What Is Climate Change and What To Do About It?

Soon I’m going to a workshop on Interdisciplinary Perspectives on Climate Change at the Balsillie School of International Affairs, or BSIA, in Waterloo, Canada. It’s organized by Simon Dalby, who has a chair in the political economy of climate change at this school.

The plan is to gather people from many different disciplines to provide views on two questions: what is climate change, and what to do about it?

We’re giving really short talks, leaving time for discussion. But before I get there I need to write a 2000-word paper on my view of climate change—‘as a mathematician’, supposedly. That’s where I want your help. I think I know roughly what I want to say, and I’ll post some drafts here as soon as I write them. But I’d like get your ideas, too.

For starters, the program looks like this:

Friday 25 October: What is Climate Change?

9:00 – 9:30 Introductory remarks
John Ravenhill, Director, BSIA
Dan Scott, University of Waterloo, Interdiscipinary Centre for Climate Change.
Simon Dalby, BSIA

9:30 – 10:45 Presentation Session 1
Chair: Sara Koopman, BSIA
John Baez, University of California (Mathematics)
Jean Andrey, University of Waterloo (Geography)
Byron Williston, Wilfrid Laurier University (Philosophy)

11:15 – 12:30 Presentation Session 2
Chair: Marisa Beck, BSIA
Chris Russill, Carleton University (Communications)
Mike Hulme, Kings’ College London (Climate Science)
Radoslav Dimitrov, Western University (Political Science)

1:30 – 2:30 Presentation Session 3
Chair: Matt Gaudreau, BSIA
Jatin Nathwani, University of Waterloo (Engineering)
Sarah Burch, University of Waterloo (New Social Media and Education)

3:00 – 5:00 Roundtable 1 (all presenters)
Chair: Lucie Edwards, BSIA
Discussant: Vanessa Schweizer, University of Waterloo

5:00 – 5:15 Wrap-up
Dan Scott and Simon Dalby

Saturday 26 October: What Should We Do About It?

9:00 – 10:15 Presentation Session 4
Chair: Matt Gaudreau, BSIA
Radoslav Dimitrov, Western University (Political Science)
Mike Hulme, Kings’ College London (Climate Science)
Jean Andrey, University of Waterloo (Geography)

10:45 – 12:00 Presentation Session 5
Chair: Lucie Edwards, BSIA
Jatin Nathwani, University of Waterloo (Engineering)
Sarah Burch, University of Waterloo (Environmental Education)
Chris Russill, Carleton University (Communications)

1:00 – 2:00 Presentation Session 6
Chair: Marisa Beck, BSIA
Byron Williston, Wilfrid Laurier University (Philosophy)
John Baez, University of California (Mathematics)

2:30 – 4:30 Roundtable 2 (all presenters)
Chair: Sara Koopman, BSIA
Discussant: James Orbinski, CIGI Chair in Global Health

4:30 – 5:00 Wrap-up
Dan Scott and Simon Dalby

Some thoughts

Though I’m playing a designated role in this workshop—the “mathematician”—I don’t think it makes sense to focus on mathematical models of climate change, or the math projects I’m working on now.

I will probably seem strange and “mathematical” enough just saying what I think about climate change! Most of the other people come from fields quite different than mine: they seem much more in tune with the nitty-gritty details of politics and economics. So, perhaps my proper role is to mention some facts and numbers that they probably know already, to remind them of the magnitude, scope and urgency of the problem.

It may also be useful to emphasize that with very high probability, we won’t do enough soon enough, so we need to study a series of fallback positions, not just an ‘optimal’ response to climate change. And these fallback positions should go as far as thinking about what happens if we burn all the available carbon. What to do then?

When I talked about this workshop with the mathematician Sasha Beilinson, he wickedly suggested that the best solution to global warming might be a global economic collapse… and he asked if anyone was looking into this.

Of course this solution comes along with huge problems, and anyone who actually advocates it is branded as a nut and excluded from the ‘serious’ discourse on global warming. But the funny thing is, a global economic collapse could be just as probable as some more optimistic scenarios, for example those that require a massive outbreak of altruism worldwide.

So it’s worth thinking about economic collapse scenarios, and ‘burn carbon until there’s none left’ scenarios, even if we don’t want them. And these are the sort of things that only the mathematician in the room may be brave—or foolish—enough to mention.

What else?

67 Responses to What Is Climate Change and What To Do About It?

  1. Berényi Péter says:

    If I were you, I would mention that entropy production in non reproducible quasi stationary nonequilibrium thermodynamic systems, to which class terrestrial climate belongs to, is not understood at all.

    It is an outstanding unresolved problem of mathematical physics, with a potential to improve computational climate models tremendously, to the point they may become actually useful.

    It would be about the state of art in science at least, not politics.

    • To answer the question of what is climate change, I would always phrase it in terms of a natural variation and a forced input.

      This combines a chaotic component, which rides on top of a steady-state average global temperature, with a response due to the forcing input . The forcing function then causes the upward temperature warming trend.

      From our best understanding, the trend follows a ln(CO2) dependence, while the major fluctuation terms that perturb the trend include the Southern Oscillation Index (SOI), aerosols from volcanic activity, Total Solar Insolation (TSI) changes, and Length-of-Day (LOD) changes reflecting fluid inertial changes.
      These 4 terms we can refer to as SALT — SOI, Aerosols, LOD,TSI.

      Combine these data sets and reduce through a multiple linear regression and we get a fit to the temperature model, in this case GISS:

      I have been working out this formulation here:

      • Berényi Péter says:

        Well, you would need at least one more variable in such a model, rate of deep turbulent mixing in oceans (driven by pure mechanical energy input), which determines the effective heat capacity of the system.

        Even then you would not get anywhere close to understanding climate. Observed close match between hemispheric albedoes is still a mystery, unaccounted for by theory.

        Journal of Climate, Volume 26, Issue 2 (January 2013)
        doi: 10.1175/JCLI-D-12-00132.1
        The Observed Hemispheric Symmetry in Reflected Shortwave Irradiance
        Aiko Voigt, Bjorn Stevens, Jürgen Bader and Thorsten Mauritsen

        “Climate models generally do not reproduce the observed hemispheric symmetry, which the authors interpret as further evidence that the symmetry is nontrivial.”

      • BP,
        OK, so you say we need one more variable to represent the system.

