Lotka-Volterra predator-prey system

The Lotka-Volterra equations, which describe a predator-prey system, must be one of the more famous dynamic systems. There are many generalizations and applications outside of biology.

Wikipedia has a nice article, which I used as the basis for this simple model.

Continue reading “Lotka-Volterra predator-prey system”

Et tu, EJ?

I’m not a cap & trade fan, but I find it rather bizarre that the most successful opposition to California’s AB32 legislation comes from the environmental justice (EJ) movement, on the grounds that cap & trade might make emissions go up in areas that are already disadvantaged, and that Air Resources failed to adequately consider alternatives like a carbon tax.

I think carbon taxes did get short shrift in the AB32 design. Taxes were a second-place favorite among economists in the early days, but ultimately the MAC analysis focused on cap & trade, because it provided environmental certainty needed to meet legal targets (oops), but also because it was political suicide to say “tax” out loud at the time.

While cap & trade has issues with dynamic stability, allocation wrangling and complexity, it’s hard to imagine any way that those drawbacks would change the fundamental relationship between the price signal’s effect on GHGs vs. criteria air pollutants. In fact, GHGs and other pollutant emissions are highly correlated, so it’s quite likely that cap & trade will have ancillary benefits from other pollutant reductions.

To get specific, think of large point sources like refineries and power plants. For the EJ argument to make sense, you’d have to think that emitters would somehow meet their greenhouse compliance obligations by increasing their emissions of nastier things, or at least concentrating them all at a few facilities in disadvantaged areas. (An analogy might be removing catalytic converters from cars to increase efficiency.) But this can’t really happen, because the air quality permitting process is not superseded by the cap & trade system. In the long run, it’s also inconceivable that it could occur, because there’s no way you could meet compliance obligations for deep cuts by increasing emissions. A California with 80% cuts by 2050 isn’t going to have 18 refineries, and therefore it’s not going to emit as much.

The ARB concludes as much in a supplement to the AB32 scoping plan, released yesterday. It considers alternatives to cap & trade. There’s some nifty stuff in the analysis, including a table of existing emissions taxes (page 89).

It seems that to some extent ARB has tilted the playing field a bit by evaluating a dumb tax, i.e. one that doesn’t adapt its price level to meet environmental objectives without legislative intervention, and heightening leakage concerns that strike me as equally applicable to cap & trade. But they do raise legitimate legal concerns – a tax is not a legal option for ARB without a vote of the legislature, which would likely fail because it requires a supermajority, and tax-equivalent fees are a dubious proposition.

If there’s no Plan B alternative to cap and trade, I wonder what the EJ opposition was after? Surely failure to address emissions is not compatible with a broad notion of justice.

Hand over your cell phones

Adam Frank @NPR says, “Science Deniers: Hand Over Your Cellphones!”

I’m sympathetic to the notion that attitudes toward science are often a matter of ideological convenience rather than skeptical reasoning. However, we don’t have a cell phone denial problem. Why? I think it helps to identify the contributing factors in circumstances in which denial occurs:

  • Non-experimental science (reliance on observations of natural experiments; no controls or randomized assignment)
  • Infrequent replication (few examples within the experience of an individual or community)
  • High noise (more specifically, low signal-to-noise ratio)
  • Complexity (nonlinearity, integrations or long delays between cause and effect, multiple agents, emergent phenomena)
  • “Unsalience” (you can’t touch, taste, see, hear, or smell the variables in question)
  • Cost (there’s some social or economic penalty  imposed by the policy implications of the theory)
  • Commons (the risk of being wrong accrues to society more than the individual)

It’s easy to believe in radio waves used by cell phones, or general relativity corrected for by GPS, because their only problematic feature is invisibility. Calling grandma is a pretty compelling experiment, which one can repeat as often as needed to dispel any doubts about those mysterious electromagnetic waves.

At one time, the debate over the structure of the solar system was subject to these problems. There was a big social cost to believing the heliocentric model (the Inquisition), and little practical benefit to being right. Theory relied on observations that were imprecise and not salient to the casual observer. Now that we have low-noise observations, replicated experiments (space probe launches), and so on, there aren’t too many geocentrists around.

