Energy, the Environment, and What Mathematicians Can Do (Part 1)

I’m preparing a talk to give at Hong Kong University next week. It’s only half done, but I could use your feedback on this part while I work on the rest:

Energy, The Environment, and What Mathematicians Can Do.

So far it makes a case for why mathematicians should get involved in these issues… but doesn’t say what they can to help! That’ll be the second part. So, you’ll just have to bear with the suspense for now.

By the way, all the facts and graphs should have clickable links that lead you to online references. The links aren’t easy to see, but if you hover the cursor over a fact or graph, and click, it should work.

107 Responses to Energy, the Environment, and What Mathematicians Can Do (Part 1)

  1. On page 8, do you have an idea of how the “long view” graph looks like? (And “the temperatures haVE gone up”.)

    • John Baez says:

      Thanks for catching that typo. Here are some graphs that provide a longer view of temperatures on Earth.

      The last 1000 years:

      Different colored lines are different reconstructions—click for details, and also a larger view.

      The last 12,000 years:

      Note what seems to be a ‘jump discontinuity’ at the far right edge of the graph. That’s because temperatures (as well as CO2) are rising very fast by geological standards. You can see that the Earth came out of the last ice age roughly around 12,000 years ago, reached its maximum temperature, started cooling down… but now it’s getting hotter.

      Going back still further:

      According to this graph, if the Earth’s temperature rises 1°C from its 2005 level, it’ll be the hottest it’s been in 1.35 million years.

      For even longer views try:

      • John Baez, Temperature.

      I really need to update this: the temperature history of the Earth is a really… umm… ‘hot topic’, so there’s a lot of new information available.

      • Thanks, that is really striking!

        • John Baez says:

          By the way, my student Mike Stay visited Singapore last week and we went through your paper on Cartesian closed 2-categories and permutation equivalence in higher-order rewriting. That’s also really striking! I’d been a bit scared to dig into the details before, but they’re not so scary now.

          He’s working on computation, concurrency, and symmetric monoidal closed bicategories. He has a paper close to finished. It would be great if you and he could talk sometime, because I’m not so knowledgeable in computer science, and on top of that I’m putting lots of energy into other things, like this environmental stuff. Also, he’s usually based at Google, in their headquarters in California, while I’m here in Singapore.

          (Ultimately I hope the environmental stuff will connect to the computation and concurrency stuff, as you can guess from my discussion of ‘networks‘ and category theory. But it will take a while to sort out.)

        • Thanks again then! It’s heartening that you could read it smoothly, I had a bit of a struggle trying to make the tons of syntax look reasonable.

          Maybe you and Mike could also be interested in Nicolas Tabareau’s Aspect Oriented Programming: a language for 2-categories. He seems to have a closely related internal language for cartesian closed 2-categories, with a more type-theoretical viewpoint.

          (And of course I know Mike, we’ve already exchanged a few mails.)

  2. Tim van Beek says:

    The first obvious feedback is: It’s 2011, not 2010 (see the date on your first slide).

    Why is the talk addressing mathematicians, but not other scientists?

    I hope that it will be possible to give this talk without getting lost in political discussions. I have a hard time to restrain myself from asking “aren’t we already busy fighting wars?”, for example, on the last slide (I’d say: “There wouldn’t be a war in Afghanistan if the Taliban had made a deal with the Bush administration – Bush senior – to allow the building of pipelines through their country”, etc.).

    • John Baez says:

      Tim wrote:

      It’s 2011, not 2010 (see the date on your first slide).

      Fixed, thanks.

      Why is the talk addressing mathematicians, but not other scientists?

      Because it’s a talk in the math department colloquium at Hong Kong University.

      I have a hard time to restrain myself from asking “aren’t we already busy fighting wars?”

      No need to restrain yourself! It serves to make my point even more clearly.

      The folks in Hong Kong are not yet busy fighting wars. But to the extent that conflicts are already being driven by the battle for oil, that may serve as a preview of how squabbling over limited resources may distract us from solving other problems.

  3. DavidTweed says:

    The only comment I’ve got is that I’d expect a question about whether the graphs are (i) artifacts of the period being graphed and (ii) if a linear trend is really supported. There are responses to all these things that I’d have on-tap if I were giving that talk.

    • Tim van Beek says:

      That’s a really good point that I did not spent much time on, partially because I thought that I would find the answer en passent while searching for discussions of climate models, but haven’t yet:

      Aren’t there claims that all the graphs can be generated by e.g. AR(1) processes and that all trends are completely random?

    • John Baez says:

      I have a certain limited ability to argue that the evidence I’m presenting is not, in fact, bullshit. When that runs out I’ll just say “if you don’t believe this stuff, you’re welcome to read the papers these claims come from: go to my website and click to get the links.”

      I plan to give a math department colloquium talk of roughly this sort over and over. It’ll take practice to get good at it, and only with practice will I get good at countering all possible objections.

      There’s a danger that I’ll spend too much time on the first part of the talk and not enough on the (unwritten!) second part, where I say what mathematicians can do. That’s the part where I may distinguish myself from a second-rate climate scientist. But I’ll probably have to give the talk a lot of times before I become happy with the second part.

      • Tim van Beek says:

        John said:

        I have a certain limited ability to argue that the evidence I’m presenting is not, in fact, bullshit.

        The whole “hockey stick” discussion is a good example of how mathematicians can help, in this case by explaining and evaluating the statistical analysis of time series. Another example that comes to mind is from Roy Spencer’s book “The Great Global Warming Blunder”, where he states that he can match the temperature time series of the 20th century with a very simple model that he implemented as an Excel time sheet: He has 4 free parameters in the model (or 5, depending on how you count). This is a nice example where a mathematician can sit down and prove that you can match any time series similar to the temperature time series with a certain class of models with 4 free parameters within a certain error bound, so people don’t have to bother to implement them and do test runs until they get a good match :-)

  4. Frederik De Roo says:

    Where you quote numbers from Pacala and Socolow’s report, it’s dated from 2004. I would say so explicitly.

    But obviously somebody may ask, what are the up-to-date numbers? I believe our page on Wind power indicates that, between 2004-2009, capacity was multiplied by four. I’m not sure if we have been able to collect other numbers on Azimuth yet.

    • John Baez says:

      Frederik wrote:

      Where you quote numbers from Pacala and Sokolow’s report, it’s dated from 2004. I would say so explicitly.

      Done.

      But obviously somebody may ask, what are the up-to-date numbers?

      I don’t know up-to-date numbers on these climate stabilization wedges, and in a sense it barely matters for this talk. My goal is mainly to give a rough sense of how hard it would be to halt the increase of carbon emissions. It’s very hard, and that hasn’t changed since 2004.

      But, I was planning to briefly mention that by continuing the current annual rate of growth of solar power for 50 years, we could meet the goal of multiplying solar power by a factor of 700. That requires a 14% annual growth rate. From 2004 to 2009, grid-connected photovoltaic solar power had a 60% average annual growth rate. Of course we cannot expect it to be easy or even possible to keep up such a high growth rate! But somehow 14% annual growth for 50 years sounds a bit easier than a factor of 700, so it’s good to realize that they’re the same thing.

      And, I’ll invite people to go to my website, read the slides there, and click on the links. That will lead them to the Azimuth Wiki page Stabilization wedges. So, any information you put there will be helpful.

      And again: I plan to keep giving this talk over and over. It’s quite hard to do a talk like this very well… so I’ll start by doing it badly, and gradually get better.

      • Joe says:

        I still think you’re missing something here using 2004 numbers.

        To me, the difference in wind between needing a factor of 50 and a factor of 12.5 is significant. We are making some progress! For some people a bit of optimism in the mix will be a reason to join in.

        In wind (and in solar) there is a new industry being created, the scale required means that we are just at the beginning. A few examples for applied mathematics: aeroelasticity of blades, layout of wind farms, grid stability – and how all of these change as turbines get bigger.

        The growth of a new industry could result in funding for mathematicians, even beyond government money. But more fundamentally the fact that wind is being built at scale will throw up interesting raw material for research problems.

        The growth of PV since 2004 is even more impressive, around a factor of 10, from about 4 to over 40GW. It only need grow by around 70, not 700, times for a wedge.

        (I think that confirms the rough picture that I have in my mind that the contribution of solar is about a decade behind wind. In 2004 wind needed to grow by a factor of 50.)

        World CO2 emissions have also risen, by around 10%, which raises the necessary size of each wedge, but I think the impressive growth rates are still important.

        • John Baez says:

          Thanks, Joe!

          I definitely plan to add some optimism in my spoken remarks, especially when it comes to wind and solar. See nad’s remark and my reply down here.

          I would like to get my numbers straight. You seem to say photovoltaic needs to grow a factor of 70 (to equal one ‘wedge’), while nad seems to be saying it only needed to grow by a factor of 35 back in 2009. It would be great if you two could straighten this out!

