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# Blog - prospects for a green mathematics

EDIT: Here the draft version: Blog (MPE) - Green mathematics for the era of environmental jeopardy.

This is a thread to discuss the article that we are writing for the MPE blog (Mathematics of Planet Earth).

I'll post a note when I have a draft up on the wiki.

This thread is a spinoff from this forum thread: Helping JB write for Azimuth.

There John said:

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

Here are the requirements for the post:

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

Here are some initial thoughts that I sent to John by email.

John,

Your slides on Energy, the Environment, and What Mathematicians Can Do already contain a lot of great material. Just converting some of that material into an expository and honestly persuasive essay could go along way. I'd be happy to make a pass at writing a draft. In doing so I would end up processing the ideas for myself, and clarifying where I stand on the points of discussion -- both in terms of my understanding of the scientific content, and my assessments about what should/can be done by mathematicians.

There is another major facet to the story, which is not unrelated to your stated goal of ending innumeracy and illogic. Our abuse of the environment is driven by societal processes. So environmental science really can't omit from the picture economics and politics as major components of the objective reality. Yet this has been a terrible quagmire for science because it is a battleground of vested interests. Much more clarity is needed here, and mathematicians are by nature truth seekers.

There is a great spiritual challenge here: how to fearlessly pursue the truth, in these most complex and heated of areas -- the social sciences -- without unwittingly becoming a doctrinaire ideologist.

I don't have answers here, but I do see a lot of questions that have yet to be addressed in a truly scientific manner.

If you think that there is room for some discussion along these lines, I could continue to write up this thread of thought.

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1.

Another facet is that these discussions about green mathematics need to be extended to larger parts of the population than just academic specialists. Searching for true mathematical insight into social dynamics, however incomplete and stumbling it may be at our present level of understanding, is bound to evoke the interests of larger sections of people, and if this is in any way connected with the green mathematics per se, we then are contributing to the elements for a larger scale discussion that involves a scientifically informed population.

Comment Source:Another facet is that these discussions about green mathematics need to be extended to larger parts of the population than just academic specialists. Searching for true mathematical insight into social dynamics, however incomplete and stumbling it may be at our present level of understanding, is bound to evoke the interests of larger sections of people, and if this is in any way connected with the green mathematics _per se_, we then are contributing to the elements for a larger scale discussion that involves a scientifically informed population.
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Hi -

Just converting some of that material into an expository and honestly persuasive essay could go along way. I'd be happy to make a pass at writing a draft.

That sounds great! Give it a try, preferably on the wiki so everyone can see it. I'm attaching the TeX file and a bunch of the figures.

This talk makes a bunch of points. To keep it the right size for a blog article, we'll have to say a bunch of these rather tersely. I think it's good to tersely describe the problems, with links so people can learn more... and spend more time on the solutions. After all, it's a lot easier to read about the problems than the solutions.

In doing so I would end up processing the ideas for myself, and clarifying where I stand on the points of discussion -- both in terms of my understanding of the scientific content, and my assessments about what should/can be done by mathematicians.

Great!

There is another major facet to the story, which is not unrelated to your stated goal of ending innumeracy and illogic. Our abuse of the environment is driven by societal processes. So environmental science really can't omit from the picture economics and politics as major components of the objective reality. Yet this has been a terrible quagmire for science because it is a battleground of vested interests. Much more clarity is needed here, and mathematicians are by nature truth seekers.

That's right. In their recent paper Can a collapse of global civilization be avoided?, the Ehrlichs write:

"Besides focusing their research on ways to avoid collapse, there is a need for natural scientists to collaborate with social scientists, especially those who study the dynamics of social movements. Such collaborations could develop ways to stimulate a significant increase in popular support for decisive and immediate action on the predicament. Unfortunately, awareness among scientists that humanity is in deep trouble has not been accompanied by popular awareness and pressure to counter the political and economic influences implicated in the current crisis. Without significant pressure from the public demanding action, we fear there is little chance of changing course fast enough to forestall disaster."

"The needed pressure, however, might be generated by a popular movement based in academia and civil society to help guide humanity towards developing a new multiple intelligence, ‘foresight intelligence’ to provide the long-term analysis and planning that markets cannot supply. Foresight intelligence could not only systematically look ahead but also guide cultural changes towards desirable outcomes such as increased socio-economic resilience. Helping develop such a movement and foresight intelligence are major challenges facing scientists today, a cutting edge for research that must slice fast if the chances of averting a collapse are to be improved."

However, we'd be a lot more persuasive about advocating that mathematicians get involved in the social sciences if we can present at least one good example of someone doing this to good effect. Otherwise readers won't see how to do it.

There is a great spiritual challenge here: how to fearlessly pursue the truth, in these most complex and heated of areas -- the social sciences -- without unwittingly becoming a doctrinaire ideologist.

Indeed.

I don't have answers here, but I do see a lot of questions that have yet to be addressed in a truly scientific manner.

If you think that there is room for some discussion along these lines, I could continue to write up this thread of thought.

There's a lot to talk about here, and it's good to talk about it on Azimuth... in fact, if you let me, I'll copy this exchange over there.

There is clearly material for many blog articles and more serious papers here, so one challenge is writing a single blog article!

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Hi -

Another facet is that these discussions about green mathematics need to be extended to larger parts of the population than just academic specialists. Searching for true mathematical insight into social dynamics, however incomplete and stumbling it may be at our present level of understanding, is bound to evoke the interests of larger sections of people, and if this is in any way connected with the green mathematics per se, we then are contributing to the elements for a larger scale discussion that involves a scientifically informed population.

That's true!

I think you're developing an idea for a different blog article, one that advocates the mathematical study of social dynamics as a way to tackle environmental problems. It's easy (but worthwhile) to make the case that social and economic issues are the hardest part about tackling global warming. It's harder to explain how math can help. One can dream that it will help, and I do, but for writing anything public about it I'd prefer to have a stock of examples I can talk about. I'm sure they exist! But I don't have them at my fingertips.

Comment Source:My second reply: <hr/> Hi - > Another facet is that these discussions about green mathematics need to be extended to larger parts of the population than just academic specialists. Searching for true mathematical insight into social dynamics, however incomplete and stumbling it may be at our present level of understanding, is bound to evoke the interests of larger sections of people, and if this is in any way connected with the green mathematics per se, we then are contributing to the elements for a larger scale discussion that involves a scientifically informed population. That's true! I think you're developing an idea for a different blog article, one that advocates the mathematical study of social dynamics as a way to tackle environmental problems. It's easy (but worthwhile) to make the case that social and economic issues are the hardest part about tackling global warming. It's harder to explain how math can help. One can dream that it will help, and I do, but for writing anything public about it I'd prefer to have a stock of examples I can talk about. I'm sure they exist! But I don't have them at my fingertips.
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I should add that there are a few different versions of my slides. In

I discuss Qinglan Xia's work on leaves. Someone - was it you, David? - said they wanted to write about this work someday. That would be a good example of what mathematicians can do: not instantly practical, but important.

In

In the related talk

I return to the leaves but spend less time outlining the problems and more time mulling over the concept of 'ecotechnology'. I also talk about how the agricultural revolution gives an earlier example of a dramatic change in energy production impacting, and being impacted by, mathematics.

Comment Source:I should add that there are a few different versions of my slides. In * [Energy, the Environment, and What Mathematicians Can Do (Hong Kong version)](http://math.ucr.edu/home/baez/what/hong_kong.html) I discuss Qinglan Xia's work on leaves. Someone - was it you, David? - said they wanted to write about this work someday. That would be a good example of what mathematicians can do: not instantly practical, but important. In * [Energy, the Environment, and What Mathematicians Can Do (Malaysia version)](http://math.ucr.edu/home/baez/what/what_malaysia.pdf) I don't talk about leaves; instead I say more about other things. In the related talk * [The Mathematics of Planet Earth](http://math.ucr.edu/home/baez/planet/) I return to the leaves but spend less time outlining the problems and more time mulling over the concept of 'ecotechnology'. I also talk about how the agricultural revolution gives an earlier example of a dramatic change in energy production impacting, and being impacted by, mathematics.
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edited January 2013

Yes that was me, I loved that leaf article.

I think you’re developing an idea for a different blog article, one that advocates the mathematical study of social dynamics as a way to tackle environmental problems.

I agree that to address this head on, a different blog article -- many of them actually -- is needed.

Nevertheless, in this blog article, which will be listing a number of "electives" for mathematicians interested in contributing to human welfare, there is a place for some mention of the great and urgent challenges involved in the understanding of social dynamics.

I also agree that concrete examples of environmentally relevant mathematical problems in social dynamics are both needed and not so easy to come by.

Here are some starter thoughts.

We could talk about the model building project at Azimuth, and the idea of starting with simple models, leading in a chain towards more and more concrete models, involving multiple factors. Even apart from the issue of the direct empirical application of the models, it is a learning process, which develops our intuitions and understanding of the various environmental factors and their interactions. I.e., the model-building effort is an educational project. These are wide open fields for mathematicians to participate in.

But eventually we do want our chains of models to closer to the empirical processes. The paper you cited by the Ehrlics mentions the fact that agriculture is one of the major producers of greenhouse gases. Let this fact sink in to the mind of the reader, it is rich in implications.

The real model of climate processes needs to include the social processes of agriculture. Climate affect harvests which affect markets and prices. The profitability of various crops affects investments, and how much of each crop will be planted. These decisions affect climate.

For the real deal, climate models are going to need to include economic models as well as models of nature. Another huge open playground for mathematicians to work in.

Furthermore, there are great challenges for applied mathematics, in which mathematicians create the models, rather than just studying the models that have been formulated by others. For climate modeling, that has meant mathematicians learning about physics and other natural sciences. For concrete climate models that include social factors, this will mean mathematicians learning about economics.

To build a model, we need to identify the key factors, and analyze their relationships and processes. What are the key economic factors, what are their relationships, and what determines their motions?

Perhaps a new generation of mathematicians, who earnestly want to understand climate dynamics, and are naive with respect to the social sciences, can bring some fresh, non-tendentious perspectives to the economic studies.