Climate, on the other hand, has all of these problems. Of particular importance, the commons and long-time-scale aspects of the problem shelter individuals from selection pressure against wrong beliefs.

Selection for deception?

Eric R. Weinstein on Edge’s 2011 question:

The sophisticated “scientific concept” with the greatest potential to enhance human understanding may be argued to come not from the halls of academe, but rather from the unlikely research environment of professional wrestling.

Evolutionary biologists Richard Alexander and Robert Trivers have recently emphasized that it is deception rather than information that often plays the decisive role in systems of selective pressures. Yet most of our thinking continues to treat deception as something of a perturbation on the exchange of pure information, leaving us unprepared to contemplate a world in which fakery may reliably crowd out the genuine. In particular, humanity’s future selective pressures appear likely to remain tied to economic theory which currently uses as its central construct a market model based on assumptions of perfect information.

If we are to take selection more seriously within humans, we may fairly ask what rigorous system would be capable of tying together an altered reality of layered falsehoods in which absolutely nothing can be assumed to be as it appears. Such a system, in continuous development for more than a century, is known to exist and now supports an intricate multi-billion dollar business empire of pure hokum. It is known to wrestling’s insiders as “Kayfabe”.

Were Kayfabe to become part of our toolkit for the twenty-first century, we would undoubtedly have an easier time understanding a world in which investigative journalism seems to have vanished and bitter corporate rivals cooperate on everything from joint ventures to lobbying efforts. Perhaps confusing battles between “freshwater” Chicago macro economists and Ivy league “Saltwater” theorists could be best understood as happening within a single “orthodox promotion” given that both groups suffered no injury from failing (equally) to predict the recent financial crisis. …

Reasoning was not designed to pursue the truth

Uh oh:

Reasoning is generally seen as a means to improve knowledge and make better decisions. However, much evidence shows that reasoning often leads to epistemic distortions and poor decisions. This suggests that the function of reasoning should be rethought. Our hypothesis is that the function of reasoning is argumentative. It is to devise and evaluate arguments intended to persuade. Reasoning so conceived is adaptive given the exceptional dependence of humans on communication and their vulnerability to misinformation. A wide range of evidence in the psychology of reasoning and decision making can be reinterpreted and better explained in the light of this hypothesis. Poor performance in standard reasoning tasks is explained by the lack of argumentative context. When the same problems are placed in a proper argumentative setting, people turn out to be skilled arguers. Skilled arguers, however, are not after the truth but after arguments supporting their views. This explains the notorious confirmation bias. This bias is apparent not only when people are actually arguing but also when they are reasoning proactively from the perspective of having to defend their opinions. Reasoning so motivated can distort evaluations and attitudes and allow erroneous beliefs to persist. Proactively used reasoning also favors decisions that are easy to justify but not necessarily better. In all these instances traditionally described as failures or flaws, reasoning does exactly what can be expected of an argumentative device: Look for arguments that support a given conclusion, and, ceteris paribus, favor conclusions for which arguments can be found. – Mercier & Sperber via Edge.org, which has a video conversation with coauthor Mercier.

This makes sense to me, but I think it can’t be the whole story. There must be at least a little evolutionary advantage to an ability to predict the consequences of one’s actions. The fact that it appears to be dominated by confirmation bias and other pathologies may be indicative of how much we are social animals, and how long we’ve been that way.

It’s easy to see why this might occur by looking at the modern evolutionary landscape for ideas. There’s immediate punishment for touching a hot stove, but for any complex system, attribution is difficult. It’s easy to see how the immediate rewards from telling your fellow tribesmen crazy things might exceed the delayed and distant rewards of actually being right. In addition, wherever there are stocks of resources lying about, there are strong incentives to succeed by appropriation rather than creation. If you’re really clever with your argumentation, you can even make appropriation resemble creation.

The solution is to use our big brains to raise the bar, by making better use of models and other tools for analysis of and communication about complex systems.

Nothing that you will learn in the course of your studies will be of the slightest possible use to you in after life, save only this, that if you work hard and intelligently you should be able to detect when a man is talking rot, and that, in my view, is the main, if not the sole, purpose of education. – John Alexander Smith, Oxford, 1914

So far, though, models seem to be serving argumentation as much as reasoning. Are we stuck with that?

