## The Mathematics of Planet Earth

Here’s a public lecture I gave yesterday, via videoconferencing, at the 55th annual meeting of the South African Mathematical Society:

Abstract: The International Mathematical Union has declared 2013 to be the year of The Mathematics of Planet Earth. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics—and be affected by it—just as dramatically as the agricultural revolution or industrial revolution. We cannot know for sure what the effect will be, but we can already make some guesses.

To watch the talk, click on the video above. To see slides of the talk, click here. To see the source of any piece of information in these slides, just click on it!

My host Bruce Bartlett, an expert on topological quantum field theory, was crucial in planning the event. He was the one who edited the video, and put it on YouTube. He also made this cute poster:

I was planning to fly there using my superpowers to avoid taking a plane and burning a ton of carbon. But it was early in the morning and I was feeling a bit tired, so I used Skype.

By the way: if you’re interested in science, energy and the environment, check out the Azimuth Project, which is a collaboration to create a focal point for scientists and engineers interested in saving the planet. We’ve got some interesting projects going. If you join the Azimuth Forum, you can talk to us, learn more, and help out as much or as little as you want. The only hard part about joining the Azimuth Forum is reading the instructions well enough that you choose your whole real name, with spaces between words, as your username.

### 27 Responses to The Mathematics of Planet Earth

1. Tobias Fritz says:

A visionary talk!

The other day a store clerk here in Waterloo told me that, paraphrasing, “winters have become much milder and more bearable”. I wonder whether she realized that this change is just the beginning and that it’s far from over.

A related issue that bugs me is that most popular accounts of climate change projections talk predominantly about the year 2100. Can we really expect the warming to stop then? For concreteness, let’s say I’m talking about a scenario in which we stop using fossil fuels by 2050 or so. Then can we expect (temporary) equilibrium to be reached by 2100?

• John Baez says:

I’m glad you liked my talk! The compliment “visionary” is the most flattering possible, because indeed I’m trying to envision the future of mathematics as affected by the global transformation that’s starting now. I hope that by doing this, we can see there can be more to global warming than just ‘doom and gloom’. We need to see the potentially positive side of this transformation to mobilize enough energy to deal with it in the ways it calls for.

Can we really expect the warming to stop then?

No, of course not—especially not if we keep going as we are now. I urge you to look at the graph that was discussed in this comment:

The reason for picking a cutoff like 2100 is that projections get less and less accurate as we go further and further into the future, and most people get less and less interested in them.

• Tobias Fritz says:

I urge you to look at the graph at the bottom of this comment!

That looks pretty scary! How is the dark red line even possible, given that we have probably passed peak oil and are not far away from peak coal? Where would all the carbon come from?

The reason for picking a cutoff like 2100 is that projections get less and less accurate as we go further and further into the future, and most people get less and less interested in them.

Ok, that’s what I figured. I think that this reason should be made more explicit in popular accounts of climate science, for otherwise “2100” may sound like the magic number after which no further change is expected to happen.

• Tobias Fritz says:

Addendum: it seems reasonable to assume that at the point of peak production, the amount of resources left should be equal in order of magnitude to the amount of resources already spent. However, the area under the dark red graph is way larger than the area under the black graph!

• John Baez says:

Tobias wrote:

That looks pretty scary! How is the dark red line even possible, given that we have probably passed peak oil and are not far away from peak coal? Where would all the carbon come from?

Now that I look into it, that’s a great question!

Currently humanity has emitted about 0.56 trillion tonnes of carbon, and people are wringing their hands about the trillionth tonne, with some estimating it will be burnt by around 2043.

The graph we’re talking about is based on data from William Nordhaus:

• William Nordhaus, The challenge of global warming: economic models and environmental policy, Technical report, accessed May 2, 2007, model version: DICE-2007.delta.v7.

• William D. Nordhaus, A Question of Balance: Weighing the Options on Global Warming Policies, Yale University Press, New Haven, 2008.

