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Sun Nov 24, 2019, 11:02 AM

Bare Metal Critical Masses of Commonly Available Plutonium Isotopes.

Last edited Sun Nov 24, 2019, 12:50 PM - Edit history (1)

The paper I'll discuss in this post is this one: Denaturing of Plutonium by Transmutation of Minor-Actinides for Enhancement of Proliferation Resistance (Saito et al, Journal of Nuclear Science and Technology, Vol 42, Issue 2, 161-168 (2005)).

The ultimate cause of our complete and technical failure to address climate change is selective attention.

And let's be clear, we are failing, we are doing nothing effective to address climate change. Here are the figures immediately available at the website of the Mauna Loa Carbon Dioxide Observatory's website:

Up-to-date weekly average CO2 at Mauna Loa

Week beginning on November 10, 2019: 410.25 ppm
Weekly value from 1 year ago: 408.91 ppm
Weekly value from 10 years ago: 385.76 ppm

Last updated: November 23, 2019

While the figure in comparison to the same week of 2018 seems low, "only" 1.34 ppm over last year, this is only the third such reading in 2019 to below 2.00. The average of such readings for 2019 as compared to 2018 is 2.98 ppm as of this writing, and in the week ending April 8 of this year, the same reading was 4.48 ppm over the same week in 2018. Of the 19 such readings over 4.00 pm, 12 have occurred in the last 5 years, 16 in the last 10 years.

We are failing. Big time.

I blame selective attention for this inasmuch as climate change is a result of our energy production practices and the criteria by which we engage in the comparative analysis is for lack of a better set of terms, completely and totally puerile, silly, and absurd.

As I frequently point out, citing the irrefutable data in this open sourced paper, Prevented Mortality and Greenhouse Gas Emissions from Historical and Projected Nuclear Power (Pushker A. Kharecha* and James E. Hansen Environ. Sci. Technol., 2013, 47 (9), pp 4889–4895), nuclear energy saves lives.

This, of course, does not imply that nuclear energy is without risk, that no one has ever been harmed by nuclear energy. This is obviously not true and never will be true. It is, I think, in the presence of a responsible cost analysis that values lost lives from any technology equally, absolutely no feasible way to make nuclear energy safer than it already is, and no rational reason for doing so, since any improvement would be minor and raise costs.

It is not, at least to sane people in my opinion, justifiable to spend tens of billions of dollars to prevent 5 future deaths or 500 future deaths from radiation leaks while we are unwilling to spend the same amount of money to provide improved sanitation to the 2 billion people who lack it, thus allowing 827,000 deaths (the WHO figure) each year from lack of clean water and fecal born diseases, 432,000 of which involve diarrhea, mostly among small children.

I a member of a generation, the so called "Baby Boomers," who proved to be, at the end of their reign, mostly concerned about money and consumption, and little else, except for some tiresome and weak gesturing, half-assed perfunctory sloganeering and cursory lip service.

It is common among members of this generation to declare, without a shred of critical thinking, that "nuclear power is dangerous" because of so called "nuclear waste," about which these same people claim, without having ever opened a science book or a scientific paper in their generally useless lives, that "nobody knows what to do with it."

The reality though is that air pollution, which again, I often point out, kills seven million people per year, and climate change to the extent it is driven by carbon dioxide are both waste problems, fossil fuel and biomass combustion waste.

The difference between so called "nuclear waste," and dangerous fossil fuel waste is essentially this: There is no record of commercial so called "nuclear waste" actually killing people beyond the fantasies of moral morons, and there is an extensive record of dangerous fossil fuel waste killing people. About 800 people will die in the next hour from fossil fuel and biomass combustion waste.

On some level, there is some excuse for Baby Boomers to have focused their fear on radiation, since many of us can remember, albeit when we were children, the Cuban Missile Crisis, when we went to school some mornings in October of 1963 expecting to be vaporized at some point in the day. Nevertheless, our focus on our childhood fears are not really excuses for having lost our ability to think critically.

There are now people who have elevated this childish fear of radiation- every human being is mildly radioactive because every human being would die without the element potassium which does not occur (except in special laboratories) in a non-radioactive form - to engage in hysterical and extremely stupid evocations of say, some crap about the Hanford weapons facility, as a justification for letting seven million people die each year from dangerous fossil fuel and biomass combustion waste. It is not worth even speaking to such moral Lilliputians.