Who moved my eigenvalues?

Change management is one of the great challenges in modeling projects. I don’t mean this in the usual sense of getting people to change on the basis of model results. That’s always a challenge, but there’s another.

Over the course of a project, the numerical results and maybe even the policy conclusions given by a model are going to change. This is how we learn from models. If the results don’t change, either we knew the answer from the outset (a perception that should raise lots of red flags), or the model isn’t improving.

The problem is that model consumers are likely to get anchored to the preliminary results of the work, and resist change when it arrives later in the form of graphs that look different or insights that contradict early, tentative conclusions.

Fortunately, there are remedies:

  • Start with the assumption that the model and the data are wrong, and to some extent will always remain so.
  • Recognize that the modeler is not the font of all wisdom.
  • Emphasize extreme conditions tests and reality checks throughout the modeling process, not just at the end, so bugs don’t get baked in while insights remain hidden.
  • Do lots of sensitivity analysis to determine the circumstances under which insights are valid.
  • Keep the model simpler than you think it needs to be, so that you have some hope of understanding it, and time for reflecting on behavior and communicating results.
  • Involve a broad team of model consumers, and set appropriate expectations about what the model will be and do from the start.

Vonnegut does the reference modes of stories

Via NPR,

All of us, even if we have no knack for science, look at the weather, at our children, at our markets, at the sky, and we see rhythms and patterns that seem to repeat, that give us the ability to predict. …

Do any of us live beyond pattern? …

I don’t think so. Artists may be, oddly, the most pattern-aware. Case in point: The totally unpredictable, one-of-a-kind novelist Kurt Vonnegut … once gave a lecture in which he presented — in graphic form — the basic plots of all the world’s great stories. Every story you’ve ever heard, he said, are reflections of a few, classic story shapes. They are so elementary, he said, he could draw them on an X/Y axis.

Systems thinkers, watch for:

  • one big reference mode diagram
  • quantification without measurement
  • a discrete event, modeled with finite slope

Wedge furor

Socolow is quoted in Nat Geo as claiming the stabilization wedges were a mistake,

“With some help from wedges, the world decided that dealing with global warming wasn’t impossible, so it must be easy,” Socolow says.  “There was a whole lot of simplification, that this is no big deal.”

Pielke quotes & gloats:

Socolow’s strong rebuke of the misuse of his work is a welcome contribution and, perhaps optimistically, marks a positive step forward in the climate debate.

Romm refutes,

I spoke to Socolow today at length, and he stands behind every word of that — including the carefully-worded title.  Indeed, if Socolow were king, he told me, he’d start deploying some 8 wedges immediately. A wedge is a strategy and/or technology that over a period of a few decades ultimately reduces projected global carbon emissions by one billion metric tons per year (see Princeton website here). Socolow told me we “need a rising CO2 price” that gets to a serious level in 10 years.  What is serious?   “$50 to $100 a ton of CO2.”

Revkin weighs in with a broader view, but the tone is a bit Pielkeish,

From the get-go, I worried about the gushy nature of the word “solving,” particularly given that there was then, and remains, no way to solve the climate problem by 2050.

David Roberts wonders what the heck Socolow is thinking.

Who’s right? I think it’s best in Socolow’s own words (posted by Revkin):

1. Look closely at what is in quotes, which generally comes from my slides, and what is not in quotes. What is not in quotes is just enough “off” in several places to result in my messages being misconstrued. I have given a similar talk about ten times, starting in December 2010, and this is the first time that I am aware of that anyone in the audience so misunderstood me. I see three places where what is being attributed to me is “off.”

a. “It was a mistake, he now says.” Steve Pacala’s and my wedges paper was not a mistake. It made a useful contribution to the conversation of the day. Recall that we wrote it at a time when the dominant message from the Bush Administration was that there were no available tools to deal adequately with climate change. I have repeated maybe a thousand times what I heard Spencer Abraham, Secretary of Energy, say to a large audience in Alexandria. Virginia, early in 2004. Paraphrasing, “it will take a discovery akin to the discovery of electricity” to deal with climate change. Our paper said we had the tools to get started, indeed the tools to “solve the climate problem for the next 50 years,” which our paper defined as achieving emissions 50 years from now no greater than today. I felt then and feel now that this is the right target for a world effort. I don’t disown any aspect of the wedges paper.