I realize that I am veering again into the terrain which is the topic of those further blog articles, but I feel a need to think this one out a bit here, because these fundamental questions can shape our whole outlook of how to work for the continuation of humanity. And, as I said before, a short gloss of some of these ideas could have a place in the MPE blog article.

Comment Source:Yes that was me, I loved that leaf article. > I think you’re developing an idea for a different blog article, one that advocates the mathematical study of social dynamics as a way to tackle environmental problems. I agree that to address this head on, a different blog article -- many of them actually -- is needed. Nevertheless, in this blog article, which will be listing a number of "electives" for mathematicians interested in contributing to human welfare, there is a place for some mention of the great and urgent challenges involved in the understanding of social dynamics. I also agree that concrete examples of environmentally relevant _mathematical_ problems in social dynamics are both needed and not so easy to come by. Here are some starter thoughts. We could talk about the model building project at Azimuth, and the idea of starting with simple models, leading in a chain towards more and more concrete models, involving multiple factors. Even apart from the issue of the direct empirical application of the models, it is a learning process, which develops our intuitions and understanding of the various environmental factors and their interactions. I.e., the model-building effort is an _educational_ project. These are wide open fields for mathematicians to participate in. But eventually we do want our chains of models to closer to the empirical processes. The paper you cited by the Ehrlics mentions the fact that agriculture is one of the major producers of greenhouse gases. Let this fact sink in to the mind of the reader, it is rich in implications. The real model of climate processes needs to include the social processes of agriculture. Climate affect harvests which affect markets and prices. The profitability of various crops affects investments, and how much of each crop will be planted. These decisions affect climate. For the real deal, climate models are going to need to include economic models as well as models of nature. Another huge open playground for mathematicians to work in. Furthermore, there are great challenges for _applied_ mathematics, in which mathematicians _create_ the models, rather than just studying the models that have been formulated by others. For climate modeling, that has meant mathematicians learning about physics and other natural sciences. For concrete climate models that include social factors, this will mean mathematicians learning about economics. To build a model, we need to identify the key factors, and analyze their relationships and processes. What are the key economic factors, what are their relationships, and what determines their motions? Perhaps a new generation of mathematicians, who earnestly want to understand climate dynamics, and are naive with respect to the social sciences, can bring some fresh, non-tendentious perspectives to the economic studies. I realize that I am veering again into the terrain which is the topic of those further blog articles, but I feel a need to think this one out a bit here, because these fundamental questions can shape our whole outlook of how to work for the continuation of humanity. And, as I said before, a short gloss of some of these ideas could have a place in the MPE blog article.
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It just sunk in to me: they want no more than 1000 words. Wow, that is a challenge, given the sweep of the subject. I'm going to have to tighten the reins on my writing style. (Just observing, not complaining.)

John, I've gone over all three versions of your slides, read the discussions on the blog, and the papers you referenced. Next I'll start reading the MPE blog itself, to see the landscape.

By the way, I edited the first message in this discussion, to contain a reference back to the parent discussion, and to restate the guidelines from MPE for the blog posts.

Comment Source:It just sunk in to me: they want no more than 1000 words. Wow, that is a challenge, given the sweep of the subject. I'm going to have to tighten the reins on my writing style. (Just observing, not complaining.) John, I've gone over all three versions of your slides, read the discussions on the blog, and the papers you referenced. Next I'll start reading the MPE blog itself, to see the landscape. By the way, I edited the first message in this discussion, to contain a reference back to the parent discussion, and to restate the guidelines from MPE for the blog posts.
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David Tanzer wrote:

It just sunk in to me: they want no more than 1000 words. Wow, that is a challenge, given the sweep of the subject.

Okay. The best solution, I think, is to tackle a more narrowly defined subject. I really think readers of this "Mathematics of Planet Earth" blog will most enjoy and benefit from concrete information about a specific problem and potential solutions that involve mathematics.

So, for one: let's not bother saying much about why global warming is a problem. Most people bothering to read the "Mathematics of Planet Earth" blog will probably agree that it is. At most we should show the graph of CO2 over recent ice age cycles, and how we're pushing the Earth into a whole new climate regime.

I should look at what if anything is already on the MPE blog and see what's most needed.

Comment Source:David Tanzer wrote: > It just sunk in to me: they want no more than 1000 words. Wow, that is a challenge, given the sweep of the subject. Okay. The best solution, I think, is to tackle a more narrowly defined subject. I really think readers of this "Mathematics of Planet Earth" blog will most enjoy and benefit from concrete information about a specific problem and potential solutions that involve mathematics. So, for one: let's not bother saying much about why global warming is a problem. Most people bothering to read the "Mathematics of Planet Earth" blog will probably agree that it is. At most we should show the graph of CO<sub>2</sub> over recent ice age cycles, and how we're pushing the Earth into a whole new climate regime. I should look at what if anything is already on the MPE blog and see what's most needed.
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By the way, if we write one really good 1000-word blog article, they'll probably be happy to have us write another.

Also: anything you want to write that's too long or otherwise inappropriate for the MPE blog, you should contribute to the Azimuth blog!

Comment Source:By the way, if we write one really good 1000-word blog article, they'll probably be happy to have us write another. Also: anything you want to write that's too long or otherwise inappropriate for the MPE blog, you should contribute to the Azimuth blog!
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9.

John, this all sounds good.

Comment Source:John, this all sounds good.
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From the MPE page of the of Isaac Newton Institute of Mathematical Sciences:

Cédric Villani, Fields Medallist and Director of the Institute Henri Poincaré (IHP) in Paris, says: “We think we are in the middle of an economic crisis, but that crisis may be nothing in comparison [with] the ecological crisis that we are, and will be facing. All of mankind’s intellectual resources will be helpful in solving these issues, and that includes mathematical sciences.”

But how can mathematics make a difference? Consider a pandemic. The mathematical modelling of infectious diseases shows that it is not necessary to vaccinate the whole population to eradicate a disease: models can identify the vaccination threshold and the groups to target. Consider now the clouds. Clouds are one of the major contributors to the uncertainty in climate predictions. But mathematicians use advanced geometry to characterise clouds and provide a more quantitative description of their role in the climate system. And what of the ubiquitous satnav? Satellite navigation systems use sophisticated optimisation algorithms to plan the best route and triangulation to determine location.

There are lots of MPE member organizations, like this one. Ideas could be gleaned from their sites.

I am going to start compiling a list of our ideas for things that mathematicians can do to help.

To set the tone in the blog, I think we should encourage the reader to adopt a broad rather than a narrow view of their skills -- that is, if they really want to make a contribution with their skills. If I start out with the position that I am an expert in transcendental invariants over Lemur sheaves with respect to coherent categories of endoworms, and I would like to know how to apply these skills to help the environment, well... More helpful would be the position that I (not me, but some hypothetical guy) have mathematical training, with emphasis in algebra; how can I find some challenging applications of my general skills, to some that will be useful to the environmental cause.

Here are a few of things to add to the list of candidate ideas:

• Help scientists to understand the mystery of turbulence, through the study of the Navier Stokes equations -- lots of uncharted terrain here

• Become an expert in signal processing, which is key to the interpretation of scientific data

• Become an expert in numerical methods, which is needed to ensure that the modeling algorithms don't give garbage outputs

• Study of network dynamics, chaotic systems, etc. -- very relevant

John you had also mentioned the analysis of time-series to detect tipping points. That fits in with the signal processing theme.

There are also lots of knowledge representation challenges posed by modeling complex systems -- this could appeal to the CS types.

Going with the theme of being willing to broaden one's self-definition for the good of the human race, we shouldn't make a dichotomy between mathematics and algorithmics -- the latter is a branch of the former.

I'd like to read more about network theory in general. So far my main contacts with it have been the Network Theory series on Azimuth, and Xia's paper on the formation of a leaf. Do you have any recommendations for survey papers, or general textbooks?

We should be able to mine network theory for some more juicy applications, no? I'll check citeseer to see what papers have referenced Xia's paper.

I'm going to poke around more to see what is going on in the area of algorithmic botany.

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If I start out with the position that I am an expert in transcendental invariants over Lemur sheaves with respect to coherent categories of endoworms

Is there an Azimuth page on that?

Comment Source:>If I start out with the position that I am an expert in transcendental invariants over Lemur sheaves with respect to coherent categories of endoworms Is there an Azimuth page on that?
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edited January 2013

I will have a draft in a few days, that will show the skeleton and spirit of how I envision the blog article.

John, we should collect as many specific applications and harbingers of what you call the "green mathematics" that will be driven by our need to understand the biosphere and our role within it. You have already provided three very substantial ones: Xia's work on the formation of a tree leaf, the application of quantum techniques to stochastic mechanics, and the problem of analyzing timeseries data to identify regions in the state space of a system that are "tipping points." That is already sufficient for me to write what I believe will be a clear and effective essay that will be both intellectually challenging, and will entice people to check out the Azimuth project, and possibly join in. What else could we hope for in a 1000 word essay?

But it would be great to have a fourth example, so keep on thinking about it.

By the way, in your MPE slides, you refer to Xia's work, but then refer to your work as being "nice mathematics" with the implication that it is not as applicable as Xia's. But it is widely applicable, because it covers Petri nets. Indeed Xia's work may be the most poetic application of green mathematics that has yet surfaced, but we can't afford to downplay the story of the quantum techniques, especially when we have so few examples of the green mathematics that have yet surfaced.

As a last note, it goes without saying that you should be the first author on this blog, because, although I will be giving to the ideas energy, spirit and form, I am new to these areas, and as of yet have not come up with new mathematical ideas. I am up for the challenge though, for the long term...

Thanks, Dave

Comment Source:I will have a draft in a few days, that will show the skeleton and spirit of how I envision the blog article. John, we should collect as many specific applications and harbingers of what you call the "green mathematics" that will be driven by our need to understand the biosphere and our role within it. You have already provided three very substantial ones: Xia's work on the formation of a tree leaf, the application of quantum techniques to stochastic mechanics, and the problem of analyzing timeseries data to identify regions in the state space of a system that are "tipping points." That is already _sufficient_ for me to write what I believe will be a clear and effective essay that will be both intellectually challenging, and will entice people to check out the Azimuth project, and possibly join in. What else could we hope for in a 1000 word essay? But it would be great to have a _fourth_ example, so keep on thinking about it. By the way, in your MPE slides, you refer to Xia's work, but then refer to your work as being "nice mathematics" with the implication that it is not as applicable as Xia's. But it is widely applicable, because it covers Petri nets. Indeed Xia's work may be the most poetic application of green mathematics that has yet surfaced, but we can't afford to downplay the story of the quantum techniques, especially when we have _so few_ examples of the green mathematics that have yet surfaced. As a last note, it goes without saying that you should be the first author on this blog, because, although I will be giving to the ideas energy, spirit and form, I am new to these areas, and as of yet have not come up with new mathematical ideas. I am up for the challenge though, for the long term... Thanks, Dave
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Let me put it a different way.