By the way, it is not sane to spend hundreds of billions of dollars to "clean up" Hanford to a standard that no one is ever, for all time, injured by its contents, at the same time that we are unwilling to spend hundreds of billions of dollars to clean up the planetary atmosphere, which is killing people continuously.

This brings me to the issue the authors of the paper cited at the outset of this post, the subject of putative nuclear war. It is a fact that for almost 3/4 of a century, 73 years to be exact, the number of people killed in nuclear wars has been zero. (This is not true of nuclear tests, but it is true of nuclear wars.) It is also a fact that millions of people have died in the last 73 years from petroleum based wars, using petroleum based weapons of mass destruction (and some dangerous natural gas based weapons of mass destruction, since nitrates are synthesized using natural gas). Yet the petroleum industry and the gas industry are not required to prove that their products and materials cannot be diverted to use in weapons of mass destruction, a task which would be futile, since they are continuously observed to do so, but the nuclear industry is so required.

The paper is written about the "Kessler proposal" (and similar proposals) to which I have paid considerable attention since it was published in 2004, which is to limit world plutonium supplies to those containing significant quantities of the 238Pu isotope, a heat generating isotope that has mostly been utilized to power deep space robots investigating the outer (and a few inner) planets in our solar system.

I am a proponent of the uranium/plutonium nuclear fuel cycle to save humanity from itself, but it largely not this cycle discussed in this paper: I propose the fast neutron (breeder) cycle, whereas this paper focuses on the thermal cycle. Inasmuch as the bare sphere metal critical mass of actinide isotopes is very much involved in my thinking, the paper nonetheless caught my eye. This is because I changed my mind a few years ago about whether large nuclear reactors were to be preferred to smaller, easily manufactured reactors: I now think small is better.

The introduction begins with a statement about the reality that selective attention exists:

Proliferation is one of the concerns limiting further peaceful use of nuclear power. Although its scope includes the entire fuel cycle, a key concern is the generation and the accumulation of weapon-usable material—especially plutonium— in power reactors. There are several proposals to burn surplus plutonium from both nuclear reactors and weapon very deeply in gas cooled reactors1,2) and light water reactor with inert matrix fuel.3) In these proposals, minimizing quantity of fissile materials is focused on the discussion of the proliferation resistance...

Later the introduction gets to the Kessler proposal and outlines it:

There are one official criterion and several proposals on this isotopic barrier of plutonium. International Atomic Energy Agency in their publication, INFCIRC/153,4) mentioned that plutonium containing 80% 238Pu or more is exempted from proliferation concerns because of high decay heat and large number of spontaneous fission neutrons (SFN). This level of plutonium content has to be considered as the upper limit. In 1980, Heissing-Goodman reported that 5% 238Pu in a critical plutonium sphere was considered enough to hinder the effort of making it into explosive metal since all the explosive lenses surrounding the plutonium sphere will be melted due to the high heat from alpha decay of 238Pu,5,6) however this proposal has never been widely accepted. The content of 238Pu in the plutonium vector that considered enough for plutonium protection was further revised by Kessler in March 2004. He improved the method developed by Heissing-Goodman and by a careful analysis and choosing the appropriate physical constants and parameters, he figured out that 12% 238Pu in a critical plutonium sphere can melt the plutonium and the explosive lenses altogether. 7)

The authors, citing a previous paper by the lead author, advance this argument further:

...Recently Saito et al. proposed the Protected Plutonium Production (PPP) by doping minor-actinide (MA) in uranium oxide fuel.8–10) In their proposal MA is utilized as a resource of 238Pu to produce the proliferation resistant plutonium fuel since 237Np and 241Am, dominant nuclides of MAs, are well transmuted to 238Pu in light water reactors (LWRs). This characteristic of MA can be also utilized for denaturing of excess plutonium to unattractive material for fission explosives.

Most of the previous researches have been devoted to the effort of increasing 238Pu as way of protection. However, exclusive and separate investigation on the effect of 238Pu on denaturing plutonium would fairly underestimate the combined effect of other even-plutonium isotopes, 240Pu and 242Pu, which have relatively large bare critical mass (BCM) and remarkably large SFNs, since fuel irradiation in LWRs inevitably produces these isotopes.

