprisingly technical - it takes me back to the days when I did lots of functional analysis. Maybe there's an easier one I didn't see!

Anyway, I'm now ready to reward myself by taking a break and doing one of the blog entries on my list.

`Papers get a life of their own and don't _want_ to be finished. At least that's my theory. It's happening now: 1. Derek Wise is not satisfied with [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf) in its current state. This was going to be a 2-part paper, and though we weren't easily able to finish the second part, there's a bunch of material in there. Derek has a plan for making the first (and now only) part better using some of that material. Luckily he's willing to do most of the work, but at some point I'll need to go back to it and polish what he's done, while simultaneously making sure I understand it! 2. I couldn't resist proving the conjecture at the end of [A Noether theorem for Markov processes](http://math.ucr.edu/home/baez/noether.pdf). I've spent the last 4 days doing that. It's almost done except for an annoying subtlety that most casual readers probably won't even notice! I still need to straighten that out. But I think I can do it. So, I've almost proved that an observable commutes with time evolution in a Markov chain iff its mean and variance don't change with each time step. More precisely: **Theorem:** Suppose $X$ is a $\sigma$-finite measure space and $U: L^1(X) \to L^1(X)$ is stochastic operator. Suppose $O$ is an observable - that is, an operator $O: L^1(X) \to L^1(X)$ given by multiplication by some function in $L^\infty(X)$. Then $[O,U] = 0$ if and only if for all probability distributions $\psi$ on $X$, $\langle O, U \psi \rangle = \langle O, \psi \rangle$ and $\langle O^2, U \psi \rangle = \langle O^2, \psi \rangle$. This in turn gives a similar theorem for continuous-time Markov processes. The proof was surprisingly technical - it takes me back to the days when I did lots of functional analysis. Maybe there's an easier one I didn't see! Anyway, I'm now ready to reward myself by taking a break and doing one of the blog entries on my list.`

Well, actually yesterday Brendan sent me a list of errors in our paper A Noether theorem for Markov processes, which I fixed. And then I felt the need to blog about it. There's some fun stuff about fat-tailed probability distributions lurking here, which I made into a puzzle, which Greg Egan solved. The idea of fat-tailed probability distributions is important for thinking about crises - financial crises, weather disasters and so on.

Today I will try to edit and maybe even post Tim van Beek's post [[Blog - fluid flows and infinite-dimensional manifolds|Fluid flows and infinite-dimensional manifolds]].

`> Anyway, I'm now ready to reward myself by taking a break and doing one of the blog entries on my list. Well, actually yesterday Brendan sent me a list of errors in our paper [A Noether theorem for Markov processes](http://math.ucr.edu/home/baez/noether.pdf), which I fixed. And then I felt the need to blog about it. There's some fun stuff about fat-tailed probability distributions lurking here, which I made into a puzzle, which Greg Egan solved. The idea of fat-tailed probability distributions is important for thinking about crises - financial crises, weather disasters and so on. Today I will try to edit and maybe even post Tim van Beek's post [[Blog - fluid flows and infinite-dimensional manifolds|Fluid flows and infinite-dimensional manifolds]].`

Here's a list of blog entries I want to work on, in no particular order:

Today I did a bunch of editing on Tim Van Beek's blog post on [[Blog - fluid flows and infinite-dimensional manifolds|fluid flows and infinite-dimensional manifolds]]. I asked him a few questions, but it's close to done.

I want to publicize Allan Erskine's simple online climate models, starting with a blog post.

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]].

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper.

I want to read and edit Staffan Lilgeren's blog post on [[Blog - carbon cycle box models (part 1)|Carbon cycle box models (part 1)]].

`Here's a list of blog entries I want to work on, in no particular order: 1. Today I did a bunch of editing on Tim Van Beek's blog post on [[Blog - fluid flows and infinite-dimensional manifolds|fluid flows and infinite-dimensional manifolds]]. I asked him a few questions, but it's close to done. 1. I want to publicize Allan Erskine's [simple online climate models](http://www.math.ntnu.no/~stacey/Mathforge/Azimuth/comments.php?DiscussionID=892&Focus=6042#Comment_6042), starting with a blog post. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]]. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. 1. I want to read and edit Staffan Lilgeren's blog post on [[Blog - carbon cycle box models (part 1)|Carbon cycle box models (part 1)]].`

Ugh... I knew I should have a look. But then, I should also have sleep... I hope I'm confused about the Markov Noether theorem, cf. blog comment...

`Ugh... I knew I should have a look. But then, I should also have sleep... I hope I'm confused about the Markov Noether theorem, cf. [blog comment](http://johncarlosbaez.wordpress.com/2012/03/07/a-noether-theorem-for-markov-processes/#comment-14214)...`

I answered your blog comment on the blog, Martin. The theorem Brendan and I proved surely isn't vacuous. It's not very profound, either... but it did take some work to prove.

`I answered your blog comment on the blog, Martin. The theorem Brendan and I proved surely isn't vacuous. It's not very profound, either... but it did take some work to prove.`

I didn't do much today except polish my paper with Brendan a bit more and put it on the arXiv.

I'm waiting for Tim to sign off on [[Blog - fluid flow and infinite-dimensional manifolds]], but in the meantime I will get to work on another blog article.

`I didn't do much today except polish my paper with Brendan a bit more and put it on the arXiv. I'm waiting for Tim to sign off on [[Blog - fluid flow and infinite-dimensional manifolds]], but in the meantime I will get to work on another blog article.`

Okay, here's what I've done recently, and what I still need to do. Papers:

I need to submit Noether's theorem for Markov processes for publication.

I'm waiting for Derek Wise to complete a new draft of our teleparallel gravity and higher gauge theory paper so I can edit that.

I want to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire. This is 'recreational mathematics' as far as I'm concerned, which makes me feel a bit guilty, but we got invited to write about it for the

AMS Notices, and it's lots of fun too, so I want to do it.I want to write a long paper on stochastic Petri nets with Jacob Biamonte, based on the network theory blog posts. This will take at least a couple of months, mixed in with other activities. I'll be happy if it's done when I leave Singapore.

Blog articles:

Today I published Tim Van Beek's blog post on fluid flows and infinite-dimensional manifolds

I want to publicize Allan Erskine's simple online climate models, starting with a blog post. Maybe a

This Week's Finds!I want to write a blog post on the master equation for monatomic/diatomic gases, for the network theory series.

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning.

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper.

There's certainly more to do, like a paper on quantropy and another blog post on fluid flows and diffeomorphisms. But this should keep me plenty busy.

`Okay, here's what I've done recently, and what I still need to do. Papers: 1. I need to submit [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) for publication. 1. I'm waiting for Derek Wise to complete a new draft of our [teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf) paper so I can edit that. 1. I want to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. This is 'recreational mathematics' as far as I'm concerned, which makes me feel a bit guilty, but we got invited to write about it for the _AMS Notices_, and it's lots of fun too, so I want to do it. 1. I want to write a long paper on stochastic Petri nets with Jacob Biamonte, based on the [network theory](http://math.ucr.edu/home/baez/networks/) blog posts. This will take at least a couple of months, mixed in with other activities. I'll be happy if it's done when I leave Singapore. Blog articles: 1. Today I published Tim Van Beek's blog post on [fluid flows and infinite-dimensional manifolds](http://johncarlosbaez.wordpress.com/2012/03/12/fluid-flows-and-infinite-dimensional-manifolds/) 1. I want to publicize Allan Erskine's [simple online climate models](http://www.math.ntnu.no/~stacey/Mathforge/Azimuth/comments.php?DiscussionID=892&Focus=6042#Comment_6042), starting with a blog post. Maybe a _This Week's Finds!_ 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. There's certainly more to do, like a paper on quantropy and another blog post on fluid flows and diffeomorphisms. But this should keep me plenty busy.`

I was sick last week with a nasty flu, and it's been taking me a while to get back up to speed. Here's the progress since last time:

Derek Wise made a lot of progress on our paper teleparallel gravity and higher gauge theory, but then he got distracted finishing writing something for the Gravity Research Foundation essay competition. That's due in a week. I really want to finish this paper, but it will take a while.

[[Jacob Biamonte]] and I started converting the network theory blog posts into a long paper or short book, tentatively called Quantum techniques for stochastic mechanics! It's 130 pages long now. It needs a lot of work.

