Letter from Middletown

I'm in Middletown, CT, this evening having just given the mathematics department colloquium at Wesleyan University.

Wesleyan is a medium sized liberal arts college which supports a PhD-granting science and math program.  My invitation was an unusual one.  It said, "We'd like to hear about your research in geometry and we'd also like to hear about your ideas on sustainability education." So I tried to come up with a one-hour talk that would combine both themes into some kind of conceptual unity.  In the end I just went with a one-word title: Growth.

I started off talking about the old chessboard legend: you know, the one where the king promises to reward the inventor of chess by granting him whatever he may desire, and the savvy inventor asks with pretended modesty for just one grain of rice on the first square of the chessboard, two on the second, four on the third, and so on.  That and so on conceals the terrifying power of exponential growth which by the 64th square would demand a rice mountain five miles high - half a trillion tons of rice or about 1000 times the amount produced each year everywhere on earth.

I went on to consider the superficial geometry of exponential growth: the fact that there is no "deep inside"   an exponentially growing system, it is all "on the surface", and the expression of this through uniformly bounded homology and Ponzi schemes.  I talked about some research mathematics here, with a bit of discussion of the index theorems that showed up in my thesis.   But then I veered back to talk about growth in the usual "economic" sense, and my perception that mathematical educators owe it to our students to give them the conceptual tools to consider whether or in what sense growth can go on for ever, and what (if anything) might come afterwards.

I've never tried to give a talk like this before.  I felt that it went pretty well, and I made some good connections; I need to let it settle though.  Meanwhile here is a link to the slides.  And if any other math department would like to invite me to give some version of this talk, I'm happy to do so!

Photo of Wesleyan University by Flickr user AmandaB3, licensed under Creative Commons

Penn State Zero

Jon Brockopp and Sylvia Neely from PAIPL have gotten involved in a new initiative - Penn State Zero.

Reposting from the blog "Spring Creek Homesteading":

A group of five faculty members including Brockopp (History and Religious Studies), Neely (History, retired), Ray Najjar (Meteorology), Andy Lau (Engineering Design) and Leland Glenna (Rural Sociology)  began meeting monthly in October 2013 to discuss two key questions:

1. “Why isn’t Penn State’s president a signatory to the American College & University Presidents’ Climate Commitment?”
2. “How can our small committee get more faculty and administrators interested in and educated about climate change so that they can influence the president to sign on?”

Read the rest here

Book Review: "Atomic Accidents"

Amazon.com: Atomic Accidents: A History of Nuclear Meltdowns and Disasters: From the Ozark Mountains to Fukushima eBook: James Mahaffey: Books via kwout

Points of Inflection has been silent for nearly two months.

I'm sorry about that.  It's been a helpful discipline to try to blog here regularly, but several unpredictable things have combined to consume a bit too much of my time recently.  I'm trying now to get back to a more regular (but probably still slow) posting schedule.

I recently read the book Atomic Accidents by James Mahaffey.  Mahaffey was a senior researcher at Georgia Tech and his book is a clear-sighted, technically detailed and yet also readable and witty account of the quest to obtain safe, clean energy from nuclear fission and the numerous ways in which safety mechanisms carefully devised by human beings have been circumvented, undermined or just messed up by other human beings (or sometimes even the same ones); quite often with fatal consequences.  From the disasters of the radium-dial factories, through the Manhattan Project and the early attempts at civilian nuclear power, to the headline-grabbing accidents at Chernobyl and Fukushima, this book covers a lot of historical ground.  Many accidents are described in extensive technical detail - though nuclear processes have many frightening features, Mahaffy believes that the instinct for secrecy, arising from military nuclear programs, has not helped teh civilian nuclear industry, and that more information may reduce unfounded anxiety.  I wonder whether he is right?