        Consider that the Gibbs free energy for a closed system is

        dG = -S dT + V dP

        If you break the SALT model down, one can see the differential components of Gibbs. The pressure differential is incorporated as the SOI measure (a pressure change between Tahiti and Darwin), the extra free energy terms in TSI radiative forcing, volcanic aerosols and logCO2 radiative filters, and the long-term Length of Day (LOD) as a proxy for kinetic energy changes.

        This is all energy balance stuff, which is remarkably well modeled by minimizing the error in the SALT terms with respect to a global average temperature, dT.

        If we want to add another term CdT representing heat capacity of the ocean, I am fine with that. The land temperatures are showing a warming that is +50% over the sea surface temperatures so that this excess heat due to an ECS=3C has to go somewhere.

        Remember, that from outer space, the earth is just another object that we can apply macro thermodynamic principles to. You can make it as complex as you want, but for now, applying an empirical variational approach may take us a way in understanding the fluctuations in the climate.

        • This is an interactive semantic web server that I am working on, with an interface to model the dynamics of climate change


          Much of the mystery behind the variability in the earth’s climate can be stripped away when one starts breaking the system down into dynamic components.

          If anyone is interested in working on the project, drop me a line with the email address at my blog linked in the handle.

        • John Baez says:

          This looks like an interesting model, WebHubTel. I’ve only looked at it a little bit. Have you tried using just some of the data to fit the parameters and then tried to ‘predict’ (retrodict) the temperature based on that? Maybe you’re already doing that, I can’t tell yet. For example, maybe you’re using 1880-1960 data to fit the parameters and then ‘predicting’ the 1960-now temperature.

        • Milan Tasic D. says:

          Dear Konstantin, I receive such e-meils from Azimuth – a Mathematician John Baez is there. They resolve global problems (climate changes) in an exact way. I didn’t read them. Hope you will find some new ideas, global as well. I am going to read them as well. M

          2013/10/27 Azimuth

          > John Baez commented: “This looks like an interesting model, WebHubTel. > I’ve only looked at it a little bit. Have you tried using just some of the > data to fit the parameters and then tried to ‘predict’ (retrodict) the > temperature based on that? Maybe you’re already doing tha” >

  2. Eric says:

    I like your ideas. I think it is also useful (sobering?) to think about what it would take to really solve the problem (i.e. stabilize the concentration of greenhouse gases in the atmosphere). Roger Pielke Jr. does this in units of nuclear power plants per week (something on the order of 1 per week for the next 30 years). It seems to me a more monumental problem than many give it credit for.

    • Berényi Péter says:

      There is nothing “monumental” about it. China alone puts a coal fired power plant online each week. You only have to make nuclear power cheaper & safer, remove unreasonable fear & political obstacles and it will happen.

      There were several successful projects on that scale in history, starting with the global railroad (and telegraph!) network in the 19th century, at a considerably lower level of technological development.

      Anyway, the enormity of this task is not unprecedented.

  3. Jimmy says:

    I think there is another problem related to global warming that we do not talk about openly. Much before we see a shift in nature, we are likely to see a change in the way major nations conduct themselves when faced with this problem. An economic collapse is not a feasible approach (though it may sound logical to allow a problem to correct its course over time) as it may cause severe civil unrest (we have seen what happened in Greece and other parts of Europe) or possibly even wars. An economic collapse will force countries to scamper to safeguard their national and political interests, which may force apart any coalition effort to fight the situation. For example, population from areas afflicted by rising ocean levels may not be allowed refuge by countries. Several industries (for example airlines and coal) may become dysfunctional and it is a huge challenge for nations to sustain the loss of jobs. At the same time, nations abundant in energy resources and food may face constant threat or pressure from powerful nations. The real challenge of global warming comes from the inability of humankind to act as one and put their political interests aside. Let’s be honest; how successful have we been to persuade developing economies to curb the GHG emissions? I don’t see any resolution until we remove the distinction and boundaries, and have one common interest.

    • Berényi Péter says:

      Removing distinction & boundaries is the worst possible course of action to solve regulation issues in a complex system.

      Any structure other than a recursively modular one with proper module boundaries, standard interfaces between them running standard protocols to facilitate traffic is utterly untenable, because regulation costs per node go up much faster than the logarithm of number of nodes. It means regulation costs become prohibitively large at some point. Then one is forced to abandon regulation attempts and the system will likely assume a state which is absolutely undesirable for any actor.

      • Jimmy says:

        By removing boundaries, I meant thinking of the benefit of the globe when deciding on an action and not individual countries. That doesn’t mean removing regulations. For example, many emerging nations refuse to curb GHG as it would hamper their growth. By removing boundaries, such nations would be inclined to think more about common interests and less about national interests.

        • Berényi Péter says:

          Ah, and who would do that thinking? The government of the U.S. of A. appointed by an elected President and overseen by an equally elected Congress and Senate or unelected officials of CPC? Or commissioners of the EU perhaps, nominated by national governments and appointed by the President of the European Commission?

          Whatever Power is entitled to think for the benefit of the globe, would it have the means to bomb Britain back to the Stone Age, should the Prime Minister refuse to oblige, pressed by the majority in Parliament, fearing a landslide failure on the next elections?

          Provided it has the power to do that, what kind of Checks and Balances should we implement to prevent it going berserk?

          Most importantly, who would pay the bill?

  4. domenico says:

    It is only an idea, but if all the coal and petroleum is burned, then it can be possible that in an old era we have had the same carbon dioxide concentration; so that it is possible that the temperature grow happened in a geological era (I am thinking that can be happen in the Silurian with sea level change and mass extinctions, but I am not an expert).

    I am thinking that can be possible to built some meteorology on the old Earth continent (so to verify the meteorology models, and compare them with geological data of atmosphere, and biostratigraphy); perhaps can be possible, to refine the meteorology model, to study other celestial body weather (for example Mars, Venus, Titan,etc.); if it is possible an experimental verify of the models, with different gases and parameters, then the criticism can be silenced.

    If there is an awareness of the critical condition of the Earth, among the people, then some changes are possible.

  5. Lee Bloomquist says:

    For the cocktail hour, maybe here’s another very low probability scenario:

    Say the mathematics turns out to support theories of dark matter where it is everywhere, for example by shadowing ordinary matter through selective obedience to physical laws. Then say that just as streams of water in early America provided almost free electric power, so in these kinds of mathematical theories would streams of dark matter give us almost free electric power. Thus enabling the design of *dark matter power plants* and saving the world. If not someone actually doing the math to say so, shouldn’t there at least be a bar bet on whether or not these kinds of theories are possible?