`I was sick last week with a nasty flu, and it's been taking me a while to get back up to speed. Here's the progress since last time: 1. Derek Wise made a lot of progress on our paper [teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf), but then he got distracted finishing writing something for the Gravity Research Foundation essay competition. That's due in a week. I really want to finish this paper, but it will take a while. 2. [[Jacob Biamonte]] and I started converting the network theory blog posts into a long paper or short book, tentatively called [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf)! It's 130 pages long now. It needs a lot of work.`

Over the last week and a half I've been doing lots of work - but unfortunately, it's work on a paper that's not even on the to-do lists I've written so far!

In short, this is a piece of 'mad scientist' mathematics of the sort I used to do. I want to finish it because it's been obsessing me for at least ten years - and while it sounds insanely esoteric, it's actually the

leastesoteric appearance of the octonions in physics. (They show up all over string theory, and help to explain why string theory works best in 10 dimensions.)Luckily this paper is almost done, and then I'll return to normal life. In fact this morning I want to finish week319.

`Over the last week and a half I've been doing lots of work - but unfortunately, it's work on a paper that's not even on the to-do lists I've written so far! 1. My former student John Huerta is visiting Singapore and we're writing up a paper called [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). It's about ball rolling on another ball without slipping or twisting. If the rolling ball is like a spin-1/2 particle (so you need to turn it around twice for it to come back to its original orientation) and the fixed one is actually a projective plane (so the rolling ball only needs to roll halfway around it to come back to its original position), the space of the rolling ball's possible positions is the same as the space of light rays seen by someone living in a 7-dimensional universe with 3 time dimensions and 4 space dimensions! And when one ball is exactly 3 times as big as the other, something even better happens: the whole problem has the same symmetries as the '[split octonions](http://en.wikipedia.org/wiki/Split-octonion)': an 8-dimensional number system closely related to the less obscure (but let's face it, still damned obscure) system called the [octonions](http://math.ucr.edu/home/baez/octonions/). The symmetry group is called $G_2$, and it's 14-dimensional. Unless the ratio of radii is 1:3, and unless we work with a rolling ball that's like a spin-1/2 particle, the symmetry group is much smaller. In short, this is a piece of 'mad scientist' mathematics of the sort I used to do. I want to finish it because it's been obsessing me for [at least ten years](http://math.ucr.edu/home/baez//rolling.html) - and while it sounds insanely esoteric, it's actually the _least_ esoteric appearance of the octonions in physics. (They show up all over string theory, and help to explain why string theory works best in 10 dimensions.) Luckily this paper is almost done, and then I'll return to normal life. In fact this morning I want to finish [week319](http://math.ucr.edu/home/baez/week319.html).`

Did you finish? Perhaps you could try cutting/pasting the fancier looking graphs of the coalbedo function I made? They have axes and everything!

`Did you finish? Perhaps you could try cutting/pasting the fancier looking [graphs of the coalbedo function](http://64.131.197.246/~aerskine/azimuth-coalbedo-example-dev/www/coalbedo.html) I made? They have axes and everything!`

Allan wrote:

Not yet - I got distracted by something else. It should just take a couple of hours. Could you write a paragraph about how you made this program, what the issues were, what you wish someone would do to make this kind of thing easier, or anything interesting about those issues? I want to include something like that.

Okay, great! Let me try that now. Yes, it works!

Excellent - thanks a lot.

`Allan wrote: > Did you finish? Not yet - I got distracted by something else. It should just take a couple of hours. Could you write a paragraph about how you made this program, what the issues were, what you wish someone would do to make this kind of thing easier, or anything interesting about those issues? I want to include something like that. > Perhaps you could try cutting/pasting the fancier looking graphs of the coalbedo function I made? They have axes and everything! Okay, great! Let me try that now. Yes, it works! Excellent - thanks a lot.`

By the way, I posted a few more blog articles:

One containing some questions about The 1990 IPCC Climate Projections.

One featuring a video of my talk Energy, the Environment and What We Should Do, given at Google via telepresence robot.

A guest post by Todd McKissick: The Living Smart Grid. I don't enough to evaluate it (much less 'endorse' it), but it seems like a good thing for people to talk about!

Here's the work I need to do on papers.

John Huerta and I need to figure out how to prove the capstone theorem of our paper G2 and the rolling ball. He's leaving tomorrow so we should do a lot of work on this today!

Derek Wise has written a new draft of our paper Teleparallel gravity and higher gauge theory paper, and he says it's basically done. I need to look at it, polish it up a bit, and finish it off!

I need to submit my paper with Brendan Fong, Noether's theorem for Markov processes for publication. What's a good math journal for a short paper on Markov processes, where I can talk about quantum theory and expect people to understand it?

Jacob Biamonte has been working away on our long paper tentatively called Quantum techniques for stochastic mechanics. I need to get back to this!

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

There are also some blog articles to write:

Week 319 is basically done - I want a paragraph or two from Allan Erskine explaining what he did to write the programs that appear in this issue, what are some of the issues he faced, what would make it easier to write such programs... or anything else interesting!

I want to write a blog post on the master equation for monatomic/diatomic gases, for the network theory series.

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning.

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.

`By the way, I posted a few more blog articles: 1. One containing some questions about [The 1990 IPCC Climate Projections](http://johncarlosbaez.wordpress.com/2012/03/27/the-1990-ipcc-climate-projections/). 1. One featuring a video of my talk [Energy, the Environment and What We Should Do](http://johncarlosbaez.wordpress.com/2012/04/05/energy-the-environment-and-what-we-can-do/), given at Google via telepresence robot. 1. A guest post by Todd McKissick: [The Living Smart Grid](http://johncarlosbaez.wordpress.com/2012/04/07/the-living-smart-grid/). I don't enough to evaluate it (much less 'endorse' it), but it seems like a good thing for people to talk about! Here's the work I need to do on papers. 1. John Huerta and I need to figure out how to prove the capstone theorem of our paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). He's leaving tomorrow so we should do a lot of work on this today! 1. Derek Wise has written a new draft of our paper [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf) paper, and he says it's basically done. I need to look at it, polish it up a bit, and finish it off! 1. I need to submit my paper with Brendan Fong, [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) for publication. What's a good math journal for a short paper on Markov processes, where I can talk about quantum theory and expect people to understand it? 1. Jacob Biamonte has been working away on our long paper tentatively called [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). I need to get back to this! 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. There are also some blog articles to write: 1. [Week 319](http://math.ucr.edu/home/baez/week319.html) is basically done - I want a paragraph or two from Allan Erskine explaining what he did to write the programs that appear in this issue, what are some of the issues he faced, what would make it easier to write such programs... or anything else interesting! 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

It's not uncommon in papers or books about best practices or the dig-out of some software project to insert standout boxes with the personal statement of a developer, like

"Finally we chose JavaScript."

I've always liked this kind of format, because besides the final solution you also get a glimpse at all the caveats that were discussed along the way.

`<blockquote> <p> I want a paragraph or two from Allan Erskine explaining what he did to write the programs that appear in this issue, what are some of the issues he faced, what would make it easier to write such programs... or anything else interesting! </p> </blockquote> It's not uncommon in papers or books about best practices or the dig-out of some software project to insert standout boxes with the personal statement of a developer, like "Finally we chose JavaScript." <blockquote> <p> <b>Allan Erskine</b>: Actually I would have preferred to... </p> </blockquote> I've always liked this kind of format, because besides the final solution you also get a glimpse at all the caveats that were discussed along the way.`

So let's hear your thoughts,

Allan Erskine!`So let's hear your thoughts, **Allan Erskine**!`

Here's the situation as of today. New stuff done since the last report:

I posted Week 319 on the blog.

I think Derek and I are basically done with our paper Teleparallel gravity and higher gauge theory. He had expanded it a lot; now I've gone through all that new stuff and polished up to the point where I'm happy with it.

Here's the work I need to do on papers:

John Huerta are a bit stuck on a result that's supposed to conclude our paper G2 and the rolling ball. We should either prove that or cut it out.

I need to submit my paper with Brendan Fong, Noether's theorem for Markov processes for publication. What's a good math journal for a short paper on Markov processes, where I can talk about quantum theory and expect people to understand it?

I need to finish off my paper with Jacob Biamonte, Quantum techniques for stochastic mechanics.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

There are also more blog articles to write:

I want to write a blog post on the master equation for monatomic/diatomic gases, for the network theory series.

I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning.

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.

