The Swinomish

25 November, 2020

The Swimonish are Native Americans who live in the southeastern part of Fidalgo Island in northern Puget Sound, about 110 kilometers north of Seattle.

They’ve been doing interesting things about climate change and ecosystem restoration. So have other tribes:

• Jim Morrison, An ancient people with a modern climate plan, The New York Times, 24 November 2020.

For 10,000 years, the Swinomish tribe has fished the waters of northwestern Washington, relying on the bounty of salmon and shellfish not only as a staple of its diet but as a centerpiece of its culture. At the beginning of the fishing season, the tribe gathers on the beach for a First Salmon ceremony, a feast honoring the return of the migratory fish that binds the generations of a tribe that calls itself the People of the Salmon.

At the ceremony’s conclusion, single salmon are ferried by boat in four directions — north to Padilla Bay, east to the Skagit River, south to Skagit Bay and west to Deception Pass — and eased into the water with a prayer that they will tell other salmon how well they were treated.

In recent years, though, the tribe’s harvest, diminished by vanishing habitat and warming waters fueled by climate change, hasn’t been sufficient to feed the hundreds of people who come to pay homage to their ancestors and to the fish that sustained them.

“We don’t have that abundance anymore,” said Lorraine Loomis, an elder who has managed the tribal fishery for 40 years. “To get ceremonial fish, we buy it and freeze it.”


The tribe has responded with an ambitious, multipronged strategy to battle climate change and improve the health of the land and the water and the plants, animals and people who thrived in harmony for generations. In 2010, the Swinomish became one of the first communities to assess the problems posed by a warming planet and enact a climate action plan. An additional 50 Native American tribes have followed, creating climate strategies to protect their lands and cultures, ahead of most U.S. communities.

The Swinomish see the tasks beyond addressing shoreline risk and restoring habitats. They look at climate adaptation and resilience with the eyes of countless generations. They recognize that the endangered “first foods” — clams, oysters, elk, traditional plants and salmon — are not mere resources to be consumed. They are central to their values, beliefs and practices and, therefore, to their spiritual, cultural and community well-being.

In recent years, the tribe has fostered salmon recovery through a variety of projects. It has restored tidelands and channels, planted trees along streambeds to cool warming waters, and collaborated with farmers to increase stream setbacks to improve water quality.

Restoring salmon populations is just part of an ambitious climate action plan to blunt the effects of increased flooding, ocean acidification, rising river temperatures, more-destructive storms and habitat loss.

The Swinomish are rebuilding oyster reefs for the native Olympia oyster. They’re planning the first modern clam garden in the United States on the reservation’s tidelands, reviving an ancient practice. They’re monitoring deer and elk populations through camera traps to understand the climate change pressures and to inform hunting limits. And they have ongoing wetland restoration projects to explore preserving native plants and to help naturally manage coastal flooding.

“They’re doing really innovative climate adaptation,” said Meade Krosby, a senior scientist with the Climate Impacts Group at the University of Washington. “They were way ahead of the curve. And that really shouldn’t be surprising, because the tribes have shown tremendous leadership in climate adaptation and mitigation.”

The Tulalip tribes, neighbors to the south, are relocating nuisance beavers from urban areas to streams with salmon to improve water quality and lower the temperature, reduce sediment flowing into streams and mitigate the effects of increasingly intense storms. The Karuk tribe of Northern California has a 232-page plan that calls for prescribed burning to reduce increasing wildfires and removing dams to help decreasing salmon and eel populations.

The Confederated Salish and Kootenai tribes of Montana have a resilience plan that calls for prescribed burns and restoring whitebark pine, a key part of tribal culture. They plan to identify trees resilient to blister rust — a fungus exacerbated by climate change — collect their seeds and eventually plant 100,000 seedlings on their lands.

And in Alaska, a partnership of 11 tribes has formed to identify harmful algae blooms so that it’s clear when shellfish can be safely harvested.

Native Americans acutely feel the effects of the changing climate because they were forced onto the most vulnerable lands, places that were of little use to others, said Nikki Cooley, co-manager of the Tribes and Climate Change Program for the Institute for Tribal Environmental Professionals.

“There’s that big push to address climate change because we’re feeling the effects more so than other places,” said Cooley, 40, who grew up without electricity or running water, herding sheep in the sprawling Navajo Nation reservations of the Arizona desert.

The Tenfold Way

22 November, 2020

I now have a semiannual column in the Notices of the American Mathematical Society! I’m excited: it gives me a chance to write short explanations of cool math topics and get them read by up to 30,000 mathematicians. It’s sort of like This Week’s Finds on steroids.

Here’s the first one:

The tenfold way, Notices Amer. Math. Soc. 67 (November 2020), 1599–1601.

The tenfold way became important in physics around 2010: it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when C. T. C. Wall classified real ‘super division algebras’. He found that besides \mathbb{R}, \mathbb{C} and \mathbb{H}, which give ‘purely even’ super division algebras, there are seven more. He also showed that these ten algebras are all real or complex Clifford algebras. The eight real ones represent all eight Morita equivalence classes of real Clifford algebras, and the two complex ones do the same for the complex Clifford algebras. The tenfold way thus unites real and complex Bott periodicity.

In my article I explain what a ‘super division algebra’ is, give a quick proof that there are ten real super division algebras, and say a bit about how they show up in quantum mechanics and geometry.

