Mathematics of Planet Earth at Banff

A while back, I mentioned that 2013 will be a special year for programs on the Mathematics of Planet Earth. I also mentioned that the Centre de Recerca Matematica in Barcelona is inviting mathematicians to organize conferences and workshops on this theme.

They’re also inviting mathematicians to organize workshops on this theme at the Banff International Research Station for Mathematical Innovation and Discovery, or BIRS. This is a famous and beautiful research center in the Canadian Rockies.

The deadline is coming up on September 30th, and I want to apply. If you’d like to join me, please drop me a note, either here on this blog or by email!

I’m open to all sorts of ideas, and I’d love help from biologists or climate scientists. If you don’t give me a better idea, I’ll probably do an application on network theory. It might look a bit like this:

Diagrammatic languages for describing complex networks made of interacting parts are used throughout ecology, biology, climate science, engineering, and many other fields. Examples include Systems Biology Graphical Notation, Petri nets in computer science, stochastic Petri nets and chemical reaction networks in chemistry and biochemistry, bond graphs in electrical, chemical and mechanical engineering, Bayesian networks in probabilistic reasoning, box models in climate science, and Harold Odum’s Energy Systems Language for systems ecology. Often these diagrammatic languages are invented by practitioners in a given field without reference to previous work in other fields. Recently mathematicians have set up the theoretical infrastructure needed to formalize, rigorously relate, and some cases unify these various languages. Doing this will help interdisciplinary work of the sort that is becoming important in theoretical ecology, climate science and ‘the mathematics of planet Earth’. The goal of this workshop is to bring together experts on various diagrammatic languages and mathematicians who study the general theory of diagrammatic reasoning.

If you’d be interested in coming to a workshop on this subject, let me know. Banff provides accommodation, full board, and research facilities—but not, I believe, travel funds! So, “interested in coming” means “interested enough to pay for your own flight”.

Banff does “full workshops” with 42 people for 5 days, and “half workshops” with 20 people for 5 days. Part of why I’m asking you to express your interest is to gauge which seems more appropriate.

Here’s what they say:

With a growing global population competing for the same global resources, an increased frequency and intensity of dramatic climatic events, and evidence pointing to more long-term patterns of general climate change, the pressure to comprehend nature and its trends is greater than ever. Leaders in politics, sociology and economics have begun to seriously take note of issues which before were confined to the natural sciences alone, and mathematical modeling is at the heart of much of the research undertaken. The year 2013 has thus been earmarked by mathematical sciences institutes around the world as a time for a special emphasis on the study of the “Mathematics of Planet Earth” (MPE 13). This theme is to be interpreted as broadly as possible, in the aim of creating new partnerships with related disciplines and casting new light on the many ways in which the mathematical sciences can help to comprehend and tackle some of the world’s most pressing problems.

The Banff International Research Station (BIRS) is a full partner in this important initiative, as the goals of MPE 13 are completely in line with the station’s commitment to pursuing excellence in a broad range of mathematical sciences and applications. BIRS has already planned to host five workshops in 2012 which deal with the themes of MPE 13:

• “Emergent Behavior in Multi-particle Systems with Non-local Interactions” (January 22-27).

• “Frontiers in the Detection and Attribution of Climate Change” (May 29–June 1).

• “Tissue Growth and Morphogenesis: from Genetics to Mechanics and Back” (July 22-27).

• “Model Reduction in Continuum Thermodynamics: Modeling, Analysis and Computation” (September 16-21).

• “Thin Liquid Films and Fluid Interfaces: Models, Experiments and Applications” (December 9-14).

BIRS also invites interested applicants to use the opportunities of its 2013 program and submit proposals in line of the MPE 2013 theme, in conjunction with BIRS’ regular format for programming. Proposals should be made using the BIRS online submission process.

Azimuth News (Part 1)

Here’s some good news about Azimuth:

1. George Musser, a science writer who is an editor for Scientific American, is coming to the Centre for Quantum Technologies here in Singapore from 10 October to 17 December 2011. I found this out in a Google Plus conversation when I happened to mention I was in Singapore. He will be visiting to write a book on “nonlocality and emergent spacetime”. But when I said I’m also interested in climate change, he suggested that we write a couple of joint blog posts on that! This is great news. He has written about “detection and attribution” questions.