`Here's the situation as of today. New stuff done since the last report: 1. I posted [Week 319](http://math.ucr.edu/home/baez/week319.html) on the blog. 1. I think Derek and I are basically done with our paper [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf). He had expanded it a lot; now I've gone through all that new stuff and polished up to the point where I'm happy with it. Here's the work I need to do on papers: 1. John Huerta are a bit stuck on a result that's supposed to conclude our paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). We should either prove that or cut it out. 1. I need to submit my paper with Brendan Fong, [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) for publication. What's a good math journal for a short paper on Markov processes, where I can talk about quantum theory and expect people to understand it? 1. I need to finish off my paper with Jacob Biamonte, [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. There are also more blog articles to write: 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

Here's my current state. For the newcomers here: if you can click on someone's name, it means they're part of the Azimuth Project and they have a page on the Azimuth Wiki. You should get one too! You can do yourself, just by typing your full name into the search box and doing the usual stuff. Ask if you need help!

First, papers that aren't related to Azimuth:

I'm almost done writing G2 and the rolling ball with John Huerta. I'n the process I've become a real expert on some obscure and useless stuff like the algebra of split octonions, to the point where the ordinary octonions seem pathetically trivial and boring. It'll make a killer talk at math department colloquia, and it wraps up a ten-year obsession I've had with this topic, but apart from that it's been a huge distraction from more important things.

I need to submit my paper with Derek Wise, Teleparallel gravity and higher gauge theory. There are some tiny changes to make, but it's done.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, papers that

arerelated to Azimuth:I need to submit my paper with [[Brendan Fong]], Noether's theorem for Markov processes for publication - I've been putting this off for no good reason.

I need to finish off my long paper with [[Jacob Biamonte]], Quantum techniques for stochastic mechanics.

Then, blog articles:

I posted an article by Todd McKissick on Personal rapid transportation.

I need to get [[Tim van Beek]]'s okay to post [[Fluid flows and infinite-dimensional manifolds II]].

I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]]

I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]].

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.

`Here's my current state. For the newcomers here: if you can click on someone's name, it means they're part of the Azimuth Project and they have a page on the Azimuth Wiki. You should get one too! You can do yourself, just by typing your full name into the search box and doing the [usual stuff](http://www.azimuthproject.org/azimuth/show/Help+edit+this+wiki). Ask if you need help! First, papers that aren't related to Azimuth: 1. I'm almost done writing [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf) with John Huerta. I'n the process I've become a real expert on some obscure and useless stuff like the algebra of [split octonions](http://en.wikipedia.org/wiki/Split-octonion), to the point where the ordinary [octonions](http://math.ucr.edu/home/baez/octonions/) seem pathetically trivial and boring. It'll make a killer talk at math department colloquia, and it wraps up a ten-year obsession I've had with this topic, but apart from that it's been a huge distraction from more important things. 1. I need to submit my paper with Derek Wise, [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf). There are some tiny changes to make, but it's done. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, papers that _are_ related to Azimuth: 1. I need to submit my paper with [[Brendan Fong]], [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) for publication - I've been putting this off for no good reason. 1. I need to finish off my long paper with [[Jacob Biamonte]], [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). Then, blog articles: 1. I posted an article by Todd McKissick on [Personal rapid transportation](http://johncarlosbaez.wordpress.com/2012/04/21/high-speed-personal-rapid-transportation/). 1. I need to get [[Tim van Beek]]'s okay to post [[Fluid flows and infinite-dimensional manifolds II]]. 1. I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]] 1. I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]]. 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

Tim said he'd make a few more corrections on [[Fluid flows and infinite-dimensional manifolds (part 2)]].

I'm going to Hong Kong the day after tomorrow, May 10th, and staying until the 25th. At first I'll be at Chinese University, but starting on the 13th I'll be at the University of Hong Kong visiting the mathematician Jiang-Hua Lu. I'll give two talks there. I've already inflicted them with an environmental talk so these will be about my old sort of stuff - two papers I just finished:

G2 and the Rolling BallTeleparallel Gravity as a Higher Gauge TheoryI don't know the dates yet.

`Tim said he'd make a few more corrections on [[Fluid flows and infinite-dimensional manifolds (part 2)]]. I'm going to Hong Kong the day after tomorrow, May 10th, and staying until the 25th. At first I'll be at Chinese University, but starting on the 13th I'll be at the University of Hong Kong visiting the mathematician Jiang-Hua Lu. I'll give two talks there. I've already inflicted them with an environmental talk so these will be about my old sort of stuff - two papers I just finished: **[G2 and the Rolling Ball](http://math.ucr.edu/home/baez/ball.pdf)** > Understanding the exceptional Lie groups as the symmetry groups of simpler objects is a longstanding challenge. Here we describe how the smallest exceptional Lie group, G2, shows up as symmetries of a simple physics problem: a ball rolling on a larger ball without slipping or twisting. G2 acts as symmetries of this problem, but only when we treat the smaller ball as a "spinor", which returns to its orientation not after one full turn but only after two — and only when the larger ball is 3 times as big as the smaller one! We show how to understand this special ratio, describe the geometry of the rolling ball system in terms of imaginary split octonions, and show how geometric quantization applied to this system lets us recover the imaginary split octonions together with their cross product. **[Teleparallel Gravity as a Higher Gauge Theory](http://math.ucr.edu/home/baez/teleparallel.pdf)** > Higher gauge theory uses '2-connections' to describe parallel transport not only along curves, but also over surfaces. Just as gauge theory uses Lie groups, higher gauge theory uses Lie 2-groups. We show that general relativity can be viewed as a higher gauge theory. On any semi-Riemannian manifold M, we construct a principal 2-bundle with the the 'teleparallel 2-group' as its structure 2-group. Any flat metric-preserving connection on M gives a flat 2-connection on this 2-bundle, and the key ingredient of this 2-connection is the torsion. Taking advantage of Einstein and Cartan's formulation of general relativity in which a flat connection and its torsion are are key ingredients, this lets us rewrite general relativity as a theory with a 2-connection for the teleparallel 2-group as its only field. I don't know the dates yet.`

Cool. Let me know if you're up for a dinner and/or beers. It would be good to see you again. If humanly possibly, I'd be interested in trying to catch one of the talks.

`Cool. Let me know if you're up for a dinner and/or beers. It would be good to see you again. If humanly possibly, I'd be interested in trying to catch one of the talks.`

Hi! I'll be at HKU starting on Sunday, so how about getting together sometime that week? I'll tell you (and everyone) when my talks will occur, as soon as I find out!

`Hi! I'll be at HKU starting on Sunday, so how about getting together sometime that week? I'll tell you (and everyone) when my talks will occur, as soon as I find out!`

Have a look at the online models we have, over at the forum thread for the blog post, I think the latest one is great!

`<blockquote> <p> I need to edit and post Tim's increasing the signal-to-noise ratio with more noise. </p> </blockquote> Have a look at the online models we have, over at the forum thread for the blog post, I think the latest one is great!`

Great! I'm sorry to be so distracted... I'll check out the stuff.

`Great! I'm sorry to be so distracted... I'll check out the stuff.`

Here's my current state:

I just gave a talk on chemical reaction networks and category theory at Paris 7. This reminded me that I need to figure out a bit more about Fock space and symmetric monoidal categories to make my paper Quantum techniques for stochastic mechanics really nice.

I wrote 3 blog entries on information theory and evolutionary game theory to help prepare for my talk in Barcelona. I need to do more.

Then there are papers that aren't related to Azimuth:

John Huerta wants to add another section to our paper G2 and the rolling ball. He's writing it, but at some point I'll need to polish it up.

I need to submit my paper with Derek Wise, Teleparallel gravity and higher gauge theory, to

Communications in Mathematical Physics. This should take 15 minutes.I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, papers that

arerelated to Azimuth:I need to submit my paper with [[Brendan Fong]], Noether's theorem for Markov processes for publication - I've been putting this off for no good reason.

I need to finish off my long paper with [[Jacob Biamonte]], Quantum techniques for stochastic mechanics.

Then, blog articles:

I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]]

I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]].

`Here's my current state: 1. I just gave a talk on chemical reaction networks and category theory at Paris 7. This reminded me that I need to figure out a bit more about Fock space and symmetric monoidal categories to make my paper [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf) really nice. 1. I wrote 3 blog entries on information theory and evolutionary game theory to help prepare for my talk in Barcelona. I need to do more. Then there are papers that aren't related to Azimuth: 1. John Huerta wants to add another section to our paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). He's writing it, but at some point I'll need to polish it up. 1. I need to submit my paper with Derek Wise, [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf), to _Communications in Mathematical Physics_. This should take 15 minutes. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, papers that _are_ related to Azimuth: 1. I need to submit my paper with [[Brendan Fong]], [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) for publication - I've been putting this off for no good reason. 1. I need to finish off my long paper with [[Jacob Biamonte]], [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). Then, blog articles: 1. I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]] 1. I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]]. 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

We could also pick up the thread with [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]...some day...