Because, for all his encyclopedic knowledge of nuclear accidents and foolishnesses, Mahaffy is a (carefully qualified) proponent of nuclear energy.  His thoughts on this can be found throughout the book, especially in its final chapter, Caught in the Rickover Trap.  Admiral Hyman Rickover devised the propulsion system for US nuclear submarines and his water-cooled reactor design, scaled up by two orders of magnitude or so, is the basis for most nuclear power stations today.  "There have been trillions of problem-free watt-hours generated by scaled-up Rickover plants", writes Mahaffy, "but there may be a problem area that was not evident when submarine reactors were tiny 12-megawatt machines but that was revealed when the Rickover model was enlarged multiple times over for industrial use.  The reactor core, the uranium fuel pellets lined up in zirconium tubes and neatly separated from each other, is terribly sensitive  for such an otherwise robust machine... There have been many engineering fixes and modifications to correct these problems, but, ironically, these fixes can present new issues as they are complex add-ons, cluttering up an otherwise simple design... most of the plumbing in a nuclear plant has nothing to do with generating electricity.  It is part of the fix." 

The message of this final chapter is that the sheer bigness of the nuclear project may have led the nuclear industry to focus prematurely on one apparently effective design.  Perhaps there are other possibilities?  Mahaffy can tell us about the exotic reactor designs of the 1950s and 1960s (some arising from the crazy project to build a nuclear airplane).  Could these be revived as an alternative?  Some of them indeed do form the basis for the futuristic Generation IV nuclear plant proposals.   Some could perhaps be made much smaller - a large power plant would consist of many identical "modules" rather than one giant reactor.  Indeed, the message I took away from this book is that the major issues with nuclear power seem less technical than political: the size and complexity of the nuclear power process in relation to the societal "containment" within which it must necessarily operate.

Math on the Rocks

I'm giving a talk next week in Baltimore.

The occasion is an evening reception sponsored by the Association of Christians in the Mathematical Sciences, which is being held during the annual joint meeting of US mathematical societies - the biggest regularly scheduled math conference in the USA (maybe the world?).

It will be a short presentation called Math on the Rocks.  I'll talk about mathematics and climbing, and my perception of overlaps, connections and creative tensions between them.  If I manage to hit an environmental theme too, that will be pretty much the whole of this blog compressed into one half-hour talk!

If you'll be in Baltimore, you're welcome to come to the event!  There's an informal reception (with refreshments) at 5:30 on January 16th in the East/West Ballrooms of the Marriott Baltimore Inner Harbor Hotel, followed by my talk at 6:30.  After the talk, there's an opportunity for dinner: we have reserved tables of 8 at ten local restaurants, and you can arrange during the reception which group you would like to be in.

A very funny presentation of the connections between math and climbing is the article: Adams, Colin. “Into Thin Air.” Mathematical Intelligencer 22, no. 1 (2000): 21–22. I'm thinking I might start by quoting some of that article...

Are People the Problem or the Solution?

Probably both.  At any rate, that is the title of an introductory lecture on demographics from Joel Cohen of Rockefeller and Columbia universities (which I learned of from the Dot Earth blog at the New York Times).  Here's a video

And here is a link to the transcript of the lecture (for those who, like me, prefer to read rather than to watch videos).

I've referred before to the command in Genesis to "fill the earth".  Looking at a graph like this, it seems that this at least is one command that humanity has succeeded in carrying out.

So what next? Professor Cohen makes his case for studying demography as follows:

I’d encourage any freshman, sophomore, junior, senior, adult, high school student—I’m not age prejudiced—anybody who wants to do three things to consider demography.  It’s not the only field that offers these attractions but it does offer them in spades.  It’s really very attractive.  First of all, demography gives you tools and analytical perspectives to understand better the world around you.  That’s understanding.  

Secondly, it gives you equipment to solve problems mentally.  It’s mentally exciting; you really have to use your noggin, and if you’ve got one use it or lose it.  So it’s use it.  And third, it is the means to intervene more wisely and more effectively in the real world to improve the wellbeing, not only of yourself—important as that may be—but of people around you and of other species with whom we share the planet.  