2. I am hiring Brendan Fong as an intern during September 2011. He has just graduated from the mathematics department at Australian National University and is starting a masters in mathematics and the foundations of computer science at Oxford in October 2011. He has written a thesis on algebraic geometry, but now he’s working on image analysis for plant growth modelling, with Jinhai Cai of the Phenomics and Bioinformatics Research Centre at the University of South Australia. He wants to help with the ‘network theory’ program we’ve been discussing here

3. On Google Plus, Cameron Smith has expressed interest in writing an article for the Azimuth Blog. He has done work on synthetic biology, but now he’s interested in gene regulatory networks and multi-level selection theory in evolutionary biology. Best of all, he’s interested in applying elegant math, like category theory, to these topics! So, I’m hoping he’ll explain some of his thoughts here, and we can discuss them, and ideally push them forwards a step or two.

As you’ll note, two of these three items are directly due to Google Plus. (The third is due to this blog, which Brendan has been reading.) So, Google Plus may be a useful way of making connections and accelerating the growth of the Azimuth Project!

Meanwhile, over on the Azimuth Forum, we’ve been having an interesting discussion of Milankovitch cycles, enlivened by the new presence of Marcel Bökstedt, an algebraic topologist who has gotten interested in climate science. A lot of what we’re discussing will eventually find its way into This Week’s Finds, so I mention it only in case you want to peek into the kitchen and see what’s cooking!

On another note, Lisa and I are going to China tomorrow. First to Beijing, where I’ll give a talk on Energy, The Environment and what Mathematicians Can Do at Capital Normal University, and she’ll try to buy a guqin:

That’s not Lisa, but you get the idea: a guqin, also simply known as a qin is a zither-like instrument. The prefix gu- means ‘old’, and this instrument is mentioned in Chinese writings dating back almost 3,000 years.

Then, on Tuesday, we’ll take a train up to Changchun, which is about 500 kilometers west of Vladivostok:

There will be a mathematics workshop at Jilin University up there, and I’ll give a series of lectures on how the octonions let us construct category-theoretic structures good for doing superstring theory.

But before the workshop, there will be an excursion to Changbai Mountain from August 3rd to 6th. This is part of a mountain range near the border with North Korea:

or, on a warmer day:

Changbai Mountain is actually a volcano, and the lake occupies a caldera formed by an explosive eruption that occurred around 969 AD. Debris from this eruption has been found as far as the island of Hokkaidō in Japan. In 2011, experts in North and South Korea met to discuss the chances of a significant eruption in the near future.

So, if it blows up while I’m in Changchun: goodbye, it was nice knowing all of you!

Otherwise, I’ll be back on August 12th.

Azimuth on Google Plus (Part 1)

Google Plus is here… and it’s pretty cool.

If you’re on Google Plus, and you want to get Azimuth-related news items, please let me know, either here or there. I’ll add you to my Azimuth circle.

Or even better, tell me how to broadcast items on Google Plus so that 1) everyone can see them, but 2) only people who want Azimuth stuff needs to see them. I can send stuff to “Public”, but so far I’ve been using that for fun stuff I think everyone would enjoy. Maybe future improvements to Google Plus will help me solve my dilemma.

Here’s a sample of Azimuth items on Google Plus. But note: these look a lot nicer on Google Plus.

• Solar panels could reduce heat reaching the rooftop by as much as 38%. So, while making electricity you also spend less energy cooling your building in the summer. Not so nice in the winter, maybe.

• Japan has been paying the dues for other countries in the International Whaling Commission — and then these countries vote against banning whaling. Japanese academic Atsushi Ishii said that this form of vote-buying was “very likely,” but added “I would not call it corruption.” Yeah, right. But the good news: now things may change a bit, since the International Whaling Commission has decided to ban this practice!

• A plastic bottle filled with water refracts sunlight and acts like a 55-watt bulb — during the day, if you have a hole in your roof. For many that would be a good thing.

• Congress may finally kill a $6 billion annual subsidy for turning corn into ethanol. This would be a good thing in many ways. Even some bioethanol producers say they don’t need this subsidy anymore. After all, there are laws requiring the use of ethanol in fuels, and as oil prices continue to rise, ethanol is becoming competitive.

• Koch Industries Inc. and Exxon Mobil helped write legislation that’s been introduced in Montana, New Mexico, New Hampshire, Oregon, Washington and other states in the USA. It includes these words: “a tremendous amount of economic growth would be sacrificed for a reduction in carbon emissions that would have no appreciable impact on global concentrations of carbon dioxide.” They did this through an organization called the American Legislative Exchange Council (ALEC).

• See all the things that are wrong with scientific publishing today. On Google Plus we’ve been discussing ways to solve these problems.