  6. John Baez says:

    Here is a first draft of my first 15-minute talk in this workshop:

    What is Climate Change?

    I wrote it in the last few hours. Comments and corrections are welcome… though if I add something I’ll need to take something out.

    It may not be obvious to you what I’ll say while showing the graphs here…

    The second talk should cover “what to do about it”.

    • John Beattie says:

      In slide 6, a first quick glance appears to show the CO2 concentration as negative numbers. Very small issue but might cause confusion.

      On slide 8, I don’t believe that there is anything new about having to balance economic growth with its effect on the biosphere. For example, consider slash-and-burn farming, where the current area is slashed, burnt and planted. After a few years, the soil is impoverished and you have to move on. For other examples, famines have occurred in Zimbabwe and China due to economic or political action.

      i think that this is important because it helps people to take something seriously when it can be seen as being not so very special.

      Yes, greenhouse gases have a global effect and so affect every human, indeed every form of life. But, consider the examples I gave above: from the perspective of J. Ordinary in the middle of one of them, the situation is just as global. It encompasses everything in his or her environment.

      • John Baez says:

        John wrote:

        On slide 8, I don’t believe that there is anything new about having to balance economic growth with its effect on the biosphere. For example, consider slash-and-burn farming, where the current area is slashed, burnt and planted. After a few years, the soil is impoverished and you have to move on. For other examples, famines have occurred in Zimbabwe and China due to economic or political action.

        Yes, that’s true. Some of these effects are old and familiar, and you’re right that it is important to see this. But there’s also something new, in part because the economy is an integrated world-wide system. And this is also important. So, I’ll have to refine my formulation, while keeping it terse if possible.

        I’ll get to be a bit more nuanced in the paper I’m supposed to be writing.

  7. Bruce Smith says:

    I don’t have any detailed idea of what you should say, but I’m sure you should try to get across the ways of thinking about climate change which come more naturally to mathematicians (or physicists, or others sympathetic to that viewpoint) than to other people. For example, one reason it’s uncertain in detail is that it’s an example of a shift of a chaotic system from one orbit-attractor to another (or something like that)… but a reason it’s not uncertain (that it will happen) from a high-level (large timescale) viewpoint is that essentially all human effects grow exponentially until something makes them not do so, and exponentially growing inputs or parameter-changes to any finite system will “soon” affect it greatly. (In other words, very basic observations can reliably predict “climate change sometime historically soon, or a disaster-for-humans which prevents it” even if the specific mechanism is entirely unknown, and the timing is uncertain by many decades.)

    But just saying these things won’t make non-mathematically-inclined people understand them, or believe them… and what to do about that, I don’t know, except try to explain them as simply and clearly as possible.

    BTW your point that it’s desirable to talk about suboptimal outcomes is a very good one. To avoid being considered “too nutty” you can just stick to the more optimistic of the pessimistic scenarios. Large-scale economic collapse is not very important to consider as a “solution” since it will happen naturally if there isn’t any other solution; if for some reason someone wanted it, they needn’t aim for it, just do nothing. (And from the human perspective it’s not a solution anyway.)

    Finally, depending on the audience, it may be worthwhile pointing out the possibility of much more powerful technology existing within a few decades (i.e. molecular manufacturing) which if not used too disastrously can be applied very usefully here (e.g. to remove unwanted gases from the atmosphere on a large scale). I’m not sure how the “mathematician” perspective fits with that… unless it’s “willingness to consider ideas which have logical foundations even if they have amazing-seeming consequences”, or an observation that for centuries now, it’s been routine for new technologies to emerge that would have amazed people a few decades before.

    • arch1 says:

      Drexler’s 2013 book “Radical Abundance” speaks to the possibility alluded to in the final paragraph, and more. In addition to removing carbon from the atmosphere, atomically precise manufacturing hold the promise of drastically localizing supply chains, greatly reducing reliance on scarce resources, yielding orders-of-magnitude better products, and doing all of the above with zero carbon impact (by using APM-fabricated solar cells). It compares the coming APM revolution with 3 other revolutions, two of which are also based on nanoscale devices: Agricultural, Industrial, and Information.

      It’s a good question whether & when (relative to the global warming timescale) this technology could start making a significant impact. Another good question is whether working to inject this prospect into the global warming debate would at this point help more than hurt.

  8. Bruce Smith says:

    Now I saw your draft… I would make sure to emphasize the different timescales of the first few graphs, since it’s easy to miss them at first glance. But it looks like a great start.

    • John Baez says:

      Thanks! In my first, talk, I can probably weave in your comment about why global warming is uncertain in detail but almost certain from a sufficiently large-scale view. But this particular crowd doesn’t need to be convinced that climate change is a serious problem. I think some of them might need to be shown that climate change is just part of a bigger phase transition, though—really the start of a new geological epoch. So that’s one of my main goals.

      I’ll point out the dramatically different timescales on the graphs. Indeed, part of the point is that people and the biosphere can adapt to large changes given enough time, but we’re imposing very sudden changes on the Earth.

      Finally, depending on the audience, it may be worthwhile pointing out the possibility of much more powerful technology existing within a few decades (i.e. molecular manufacturing) which if not used too disastrously can be applied very usefully here (e.g. to remove unwanted gases from the atmosphere on a large scale).

      This sort of thing will fit in better with my second talk, “What To Do About It”.

      I’m not sure how the “mathematician” perspective fits with that… unless it’s “willingness to consider ideas which have logical foundations even if they have amazing-seeming consequences”…

      That’s a good enough excuse. Most of the people in the room will be into public policy, economics, and climate science, so it’s my job to inject things like this. I might mention how in 1930 a mathematician named Turing wrote a paper about how in theory a simple machine could do arbitrary computations…

  9. morgan knapp says:

    I still say to look at the Antartica researcher that found arecheons eating methane in every single ice core he looked at. They all showed those elevated CO2 where they were converting CH4 to CO2 over millennia, at very slow respiration.

    Focusing on carbon is the wrong point, it is the LEAST active greenhouse gas.

    If warming slowly builds, from soot and bromine/sulfur (fires and volcanic), until the methane gun goes off, then a catastrophic population decline will happen, to all the folks on the coasts along those ocean boundaries.