          If you know any specific papers about ‘math and solar power’, or people who do that sort of thing, that would also be great.

  5. Frederik De Roo says:

    If my impression is correct, the main focus on why seems to be that you want them to work on it because of the environmental problems (emotional plea – although one could make some arguments related to the economical costs related to the loss of biodiversity etc). Perhaps some other reasons for those who are not very interested in that?

    * there is also a variety of interesting mathematics involved in environmental problems, see your talk part 2

    * somewhat cynical (and already hinted at in slide 41-42) maybe it could be expected that budgets funding environmentally-related math will become bigger (relatively to other funds) when problems become bigger – even before waiting another 20 years? Of course, this also presupposes that you can convince them to believe that problems will become bigger…

    • John Baez says:

      Thanks for the tips.

      I certainly want to mention some interesting math problems related to environmental and energy issues.

      And yes, I’m not-too-subtly hinting that mathematicians who want government grants in 20 years should consider starting work on environmental and energy issues now! One may consider this cynical, but since many mathematicians tell me they would work on these issues if they were more idealistic, it might be a useful observation.

      The real challenge is covering so much material in 50 minutes.

      • Tim van Beek says:

        John said:

        I certainly want to mention some interesting math problems related to environmental and energy issues.

        Of course there are the Navier-Stokes equations: being an expert in an interesting class of solutions can get you an invitation to Oberwolfach (no need to mention the millenium problem, as I suppose that everybody knows about it).

        If you add random forcing you get to the topic of stochastic partial differential equations, which leads you to stochastic processes in infinite dimensional spaces, which is a really nice topic if you already chastened yourself with quantum field theory.

  6. Arrow says:

    So the floods in Pakistan were due to global warming? What about Japanese earthquake and tsunami? I’m sure they too can be linked to global warming (what cannot?), it could go like this – as the Earths crust warms it gets slightly more fluid which lowers it’s strain resistance and prompts release of the accumulated tensions – more earthquakes. Moreover the higher water level makes tsunamis more damaging.

    • John Baez says:

      Cheap sarcasm aside, you’ll note I didn’t say the floods in Pakistan were due to global warming. I was asking how many events of this magnitude must occur for people to 1) decide that global warming is increasing the risk of weather disasters and 2) decide it’s worth doing something about it. Clearly the answer to question 2) is ‘more than one’.

      The question of whether an individual event is ‘due to’ a general trend doesn’t have a definitive yes-or-no answer. We can talk about the extent to which a trend like global warming changes the probability of an event like the Pakistan flood, and there has been recent progress in studying questions of this sort.

      In February 2011 two papers appeared on this topic.

      • Pardeep Pall, Tolu Aina, Dáithí Stone, Peter Stott, Toru Nozawa, Arno Hilberts, Dag Lohmann, and Myles Allen, Anthropogenic greenhouse gas contribution to flood risk in England and Wales in autumn 2000, Nature 470> (17 February 2011), 382–385.

      Abstract: Interest in attributing the risk of damaging weather-related events to anthropogenic climate change is increasing. Yet climate models used to study the attribution problem typically do not resolve the weather systems associated with damaging events such as the UK floods of October and November 2000. Occurring during the wettest autumn in England and Wales since records began in 1766, these floods damaged nearly 10,000 properties across that region, disrupted services severely, and caused insured losses estimated at £1.3 billion. [...] Here we present a multi-step, physically based ‘probabilistic event attribution’ framework showing that it is very likely that global anthropogenic greenhouse gas emissions substantially increased the risk of flood occurrence in England and Wales in autumn 2000.

      This paper is not freely available online yet, but the supplementary online information is free and interesting. It begins:

      A popular simple thermodynamic argument assumes precipitation extremes are constrained to change with the water vapour capacity of the atmosphere that can be determined, under conditions of constant relative humidity, using change in mean surface temperature alone according to the Clausius-Clapeyron relation. This argument is typically invoked in the aftermath of floods as an explanation for possible increases in such severe wet events under an anthropogenically warming climate.

      While this is an oversimplified treatment not fully accounting for the complex hydrometeorology typically associated with UK flooding, it may nevertheless provide a physically plausible first guess of increases in mid-latitude precipitation extremes under warming. Indeed, a recently updated analysis of observed atmospheric column water vapour for past decades finds increasing trends over the UK and western Europe, and a significant autumnal increase more generally over Europe and the Northern Hemisphere; and this appears in agreement with a similar analysis finding increases in observed atmospheric humidity under warming for these regions that are within expected moistening rates for near-constant relative humidity.This latter analysis in particular appears broadly consistent with observations of Clausius-Clapeyron scale increases in surface specific humidity (the principle source for the free-troposphere) under warming over past decades, again with near-constant relative humidity – including for an European region incorporating the UK. Since these surface specific humidity increases have been attributed to mainly anthropogenic drivers, this lends support to a thermodynamic mechanism for increasing UK precipitation, and hence flooding, under anthropogenic warming.

      Here we use this thermodynamic argument to deduce the reduction in observed England and Wales total daily precipitation extremes for an autumn 2000 climate, had estimated twentieth-century surface warming attributable to anthropogenic greenhouse gas emissions not occurred. Then regarding this reduction in precipitation extremes as a direct measure of reduction in flooding, we calculate the fraction of attributable risk (FAR) of these extremes, and compare it to the FAR of autumn 2000 flooding explicitly modelled in terms of severe daily river runoff using our more rigorous multi-step probabilistic event attribution (PEA) framework of the main text.

      This related abstract is also available:

      • Pardeep Pall, Tolu Aina, Dáithí Stone, Peter Stott, Toru Nozawa, Arno Hilberts, Dag Lohmann, and Myles Allen, Anthropogenic greenhouse gas contribution to UK autumn flood risk, Geophysical Research Abstracts 12, EGU2010-12930, 2010.

      The second paper appearing in February 2011 is:

      • Seung-Ki Min, Xuebin Zhang, Francis W. Zwiers and Gabriele C. Hegerl, Human contribution to more-intense precipitation extremes, Nature 470 (17 February 2011), 378-381.

      Abstract: Here we show that human-induced increases in greenhouse gases have contributed to the observed intensification of heavy precipitation events found over approximately two-thirds of data-covered parts of Northern Hemisphere land areas. […] Changes in extreme precipitation projected by models, and thus the impacts of future changes in extreme precipitation, may be underestimated because models seem to underestimate the observed increase in heavy precipitation with warming.

      Again this paper is not yet available for free online, but there’s a discussion of it here:

      • Alyson Kenward, Scientists identify human connection to precipitation extremes, Climate Central, 16 February 2011.

      • Frederik De Roo says:

        I seem to have troubles with replying too slowly today…

      • Arrow says:

        While you did not state it explicitly, the question certainly implies that you consider global warming at least partly responsible, otherwise asking how many events like that we would need before acting makes no sense.

        As for assigning the risks there are two problems with such attributions – they are biased and they lack experimental support.

        A neutral approach would have to take into account all the effects – not only negative ones but also positive ones. For example if global warming does indeed lead to increased precipitation then in addition to floods in some areas it also helps avert droughts in others, if it leads to exceptionally hot summers then it should lead to milder winters too, and so on.

        But following the media and the “experts” they cite, one learns that both floods and droughts, heatwaves and cold spells, are all attributable to global warming. On the other hand no one ever mentions positive effects that may also be attributed to global warming. This is an obvious example of bias.

        The other problem is that all those attributions carry little to no weight. Due to complexity of the climate, motivated people can always devise plausible sounding hypotheses (and models purporting to support them) which show how this or that disaster might be attributed to global warming. But Earth’s climate is way to complex and poorly understood for such hypotheses to be taken seriously without experimental support to back them up. However experiments which could offer such support are pretty much impossible to perform.

        • Tim van Beek says:

          Arrow wrote:

          While you did not state it explicitly, the question certainly implies that you consider global warming at least partly responsible, otherwise asking how many events like that we would need before acting makes no sense.

          I second that, without further explanation it does look like a claim that the flood was caused by AGW.

          A neutral approach would have to take into account all the effects – not only negative ones but also positive ones.

          I think we had this discussion on this blog before, but it does no harm to repeat some points: The problem is that humanity is performing a global climate experiment which could lead to a very fast change of the climate, too fast for the biosphere to adapt. There may be “positive” effects too, of course, and we should try to understand them, too.

          Due to complexity of the climate, motivated people can always devise plausible sounding hypotheses (and models purporting to support them) which show how this or that disaster might be attributed to global warming.

          Climate models have a grid resolution between 300 km and 50 km and thus cannot resolve most mesoscale effects (mesoscale = 2km to 2000 km). Cloud formation and precipitation, for example, have to be added as subgrid parameterizations, which makes most predictions of climate models about local precipitation uncertain. AFAIK there are no climate modelers who claim that their models can predict singular events like the flood in Pakistan, and the IPCC makes no claims in this direction, either.