• Paleoecologist Micha Ruhl of Utrecht University has a new paper on the Permian-Triassic extinction. It argues that a fairly small release in CO₂ from volcanoes was enough to make the sea floor release methane and cause the world’s worst mass extinction event. How much is “fairly small”, I wonder?

• There’s a new Canadian study on “astroturfing”. Students who viewed a fake “grassroots” website with arguments against the existence of manmade global warming not only became less certain about the cause of global warming; they also believed that the issue was less important than before! Worst, the responses of participants who had viewed sites “Funded by Exxon-Mobil” weren’t different than those who had viewed sites funded by the “Conservation Heritage Fund,” by “donations by people like you,” or sites that didn’t list the source of funding at all.

And just for fun, especially for those of you suffering from the US heat wave… here’s what happens when you throw boiling water into the air at -35 °C:

But why isn’t she wearing a hat?

The One Best Thing Everyone Could Do to Slow Climate Change

There’s a website called Quora where people can ask and answer questions of all sorts. Lots of people use it, so Curtis Faith suggested that we—that is, everyone here reading this blog—try answering some of the questions there. That sounded like a nice idea, so now there’s a ‘topic’ on Quora called Azimuth Project. The questions we tackle will be listed there, so people can easily find them.

To get the ball rolling, Curtis posted this question:

What is the one best thing everyone could do to slow down climate change?

If you’re like me, the first thing you’ll want to do is question the question. Are we really looking for the one best thing everyone could do? Everyone in the world, including the billion poorest people?

In that case, many answers that leap to mind are no good. We can’t say “take fewer airplane trips” because most of those people don’t take airplane trips to begin with. We can’t say “drive less” because most of those people don’t have cars. And so on. It’s no fair! We need an easier question!

Well… let’s not try to second-guess the question. It’s actually fun to take it seriously and try to answer it. It’ll force us to think about the world as a whole, instead of the sins of our rich neighbors.

Here are 50 tips for how to fight global warming from Global Warming Facts. Could any of these be the right answer? How many of these are things that everyone on this Earth can do?

1. Replace a regular incandescent light bulb with a compact fluorescent light bulb (cfl)
   CFLs use 60% less energy than a regular bulb. This simple switch will save about 300 pounds of carbon dioxide a year.
   We recommend you purchase your CFL bulbs at 1000bulbs.com, they have great deals on both screw-in and plug-in light bulbs.

2. Install a programmable thermostat
   Programmable thermostats will automatically lower the heat or air conditioning at night and raise them again in the morning. They can save you $100 a year on your energy bill.

3. Move your thermostat down 2° in winter and up 2° in summer
   Almost half of the energy we use in our homes goes to heating and cooling. You could save about 2,000 pounds of carbon dioxide a year with this simple adjustment.

4. Clean or replace filters on your furnace and air conditioner
   Cleaning a dirty air filter can save 350 pounds of carbon dioxide a year.

5. Choose energy efficient appliances when making new purchases
   Look for the Energy Star label on new appliances to choose the most energy efficient products
   available.

6. Do not leave appliances on standby
   Use the “on/off” function on the machine itself. A TV set that’s switched on for 3 hours a day (the average time Europeans spend watching TV) and in standby mode during the remaining 21 hours uses about 40% of its energy in standby mode.

7. Wrap your water heater in an insulation blanket
   You’ll save 1,000 pounds of carbon dioxide a year with this simple action. You can save another 550 pounds per year by setting the thermostat no higher than 50°C.

8. Move your fridge and freezer
   Placing them next to the cooker or boiler consumes much more energy than if they were standing on their own. For example, if you put them in a hot cellar room where the room temperature is 30-35ºC, energy use is almost double and causes an extra 160 kg of CO₂ emissions for fridges per year and 320 kg for freezers.

9. Defrost old fridges and freezers regularly
   Even better is to replace them with newer models, which all have automatic defrost cycles and are generally up to two times more energy-efficient than their predecessors.

10. Don’t let heat escape from your house over a long period
    When airing your house, open the windows for only a few minutes. If you leave a small opening all day long, the energy needed to keep it warm inside during six cold months (10ºC or less outside temperature) would result in almost 1 ton of CO₂ emissions.

11. Replace your old single-glazed windows with double-glazing
    This requires a bit of upfront investment, but will halve the energy lost through windows and pay off in the long term. If you go for the best the market has to offer (wooden-framed double-glazed units with low-emission glass and filled with argon gas), you can even save more than 70% of the energy lost.