    Looking at a probable 25% reduction of population globally, no water which basin decompresses. Once a ocean basin hydrate deposit starts to release, it drops the density of the water above it, lowering the pressure,. and allowing for acellerating release.
    At about 17% mix with oxy, you are looking at the explosive potential of a military air/fuel bomb. CO poisoning, explosive air burst, coast length fires, and carbon lofting equal to nuc winter.
    Apocalypse Now ! Guess you shouldn’t use that as a title.

    Look up some of the studies on the rise of noctilucent, high altitude clouds. About the only explanation that has been postulated to cover them, is increased methane in the upper atmo. The shallow ocean along the old Bering Straight is leaking way above any historical level.





    Click to access paull-plfs.pdf


    The failure of wind turbines as a large scale commercial source can not be overstated. Over 50% of the subsidized turbines in CA are now disabled because of wind damage or bearing failures.

    You might look at Brillouin Energy systems. Just the idea that neutron synthesis is happening in their design is enough to fill a few workbooks.


  10. I think you really should explain that given enough CO2 in the atmosphere temperature has to rise. This is obvious, to you, and I may be underestimating your public, but this isn’t at all obvious for people in economics, politics, and communication etc. They take the relation between CO2 and climate change as some sort of belief like, “interest rates should go down to improve the economy”, or “because of social media we are in a new era of business to consumer relations”, i.e. as something some people including professors say but other people including professors deny and that is not directly supported by hands on experience, rather than hard, first principle physics. Perhaps the best way to show this is through this little video of Ian Steward http://www.youtube.com/watch?v=Ot5n9m4 and mentioning the climate on Venus. Now there are all sorts of feedback mechanisms and subtleties that can and will effect the direct naive relationship, but

    A) if we keep on blowing exponentially more CO2 in the atmosphere we will inevitably see climate change (see above),

    B) at the relatively small concentrations of CO2 (compared to Venus, say) we are, there are lots competing mechanisms and feedback loops on earth that change a naive climate change is proportional to CO2 change, but the burden of proof is on the nay sayers_ that the subtle feedback mechanisms make the unsubtle change due to changing CO2 levels negligible,
    C) It is an important and unfortunately really difficult problem to take into account all the feedback loops precisely. However, meteorologists, physicists and mathematicians are steadily getting better grips on the problem and unfortunately the answer is not reassuring and is in line with all the (also difficult) paleo and historic -climate change findings.

    Note that because you are a mathematical physicist you are by far the most obvious speaker to present this perspective, and will be by far the most convincing one to tell it.

  11. The question of whether climate change is anthropogenetic is of secondary importance.

    The primary questions are (a) does climate change exist? (b) if so, should we do anything about it? (c) if so, what can we do?

    More briefly : can we do anything to improve the future climate?

  12. Charlie Clingen says:

    If you could present only one chart, or more realistically, if you had to summarize your presentation in one chart, what would it be?

    • John Baez says:

      I would prefer to summarize it in a couple of paragraphs, namely these, because it’s really an idea rather than some data:

      We have entered the Anthropocene, a new geological epoch.

      Before, we could treat nature’ as distinct from ‘civilization’. Now, there is no nature separate from civilization—but also no civilization separate from nature!

      Before, we might treat ‘economic growth’ as an almost unalloyed good. Now, every form of economic growth must also be assessed for its effect on the biosphere.

      For better or worse, we will adapt to this new epoch.

      I’m rewriting my first talk to make this point a bit clearer, and flesh it out some more. The graphs will go along with narrative that leads up to these points.

      • Charlie Clingen says:

        Powerful! The Anthropocene, a new geological era. I think your audience will remember this point a year from now, and probably much longer than that. I know I will.

  13. Milan TASIĆ D. says:

    If you think like this, you can suggest: Scientists of all countries should be organized – as a legal mean to take a power – in political parties, which would include the higher levels of organizations etc. – as once was the labor movement. So instead of: Proletarians of the world unite, it would be as: Scientists of all countries, unite. dr Milan Tasić D., Serbia

  14. Jim Stuttard says:

    With respect to carbon taxes, Myles Allen, argued in a recent article that:

    Trillion-tonne budget means carbon capture is not optional.

    The article is based on the:

    Global CCS Institute Report (2013).

    Agreeing on their fifth assessment report two weeks ago, the 195 member governments of the Intergovernmental Panel on Climate Change accepted that to meet their goal of limiting global warming to 2°C, the planetary carbon budget – total carbon emissions released from the dawn of the industrial age – must be limited to one trillion tonnes.

    But today’s latest report from the Global Carbon Capture and Storage Institute suggests the governments did not comprehend what this really entails.

    Carbon capture and storage (CCS) projects are struggling, with five cancelled and seven put on hold in the past year alone. As the IPCC gathered in Stockholm, neighbouring Norway announced the cancellation of their flagship Mongstad CCS project, which would have stripped CO2 from a petrochemical and power plant and injected it into geological formations below the North Sea.

    We have already burned through more than half of those trillion tonnes of carbon, with at least double the remainder lying in economically viable reserves of fossil fuels, and an energy industry that keeps finding more.

    Don’t blame the industry. The value of our pensions is based on the assumption that these reserves will be sold and burnt. So limiting carbon emissions to a trillion tonnes means either we accept global warming beyond 2°C, or we develop CCS to use fossil fuels without releasing CO2, or the value of our pensions takes a hit.

    CCS is often seen as “one of a suite of options” in combating climate change. But once we accept that the world’s fossil energy stores will be used someday (and what right have we to tell the citizens of India in 2080 no to burn their coal?) then the only question that really matters is what fraction of remaining reserves will be captured and stored. If we are to meet the 2°C goal, that fraction needs to be at 50% by mid-century and heading for 100% by 2100. We might even need to “go negative” – pulling CO2 out of the air in order to stabilise the climate. That’s not something that can be done with low-energy lightbulbs.

    The maths are simple: to limit remaining carbon emissions to 450 billion tonnes, the fraction of extracted carbon we sequester must increase by 1/450th, or 0.22%, for every billion tonnes of carbon released into the atmosphere. That’s not a policy, that’s a fact.

    Many environmentalists find this fact uncomfortable, and complain that CCS is “unproven technology” – this isn’t true, the industry has been doing it for decades – or worry the reservoirs may leak.