The "green reality" which is the environment is a massively complex network. The green is a network. Therefore network theory is a theory of the green. In Xia's work, the connection is very literal: the vein system of a green leaf is modeled as a transport network for nutrients, in the form of a directed graph. The math of these graphs, and of the optimization algorithms used to find the trees that minimize the transport cost functions, are therefore an example of network = green math.

Stochastic Petri nets, on the other hand, are an abstract formalism for reaction networks, with an abundance of applications. And they do have environmental applications, e.g., to oceanic chemical reaction networks, and to ecological networks such as food chains. Interestingly, they turn out to have a deeper mathematics than it might at first appear. In fact, as the work in the Azimuth Network Theory series has been showing, some of the mathematical structures of quantum theory can be brought to bear on these reaction networks. This may lead us to further insight into the deeper systemic structures of such networks, and so to green networks. So this is another avenue of green mathematics.

By the way, I'm not planning to use the phrase "green mathematics" so repetitively in the text, I'm just trying to iron out some of the connections here.

Also, I don't mean to be heavy-handed about what should go in the article and what shouldn't. I got emphatic in my previous message because I an idea about how it could all tie together well! So I'll write it up, and then announce it here, and then see what you think.

As I mentioned, it would be cool, but not necessary, to have one more "juicy" application, though they don't look so easy to come by at the moment. Another thing that would be helpful would be some description of a nice juicy green stochastic Petri net. Yes we have Lotka Volterra, and the ocean acidification network, but does anyone know of some more complex ecological applications of Petri nets. I'm just looking for a few sentences that summarize it, not a diagram.

Thanks

Comment Source:Let me put it a different way. The "green reality" which is the environment is a massively complex network. The green is a network. Therefore network theory is a theory of the green. In Xia's work, the connection is very literal: the vein system of a green leaf is modeled as a transport network for nutrients, in the form of a directed graph. The math of these graphs, and of the optimization algorithms used to find the trees that minimize the transport cost functions, are therefore an example of network = green math. Stochastic Petri nets, on the other hand, are an abstract formalism for _reaction_ networks, with an abundance of applications. And they do have environmental applications, e.g., to oceanic chemical reaction networks, and to ecological networks such as food chains. Interestingly, they turn out to have a deeper mathematics than it might at first appear. In fact, as the work in the Azimuth Network Theory series has been showing, some of the mathematical structures of quantum theory can be brought to bear on these reaction networks. This may lead us to further insight into the deeper systemic structures of such networks, and so to green networks. So this is another avenue of green mathematics. By the way, I'm not planning to use the phrase "green mathematics" so repetitively in the text, I'm just trying to iron out some of the connections here. Also, I don't mean to be heavy-handed about what should go in the article and what shouldn't. I got emphatic in my previous message because I an idea about how it could all tie together well! So I'll write it up, and then announce it here, and then see what you think. As I mentioned, it would be cool, but not necessary, to have one more "juicy" application, though they don't look so easy to come by at the moment. Another thing that would be helpful would be some description of a nice juicy green stochastic Petri net. Yes we have Lotka Volterra, and the ocean acidification network, but does anyone know of some more complex ecological applications of Petri nets. I'm just looking for a few sentences that summarize it, not a diagram. Thanks
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This paper: Reconstruction of extended Petri nets from time-series data by using logical control functions landed in my email recently. http://link.springer.com/article/10.1007%2Fs00285-012-0511-3. This is aimed at molecular biology, gene regulatory networks, etc.

Earlier papers, open access:

http://www.biomedcentral.com/1752-0509/5/113

http://www.sciencedirect.com/science/article/pii/S0303264708000701

Comment Source:This paper: _Reconstruction of extended Petri nets from time-series data by using logical control functions_ landed in my email recently. [http://link.springer.com/article/10.1007%2Fs00285-012-0511-3](http://link.springer.com/article/10.1007%2Fs00285-012-0511-3). This is aimed at molecular biology, gene regulatory networks, etc. Earlier papers, open access: [http://www.biomedcentral.com/1752-0509/5/113](http://www.biomedcentral.com/1752-0509/5/113) [http://www.sciencedirect.com/science/article/pii/S0303264708000701](http://www.sciencedirect.com/science/article/pii/S0303264708000701)
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edited January 2013

David Tanzer wrote:

I am going to start compiling a list of our ideas for things that mathematicians can do to help.

Great! Mathematicians keep asking me about this. I'd love it if you started an Azimuth Wiki page on this subject, and announcing it here. I've been meaning to do it! That'll be easier to find, in the long run, than comments here. We've got a mathematical methods category that such a page belongs in. It could be a very simple list at first, like you started here.

By the way, in your MPE slides, you refer to Xia’s work, but then refer to your work as being “nice mathematics” with the implication that it is not as applicable as Xia’s.

That was one of my rare half-hearted attempts at modesty. Of course I hope network theory will be very useful in a while, but I don't feel I've contributed anything practical yet - I'm just getting started, in my usual top-down way. So I wanted to deflect the question of how immediately useful this work was, and called it "nice mathematics".

I’d like to read more about network theory in general. So far my main contacts with it have been the Network Theory series on Azimuth, and Xia’s paper on the formation of a leaf. Do you have any recommendations for survey papers, or general textbooks?

I recently saw a book that looks worth reading:

Oxford University Press seems to be getting into this stuff; here are some books I haven't even glanced at yet:

The first of these is 720 pages long, the second a measly 152 pages.

Clearly a bandwagon is forming, upon which we should ride!

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edited January 2013

Graham wrote:

This paper: 'Reconstruction of extended Petri nets from time-series data by using logical control functions' landed in my email recently...

Groovy! This is an important ‘inverse problem' I haven't started thinking about: not starting with a reaction network and deriving predictions, but starting with empirical data and trying to fit it to a reaction network.

In some way that I haven't begun to ponder, this should connect reaction networks to machine learning and Bayesian networks. Brendan Fong did his master's thesis on Bayesian networks and category theory, and I want to explain that someday!

There's something big going on here... but it's not a simple case of "I see a network here and a network there, so they must be somehow the same". In Bayesian networks the edges indicate causality, some random variable affecting another. That's a seemingly different use of edges from reaction networks, where they mean something turning into something else! So we'll need to invent a sufficiently rich framework to fit these two together.

Comment Source:Graham wrote: > This paper: 'Reconstruction of extended Petri nets from time-series data by using logical control functions' landed in my email recently... Groovy! This is an important ‘inverse problem' I haven't started thinking about: not starting with a reaction network and deriving predictions, but starting with empirical data and trying to fit it to a reaction network. In some way that I haven't begun to ponder, this should connect reaction networks to machine learning and [Bayesian networks](http://en.wikipedia.org/wiki/Bayesian_network). Brendan Fong did his master's thesis on Bayesian networks and category theory, and I want to explain that someday! There's something big going on here... but it's not a simple case of "I see a network here and a network there, so they must be somehow the same". In Bayesian networks the edges indicate causality, some random variable affecting another. That's a seemingly different _use_ of edges from reaction networks, where they mean something turning into something else! So we'll need to invent a sufficiently rich framework to fit these two together.
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Here is some stuff on networks and machine learning I bumped into on Google+. It's yet another bunch of people doing something different with networks:

Comment Source:Here is some stuff on networks and machine learning I [bumped into on Google+](https://plus.google.com/u/0/106477459404474214513/posts/GTvauSD1b9q). It's yet another bunch of people doing something different with networks: * Mallat. Classification with Deep Invariant Scattering Networks. [http://nips.cc/Conferences/2012/Program/event.php?ID=3127](http://nips.cc/Conferences/2012/Program/event.php?ID=3127) * Dean et. al. Large Scale Distributed Deep Networks. [http://books.nips.cc/papers/files/nips25/NIPS2012_0598.pdf](http://books.nips.cc/papers/files/nips25/NIPS2012_0598.pdf) * Krizhevsky, Sutskever, Hinton. ImageNet Classification with Deep Convolutional Neural Networks. [http://books.nips.cc/papers/files/nips25/NIPS2012_0534.pdf](http://books.nips.cc/papers/files/nips25/NIPS2012_0534.pdf)
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edited January 2013

John wrote:

Great! Mathematicians keep asking me about this. I’d love it if you started an Azimuth Wiki page on this subject, and announcing it here.

Sure thing.

I have a draft of my conception for a good MPE blog article. It is a kind of understated manifesto for "green mathematics" and the Azimuth project. The main goal is provide insight, at a high level, about our current situation and historical context, and the general prospects for mathematics to contribute. The second goal, which is related, is to subtly recruit new members. The ideas are based on your slides, and everything that I have read in the forum and on the wiki, sprinkled with a few of my own perspectives.

To add some specific color to the presentation, I give a high-level summary of Xia's work on the formation of the vein patterns in leaves, and on the new mathematical framework for stochastic Petri nets that has been presented in the Azimuth Network Series.

There isn't room to present all of this, and to elaborate a list of specific things for mathematicians to do. Once the reader is interested in the overall picture and the Azimuth project, then we are well positioned to write a followup article with specific ideas. We can mention that this will be upcoming, either on the MPE blog or the Azimuth blog.

And this will be good for another reason, which is that, frankly speaking, in my opinion we have a lot more work to do in order to come up with a compelling list of ways that mathematicians can contribute to the environment.

It needs one more pass on my part, to put the writing in good order, before I'm ready to show it. I am aiming to post this by Wednesday, or, at the very latest, by Friday.