12. Get a home energy audit
    Many utilities offer free home energy audits to find where your home is poorly insulated or energy inefficient. You can save up to 30% off your energy bill and 1,000 pounds of carbon dioxide a year. Energy Star can help you find an energy specialist.

13. Cover your pots while cooking
    Doing so can save a lot of the energy needed for preparing the dish. Even better are pressure cookers and steamers: they can save around 70%!

14. Use the washing machine or dishwasher only when they are full
    If you need to use it when it is half full, then use the half-load or economy setting. There is also no need to set the temperatures high. Nowadays detergents are so efficient that they get your clothes and dishes clean at low temperatures.

15. Take a shower instead of a bath
    A shower takes up to four times less energy than a bath. To maximize the energy saving, avoid power showers and use low-flow showerheads, which are cheap and provide the same comfort.

16. Use less hot water
    It takes a lot of energy to heat water. You can use less hot water by installing a low flow showerhead (350 pounds of carbon dioxide saved per year) and washing your clothes in cold or warm water (500 pounds saved per year) instead of hot.

17. Use a clothesline instead of a dryer whenever possible
    You can save 700 pounds of carbon dioxide when you air dry your clothes for 6 months out of the year.

18. Insulate and weatherize your home
    Properly insulating your walls and ceilings can save 25% of your home heating bill and 2,000 pounds of carbon dioxide a year. Caulking and weather-stripping can save another 1,700 pounds per year. Energy Efficient has more information on how to better insulate your home.

19. Be sure you’re recycling at home
    You can save 2,400 pounds of carbon dioxide a year by recycling half of the waste your household generates.

20. Recycle your organic waste
    Around 3% of the greenhouse gas emissions through the methane is released by decomposing bio-degradable waste. By recycling organic waste or composting it if you have a garden, you can help eliminate this problem! Just make sure that you compost it properly, so it decomposes with sufficient oxygen, otherwise your compost will cause methane emissions and smell foul.

21. Buy intelligently
    One bottle of 1.5l requires less energy and produces less waste than three bottles of 0.5l. As well, buy recycled paper products: it takes less 70 to 90% less energy to make recycled paper and it prevents the loss of forests worldwide.

22. Choose products that come with little packaging and buy refills when you can
    You will also cut down on waste production and energy use… another help against global warming.

23. Reuse your shopping bag
    When shopping, it saves energy and waste to use a reusable bag instead of accepting a disposable one in each shop. Waste not only discharges CO2 and methane into the atmosphere, it can also pollute the air, groundwater and soil.

24. Reduce waste
    Most products we buy cause greenhouse gas emissions in one or another way, e.g. during production and distribution. By taking your lunch in a reusable lunch box instead of a disposable one, you save the energy needed to produce new lunch boxes.

25. Plant a tree
    A single tree will absorb one ton of carbon dioxide over its lifetime. Shade provided by trees can also reduce your air conditioning bill by 10 to 15%. The Arbor Day Foundation has information on planting and provides trees you can plant with membership.

26. Switch to green power
    In many areas, you can switch to energy generated by clean, renewable sources such as wind and solar. In some of these, you can even get refunds by government if you choose to switch to a clean energy producer, and you can also earn money by selling the energy you produce and don’t use for yourself.

27. Buy locally grown and produced foods
    The average meal in the United States travels 1,200 miles from the farm to your plate. Buying locally will save fuel and keep money in your community.

28. Buy fresh foods instead of frozen
    Frozen food uses 10 times more energy to produce.

29. Seek out and support local farmers markets
    They reduce the amount of energy required to grow and transport the food to you by one fifth. Seek farmer’s markets in your area, and go for them.

30. Buy organic foods as much as possible
    Organic soils capture and store carbon dioxide at much higher levels than soils from conventional farms. If we grew all of our corn and soybeans organically, we’d remove 580 billion pounds of carbon dioxide from the atmosphere!

31. Eat less meat
    Methane is the second most significant greenhouse gas and cows are one of the greatest methane emitters. Their grassy diet and multiple stomachs cause them to produce methane, which they exhale with every breath.

32. Reduce the number of miles you drive by walking, biking, carpooling or taking mass transit wherever possible
    Avoiding just 10 miles of driving every week would eliminate about 500 pounds of carbon dioxide emissions a year! Look for transit options in your area.

33. Start a carpool with your coworkers or classmates
    Sharing a ride with someone just 2 days a week will reduce your carbon dioxide emissions by 1,590 pounds a year. eRideShare.com runs a free service connecting North American commuters and travelers.