For a lot more about the tenfold way, try this:

The tenfold way.

Ramanujan’s Easiest Formula

18 November, 2020

A while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once.

I picked the easiest one I could find. Hardy called it one of the “least impressive”. Still, it was pretty interesting: it turned out to be a puzzle within a puzzle. It has an easy outer layer which one can solve using standard ideas in calculus, and a tougher inner core which requires more cleverness. This inner core was cracked first by Laplace and then by Jacobi. Not being clever enough to do it myself, I read Jacobi’s two-page paper on this subject to figure out the trick. It was in Latin, and full of mistakes, but still one of the most fun papers I’ve ever read.

On Friday November 20th I’m giving a talk about this at the Whittier College Math Club, which is run by my former student Brandon Coya. Here are my slides:

Ramanujan’s easiest formula.

Here is Ramanjuan’s puzzle in the The Journal of the Indian Mathematical Society:

Octonions and the Standard Model

13 November, 2020

I avoid talking about fundamental physics or pure math here—I do that on the n-Category Café. I also avoid talking about category theory, except for its applications to electrical circuits, chemical reaction networks and the like. I discuss more ‘pure’ aspects of category theory on the n-Category Café and the Category Theory Community Server.

I’ve been fascinated by the octonions for a long time now: they’re an enigmatic link between many ‘exceptional’ structures in geometry and group theory.

• John Baez, The octonions.

There have been various attempts to use the octonions in physics. While they play a clear role in superstring theory, which is mathematically beautiful but distant from what we observe in nature, there are also some hopes that they could explain the quirky patterns in the forces and particles we actually see. I’m not extremely optimistic about these hopes, but there are some tantalizing facts here and there, so I’ve decided to write some blog articles explaining them.

I should emphasize that I’m not proposing or even advocating any theory of physics here! Instead, I’m just collecting and explaining some interesting relations between octonionic mathematics and the Standard Model. I thought about this stuff for a long time, so I wanted to write it up before I forget it all—especially some work I did with Greg Egan and John Huerta back in November 2015.

Here are the posts so far:

Octonions and the Standard Model 1. How to define octonion multiplication using complex scalars and vectors, much as quaternion multiplication can be defined using real scalars and vectors. This description requires singling out a specific unit imaginary octonion, and it shows that octonion multiplication is invariant under SU(3).

Octonions and the Standard Model 2. A more polished way to think about octonion multiplication in terms of complex scalars and vectors, and a similar-looking way to describe it using the cross product in 7 dimensions.

Octonions and the Standard Model 3. How a lepton and a quark fit together into an octonion – at least if we only consider them as representations of SU(3), the gauge group of the strong force. Proof that the symmetries of the octonions fixing an imaginary octonion form precisely the group SU(3).

Octonions and the Standard Model 4. Introducing the exceptional Jordan algebra: the 3×3 self-adjoint octonionic matrices. A result of Dubois-Violette and Todorov: the symmetries of the exceptional Jordan algebra preserving their splitting into complex scalar and vector parts and preserving a copy of the 2×2 adjoint octonionic matrices form precisely the Standard Model gauge group.

I didn’t give the proof of that result.   Instead I moved in a different direction, which should eventually loop back:

Octonions and the Standard Model 5. How to think of the 2×2 self-adjoint octonionic matrices as 10-dimensional Minkowski space, and pairs of octonions as left- or right-handed Majorana-Weyl spinors in 10 dimensional spacetime.

Octonions and the Standard Model 6.  The linear transformations of the exceptional Jordan algebra that preserve the determinant form the exceptional Lie group E6. How to compute this determinant in terms of 10-dimensional spacetime geometry: that is, scalars, vectors and left-handed spinors in 10d Minkowski spacetime.

Octonions and the Standard Model 7. How to describe the Lie group E6 using 10-dimensional spacetime geometry. This group is built from the double cover of the Lorentz group, left-handed and right-handed spinors, and scalars in 10d Minkowski spacetime.

Octonions and the Standard Model 8.  A geometrical way to see how E6 is connected to 10d spacetime, based on the octonionic projective plane.

As usual, once I start writing about something I get more interested in it. There’s a lot more left to say, and it’s a lot of fun, so there will be more posts.

US Environmental Policy (Part 2)

12 November, 2020

On his first day in office, President-elect Biden plans to have the US rejoin the Paris climate accord. He has also pledged to sign ten executive orders on his first day in office:

• Requiring aggressive methane pollution limits for new and existing oil and gas operations.

• Using the Federal government procurement system—which spends $500 billion every year—to drive towards 100% clean energy and zero-emissions vehicles.

• Ensuring that all U.S. government installations, buildings, and facilities are more efficient and climate-ready, harnessing the purchasing power and supply chains to drive innovation.

• Reducing greenhouse gas emissions from transportation—the fastest growing source of U.S. climate pollution—by preserving and implementing the existing Clean Air Act, and developing rigorous new fuel economy standards aimed at ensuring 100% of new sales for light- and medium-duty vehicles will be electrified and annual improvements for heavy duty vehicles.

• Doubling down on the liquid fuels of the future, which make agriculture a key part of the solution to climate change. Advanced biofuels are now closer than ever as we begin to build the first plants for biofuels, creating jobs and new solutions to reduce emissions in planes, ocean-going vessels, and more.

• Saving consumers money and reduce emissions through new, aggressive appliance- and building-efficiency standards.