          But Earth’s climate is way to complex and poorly understood for such hypotheses to be taken seriously without experimental support to back them up. However experiments which could offer such support are pretty much impossible to perform.

          There is a lot known about the climate and the weather of the earth, so generic claims that the whole topic is obviously too complex to do any research and make progress is neither warranted nor helpful. It is rather easy to validate weather models, for example. It is also easy to validate climate models by comparing effects at the synoptic scale to observations qualitatively.

        • Frederik De Roo says:

          Arrow said:

          On the other hand no one ever mentions positive effects that may also be attributed to global warming. This is an obvious example of bias.

          Actually I wouldn’t be surprized if there is evolutionary pressure for scientists to better motivated to come up with negative consequences. Risk-averse humans are perhaps more inclined to think twice, than risk-seeking people.

          If there were global cooling, I guess it would also be easier to come up with negative consequences (e.g. more land due to receding oceans but less inhabitable land near the Arctic and a drier Africa)

          Conversely, one positive side of warming would be that the Arctic becomes more habitable (for the Antartic we’ll have to burn more carbon) but on the other hand, in land climates it could simulaneously lead to more risk for heat waves and bog fires… (sorry, couldn’t resist)

          In any case, rapid climate change have their implications on biodiversity and that’s a big worry for some. Of course, moving away from fossile fuels would probably demand rapid changes in our consumption patterns, so it’s no big surprize that there are other risk-averse people looking for negative consequences of economic changes (instead of also including possible positive consequences).

          For example if global warming does indeed lead to increased precipitation then in addition to floods in some areas it also helps avert droughts in others, if it leads to exceptionally hot summers then it should lead to milder winters too, and so on.

          I don’t think those are necessary consequences. Global warming could also tend to push climates to extremes: both hotter summers and colder winters, e.g. in Europe because of changes in the Atlantic ocean circulations. I’m not an expert, so I can’t argue whether this is likely. Well, anyway, because of this observation about likeliness I tend to agree with your following comment:

          Due to complexity of the climate, motivated people can always devise plausible sounding hypotheses

          On the other hand, I think your preceding conclusion is a little lazy (“the best steersmen are ashore”):

          The other problem is that all those attributions carry little to no weight.

          I think if it would be possible to point out scientific flaws in other papers, it would earn a scientist a lot of publications (unless you would argue that the publishers are biased too).

        • DavidTweed says:

          Arrow wrote

          For example if global warming does indeed lead to increased precipitation then in addition to floods in some areas it also helps avert droughts in others, if it leads to exceptionally hot summers then it should lead to milder winters too, and so on.

          I really don’t think the earth is a homogeneous enough system for this “should” (rather than “might”) to be supportable on logic alone.

          An analogy I sometimes use is a pinball machine: just because you increase the initial energy of the ball doesn’t automatically mean it’s speed at various points in its path is uniformly increased from it’s previous values at all points: indeed depending on the configuration of barriers, etc, it may hit new ones and actually have a lower speed.

          You can say that mainstream AGW research is model based, but then your statement above is also a model based prediction, just one based on a very basic mental model that everything is incredibly homogeneous. All models require attempts to validate their accuracy, even loose mental ones.

      • John Baez says:

        Tim wrote:

        I second that, without further explanation it does look like a claim that the flood was caused by AGW.

        A few points:

        1. The slides for a talk always come with further explanation. I’ve given you guys that explanation here.

        2. Every unnecessary word written on a slide is an evil thing, to be avoided at all costs. However, since more people may read the slides than attend the talk, and you seem to have misunderstood that passage in the absence of verbal clarification, I’ll try to make this passage clearer without making it much longer.

        3. The sentence in question appears in a section labelled “My personal thoughts, right now.” Nothing in this section is any sort of scientific claim. People can’t help having opinions they can’t prove, and I think it’s good to come out and state them, labelled as such. Pretending to be perfectly objective is worse—people who pretend that tend to be the least objective of all! I believe, but can’t prove and don’t expect anyone else to believe, that events like the floods in Pakistan are more likely thanks to human-caused global warming.

        Anyway, the passage said:

        My personal thoughts, right now:

        Each wedge is a massive undertaking, and we need to do seven of them just to hold carbon emissions constant.

        We probably won’t bother unless conditions get worse in a fairly dramatic way. The floods in Pakistan covered 800,000 square kilometers, affecting 20 million people. That was not enough. How many events like this do we need?

        In the final version it will say:

        My personal thoughts, right now:

        Each wedge is a massive undertaking, and we need to do seven of them just to hold carbon emissions constant.

        We probably won’t bother unless conditions get worse in a fairly dramatic way.

        The floods in Pakistan covered 800,000 square kilometers, affecting 20 million people. Suppose events like this become more common. How many will it take before we 1) decide global warming is to blame and 2) decide to do something very difficult to stop it?

        • Peter Morgan says:

          “2. Every unnecessary word written on a slide is an evil thing, to be avoided at all costs. However, since more people may read the slides than attend the talk, and you seem to have misunderstood that passage in the absence of verbal clarification, I’ll try to make this passage clearer without making it much longer.” Someone here must have a contact at PI or somewhere else that makes videos of talks freely available. Invite the Baez!

          I suppose an annotated PDF for distribution might be possible, after you’ve given the talk enough times to refine it. At PIRSA I usually look through the PDFs when a talk is of general rather than specific interest. If there were obvious annotations, however, I would probably start by looking at them, and keep looking at them if the annotations proved to be worthwhile.

    • Frederik De Roo says:

      An amplification of the depletion of the ozone layer can also be linked to global warming, indeed.

      About the floods in Pakistan “due” to global warming, it’s more like a particular human individual suffering cancer “due” to some radioactive fallout, who can prove that? In general events of extreme precipitation can be linked to higher average temperatures because a hotter atmosphere can hold more water, simply speaking.

      If you had written “floods in Pakistan due to anthropogenic carbon emissions?” it would be more difficult to argue against it, at least for me.

      • John Baez says:

        Frederik wrote:

        If you had written “floods in Pakistan due to anthropogenic carbon emissions?” it would be more difficult to argue against it, at least for me.

        I’m having trouble guessing who “you” is, here.

        • Frederik De Roo says:

          Oh, I’m sorry, it’s Arrow.

          But I wrote my comment before yours appeared, so mine seemed directly below his comment.

          I’ll be more specific from now one, especially because in this single topic I’ve had three times that somebody overtook me in posting a comment, so my comments look quite delayed.

  7. Bruce Bartlett says:

    Hooray, this will be useful material for those of us thinking of giving similar talks in our own departments, etc.

    Some quick comments:

    1. I vote for serif fonts! You always used to use them, I think they look much better, even in a presentation. In Beamer you can include the line \usefonttheme{serif}.

    2. People will definitely want to see much longer time scales in the graphs, such as the land-ocean temperature (pg 8), arctic ice (pg 9), Antarctica + Greenland (pg 10).

    3. The graph on page 12 looks a bit blurry and ugly. Can you get a nicer and clearer one? The Copenhagen Diagnosis seems to contain one or two similar, more “attractive”, graphs.

    • John Baez says:

      Hi, Bruce! Great to hear from you!

      1. I vote for serif fonts! You always used to use them…

      That’s because I didn’t know how to get rid of them. I think my old slides look gauche—too much like a math paper written in LaTeX!

      But I’ll see what \usefonttheme{serif} looks like.

      People will definitely want to see much longer time scales in the graphs, such as the land-ocean temperature (pg 8), arctic ice (pg 9), Antarctica + Greenland (pg 10).

      I think the only one where we have data available for ‘much longer scales’ is the global temperature—see my response to Tom Hirschowitz. However, as soon as one goes back much before 1880, accurate human-created temperature records become thin on the ground and we need to rely on ‘temperature proxies': things that correlate to temperature. So, the uncertainties grow.

      That’s just life… but it’s a good reason to have separate graphs for post-1880 temperatures and longer time scales.

      Maybe I’ll put a few extra graphs at the back of my talk, so I can summon them up if people have questions. I think this is better than overwhelming people with data.

      Indeed, I’m trying to keep the ‘data’ part of the talk to a bare minimum, since this is not a talk about ‘why I believe global warming is a problem and you should too’, but rather, ‘what mathematicians can do’.

      The graph on page 12 looks a bit blurry and ugly. Can you get a nicer and clearer one? The Copenhagen Diagnosis seems to contain one or two similar, more “attractive”, graphs.

      I’ll check it out. I like the one I’ve got because it comes straight out of the IPCC report.

    • DavidTweed says:

      FWIW, I find serif fonts, particularly at large sizes, ugly and trite. But maybe that’s because I do so much reading online — where sans-serif fonts seem to be the norm — and I’ve set the default font in my text editor to sans-serif as well.

      • John Baez says:

        I find the default TeX font ‘gauche’ at large sizes (it’s a bit hard to describe what I don’t like about it, but that’s the best word that comes to mind). However, the serif font Bruce’s recommendation yielded seems nicer.