34. Don’t leave an empty roof rack on your car
    This can increase fuel consumption and CO₂ emissions by up to 10% due to wind resistance and the extra weight – removing it is a better idea.

35. Keep your car tuned up
    Regular maintenance helps improve fuel efficiency and reduces emissions. When just 1% of car owners properly maintain their cars, nearly a billion pounds of carbon dioxide are kept out of the atmosphere.

36. Drive carefully and do not waste fuel
    You can reduce CO₂ emissions by readjusting your driving style. Choose proper gears, do not abuse the gas pedal, use the engine brake instead of the pedal brake when possible and turn off your engine when your vehicle is motionless for more than one minute. By readjusting your driving style you can save money on both fuel and car maintenance.

37. Check your tires weekly to make sure they’re properly inflated
    Proper tire inflation can improve gas mileage by more than 3%. Since every gallon of gasoline saved keeps 20 pounds of carbon dioxide out of the atmosphere, every increase in fuel efficiency makes a difference!

38. When it is time for a new car, choose a more fuel efficient vehicle
    You can save 3,000 pounds of carbon dioxide every year if your new car gets only 3 miles per gallon more than your current one. You can get up to 60 miles per gallon with a hybrid! You can find information on fuel efficiency on FuelEconomy and on GreenCars websites.

39. Try car sharing
    Need a car but don’t want to buy one? Community car sharing organizations provide access to a car and your membership fee covers gas, maintenance and insurance. Many companies – such as Flexcar – offer low emission or hybrid cars too! Also, see ZipCar.

40. Try telecommuting from home
    Telecommuting can help you drastically reduce the number of miles you drive every week. For more information, check out the Telework Coalition.

41. Fly less
    Air travel produces large amounts of emissions so reducing how much you fly by even one or two trips a year can reduce your emissions significantly. You can also offset your air travel carbon emissions by investing in renewable energy projects.

42. Encourage your school or business to reduce emissions
    You can extend your positive influence on global warming well beyond your home by actively encouraging other to take action.

43. Join the virtual march
    The Stop Global Warming Virtual March is a non-political effort to bring people concerned about global warming together in one place. Add your voice to the hundreds of
    thousands of other people urging action on this issue.

44. Encourage the switch to renewable energy
    Successfully combating global warming requires a national transition to renewable energy sources such as solar, wind and biomass. These technologies are ready to be deployed more widely but there are regulatory barriers impeding them. U.S. citizens, take action to break down those barriers with Vote Solar.

45. Protect and conserve forest worldwide
    Forests play a critical role in global warming: they store carbon. When forests are burned or cut down, their stored carbon is release into the atmosphere – deforestation now accounts for about 20% of carbon dioxide emissions each year. Conservation International has more information on saving forests from global warming.

46. Consider the impact of your investments
    If you invest your money, you should consider the impact that your investments and savings will have on global warming. Check out SocialInvest and Ceres to can learn more about how to ensure your money is being invested in companies, products and projects that address issues related to climate change.

47. Make your city cool
    Cities and states around the country have taken action to stop global warming by passing innovative transportation and energy saving legislation. If you’re in the U.S., join the cool cities list.

48. Tell Congress to act
    The McCain Lieberman Climate Stewardship and Innovation Act would set a firm limit on carbon dioxide emissions and then use free market incentives to lower costs, promote efficiency and spur innovation. Tell your representative to support it.

49. Make sure your voice is heard!
    Americans must have a stronger commitment from their government in order to stop global warming and implement solutions and such a commitment won’t come without a dramatic increase in citizen lobbying for new laws with teeth. Get the facts about U.S. politicians and candidates at Project Vote Smart and The League of Conservation Voters. Make sure your voice is heard by voting!

50. Share this list!
    Spread this list worldwide and help people doing their part: the more people you will manage to enlighten, the greater YOUR help to save the planet will be (but please take action on first person too)! If you like, you are free to republish, adapt or translate the list and post it in your blog, website or forum as long as you give us credit with a link to the original source.

There are a lot of great ideas here, but if we look for those that everyone can do, there aren’t many.

What’s the most important item that was left off this list?

I’ll give my answer to Curtis’ question after I’ve heard some of yours. It’s a tough question but I have an idea. And no, it’s not “join the Azimuth Project”.

A Question About Graduate Schools

I got an email from a physics major asking for some advice about graduate programs. He said it would be okay if I posted it here. Maybe you can help out!