    With the right geology, nature herself has demonstrated that CCS works: ancient CO2 is often found in oil and gas fields. But finding the right formations, and learning to avoid less reliable ones, is indeed one of the biggest challenges facing the CCS industry. All the more reason to roll out CCS progressively – and why a global carbon tax or cap-and-trade regime won’t work. The price of CCS is relatively inelastic, so we cannot afford to wait until the carbon price is high enough for CCS to be viable and then expect to deploy it overnight.

    • John Baez says:

      Thanks! In my talk on What To Do About It, I’ll say something like this about carbon sequestration:

      In China, Huaneng Group says it’s scrubbing CO2 from a coal-fired plant at less than $35 per tonne.

      Sucking CO2 from the air or sea could be a safe way to `ratchet back’ global warming, but it’s hard to do on a large enough scale.

      If you grind up a common mineral called serpentine, it absorbs 2/3 its own weight in CO2. But to absorb all 37 gigatonnes of CO2 emitted in 2010 would require 55 gigatonnes of serpentine. The total amount of material handled by US mines is only 6 gigatonnes.

      Plants already suck CO2 from the air! Suppose we could make farmers deposit all crop residues on the deep ocean floor. That's about 5 gigatonnes of stuff, not nearly enough to equal 37 gigatonnes of CO2, but significant. See Strand and Benford.

      Sustenance farmers can already do something similar by making biochar, which also fertilizes the soil.

      Iron fertilization of algae growth in the ocean is worth looking at — but so far the results have been poor.

      In the future, nanotechnology may make it easier to sequester lots of CO2. It sounds far-out, but a century ago so did computers. We need to do things now, though.

      I should also mention preventing deforestation, but the audience will probably be familiar with that, so I want to spend more time on these less familiar options.

  15. alQpr says:

    Odd to see no-one designated as representing ‘Physics’ but I suppose you can carry that ball well enough if you want to!

    (I don’t know what the intended audience is, but I would expect a discussion of ‘What is Climate Change?’ to include some discussion of planetary thermodynamics and the fact that we had good, or at least quite plausible, reasons to expect all this more than a century ago)

    • John Baez says:

      I believe Lee Smolin from the nearby Perimeter Institute was invited to represent ‘Physics’. Apparently he was unable to come.

      Mike Hulme of Kings’ College London is representing ‘Climate Science’, and I’m hoping he will carry that burden.

      The main audience in this workshop is the other workshop participants, and the goal is to reconcile and synthesize how people from different fields think about climate change.

      I don’t think there will be any need to convince other participants that climate change exists and is a problem. So, I don’t really want to spend part of my 15 minute talk What is Climate Change? saying “Arrhenius told you so!”

      As you can see from the draft of my talk, I want to convince people that climate change is part of a bigger ‘phase transition’, really a shift to a new geological epoch, which has many aspects. I don’t want the experts on international diplomacy to think that climate change is just a little item on their menu like any other. We’re talking about things like losing the polar ice caps, breaking out of the glacial cycle, massive ‘dead zones’ in oceans… and ultimately humanity finding out if it’s up to the task of managing the biosphere. In a way the last comparable event was when blue-green algae started photosynthesizing and spewing what was then a poisonous gas into the atmosphere: oxygen. But the changes now are happening much faster, in hundreds rather than millions of years.

      The workshop’s website explains its goals in somewhat more bureaucratic language:

      Each day will consist of three sessions for presentations followed by a lengthy roundtable where the commonalities and differences between the various disciplines can be teased out, with the aid of some BSIA and MCC graduate student facilitators. Presentations, and the papers they are based on, will not be circulated prior to the workshop so that there is a certain surprise element during the event to focus attention on the details of both definition and response.

      This workshop will address questions of definition and governance and crucially how they are related in terms of how definitions of the problem are related to proposed social and governmental “solutions”. In the process cross-disciplinary dialogue will be facilitated and the commonalities and differences between disciplinary perspectives elucidated. This should shed light on the very difficult problems of how to deal with climate change as a matter of international affairs, and how university educators can better address these issues too.

      If interdisciplinary efforts are to bear fruit on this problem, being explicit about the various assumptions structuring the viewpoints in the discussion is necessary for effective dialogue and common research efforts subsequently. Comparing and contrasting different disciplinary specifications of the problem and the related proposals for tackling climate change will add an explictly interdisciplinary perspective to understanding the issue.

      • alQpr says:

        ok – if the audience members are all already convinced that AGW exists, then to best put forward your idea of a phase change to a new geological era I’d drop the relatively unimpressive short term arctic ice cover graph and only give 1 second or so to each of the others (which an informed audience will all be familiar with anyhow), and spend more time on looking at past major phase changes – maybe including something about periods of rapid reduction in biological diversity and the time taken (and/or expected from math models of evolution) to recover from them (would be nice to have biologists and paleontologists represented there also). And I’d drop the stuff about wedges as that’s more related to what we do to mitigate CC than what it really is (especially since the P&S analysis opens the question of why do that mix rather than just multiply current solar by 140, or, more plausibly, nuclear by 14).

      • John Baez says:

        alQpr wrote:

        I’d drop the relatively unimpressive short term arctic ice cover graph and only give 1 second or so to each of the others (which an informed audience will all be familiar with anyhow)…

        I will go through these very fast, but I’ll be telling a story that leads up to the idea of the Anthropocene.

        To me, the fact that we’ve cut the extent of summer Arctic sea ice in half in just 30 years is actually very impressive!

        …. including something about periods of rapid reduction in biological diversity and the time taken (and/or expected from math models of evolution) to recover from them (would be nice to have biologists and paleontologists represented there also).

        Yes, these are good ideas. There won’t be biologists and paleontologists there, so I will have to fill that role. Most of the other participants see to be focused on economics, politics, society and diplomacy, so I need to be a counterweight.

        And I’d drop the stuff about wedges as that’s more related to what we do to mitigate CC than what it really is (especially since the P&S analysis opens the question of why do that mix rather than just multiply current solar by 140, or, more plausibly, nuclear by 14).

        I’ve moved that to my second talk, What To Do About Climate Change. When recalling the work of Pacala and Socolow, I will be very clear that I’m not advocating any particular mix of strategies; I am just listing 7 strategies that each reduce carbon emissions by 1 gigatonne by 2054. The audience is free to think “hmm, I’d prefer to multiply nuclear power by 14 and not do any of the other strategies”—or whatever they want. I’m just presenting a menu, they can choose their dinner.