Thanks

Comment Source:John wrote: > Great! Mathematicians keep asking me about this. I’d love it if you started an Azimuth Wiki page on this subject, and announcing it here. Sure thing. I have a draft of my conception for a good MPE blog article. It is a kind of understated manifesto for "green mathematics" and the Azimuth project. The main goal is provide insight, at a high level, about our current situation and historical context, and the _general_ prospects for mathematics to contribute. The second goal, which is related, is to subtly recruit new members. The ideas are based on your slides, and everything that I have read in the forum and on the wiki, sprinkled with a few of my own perspectives. To add some specific color to the presentation, I give a high-level summary of Xia's work on the formation of the vein patterns in leaves, and on the new mathematical framework for stochastic Petri nets that has been presented in the Azimuth Network Series. There isn't room to present all of this, _and_ to elaborate a list of specific things for mathematicians to do. Once the reader is interested in the overall picture and the Azimuth project, then we are well positioned to write a followup article with specific ideas. We can mention that this will be upcoming, either on the MPE blog or the Azimuth blog. And this will be good for another reason, which is that, frankly speaking, in my opinion we have a lot more work to do in order to come up with a compelling list of ways that mathematicians can contribute to the environment. It needs one more pass on my part, to put the writing in good order, before I'm ready to show it. I am aiming to post this by Wednesday, or, at the very latest, by Friday. Thanks
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edited January 2013

There is another reason why I recommend this presentation strategy.

The MPE is a world-wide consortium of some 100 institutions. This is reflected in the character of the blog, which contains a widely heterogeneous collection of posts. This is a risk that whatever we write will just quickly fall off the radar, especially given the fact that they aim to post a new article each day.

So how do we make best use of our quick sound-bite of up to 1000 words? If we just gave our list of ideas for ways for mathematicians to contribute, it could come off as kind of bland, subjective and arbitrary. The whole idea of MPE is finding ways for mathematics to contribute, and many people will be oriented towards that in their posts. But if we catch their attention with the really excellent perspectives that have been developed at Azimuth, and the fascinating ideas behind the "green mathematics," which are urgently needed, incipient, and mind-expanding, then we've cleared out throats and will have an audience for the more specific ideas that we will present later (which we need to work out amongst ourselves first!)

Let's see what you think of all this, once I post the draft this week.

Comment Source:There is another reason why I recommend this presentation strategy. The MPE is a world-wide consortium of some 100 institutions. This is reflected in the character of the blog, which contains a widely heterogeneous collection of posts. This is a risk that whatever we write will just quickly fall off the radar, especially given the fact that they aim to post a new article each day. So how do we make best use of our quick sound-bite of up to 1000 words? If we just gave our list of ideas for ways for mathematicians to contribute, it could come off as kind of bland, subjective and arbitrary. The whole idea of MPE is finding ways for mathematics to contribute, and many people will be oriented towards that in their posts. But if we catch their attention with the really excellent perspectives that have been developed at Azimuth, and the fascinating ideas behind the "green mathematics," which are urgently needed, incipient, and mind-expanding, then we've cleared out throats and will have an audience for the more specific ideas that we will present later (which we need to work out amongst ourselves first!) Let's see what you think of all this, once I post the draft this week.
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edited January 2013

David wrote:

It is a kind of understated manifesto for “green mathematics”

I give a high-level summary of Xia’s work on the formation of the vein patterns in leaves,

In Xia’s work, the connection is very literal: the vein system of a green leaf is modeled as a transport network for nutrients, in the form of a directed graph. The math of these graphs, and of the optimization algorithms used to find the trees that minimize the transport cost functions, are therefore an example of network = green math.

Why is Xia's work "green mathematics" in the sense "how does it help the environment"? In my understanding it is rather basic research and probably currently mostly applicable in computer graphics.

Comment Source:David wrote: > It is a kind of understated manifesto for “green mathematics” >I give a high-level summary of Xia’s work on the formation of the vein patterns in leaves, >In Xia’s work, the connection is very literal: the vein system of a green leaf is modeled as a transport network for nutrients, in the form of a directed graph. The math of these graphs, and of the optimization algorithms used to find the trees that minimize the transport cost functions, are therefore an example of network = green math. Why is Xia's work "green mathematics" in the sense "how does it help the environment"? In my understanding it is rather basic research and probably currently mostly applicable in computer graphics.
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The needed pressure, however, might be generated by a popular movement based in academia and civil society to help guide humanity towards developing a new multiple intelligence, ‘foresight intelligence’ to provide the long-term analysis and planning that markets cannot supply.

Since when is "foresight" a new type of intelligence?

Comment Source:>The needed pressure, however, might be generated by a popular movement based in academia and civil society to help guide humanity towards developing a new multiple intelligence, ‘foresight intelligence’ to provide the long-term analysis and planning that markets cannot supply. Since when is "foresight" a new type of intelligence?
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edited January 2013

Why is Xia’s work “green mathematics” in the sense “how does it help the environment”?

I suppose I have some similar opinion in the sense that I would also say there is not really such a thing as "green mathematics" (except as a fancy term) but there is mathematics that can be used to study green topics.

Since when is “foresight” a new type of intelligence?

Does that actually matter to the conversation on this thread?

Comment Source:> Why is Xia’s work “green mathematics” in the sense “how does it help the environment”? I suppose I have some similar opinion in the sense that I would also say there is not really such a thing as "green mathematics" (except as a fancy term) but there is mathematics that can be used to study green topics. > Since when is “foresight” a new type of intelligence? Does that actually matter to the conversation on this thread?
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edited January 2013

Does that actually matter to the conversation on this thread?

I just want to know what the authors mean by "foresight intelligence" that is how does it differ from the usual term: Foresight, which I understand as some old aspect of human intelligence and not as some "new multiple intelligence", so I wondered what they meant.

So to make things more precise I should have asked: Since when is “foresight intelligence” a new type of intelligence?

Comment Source:>Does that actually matter to the conversation on this thread? I just want to know what the authors mean by "foresight intelligence" that is how does it differ from the usual term: <a href="http://en.wikipedia.org/wiki/Foresight_%28psychology%29">Foresight</a>, which I understand as some old aspect of human intelligence and not as some "new multiple intelligence", so I wondered what they meant. So to make things more precise I should have asked: Since when is “foresight intelligence” a new type of intelligence?
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Nad, see if the draft that I will be posting this week will address your question. Thanks

Comment Source:Nad, see if the draft that I will be posting this week will address your question. Thanks
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edited January 2013

Why is Xia’s work “green mathematics” in the sense “how does it help the environment”? In my understanding it is rather basic research [...]

It's basic research. I imagine that "green mathematics" will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other 'living systems'.

I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. I even feel that this is a necessary condition for modern civilization to become more friendly to the biosphere without collapsing.

A sufficiently big collapse, e.g. a massive dieoff of the human species and a return to the days of small bands of hunter-gatherers, might also help the biosphere. But this is not what I want. And a small collapse might actually hurt the biosphere, for example if people run out of fossil fuels and then burn all the trees they can find. So I believe the only good way is 'forward', not 'back' to previous conditions.

and probably currently mostly applicable in computer graphics.

I think Xia's work helps us understand leaves. This is different than, say, Barnsely's fractal fern, which is great for drawing pictures of ferns - or at least some ferns - but doesn't actually help us understand ferns.

Comment Source:Nad wrote: > Why is Xia’s work “green mathematics” in the sense “how does it help the environment”? In my understanding it is rather basic research [...] It's basic research. I imagine that "green mathematics" will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other 'living systems'. I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. I even feel that this is a _necessary_ condition for modern civilization to become more friendly to the biosphere without collapsing. A sufficiently big collapse, e.g. a massive dieoff of the human species and a return to the days of small bands of hunter-gatherers, might also help the biosphere. But this is not what I want. And a small collapse might actually hurt the biosphere, for example if people run out of fossil fuels and then burn all the trees they can find. So I believe the only good way is 'forward', not 'back' to previous conditions. > and probably currently mostly applicable in computer graphics. I think Xia's work helps us understand leaves. This is different than, say, <a href = "http://en.wikipedia.org/wiki/Barnsley_fern">Barnsely's fractal fern</a>, which is great for _drawing pictures of ferns_ - or at least some ferns - but doesn't actually help us understand ferns. <img src = "http://upload.wikimedia.org/wikipedia/commons/thumb/7/76/Barnsley_fern_plotted_with_VisSim.PNG/220px-Barnsley_fern_plotted_with_VisSim.PNG" alt = ""/>
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David wrote:

frankly speaking, in my opinion we have a lot more work to do in order to come up with a compelling list of ways that mathematicians can contribute to the environment.

I agree with that! This is the big dilemma of my life, right now.

By the way, read this blog comment and my answer. It's about a way mathematicians could contribute to the environment.

Comment Source:David wrote: > frankly speaking, in my opinion we have a lot more work to do in order to come up with a compelling list of ways that mathematicians can contribute to the environment. I agree with that! This is the big dilemma of my life, right now. By the way, read [this blog comment](http://johncarlosbaez.wordpress.com/2013/01/22/why-its-getting-hot/#comment-24462) and my answer. It's about a way mathematicians could contribute to the environment.
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edited January 2013

Since we've already gotten into it, here is the part of my manuscript, that concerns the work of Xia. I will say it better in the draft that I post. Note, I was making some guesses about the rationale behind the cost function, since it wasn't stated, so feel free to chime in or correct.

First, is there math in a leaf? In a recent paper by Qinglan Xia, called The Formation of a Tree Leaf, we see an explanation of what might be the secret key to one of Nature’s algorithms – the formation of the vein patterns in a tree leaf. The system of veins is modeled, quite plausibly, as a transport network for nutrients, which takes the form of a directed acyclic graph – a tree actually – where the nodes represent cells, and the edges are the “pipes” that connect the cells. Every cell generates a “revenue” of energy from photosynthesis, but it also extracts the cost of transporting nutrients to it from the base of the leaf (and of transporting other materials back towards the base). In this model, new cells are grown only if their revenue exceeds their cost.

Moreover, the total cost of transporting to a given collection of cells is a function of the network structure. Changes of angle in the veins extract a cost, because there is energy loss involved in the changing of the direction of the fluid flow. Furthermore, it is cheaper to transport a lot of material through a thick pipe to a distribution point, and then use thin pipes from there to distribute to the end destinations, rather than using many thin pipes from the root to each of the cells. (Less loss due to friction with the pipe walls).