Prof. Baez,

My name is Blake Pollard, I am an undergraduate physics major at Columbia University graduating next week. I agree very much with the premise of and the need for the Azimuth Project and would like to help out. Though my passion is physics, most of my undergraduate research has been in climate and sustainability. I would really like to find a graduate program enabling me to do both physics and something useful for the environmental movement, hence I haven’t committed to a Ph.D. program in pure physics. I studied category theory a bit here at Columbia from Lauda, and took some representation theory with Khovanov, but I think (at least at this point in time) my calling in physics is geometrical algebras. I was planning on spending a year off reading on my own, trying to do some work, and making the decision between environmental, physics, or mathematics graduate studies. Your blog served me well as a guidepost in my early college years for reading good stuff, and would appreciate any advice you have on:

1) graduate programs where I could do work on both mathematical physics and the environment

2) good people/places/projects that I could participate in in the coming year.

The Azimuth Project web resources have already been helpful in finding people to reach out to, but I figured you might have something or someone popping out of your head in particular.

I have programming experience in data mining, numerical simulations, remote sensing, and just having fun programming; decent math/physics background; and really just want to find a good place where good people are working hard. Like Göttingen way back in the day. Sorry for the longish email.

Thank you in advance for your time,

Blake S. Pollard
Applied Physics 2011

In a later email he added a bit more detail:

I think most people, though, would associate my goals with doing some physical modeling/analysis of environmental systems/problems, maybe a statistical-physical hybrid. That is probably what I would do in a PhD program on the environmental side of things. But I’m more thinking of having an advisor who does research in mathematical physics, while applying myself on the side to some problem related to the environment, like Google’s 20% projects. Probably it’s a bit too inter-departmental and too flexible for there to be a formal program for this (plus I’d likely be too busy!).

It seems though the answer might be simply doing a PhD in environmental sciences and doing physics in my spare time. Just organizing my own thoughts.

Are there any good grad programs that involve a mix of mathematical or theoretical physics and environmental science? I’ll take any good answers I get and add them to the Azimuth Wiki.

Networks and Population Biology (Part 4)

Today was the last day of the tutorials on discrete mathematics and probability in networks and population biology. Persi Diaconis gave two talks, one on ‘exponential families’ of random graphs and one on ‘exchangeability’. Since there’s way too much to summarize, I’ll focus on explaining ideas from the first talk, leaving you to read about the second here:

• Persi Diaconis and Svante Janson, Graph limits and exchangeable random graphs.

Susan Holmes also gave two talks. The first was on metagenomics and the human microbiome—very cool stuff. Did you know that your body contains 100 trillion bacteria, and only 10 trillion human cells? And you’ve got 1000 species of bacteria in your gut? Statistical ecologists are getting very interested in this.

Her second talk was about doing statistics when you’ve got lots of data of different kinds that need to be integrated: numbers, graphs and trees, images, spatial information, and so on. This is clearly the wave of the future. You can see the slides for this talk here:

• Susan Holmes, Heterogeneous data challenge: combining complex data.

The basic idea of Persi Diaconis’ talk was simple and shocking. Suppose you choose a random graph in the most obvious way designed to heighten the chance that it contains a triangle, or some other figure. Then in fact all you’ve done is change the chance that there’s an edge between any given pair of vertices!

But to make this precise—to make it even true—we need to say what the rules are.

For starters, let me point you back to part 2 for Persi’s definitions of ‘graph’ and ‘graph homomorphism’. If we fix a finite set , there will be a big set of graphs with exactly these vertices. To define a kind of ‘random graph’, we first pick a probability measure on each set . Then, we demand that these probability measures converge in a certain sense as .

However, we can often describe random graphs in a more intuitive way! For example, the simplest random graphs are the Erdős–Rényi random graphs. These depend on a parameter . The idea here is that we take our set of vertices and for each pair we flip a coin that lands heads up with probability . If it lands heads up, we stick in an edge between those vertices; otherwise not. So, the presence or absence of each edge is an independent random variable.

Here’s a picture of an Erdős–Rényi random graph drawn by von Frisch, with a 1% chance of an edge between any two vertices. But it’s been drawn in a way so that the best-connected vertices are near the middle, so it doesn’t look as random as it is:

People have studied the Erdős–Rényi random graphs very intensively, so now people are eager to study random graphs with more interesting correlations. For example, consider the graph where we draw an edge between any two people who are friends. If you’re my friend and I’m friends with someone else, that improves the chances that you’re friends with them! In other words, friends tend to form ‘triangles’. But in an Erdős–Rényi random graph there’s no effect like that.