`We could also pick up the thread with [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]...some day...`

Okay, Tim, I'll add that to my to-do list. Are you waiting for me to do something regarding part 4?

`Okay, Tim, I'll add that to my to-do list. Are you waiting for me to do something regarding part 4?`

Sorry all you Azimuthers: I'm extremely distracted by the program on The Mathematics of Biodiversity here in Barcelona. I think it will help me shift my career toward 'green mathematics', so I want to spend as much time as possible talking to biologists here. That means I'm neglecting the Azimuth Forum for a while.

But at least I'm getting some work done. Here's my current state. First, talks:

Then, papers that aren't related to Azimuth:

I submitted my paper with Derek Wise, Teleparallel gravity and higher gauge theory, to

Communications in Mathematical Physics.John Huerta wants to add another section to our paper G2 and the rolling ball. He's still writing it - he had surgery for an old eye injury, so he's a bit distracted.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, papers that

arerelated to Azimuth:I submitted my paper with [[Brendan Fong]], Noether's theorem for Markov processes to

Journal of Mathematical Physics.I need to finish off my long paper with [[Jacob Biamonte]], Quantum techniques for stochastic mechanics.

Then, blog articles:

First, blogging:

I wrote The Mathematics of Biodiversity (Part 1) and The Mathematics of Biodiversity (Part 2) about estimating the fraction of species haven't been observed yet, a notoriously difficult problem in biology.

I wrote Information Geometry (Part 12), about evolutionary game theory. I have part 13 almost but not quite done.

I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]]

I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]].

`Sorry all you Azimuthers: I'm extremely distracted by the program on [The Mathematics of Biodiversity](http://www.maths.gla.ac.uk/~tl/tmob.html) here in Barcelona. I think it will help me shift my career toward 'green mathematics', so I want to spend as much time as possible talking to biologists here. That means I'm neglecting the Azimuth Forum for a while. But at least I'm getting some work done. Here's my current state. First, talks: 1. I gave an informal talk here about how natural selection reduces the information 'left to learn' as the population approaches an evolutionarily stable state. As a result someone told me about some interesting papers: N. H. Barton and J. B. Coe's [On the application of statistical physics to evolutionary biology](http://www.ncbi.nlm.nih.gov/pubmed/19348811), and Y. Iwasa's [Free fitness that always increases in evolution](http://www.ncbi.nlm.nih.gov/pubmed/3256719). (Not free online, but you can read the abstract.) These use a stochastic rather than deterministic approach to natural selection. That's a good next step. Then, papers that aren't related to Azimuth: 1. I submitted my paper with Derek Wise, [Teleparallel gravity and higher gauge theory](http://math.ucr.edu/home/baez/teleparallel.pdf), to _Communications in Mathematical Physics_. 1. John Huerta wants to add another section to our paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). He's still writing it - he had surgery for an old eye injury, so he's a bit distracted. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, papers that _are_ related to Azimuth: 1. I submitted my paper with [[Brendan Fong]], [Noether's theorem for Markov processes](http://math.ucr.edu/home/baez/teleparallel.pdf) to _Journal of Mathematical Physics_. 1. I need to finish off my long paper with [[Jacob Biamonte]], [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). Then, blog articles: First, blogging: 1. I wrote [The Mathematics of Biodiversity (Part 1)](http://johncarlosbaez.wordpress.com/2012/06/21/the-mathematics-of-biodiversity-part-1/) and [The Mathematics of Biodiversity (Part 2)](http://johncarlosbaez.wordpress.com/2012/06/24/the-mathematics-of-biodiversity-part-2/) about estimating the fraction of species haven't been observed yet, a notoriously difficult problem in biology. 1. I wrote [Information Geometry (Part 12)](http://johncarlosbaez.wordpress.com/2012/06/24/information-geometry-part-12/), about evolutionary game theory. I have part 13 almost but not quite done. 1. I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]] 1. I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]]. 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

John asked

It would be great if you would skim it and tell me if it is at all interesting. I will come back to it during the next weeks, as soon as I no longer stand learning C++.

`John asked <blockquote> <p> Okay, Tim, I'll add that to my to-do list. Are you waiting for me to do something regarding part 4? </p> </blockquote> It would be great if you would skim it and tell me if it is at all interesting. I will come back to it during the next weeks, as soon as I no longer stand learning C++.`

I'm back from Barcelona and able to focus more on Azimuth, especially now that I'm getting over my jetlag. Here's the state of things. Papers that aren't related to Azimuth:

John Huerta just finished all the remaining proofs in our paper G2 and the rolling ball, so now I need to edit it and send it out.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, papers that

arerelated to Azimuth:Then, blog articles:

While in Barcelona, I wrote more posts on The Mathematics of Biodiversity: Part 3, Part 4, Part 5, and Part 6. There's a lot more to say about this workshop - I learned a lot of interesting stuff! - but I'm not sure how much I'll get around to. Ugh, I should just write it down before I forget it all.

In preparation for my Barcelona talk, I wrote another post on evolutionary game theory in the Information Geometry series: Information Geometry (Part 13).

I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]] and [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

`I'm back from Barcelona and able to focus more on Azimuth, especially now that I'm getting over my jetlag. Here's the state of things. Papers that aren't related to Azimuth: 1. John Huerta just finished all the remaining proofs in our paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf), so now I need to edit it and send it out. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, papers that _are_ related to Azimuth: 1. I need to finish off my long paper with [[Jacob Biamonte]], [Quantum techniques for stochastic mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf). He is now here at the Centre for Quantum Technologies and we have a game plan for doing this. Then, blog articles: 1. While in Barcelona, I wrote more posts on The Mathematics of Biodiversity: [Part 3](http://johncarlosbaez.wordpress.com/2012/06/21/the-mathematics-of-biodiversity-part-1/), [Part 4](http://johncarlosbaez.wordpress.com/2012/07/02/the-mathematics-of-biodiversity-part-4/), [Part 5](http://johncarlosbaez.wordpress.com/2012/07/03/the-mathematics-of-biodiversity-part-5/), and [Part 6](http://johncarlosbaez.wordpress.com/2012/07/06/the-mathematics-of-biodiversity-part-6/). There's a lot more to say about this workshop - I learned a lot of interesting stuff! - but I'm not sure how much I'll get around to. Ugh, I should just write it down before I forget it all. 1. In preparation for my Barcelona talk, I wrote another post on evolutionary game theory in the Information Geometry series: [Information Geometry (Part 13)](http://johncarlosbaez.wordpress.com/2012/06/26/information-geometry-part-13/). 1. I need to edit and post [[Staffan Liljgeren]]'s article [[Blog - carbon cycle box models (part 1)|carbon cycle box models (part 1)]] 1. I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]] and [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I want to write a blog post on the master equation for monatomic/diatomic gases, for the [network theory](http://math.ucr.edu/home/baez/networks/) series. 1. I want to edit and publish Jacob Biamonte's blog post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], also for the network theory series. These two blog articles will go into the long paper we're envisioning. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are busy writing the software for that now.`

First, papers not related to Azimuth:

I've been editing G2 and the rolling ball but there's one proof by John Huerta where I don't follow all the steps, so I've asked him to fill in details.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, papers that

arerelated to Azimuth:Quantum Techniques for Stochastic Mechanics.Then, blog articles:

I posted [[Staffan Liljgeren]]'s article Carbon cycle box models.

I posted Networks Theory (Part 19), on the master equation for a diatomic gas. Next I need to edit and publish Jacob Biamonte's post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], which will become Part 20. These two blog articles will become chapters of our book. I think we need to write about 4 more chapters: two on the proof of the deficiency zero theorem, one on software for simulating stochastic Petri nets, and one on the category theoretic aspects of stochastic Petri nets.

I posted two more articles on The Mathematics of Biodiversity: Part 7 and [Part 8)(http://johncarlosbaez.wordpress.com/2012/07/14/the-mathematics-of-biodiversity-part-8/), on the estimation of entropy from empirical data. I should post at least one more, on Hans Metz's work on mathematical models evolution and/or the concepts of alpha, beta and gamma diversity.

I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]] and [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to start posting articles about online climate models that people have created here! Logically, the first should be the time-dependent version of ice albedo model. This should become a

This Week's Finds.I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are still writing the software for that.