The present paper therefore focuses on the intrinsic feature of proliferation resistance of plutonium with consideration of the dilution of fissile-plutonium isotope with evenmass- number-plutonium-isotopes. Increasing the fraction of even-mass-number-plutonium-isotopes by plutonium irradiation and MA transmutation in LWRs, the denaturing of reactor- grade-plutonium to unattractive material for fission explosives by utilizing MA transmutation in LWRs is also studied in the present paper...

"SFN" refers to "spontaneous fission neutrons" which are the neutrons released in a subcritical state by the inherent property of both naturally occurring actinides (except thorium) and synthetic actinides to fission spontaneously, without being hit by an external neutron. The presence of to many such neutrons makes nuclear weapon manufacture problematic, and limits their lifetime considerably.

Again, this paper focuses on the thermal cycle, which is not my primary interest, but the tables supporting the discussion are of interest, so I won't discuss much more of the text.

The first table does what the title of this post promises, and gives the bare metal critical masses of plutonium isotopes (presumably spherical geometry, since this is what nuclear weapons utilize).

The column BCM stands for "Bare Critical Mass."

The high figure for the decay heat associated with 238Pu, 567 watts per kg, shows why it is useful on space vehicles.

A second table is also of interest since it shows the composition vectors of the main actinide constituents of used nuclear fuel.

These figures are for "once through" plutonium, that generated utilizing enriched uranium at start up. Of note to me is the relatively low concentration of Pu-242, which is a wonderful isotope since it is fairly but not completely (as it has a critical mass) inert nuclide. Its presence has the effect of increasing the critical mass of any plutonium sample containing it.

In the area of nuclear engineering in which I focus most of my attention, specifically liquid metal fuels, this has an important consequence in terms of a difficult issue, which is heat transfer.

Plutonium is one of three metals exhibiting a very long thermal liquid phase temperature range; the other two are neptunium and gallium. This means it is not easy to get plutonium to boil (although it does so in nuclear weapons explosions). I have in my library a report dating from 1966, when a generation less stupid than mine was working on breeder reactor concepts - indicating that the specific power of a liquid plutonium fueled reactor (the LAMPRE reactor) was 1MW/kg. (cf. Whitman, "Fast Breeder Reactor Development in the United States" in Fast Breeder Reactors, Proceedings of the London Conference on Fast Breeder Reactors, 17-19 May, 1966, P.V. Evans, Ed. page 286.)

Presumably the plutonium utilized in this reactor was or almost was weapons grade plutonium, nearly pure 239Pu. It was, however in the form of an iron plutonium eutectic. The density of this fuel at 760°C, the temperature at which the reactor was said to have operated is approximately 15.53 g/ml. (cf Wittenberg and Ofte, Fluid Flow of Liquid Plutonium Alloys in an Oscillating‐Cup Viscosimeter J. Chem. Phys. 48, 3253 (1968)) The eutectic point in the iron plutonium system exists at about 10% iron, suggesting that at this power density, if we assume that the 1MW/kg figure refers only to the plutonium content, involved 70 ml of fuel putting out 900 kW of energy.

The LAMPRE reactor utilized tantanlum crucibles, and small amounts of plutonium, and thus heat transfer may not have been an issue, if, in fact, this 1MW/kg figure is real, which it may not be.

This suggests a role for 242Pu in reactors of this type, which is to lower the energy density of the fuel.

There is nuclear fuel available with a higher 242Pu content, largely available in France, which is "twice through" MOX. The vectors I've seen for it, show much higher concentrations of 242Pu.

I hope the French protect this fuel. It will be important for future generations to have it.

Have a nice day.

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Reply Bare Metal Critical Masses of Commonly Available Plutonium Isotopes. (Original post)
NNadir Nov 2019 OP
rlegro Dec 2019 #1
NNadir Dec 2019 #2
rlegro Dec 2019 #3

Response to NNadir (Original post)

Tue Dec 3, 2019, 05:59 PM

1. Thanks.

Excellent piece worthy of many further reads. Here is a sidebar. I am a lay person, albeit one who did take a couple of physics classes in college decades ago, and one who worked some years in the electric power industry when nuclear generation still looked like da bomb -- uh, maybe i should rephrase that last remark.