• Committing that every federal infrastructure investment should reduce climate pollution, and require any federal permitting decision to consider the effects of greenhouse gas emissions and climate change.

• Requiring public companies to disclose climate risks and the greenhouse gas emissions in their operations and supply chains.

• Protecting biodiversity, slowing extinction rates and helping leverage natural climate solutions by conserving 30% of America’s lands and waters by 2030.

• Protecting America’s natural treasures by permanently protecting the Arctic National Wildlife Refuge and other areas impacted by President Trump’s attack on federal lands and waters, establishing national parks and monuments that reflect America’s natural heritage, banning new oil and gas permitting on public lands and waters, modifying royalties to account for climate costs, and establishing targeted programs to enhance reforestation and develop renewables on federal lands and waters with the goal of doubling offshore wind by 2030.

According to article in today’s Washington Post:

In a sign of how Biden has already elevated the issue, he discussed the topic with every European head of state with whom he spoke on Tuesday, including the leaders of Britain, France, Germany and Ireland. Biden has started frequently referring to the climate “crisis,” suggesting a heightened level of urgency.

A team of former Obama administration officials and experts have created a 300-page blueprint laying out a holistic approach to the climate while avoiding some of the pitfalls that hampered President Barack Obama, who shared some of the same goals but was unable to enact all of them. Dubbed the Climate 21 Project, it took a year and a half to develop and was delivered recently to Biden’s transition team. The document outlines how the incoming administration could restructure aspects of the government to move faster on global warming.

For more, see:

Climate 21 Project.

US Environmental Policy (Part 1)

8 November, 2020

This blog does not allow discussion of partisan politics. But I can still list some ways in which US environmental policy will change if Biden becomes president.

First and foremost, the US will rejoin the Paris Climate Agreement.

Besides leaving the Paris Climate Agreement, the Trump administration did many other things that didn’t require approval from Congress:

• Nadja Popovich, Livia Albeck-Ripka and Kendra Pierre-Louis, The Trump administration is reversing nearly 100 environmental rules. Here’s the full list, New York Times, 15 October 2020.

Here’s the list. Biden can reverse or halt all these actions without approval from Congress:

Air pollution – completed:

  1. Weakened Obama-era fuel economy and greenhouse gas standards for passenger cars and light trucks.
    E.P.A. and Transportation Department
  2. Revoked California’s ability to set stricter tailpipe emissions standards than the federal government.
  3. Withdrew the legal justification for an Obama-era rule that limited mercury emissions from coal power plants.
  4. Replaced the Obama-era Clean Power Plan, which would have set strict limits on carbon emissions from coal- and gas-fired power plants, with a new version that would let states set their own rules.
    Executive Order; E.P.A.
  5. Canceled a requirement for oil and gas companies to report methane emissions.
  6. Revised and partially repealed an Obama-era rule limiting methane emissions on public lands, including intentional venting and flaring from drilling operations. A federal court struck down the revision in July 2020, calling the Trump administration’s reasoning “wholly inadequate” and mandating enforcement of the original rule. However, the Obama-era rule was later partially struck down in a separate court case, during which the Trump administration declined to defend it.
    Interior Department
  7. Withdrew a Clinton-era rule designed to limit toxic emissions from major industrial polluters, and later proposed codifying the looser standards.
  8. Revised a program designed to safeguard communities from increases in pollution from new power plants to make it easier for facilities to avoid emissions regulations.
  9. Amended rules that govern how refineries monitor pollution in surrounding communities.
  10. Weakened an Obama-era rule meant to reduce air pollution in national parks and wilderness areas.
  11. Weakened oversight of some state plans for reducing air pollution in national parks.
  12. Relaxed air pollution regulations for a handful of plants that burn waste coal for electricity.
  13. Repealed rules meant to reduce leaking and venting of powerful greenhouse gases known as hydrofluorocarbons from large refrigeration and air conditioning systems.
  14. Directed agencies to stop using an Obama-era calculation of the social cost of carbon, which rulemakers used to estimate the long-term economic benefits of reducing carbon dioxide emissions.
    Executive Order
  15. Withdrew guidance directing federal agencies to include greenhouse gas emissions in environmental reviews. But several district courts have ruled that emissions must be included in such reviews.
    Executive Order; Council on Environmental Quality
  16. Revoked an Obama executive order that set a goal of cutting the federal government’s greenhouse gas emissions by 40 percent over 10 years.
    Executive Order
  17. Repealed a requirement that state and regional authorities track tailpipe emissions from vehicles on federal highways.
    Transportation Department
  18. Lifted a summertime ban on the use of E15, a gasoline blend made of 15 percent ethanol. (Burning gasoline with a higher concentration of ethanol in hot conditions increases smog.)
  19. Changed rules to allow states and the E.P.A. to take longer to develop and approve plans aimed at cutting methane emissions from existing landfills.
  20. Withdrew a proposed rule aimed at reducing pollutants, including air pollution, at sewage treatment plants.
  21. Relaxed some Obama-era requirements for companies to monitor and repair leaks at oil and gas facilities, including exempting certain low-production wells – a significant source of methane emissions – from the requirements altogether. (Other leak regulations were eliminated.)