‘Exponential families’ of random graphs seem like a way around this problem. The idea here is to pick a specific collection of graphs and say how commonly we want these to appear in our random graph. If we only use one graph , and we take this to be two vertices connected by an edge, we’ll get an Erdős–Rényi random graph. But, if we also want our graph to contain a lot of triangles, we can pick to be a triangle.

More precisely, remember from part 2 that is the fraction of functions mapping to vertices of that are actually graph homomorphisms. This is the smart way to keep track of how often shows up inside . So, we pick some numbers and define a probability measure on as follows: the probability of any particular graph should be proportional to

If you’re a physicist you’ll call this a ‘Gibbs state’, and you’ll know this is the way to get a probability distribution that maximizes entropy while holding the expected values of constant. Statisticians like to call the whole family of Gibbs states as we vary the number an ‘exponential family’. But the cool part, for me, is that we can apply ideas from physics—namely, statistical mechanics—to graph theory.

So far we’ve got a probability measure on our set of graphs with vertices. These probability measures converge in a certain sense as . But Diaconis and Chatterjee proved a shocking theorem: for almost all choices of the graphs and numbers , these probability measures converge to an Erdős–Rényi random graph! And in the other cases, they converge to a probabilistic mixture of Erdős–Rényi random graphs.

In short, as long as the numbers are positive, exponential families don’t buy us much. We could just work with Erdős–Rényi random graphs, or probabilistic mixtures of these. The exponential families are still very interesting to study, but they don’t take us into truly new territory.

The theorem is here:

• Sourav Chatterjee and Persi Diaconis, Estimating and understanding random graph models.

To reach new territory, we can try letting some be negative. The paper talks about this too. Here many questions remain open!

What To Do? (Part 1)

In a comment on my last interview with Yudkowsky, Eric Jordan wrote:

John, it would be great if you could follow up at some point with your thoughts and responses to what Eliezer said here. He’s got a pretty firm view that environmentalism would be a waste of your talents, and it’s obvious where he’d like to see you turn your thoughts instead. I’m especially curious to hear what you think of his argument that there are already millions of bright people working for the environment, so your personal contribution wouldn’t be as important as it would be in a less crowded field.

I’ve been thinking about this a lot.

Indeed, the reason I quit work on my previous area of interest—categorification and higher gauge theory—was the feeling that more and more people were moving into it. When I started, it seemed like a lonely but exciting quest. By now there are plenty of conferences on it, attended by plenty of people. It would be a full-time job just keeping up, much less doing something truly new. That made me feel inadequate—and worse, unnecessary. Helping start a snowball roll downhill is fun… but what’s the point in chasing one that’s already rolling?

The people working in this field include former grad students of mine and other youngsters I helped turn on to the subject. At first this made me a bit frustrated. It’s as if I engineered my own obsolescence. If only I’d spent less time explaining things, and more time proving theorems, maybe I could have stayed at the forefront!

But by now I’ve learned to see the bright side: it means I’m free to do other things. As I get older, I’m becoming ever more conscious of my limited lifespan and the vast number of things I’d like to try.

But what to do?

This a big question. It’s a bit self-indulgent to discuss it publicly… or maybe not. It is, after all, a question we all face. I’ll talk about me, because I’m not up to tackling this question in its universal abstract form. But it could be you asking this, too.

For me this question was brought into sharp focus when I got a research position where I was allowed—nay, downright encouraged!—to follow my heart and work on what I consider truly important. In the ordinary course of life we often feel too caught up in the flow of things to do more than make small course corrections. Suddenly I was given a burst of freedom. What to do with it?

In my earlier work, I’d always taken the attitude that I should tackle whatever questions seemed most beautiful and profound… subject to the constraint that I had a good chance of making some progress on them. I realized that this attitude assumes other people will do most of the ‘dirty work’, whatever that may be. But I figured I could get away with it. I figured that if I were ever called to account—by my own conscience, say—I could point to the fact that I’d worked hard to understand the universe and also spent a lot of time teaching people, both in my job and in my spare time. Surely that counts for something?

I had, however, for decades been observing the slow-motion train wreck that our civilization seems to be engaged in. Global warming, ocean acidification and habitat loss may be combining to cause a mass extinction event, and perhaps—in conjunction with resource depletion—a serious setback to human civilization. Now is not the time to go over all the evidence: suffice it to say that I think we may be heading for serious trouble.