        If the worst thing someone says about my talk is that they hate the font, I’ll count it as a success.

  8. p1, double “and”
    p9,p10, what are these straight lines exactly? First impression – cheap tricks to convince the opponents.
    p18, more of a personal thing, is it really just about US or about north America?

    • sorry, double “and” is p2

    • Tim van Beek says:

      Likasz asked:

      …what are these straight lines exactly?

      Unless stated otherwise these things are linear least squares fits. I don’t think that they are really needed to see a trend. What bothers me more is that the axes are usually scaled such that the graph fills all the space, if CO2 levels go from 300 ppm to 380 ppm then the y-axis goes from 300 ppm to 380 ppm, too, so all you see is a graph that starts on the left at the lower end and ends on the right on the upper end. It would be more informative to have the y-axis go from 0 to 400, say, to see the absolute increase, instead.

    • Frederik De Roo says:

      The linear trends are probably more cheap statistics than tricks to convince the neutral public (I doubt the opponents will be listening, though they will probably attend)

      But on p10 it’s actually a “clever” linear fit to discover a quadratic trend ;-)

  9. Frederik De Roo says:

    @Tim: I didn’t see your reply before I posted mine

  10. Kelly says:

    I suggest you add a slide on polar amplification to make sure that attendees understand the implications of a global change of 1 C will cause rise of 3 C in Arctic.

    Would also suggest that you demonstrate impact of current global warming, Arctic Sea Ice extent trends provide a illustration.

    • John Baez says:

      Thanks for the suggestion!

      Since the talk will be 50 minutes long and the slides I’ve prepared so far are supposed to cover just the first half (i.e., 25 minutes), I don’t think I should include much more material.

      I already have slides on Arctic sea ice trends and—a more recent and less well-understood, but important subject—the apparent acceleration of the melting of Greenland and Antarctica.

      After I learn more about all these subjects I might risk running a seminar on them. That would be a great excuse to make a much more detailed set of slides and/or notes. If I do this, I’ll need all the help I can get from experts… and you’ll probably see my pleas here!

  11. Peter Morgan says:

    I react somewhat against the last slide. Introducing wars introduces a much wider range of resource competition than you have been discussing. Water, minerals, precious metals, diamonds, etc., not just energy, even if many resources are very directly affected by energy scarcity. Introducing wars also throws politics and religion into the mix. It’s messy. When you’re trying to convince mathematicians, many of whom want a more idealistic problem, might you be better not to introduce these complications? Perhaps the problem is that your comment is too flippant — if you mention wars, say explicitly that the aim is to avoid wars by finding ways to use resources more efficiently, in innovative ways, in whatever way we can find that avoids wars. At some point, though, I suppose someone is going to ask about allocating resources fairly, and it will get messy.

    Most mathematicians perhaps prefer ordered lives, but there is a type of businessman, politician, and soldier who profits enormously from chaos, even to the extent of preferring war to peace.

    • John Baez says:

      Peter wrote:

      Introducing wars also throws politics and religion into the mix. It’s messy.

      I can’t avoid mentioning it, because I believe that if global warming and peak oil cause human suffering, this suffering will be vastly amplified by wars and other nasty things that people do when the pie starts shrinking.

      When you’re trying to convince mathematicians, many of whom want a more idealistic problem, might you be better not to introduce these complications?

      To give people a fair sense of the magnitude of the problems we’re likely to face, it seems necessary to mention war. Ignoring it seems like trying to understand the fall of feather in an approximation where you ignore friction.

      But I agree with one thing you seem to be suggesting: I won’t try to convince mathematicians to tackle the ‘human’ aspects of energy and the environment: the political, military and economic aspects.

      These are in fact the most important aspects! But mathematicians are, in general, repelled by their intractable and ugly complexity. And so, to get them on board, we will have to find things for them to do that they can stomach.

      Perhaps the problem is that your comment is too flippant…

      Maybe. It wasn’t supposed to be flippant. You should imagine me saying it in a very somber way.

      • Peter Morgan says:

        “flippant” isn’t the right word. I know you aren’t joking here. It’s a subordinate clause in the middle of a sentence, but it’s the elephant in the room. War will likely displace more people than rising sea levels will [is the study of migrations in response to resource competition open to realistic modeling? Differential equations, etc? The prospect that 1000 million people might have to be absorbed in Europe and the Americas from the third world might focus political will, although any such analysis would probably be more open to dispute even than current climate analyses are.] IIRC, just the second Iraq war displaced more than a million people. Perhaps the trouble is that it needs more detail — perhaps make it something like “War will likely displace and kill more people than rising sea levels will.”

  12. Phil Henshaw says:

    What about the critical importance of asking why neither the Japanese (as the client), nor the GE engineers (as the designer), thought put the emergency power generators above sea level (for their most critical emergency condition)?

    It’s such a completely obvious mistake, in hind sight, made by such highly talented and sophisticated problem solvers…. They evidently were not very good problem FINDERS, though. So why is that? It’s evidently because of some sort of blindness to the reality of what they were designing, right, a lack of awareness of their real environment?

    What is going on with mega-errors like these is often a simple matter of using trusted principles for one circumstance when planning for another. If people are not good at “problem finding”, looking at things from previously unnoticed perspectives to find the hidden new issues, they just don’t end up solving the right problem. That’s what’s called a “Type III” error, asking the wrong question.

    That’s why environmental search methods that mimic how nature’s design processes work (like Alexander’s or mine or any other) are so important to use to connect your “problem solving” to the real problems of the natural world. Solving the wrong problem may be highly sophisticated, profitable and satisfying, but just not apply. Relying on stand-along equations won’t help. Learning how to connect them to the shifting circumstances of the natural world is what’s needed.

    Today there are lots of much bigger things than just power plant melt-downs in jeopardy, for people persistently clinging to “trusted rules” that now lead to disaster. One example is the variety of very profitable investment practices, like the ones you had in the housing bubble, making our whole economic world increasingly unstable. Nothing wrong with them except that trusting them in our present circumstance has rather unwanted effects.

    To find the questions a problem solver is missing involves more than staring at blank sheets of paper, though, but realizing that can be the first step.

    • John Baez says:

      Phil wrote:

      What about the critical importance of asking why neither the Japanese (as the client), nor the GE engineers (as the designer), thought put the emergency power generators above sea level (for their most critical emergency condition)?

      That sounds like a great subject for a talk—the talk I’d expect you to give.

      It could be a great talk, but I doubt it would succeed in luring mathematicians into working on energy and the environment, which is my goal here.

      Once they get interested in these topics, they will read my blog and hear what you have to say.

  13. Florifulgurator says:

    You counter balance Al Gore’s slideshow with stating just the humblest numbers on sea level rise. :-)

    Regarding the last slide; methinks when leading hominids start requesting scientists to find solutions, then it will be utterly too late: With depleting resources, the economy tanked, the biosphere shrinking, billions starving and rioting, etc., what to do? … To such a request the obvious mathematical answer would be: Sorry folks, you’ve insisted in stupidity for centuries; not understanding the exponential function, not appreciating a simple topological consequence of the planet being positively curved, etc. etc. – now it’s time to pay and learn the hard way…

    • John Baez says:

      Florifulgurator wrote:

      Regarding the last slide; methinks when leading hominids start requesting scientists to find solutions, then it will be utterly too late…

      I don’t plan to discuss this in my talk, but it was extremely important for me personally to come to an emotional equilibrium where I feel that:

      1) In one sense it’s already too late: we’re set on a course that’s bound to lead to serious trouble, and the only way to wriggle out of it would be a wholly implausible mass transformation of human psychology.

      2) In other sense it’s never too late: no matter how bad things are likely to get, they can still get worse… or not. So, there’s always room for decisions to make a difference.

      For example, if we go ahead and kill off 99% of the species on the planet, we’re still left with the freedom to kill 99% the remaining species, or not. I don’t consider it plausible that we’ll kill off all life on this planet, or even all human life. At least, not in the next century. Either of these would count as a kind of ‘worst possible scenario’, a kind of floor on how bad things can get. But I don’t think we’ll reach that sort of floor—and as long as we don’t, my choices now may have significant consequences!

      Note: all this is more about feelings than facts. But it’s my way of avoiding the usual trap where people either think

      1) things will be all right no matter what I do, so there’s no point in doing anything,

      or

      2) we’re doomed no matter what I do, so there’s no point in doing anything.

      • Peter Morgan says:

        99% killed is the nightmare. There are typically strong correlations here, so if I die the conditional probability that everyone in my close family dies is even closer to 1. Most people know far fewer than 100 people well; almost everyone most people know well, and their children and grandchildren, all die. If they die, more probably you do too. Poor people, who are more likely not to be geographically distributed, fare worst as a group. Groups can improve their chances as a group by taking steps to ensure that individuals survive other individuals dying. All of which, as they say, dehumanizes. I’m surprised you introduce this, and this response is at the edge of my comfort zone. In post-apocalyptic movies, the hero survives, we identify with them, we don’t think of being the 99%. This is shock tactics.