Air pollution – in progress:

  1. Eliminated Obama-era methane emissions standards for oil and gas facilities and narrowed standards limiting the release of other polluting chemicals known as “volatile organic compounds” to only certain facilities. A federal court temporarily halted the rollback from going into effect after environmental groups and several states filed suit.
  2. Proposed revisions to standards for carbon dioxide emissions from new, modified and reconstructed coal power plants, eliminating Obama-era restrictions that, in effect, required them to capture and store carbon dioxide emissions.
  3. Began a review of emissions rules for power plant start-ups, shutdowns and malfunctions. One outcome of that review: In February 2020, E.P.A. reversed a requirement that Texas follow emissions rules during certain malfunction events.
  4. Proposed a rule limiting the ability of individuals and communities to challenge E.P.A.-issued pollution permits before a panel of agency judges.

Drilling and extraction – completed:

  1. Made significant cuts to the borders of two national monuments in Utah and recommended border and resource-management changes to several more.
    Presidential Proclamation; Interior Department
  2. Lifted an Obama-era freeze on new coal leases on public lands. In April 2019, a judge ruled that the Interior Department could not begin selling new leases without completing an environmental review. In February 2020, the agency published an assessment that concluded restarting federal coal leasing would have little environmental impact.
    Executive Order; Interior Department
  3. Finalized a plan to open up part of the Arctic National Wildlife Refuge in Alaska for oil and gas development, a move that overturns six decades of protections for the largest remaining stretch of wilderness in the United States.
    Congress; Interior Department
  4. Approved construction of the Dakota Access pipeline, less than a mile from the Standing Rock Sioux Reservation. (The Obama administration had halted the project, with the Army Corps of Engineers saying it would explore alternative routes.) The pipeline is embroiled in a lengthy legal battle, but has been allowed to continue operating by the Army Corps of Engineers even though a federal court reversed the Corps’ decision to allow the pipeline to run along its current path.
    Executive Order; Army
  5. Rescinded water pollution regulations for fracking on federal and Indian lands.
    Interior Department
  6. Scrapped a proposed rule that required mines to prove they could pay to clean up future pollution.
  7. Withdrew a requirement that Gulf oil rig owners prove they can cover the costs of removing rigs once they stop producing.
    Interior Department
  8. Moved the permitting process for certain projects that cross international borders, such as oil pipelines, to the office of the president from the State Department, exempting them from environmental review.
    Executive Order
  9. Changed how the Federal Energy Regulatory Commission considers the indirect effects of greenhouse gas emissions in environmental reviews of pipelines.
    Federal Energy Regulatory Commission
  10. Revoked an Obama-era executive order designed to preserve ocean, coastal and Great Lakes waters in favor of a policy focused on energy production and economic growth.
    Executive Order
  11. Loosened offshore drilling safety regulations implemented by the Obama after following the 2010 Deepwater Horizon explosion and oil spill, including reduced testing requirements for blowout prevention systems.
    Interior Department

Drilling and extraction – in progress

  1. Proposed opening most of America’s coastal waters to offshore oil and gas drilling, but delayed the plan after a federal judge in 2019 ruled that reversing a ban on drilling in the Atlantic and Arctic Oceans was unlawful. Ahead of the 2020 election, Mr. Trump announced he would exempt from drilling coastal areas around Florida, a crucial battleground state, Georgia and South Carolina.
    Interior Department
  2. Repealed an Obama-era rule governing royalties for oil, gas and coal leases on federal lands, which replaced a 1980s rule that critics said allowed companies to underpay the federal government. A federal judge struck down the Trump administration’s repeal, but another court froze the original rule pending litigation.
    Interior Department
  3. Proposed easing the approval process for oil and gas drilling in national forests by curbing the power of the Forest Service to review and approve leases, among other changes.
    Agriculture Department; Interior Department
  4. Withdrew proposed restrictions on mining in Bristol Bay, Alaska, despite concerns over environmental impacts on salmon habitat, including a prominent fishery. The U.S. Army Corps of Engineers has so far denied a permit for a proposed project, known as the Pebble Mine, noting it “could have substantial environmental impacts,” but left the door open for a revised plan.
    E.P.A.; Army
  5. Proposed revising regulations on offshore oil and gas exploration by floating vessels in the Arctic that were developed after a 2013 accident. The Interior Department previously said it was “considering full rescission or revision of this rule.”
    Executive Order; Interior Department
  6. Proposed opening more land for drilling in the Alaska National Petroleum Reserve, a vast swath of public land on the Arctic Ocean. The Obama administration had designated about half of the reserve as a conservation area.
    Interior Department
  7. Finalized a plan to allow logging and road construction in Tongass National Forest, Alaska, by exempting the area from a Clinton-era policy known as the roadless rule, which applied to much of the national forest system.
    Interior Department
  8. Approved the Keystone XL pipeline rejected by President Barack Obama, but a federal judge blocked the project from going forward without an adequate environmental review process. The Supreme Court in July 2020 upheld that ruling, further delaying construction of the pipeline.
    Executive Order; State Department
  9. Approved the use of seismic air guns for gas and oil exploration in the Atlantic Ocean. The Obama administration had denied permits for such surveys, which can kill marine life and disrupt fisheries. However, the Trump administration’s permits to allow seismic surveys expired following a protracted lawsuit, ending the possibility of seismic air gun surveys in the Atlantic in the near term. Companies would need to restart the months-long permitting process.
    National Oceanic and Atmospheric Administration

Infrastructure – completed:

  1. Weakened the National Environmental Policy Act, one of the country’s most significant environmental laws, in order to expedite the approval of public infrastructure projects, such as roads, pipelines and telecommunications networks. The new rules shorten the time frame for completing environmental studies, limit the types of projects subject to review, and no longer require federal agencies to account for a project’s cumulative effects on the environment, such as climate change.
    Council on Environmental Quality
  2. Revoked Obama-era flood standards for federal infrastructure projects that required the government to account for sea level rise and other climate change effects.
    Executive Order
  3. Relaxed the environmental review process for federal infrastructure projects.
    Executive Order
  4. Overturned an Obama-era guidance that ended U.S. government financing for new coal plants overseas except in rare circumstances.
    Executive Order; Treasury Department
  5. Revoked a directive for federal agencies to minimize impacts on water, wildlife, land and other natural resources when approving development projects.
    Executive Order
  6. Revoked an Obama executive order promoting climate resilience in the northern Bering Sea region of Alaska, which withdrew local waters from oil and gas leasing and established a tribal advisory council to consult on local environmental issues.
    Executive Order
  7. Reversed an update to the Bureau of Land Management’s public land-use planning process.
  8. Withdrew an Obama-era order to consider climate change in the management of natural resources in national parks.
    National Park Service
  9. Restricted most Interior Department environmental studies to one year in length and a maximum of 150 pages, citing a need to reduce paperwork.
    Interior Department
  10. Withdrew a number of Obama-era Interior Department climate change and conservation policies that the agency said could “burden the development or utilization of domestically produced energy resources.”
    Interior Department
  11. Eliminated the use of an Obama-era planning system designed to minimize harm from oil and gas activity on sensitive landscapes, such as national parks.
    Interior Department
  12. Withdrew Obama-era policies designed to maintain or, ideally, improve natural resources affected by federal projects.
    Interior Department

Infrastructure – in progress:

  1. Proposed plans to speed up the environmental review process for Forest Service projects.
    Agriculture Department

Animals – completed:

  1. Changed the way the Endangered Species Act is applied, making it more difficult to protect wildlife from long-term threats posed by climate change.
    Interior Department; National Oceanic and Atmospheric Administration
  2. Ended the automatic application of full protections for ‘threatened’ plants and animals, the classification one step below ‘endangered’ in the Endangered Species Act.
    Interior Department
  3. Relaxed environmental protections for salmon and smelt in California’s Central Valley in order to free up water for farmers.
    Executive Order; Interior Department
  4. Overturned a ban on the use of lead ammunition and fishing tackle on federal lands.
    Interior Department
  5. Overturned a ban on the hunting of predators in Alaskan wildlife refuges.
  6. Reversed an Obama-era rule that barred using bait, such as grease-soaked doughnuts, to lure and kill grizzly bears, among other sport hunting practices that many people consider extreme, on some public lands in Alaska.
    National Park Service; Interior Department
  7. Amended fishing regulations to loosen restrictions on the harvest of a number of species.
    National Oceanic and Atmospheric Administration
  8. Removed restrictions on commercial fishing in a protected marine preserve southeast of Cape Cod that is home to rare corals and a number of endangered sea animals. The Trump administration has suggested changing the management or size of two other marine protected areas in the Pacific Ocean.
    Executive Order; National Oceanic and Atmospheric Administration
  9. Proposed revising limits on the number of endangered marine mammals and sea turtles that can be unintentionally killed or injured with sword-fishing nets on the West Coast. (The Obama-era rules were initially withdrawn by the National Oceanic and Atmospheric Administration, but were later finalized following a court order. The agency has said it plans to revise the limits.)
    National Oceanic and Atmospheric Administration
  10. Loosened fishing restrictions intended to reduce bycatch of Atlantic Bluefin Tuna. Nonprofits have filed a lawsuit challenging the rollback.
    National Oceanic and Atmospheric Administration
  11. Overturned a ban on using parts of migratory birds in handicrafts made by Alaskan Natives.
    Interior Department

Animals – in progress:

  1. Proposed weakening critical habitat protections under the Endangered Species Act by making it easier to exclude certain areas, including for public-works projects, such as schools and hospitals, and for public lands leased to non-government businesses.
    Interior Department
  2. Opened nine million acres of Western land to oil and gas drilling by weakening habitat protections for the sage grouse, an imperiled bird. The Idaho District Court temporarily blocked the measure. The Montana District Court also invalidated the directive, nullifying 440 oil and gas leases, but the ruling is on hold pending appeal.
    Interior Department

Water pollution – completed:

  1. Scaled back pollution protections for certain tributaries and wetlands that were regulated under the Clean Water Act by the Obama administration. (A federal judge in Colorado halted implementation of the rule within the state, but it is in effect elsewhere.)
    E.P.A.; Army
  2. Revoked a rule that prevented coal companies from dumping mining debris into local streams.
  3. Weakened a rule that aimed to limit toxic discharge from power plants into public waterways.
  4. Weakened a portion of the Clean Water Act to make it easier for federal agencies to issue permits for federal projects over state objections if the projects don’t meet local water quality standards, including for pipelines and other fossil fuel facilities.
    Executive Order; E.P.A. holding areas, which can spill their contents because they lack a protective underlay.
  5. Withdrew a proposed rule requiring groundwater protections for certain uranium mines. Recently, the administration’s Nuclear Fuel Working Group proposed opening up 1,500 acres outside the Grand Canyon to nuclear production.