It’s hard to know just how much trouble. If it were just routine ‘misery as usual’, I’ll admit I’d be happy to sit back and let everyone else deal with these problems. But the more I study them, the more that seems untenable… especially since so many people are doing just that: sitting back and letting everyone else deal with them.

I’m not sure this complex of problems rises to the level of an ‘existential risk’—which Nick Bostrom defines as one where an adverse outcome would either annihilate intelligent life originating on Earth or permanently and drastically curtail its potential. But I see scenarios where we clobber ourselves quite seriously. They don’t even seem unlikely, and they don’t seem very far-off, and I don’t see people effectively rising to the occasion. So, just as I’d move to put out a fire if I saw smoke coming out of the kitchen and everyone else was too busy watching TV to notice, I feel I have to do something.

But the question remains: what to do?

Eliezer Yudkowsky had some unabashed advice:

I honestly don’t see how a rationalist can avoid this conclusion: At this absolutely critical hinge in the history of the universe—Earth in the 21st century—rational altruists should devote their marginal attentions to risks that threaten to terminate intelligent life or permanently destroy a part of its potential. Those problems, which Nick Bostrom named ‘existential risks’, have got all the scope. And when it comes to marginal impact, there are major risks outstanding that practically no one is working on. Once you get the stakes on a gut level it’s hard to see how doing anything else could be sane.

So how do you go about protecting the future of intelligent life? Environmentalism? After all, there are environmental catastrophes that could knock over our civilization… but then if you want to put the whole universe at stake, it’s not enough for one civilization to topple, you have to argue that our civilization is above average in its chances of building a positive galactic future compared to whatever civilization would rise again a century or two later. Maybe if there were ten people working on environmentalism and millions of people working on Friendly AI, I could see sending the next marginal dollar to environmentalism. But with millions of people working on environmentalism, and major existential risks that are completely ignored… if you add a marginal resource that can, rarely, be steered by expected utilities instead of warm glows, devoting that resource to environmentalism does not make sense.

Similarly with other short-term problems. Unless they’re little-known and unpopular problems, the marginal impact is not going to make sense, because millions of other people will already be working on them. And even if you argue that some short-term problem leverages existential risk, it’s not going to be perfect leverage and some quantitative discount will apply, probably a large one. I would be suspicious that the decision to work on a short-term problem was driven by warm glow, status drives, or simple conventionalism.

With that said, there’s also such a thing as comparative advantage—the old puzzle of the lawyer who works an hour in the soup clinic instead of working an extra hour as a lawyer and donating the money. Personally I’d say you can work an hour in the soup clinic to keep yourself going if you like, but you should also be working extra lawyer-hours and donating the money to the soup clinic, or better yet, to something with more scope. (See “Purchase Fuzzies and Utilons Separately” on Less Wrong.) Most people can’t work effectively on Artificial Intelligence (some would question if anyone can, but at the very least it’s not an easy problem). But there’s a variety of existential risks to choose from, plus a general background job of spreading sufficiently high-grade rationality and existential risk awareness. One really should look over those before going into something short-term and conventional. Unless your master plan is just to work the extra hours and donate them to the cause with the highest marginal expected utility per dollar, which is perfectly respectable.

Where should you go in life? I don’t know exactly, but I think I’ll go ahead and say “not environmentalism”. There’s just no way that the product of scope, marginal impact, and John Baez’s comparative advantage is going to end up being maximal at that point.

When I heard this, one of my first reactions was: “Of course I don’t want to do anything ‘conventional’, something that ‘millions of people’ are already doing”. After all, my sense of being just another guy in the crowd was a big factor in leaving work on categorification and higher gauge theory—and most people have never even heard of those subjects!

I think so far the Azimuth Project is proceeding in a sufficiently unconventional way that while it may fall flat on its face, it’s at least trying something new. Though I always want more people to join in, we’ve already got some good projects going that take advantage of my ‘comparative advantage’: the ability to do math and explain stuff.

The most visible here is the network theory project, which is a step towards the kind of math I think we need to understand a wide variety of complex systems. I’ve been putting most of my energy into that lately, and coming up with ideas faster than I can explain them. On top of that, Eric Forgy, Tim van Beek, Staffan Liljgeren, Matt Reece, David Tweed and others have other interesting projects cooking behind the scenes on the Azimuth Forum. I’ll be talking about those soon, too.

I don’t feel satisfied, though. I’m happy enough—that’s never a problem these days—but once you start trying to do things to help the world, instead of just have fun, it’s very tricky to determine the best way to proceed.

One can, of course, easily fool oneself into thinking one knows.