        • John Baez says:

          Peter Morgan wrote:

          99% killed is the nightmare…

          I’m surprised you introduce this…

          I was responding to Florifulgurator’s suggestion that by the time we get around to doing something serious about energy and the environment, it’ll be ‘too late’. I was trying to explain why in practice it’ll never be too late for our actions to make a significant difference. It was an argument against giving up.

          And it went like this: consider the nightmare scenario where we kill off 99% of the Earth’s species. (Note I’m talking about species, while you seem to be talking about people.) That means that instead of somewhere between 2 and 100 million species (we’re appallingly ignorant of their number) there will be only between 20,000 and 1 million. There will still be a vast difference between keeping these remaining species alive and killing off 99% more. And even if we kill off 99% more, reducing the number to between 200 and 10,000, there will still be a vast difference between keeping these remaining ones alive and killing off 99% of them.

          So, I’m not at all saying that these nightmare scenarios are likely: I’m just trying to say that for all practical purposes there’s no ‘floor’, no ‘lower limit’ on how bad things can get. And I actually find this very reassuring, because it suggests that my natural tendency to want to go on fighting for good is not a pointless reflex, even under highly pessimistic assumptions.

          Hmm… perhaps some further explanation is in order.

          I don’t know how much stuff you read about global warming, peak oil and related problems, but if you nose around, you’ll find that in addition to a large community of people who think these problems are overblown and not really worth worrying about, there’s a community of people who take them seriously but are extremely pessimistic about our chances of doing anything effective about them. A good example is this:

          • George Mobus, Past the point of no return.

          He’s a smart guy (if you don’t believe me, read some of his other posts), but here he suggests that the only way to ensure the survival of the human race is to…

          … do something so horrible he refuses to come straight out and say what it is! If you read between the lines, you can guess. In any event, it’s something he thinks we won’t do. So, he seems to think we’re doomed.

          So: just as overoptimism can lead to inaction, so can overpessimism—and it was psychologically necessary for me to find a robust counterargument against the idea that “if things are bound to get really bad, why even bother?”

          But I don’t plan to mention any of this in my talk, because I doubt that a significant fraction of the audience is so deeply pessimistic about the future. If they’re like most mathematicians I know, they’re more concerned about proving cool theorems than the future of the human race, or the biosphere.

        • Phil Henshaw says:

          John, George Mobus is indeed a brilliant guy, and I like much of the way he arranges his theoretical approach. He doesn’t look at the things nature seems to solve easily but his equations can’t, as a challenge to his assumptions, though.

          When growth systems switch from multiplying to maturing, for example, it displays something like a grand change of purposes and organizational strategies. It lets them meet its otherwise dangerous limits of growth with a soft landing. It’s direction of development changes in mid-stream, letting it fit in with its discovered environment, as if growth of that kind was an independently animated process that reshaped itself to fit what it runs into. Equations don’t seem able to do that, to reinvent themselves without guidance when they change scale and need to interact with new environments.

          As growth is a kind of self-investment in expanding organizational scale, it would naturally become very unprofitable at some point. It makes it seem as if systems that switch how they invest their net-energy from expanding themselves to finding how to succeed in a new environment, and so a particular curiosity. It makes it look as if systems that do that are learning as they go, and actively choosing the most profitable options at the time.

          Equations may not now or ever be able to break the bonds of their own definitions, but a huge variety of natural system do display that very phenomenon.

  14. Giampiero Campa says:

    So, in the last few slides, is not the mentioning of wars that i find puzzling (in fact we should expect wars in situations of intensified resource competition).

    It is the reference to “the mess we’re in” that leaves me wondering exactly what mess are you talking about, the declining oil supply (which might be perceived to be more problematic than warming), or the warming, or the wars.

    I am a little hesitant to add everything up into a single “mess” because, for example, the “declining oil supply mess” would in part counteract the “warming mess”, (and so it would a confined thermonuclear war in the middle east, by the way, which obviously i am not advocating).

    So i guess my point is that you need to be more clear/convincing about exactly what problem you think the “governments will push scientists to do something about”, otherwise you will leave people silently wondering about this, exactly in the point in your presentation when you want everybody to be convinced, so they can be 100% on your side for the second part of the presentation.

    • Giampiero Campa says:

      In other words, peak oil is another huge problem, so it’s good to bring it up, bit it would be even better to explain the connections with the warming problem.

  15. Tom Leinster says:

    Hi John. I like it so far. Two comments.

    First, as a mathematician who needs no persuading of the trouble we’re in, I found myself a little bit impatient to get to the second half. Of course I don’t know how fast you plan to go or what entertaining things you might be saying while presenting the first half. And I understand that not everyone is as persuaded as me.

    Second, on page 22, would a 60cm sea rise really only displace 3 million people? That seems awfully low. According to Wikipedia, there are about 80 cities in China with a population bigger than that. Compare also the figures you give on the Pakistan flood.

    • John Baez says:

      Tom wrote:

      First, as a mathematician who needs no persuading of the trouble we’re in, I found myself a little bit impatient to get to the second half. Of course I don’t know how fast you plan to go or what entertaining things you might be saying while presenting the first half. And I understand that not everyone is as persuaded as me.

      Hi! The “first half” really consists of 3 parts:

      1) review of the current scientific consensus on global warming and its effects,

      2) summary of Pacala and Socolow’s paper, which gives some idea of the magnitude of the difficulty of ending global warming by cutting carbon emissions,

      3) my personal conclusions from all this.

      I plan to whiz through 1) fairly quickly. I’m certain not expecting that climate skeptics will decide they were wrong and leave the lecture committed to work on environmental issues! That would be unrealistic.

      I think 2) is a bit more important: a lot of people have heard global warming is a problem but have no sense of the magnitude of the problem. I’ve heard quite educated people say that it’s something scientists will figure out how to solve—presumably leaving ‘us’ to carry on life as usual. Only after I started studying this problem pretty carefully did I realize how insanely hard it is.

      And that leads to part 3): my personal (unproven!) conviction that nobody will do anything truly significant about global warming unless and until it becomes much worse than now—say, 10-30 years from now. At that point, I believe (but cannot prove!) that depletion of oil reserves will also be quite severe. The two problems will be thoroughly intertwined, and a lot of ways of solving one will aggravate the other.

      So, I’m trying to proceed now with this sort of future in view… and I’m trying to figure out what ‘people like me’ (say, mathematicians) should do to have maximal impact.

      I’m not really ready to give the second half of the talk as well as I should! But the first half is supposed to make it clear why certain activities seem useful to me, while others seem relatively pointless.

      Second, on page 22, would a 60cm sea rise really only displace 3 million people?

      Hmm, rechecking my source:

      • National Research Council, Climate Stabilization Targets: Emissions, Concentrations, and Impacts over Decades to Millennia, 2010. 20th and 21st Century Changes in Sea Level and Impacts of 21st Century Sea Level Rise.

      Thanks for asking!

      They predict 0.6±.11 meters of sea level rise. They say 0.5 meters would cause increased risk of flooding for 5-200 million people (some error bars, those!), and “as many as 4 million people could be permanently displaced”.

      Right now I’m not seeing the figure of 3 million that I’d quoted… it could easily be lurking elsewhere.

      It’s consistent with what I just said, but more important is the big difference between “permanently displaced” and “at risk for flooding”. I left out the word “permanently” in my slides, since every word is precious—but if you get caught in a flood, it may be little consolation that the flood waters will recede.

      • Tom Leinster says:

        I guess I’d slightly forgotten how impressive the wedge story is. I’ve already heard it enough times (thanks to you) that I’m no longer so surprised by the magnitude of what apparently needs doing.

        Thanks for checking on the flood thing. I agree, there’s a spectrum of meanings of “displaced”.

        (Incidentally, I realized after posting my comment that my figure of “80 Chinese cities bigger than 3 million”, taken from Wikipedia, was a bit misleading. I used “administrative area population”, not noticing the “metro area population” column, which presumably is more like what people think of as the population of a city. Using this, it drops to a mere 25.)

  16. jack fuller says:

    According to my mathematician daughter (an anomaly, if not a freakish occurrence according to a certain highly placed educator and various others) there is an increasing “Darwinian” learning interval progressing from, among many other things, automotive design to aerospace engineering to nuclear plant design and finally to climate change effects.

    We clearly witness the consequences of ‘too late smart’ for the first three. When, indeed, will they ever learn on the last?

  17. nad says:

    “Solar: Replace 700 gigawatts of coal power by solar power. This requires multiplying existing solar power by 700!”