        • alQpr says:

          Re the arctic ice, what is impressive about your other graphs is not the amount or rate of change, but the sudden dramatic acceleration into a range of rates never seen before. I don’t know how stable the arctic summer ice cover was prior to 1979, but it is conceivable to one who doesn’t know the long term record that it often varied widely and that the current rate of change is not unusual.

          If you now have a bit more space in part one then I’d recommend actually putting in a plug for the need for mathematical modeling to understand *all* of these effects – including eg speaking in place of biologists re the rate of re-speciation following a collapse of diversity. (And there may even be a spot there for a brief “And hey we DID warn you about this over 100 years ago!” just to remind people that we do have a good record)

          Re P&S, I like your rephrasing here “listing 7 strategies that each reduce carbon emissions by 1 gigatonne by 2054” rather than saying “one way would be to do all seven” and would encourage a bit more explicit thinking about both the relative feasibilities of each – both to reach the 1G contribution and to be scaled up to do more. Maybe pointing there again to the possibility of using mathematics and a more serious kind of decision theory for making these choices.

          P.S. Is this all going to be recorded? (PI usually do a pretty good job of that sort of thing so I am looking forward to being a fly on the wall – albeit maybe sometime after the fact)

        • John Baez says:

          Thanks for the further comments.

          This workshop is at the Balsillie School of International Affairs, not the Perimeter Institute. Some of the workshop will be videotaped, but unfortunately these videotapes will not be made publicly available. I urged that everything should be made public, but the organizers didn’t go for that:

          This workshop, open to the public, but drawing heavily on BSIA, MCC, SEED, geography and other local graduate students (session chairs, registration assistants etc, and rapporteurs,) is designed to facilitate such a dialogue. (Round tables will be recorded for the use of all participants, not for broadcast.)

          Please register by emailing IC3@uwaterloo.ca so we can keep track of numbers. There is no cost to attend this workshop.

          A book will appear, probably not free—though I’ll suggest that too. But of course I’ll make my article freely available. I think it’s absurd not to make these discussions as easy to access as possible: whether you like what people or saying or hate it, it’s too important to keep buried.

  16. Arrow says:

    You should mention that despite all the panic and unlike the many real problems each of us faces in our everyday lives global warming has been a complete non-issue and will remain that way for the reminder of our lives.
    Everyone needs to:
    1. realize that climate is completely beyond our conscious control,
    2. be grateful extra CO2 helps avert the next ice age,
    3. appreciate it’s fertilization effects on global agricultural production,
    4. stop wasting time on it and focus on more productive pursuits like economy, health, crime, true pollution or anything really. Almost anything one can think of is more productive then “fighting global warming.”

  17. I think slides 9 to 11 might belong to the second talk about what to do about it, so if you absolutely need space you might start by cutting that part.

    To me climate change is just an ongoing millennium-long dangerous geoenginering experiment which was started really a couple of centuries ago.

    We are all passengers in a big truck that is going at full speed into unknown territory, and we have to, simultaneously:
    1) take control of the truck,
    2) understand where we are and where we are going,
    3) decide where we want to go,
    4) figure out how to actually drive the bus to get there.
    All of this hopefully before we’re off a cliff :)

    I really like the second paragraph on slide 8, and i think you should try to insist more on that point.

    In fact, i think that the concept of a trade off between global warming and economic growth has not yet settled in for most people, but this is really what we are looking at for the next century.

    I believe that if you do some back of the envelope calculations it turns out that for every dollar of global GDP we currently have to burn about a Kg of coal (obtaining, with a 30% efficiency, which is the average for existing coal power plants, about 7M Joule).

    I would personally put a slide with just one dollar on the right, an equal sign in the middle, and a burning Kg of coal on the right! Images gets understood much faster and better than words …

    Now, when it comes to the “what to do about it” part, i think we will need to engage in geoengineering ASAP if we are serious about mitigating GW effects. Everything we know so far tells us that the dangers of not doing so are higher, and that it’s the only way we can attempt to preserve both civilization and nature as we know them, while we switch to better energy sources like wind and thorium.

    • John Baez says:

      Giampero wrote:

      I think slides 9 to 11 might belong to the second talk about what to do about it…

      Yes, they do. I’m moving them there, freeing me to focus on my more novel points.

      I really like the second paragraph on slide 8, and i think you should try to insist more on that point.

      Thanks. That’s this, for anyone too busy to look at the slides:

      Before, we might treat `economic growth’ as an almost unalloyed good. Now, every form of economic growth must also be assessed for its effect on the biosphere.

      In fact, i think that the concept of a trade off between global warming and economic growth has not yet settled in for most people, but this is really what we are looking at for the next century.

      I believe that if you do some back of the envelope calculations it turns out that for every dollar of global GDP we currently have to burn about a Kg of coal (obtaining, with a 30% efficiency, which is the average for existing coal power plants, about 7M Joule).

      Are you doing this just by dividing global annual coal consumption by global GDP? That’s interesting. Of course to be careful I wouldn’t say we “have to burn” that much, simply that we “do burn” that much.

  18. Are you doing this just by dividing global annual coal consumption by global GDP? That’s interesting.

    No i was mostly referring to the 7 MJ figure because of what i remembered from this post. Then i asked myself how much coal we burn – with current efficiency – to have that energy, and it turns out that it’s very close to 1Kg.

    In reality we do burn mostly fossil fuels (not just coal but oil and gas) to get that energy, so the right amount might be perhaps a quarter of that Kg. But then again the carbon impact is higher than just 250gr of burned coal …

    Of course to be careful I wouldn’t say we “have to burn” that much, simply that we “do burn” that much.

    Yes you are right, i didn’t mean we “have to” burn that, only that that’s what we do right now (and probably what we’ll be doing for at least another decade).

    • Sorry i should have answered as a reply to your post.

      Anyway, in 2008 we obtained 38497TWh from coal.

      38497 TWh are 1.385892e+014 MJ (to be double-checked) which, divided by 7MJ yield 1.9798e+13 Kg.

      In 2008 the global GDP was 61T$, which means really almost exactly 3Kg of coal for each dollar !!

      So which one is the right amount now ? what am i missing ? need to get back to that !!

      • Giampiero Campa says:

        Ok, i was doing things in a hurry, it’s almost exactly 3$ per Kg of coal, which means 0.32 Kg for each dollar, which makes a lot more sense and it’s close to the previous result.

  19. John Baez says:

    Here are drafts of my two talks:

    What Is Climate Change?

    What To Do About Climate Change?