So it prepares you to go out and do something that’s worth doing for a larger good than only yourself.  So there’s an old saying, “If I am not for myself who will be; but if I am only for myself what am I; and if not now, when”?  So now is the time.  Pull up your pants and get to work.

Inexhaustible

Things run out.  The oil in the ground; the food we can grow; the days of our lives.  The nature of this blog (or maybe of its author) is to focus attention on such limits.  To live wisely is to live within bounds.  "So teach us to number our days", says the psalm attributed to Moses, "that we may gain a heart of wisdom". (Psalm 90:12)

Not just our physical resources run out.  Our emotional strength, our ability to forgive, even to pity.  There are limits to all of these, perhaps closer to the surface than we realize.  In Chesterton's story The Chief Mourner of Marne, the characters claim to "forgive" a crime whose nature they do not understand.  When realization dawns on them, they swing over to the opposite side like a door slamming. "There is a limit to human charity" cries the most sympathetic of them, 'trembling all over'.

Christians (in Chesterton's story represented by Father Brown) make the outrageous claim that there is one inexhaustible force at work in the world: the love of God.  Unlike "human charity",  Love never ends. (I Cor 13:8)  Christmas is the sign and token and proclamation that this love - electing, purifying, creative - has come among us and will persist - patiently, and at great cost - in bringing to fulfillment human beings and the world in which they share.  This love will not let go.  This love will not give up.  This love will not run out.  This love will win.

So, if I speak in the tongues of scientists and activists, but have not love, I am a noisy gong or a clanging cymbal.

And if I have prophetic powers, and my climate model is more accurate than any other; and if I have faith enough for geoengineering, but have not love, I am nothing.

And if I give away all that I have, and live off the grid an an ecovillage, and return my body to the cycle of nature through cremation, but have not love, I gain nothing.

For natural resources may be exhausted; tongues will cease; as for knowledge, it too will pass away.

But love never ends. 

Photo by Flickr user Fiona Shields, licensed under Creative Commons

Recycling Heat

ReTherm™ - Get 60% Energy Savings every shower with Drain Water Heat Recovery via kwout

A lot of water flows to waste each day from the average American home. (Over 300 gallons per day according to the EPA.)  What's more, quite a bit of that water is hot. To heat a gallon of water (from domestic cold to hot temperatures) takes about 750 kilojoules of energy so 100 gallons a day of hot water represents 75 megajoules -  something like 800 watts of energy, all day, every day.

Even if cleaning and reusing the water itself might not be economic in a domestic context (and by the way, that is not so clear - especially as regards using "grey" water to flush toilets) it still makes sense to try to recover some of that heat before it goes down the drain. The most effective, but somewhat high-tech, way to do that would be to store the warm "grey" water somewhere and use it as the source for a heat pump.  However, simpler devices can be effective too. 

For instance, one can fit a shower drain with a heat exchanger like the one illustrated from ReTherm.  The idea is that the cold water supply to the shower exchanges heat with the waste water running down the drain.  The cold supply therefore arrives at the showerhead somewhat pre-warmed, and this reduces the demand on the hot water heater.

It is pretty easy to do an idealized mathematical analysis of the performance of this system.   What one finds is the following.  If a denotes the setting of the shower temperature mixer, then with the usual plumbing arrangement the showerhead temperature is

ah + (1-a)c

where h is the hot supply temperature and c the cold.  With the (idealized) heat exchanger in play this changes to

(2a-a²)h + (1-a)²c

If you know a little calculus you'll see immediately that this means the shower temperature control becomes "twice as effective" when it is at the lower end of its range.  Towards the upper end (i.e. if your shower is as hot as your hot water supply) recycling heat becomes less effective because the relative amount of cold water used is less.

Note  The ReTherm device illustrated is installed in a slightly different way than described above - it preheats the cold water supply to the hot water heater rather than the cold water supply to the shower.  Although this changes some of the details of the above analysis, the overall energy savings are the same.