    (page 30)

    If I understand correctly then the cumulative installed PV power in selected countries of the Photovoltaic Power Programme was in 2003 already about 1.8 Gigawatts, in 2009 it was already about 20.4 Gigawatts. Those alone would give rather a factor of 35 then a factor of 700:

    page 5 Table 2 of:
    http://www.iea-pvps.org/fileadmin/dam/public/report/statistics/tr_2009_neu.pdf

    • John Baez says:

      nad wrote:

      If I understand correctly then the cummulative installed PV power in selected countries of the Photovoltaic Power Programme was in 2003 already about 1.8 Gigawatts, in 2009 it was already about 20.4 Gigawatts. Those alone would give rather a factor of 35 then a factor of 700.

      Thanks! Yes, if you go to my talk or look at the Azimuth Project page you’ll see me say that currently photovoltaic power production is growing at a rate that vastly exceeds the rate required to grow by a factor of 700 in 50 years.

      So, my slides here are punching the audience in the gut with the bad news… but then I’ll give them some good news:

      To grow by a factor of 700 in 50 years, photovoltaic solar power must grow at an annual average rate of 14%. My sources say that from 2004 to 2009 it was growing at an annual average rate of 60%.

      So, the question is: how high a growth rate can be sustained? I don’t know what the experts think.

      In case it’s not clear, I’m not “knocking solar power”. I’m trying to say that each of Pacala and Socolow’s climate stabilization wedges is a big job. Each one is hard, doing seven is hard… and doing seven is not enough to stop global warming.

      I will make it clear that the numbers I’m presenting come from Pacala and Socolow’s 2004 paper and are not up to date. It would be nice to redo their whole paper with current numbers, but I don’t have the time to do that now. So, I’ll just make a few comments here and there in my talk.

      Since 2004, some things have gotten better—for example, we have a lot more solar and wind power. But other things have gotten worse. I’ll talk about that soon on the blog…

      • John Baez says:

        I’m looking for more numbers on photovoltaic solar power.

        Solarbuzz reports world solar photovoltaic market grew to 18.2 gigawatts in 2010, Up 139%, Solarbuzz, 15 March 2011.

        I’m a bit worried about whether I understand all the terms in these statements:

        Worldwide solar photovoltaic (PV) market installations reached a record high of 18.2 gigawatts (GW) in 2010.

        What are ‘market installations’? Newly installed solar power plants or total existing solar power plants?

        Worldwide solar cell production reached 20.5 GW in 2010, up from 9.86 GW a year earlier, with thin film production accounting for 13.5% of total production.

        What is ‘solar cell production’? Newly produced solar cells or total existing solar cells?

        On a side note, it seems percentage growth rates will decline a bit now that subsidies are declining:

        After addressing 2010 outcomes, the Marketbuzz 2011 report sets out three scenarios for supply, demand, and prices over the next five years. By 2015, Solarbuzz projects the European market share to fall to between 45-54% as North America and several Asian markets grow rapidly. The US will be the fastest growing major country market over this period. Over the next five years, factory gate module prices are projected to drop between 37% and 50% from 2010 levels.

        You can get more information if you buy the 2011 Marketbuzz report… alas, the Azimuth Project can’t afford this now.

      • John Baez says:

        Here’s another source:

        Another sunny year for solar power, Worldwatch Institute, 20 March 2011 (?).

        Global production of photovoltaic (PV) or solar cells-which convert the sun’s light directly to electricity-increased 51 percent in 2007, to 3,733 megawatts. According to early estimates, more than 2,935 megawatts of solar modules were installed that year, bringing cumulative global installations of PVs since 1996 to more than 9,740 megawatts-enough to meet the annual electricity demand of more than 3 million homes in Europe. Over the past five years, annual global production of PV cells has increased nearly sevenfold, and cumulative installations have grown more than fivefold.

        The whole article is worth reading if you’re interested in solar power.

        So, this says “cumulative global installations of PVs since 1996″ equal 9.740 gigawatts. If I knew the total installations up to 1996, I could add those two figures and get the grand total.

      • Sorry, but your projected numbers on solar PV simply do not make sense until economic storage is developed. The sun does not shine at night at all, not much during the winter and accumulators are just too inefficient and expensive.

        What we need is not PV, but molecular engines manufacturing some energy rich chemical using sunlight, not flammable, non-toxic, not explosive like e.g. sugar.

        To close the cycle one also needs micron sized fuel cells in the array which turn the energy stored into electricity on demand.

        There’s nothing inherently impossible in such a solution, just needs advanced molecular nanotechnology with self-replicating programmable molecular assemblers to bring costs down.

        The default construction material for such a large scale industrial project is carbon, extracted from airborne carbon dioxide (to avoid mining and transportation costs). The only caveat is that eventually atmospheric carbon dioxide should be replenished for as soon as it gets depleted too much, plant life suffers.

        Unfortunately we do not know the time frame necessary to accomplish such a technological advance. Anyway, it makes sense to advise bright young people, mathematicians included, to go for nanotech.

        However, even in this case average solar flux is pretty low which means land use can never be efficient. One can of course put surfaces like roads and rooftops to dual use, but going beyond that is plain crazy. Raw land area is one of the two resources for which expanded reproduction does not work, not even with the most advanced technology imaginable (the other one is span of human attention).

        Therefore we also need to develop sustainable compact energy sources like thorium breeder reactors and need them fast.

    • John Baez says:

      Okay, here’s the updated story on wind power:

      As Pacala and Socolow pointed out, to use wind power to reduce our coal burning by 1 gigatonne of carbon per year, we would need to increase the amount of wind power produced worldwide by a factor of 50, starting from its 2004 level. This sounds difficult, but to grow by a factor of 150 over 50 years, wind power would only need to grow at an average annual rate of 10.5%.

      And according to the Renewables 2010 Global Status Report, the average annual growth rate over the five-year period from the end of 2004 to 2009 was much higher than this: namely, 27%!

      According to the same source, peak wind power capacity reached 159 gigawatts in 2009. So, reaching Pacala and Socolow’s goal of 2000 gigawatts now requires multiplying the world production of wind power by a factor of 12.5. To reach this goal by 2054 now requires an average annual growth rate of only 5.8%.

    • John Baez says:

      And here’s the updated story on solar power!

      As Pacala and Socolow pointed out, to use photovoltaic solar power to reduce our coal burning by 1 gigatonne of carbon per year, we would need to increase the amount of peak photovoltaic solar power worldwide by a factor of 700, starting from its 2004 level. This sounds difficult, but to grow by a factor of 700 over 50 years, it would only need to grow at an average annual rate of 14%.

      And according to Renewables 2010, the average annual growth rate over the five-year period from the end of 2004 to 2009 was much higher than this: namely, 60%.

      According to the same source, by 2009 peak photovoltaic power reached 24-25 gigawatts worldwide. (Of this, only 21 gigawatts were grid-connected). So, reaching Pacala and Socolow’s goal of 2000 gigawatts now requires multiplying the world production of wind power by a factor of 80.

      To reach this goal by 2054 now requires an average annual growth rate of 10.3%.

      I’ve added all this info on wind and solar power to:

      Stabilization wedges, Azimuth Project.

      and also to the webpage for my talk.

      • nad says:

        According to the same source, by 2009 peak photovoltaic power reached 24-25 gigawatts worldwide. (Of this, only 21 gigawatts were grid-connected). So, reaching Pacala and Socolow’s goal of 2000 gigawatts now requires multiplying the world production of wind power by a factor of 80.

        ? … requires multiplying the world production of wind power by a factor of 80 … ?

      • John Baez says:

        I’m terrible at division, but I checked, and 2000 divided by 25 is 80. Or is it something else you’re puzzled by?

        • nad says:

          2000 divided by 25 is 80.

          I currently don’t doubt that (even without a calculator at hand…) but it is somewhat mysterious how you get wind power by dividing through photovoltaic power.

        • John Baez says:

          Whoops! It was a cut-and-paste error: I did the calculations for wind, wrote them up here, did the analogous calculations for solar, and wrote them up here by copying the wind article word-for-word and then changing only the relevant words… well, most of the relevant words.

          I make this type of mistake a lot.

          I’ll fix that typo on the Azimuth Project, but leave it here to entertain future generations.

        • nad says:

          @Giampiero

          I was quite sure that this was a cut and paste error and that he meant solar power…if not I wouldn’t have dared joking!

        • John Baez says:

          You’re too sneaky for me, nad. You know how it is when a lecturer makes a typo in an equaion at the blackboard: everyone else can see it except him, because he sees what he meant.

        • nad says:

          John Baez says:
          March 22, 2011 at 10:57 am

          You’re too sneaky for me, nad. You know how it is when a lecturer makes a typo in an equaion at the blackboard: everyone else can see it except him, because he sees what he meant.

          I am sorry, I find these scientifc discussions sometimes just overly dry and machinelike and they make me go all tingly. I didn’t mean to insult you.

        • John F says:

          A couple of math professors got mad at being corrected while busy writing at the blackboard, usually by slower students. Mutatis mutandis isn’t quite right. What is Latin for “you can make the obvious corrections yourself”?