`First, papers not related to Azimuth: 1. I've been editing [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf) but there's one proof by John Huerta where I don't follow all the steps, so I've asked him to fill in details. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, papers that _are_ related to Azimuth: 1. I need to finish off my book with [[Jacob Biamonte]], tentatively called _[Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf)_. Then, blog articles: 1. I posted [[Staffan Liljgeren]]'s article [Carbon cycle box models](http://johncarlosbaez.wordpress.com/2012/07/24/carbon-cycle-box-models/). 1. I posted [Networks Theory (Part 19)](http://johncarlosbaez.wordpress.com/2012/07/18/network-theory-part-19/), on the master equation for a diatomic gas. Next I need to edit and publish Jacob Biamonte's post on [[Blog - forbidden states in stochastic mechanics|forbidden eigenstates in stochastic mechanics]], which will become Part 20. These two blog articles will become chapters of our book. I think we need to write about 4 more chapters: two on the proof of the deficiency zero theorem, one on software for simulating stochastic Petri nets, and one on the category theoretic aspects of stochastic Petri nets. 1. I posted two more articles on The Mathematics of Biodiversity: [Part 7](http://johncarlosbaez.wordpress.com/2012/07/12/the-mathematics-of-biodiversity-part-7/) and [Part 8)(http://johncarlosbaez.wordpress.com/2012/07/14/the-mathematics-of-biodiversity-part-8/), on the estimation of entropy from empirical data. I should post at least one more, on Hans Metz's work on mathematical models evolution and/or the concepts of alpha, beta and gamma diversity. 1. I need to edit and post Tim's [[Blog - increasing the signal-to-noise ratio with more noise|increasing the signal-to-noise ratio with more noise]] and [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to start posting articles about online climate models that people have created here! Logically, the first should be the time-dependent version of ice albedo model. This should become a _This Week's Finds_. 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that.`

First, papers not related to Azimuth:

I put my paper with John Huerta, G2 and the rolling ball, on the arXiv! Now I just need to submit it for publication.

I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, a book that

isrelated to Azimuth:Quantum Techniques for Stochastic Mechanics.Then, blog articles:

I posted [[Tim van Beek]] and [[Glyn Adgie]]'s article Increasing the signal-to-noise ratio with more noise.

I polished up Jacob Biamonte's post [[Blog - network theory (part 20)|Network theory (part 20)]] and I'll post it this week. I've been working hard on coming up with a proof of the deficiency zero theorem that mathematicians can enjoy, and made lots of progress yesterday. This will all go into the book.

I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to post more articles about online models that people have created here!

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are still writing the software for that.

`First, papers not related to Azimuth: 1. I put my paper with John Huerta, [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf), on the arXiv! Now I just need to submit it for publication. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, a book that _is_ related to Azimuth: 1. I need to finish off my book with [[Jacob Biamonte]], tentatively called _[Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf)_. Then, blog articles: 1. I posted [[Tim van Beek]] and [[Glyn Adgie]]'s article [Increasing the signal-to-noise ratio with more noise](http://johncarlosbaez.wordpress.com/2012/07/30/increasing-the-signal-to-noise-ratio-with-more-noise/). 1. I polished up Jacob Biamonte's post [[Blog - network theory (part 20)|Network theory (part 20)]] and I'll post it this week. I've been working hard on coming up with a proof of the deficiency zero theorem that mathematicians can enjoy, and made lots of progress yesterday. This will all go into the book. 1. I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that.`

First, papers not related to Azimuth:

I submitted my paper with John Huerta, G2 and the rolling ball, for publication in

Transactions of the American Mathematical Society. So, that's out of my hair for a while.I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

Then, a book that

isrelated to Azimuth:Quantum Techniques for Stochastic Mechanics.Then, blog articles:

I posted Network theory (part 21) and Network theory (part 22). Need to keep soldiering on.

I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to post more articles about online models that people have created here!

I want to blog about the selected papers network being developed by Chris Lee and Marc Harper. They are still writing the software for that.

`First, papers not related to Azimuth: 1. I submitted my paper with John Huerta, [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf), for publication in _Transactions of the American Mathematical Society_. So, that's out of my hair for a while. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire. Then, a book that _is_ related to Azimuth: 1. I need to finish off my book with [[Jacob Biamonte]], tentatively called _[Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf)_. Then, blog articles: 1. I posted [Network theory (part 21)](http://johncarlosbaez.wordpress.com/2012/08/14/network-theory-part-21/) and [Network theory (part 22)](http://johncarlosbaez.wordpress.com/2012/08/16/network-theory-part-22/). Need to keep soldiering on. 1. I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that.`

First, blog articles:

I posted Network theory (part 23) and Network theory (part 24). Jacob needs to write something about a predator-prey model with spatial dependence, and then I need to write a kind of conclusion for this part of the series. This stuff will become the book below.

I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to post more articles about online models that people have created here!

Then, a book related to Azimuth:

Quantum Techniques for Stochastic Mechanics. I hope to have a draft on the arXiv when I go back to California on September 21st.Finally, papers not related to Azimuth:

My paper with John Huerta, G2 and the rolling ball, was rejected by the editor of

Transactions of the American Mathematical Society. But then 15 minutes he sent another email saying no, it wasn't rejected after all! The first reader didn't think it was important enough to be worth publishing in this journal... but the second reader thought it might be. So now we wait for an actual verdict.I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

`First, blog articles: 1. I posted [Network theory (part 23)](http://johncarlosbaez.wordpress.com/2012/08/21/network-theory-part-23/) and [Network theory (part 24)](http://johncarlosbaez.wordpress.com/2012/08/23/network-theory-part-24/). Jacob needs to write something about a predator-prey model with spatial dependence, and then I need to write a kind of conclusion for this part of the series. This stuff will become the book below. 1. I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that. Then, a book related to Azimuth: 1. I need to finish off my book with [[Jacob Biamonte]], tentatively called _[Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/quantum-mathematics.pdf)_. I hope to have a draft on the arXiv when I go back to California on September 21st. Finally, papers not related to Azimuth: 1. My paper with John Huerta, [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf), was rejected by the editor of _Transactions of the American Mathematical Society_. But then 15 minutes he sent another email saying no, it wasn't rejected after all! The first reader didn't think it was important enough to be worth publishing in this journal... but the second reader thought it might be. So now we wait for an actual verdict. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire.`

First, blog articles:

I'm starting to blog about my paper with John Huerta, G2 and the rolling ball. I'm taking a rather leisurely and digressive route. Our paper is about one ball rolling on another ball that's 3 times as big. But in Rolling Balls and Circles (Part 1), I wrote about a

circlerolling on another circlethe same size, and in Rolling Balls and Circles (Part 2), I wrote about a circle rolling on another circletwice as big. These situations hold delights that are almost completely unrelated to our paper, so it's pure decadent self-indulgence to be writing about them. I'm probably doing it because I'm dreading the amount of real work I'll need to do soon!I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to post more articles about online models that people have created here!

Then, a book related to Azimuth:

Quantum Techniques for Stochastic Mechanics. I hope to have a draft on the arXiv when I go back to California on September 21st.Then, a course related to Azimuth:

Finally, papers not related to Azimuth:

`First, blog articles: 1. I'm starting to blog about my paper with John Huerta, [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf). I'm taking a rather leisurely and digressive route. Our paper is about one ball rolling on another ball that's 3 times as big. But in [Rolling Balls and Circles (Part 1)](http://johncarlosbaez.wordpress.com/2012/08/31/rolling-circles-and-balls-part-1/), I wrote about a _circle_ rolling on another circle _the same size_, and in [Rolling Balls and Circles (Part 2)](https://johncarlosbaez.wordpress.com/2012/09/03/rolling-balls-and-circles-part-2/), I wrote about a circle rolling on another circle _twice as big_. These situations hold delights that are almost completely unrelated to our paper, so it's pure decadent self-indulgence to be writing about them. I'm probably doing it because I'm dreading the amount of real work I'll need to do soon! 1. I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that. Then, a book related to Azimuth: 1. After a week of procrastination, I'm finally doing a lot of edits on my book with [[Jacob Biamonte]], _[Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/stoch.pdf)_. I hope to have a draft on the arXiv when I go back to California on September 21st. Then, a course related to Azimuth: 1. My graduate seminar will be called 'The Mathematics of Climate Change', and I have to start preparing that. It'll be easy for the first few weeks, as I sketch the basic information about climate change and how nasty our future will be if we don't shape up. But then I'll want to talk about climate models, and that will take more work. Finally, papers not related to Azimuth: 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire.`

Just a little update... Jacob and I are hard at work on this book:

Notes on Quantum Techniques for Stochastic Mechanics.You can get a draft here. I'd love to hear about typos! I don't have time to make major changes now, since in about a week I'll put a version on the arXiv. Later we'll polish this stuff a bit more and try to publish it as a book, without 'Notes on' in the title. But for those of you interested in stochastic Petri nets, this may already be more convenient than the blog version.