All told, there is a cost function associated with the structure of the graph, and the model of growth is an incremental one, in which the leaf is constantly altering the vein structure (making local adjustments) to to find a local minimum in the cost function.

There overarching point here, from our purposes, is that, as an examination of the article shows, the work that is being done in that paper, is completely mathematical, involving lemmas, theorems, algorithms, etc.

This work also has the remarkable property that, by changing the parameters of the cost function, the algorithm will generate realistic images of various types of leaves found in nature, such as the maple, oak, etc. Note that this work is to be distinguished from other approaches to “artificial life,” which use synthetic models, e.g. L-systems, to produce more or less realistic images of plants. This model is based on an empirical concept of how plants really work.

Comment Source:Since we've already gotten into it, here is the part of my manuscript, that concerns the work of Xia. I will say it better in the draft that I post. Note, I was making some guesses about the rationale behind the cost function, since it wasn't stated, so feel free to chime in or correct. * * * First, is there math in a leaf? In a recent paper by Qinglan Xia, called [The Formation of a Tree Leaf](http://www.ma.utexas.edu/users/qlxia/Research/leaf.pdf), we see an explanation of what might be the secret key to one of Nature’s algorithms – the formation of the vein patterns in a tree leaf. The system of veins is modeled, quite plausibly, as a transport network for nutrients, which takes the form of a directed acyclic graph – a tree actually – where the nodes represent cells, and the edges are the “pipes” that connect the cells. Every cell generates a “revenue” of energy from photosynthesis, but it also extracts the cost of transporting nutrients to it from the base of the leaf (and of transporting other materials back towards the base). In this model, new cells are grown only if their revenue exceeds their cost. Moreover, the total cost of transporting to a given collection of cells is a function of the network structure. Changes of angle in the veins extract a cost, because there is energy loss involved in the changing of the direction of the fluid flow. Furthermore, it is cheaper to transport a lot of material through a thick pipe to a distribution point, and then use thin pipes from there to distribute to the end destinations, rather than using many thin pipes from the root to each of the cells. (Less loss due to friction with the pipe walls). All told, there is a cost function associated with the structure of the graph, and the model of growth is an incremental one, in which the leaf is constantly altering the vein structure (making local adjustments) to to find a local minimum in the cost function. There overarching point here, from our purposes, is that, as an examination of the article shows, the work that is being done in that paper, is completely mathematical, involving lemmas, theorems, algorithms, etc. This work also has the remarkable property that, by changing the parameters of the cost function, the algorithm will generate realistic images of various types of leaves found in nature, such as the maple, oak, etc. Note that this work is to be distinguished from other approaches to “artificial life,” which use synthetic models, e.g. L-systems, to produce more or less realistic images of plants. _This_ model is based on an empirical concept of how plants really work.
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edited January 2013

This looks great. For the MPE blog we might also actually say what the cost function is - I don't think it's so terribly complicated, and mathematicians value precise statements, so they might enjoy knowing the actual cost function that leaves apparently minimize! There's nothing like an equation to convince mathematicians that math is being done.

Comment Source:This looks great. For the MPE blog we might also actually say what the cost function _is_ - I don't think it's so terribly complicated, and mathematicians value precise statements, so they might enjoy knowing the actual cost function that leaves apparently minimize! There's nothing like an equation to convince mathematicians that math is being done.
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edited January 2013

John wrote:

It’s basic research. I imagine that “green mathematics” will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other ’living systems’.

I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. So I believe the only good way is ’forward’, not ’back’ to previous conditions.

Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go "forward", this may also have the consequence that an enhanced knowledge of "living systems" might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons. That is I think that in the long run one probably can't conceal or prevent the growth of human knowledge, a big question is here thus at what pace, how and in which direction this growth should take place. Or in short: "green mathematics" might be very "ungreen" depending on circumstances.

In this context I just cite: "Turning lab innovations into high impact products"

I think Xia’s work helps us understand leaves. This is different than, say, Barnsely’s fractal fern, which is great for drawing pictures of ferns - or at least some ferns - but doesn’t actually help us understand ferns.

I agree, that Xia's work gives a deeper insight into ferns then just imitating forms via fractals. And the "solutions" will probably be mathematically related. For an even more realistic application one could try to add one dimension and then do some buckling:

Comment Source:John wrote: >It’s basic research. I imagine that “green mathematics” will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other ’living systems’. > I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. So I believe the only good way is ’forward’, not ’back’ to previous conditions. Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go "forward", this may also have the consequence that an enhanced knowledge of "living systems" might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons. That is I think that in the long run one probably can't conceal or prevent the growth of human knowledge, a big question is here thus at what pace, how and in which direction this growth should take place. Or in short: "green mathematics" might be very "ungreen" depending on circumstances. In this context I just <a href="http://wyss.harvard.edu/">cite</a>: "Turning lab innovations into high impact products" >I think Xia’s work helps us understand leaves. This is different than, say, Barnsely’s fractal fern, which is great for drawing pictures of ferns - or at least some ferns - but doesn’t actually help us understand ferns. I agree, that Xia's work gives a deeper insight into ferns then just imitating forms via fractals. And the "solutions" will probably be mathematically related. For an even more realistic application one could try to add one dimension and then do some buckling: <a href="http://www.seas.harvard.edu/softmat/downloads/2009-16.pdf">http://www.seas.harvard.edu/softmat/downloads/2009-16.pdf</a>
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I have posted a draft my my vision of a good article to contribute to the MPE blog.

Aside from any content revisions, the word count needs to be reduced. The word count is just under 1600. I will keep chipping away at the phrases, to make them shorter and nicer.

Comment Source:I have posted a draft my my vision of a good article to contribute to the MPE blog. Here it is [[Blog (MPE) - Green mathematics for the era of environmental jeopardy]]. Aside from any content revisions, the word count needs to be reduced. The word count is just under 1600. I will keep chipping away at the phrases, to make them shorter and nicer. Ready for review. Thanks.
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31.

David Tanzer wrote:

I have posted a draft my my vision of a good article to contribute to the MPE blog.

and

Nad, see if the draft that I will be posting this week will address your question. Thanks

Sorry I don't see where there is an explanation for the term "forsight intelligence".

Comment Source:David Tanzer wrote: >I have posted a draft my my vision of a good article to contribute to the MPE blog. and >Nad, see if the draft that I will be posting this week will address your question. Thanks Sorry I don't see where there is an explanation for the term "forsight intelligence".
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Looks good. Needs some pictures. Some comments...

Hence network theory finds an important partner in the the science of complexity itself, which can now be seen in the particular forms like computational complexity theory, chaos theory, and organizational complexity theory.

I would delete this sentence. 'Complexity' means too many different things to different people - a lot of poorly understood concepts are bundled together under one word, which obscures possible connections instead of revealing them.

Computation itself is a partner to network theory,

I'd delete itself'

in turn, scientists may call on mathematicians to make in-depth analysis of environmental time-series data.

I suggest: In turn, scientists need mathematicians and statisticians to analyse environmental data.

Some environmental data is not a time series. For example, you can tell a lot about the history of a population if you have a lot of DNA sampled at one time. And mathematicians always study things in depth.

What are the repair processes that take place when a tree, or a worm, is cut?

A lot is known about this already, so the question sounds a bit silly. See http://www.biologie.uni-hamburg.de/b-online/e04/04c.htm for example. I'm not even sure that 'repair processes' make sense in the context of plants. Plants don't repair damaged parts, they replace them with new parts, roughly speaking.

Next we assert that the

I would delete this.

work by Xia takes a truly biological

I suggest: work by Xia takes a more biological

We take these results as further evidence that

I would delete this.

Comment Source:Looks good. Needs some pictures. Some comments... > Hence network theory finds an important partner in the the science of complexity itself, which can now be seen in the particular forms like computational complexity theory, chaos theory, and organizational complexity theory. I would delete this sentence. 'Complexity' means too many different things to different people - a lot of poorly understood concepts are bundled together under one word, which obscures possible connections instead of revealing them. > Computation itself is a partner to network theory, I'd delete itself' > in turn, scientists may call on mathematicians to make in-depth analysis of environmental time-series data. I suggest: In turn, scientists need mathematicians and statisticians to analyse environmental data. Some environmental data is not a time series. For example, you can tell a lot about the history of a population if you have a lot of DNA sampled at one time. And mathematicians always study things in depth. > What are the repair processes that take place when a tree, or a worm, is cut? A lot is known about this already, so the question sounds a bit silly. See [http://www.biologie.uni-hamburg.de/b-online/e04/04c.htm](http://www.biologie.uni-hamburg.de/b-online/e04/04c.htm) for example. I'm not even sure that 'repair processes' make sense in the context of plants. Plants don't repair damaged parts, they replace them with new parts, roughly speaking. > Next we assert that the I would delete this. > work by Xia takes a truly biological I suggest: work by Xia takes a more biological > We take these results as further evidence that I would delete this.
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33.

I think you should point at human activity rather than fortune as the important, tractable contributor to these environmental events :)

Comment Source:I think you should point at human activity rather than fortune as the important, tractable contributor to these environmental events :)
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edited January 2013

"Global warming.,...etc. are causing measurable damage to life on earth".

Measurable doesn't necessarily mean accurately measured; which I think is an important campaigning issue.

If you assume that the audience knows what power series are then the first few paragraphs come across to me as a bit too babyish.

Comment Source:And I think your initial claim isn't strong enough. I'd start with the what first. "Global warming.,...etc. are causing measurable damage to life on earth". Measurable doesn't necessarily mean accurately measured; which I think is an important campaigning issue. If you assume that the audience knows what power series are then the first few paragraphs come across to me as a bit too babyish.
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edited January 2013

John wrote:

It’s basic research. I imagine that “green mathematics” will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other ’living systems’.

I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. So I believe the only good way is ’forward’, not ’back’ to previous conditions.

Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go "forward", this may also have the consequence that an enhanced knowledge of "living systems" might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons.