        • streamfortyseven says:

          John, it’s probably pretty close to the Latin for “the proof is obvious and is left to the reader as an exercise…” Wind power is, indirectly, solar power.

        • John Baez says:

          nad wrote:

          I am sorry, I find these scientific discussions sometimes just overly dry and machinelike and they make me go all tingly. I didn’t mean to insult you.

          Don’t worry, I know that. I just had no idea what you were saying at first.

  18. Thomas says:

    Here one finds some remarks around the theme “science communication” in the blog of a mathematician-physicist.

  19. Web Hub Tel says:

    John,
    You might also want to add Entropy to the Energy and the Environment in the title of the talk. We can’t escape entropy.

  20. Energy, the Environment, and What Mathematicians Can Do (Part 2). A couple of days ago I begged for feedback on a math colloquium talk I’m giving this Wednesday at Hong Kong University. The response was immediate…

  21. westy31 says:

    I had not seen the concept of a Petri net before.

    Thinking about it, the circles in Petri nets can each be of a different data type, whereas in electric network, each vertex has the same data type. You could try and generalize by allowing a state-vector of quantities on each vertex, so that the vector includes an entry for each data type, eg (C,O,CO2 ).

    The movement of tokens suggests the use of conserved quantities, and reminds me of a related concept that I call a bucket. I was trying to implement the Navier Stokes equation as an electric network, but I couldn’t do it without introducing a new concept. Basically, a bucket transports not just charge, but all extensity quantities present in one vertex to another. (eg momentum, mols of chemical species) You can visualize a container on each vertex, with buckets traveling along edges, transporting quantities.

    Thinking about ‘Green mathematics’, I guess you can split the problem of modeling problems related to global energy into a number of parts. One of the parts is how you translate the physical problem into a mathematical model. This is perhaps not normally ‘part of mathematics’. Another part is to figure out mathematical properties of the model, such as existence and uniqueness. Or establish relations and analogies with other problems. A third part is how to get mathematicians interested in helping to solve the problems of the world.

    Gerard

    • John Baez says:

      Hi, Gerard!

      The movement of tokens suggests the use of conserved quantities…

      Of course a Petri net allows for transitions where one token goes in and two go out. We might want this, for example, to describe the dissociation of molecular hydrogen:

      H2 → H + H

      But as you’ll note, in this reaction hydrogen atoms are conserved! So, especially in examples from chemistry, Petri nets tend to have lots of interesting conserved quantities that aren’t the token number: namely, numbers of various kind of atoms.

      There’s been some interesting work on this using algebraic geometry…

      Thinking about ‘Green mathematics’, I guess you can split the problem of modeling problems related to global energy into a number of parts.

      [...]

      A third part is how to get mathematicians interested in helping to solve the problems of the world.

      That’s the part this talk is focused on. I’ll have to give this talk over and over, a bit better each time. By the time it’s really good, I’ll have a few ‘subtalks’ prepared where I can describe nice math problems related to environmental and energy issues—problems that are mathematically well-defined, not too easy, and not too hard. I think that’s what mathematicians want.

  22. streamfortyseven says:

    First, IANAM, I Am A Lawyer… You’re looking for ways to get mathematicians and physicists interested in this, and you’re citing various potentially interesting bits and pieces of math and physics which could be applicable to a part of a climate/weather prediction model.

    Nobody works for free, not mathematicians or physicists, and definitely not lawyers. I haven’t seen anything here on Azimuth about sources of funding for research in any of these topics. If there’s no funding to be had, it might be a good idea for Azimuth to figure out how to make a case for funding this research. One of the things that might be particularly convincing could be to use existing models to predict some near-term effects of climate change which would have significant negative economic impact – and hit the nail on the head. Do that twice or three times, and people with money will start looking at Azimuth and begin to take it seriously, and if enough of that happens, then people and governments and suchlike will begin to pay attention. It might be a good idea to open up a couple of topics with these two things in mind: 1. Sources of funding 2. Making a case for funding

    • DavidTweed says:

      The situation is a bit more complicated. There’s very clearly money available for funding various environmental research. Even though it’s not the riches of croesus the right-wing conspiracy theorists paint, it clearly is able to support large amounts of academic environmental research over the globe. However, it’s the short-term directed funding that is based upon producing a significant number of publishable results within 2-5 years. This leads to the issue that some people, both in general and on Azimuth, complain about, namely that the code written is the minimum that will do the analysis required, and is often not portable outside the machines it was developed on.

      So a key question is whether conventional modes of funding will lead to acheiving the desired goals.

      (Incidentally, I thought lawyers were so proud that they very occasionally did work for no payment that they made up a latin phrase for it: pro bono?)

      • streamfortyseven says:

        I once defended an anarchist who was falsely accused of assaulting the local chief of police at a demonstration and won a two-day jury trial in a unanimous verdict – and did it for free because he had no money. So yes, lawyers occasionally work for free.

    • John F says:

      “Make a case”. Literally. I happen to work for a funding source, and one thing I can say is that almost all the environmental funding is driven by lawsuits and/or regulations that were only promulgated because of lawsuits.

    • Phil Henshaw says:

      What you need for funding is a demonstrated path of inquiry leading to successively more important results. I see that in other fields, but the gaping hole in modeling natural systems, only occasionally explored by others, seems entirely neglected by math.

      It would mean using math to reflect rather than define the working parts of natural systems, as if for making “leaf prints” to expose natural system structures. That would help physical system scientists visualize the working parts… and the changing relationships of the complex natural systems they are studying.

      Some network science people have gotten funding for that, but the dilemma persists that math is so dominantly used for representing nature as made of inanimate categories connected by unchanging logic, and that is phenomenologically different from physical systems in numerous ways. That’s a primary reason math works so poorly for modeling open networks composed of energetic learning parts, i.e. “the real things”.

      People don’t seem to be using math to make even the least attempt to usefully record and display the actual patterns and structures of natures complex systems. How’s anyone supposed to successfully study them with that kind of broad disinterest in how they actually work from mainstream science?

  23. Tim van Beek says:

    streamfortyseven wrote:

    I haven’t seen anything here on Azimuth about sources of funding for research in any of these topics.

    I think John has some ideas, but of course any kind of funding that Azimuth could get would be through academic research. To this end, we first need to figure out interesting projects that involve some first class mathematics and maybe physics, and it would seem that we are still doing that.

    One of the things that might be particularly convincing could be to use existing models to predict some near-term effects of climate change which would have significant negative economic impact – and hit the nail on the head.

    The only chance I see is starting interesting collaborations with already existing projects and teams in academia and achieve nontrivial contributions to those. There is already a lot of research going on about weather and climate models in general, and especially about decadal forecasts. Azimuth is about figuring out how mathematicians and physicists can contribute to these kinds of projects, and this should be enough to get funding for those people who would like to work on this full time in academia. (Some kind of breakthrough like you describe seems to be unrealistic and hopefully unnecessary to get funding.) Of course, these people won’t work for free, but in the mean time there are some people who do it as a hobby, for free :-)

    • nad says:

      If you see how already “basic arithmetic” projects are struggling (I just wrote something on economic growth and labour using the beta version of the ILO Index at: http://www.azimuthproject.org/azimuth/show/economic+growth+and+labour then I have my doubts about appropriate funding.

      By the way I don’t see myself as working for “free”, but feel rather forced to do so by the possibility that a contribution may eventually marginally mitigate the troubles of future inhabitants of this planet. I could think definitely of more fun things than editing the Azimuth project.

    • DavidTweed says:

      As a data-point, in the UK it’s typical for a staff member to have a basic “cost” the organisation he works at least twice his untaxed salary (their proportion of building costs, heating/electricty and insurance, pension contributions, etc). This figure doesn’t include role specific expenses such as a dedicated computer, data collection trips, funds to pay students for data entry, etc. In some cases, such as pure mathematics, many of these expenses will be very low level, for many ecological fields they’ll be relatively high (although not at the level of a mega-project like CERN).

  24. WebHubTel says:

    Nobody works for free

    Define “work”

    • streamfortyseven says:

      Work is the set of tasks you perform in order to get enough income to get food and water, get a place to stay, and get clothing, for a start. Quite a few people I know here in the US haven’t been able to find work for at least the past year, hence they live in squats, and get food and suchlike from dumpsters. Occasionally they take the train to visit other places, but they catch out freights; grainers are preferable to box cars, which are in turn preferable to coal trains, which are the worst…

      • nad says:

        streamfortyseven wrote:

        Work is the set of tasks you perform in order to get enough income to get food and water, get a place to stay, and get clothing, for a start.

        You might want to read a blog post I wrote
        on this topic at:

        http://www.randform.org/blog/?p=2635

        There I tried to explain, that I think that work should rather be seen as something that one wouldn’t like to do without some kind of compensation. In particular unpleasant work should be paid higher and pleasant work lower, if at all. That leaves you of course with the question how people who have a rather pleasant work should survive.