    I pulled some material from the first and put it in the second, following suggestions by Giampiero Campa and alQpr. Now the first one is a bit short, which is good. I’ll add some more material about the Anthropocene, perhaps comparing it to the Paleocene-Eocene Thermal Maximum or (going back much further) the Oxygen Catastrophe.

    • Frederik De Roo says:

      Hi John,

      some suggestions:

      Regarding what to do, and when:

      * Because you are the mathematician of the group, perhaps you could mention the possible existence of “positive” feedback mechanisms so that once the Earth’s state moves too far out of yesterday’s (sort of) equilibrium, it will be much harder to get it back there.

      * In the “what is” slide 8:

      With respect to “Before” the phase transition: books like Collapse suggest that in isolated communities, such phase transitions have taken place in the past. Perhaps you could mention that sometimes humans adapted cleverly, sometimes they hit a wall and their civilization crashed. It’s not backed by a model, but perhaps two pictures (x: time, y: comfort ) comparing (a) large overshoot and a lower equilibrium and (b) a smaller overshoot and a higher equilibrium, help to visualize the possible outcomes.

      * What to do (some very minor comments):

      -slide 9 renewables wood perhaps within quotation marks? (Or maybe this will be obvious by the way you mention it)
      -slide 10 what about ‘will have to adapt’? (sounds less easy-going than ‘will adapt’ to me)

      • John Baez says:

        Thanks for your wise and helpful comments!

        Since my message may seem overly grim to some, I wanted to end with something resembling a message of hope… but something that I believe is actually true: we will adapt to life in the Anthropocene.

        I doubt Homo sapiens will go extinct soon. The process of adaptation may be very unpleasant: for example, we could be reduced to bands of hunter-gatherers living in Canada and Siberia after most of the world has become uninhabitable due to a 12°C average temperature increase, due to people burning all available carbon, perhaps combined with a catastrophic methane release from permafrost and the ocean floor. This is close to a worst-case scenario, but I still think that people would adapt and survive.

        In short: I believe we will adapt. But I’ll explain that this doesn’t imply life will be nice. Some ways of adapting lead to better results than others.

        (Of course I also think Homo sapiens will eventually go extinct, either by simply dying out, by evolving into other species, or by creating artificial replacements for ourselves. But this is looking a bit too far into the future for the purposes of this workshop!)

    • In slide #2 of the “what to do” part, I would maybe replace “So, we will:”, with “So, we will choose among the following possibilities (or a mix of them):”.

      I think that the (unlikely) scenario in which an economic collapse actually causes fossil fuels to stay unburnt naturally belongs to the first group.

      It’s also possible that as we run out of easily exploitable oil the resulting higher energy prices will cause a strong reduction in fossil fuels dependence, (either by reducing energy consumption or by incentivizing renewables, or both).

      Some have also theorized that higher energy prices will cause an economics (or civilization) collapse, thereby in the end leaving a lot of fossil fuel unburnt.

      I think all these scenarios are unlikely, especially the first and the last (which are really the same one), but nevertheless they are possible so you might want to briefly talk about them (if not dedicate a slide) when discussing option #1, that is “leave fossil fuels unburnt”.

      By the way, for sake of completeness, a nuclear war could also “actively cool the earth”, but I wouldn’t mention it …

  20. Dilip Kale says:

    Climate change is a geological phenomenon ad has taken place before. The immediate cause has been global warming in the five geologically preserved events it has led to extinction of large number of species. The evolution of methane from the hydrate melting is the ultimate positive feed back loop responsible for warming. For a change, this time round the role of detonator is played by one of the species namely homo sapiens. That it can be averted or controlled is simply reflection of failure to grasp the physics behind it. The strong ingrained optimism and hubris about the prowess of technology makes most people believe in the myth of solution ! Finally it is a mathematically certainty is what a mathematician can stress!

  21. Thomas Larsson says:

    Depletion of fossil fuels and anthropogenic climate change: a review

    Mikael Höök and Xu Tang


    Future scenarios with significant anthropogenic climate change also display large increases in world production of fossil fuels, the principal CO2 emission source. Meanwhile, fossil fuel depletion has also been identified as a future challenge. This chapter reviews the connection between these two issues and concludes that limits to availability of fossil fuels will set a limit for mankind’s ability to affect the climate. However, this limit is unclear as various studies have reached quite different conclusions regarding future atmospheric CO2 concentrations caused by fossil fuel limitations.

    It is concluded that the current set of emission scenarios used by the IPCC and others is perforated by optimistic expectations on future fossil fuel production that are improbable or even unrealistic. The current situation, where climate models largely rely on emission scenarios detached from the reality of supply and its inherent problems is problematic. In fact, it may even mislead planners and politicians into making decisions that mitigate one problem but make the other one worse. It is important to understand that the fossil energy problem and the anthropogenic climate change problem are tightly connected and need to be treated as two interwoven challenges necessitating a holistic solution.

    And the shale bubble may be about to burst; Shell is pulling out of the shale play with major losses.

    • The Bakken extraction rates are a good example of modeling diffusional flow.

      We are trying to figure out how long the Bakken will last assuming it is essentially showing Red Queen behavior. The models are very simple and show good historical agreement so we are trying to project assuming well growth rates and ultimate reserve.

    • John Baez says:

      Webhubtel: what’s your opinion of this?

      Economic dangers of ‘peak oil’ addressed, Science Daily, 16 October 2013.

      Sorry I’m too busy to find the original paper(s) on which this news report is based!

      • John, thanks, I will read the paper when I can get access to it. They do appear to cover the two significant issues of fracked shale wells —

        “Shale developments are, so we believe, largely overrated, because of the huge amounts of financial resources that went into them (danger of bubble) and because of their apparent steep decline rates (shale wells tend to peak fast),” according to Dr. Kerschner.

  22. Maicol Ochoa says:

    Dear Professor Baez,
    While I’m not a mathematician, I have enough background in mathematics to understand the mathematical theory of dynamical systems. My background is in Chemistry, and I believe it will be important to describe (if possible) the minimum mathematical elements of a good theory of climate change, i.e., one that can make unambiguous predictions that can be contrasted with experimental observation. This is an important topic, equivalent to the discussion on the right mathematical structure that describe classical and quantum mechanical systems. In particular, it would be important to understand how it is possible to make predictions about the global climate change in the long term (years) and, at the same time, it is impossible to anticipate the weather twenty days ahead. I’m seriously concerned about the chaotic nature of the equations that may describe the climate evolution in such a theory.