I guess we can't get much more destructive. The moral-apperceptive problem is, most hominids have completely lost touch with their habitat. They have no grasp of the obscene destruction perpetrated these days. It started perhaps in bonze age city civilization and their Earth-detached sky gods, but the hallmark is Descartes' split of the world into mind/ego and matter. Poor Blaise Pascal was whining about being thrown into vast empty space. We have to get over this nihilist thrownness and start perceiving that we are not detached from earth. I.e. we have to get our head out of the clouds (marvelling at cosmology and quantum foams) and get the feet back on the ground (and have a look there). That's the purely natural philosophic reason why we need green mathematics. The mud under the boots is actually vastly more complex and fascinating than all the irrelevant galaxies and black holes and Hubble stuff. And it is actually relevant.

Here's a still valid quote from Leonardo da Vinci:

• We know more about the movement of celestial bodies than about the soil underfoot.

and he notes:

• nothing can be loved or hated unless it is first known.
Comment Source:nad wrote: >John wrote: >>It’s basic research. I imagine that “green mathematics” will range from immediately practical mathematics to basic research that helps us understand organisms, ecosystems, social systems and other ’living systems’. >> I imagine that in the long term, understanding living systems can help us become more friendly to the biosphere. So I believe the only good way is ’forward’, not ’back’ to previous conditions. >Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go "forward", this may also have the consequence that an enhanced knowledge of "living systems" might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons. I guess we can't get much more destructive. The moral-apperceptive problem is, most hominids have completely lost touch with their habitat. They have no grasp of the obscene destruction perpetrated these days. It started perhaps in bonze age city civilization and their Earth-detached sky gods, but the hallmark is Descartes' split of the world into mind/ego and matter. Poor Blaise Pascal was whining about being thrown into vast empty space. We have to get over this nihilist thrownness and start perceiving that we are not detached from earth. I.e. we have to get our head out of the clouds (marvelling at cosmology and quantum foams) and get the feet back on the ground (and have a look there). _That's the purely natural philosophic reason why we need green mathematics._ The mud under the boots is actually vastly more complex and fascinating than all the irrelevant galaxies and black holes and Hubble stuff. And it is actually relevant. Here's a still valid quote from Leonardo da Vinci: * We know more about the movement of celestial bodies than about the soil underfoot. and he notes: * nothing can be loved or hated unless it is first known.
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36.

Graham and Jim, thanks for your feedback. I will respond to your points over the course of a few messages.

Graham wrote:

Ok, to put my sentence in perspective, here what I had originally:

Another key area is the study of shocks to systems. When is it possible for a system, or an organism, to recover from a major blow to one of its subsystems? What are the repair processes that take place, for example, when a tree, or a worm, is cut?

Then to trim away two words, I changed the last sentence to become:

What are the repair processes that take place when a tree, or a worm, is cut?

Which you are saying doesn't make that much sense.

True, it was a hastily constructed example -- which may not hold water.

But can we think of a more solid example?

I have an intuition that the study of shocks and recovery can be studied at an abstract systems-theoretic level (is it already?) What I'm getting at, of course, is the prospect that one day, for example, a major food chain may collapse, and the "social metabolism" will be pressed adapt to such a shock.

Here I'll fish around for another example. What happens in the brain when there is a major loss of information from the visual fields. Isn't there some kind of adaptation, where there is a neural organization, and the person's visual cognition may partially recover, under the less favorable circumstances? I'm envisioning optimization processes that kick into place, that lead to reallocation of resources, under conditions of damage.

Or, more palpably, consider how animals adjust to the loss of a major organ.

Mostly I wanted to raise this as an avenue for research, that could both have vital applications, and be of theoretical interest in itself.

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edited January 2013

I wrote:

Hence network theory finds an important partner in the the science of complexity itself, which can now be seen in the particular forms like computational complexity theory, chaos theory, and organizational complexity theory.

Graham replied:

I would delete this sentence. ’Complexity’ means too many different things to different people - a lot of poorly understood concepts are bundled together under one word, which obscures possible connections instead of revealing them.

I'm open to reformulating it to make it more clear, but, in my opinion, something would be lost by just deleting it.

First, even apart from the notion of complexity at a generic level, when dealing with networks, especially at a biological scale, complexity is one of their salient attributes. So measures of network complexity, and the study of this complexity, would be part and parcel of network theory.

I really can't say anything much more specific here, because I'm a relative newcomer to network theory. In this draft, I'm taking my best shot at these ideas, but they will have to be vetted by the group and by John.

Now I have a further intuition that there will eventually be a coherent science of complexity, that, being related to the concept of information, it can be abstracted to a generic level. Is this done already? Do we have any complexity theorists in the house?

In any case, the pursuit of a general theory of complexity merits research, in my opinion.

But I agree that if no such coherent study exists at this moment, then I shouldn't write about it as if it exists, and, if we are going to introduce any speculations into our writing, then they should identified as such.

Comment Source:I wrote: > Hence network theory finds an important partner in the the science of complexity itself, which can now be seen in the particular forms like computational complexity theory, chaos theory, and organizational complexity theory. Graham replied: > I would delete this sentence. ’Complexity’ means too many different things to different people - a lot of poorly understood concepts are bundled together under one word, which obscures possible connections instead of revealing them. I'm open to reformulating it to make it more clear, but, in my opinion, something would be lost by just deleting it. First, even apart from the notion of complexity at a generic level, when dealing with networks, especially at a biological scale, complexity is one of their salient attributes. So measures of _network complexity_, and the study of this complexity, would be part and parcel of network theory. I really can't say anything much more specific here, because I'm a relative newcomer to network theory. In this draft, I'm taking my best shot at these ideas, but they will have to be vetted by the group and by John. Now I have a further _intuition_ that there will eventually be a coherent science of complexity, that, being related to the concept of information, it can be abstracted to a generic level. Is this done already? Do we have any complexity theorists in the house? In any case, the pursuit of a general theory of complexity merits research, in my opinion. But I agree that if no such coherent study exists at this moment, then I shouldn't write about it as if it exists, and, if we are going to introduce any speculations into our writing, then they should identified as such.
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38.

By way of association, I'd like to raise another point here.

To what extent does there exist a single coherent theory of networks? It sounds like, at present, network theory is an umbrella term that covers a heterogeneous variety of kinds of networks: Petri nets, pi-calculus, ... I saw that somewhere John used the term "sprawling" for network theory, which led me to the phrase that it is a "sprawling and incipient area of investigation."

This isn't any kind of show-stopper, but it's important to get the phrasing right, so that we don't imply that it is -- as yet -- a single crystallized theory. Also this doesn't invalidate the term "network theory." For the longest time, "biology" has been the study of a wildly disparate collection of forms of life. It's coherence as a unified theory has come along way...and it also has a long way to go.

John you have mentioned that you have ideas, rooted in category theory, for unifying various forms of network theory. Very interesting!! We could add a small mention that one part of the research at Azimuth -- or of John Baez's research at Azimuth -- however you want to work out the attributions -- is work on using category theory to connect various forms of network theory.

Comment Source:By way of association, I'd like to raise another point here. To what extent does there exist a single coherent theory of networks? It sounds like, at present, network theory is an umbrella term that covers a heterogeneous variety of kinds of networks: Petri nets, pi-calculus, ... I saw that somewhere John used the term "sprawling" for network theory, which led me to the phrase that it is a "sprawling and incipient area of investigation." This isn't any kind of show-stopper, but it's important to get the phrasing right, so that we don't imply that it is -- as yet -- a single crystallized theory. Also this doesn't invalidate the term "network theory." For the longest time, "biology" has been the study of a wildly disparate collection of forms of life. It's coherence as a unified theory has come along way...and it also has a long way to go. John you have mentioned that you have ideas, rooted in category theory, for unifying various forms of network theory. Very interesting!! We could add a small mention that one part of the research at Azimuth -- or of John Baez's research at Azimuth -- however you want to work out the attributions -- is work on using category theory to connect various forms of network theory.
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edited January 2013

I have an intuition that the study of shocks and recovery can be studied at an abstract systems-theoretic level (is it already?) What I’m getting at, of course, is the prospect that one day, for example, a major food chain may collapse, and the “social metabolism” will be pressed adapt to such a shock.

I understand better what you are talking about now. A key word is resilience http://www.resilience.org/, http://www.ecologyandsociety.org/vol9/iss2/art5/. You could ask the question: is there a maths of resilience? (I guess there is, but I don't know of examples.)

I won't say more about complexity, because my intuition is very different from yours, and I think John shares your intuition---and it is your blog!

Comment Source:> I have an intuition that the study of shocks and recovery can be studied at an abstract systems-theoretic level (is it already?) What I’m getting at, of course, is the prospect that one day, for example, a major food chain may collapse, and the “social metabolism” will be pressed adapt to such a shock. I understand better what you are talking about now. A key word is resilience [http://www.resilience.org/](http://www.resilience.org/about), [http://www.ecologyandsociety.org/vol9/iss2/art5/](http://www.ecologyandsociety.org/vol9/iss2/art5/). You could ask the question: is there a maths of resilience? (I guess there is, but I don't know of examples.) I won't say more about complexity, because my intuition is very different from yours, and I think John shares your intuition---and it is your blog!
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40.

David wrote:

Now I have a further intuition that there will eventually be a coherent science of complexity, that, being related to the concept of information, it can be abstracted to a generic level. Is this done already?

One example for a "generic" approach is by John Harte, whom John mentioned on the blog 2 months ago (click). Harte has applied Jaynes' maximum information entropy principle to ecology and gets a theory describing the major observed patterns in macroecology. But this is just ecologic "statics". Some interesting information geometry might be lurking here. Alas me dunno much. For a "dynamics" of ecosystems (e.g. due to perturbation by climate change) Harte suggests a variation of the maximum entropy production principle. But still conjecture. See his recent excellent book.