Water pollution – in progress:

  1. Proposed doubling the time allowed for utilities to remove lead pipes from water systems with high levels of lead.
  2. Attempted to weaken federal rules regulating the disposal and storage of coal ash waste from power plants, but a court determined the original rules were already insufficient to protect the environment. The E.P.A. then proposed a new rule that would allow unlined coal ash ponds, previously deemed unsafe, to continue operating.
  3. Proposed a regulation limiting the scope of an Obama-era rule under which companies had to prove that large deposits of recycled coal ash would not harm the environment.

Toxic substances and safety – completed:

  1. Rejected a proposed ban on chlorpyrifos, a pesticide linked to developmental disabilities in children. In 2020, the E.P.A. also rejected its own earlier finding that the pesticide can cause serious health problems. (Several states have banned use of the pesticide and its main manufacturer said it would stop producing the product because of shrinking demand.)
  2. Narrowed the scope of a 2016 law mandating safety assessments for potentially toxic chemicals like dry-cleaning solvents. The updated rules allowed the E.P.A. to exclude some chemical uses and types of exposure in the review process. In November 2019, a court of appeals ruled the agency must widen its scope to consider full exposure risks, but watchdog groups say the agency has not done so in some assessments.
  3. Reversed an Obama-era rule that required braking system upgrades for “high hazard” trains hauling flammable liquids like oil and ethanol.
    Transportation Department
  4. Changed safety rules to allow for rail transport of highly flammable liquefied natural gas.
    Transportation Department

Toxic substances and safety – in progress:

  1. Proposed limiting pesticide application buffer zones that are intended to protect farmworkers and bystanders from accidental exposure.
  2. Announced a review of an Obama-era rule lowering coal dust limits in mines. The head of the Mine Safety and Health Administration said there were no immediate plans to change the dust limit but has extended a public comment period until 2022.
    Labor Department

Other – completed:

  1. Repealed an Obama-era regulation that would have nearly doubled the number of light bulbs subject to energy-efficiency standards starting in January 2020. The Energy Department also blocked the next phase of efficiency standards for general-purpose bulbs already subject to regulation.
    Energy Department
  2. Changed a 25-year-old policy to allow coastal replenishment projects to use sand from protected ecosystems.
    Interior Department
  3. Limited funding of environmental and community development projects through corporate settlements of federal lawsuits.
    Justice Department
  4. Stopped payments to the Green Climate Fund, a United Nations program to help poorer countries reduce carbon emissions.
    Executive Order
  5. Reversed restrictions on the sale of plastic water bottles in national parks desgined to cut down on litter, despite a Park Service report that the effort worked.
    Interior Department

Other – in progress:

  1. Proposed limiting the studies used by the E.P.A. for rulemaking to only those that make data publicly available. (Scientists widely criticized the proposal, saying it would effectively block the agency from considering landmark research that relies on confidential health data.)
  2. Proposed changes to the way cost-benefit analyses are conducted under the Clean Air Act. Similar rules for the Clean Water Act and other environmental statutes are in development.
  3. Proposed freezing efficiency standards for residential furnaces and commercial water heaters designed to reduce energy use.
    Energy Department
  4. Created a product category that would allow some dishwashers to be exempt from energy efficiency standards.
    Energy Department
  5. Initially withdrew, and then delayed, a proposed rule that would inform car owners about fuel-efficient replacement tires.
    Transportation Department

Reducing Bird Deaths Caused by Wind Turbines

3 November, 2020

According to the United States Fish and Wildlife Service, about 300,000 birds were killed by wind turbines in the US in 2015. Another study estimated that wind turbines killed about 500,000 birds and 900,000 bats in the US in 2012.

This sounds bad. But it’s actually tiny compared to some other causes of death! A 2014 paper estimated that power lines kill somewhere between 12 and 64 million birds each year in the US. And another paper estimates that between 1.3 to 4 billion birds are killed by domestic cats each year in the US.

So if you really want to save birds, do something about cats. But it’s interesting to read that there may be an easy way to reduce bird mortality due to wind turbines. Just paint one blade black!

That’s what this laboratory study suggested, back in 2003:

• W. Hodos, Minimization of motion smear: reducing avian collisions with wind turbines, National Renewable Energy Laboratory, NREL/SR-500-33249, August 2003.

Hodos studied the perceptual psychology of birds and recommended field testing. And that’s what these folks did, with a nice hat tip to the Rolling Stones song:

• Roel May, Torgeir Nygård, Ulla Falkdalen, Jens Åström, Øyvind Hamre and Bård G. Stokke, Paint it black: Efficacy of increased wind turbine rotor blade visibility to reduce avian fatalities, Ecology and Evolution 10 (2020), 8927–8935.

With a rather small sample size, they concluded that painting one blade of a wind turbine black reduced the fatality rate by about 70% compared to to the neighboring unpainted turbines. And the treatment had the largest effect on reduction of raptor fatalities.

Audubon Magazine is cautiously optimistic… but the Federal Aviation Authority would need to be persuaded:

The results are promising, says Garry George, director of Audubon’s Clean Energy Initiative, but they’re also preliminary. Eight turbines—half of which were treated with black paint—is not a large sample size, he says, and the researchers found relatively few bird carcasses both before and after painting the blades: A total of 42 dead birds, found at all eight turbines during the study period, were included in the analysis. It’s also not clear if the paint solution achieves the same results across various species of birds. May himself agrees: “Although we found a significant drop in bird collision rates, its efficacy may well be site- and species-specific,” he says. “It is surely not a golden egg solving all bird-collision problems in the world.” He recommended that more turbine operators test the approach around the world to see whether it works in different places and with different bird species.