I expect many folks here will not want to get into the physics and engineering of any type of nuclear power reactor, nor potential fusion reactor designs that may be perfected later on. It isn't a taboo subject, but it's too often a wired one, case closed for the moment.

You are correct that a confluence of events and memes have soured many individuals and also institutions -- public and private including the insurance industry and commercial utility sector itself -- on fission-based generation. Clearly, some of this concern is not unfounded -- Chernobyl and more pertinently the Fukushima disasters weigh heavily in the collective mind, and rightfully so. So does terrorism and the idea that fanatics will gain nuclear technology if we have it lying around.

Re-introduction of the pressurized water reactor is virtually a dead prospect, not just due to problems of scale but especially given that design's physical and economic need to be near large bodies of water where rising oceans and wilder weather will be even more problematic. Still, in a world where wildfire holocausts and superstorms are ravaging continents regularly, some citizens might understand the need to draw on that technology again. Not many, in all likelihood. but would they accept programmed brownouts and blackouts over nuclear? No.

So you have identified a key problem for planners, public leaders and the utility industry, namely, how humankind might transit quickly yet safely to alternative power technologies in time to avert the worst (and perhaps irreversible) effects of a runaway greenhouse environment.

Wind, solar, tidal and some other technologies might eventually come on line in sufficient quantity to supplant remaining fossil-fuel power plants (including those using natural gas). Indeed, capital costs, at least for solar, are going down quickly, now below that of coal. However, further ramping up alternate technologies is going to take time and lots of alternative resources. For instance, a new study suggests lithium supplies will not be sufficient to convert to more than a fraction of the production we'd need to bring on line to halt production and transportation-related C02 releases. And then there are those natural greenhouse-gas sources, like methane, which are likely to account for greater releases as the planet thaws further.

Therefore we will need an interim technology. If it's well designed and works safely for a decade or three, nuclear might win back public approval.

As you indicate, there are a number of possible new approaches to nuclear power generation. Thorium-cycle designs looked good but even those aren't without their downsides, from what I am able to discern Smaller nuclear plants would seem to have many advantages but also new drawbacks -- real and imagined.

Besides small-is-beautiful thinking we are going to need to get into space in a big way if we are to contain global warming to a manageable level and in time. Reasons include finding suitable raw materials in new quantity and building orbital solar collectors that can beam power to Earth -- which designs might be just as controversial as nuclear of any kind.

Longer term solutions also must rely on energy conservation and -- probably -- a reduction in the planetary human population. Some humans may leave Earth and settle elsewhere in the Solar system -- not enough to matter physically, but enough to spur more positive and creative thinking. On a generational scale (i.e., slow), if we could get back to the still-crowded but not bursting-at-seams world population of, say, the mid 20th century, we would resolve a chunk of the present problem but that would require rejiggering our economic structures -- which by their nature are both decaying yet resistant to reform. All this may be a genie we can't put back into the bottle, at least not without authoritarian controls most of us would not like. Which is to say the technological obstacles might be more malleable than the sociopolitical ones.

The trick in solving this therefore is to leave nothing on the table. We likely will need many approaches, some in tandem, others triggered along a careful timeline. Task One is to break down not just the flat earthers but also, when they are ready to listen, those who are capable of reason yet badly under-informed. Your well-laid-out discussion and similar treatises certainly will go over the heads of such people, so we'll need a much greater educational emphasis employing sociology, psychology, political science, and the physical sciences.

Anyway, that's off the top of my head and I'm certainly not Mr. Know It All. It'll take tens or hundreds of millions of heads to fix this in time; have to start somewhere. In that regard, thanks again for your well-documented and thoughtful piece.

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Response to rlegro (Reply #1)

Tue Dec 3, 2019, 09:18 PM

2. I disagree with the "rightly so" statement about Chernobyl and Fukushima.

It is entirely based on selective attention.

On the scale of human tragedy connected with energy, air pollution is a tragedy that dwarfs, by at least 5 orders of magnitude, the combined effects of Chernobyl and Fukushima combined.

Seven million people die every damned year from air pollution. This means that since Fukushima occurred in 2011, 56 million people have died from air pollution. How many people died from radiation at Fukushima again?

How anyone can consider this an issue that is "rightly so" escapes my ethical purview completely.