Comment Source:David wrote: > Now I have a further _intuition_ that there will eventually be a coherent science of complexity, that, being related to the concept of information, it can be abstracted to a generic level. Is this done already? One example for a "generic" approach is by [John Harte](http://johncarlosbaez.wordpress.com/2012/10/27/john-harte), whom John mentioned on the blog 2 months ago (click). Harte has applied Jaynes' maximum information entropy principle to ecology and gets a theory describing the major observed patterns in macroecology. But this is just ecologic "statics". Some interesting information geometry might be lurking here. Alas me dunno much. For a "dynamics" of ecosystems (e.g. due to perturbation by climate change) Harte suggests a variation of the maximum entropy production principle. But still conjecture. See his recent excellent [book](http://ukcatalogue.oup.com/product/9780199593422.do#.UQfyI3J47QM).
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edited January 2013

In the draft blog article, I wrote:

It is becoming increasingly clear that we are witnessing the beginning of a series of unfortunate environmental events. The problems include global warming, ice melting, permafrost melting, sea level rise, extreme weather events, wars, peak oil, loss of habitats, mass extinctions, deforestation, soil erosion, acid rain, air pollution, famines, pathogen mutations, antibiotic resistant diseases, epidemics, ocean acidification, ocean dead zones, radioactive waste, ozone depletion, the water crisis, and the accumulation of toxins.

Deep changes will be required to stabilize and regenerate the environment, but, unfortunately, the true political will for such difficult changes may not be mustered until things get significantly worse. Whether it comes sooner, or later, the recovery of an injured biosphere will be recognized as the top priority for continued social development. This will – and does – pose a great challenge for science and its twin, mathematics. At the Azimuth project, we want to get started now to help with the mathematical foundations for this science project, which is bound to become socially urgent as things progress.

Jim Stuttard wrote:

I think you should point at human activity rather than fortune as the important, tractable contributor to these environmental events :)

And I think you initial claim isn’t strong enough. I’d start with the what first.

Jim, there is merit in what you suggest. I also believe that the writing strategy that I adopted is viable -- I will explain. the right approach depends upon the goal of the article and the intended audience. That has yet to be established, as this draft was just my vision -- as one of the authors -- of how it could go. I'm not wedded to any particular handling of the introduction.

Here is the thinking that went behind the presentation as it now stands. No doubt that it is understated. I was using understatement as a writing device to emphasize the point. In our given context, I believe that by and large people know about global warming, etc., and they know that it has anthropogenic causes. It is becoming more and more manifest, and one has to be a committed "skeptic" to staunchly resist both the consensus of science and the news itself. As evidenced in the quotation page that I started, even in the U.S., which has been a stronghold of climate-change skepticism, public opinion is sobering up. (Sure, there are those who have made prior commitments to the denial of climate change, but no amount of graphs will persuade them otherwise.)

Furthermore, the readers of the MPE blog can be presumed to be interested in both mathematics and the environment, which points to a commitment to truth.

So the seriousness of the situation, and its anthropogenic causes, is not such a hard point to make!

I think that by understating the point, and simply enumerating the major environmental problems of the day, the logic in the readers mind will say Anthropogenic Causes. Kind of like the way that a syncopated beat, which is palpably missing, can be very strongly felt.

The other advantage of this, from a writing perspective, is that it economizes on the space (it's already over the limit), and it doesn't trigger off the standard "debate" dialogues in the reader's mind, leading more quickly to what I feel to be the most novel and interesting part of the article, which is John's thesis about green mathematics, it's historical significance, and the role of network theory in this next-era mathematics.

But, as I said, I also see the value in what you are suggesting, to make a more assertive introduction. A solution could be to keep it short and sweet, so that it puts some more focus on the problems, without interfering with the main line of vision of the article.

I will experiment with this, and put it into a second draft. It will also be useful for me to engage more closely with the data. We can worry about the word count a little be later on, once we have settled on a message and thread of discourse for the article.

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42.

Jim, I would also like to address your other point, which I would paraphrase here in neutral terms by the following: for the given level of sophistication of our readers -- who know about power series -- the introduction is too simplistic.

As I see it, an effective introduction can be tuned to a lower octane than the heart of an article. I'll go further, and say that in good writing, at least the very beginning should make some sense to any intelligent human being. If our goal is to educate, with a human purpose in mind, then we should seek to get the maximum social mileage out of everything that we write.

I have two metaphors in mind for this. First, if you'll pardon the aggressive imagery, think of a multi-pronged fish hook, that has hooks of varying sizes, each holding different kinds of baits. With such a hook, you could hope to catch a variety of fish. There is some food there for everyone. (It's a bad metaphor in another way, because we are really trying to give ideas to the reader, and not prey upon them.)

Second, think of leading the reader along a path that leads upwards, starting at a ground level, and which has to reach a certain height. How should you design the upwards curvature of your path, to maximize aggregate educational value of the writing? The final height represents the full idea that you want to transmit, to the maximally advanced reader that you have in mind. The slope at each point represents the "conceptual gradient" at each point in the text. Do you make it a linear path, with constant slope?

But there may be more optimal paths. If we start out flatter, then more people can get on board at the beginning. The slope will have to increase even more quickly later, so different levels of readers will drop off at different points. But if you give a reader something to work with, and they follow the first 40%, then you really have given them something, and they may be emboldened to try again later, and get 50% of the way through.

But, on the other hand, you don't want to alienate your more advanced readers. So there should be some bits of spice, challenge, or promise of challenge soon to come, in the lower-sloped sections. You don't want to talk down to anybody. And you do reach your advanced material by the end of the text, without fuzzing over it, ultimately with all the precision that it deserves. But you try to delay the point in the text where the less advanced readers will no longer be able to follow it.

This is a very difficult optimization problem to solve, but it is worth trying.

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43.

The metaphor of a single slope at each point it itself oversimplified. At each point in the text there are multiple threads of meaning that are being developed. So, informally speaking, it's some kind of "complex semantic manifold."

Comment Source:The metaphor of a single slope at each point it itself oversimplified. At each point in the text there are multiple threads of meaning that are being developed. So, informally speaking, it's some kind of "complex semantic manifold."
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44.
edited January 2013

Now I'd like to address the question of what could a mathematician, who knows about power series, possibly get out of a lower-sloped introduction, such as the one that I gave in the blog article?

First, I should acknowledge where some of my ideas for those first paragraphs came from. It was the following, very simple, but very meaningful idea that I found in one of John's slide presentations. I will paraphrase, as follows. In once sense, it is already too late, because the crises are underway, and we haven't even begun to make the changes that would merely stabilize the levels of atmospheric carbon dioxide. But in another sense, it is never too late, because no matter how bad things get, as long as we are still alive, we have choices to make, which will have consequences. And that at the Azimuth project, we are trying to work now to build the science that will become more and more urgently needed as the problems progress.

Now I think that these are useful perspectives, even to the world's leading experts on time series. They share the same basic human concerns as all the intelligent laymen, and they are subject to the same issues of fear, despair, and questions about the real meaningfulness of their work.

A lower-sloped introduction can connect to an advanced reader on these levels. That's the kind of things that introductions (and conclusions) are good for.

To me it's not "babyish" to engage a reader on this kind of level while leading towards the delivery of the target intellectual content.

So my plan, for the draft amendment, is to retain a human oriented-initial section, which will lead into a telescoped summary of some of the frightening mathematics of planet Earth.

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45.
edited January 2013

Dave wrote:

A solution could be to keep it short and sweet, so that it puts some more focus on the problems, without interfering with the main line of vision of the article.

+1.

I did baulk at leaving the adjective babyish in case it appeared offensive: which it obviously did so I apologise. I just thought I'd report my initial gut feeling in case others might have a similar response.

I think this is particularly good although I haven't checked the equivalent part of the blog.

In once sense, it is already too late, because the crises are underway, and we haven’t even begun to make the changes that would merely stabilize the levels of atmospheric carbon dioxide. But in another sense, it is never too late, because no matter how bad things get, as long as we are still alive, we have choices to make, which will have consequences. And that at the Azimuth project, we are trying to work now to build the science that will become more and more urgently needed as the problems progress.

And I did think the last version I read was really good.

As punishment I'll try to work out if there's any aspect of a semantic network which could usefully be described as commutative and thus possibly part of John's symmetrical monoidal category campaign :)

Comment Source:Dave wrote: > A solution could be to keep it short and sweet, so that it puts some more focus on the problems, without interfering with the main line of vision of the article. +1. I did baulk at leaving the adjective babyish in case it appeared offensive: which it obviously did so I apologise. I just thought I'd report my initial gut feeling in case others might have a similar response. I think this is particularly good although I haven't checked the equivalent part of the blog. > In once sense, it is already too late, because the crises are underway, and we haven’t even begun to make the changes that would merely stabilize the levels of atmospheric carbon dioxide. But in another sense, it is never too late, because no matter how bad things get, as long as we are still alive, we have choices to make, which will have consequences. And that at the Azimuth project, we are trying to work now to build the science that will become more and more urgently needed as the problems progress. And I did think the last version I read was really good. As punishment I'll try to work out if there's any aspect of a semantic network which could usefully be described as commutative and thus possibly part of John's symmetrical monoidal category campaign :)
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edited January 2013

David - I'll look at this blog article this weekend; I've been busy, but I'm extremely happy to read the criticisms and discussion here.

My general rule of thumb in writing is that whenever an intelligent and non-cranky person makes a criticism, there's probably some merit to it, so it probably calls for some modification of what I've written. My first reaction when people criticize my writing is always to defend what I'd done... so I try very hard to go past this and make changes. It's impossible to guess what all the reactions to a sentence might be, but every little bit of feedback helps. So, I hope each criticism here causes some change, perhaps small, that defuses that criticism.

In once sense, it is already too late, because the crises are underway, and we haven’t even begun to make the changes that would merely stabilize the levels of atmospheric carbon dioxide. But in another sense, it is never too late, because no matter how bad things get, as long as we are still alive, we have choices to make, which will have consequences. And that at the Azimuth project, we are trying to work now to build the science that will become more and more urgently needed as the problems progress.

As you probably know, I find these ideas extremely important. I need to keep reminding myself of them, to keep from sinking into despair and inaction. So, I'm glad you like them and I hope they find a clear expression in this blog article (which I haven't looked at yet ).

I think it pays to bite the bullet, confront our worst fears, and use the simple phrase we all don't want to hear: "too late".