`Just a little update... Jacob and I are hard at work on this book: * John Baez and Jacob Biamonte, _[Notes on Quantum Techniques for Stochastic Mechanics](http://math.ucr.edu/home/baez/stoch_stable.pdf)_. You can get a draft here. I'd love to hear about typos! I don't have time to make major changes now, since in about a week I'll put a version on the arXiv. Later we'll polish this stuff a bit more and try to publish it as a book, without 'Notes on' in the title. But for those of you interested in stochastic Petri nets, this may already be more convenient than the blog version.`

Thanks for sharing this Amazing book! I'm having so much fun with it, that I have to keep reminding myself about my employment :)

A couple of remarks on the text of Chapter 4, Probabilities vs. amplitudes.

In sections 4.3, Stochastic versus unitary operators, and 4.4, in Infinitesmal stochastic vs. self-adjoint operators, it looks like wherever you mean to write $\ge$, it is showing up in the pdf as $\gt$. For instance on p. 40 you say that a stochastic operator gives a square matrix with non-negative entries, but the formula prints as $U_{i j} \gt 0$. For another example, the second condition for a stochastic operator shows up as $\psi \ge 0 \quad \implies \quad U \psi \ge 0$.

On page 36, you gave the corrected value for as $H = r(a^\dagger - 1)$, after showing that your initial guess of $H = r a^\dagger$ failed to map probability distributions to probability distributions. After giving the algebraic explanation that you gave for why the one operator works and the other one doesn't, it could make the reader even happier if you pointed out the meaning of the "fudge factor" -1. The creation operator $r a^\dagger$ was a correct guess for part of the story, which is the contribution of $\Psi_n$ to the positive derivative of $\Psi_{n+1}$ (scaled by the rate constant $r$). But but because the probabilities have to add up to one, they must "flow" among the components. In this case, the rising probability of $\Psi_{n+1}$ is accompanied by an equally falling component of $\Psi_{n}$. This second contribution is the "destruction" of probability in $\Psi_n$ due to the existence of probability in $\Psi_n$. This is the content of the factor $-1$ in the adjusted formula.

`Thanks for sharing this Amazing book! I'm having so much fun with it, that I have to keep reminding myself about my employment :) A couple of remarks on the text of Chapter 4, Probabilities vs. amplitudes. 1. In sections 4.3, Stochastic versus unitary operators, and 4.4, in Infinitesmal stochastic vs. self-adjoint operators, it looks like wherever you mean to write $\ge$, it is showing up in the pdf as $\gt$. For instance on p. 40 you say that a stochastic operator gives a square matrix with non-negative entries, but the formula prints as $U_{i j} \gt 0$. For another example, the second condition for a stochastic operator shows up as $\psi \ge 0 \quad \implies \quad U \psi \ge 0$. 2. On page 36, you gave the corrected value for as $H = r(a^\dagger - 1)$, after showing that your initial guess of $H = r a^\dagger$ failed to map probability distributions to probability distributions. After giving the algebraic explanation that you gave for why the one operator works and the other one doesn't, it could make the reader even happier if you pointed out the meaning of the "fudge factor" -1. The creation operator $r a^\dagger$ was a correct guess for part of the story, which is the contribution of $\Psi_n$ to the positive derivative of $\Psi_{n+1}$ (scaled by the rate constant $r$). But but because the probabilities have to add up to one, they must "flow" among the components. In this case, the rising probability of $\Psi_{n+1}$ is accompanied by an equally falling component of $\Psi_{n}$. This second contribution is the "destruction" of probability in $\Psi_n$ due to the existence of probability in $\Psi_n$. This is the content of the factor $-1$ in the adjusted formula.`

Today I read chapter 5, and I see that you addressed my second point above. So I retract that suggestion about how to address the reader.

Best Regards

`Today I read chapter 5, and I see that you addressed my second point above. So I retract that suggestion about how to address the reader. Best Regards`

Thanks for catching that error number 1, David! I've fixed it now, along with zillions of other things. By Tuesday I hope to put a reasonably nice draft on the arXiv, including one more section that wraps up the story. On Wednesday the movers are coming, and on Friday we're flying from Singapore back to California!

`Thanks for catching that error number 1, David! I've fixed it now, along with zillions of other things. By Tuesday I hope to put a reasonably nice draft on the arXiv, including one more section that wraps up the story. On Wednesday the movers are coming, and on Friday we're flying from Singapore back to California!`

I'm leaving for California on Friday. Tomorrow the movers come to pick up our stuff. But I got some work done, just in time:

There's plenty left to do. First, blog articles:

I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to post more articles about online models that people have created here!

Then, a course related to Azimuth:

Finally, papers not related to Azimuth:

`I'm leaving for California on Friday. Tomorrow the movers come to pick up our stuff. But I got some work done, just in time: 1. I put a draft of [A Course in Quantum Techniques for Stochastic Mechanics](http://arxiv.org/abs/1209.3632) on the arXiv. There's plenty left to do. First, blog articles: 1. I need to edit and post Tim's [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that. Then, a course related to Azimuth: 1. My graduate seminar will be called 'The Mathematics of Climate Change', and I have to start preparing that. Finally, papers not related to Azimuth: 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire.`

Life has become quite busy now that I'm back in California, but in a fun way so far. I have some talks to think about:

On Wednesday October 24 I'm giving the colloquium at 3:30 at the mathematics department of the University of Southern California. I will probably talk about The Mathematics of Planet Earth, to help me prepare the slides for a bigger talk coming up shortly.

On October 30th I'm giving a public lecture on The Mathematics of Planet Earth at Stellenbosch University in South Africa, as part of the 50th annual meeting of the South African Mathematical Society. I'll do it remotely, via videoconferencing, so there will be technical issues to sort out. I'm going to test out some things with my host, Bruce Bartlett, this Monday at the awful hour of 9:30 am. That's when the talk will be, too!

On Friday November 16 I'm giving the Lang Lecture, an annual lecture at at the math department of U. C. Berkeley. I don't know what I'll talk about yet - either fun math or The Mathematics of Planet Earth.

On December 6 I'll be giving a talk on The Azimuth Project: an Open-Access Educational Resource at Climate Modeling in an Open, Transparent World, organized by Steve M. Easterbrook, V. Balaji

et alas part of the AGU (American Geophysical Union) Fall Meeting in San Francisco. Yes, our application got accepted! This talk is at 9:00 am, and it's for just 15 minutes. It wouldn't be worth bothering with except that I'll meet a bunch of climate scientists.I also have some classes to teach:

This quarter I'm teaching an undergraduate course on ordinary differential equations. I want to use some examples from population biology - indeed I've already started. And I want to get the students to solve some first-order ODE using the simplest possible numerical method, the Euler method. I would like them to do this using online software that runs on a browser! I know such software is already out there, but I have to find it. Can you help me? I think the Sage website Staffan likes is an option. I believe there are also webpages that do nothing but solve first-order ODE. The math department also has Mathematica on its computers, but there are 90 students in this class, so they'll overwhelm the facilities if we proceed that way. I'll post about this on the blog later.

I'm also teaching a graduate seminar, Mathematics of the Environment. This meets on Tuesdays from 3:30 to 5 and hasn't met yet. I'll start either with my Energy, the Environment, and What Mathematicians Can Do talk or a warmup version of my 'Mathematics of Planet Earth' talk, which will be more optimistic in tone. Not sure I'll have time to make slides for that by Tuesday, though!

Next quarter I'll be teaching an upper-level undergraduate course on game theory, where I can do whatever I want - as long as it's game theory. So, I'll probably talk about 2-person games, Nash equilibria, and then evolutionary game theory - as I began to do in the information geometry series. This would be a fun excuse to talk about game theory, evolution and information theory in a low-tech, no-frills way. It would be fun to blog about this. But....

Next quarter I'll also be teaching a graduate course on classical mechanics, using my book with Derek Wise. Ideally I would use this time to refine that book and get it ready for publication, but it looks like I'll be quite busy, since...