    Maicol Ochoa

    • John Baez says:

      Indeed, the separation of variables into ‘slow’ and ‘fast’ ones, and the approximate decoupling of slow and fast ones, is very interesting and complicated. We can predict that it will be colder in winter, we can predict that in different locations rainfall varies in different ways with the seasons, and we can predict the El Niño cycle for years in advance, while being unable to predict the weather in detail for more than a week or so.

      • alQpr says:

        I know you don’t want to lose your audience by getting too technical, but if you can find time in your first talk to briefly allude to this as well as the fact that there are really interesting mathematical issues around the definition of a “phase transition” I think that would be great.
        P.S. Perhaps you should demand extra time as you are now wearing (at the latest count) 5 hats: math, stats, physics, biology, and (see below) economics (but at least I think you can save that last one for the second talk).

  23. svein vik says:

    The “suggested economic collapse” may not be far off considering how the US just bumped the debt limit without even discussing a real balancing of the budget (via cutting salaries in half and cutting other pet projects). In fact nobody in the media or otherwise even considered a real balanced budget. Unless some drastic measures are taken sooner than later the exponential debt increase will hit the real ceiling soon enough and then the consequences will be much much worse.

  24. svein vik says:

    I recently read a book with some suggestion:

    (1) Eat ostrich instead of beef (no more burgers) to stop methane.
    >>> i.e. In Scientific Amer. an old article says rice and beef production has prevented the start of the next ice age.

    (2) Restore whales as they seed (poop) the oceans with iron from eating deep squid. There are papers out about this.
    This of course means stopping or slowing shipping which kills whales. (i.e. no more plastic junk toys and iphones from china).

    (3) Give poor people all the oil (i.e. free) they want to prevent burning wood and increasing the deserts of the world. And replant the sahara and other deserts. Apparently vegetation prevents temp. increases. Stop C++.

    That’s all.
    S. Vik

  25. Blake Pollard says:

    One way to look at global warming is as an opportunity to observe a single output of a complex system when you start turning the knobs on the parameters slightly faster than the system has been used to.

  26. Andrew Robinson says:

    I would like someone to do the math and show how: (1) at the height of the last glaciation, CO2 levels were at 180ppm and the avg global temp was 10C lower than today’s, (2) how tacking on an additional 100ppm to that 180ppm results in a whopping 10C increase, yet (3) tacking on yet another 100ppm to that 280ppm resulted in a measly 0.5C increase in global avg temps instead of another 10C? Another way of looking at this is why we would ever need to fear an additional 100ppm increase in CO2 in the next 100 years when we have gone through a 100ppm increase in the last 100 years yet avg global temps have only risen a mere 0.5C?

    I would also like someone to explain why all the “unprecedented” and “record breaking” ice has melted in Greenland, yet the Viking settlements that were once ice-free during the Medieval Warming period (950-1250), are still frozen solid after the Little Ice Age (1350-1850) occurred? Obviously we have broken this ice melt record before in recent history with no ill consequences whatsoever.

    I would like someone to explain how no one is certain how the current multiple cycles of glaciation are caused, yet so many scientists are absolutely certain that those unknown cycles have currently ceased due to the influence of man? I have seen the lame guesses of how variations in orbital cycles could cause glaciations, but those particular orbital variations have been around much longer (50my) than the current Ice Age (6my).

    According to popular opinion, ALL or almost all of the current warming trend is due to oh so powerful men and their wonderful machines. So if man didn’t exist, neither would the current warming trend? If man didn’t exist, we would still be in the throes of the Little Ice Age, forever and ever? Nothing ever changes of it’s own accord?

    Whatever happened to real science? Whatever happened to the separation of science from unscientific influence of money and politics? I guess they don’t make scientists like they used to. :)

    • Frederik De Roo says:

      yet another 100ppm to that 280ppm resulted in a measly 0.5C increase in global avg temps instead of another 10C

      I haven’t checked your numbers (references/links would be nice) but in any case if you do the math/radiation physics the relation between tenperature rise and carbon dioxide concentration can be shown to be logarithmic, not linear, so I’m not sure which point you want to make here…

      (In the presence of earth system feedback processes the derivation will of course become more complicated and will only be valid insofar the feedback processes are correctly accounted for)

      I would like someone to do the math

      I think it’s better if you do the math yourself. It’s more insightful and I’m not sure if you would really trust the result if someone else does the math for you instead.

  27. Notable is the lack of any expert on economists on the panel. Yes, there’s a political scientist, but that’s a different beast.

    The point of climate change is human misery and suffering, which we currently measure in mostly economic terms. So, we have models that predict meters of sea-level rise, but I can’t say I’ve seen any estimates of economic impact. Yes, if Bangladesh goes under-water, there will be war; the political scientist can tell you that.

    But what about tedious, mundane things: loss of fisheries, disruption to farming (e.g see Australia in recent decades) Water scarcity issues in American southwest, and the economic impact of that.

    Yes, all this can be hotly debated, and economists are often woefully wrong; but they do know the sizes of things, measured in money — no one else does. This is the background needed for discussing “global economic collapse”.

    I doubt you’re able to play economist-and-mathematician; but who can?

  28. domenico says:

    I am thinking that climate change is that is a problem of only a political part, and this is not true.
    The governments changes, and the problem remains.
    The view of the people is that the climate change is a political left problem, that give more taxes and constraints, so that the persons are less free.
    The occidental countries depend on other countries for energy source: in these countries the sun energy was trasformed in energy source (oil, gas, coal).
    I think that in some years the performance of the solar, and wind, domestic plants can give energy for drive a car, or for domestic use, or for industrial use, without cost: no tax to the country (I produce, I use); there is a complete freedom, that is a political right fight, but also a fight of hippies.
    We can start before of others countries in the technological research to obtain free energy (solar energy converted in winds, tides,organic carbon,biocarburant) for all (low cost and without taxes), and I think this is inevitable, and this can be only slowed politically.

  29. This will be the first talk at the Interdisciplinary Climate Change Workshop at the Balsillie School of International Affairs, so I wanted to set the stage with a broad perspective…

  30. Here are the slides for my second talk in the Interdisciplinary Climate Change Workshop at the Balsillie School of International Affairs…

  31. There were many interesting talks at the Interdisciplinary Climate Change Workshop last week—too many for me to describe them all in detail. But I really must describe the one by Radoslav Dimitrov.

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