b. “The wedges paper made people relax.” I do not recognize this thought. My point is that the wedges people made some people conclude, not surprisingly, that if we could achieve X, we could surely achieve more than X. Specifically, in language developed after our paper, the path we laid out (constant emissions for 50 years, emissions at stabilization levels after a second 50 years) was associated with “3 degrees,” and there was broad commitment to “2 degrees,” which was identified with an emissions rate of only half the current one in 50 years. In language that may be excessively colorful, I called this being “outflanked.” But no one that I know of became relaxed when they absorbed the wedges message.

c. “Well-­?intentioned groups misused the wedges theory.” I don’t recognize this thought. I myself contributed the Figure that accompanied Bill McKibben’s article in National Geographic that showed 12 wedges (seven wedges had grown to eight to keep emissions level, because of emissions growth post-­?2006 and the final four wedges drove emissions to half their current levels), to enlist the wedges image on behalf of a discussion of a two-­?degree future. I am not aware of anyone misusing the theory.

2. I did say “The job went from impossible to easy.” I said (on the same slide) that “psychologists are not surprised,” invoking cognitive dissonance. All of us are more comfortable with believing that any given job is impossible or easy than hard. I then go on to say that the job is hard. I think almost everyone knows that. Every wedge was and is a monumental undertaking. The political discourse tends not to go there.

3. I did say that there was and still is a widely held belief that the entire job of dealing with climate change over the next 50 years can be accomplished with energy efficiency and renewables. I don’t share this belief. The fossil fuel industries are formidable competitors. One of the points of Steve’s and my wedges paper was that we would need contributions from many of the available option. Our paper was a call for dialog among antagonists. We specifically identified CO2 capture and storage as a central element in climate strategy, in large part because it represents a way of aligning the interests of the fossil fuel industries with the objective of climate change.

It is distressing to see so much animus among people who have common goals. The message of Steve’s and my wedges paper was, above all, ecumenical.

My take? It’s rather pointless to argue the merits of 7 or 14 or 25 wedges. We don’t really know the answer in any detail. Do a little, learn, do some more. Socolow’s $50 to $100 a ton would be a good start.

this
three 

a. “It
It
time
available
thousand
audience
akin
the
tools
to
get
started,
indeed
the
tools
to
“solve
the
climate
problem
for
the
next
50

years,”
than
disown
any
aspect
of
the
wedges
paper.

b. “The
wedges
paper
made
people
relax.”
I
do
not
recognize
this
thought.
My
point
is
that

the
wedges
people
made
some
people
conclude,
not
surprisingly,
that
if
we
could

achieve
after
our
paper,
the
path
we
laid
out
(constant
emissions
for
50
years,
emissions
at

stabilization
was
only
half
the
current
one
in
50
years.
In
language
that
may
be
excessively
colorful,
I

called
this
being
“outflanked.”
But
no
one
that
I
know
of
became
relaxed
when
they

absorbed
the
wedges
message.

c.
“Well-­?intentioned
myself
contributed
the
Figure
that
accompanied
Bill
McKibben’s
article
in
National

Geographic
emissions
emissions
discussion

Bigfoot II

I just rediscovered the Carnegie Mellon EIO-LCA tool, an online model for input-output lifecycle analysis. I ran it for the “Electronic computer manufacturing” sector to see how the results compare with Apple’s lifecycle analysis of my new MacBook.

The result: 284 tons CO2eq per million dollars of output. That translates to 340 kg for a $1200 computer. This is almost the same as Apple’s number, except that the Apple figure includes lifecycle emissions from use, for about a third of the total, so Apple’s manufacturing emissions are about a third lower than the generic computer sector in the EIO-LCA tool.

Directionally, it’s interesting that Apple’s estimate (presumably a process-based accounting) is lower, given that manufacturing happens in China, where electricity and GDP are both carbon-intensive on average. I wouldn’t read too much into the differences without digging much deeper though.