Comment Source:David - I'll look at this blog article this weekend; I've been busy, but I'm extremely happy to read the criticisms and discussion here. My general rule of thumb in writing is that whenever an intelligent and non-cranky person makes a criticism, there's probably _some_ merit to it, so it probably calls for _some_ modification of what I've written. My first reaction when people criticize my writing is always to defend what I'd done... so I try very hard to go past this and make changes. It's impossible to guess what all the reactions to a sentence might be, but every little bit of feedback helps. So, I hope each criticism here causes some change, perhaps small, that defuses that criticism. > In once sense, it is _already_ too late, because the crises are underway, and we haven’t even begun to make the changes that would merely stabilize the levels of atmospheric carbon dioxide. But in another sense, it is _never_ too late, because no matter how bad things get, as long as we are still alive, we have choices to make, which will have consequences. And that at the Azimuth project, we are trying to work now to build the science that will become more and more urgently needed as the problems progress. As you probably know, I find these ideas extremely important. I need to keep reminding myself of them, to keep from sinking into despair and inaction. So, I'm glad you like them and I hope they find a clear expression in this blog article (which I haven't looked at yet <img src = "http://math.ucr.edu/home/baez/emoticons/uhh.gif" alt = ""/>). I think it pays to bite the bullet, confront our worst fears, and use the simple phrase we all don't want to hear: **"too late"**.
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47.
edited January 2013

David wrote:

To what extent does there exist a single coherent theory of networks?

I don't think it exists; that's why I'm trying to invent it.

If you can get ahold of these books or even just read the blurbs linked to here, I think you'll see what I mean:

Oxford University Press seems to be getting into this stuff; here are some books I haven't even glanced at yet:

Their titles make them sound like general introductions to networks, but I think you'll find that many important ideas are completely missing, including most of the ideas I've been talking about: chemical reaction networks, stochastic Petri nets, electrical circuits as metaphors for general systems, etc. A lot of people use 'network theory' to mean the study of the statistical properties of large random graphs, and random growth processes for graphs. This should ultimately be just a portion of network theory.

This is why I said network theory was a "sprawling" subject. Pieces of it are being developed in many different disciplines, but nobody has integrated this work... as far as I can see.

John you have mentioned that you have ideas, rooted in category theory, for unifying various forms of network theory. Very interesting!! We could add a small mention that one part of the research at Azimuth – or of John Baez’s research at Azimuth – however you want to work out the attributions – is work on using category theory to connect various forms of network theory.

I think a very very short plug for our work here on Azimuth would be good: e.g., simply to say that one of the things we're doing is trying to develop (or unify) network theory. I suspect a mention of category theory would repulse as many mathematicians as it would attract, so I don't we should mention that.

Comment Source:David wrote: > To what extent does there exist a single coherent theory of networks? I don't think it exists; that's why I'm trying to invent it. If you can get ahold of these books or even just read the blurbs linked to here, I think you'll see what I mean: * Ernesto Estrada, _[The Structure of Complex Networks: Theory and Applications](http://oup.com/us/catalog/general/subject/Physics/AtomicMolecularOpticalphysics/?view=usa&ci=9780199591756)_, Oxford U. Press, 2011. Oxford University Press seems to be getting into this stuff; here are some books I haven't even glanced at yet: * Mark Newman, [Networks: An Introduction](http://oup.com/us/catalog/general/subject/Physics/?view=usa&ci=9780199206650)_, Oxford U. Press, 2010. * Guido Caldarelli and Michele Catanzaro, _[Networks: A Very Short Introduction](http://oup.com/us/catalog/general/subject/Sociology/?view=usa&ci=9780199588077)_, Oxford U. Press, 2012 Their titles make them sound like general introductions to networks, but I think you'll find that many important ideas are completely missing, including most of the ideas I've been talking about: chemical reaction networks, stochastic Petri nets, electrical circuits as metaphors for general systems, etc. A lot of people use 'network theory' to mean the study of the statistical properties of large random graphs, and random growth processes for graphs. This should ultimately be just a _portion_ of network theory. This is why I said network theory was a "sprawling" subject. Pieces of it are being developed in many different disciplines, but nobody has integrated this work... as far as I can see. > John you have mentioned that you have ideas, rooted in category theory, for unifying various forms of network theory. Very interesting!! We could add a small mention that one part of the research at Azimuth – or of John Baez’s research at Azimuth – however you want to work out the attributions – is work on using category theory to connect various forms of network theory. I think a very _very_ short plug for our work here on Azimuth would be good: e.g., simply to say that one of the things we're doing is trying to develop (or unify) network theory. I suspect a mention of category theory would repulse as many mathematicians as it would attract, so I don't we should mention that.
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edited January 2013

John wrote:

My general rule of thumb in writing is that whenever an intelligent and non-cranky person makes a criticism, there’s probably some merit to it, so it probably calls for some modification of what I’ve written.

Yes, I know, that is why I have been discussing, above, the second draft that I am now writing, which is largely in response to Jim's suggestions about the writing.

Jim, the point which threw me off balance was the term "babyish" for the writing, which to my reading, ambiguously says as much about the author as it does about the text itself. There are more objective ways of stating what you meant, as, for example, that the level is too simple for the intended audience, the presentation is too simplistic, it is too light, etc. By the way, I am coming to agree with you on this point, especially as I dig into the second draft.

Anyhow, no problem, and I appreciated your last message. We should have a virtual beer one of these days. I'll be sure to bring my bib :) Do you have any baseball cards?

Comment Source:John wrote: > My general rule of thumb in writing is that whenever an intelligent and non-cranky person makes a criticism, there’s probably some merit to it, so it probably calls for some modification of what I’ve written. Yes, I know, that is why I have been discussing, above, the second draft that I am now writing, which is largely in response to Jim's suggestions about the writing. Jim, the point which threw me off balance was the term "babyish" for the writing, which to my reading, ambiguously says as much about the author as it does about the text itself. There are more objective ways of stating what you meant, as, for example, that the level is too simple for the intended audience, the presentation is too simplistic, it is too light, etc. By the way, I am coming to agree with you on this point, especially as I dig into the second draft. Anyhow, no problem, and I appreciated your last message. We should have a virtual beer one of these days. I'll be sure to bring my bib :) Do you have any baseball cards?
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49.

Yes, I know, that is why I have been discussing, above, the second draft that I am now writing, which is largely in response to Jim’s suggestions about the writing.

Okay, good. Reading just the comments on this forum here, you seemed to be spending time explaining, or, umm, "defending" what you'd already written. When I respond to referee's reports I try to avoid doing that... because it never helps, and I figure it's best to try to extract some constructive advice from even the most nasty, sharp-tongued criticism.

Maybe I was forgetting that this is a much more friendly environment, and a bit of 'pushback' may help find the best way to make both the author and the critic happy.

So never mind!

Comment Source:> Yes, I know, that is why I have been discussing, above, the second draft that I am now writing, which is largely in response to Jim’s suggestions about the writing. Okay, good. Reading just the comments on this forum here, you seemed to be spending time explaining, or, umm, "defending" what you'd already written. When I respond to referee's reports I try to avoid doing that... because it never helps, and I figure it's best to try to extract some constructive advice from even the most nasty, sharp-tongued criticism. Maybe I was forgetting that this is a much more friendly environment, and a bit of 'pushback' may help find the best way to make both the author and the critic happy. So never mind!
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edited January 2013

Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go “forward”, this may also have the consequence that an enhanced knowledge of “living systems” might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons.

That's true. However, I don't think that avoiding understanding organisms, ecosystems will help save us. As Martin points out, we're already doing an excellent job of destroying the biosphere, merely by not understanding it and ignoring it. But the trick is to find modes of understanding that will help us understand and preserve what is precious about the biosphere.

So, my own goal will be to avoid doing research that helps people produce, e.g., glow-in-the-dark fish. Instead, I'll try to think about things like biodiversity, tipping points, how evolution is related to information theory, what causes the ice ages, etcetera.

I guess you could say, in a vague way, that I'm trying to seek "holistic" rather than "reductionist" understandings. I put these words in quotes because I can barely stand saying them - they're so clichéd, and not exactly accurate for what I'm trying to express. I don't really think reductionism is bad when it's appropriate. I spent a lot of time thinking about particle physics, for example, and this is as reductionist as it gets! I don't think particle physics is bad, except that it's a bit useless, and it distracts smart people from more important problems.

Here's the kind of thing I mean. Right now we're getting good at modifying individual genes in organisms, and producing things like crops that resist certain pesticides, or glow-in-the-dark fish... but we're not so good at understanding the effects of such actions. We tend to manipulate the biosphere without an adequate understanding of how the biosphere as a whole will respond, and then be surprised at what we've done.

The biosphere, like a leaf, is a "network" of some sort. So I think we need to understand networks.

Comment Source:Nad wrote: > Understanding organisms, ecosystems etc. is a prerequisite to control them. So in that sense if you want to go “forward”, this may also have the consequence that an enhanced knowledge of “living systems” might be used in a very regulatory and eventually rather destructive way, as one can see at the example of weapons. That's true. However, I don't think that _avoiding_ understanding organisms, ecosystems will help save us. As Martin points out, we're already doing an excellent job of destroying the biosphere, merely by _not_ understanding it and ignoring it. But the trick is to find modes of understanding that will help us understand and preserve what is precious about the biosphere. So, my own goal will be to _avoid_ doing research that helps people produce, e.g., [glow-in-the-dark fish](http://www.theworld.org/2012/09/glow-in-the-dark-fish/). Instead, I'll try to think about things like biodiversity, tipping points, how evolution is related to information theory, what causes the ice ages, etcetera. I guess you could say, in a vague way, that I'm trying to seek "holistic" rather than "reductionist" understandings. I put these words in quotes because I can barely stand saying them - they're so clich&eacute;d, and not exactly accurate for what I'm trying to express. I don't really think reductionism is bad when it's appropriate. I spent a lot of time thinking about particle physics, for example, and this is as reductionist as it gets! I don't think particle physics is bad, except that it's a bit useless, and it distracts smart people from more important problems. Here's the kind of thing I mean. Right now we're getting good at modifying individual genes in organisms, and producing things like crops that resist certain pesticides, or glow-in-the-dark fish... but we're not so good at understanding the effects of such actions. We tend to manipulate the biosphere without an adequate understanding of how the biosphere as a whole will respond, and then be surprised at what we've done. The biosphere, like a leaf, is a "network" of some sort. So I think we need to understand networks.