Next quarter I'll also be continuing my seminar Mathematics of the Environment. Since it's quite hard to prepare interesting classes on 3 new subjects, I'll probably slack off at this point and teach this from my book with Jacob, A Course on Quantum Techniques for Stochastic Physics, following it fairly closely so I don't have to prepare too much. This will at least help me think about how I want to refine

thatbook.Then there are blog articles:

I posted Azimuth News (Part 2), to make people aware that a lot of stuff is going on here. I got about 3 or 4 people applying for membership in the Forum thanks to this.

On Monday I want to post the article by [[David Tanzer]], [[Blog - Petri net programming (part 1)]].

Then I want to post the article by Matteo Smerlak, [[Blog - the mathematical origin of irreversibility]]. This is almost polished up, but there's so much material that could stand longer explanations! I'd like to do all the calculations that prove all the results here...

I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. This has been sitting in my to-do list for a long time - sorry, Tim.

I need to post more articles about online models that people have created here!

Finally, papers not related to Azimuth:

My paper G2 and the rolling ball seems to have been accepted by

Transactions of the American Mathematical Society, modulo some small corrections. I uploaded a corrected version today.I need to finish the paper The beauty of roots, written with Dan Christensen and Sam Derbyshire.

`Life has become quite busy now that I'm back in California, but in a fun way so far. I have some talks to think about: 1. On Wednesday October 24 I'm giving the colloquium at 3:30 at the mathematics department of the University of Southern California. I will probably talk about The Mathematics of Planet Earth, to help me prepare the slides for a bigger talk coming up shortly. 1. On October 30th I'm giving a public lecture on [The Mathematics of Planet Earth](http://www.sams2012.org/public-lecture/) at Stellenbosch University in South Africa, as part of the 50th annual meeting of the South African Mathematical Society. I'll do it remotely, via videoconferencing, so there will be technical issues to sort out. I'm going to test out some things with my host, Bruce Bartlett, this Monday at the awful hour of 9:30 am. That's when the talk will be, too! 1. On Friday November 16 I'm giving the Lang Lecture, an annual lecture at at the math department of U. C. Berkeley. I don't know what I'll talk about yet - either fun math or The Mathematics of Planet Earth. 1. On December 6 I'll be giving a talk on The Azimuth Project: an Open-Access Educational Resource at <a href = "http://fallmeeting.agu.org/2012/session-search/single/climate-modeling-in-an-open-transparent-world/">Climate Modeling in an Open, Transparent World</a>, organized by Steve M. Easterbrook, V. Balaji <i>et al</i> as part of the AGU (American Geophysical Union) Fall Meeting in San Francisco. Yes, our application got accepted! This talk is at 9:00 am, and it's for just 15 minutes. It wouldn't be worth bothering with except that I'll meet a bunch of climate scientists. I also have some classes to teach: 1. This quarter I'm teaching an undergraduate course on ordinary differential equations. I want to use some examples from population biology - indeed I've already started. And I want to get the students to solve some first-order ODE using the simplest possible numerical method, the Euler method. I would like them to do this using online software that runs on a browser! I know such software is already out there, but I have to find it. Can you help me? I think the Sage website Staffan likes is an option. I believe there are also webpages that do nothing but solve first-order ODE. The math department also has Mathematica on its computers, but there are 90 students in this class, so they'll overwhelm the facilities if we proceed that way. I'll post about this on the blog later. 1. I'm also teaching a graduate seminar, Mathematics of the Environment. This meets on Tuesdays from 3:30 to 5 and hasn't met yet. I'll start either with my <a href = "math.ucr.edu/home/baez/what/what_hong_kong.pdf">Energy, the Environment, and What Mathematicians Can Do</a> talk or a warmup version of my 'Mathematics of Planet Earth' talk, which will be more optimistic in tone. Not sure I'll have time to make slides for that by Tuesday, though! 1. Next quarter I'll be teaching an upper-level undergraduate course on game theory, where I can do whatever I want - as long as it's game theory. So, I'll probably talk about 2-person games, Nash equilibria, and then evolutionary game theory - as I began to do in the <a href = "http://math.ucr.edu/home/baez/information/information_geometry_8.html">information geometry</a> series. This would be a fun excuse to talk about game theory, evolution and information theory in a low-tech, no-frills way. It would be fun to blog about this. But.... 1. Next quarter I'll also be teaching a graduate course on classical mechanics, using my <a href = "http://math.ucr.edu/home/baez/classical/">book with Derek Wise</a>. Ideally I would use this time to refine that book and get it ready for publication, but it looks like I'll be quite busy, since... 1. Next quarter I'll also be continuing my seminar Mathematics of the Environment. Since it's quite hard to prepare interesting classes on 3 new subjects, I'll probably slack off at this point and teach this from my book with Jacob, <a href = "http://math.ucr.edu/home/baez/stoch_stable.pdf">A Course on Quantum Techniques for Stochastic Physics</a>, following it fairly closely so I don't have to prepare too much. This will at least help me think about how I want to refine <i>that</i> book. Then there are blog articles: 1. I posted [Azimuth News (Part 2)](http://johncarlosbaez.wordpress.com/2012/09/28/azimuth-news-part-2/), to make people aware that a lot of stuff is going on here. I got about 3 or 4 people applying for membership in the Forum thanks to this. 1. On Monday I want to post the article by [[David Tanzer]], [[Blog - Petri net programming (part 1)]]. 1. Then I want to post the article by [Matteo Smerlak](http://aei-mpg.academia.edu/MatteoSmerlak), [[Blog - the mathematical origin of irreversibility]]. This is almost polished up, but there's so much material that could stand longer explanations! I'd like to do all the calculations that prove all the results here... 1. I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. This has been sitting in my to-do list for a long time - sorry, Tim. 1. I need to post more articles about online models that people have created here! 1. I want to blog about the [selected papers network](http://www.math.ntnu.no/~stacey/Mathforge/Math2.0/comments.php?DiscussionID=27&Focus=259#Comment_259) being developed by Chris Lee and Marc Harper. They are still writing the software for that. Finally, papers not related to Azimuth: 1. My paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf) seems to have been accepted by _Transactions of the American Mathematical Society_, modulo some small corrections. I uploaded a corrected version today. 1. I need to finish the paper [The beauty of roots](http://math.ucr.edu/home/baez/roots.pdf), written with Dan Christensen and Sam Derbyshire.`

Small updates:

My paper G2 and the rolling ball was actually

reallyaccepted byTransactions of the American Mathematical Societythis morning.I posted the article by [[David Tanzer]], [[Blog - Petri net programming (part 1)]].

I'll post a blog article linking to the first day of my course Mathematics of the Environment. I plan to march ahead describing stuff we've done here on the Azimuth Project: simple climate models, and also stuff about the Milankovich cycles and their role in causing glacial cycles.

`Small updates: 1. My paper [G2 and the rolling ball](http://math.ucr.edu/home/baez/ball.pdf) was actually _really_ accepted by _Transactions of the American Mathematical Society_ this morning. 1. I posted the article by [[David Tanzer]], [[Blog - Petri net programming (part 1)]]. 1. I'll post a blog article linking to the first day of my course Mathematics of the Environment. I plan to march ahead describing stuff we've done here on the Azimuth Project: simple climate models, and also stuff about the Milankovich cycles and their role in causing glacial cycles.`

Talks:

I gave my talk The Mathematics of Planet Earth at the University of Southern California and people seemed to really like it. As usual, at dinner afterward there were a lot of nervous jokes whenever anyone mentioned flying somewhere, since I'd said the best easy way to cut our carbon footprints was to fly less. (Small-talk among successful academics usually involves lots of discussion of where you were last and where you're flying next.) Someone suggest that I read the work of John Harte, about maximum entropy and ecology. He's at U.C. Berkeley.

I've videotaped a version of that talk and it'll be shown next Tuesday, October 30th, at Stellenbosch University in South Africa, as part of the 50th annual meeting of the South African Mathematical Society. At 9 am my time I'll turn on Skype. At 9:30am Barry Green will show up and and introduce Mark Swilling. At 9:40am Mark Swilling will speaks for about 10 minutes. At 9:55am Barry will introduce me. At 10am I'll say hi via Skype, and then they'll start my video. At 10:50 am Mark Swilling and I will answer questions. Barry Green is the director of the African Institute for Mathematical Sciences, which has institutes in Cape Town, Senegal and Ghana. It is the brainchild of Neil Turok, who is currently the head of the Perimeter Institute. Mark Swilling is the head of the Sustainability Institute in Stellenbosch.

Bruce Bartlett, who masterminded this talk in South Africa, will eventually put it on YouTube.