To this, we may add the results of climate change, another related effect to the accumulation of dangerous fossil fuel waste, the total destruction of entire oceanic ecosystems such as the Great Barrier Reef.

It is pure ignorance to oppose nuclear energy because of Fukushima, and there is nothing moral or remotely ethical in even the weakest sense of deciding that fear of radiation from Fukushima justifies the death of 70 million people every decade from combustion wastes.

The idea that wind, solar and tidal energy is cheap, environmentally sustainable or desirable does not stand up to critical examination. The cost of this experiment is in the trillions of dollars. I pointed out in another post here (see below), with IEA data, that the results have been negligible.

If we are to speak of destruction of ecosystems, I note that worship at the altar of so called "renewable energy" has destroyed both the Mississippi River Delta system by eutrophication because of fertilizer runoff from Iowa farms growing corn for corn ethanol, and Borneo's rain forests being destroyed to make palm oil plantations to feed into Germany's biodiesel supplies for its "renewable fuel portfolio standards."

I'm an environmentalist, not an industrial agronomist. I object.

I also object to converting pristine wildernesses into industrial parks for wind turbines serviced by huge diesel trucks.

Look, I'm a political liberal and for many years I towed the party line - actually believing it and advocating for so called "renewable energy - believing that advancing so called "renewable energy" was a worthy cause. I note that this has become a feature of our culture of pablum, that you can make anything acceptable if you put a picture of a wind turbine next to it. But I have come understand that the means has become more important that what I personally regard as the ends of liberalism's stated goal of caring for the environment. This public meme is counterfactual. If the goal is to prevent climate change and to save the environment, it is experimentally clear that solar and wind haven't cut it, aren't cutting it and won't cut it.

It has become a sordid religion that we must worship solar and wind energy without giving a crap about what should have been its ends, which is a safe and sustainable environment.

Do you know what the fastest growing source of energy in the 21st century has been? I do. I wrote about recently in this space.

World Energy Outlook, 2017, 2018, 2019. Data Tables of Primary Energy Sources.

An improved and less confusing data table combining the 2017, 2018, and 2019 WEO reports.

Let me quote from the former:

In absolute numbers, exajoules, the fastest growing source of energy on this planet in this century has been coal. Coal use grew in the world at large between 2017 and 2018, despite what one may have heard in the American provinces.

In absolute numbers, dangerous natural gas was the second fastest growing source of energy in this century.

In absolute numbers, dangerous petroleum was the third fastest growing source of energy on this planet.

In this century, world energy demand grew by 179.15 exajoules to 599.34 exajoules.

In this century, world gas demand grew by 50.33 exajoules to 137.03 exajoules.

In this century, the use of petroleum grew by 34.79 exajoules to 188.45 exajoules.

In this century, the use of coal grew by 63.22 exajoules to 159.98 exajoules.

In this century, the solar, wind, geothermal, and tidal energy on which people so cheerfully have bet the entire planetary atmosphere, stealing the future from all future generations, grew by 9.76 exajoules to 12.27 exajoules.

The ends of liberalism as I define them are caught up in Article 25 Section 1 of the Universal Declaration of Human Rights passed by the UN in 1948, and they honored only in the breech. They are still worthy human goals. This section reads as follows:

Article 25.

(1) Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.

I am tired of hearing about conservation from people living in the Western World, particularly when said people complain about China's carbon emissions. The per capita consumption of a Chinese citizen is roughly 1/10 of an American. When the Chinese were consuming 1/50th of an American, should we have been lecturing them on conservation? Were they within their rights to look at our lifestyle and think, as we do, that we had a "right" to it? Why are we allowed to live on average continuous power consumption rates nearly 10,000 watts, while they live on 900? Because most of us doing this are white? Because of George Washington? Herbert Hoover? Donald Trump?

Two billion people on this planet lack access to even primitive sanitation systems; more than 600 million need to defecate in the open.

WHO fact sheet, Sanitation.

Is it ethical to talk about energy conservation to these people? Do we really believe that if we all switch to LED light bulbs that we will save the world? Might we do better at saving the world by giving these people a light bulb in a latrine?

I have been studying issues in energy flows for more than 30 years, based on an ethical view very much connected with Article 25 Section 1 of the Universal Declaration of Human Rights. Realizing these rights will require broad access to energy, we must make that energy in a sustainable fashion.