On page 127 of A Question of Balance, Nordhaus estimates that a total of 6±1.2 trillion tonnes of carbon are available to be burnt.

However, environmentalist Bill McKibben writes:

Scientists estimate that humans can pour roughly 565 more gigatons of carbon dioxide into the atmosphere by midcentury and still have some reasonable hope of staying below two degrees. (“Reasonable,” in this case, means four chances in five, or somewhat worse odds than playing Russian roulette with a six-shooter.)

[….]

#### The Third Number: 2,795 Gigatons

This number is the scariest of all – one that, for the first time, meshes the political and scientific dimensions of our dilemma. It was highlighted last summer by the Carbon Tracker Initiative, a team of London financial analysts and environmentalists who published a report in an effort to educate investors about the possible risks that climate change poses to their stock portfolios. The number describes the amount of carbon already contained in the proven coal and oil and gas reserves of the fossil-fuel companies, and the countries (think Venezuela or Kuwait) that act like fossil-fuel companies. In short, it’s the fossil fuel we’re currently planning to burn. And the key point is that this new number – 2,795 – is higher than 565. Five times higher.

The Carbon Tracker Initiative – led by James Leaton, an environmentalist who served as an adviser at the accounting giant PricewaterhouseCoopers – combed through proprietary databases to figure out how much oil, gas and coal the world’s major energy companies hold in reserve. The numbers aren’t perfect – they don’t fully reflect the recent surge in unconventional energy sources like shale gas, and they don’t accurately reflect coal reserves, which are subject to less stringent reporting requirements than oil and gas. But for the biggest companies, the figures are quite exact: If you burned everything in the inventories of Russia’s Lukoil and America’s ExxonMobil, for instance, which lead the list of oil and gas companies, each would release more than 40 gigatons of carbon dioxide into the atmosphere.

Which is exactly why this new number, 2,795 gigatons, is such a big deal. Think of two degrees Celsius as the legal drinking limit – equivalent to the 0.08 blood-alcohol level below which you might get away with driving home. The 565 gigatons is how many drinks you could have and still stay below that limit – the six beers, say, you might consume in an evening. And the 2,795 gigatons? That’s the three 12-packs the fossil-fuel industry has on the table, already opened and ready to pour.

That’s scary.

But notice, this is 2,795 gigatons of carbon dioxide, which we must divide by 3.666… to get the amount of carbon. So the Carbon Tracker initiative is saying we have the potential to emit just 0.76 gigatonnes more carbon. This is a lot less than Nordhaus’ estimate of about 6 gigatonnes.

So, I conclude that either I am very confused, or someone is very confused, or everyone is very confused about how much carbon we have left to burn.

(There’s also carbon emissions due to cement and changes in land use, but these can’t possibly explain such a vast discrepancy. There’s also a difference between tons and tonnes, but again, it’s nowhere near enough to explain the vast discrepancy!)

• Nathan Urban says:

I am not an expert on fossil energy, but let me point out a semantic issue.

The “2,795 gigatons” figure (analyzed here) refers to proven reserves. “Proven reserves” refer to sources that are recoverable from known reservoirs under current economic and technological conditions. That is, they’re reserves that we know about with reasonable certainty and are currently possible and profitable to exploit.

By contrast, the ~5000 gigaton worst-case figure that economists like Nordhaus use refers to estimates of all the fossil carbon, including “unconventional” sources like oil sands and shales (which actually are already being exploited to some degree), and including some more speculative estimates of “unknown” reserves. These scenarios assume that if energy demand is high enough, and technology progresses far enough, all of this carbon will eventually be exploited, even if it’s more expensive and difficult to do so than it is now. (In other words, our “proven reserves” expand with demand and technological progress.) I haven’t really dug deeply into where that figure comes from in the first place, though.