Blogging:

I've been posting lectures notes for my course on Mathematics and the Environment: Part 1, Part 2, Part 3 and Part 4.

I posted [[Matteo Smerlak]]'s article The Mathematical Origin of Irreversibility.

I posted [[John Roe]]'s article Mathematics for Sustainability (Part 1). I need to post Part 2.

I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to see if [[Ken Webb]] is ready for any of his material to be posted.

I need to finish my interview with Didier Paillard about the glacial cycles.

I need to find and post the online simulations people here did about a simple time-dependent climate model. I can't find them!

Papers:

Grant proposals:

`Talks: 1. I gave my talk [The Mathematics of Planet Earth](http://math.ucr.edu/home/baez/planet/planet.pdf) at the University of Southern California and people seemed to really like it. As usual, at dinner afterward there were a lot of nervous jokes whenever anyone mentioned flying somewhere, since I'd said the best easy way to cut our carbon footprints was to fly less. (Small-talk among successful academics usually involves lots of discussion of where you were last and where you're flying next.) Someone suggest that I read the work of [John Harte](http://socrates.berkeley.edu/~hartelab/Publications.html), about maximum entropy and ecology. He's at U.C. Berkeley. 1. I've videotaped a version of that talk and it'll be shown next Tuesday, October 30th, at Stellenbosch University in South Africa, as part of the 50th annual meeting of the South African Mathematical Society. At 9 am my time I'll turn on Skype. At 9:30am Barry Green will show up and and introduce Mark Swilling. At 9:40am Mark Swilling will speaks for about 10 minutes. At 9:55am Barry will introduce me. At 10am I'll say hi via Skype, and then they'll start my video. At 10:50 am Mark Swilling and I will answer questions. Barry Green is the director of the [African Institute for Mathematical Sciences](http://www.aims.ac.za/), which has institutes in Cape Town, Senegal and Ghana. It is the [brainchild of Neil Turok](http://blog.ted.com/2008/03/20/neil_turok/), who is currently the head of the Perimeter Institute. [Mark Swilling](http://www.youtube.com/watch?v=GBnN62-Lp7U) is the head of the [Sustainability Institute](http://www.sustainabilityinstitute.net/) in Stellenbosch. 1. Bruce Bartlett, who masterminded this talk in South Africa, will eventually put it on YouTube. Blogging: 1. I've been posting lectures notes for my course on Mathematics and the Environment: [Part 1](http://johncarlosbaez.wordpress.com/2012/10/04/mathematics-of-the-environment/), [Part 2](http://johncarlosbaez.wordpress.com/2012/10/11/mathematics-of-the-environment-part-2/), [Part 3](http://johncarlosbaez.wordpress.com/2012/10/13/mathematics-of-the-environment-part-3/) and [Part 4](http://johncarlosbaez.wordpress.com/2012/10/22/mathematics-of-the-environment-part-4/). 1. I posted [[Matteo Smerlak]]'s article [The Mathematical Origin of Irreversibility](http://johncarlosbaez.wordpress.com/2012/10/08/the-mathematical-origin-of-irreversibility/). 1. I posted [[John Roe]]'s article [Mathematics for Sustainability (Part 1)](http://johncarlosbaez.wordpress.com/2012/10/21/mathematics-for-sustainability-part-1/). I need to post Part 2. 1. I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to see if [[Ken Webb]] is ready for any of his material to be posted. 1. I need to finish my [interview with Didier Paillard](http://www.azimuthproject.org/azimuth/show/Blog+-+interview+with+Didier+Paillard) about the glacial cycles. 1. I need to find and post the online simulations people here did about a simple time-dependent climate model. I can't find them! Papers: 1. I need to finish [The Beauty of Roots](http://math.ucr.edu/home/baez/roots.pdf) with Dan Christensen and Sam Derbyshire. Dan is on sabbatical in Lisbon, but apparently quite absorbed with other fun math activities. Grant proposals: 1. I need to finish 2 NSF grant proposals in the next week or two: [Quantum techniques for stochastic physics](http://azimuth.mathforge.org/discussion/1075/grant-proposals/?Focus=7733#Comment_7733) and [Information geometry and Markov processes](http://azimuth.mathforge.org/discussion/1075/grant-proposals/?Focus=7739#Comment_7739).`

Good news: my paper with [[Brendan Fong]] called A Noether theorem for Markov processes has been accepted for publication by

Journal of Mathematical Physics, subject to lots of small corrections.`Good news: my paper with [[Brendan Fong]] called [A Noether theorem for Markov processes](http://math.ucr.edu/home/baez/noether.pdf) has been accepted for publication by _Journal of Mathematical Physics_, subject to lots of small corrections.`

Talks:

I'm giving the annual 'Lang Lecture' at the U.C. Berkeley math department next Friday, 16 November 2012. I'll give a version of The Mathematics of Planet Earth.

I'm giving a 15-minute talk 'The Azimuth Project: an Open-Access Educational Resource' at Climate Modeling in an Open, Transparent World, organized by Steve M. Easterbrook, V. Balaji

et alas part of the AGU (American Geophysical Union) Fall Meeting in San Francisco on Thursday, 6 December 2012 from 9:00 to 9:15 am. I have to write that talk.Blogging:

I posted Network Theory (Part 25) and got a great email reply from Luca Cardelli, who works on biology and computation! I'll try to post something based on that.

I posted Mathematics and the Environment (Part 5) and am almost ready to post part 6.

I posted [[John Roe]]'s article Mathematics for Sustainability (Part 1). I need to post Parts 2 and 3.

I copied 5 blog posts to my Information Geometry webpages.

I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]].

I need to see if [[Ken Webb]] is ready for any of his material to be posted.

I need to finish my interview with Didier Paillard about the glacial cycles.

Papers:

Brendan Fong and I made the changes in A Noether Theorem for Stochastic Mechanics requested by the referee.

I need to finish The Beauty of Roots with Dan Christensen and Sam Derbyshire.

`Talks: 1. I'm giving the annual 'Lang Lecture' at the U.C. Berkeley math department next Friday, 16 November 2012. I'll give a version of [The Mathematics of Planet Earth](http://math.ucr.edu/home/baez/planet.pdf). 1. I'm giving a 15-minute talk 'The Azimuth Project: an Open-Access Educational Resource' at <a href = "http://fallmeeting.agu.org/2012/session-search/single/climate-modeling-in-an-open-transparent-world/">Climate Modeling in an Open, Transparent World</a>, organized by Steve M. Easterbrook, V. Balaji <i>et al</i> as part of the AGU (American Geophysical Union) Fall Meeting in San Francisco on Thursday, 6 December 2012 from 9:00 to 9:15 am. I have to write that talk. Blogging: 1. I posted [Network Theory (Part 25)](http://johncarlosbaez.wordpress.com/2012/11/03/network-theory-part-25/) and got a great email reply from [Luca Cardelli](http://lucacardelli.name/), who works on biology and computation! I'll try to post something based on that. 1. I posted [Mathematics and the Environment (Part 5)](http://johncarlosbaez.wordpress.com/2012/11/06/mathematics-and-the-environment-part-5/) and am almost ready to post part 6. 1. I posted [[John Roe]]'s article [Mathematics for Sustainability (Part 1)](http://johncarlosbaez.wordpress.com/2012/10/21/mathematics-for-sustainability-part-1/). I need to post Parts 2 and 3. 1. I copied 5 blog posts to my [Information Geometry](http://math.ucr.edu/home/baez/information/) webpages. 1. I need to edit and post [[Tim van Beek]]'s article [[Blog - fluid flows and infinite dimensional manifolds (part 4)]]. 1. I need to see if [[Ken Webb]] is ready for any of his material to be posted. 1. I need to finish my [interview with Didier Paillard](http://www.azimuthproject.org/azimuth/show/Blog+-+interview+with+Didier+Paillard) about the glacial cycles. Papers: 1. Brendan Fong and I made the changes in [A Noether Theorem for Stochastic Mechanics](http://math.ucr.edu/home/baez/noether.pdf) requested by the referee. 1. I need to finish [The Beauty of Roots](http://math.ucr.edu/home/baez/roots.pdf) with Dan Christensen and Sam Derbyshire.`

It occurred to me that if you have any more climate blog posts queued up, you might want to save them and start posting them again just before your AGU talk. That way, there will be a stream of them afterward to engage any new geoscientists your talk my attract.

`It occurred to me that if you have any more climate blog posts queued up, you might want to save them and start posting them again just before your AGU talk. That way, there will be a stream of them afterward to engage any new geoscientists your talk my attract.`