There is nothing, absolutely nothing, sustainable about the material requirements, owing to the low energy to mass ratio of so called "renewable energy." The worship of it is a crime against all future generations. It is, in fact, not liberal, and not connected with human development goals or compatible with them. It is rather, to the contrary, reactionary. I remind everyone that humanity existed on so called "renewable energy" for thousands of years and abandoned it during the 19th and early 20th century. Does anyone ever pause from chanting mantras about solar and wind to consider why that is?

The idea that solar and wind are cheap is also based on bad thinking. What is the use of the capital cost of a solar installation at midnight? At midnight it doesn't matter if the capital cost was zero, because the value is zero. In fact, it requires both the external and internal costs of the redundant system. If, in fact, there is so much electricity available on a bright sunny windy day that electricity prices go negative - this actually happens - the solar and wind systems are worthless to the investors, and the redundant systems are also worthless. Does anyone ever pause from chanting the mantra to ask how it is that the highest consumer electricity prices in the OECD belong to Germany and that off shore oil and gas drilling hellhole Denmark? I finally understood why and how this is from a wonderful publication by MIT's Charles Forsberg.

It is one thing to despise the right for its willful denial of climate change. It is another thing to understand that climate change is real, is driven by human activities, but otherwise to insist that a fixed belief in a pet system, as we do on the left, that has clearly and unambiguously failed is the only acceptable solution.

You sound as if you are a person who cares, or who at least wants to care. I'm an old man. I've been hearing this Amory Lovins anti-nuke "conservation and solar energy will save us" rhetoric for my entire adult life. Again, I even believed in it once. I am a political liberal; but my liberalism is secondary to my life as a scientist, because in science, no theory is valid unless it is tested by experiment.

The results of the trillion dollar experiment in "renewable energy will save us" are in. We are going to see carbon dioxide concentrations measured at Mauna Loa of over 417 ppm, maybe more, in May of 2020.

It is time to let go of dogma and wishful thinking and to get serious.

There is nothing "rightly so" about anti-nuke fear and ignorance. Nothing. It is a crime against all future generations.

History will not forgive us, nor should it.

Have a nice day tomorrow.

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Response to NNadir (Reply #2)

Wed Dec 4, 2019, 11:20 AM

3. I'm not questioning the supremacy of fossil fuel pollution...

... nor do I "worship" alternative energies, which as I noted have their own costs and benefits. [Storing solar-derived or wind-derived power for night-time use isn't unsolvable, though. Mechanical and electronic storage technologies do exist, and lithium-ion batteries are not likely to be a large component in such storage for reasons I shared earlier.]

However, in social and economic measures for the moment excluding environmental, the damage caused at Fukushima and Chernobyl was and will remain significant. And just because one component of that damage is (merely?) perceptual doesn't overcome popular resistance. Humans after all required millennia before they were comfortable harnessing fire. I trust large-scale engineering more than I trust, say, the people who design, build, and maintain modern corkscrew roller-coaster designs. But in that comparison I'm a distinct minority.

Engineering and management of complex technologies (anyone want to fly the 737 Max, yet?) are inevitably imperfect, and rushing new technologies to commercialization is often a mistake. Smaller scale nuclear generators do make some kind of sense. But until the insurance companies decide they can reliably cover nuclear accidents (meaning the federal government wouldn't have to underwrite those risks), the high probability is that we're not going to see a resurgence in commercial nuclear power on any scale.

I am an old man, as well, one who studied sociology, psychology, and political science. In my view, you needn't worry for now about the vast majority of Americans falling under the spell of "alternative energy." So far, a serious plurality of them still follow handy memes that deride those alternatives -- for wrong and usually non-technical reasons. I mean, wind farms are uglier than smoke stacks and kill more birds, right?

Society will remain at an impasse until more citizens are willing to sit down and learn more about necessary choices. And until they are represented by elected representatives who will follow the science and do the right things. Instead of, for example, what the Koch conglomerates or the American Petroleum Institute pay them to do.

Human nature tends toward favoring things as they are. Too bad, because as the late Marshall McLuhan pointed out, "Our museums depict ways of life that we have made impossible." I just hope there's a place on a future Earth for a museum that depicts our current way of life.

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