2. […] John Baez alludes to this in his very nice talk The Mathematics of Planet Earth, at his new blog […]

• John, you probably already know this, but AIMS is a place where researchers like yourself go and give three-weeks courses to students from all over Africa. (I worked there as teaching assistant in 2007-2008.) It’s a great teaching experience, one that makes you feel you’re really making a difference. I’d love to learn some day that AIMS students have got the chance to learn from you!

• John Baez says:

That would be really cool. I am trying to avoid unnecessary plane trips, but if I can find a geodesic between Riverside and Singapore that goes through South Africa, and arrange to spend three weeks there sometime en route to my summer job, it would be a fascinating thing to do.

• Unfortunately I don’t think any such geodesic exists! I know that AIMS will be happy to have you over. But it was great to arrange this one public lecture which linking John and AIMS in some small way.

3. Great talk John…great job.

• John Baez says:

Thanks! Are you the same Heather I always talk to, whose last name starts with V? If so, you’re posting under a slightly different address.

4. Let me add some virtual applause:

knock … knock … knock …

5. … and a question: Under the assumption that the Azimuth project has some impact. Aren’t you then hitting the Object-subject problem (cf.http://en.wikipedia.org/wiki/Subject%E2%80%93object_problem)?

I mean, you either have to assume that the the project has no influence on the object (which makes it obsolete) or to estimate the influence of your own project to make correct predictions.

We have no mathematics to deal with such situations and it is widely believed that there is no science without a somewhat strict object – subject distinction (e.g. economists advising goverments $\not=$ science).

Once you give that up you are in a very circular terrain. Maybe that is the ‘new’ mathematics you are looking for.

• John Baez says:

Glad to see you here again, Uwe! And I’m glad you enjoyed the talk!

When it comes to environmental problems, I’m less interested in predicting the future than influencing it in ways I like. So, it’s fine if the Azimuth Project makes predictions that turn out to be inaccurate because the Azimuth Project makes the future better than expected! But in fact our main thrust so far seems to be not predicting anything, but rather educating people, inspiring people, and coming up with new math.

I am also more interested in creating the math of the future than predicting what the math of the future will be. But I don’t mind predicting it and then doing things that make those predictions come true.

6. I hope someone out there enjoyed the audio clip I put in by Vusi Mahlesela, taken from when he performed live at AIMS at the launch of the Next Einstein Initiative:

Quiz question: What famous 60’s era folk-song, has exactly the same tune as the two opening lines of the Siswati harvest-time song hummed by Vusi?

• John Baez says:

No idea! Did my cousin sing it?

• Todd Trimble says:

Well, by no means does it have exactly the same tune, but the first few bars as hummed did remind me of “Blowin’ in the Wind”, most famously sung by Bob Dylan but also covered by Joan Baez.

• Todd Trimble says:

Okay, I might know the answer now, although I didn’t really know the song and had to “cheat” to find out. (I thought I was reasonably familiar with many folk songs from that era, but maybe not.) Could it be (rot 13) “Jr Funyy Birepbzr”?

• Gosh, I never heard of that one. The song I was looking for was “We shall overcome”. It has exactly the same tune as the first two lines of the song Vusi hums, do you agree? Quite bizarre, since I originally had Joan Baez down as the soundtrack, then I replaced her with Vusi, then I realized that, bizarrely, the songs have the same tune, even though they come from completely different times and cultures!

7. Bruce, Todd encoded his answer with ROT13 to prevent other people getting the answer before they’d had chance to guess. That’s why you’d never heard of that song before.

I have to say that I did wonder if it was actually you humming the tune at the beginning of John’s video.

• Oh – that was really silly of me. Apologies, folks.

• John Baez says:

Ah yes, I remember my cousin and a huge crowd singing:

Junior Funny Birepbzr
Junior Funny Birepbzr
Junior Funny Birepbzr someday!

• Todd Trimble says:

Dammit, now I have Junior Funny Birepbzr stuck in my head!