If it does work, Allison says, painting blades black would be an effective, low-cost solution. But giving birds visual cues with paint isn’t the only solution researchers are testing. More thought is being put into siting, or figuring out where to physically place turbines. By studying nesting areas and common flight paths near potential wind farm locations, Allison says, wind companies can build turbines as far as possible from frequented bird routes. Additionally, wind farms are experimenting with radar, camera, and GPS tech to track birds and automatically shut off turbines as the birds approach. Still, since birds use wind to navigate and soar, there’s inevitably going to be some overlap between the best locations for wind farms and the best migratory pathways for birds.

Researchers are also experimenting with deterrence systems. “When you detect something that you think might be an eagle within a certain distance of a turbine, you emit sounds that will first alert the bird,” Allison says. “If the bird keeps coming, you send a second signal that—you know, the hope is it will persuade the bird to change its flight path.” The turbines will, in essence, scream at birds to stay away, and a report published by AWWI suggests this method could reduce collisions by somewhere between 33 and 53 percent.

Future research might prove that black turbine blades are the wind energy panacea we’ve been waiting for, but for now the idea of seeing painted blades dotted across the landscape is still up in the air in the United States. That’s because painted turbine blades are currently prohibited by Federal Aviation Administration (FAA) regulations, in part due to concern about reduced visibility for aircraft flying at night. “However, we do have a process for considering such changes,” an FAA spokesperson wrote in an email to Audubon—which sounds like they might consider changing their rules.

• Neel Dhanesha, Can painting wind turbine blades black really save birds?, Audubon, 18 September 2020.

Exponential Discounting

25 October, 2020

Most of us seem to agree that the promise of a dollar in the future is worth less to us than a dollar today, even if the promise is certain to be fulfilled. Economists often assume ‘exponential discounting’, which says that a dollar promised at some time s is worth

\exp(-\alpha(s - t))

dollars in hand at time t. The constant \alpha is connected to the ‘interest rate’.

Why are economists so wedded to exponential discounting? The main reason is probably that it’s mathematically simple. But one argument for it goes roughly like this: if your decisions today are to look rational at any future time, you need to use exponential discounting.

In practice, humans, pigeons and rats do not use exponential discounting. So, economists say they are ‘dynamically inconsistent’:

• Wikipedia, Dynamic inconsistency.

In economics, dynamic inconsistency or time inconsistency is a situation in which a decision-maker’s preferences change over time in such a way that a preference can become inconsistent at another point in time. This can be thought of as there being many different “selves” within decision makers, with each “self” representing the decision-maker at a different point in time; the inconsistency occurs when not all preferences are aligned.

I this ‘inconsistent’ could be a misleading term for what’s going on here. It suggests that something bad is happening. That may not be true.

Anyway, some of the early research on this was done by George Ainslie, and here is what he found:

Ainslie’s research showed that a substantial number of subjects reported that they would prefer $50 immediately rather than $100 in six months, but would NOT prefer $50 in 3 months rather than $100 in nine months, even though this was the same choice seen at 3 months’ greater distance. More significantly, those subjects who said they preferred $50 in 3 months to $100 in 9 months said they would NOT prefer $50 in 12 months to $100 in 18 months—again, the same pair of options at a different distance—showing that the preference-reversal effect did not depend on the excitement of getting an immediate reward. Nor does it depend on human culture; the first preference reversal findings were in rats and pigeons.

Let me give a mathematical argument for exponential discounting. Of course it will rely on some assumptions. I’m not claiming these assumptions are true! Far from it. I’m just claiming that if we don’t use exponential discounting, we are violating one or more of these assumptions… or breaking out of the whole framework of my argument. The widespread prevalence of ‘dynamic inconsistency’ suggests that the argument doesn’t apply to real life.

Here’s the argument:

Suppose the value to us at any time t of a dollar given to us at some other time s is V(t,s).

Let us assume:

1) The ratio

\displaystyle{ \frac{V(t,s_2)}{V(t,s_1)} }

is independent of t. E.g., the ratio of value of a “dollar on Friday” to “a dollar on Thursday” is the same if you’re computing it on Monday, or on Tuesday, or on Wednesday.

2) The quantity V(t,s) depends only on the difference s - t.

3) The quantity V(t,s) is a continuous function of s and t.

Then we can show

V(t,s) = k \exp(-\alpha(s-t))

for some constants \alpha and k. Typically we assume k = 1 since the value of a dollar given to us right now is 1. But let’s just see how we get this formula for V(t,s) out of assumptions 1), 2) and 3).

The proof goes like this. By 2) we know

V(t,s) = F(s-t)

for some function F. By 1) it follows that

\displaystyle{ \frac{F(s_2 - t)}{F(s_1 - t)} }

is independent of t, so

\displaystyle{ \frac{F(s_2 - t)}{F(s_1 - t)} =  \frac{F(s_2)}{F(s_1)} }

or in other words

F(s_2 - t) F(s_1) = F(s_2) F(s_1 - t)

Ugh! What next? Well, if we take s_1 = t, we get a simpler equation that’s probably still good enough to get the job done:

F(s_2 - t) F(t) = F(s_2) F(0)

Now let’s make up a variable t' = s_2 - t, so that s_2 = t + t'. Then we can rewrite our equation as

F(t') F(t) = F(t+t') F(0)


F(t) F(t') = F(t+t') F(0)

This is beautiful except for the constant F(0). Let’s call that k and factor it out by writing

F(t) = k G(t)

Then we get

G(t) G(t') = G(t+t')

A theorem of Cauchy implies that any continuous solution of this equation is of the form

G(t) = \exp(-\alpha t)

So, we get

F(t) = k \exp(-\alpha t)


V(t,s) = k \exp(-\alpha(s-t))

as desired!