        In Europe a lot of people favorize a basic income, which you get even without any work. However I am sceptic about that concept. It might not work in our current economy for pure systemic reasons. One probably has rather to provide an out-of-market basic income, like in form of free basic housing, free basic food, free basic clothing etc.

        I am currently writing up ideas which you can
        find in this blog post:

        http://www.randform.org/blog/?p=2312

        In this post I propose to use games to help to determine the realizability of economic schemes. Moreover in that post I sketched one proposal of such a scheme.

        In that paper I want to adress the questions of basic income/work etc. thats why I started to investigate the current role of labour at:

        http://www.azimuthproject.org/azimuth/show/economic+growth+and+labour

        • Web Hub Tel says:

          Somehow my comment below got disconnected from this thread, but my point is doing “work” independent of outside influence and simply by self-motivating factors.

        • nad says:

          A draft of the paper about new economic schemes in games about which I was talking in the above comment can be found here:
          http://www.randform.org/blog/?p=3827

        • John Baez says:

          Nad—I liked the article you sent me about games, the role of labour, etcetera. When reading it, I wanted to help polish the English spelling, grammar and style. (My dad was an editor, so this is something I can’t resist doing.)

          So, I was going to suggest that you put some of this material on the Azimuth Wiki—that will make it easy to edit. But now I see you’ve already put some on. Great!

        • nad says:

          John wrote:

          … I wanted to help polish the English spelling, grammar and style. (My dad was an editor, so this is something I can’t resist doing.)

          I find my english is still better than google translate, … ? ? isnt??

          So, I was going to suggest that you put some of this material on the Azimuth Wiki—that will make it easy to edit. But now I see you’ve already put some on. Great!

          -Just look what you have put on!

          …I made only this little page.

          I don’t really know where to put the other sections of the article. Like I don’t think that the Azimuth project needs the overview about games. I don’t know.

          I regard my description of a possible game scheme in blog post On the return of investments as a very rough outline of a so-called “design treatment” (see the article The Game Design Process by Francois Laramee). According to Laramee the next step includes:

          Then, you should move to a preliminary design, discussing the game’s rules, content and behaviour in a purely qualitative way. This document should be circulated and discussed as widely as possible given the situation.

          so this could be something for the wiki.

          Moreover the game scheme in the blog post is just a more or less concrete suggestion and one point of the article was that there may be other schemes, that one may want to use the schemes as a research tool etc. so the proposed game scheme is rather just intended for having at least one concrete guideline (there is already enough theoretical blabla in the internet). The flexibility towards other schemes may also be interesting to discuss.

          I don’t know when I am going to continue writing at this article, it takes a lot of time and besides the fact that I think something like what I proposed should be done I haven’t yet developed a sufficient passion for the subject that I would like to spend too much free time on it. So it may take me another year until I write more. That depends on also on outer circumstances.

        • John Baez says:

          nad wrote:

          I find my english is still better than google translate, … ? ? isnt??

          Definitely, yes! But a native English speaker could improve your prose and make it really nice.

          For example, I’d say “Isn’t it?” instead of “isnt?”

          Whenever I read things on the Azimuth Wiki, I try to make them nicer. Sometimes it doesn’t take much more work than reading them. Sometimes I get interested in the details and put a lot of work into it. It depends a lot on how much time I have that day.

          I don’t know when I am going to continue writing at this article, it takes a lot of time and besides the fact that I think something like what I proposed should be done I haven’t yet developed a sufficient passion for the subject that I would like to spend too much free time on it. So it may take me another year until I write more.

          That’s okay. Of course I want everyone (or at least everyone smart and sensible) to join the Azimuth Project and become very passionate about it and put a lot of time into it. But I don’t think that pressuring people makes them more passionate. So: do whatever you like!

        • John Baez says:

          I edited Nad’s page a little:

          Economic growth and labour, Azimuth Project.

          I made a guess that the “employment ratio” is what Wikipedia calls the “employment-to-population ratio”, and added a link to that. If I’m wrong, I hope someone (like Nad) corrects me.

        • nad says:

          John wrote:

          I edited Nad’s page a little

          Thats fine. Go ahead.

          John wrote:

          I made a guess that the “employment ratio” is what Wikipedia calls the “employment-to-population ratio”, and added a link to that.

          The ILO writes about the employment-to-population ratio:

          Table 2a. Employment-to-population ratio (ILO estimates, by sex and age group)

          The employment-to-population ratio is defined as the proportion of a country’s working-age population that is employed. A high ratio means that a large proportion of a country’s population is employed, while a low ratio means that a large share of the population is not involved directly in market-related activities, because they are either unemployed or (more likely) out of the labour force altogether. The ILO estimates in table 2a are harmonized to account for differences in national data collection and tabulation methodologies as well as for other country-specific factors such as military service requirements. The series includes both nationally reported and imputed data and only estimates that are national, meaning there are no geographic limitations in coverage.

          I have no idea what they mean by

          “The ILO estimates in table 2a are harmonized to account for differences in national data collection…”

          This strange attempt in “harmonizing” may explain the differences between the International Labour Organisation (ILO) (compare
          their KILM table at
          Employment-to-population-ratio)

          and the OECD data listed on the Wikipedia site.

          I had asked ILO meanswhile a couple of times for formulas via email (partially sending the request to other adresses) but got only some phrases or no reply at all. I had sent them the link to the economic growth page and I had written them they should put formulas next to the tables in KILM.

          In short: the ILO doesnt seem to be overly interested in my free consulting efforts, nor is their CRM very attractive.

          I am really fed up with spending my time (and this is my free time!) with trying to make sense of incomplete information. (see also the discussion between Frederik and me about the elasticity).

          So everybody please go ahead and edit this page!

  25. Web Hub Tel says:

    That’s funny because as a lark, I wrote the applied math treatise The Oil ConunDrum as a free download on Google Docs. According to the classification system, I fit in the category of a crank.

    Moral to the story: everyone has got hobbies in which they pass their time. It just so happens that some people might choose to do math, instead of oil painting, gaming or whatever. I don’t understand the need for funding if it is just a hobby, albeit a fairly intense one.

    • DavidTweed says:

      Certainly at the hobbyist level there’s no need for funding, but at the higher level where one attempts to gather data, and even more signficantly makes predictions in advance of gathering further data in order to attempt to validate the theories being developed, these generally unavoidably involve things that cost money. (I’m sure you’re used to this in your day job.)

      • WebHubTel says:

        My oh my, do I get the data. The whole book is full of data. I go to various web sites and pull down megabytes of data and statistically analyze the numbers to verify the models. Some of the latest data includes hourly wind speeds over the span of a year and one massive pull from all the DTED databases of the USA to get statistical terrain elevation data. I realize this isn’t original experimental data on my part, but neither is it something that an agency will pay anyone to do. I haven’t really looked too hard, but I don’t think the government or any agency has ever funded studies directly related to oil depletion, as one example. Yes, they do fund the USGS and the one report by Robert Hirsch, but these barely tap the interesting issues.

        By my not having any strings attached to what we can research, comes great freedom. I do tend to run “open loop” because no one is looking over my shoulder. I kind of thought that this is what Azimuth is all about. I figured to have gotten a head start and so put everything in the can that I spent the last 6 blog-years working on.

        • DavidTweed says:

          Part of the background is that I come from a statistical machine learning background, so one of the things heavily imprinted on me is that one can often fit a curve from a reasonably “expressive” family to most data sets, but that without additional validation this can’t be taken to demonstrate either level of model predicitivity or, even harder, that the model is the “actual” mechanism of the studied phenomenon. Techniques like threefold cross validation (or in the case of very low data volume, leave-one-out validation), where some of the data is deliberately only ever “seen” to score a fitted model, have been devised by the community in order to solve the real, serious problem of being able to meaningfully look at if one model is “better” than another (or in the extreme if a model is significantly better than expected by general “pick the closest curve from this set” considerations). This is a really important consideration in stat mach learning, since we’ve generally decided we don’t understand the system enough to input/extract the “true” model, so unless we assess predictivity meaningfully (eg, using data unseen in the model fitting process) there’s no point to what we’re doing.

          If one thinks that one of the goals of Azimuth is synthesising an accurate “effective theory”, let alone a “physically correct” theory (to nick a bit of physics jargon) of various environmental issues, then doing meaningful model evaluation is going to be important. And that will generally requires collecting new evaluation data, which in turn does cost money. (I’m not saying that this is remotely easy: part of the reason I left my academic niche was realising that, despite large amounts of money being spent on it, the data collected in that field wasn’t really capable of validating the model research I and others were doing, and that addressing that would put me in the position of trying to write grants for data collection rather than doing model building.)

      • John Baez says:

        WebHubTel wrote:

        I kind of thought that this is what Azimuth is all about.

        That’s certainly part of what it’s all about. So, I’m hoping you’ll use the Azimuth Wiki as a place to put some of your analyses of (for example) oil depletion. Links to data are also much appreciated.

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