By the way, we don’t need to assume G is continuous: it’s enough to assume G is measurable. You can get bizarre nonmeasurable solutions of G(t) G(t') = G(t+t') using the axiom of choice, but they are not of practical interest.

So, assumption 3) is not the assumption I’d want to attack in trying to argue against exponential discounting. In fact both assumptions 1) and 2) are open to quite a few objections. Can you name some? Here’s one: in real life the interest rate changes with time. There must be some reason.

By the way, nothing in the argument I gave shows that \alpha \ge 0. So there could be people who obey assumptions 1)–3) yet believe the promise of a dollar in the future is worth more than a dollar in hand today.

Also, nothing in my argument for the form of V(t,s) assumes that s \ge t. That is, my assumptions as stated also concern the value of a dollar that was promised in the past. So, you might have fun seeing what changes, or does not change, if you restrict the assumptions to say they only apply when s \ge t. The arrow of time seems to be built into economics, after all.

Also, you may enjoy finding the place in my derivation where I might have divided by zero, and figure out to do about that.

If you don’t like exponential discounting—for example, because people use it to argue against spending money now to fight climate change—you might prefer hyperbolic discounting:

• Wikipedia, Hyperbolic discounting.

The SPARC Fusion Reactor

21 October, 2020

There’s a lot of excitement about a new approach to fusion power:

• Henry Fountain, Compact nuclear fusion reactor is ‘very likely to work,’ studies suggest, The New York Times, 29 September 2020.

Scientists developing a compact version of a nuclear fusion reactor have shown in a series of research papers that it should work, renewing hopes that the long-elusive goal of mimicking the way the sun produces energy might be achieved and eventually contribute to the fight against climate change.

Construction of a reactor, called SPARC, which is being developed by researchers at the Massachusetts Institute of Technology and a spinoff company, Commonwealth Fusion Systems, is expected to begin next spring and take three or four years, the researchers and company officials said.

Although many significant challenges remain, the company said construction would be followed by testing and, if successful, building of a power plant that could use fusion energy to generate electricity, beginning in the next decade.

This ambitious timetable is far faster than that of the world’s largest fusion-power project, a multinational effort in Southern France called ITER, for International Thermonuclear Experimental Reactor. That reactor has been under construction since 2013 and, although it is not designed to generate electricity, is expected to produce a fusion reaction by 2035.

But fusion has been twenty years off since the 1950s. What’s the evidence that Sparc will work? I guess most of the evidence is here—a series of seven papers, which luckily are available open-access:

Status of the SPARC physics basics, Journal of Plasma Physics 86 (2020).

I have not read these! And even if I did, since I’m not an expert on fusion reactors—obviously a tricky subject—I’m not sure how much my impression would help.

Do you know any commentary on SPARC from other experts on fusion reactors? The more detailed, the better. All I’ve seen so far are very sketchy remarks from people who don’t seem to know what they’re talking about.

Epidemiological Modeling With Structured Cospans

19 October, 2020

This is a wonderful development! Micah Halter and Evan Patterson have taken my work on structured cospans with Kenny Courser and open Petri nets with Jade Master, together with Joachim Kock’s whole-grain Petri nets, and turned them into a practical software tool!

Then they used that to build a tool for ‘compositional’ modeling of the spread of infectious disease. By ‘compositional’, I mean that they make it easy to build more complex models by sticking together smaller, simpler models.

Even better, they’ve illustrated the use of this tool by rebuilding part of the model that the UK has been using to make policy decisions about COVID19.

All this software was written in the programming language Julia.

I had expected structured cospans to be useful in programming and modeling, but I didn’t expect it to happen so fast!

For details, read this great article:

• Micah Halter and Evan Patterson, Compositional epidemiological modeling using structured cospans, 17 October 2020.

Abstract. The field of applied category theory (ACT) aims to put the compositionality inherent to scientific and engineering processes on a firm mathematical footing. In this post, we show how the mathematics of ACT can be operationalized to build complex epidemiological models in a compositional way. In the first two sections, we review the idea of structured cospans, a formalism for turning closed systems into open ones, and we illustrate its use in Catlab through the simple example of open graphs. Finally, we put this machinery to work in the setting of Petri nets and epidemiological models. We construct a portion of the COEXIST model for the COVID-19 pandemic and we simulate the resulting ODEs.

You can see related articles by James Fairbanks, Owen Lynch and Evan Patterson here:

AlgebraicJulia Blog.

Also try these videos:

• James Fairbanks, AlgebraicJulia: Applied category theory in Julia, 29 July 2020.

• Evan Patterson, Realizing applied category theory in Julia, 16 January 2020.

I’m biased, but I think this is really cool cutting-edge stuff. If you want to do work along these lines let me know here and I’ll get Patterson to take a look.

Here’s part of a network created using their software: