Cabbie Philosophy

 kw: book reviews, nonfiction, astrobiology, cab drivers, philosophy, speculation

The idea for the book gelled when Dr. Charles S. Cockell was asked by a taxi driver in London, "Are there alien taxi drivers? People like me elsewhere in the universe?" The conversation, held during a taxi ride between King's Cross railway station and 10 Downing Street, Westminster, is recorded and enlarged upon in the first chapter of Taxi From Another Planet: Conversations with Drivers about Life in the Universe.

The book's 18 chapters deal with similarly searching questions the author discussed with various taxi drivers over a period of a few years (he rides a lot of taxis). I'll touch on a few of my favorites.

Ch. 4: "Should We Solve Problems on Earth before Exploring Space"? This is a common question, and the discussion ranged over several topics, such as the utility of weather forecasting aided by satellite data, resource discovery and conservation, and the numerous products that had to be developed just to get people into orbit and keep them alive and useful (think fountain pens and more secure ways of sealing diapers).

My father was once asked after a speech about the Apollo program and the Moon landings, "The astronauts left millions of dollars worth of machinery on the Moon. Of what use is that?" Dad replied, "Do you know where those millions of dollars are? Right here on Earth! Every dollar spent on the space program eventually wound up in someone's pocket: from technicians to miners to metal workers to computer programmers. Those dollars circulated in the economy, as space industry workers bought houses and groceries, paid workers to mow lawns or remodel kitchens, and bought fuel for their cars."

The author's discussion, on a taxi ride between Paddington station and Heathrow airport, eventually settled on defense from asteroids. The author mentioned the 10km asteroid that drove most dinosaurs extinct 66 million years ago; those not wiped out became birds. It would be scientifically accurate for a chicken-burger joint to label their wares "Dinosaur Burgers". He went on to tell of Barringer Crater in Arizona, where a smaller meteorite blasted out a mile-wide crater a lot more recently, about 50,000 years ago. He called it "a tiny rock"; for the record its size was about 150 feet (45 m) and it weighed something like 200,000 tons. Its velocity upon impact was about 20 km/s, or 70,000 km/hr (12-13 mi/s or 45,000 mph). NASA and other space agencies are spending significant amounts of money on telescopes, both on land and in orbit, to locate all the asteroids big enough to wipe out cities or states or continents. The DART (Double Asteroid Redirection Test) project was to learning how hard it is to deflect a small asteroid. Just for the record, those "significant funds" are a small fraction of the various "stimulus" packages perpetrated by the US government in reaction to the pandemic. That's where the cabbie's question should be aimed!

Ch 10: "Will We Understand the Aliens?" In Glasgow, a discussion ensued about whether we and aliens would be able to communicate. Consider this: Without the Rosetta Stone, it might still be impossible to decipher early Egyptian hieroglyphics. There are a few dozen scripts that are still unknown, and until about 20 years ago Mayan was one of them, until my brother's mentor, Linda Schiele, cracked the code. It helped that there are living Mayans, who still speak the language. Even though the written script fell completely out of use about a thousand years ago, the linguistic characteristics of spoken Mayan led Dr Schiele and her collaborators toward the right path. Also, what of dolphins and other vocal whales? Only recently has it been learned that sperm whales seem to have names. It's a start. But alien-human linguistics will be really hard. Dr. Cockell thinks that, because the scientific method has to be the same everywhere, and the basic scientific laws are universal, that scientific and technical terms will be the first terms we and aliens will be able to share, and much can then be derived from that.

Ch 17: "What is the Meaning of Life?" There is no person anywhere who has never asked this question. In the author's estimation, the answer, if there is one, depends on how rare or how abundant life is, particularly life with sufficient consciousness to ask the question. I'd put it in reverse: Live has meaning of we live a meaningful life. If there is no life, there is no need for anything to "mean" anything. We are defined primarily by the quality of our relationships. You or I may be a wonderful person; this will remain unknown unless we are wonderful to or for someone. Or if a person is evil, that is only manifested when he or she is evil towards others (even if the "others" are frogs being stomped "for fun" or flies getting their wings pulled off).

This delightful book is full of meaningful insights about "life, the universe, and everything", with no trace of the whimsy of  Douglas Adams. The author has the privilege of thinking about these things for his day job as an astrobiologist and an adviser to NASA. His humility and grace, relating to taxi drivers from sundry backgrounds, come through and confer wisdom to us, his readers.

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Coda: While persuading various generative art programs to produce the image above, generated by the Stable Diffusion engine in Playground, I kept a couple of others that I particularly liked, that were "almost there". The first was drawn by Dall-E3, the second by Playground 2.5.

Herd Immunity versus Herd Mentality

 kw: book reviews, nonfiction, pandemics, covid-19, sars-cov-2, politics, epidemiology, sociology

During what we now know was an early stage of the Covid-19 pandemic, Johan Anderberg wrote his analysis of the unique approach taken by Sweden, as compared to all the other First World nations: The Herd: How Sweden Chose Its Own Path Through the Worst Pandemic in 100 years, translated from Swedish by Alice E. Olsson and published in English in 2022.

The book covers from early March 2020 until the end of the year. Writing in 2021 a book to be published the following year, the author could not have foreseen how absolutely middle-of-the road the results would be in Sweden, or how the pandemic would play out for another two full years, followed by a sputtering endemic infection that has become a slightly-worse-than-usual type of flu. Four other coronaviruses are known to cause fall-to-winter colds, and now there is a fifth, that is a little more deadly than the other four, but on a par with Type A influenza.

The action centers on two significant men, Anders Tegnell, Sweden's state epidemiologist, and Johan Giesecke, advisor of WHO to the Public Health Agency of Sweden. Other important men and women played their parts, including the Prime Minister of Sweden, but these two, with Tegnell in the lead, helmed the Swedish strategy for coping with the pandemic, for at least the year 2020.

Just as the two men began to collaborate, on March 12, Giesecke quoted a 17th Century noble who had written to his son, "An nescis, mi fili, quantilla prudentia mundus regulatur" and thoughtfully provided a translation, "Don't you know, my son, with how little wisdom the world is governed?" (p.73) This attitude was the underlying basis for dealing with the hundred-odd world governments and hundreds of news agencies that questioned, then decried, then condemned the light touch taken by the Swedes.

Early on Tegnell and Giesecke sought not to limit transmission but, in the absence of a viable vaccine, to allow the infection to spread while taking measures to protect the frail elderly and other vulnerable persons, with the goal of establishing herd immunity. There is much discussion of this concept in the book, with an equation or two related to R₀, the expected number of persons one infected person infects. Later, discussion moved to such buzz phrases as "limit the spread" and "flatten the curve", which caused confusion and had no discernible effect.

I remember well that President Trump authorized the military to make available great numbers of hospital beds and ventilator equipment, many on Navy ships. These went largely unused. To my discernment, being put on a ventilator was a death sentence for 50% of patients who were thus treated, and a great way to lose a quarter to half of one's body weight and muscle mass for those who survived, leading to months of recuperation. 

This is as good a time as any to note that a good friend of mine, a physician, and I worked out a plan: 

1. Since the main killer of Covid patients is pneumonia, and the lung-filling fluids of pneumonia are primarily composed of sugars, at the first symptom it is best to stop eating, ingesting only water, for at least 2-3 days.
2. Rather than fighting a fever, seek to enhance it into the 102°F range (39°C), to support the T-cells that are fighting the virus. He intended to use hot water baths or to get in the car on a sunny day and turn up the heat all the way. I preferred to not use anti-fever medications such as Tylenol.

As it happens, the doctor and I, in spite of being "fully vaccinated", both contracted Covid-19 twice, and survived quite well. In my case, effective antivirals were available by that time, which no doubt helped a lot.

The Swedish epidemiologists didn't stay "in the silo" of epidemiology, but took a more sociological approach. They disdained the notion of locking down a society, and while the rest of the world (or at least Europe and North America and developed Asia) was mandating masks, forbidding church and other gatherings, closing schools, and issuing "6-foot spacing" guidelines, they kept Swedish society almost completely open.

It seems the rest of the world took their cue from an amateur scientist with no epidemiological training, Tomas Puevo, who published an essay, "The Hammer and the Dance", predicting that the attempt to attain herd immunity would result in 10 million deaths in the USA (pp. 124-5). The actual total by end-April 2024 was 1.2 million, and at the end of 2020, about 380,000. But politicians and some scientists worldwide bought into this totally, and we were all locked down.

I'll jump forward to the denouement, which begins on p. 288 with a bit of genuine epidemiology: comparing year-on-year death statistics to discern "excess deaths" that might more properly be attributed to Covid-19 (or any other epidemic agent). 

• In 2020, the total number who died of all causes in Sweden was 98,124. 
• The annual average for 2015-2019 was 90,962. 
• In 1993, the year of a bad flu outbreak ("the Beijing flu"), the figure was 97,008. 
• Swedish population in 2020 and in 1993 (rounded): 10,369,000 and 8,574,000. 
• Divide deaths by population. 
• In 2020: 9,463 per million
• In 1993: 11,310 per million 
• Population average 2015-2019: 10,109,000. Divide it out: 8,998
• Delta per million in 2020 = 465 excess deaths per million
• Delta per million in 1993 = 2,312 (almost 5x!).

Conclusion: The Covid-19 pandemic was far from being "the worst pandemic in 100 years". It was probably second-worse.

Note: CDC data (https://www.cdc.gov/mmwr/preview/mmwrhtml/00016654.htm) indicates that in an "ordinary" flu season, flu leads to about 10,000 deaths in the USA. In the 1992-1993 seasons, 45,000 such deaths occurred each of the two years. Dividing these figures by a population of about 330 million, we find that flu deaths are "usually" about 30 per million, while the sum of 1992 and 1993 deaths by flu comes to 273. The Beijing flu hit Sweden 8.5 times as hard as it did the USA.

Backing up to p. 223, where the scientific community "turned from evidence-based reasoning to the precautionary principle": One scientist wrote of the reasoning of Anders Tegnell, "If he's wrong, it costs life. If I'm wrong, what harm does it do?" This is a markedly false dichotomy, for the lockdowns and other draconian measures not only did much harm, they cost many lives in themselves, including a great increase in suicide among younger people. The scientist who wrote that statement doesn't deserve to be called scientific.

Even in Sweden, by the end of 2020 the situation was no longer driven by science (protestations by fraudulent scientist Andrew Fauci notwithstanding), but by politics, specifically the totalitarian politics of control and the amassing of power. So-called "cancel culture" took control, such that the final sentence in the chapter titled "Science!" is, "What was regarded as a scientific discussion in Sweden was deemed to be misinformation in other countries." (p. 247). This is still true!

Considering the polarizing politics that arose from this, or rather that took advantage of it, I need to point out that on p. 243 the author quotes Glenn Kessler's article in The Washington Post that claimed Donald Trump issued 16,241 false and misleading claims in his first three years in office. He is apparently unaware that the article was debunked within a week by real journalists at the New York Post and The Atlantic. They found that at most, Mr. Trump lied outright no more than a handful of times; rather, Kessler printed thousands of lies in his article. True to form, Kessler just doubled down and issued further claims. The debunking has been so covered up it is hard to track down the truth. In actuality, since 2015 The WaPo, NYT and other "leading" publishers committed tens of thousands of lies against Donald Trump weekly, and continue to do so.

Let's look at some charts from Worldometer, which is cited a few times in the book. Note that the last update to their figures was April 13, 2024. Reporting has become too sporadic and unreliable for them to continue. I must add that early reporting is also somewhat questionable, and in particular, nothing that was "reported" by China or North Korea (DPRK in Worldometer) should be relied upon.

First, to discuss the summary for the whole world:

The fluctuating death rate shows the progress of the different "waves", ten of them, counting the late, rather tiny, bump from November 2023 to February 2024. The biggest wave of cases, in early 2022, with a wave of deaths that is lower than two of the others, shows how infectious the Omicron variant of the virus was, and how much less deadly it was.

When The Herd was written, the third wave, counted worldwide, was just ending. These figures help us establish some criteria. New daily cases in 2022 peaked at 500 per million persons, and exceeded 100 for much of the year; at all other times there were fewer than 100. The current case rate is 2/million or less.

The worldwide Covid-19 death rate exceeded 1/million persons for all of 2021 and the first third of 2022, and then, as the Delta variant petered out, it dropped very low and apparently remains well below 100 total deaths daily, or some 0.012 deaths daily per million population. As mentioned, this is in line with seasonal influenza. This is why, although some nutty politicians continue calling for restrictions to be imposed again, nobody is paying attention.

Next, let's look at how Sweden fared in all this:

It is worth noting that, while the daily case rate prior to August 2020, worldwide and in Sweden, is almost not visible on these charts, the daily death rates in this period were quite high. The very early death rate exceeded 10% of (known) cases. Two factors combine: figuring out how many actual cases there were was very difficult early on, and the large number of deaths represent "low-hanging fruit", or people who were at death's door already. In the USA, this was exacerbated in five states whose governors required nursing homes to take in people dying of Covid-19, which spread through those nursing homes like wildfire, killing many. I contend that those five governors are the five greatest mass murderers of the early 21st Century.

During the second wave at the end of 2020, Swedish politicians were spooked that Covid-19 deaths had again exceeded 100 per day (10/million in a population of just over 10 million), and as is noted in The Herd, began to swerve from the open stance of the prior year.

The figures in brown at top right of these charts show that the total case rate in Sweden was three times the world average, and the total death rate was just under three times as much.

Arguably, the country worst hit by the pandemic was the USA:

I am not sure whether the lockdowns in the USA were the worst in the Free World, but in my experience they were pretty bad. They varied from state to state. The first wave of deaths was not quite as bad, on a per-capita basis, as for Sweden, but the second wave was clearly worse. After the end of 2021, the USA case rate was much higher than that for Sweden, and this apparently continues, but after the middle of 2022 the Covid-19 death rate in the USA is quite a bit lower than Sweden's.

Compared to the world, the total case rate for the USA is 3.7 times higher and the total death rate is just over 4.0 times as high.

I originally prepared two more similar graphs, for the UK and for Norway, but instead I'll present the following:

The vertical axis is deaths from Covid-19 per million population of a country. Sweden, shown as "Swe", is right in the middle. The USA is to its upper right, with the UK in between. Among more authoritarian European countries, I've marked Bulgaria, Hungary, and Bosnia/Herzegovina, which had three of the four highest death rates in the world. The highest was Peru, for reasons I won't plumb here. By contrast, look at Canada and Norway ("Nor"; in each case except "World" the title is to the right of the dot). Nearly all the dots below them are countries in Africa and poorer parts of Asia, places which had few infections and very low death rates. 

I would think an ambitious epidemiologist could make a career of finding out whether there was something more than dumb luck that "blessed" the Third World. But I also must note that I have, from the beginning, strongly suspected that the USA was targeted by China, which released this bug with malice aforethought. I am flabbergasted by the number of American pundits who defend China at every turn. I know enough Chinese people to have an inkling of their way of thinking. Not every war goes fast. The Chinese way is patient, slow, and—insofar as they can ensure it—irresistible. To their way of thinking, WW3 has begun, and if they can manage it, our enemy will remove our head before we notice we have died.

The core message of this chart is that lockdowns had no discernible effect. Every European nation and most others locked down a great deal more than Norway, which stayed open during that very crucial first year, and has remained more open than most other countries thereafter. As a preacher once said about faith healing, "God may heal you today, but eventually you are going to die of something."

We learned from this pandemic that we have more to fear from totalitarian politicians than we do from a global disease outbreak. Sweden showed that society could remain open, taking only certain rather cautious measures, without harming the citizens either medically or politically. It is hard to tell whether any country achieved herd immunity, but it is certain that with the exception of Sweden, most countries fell victim to herd mentality, from which they are still in a very slow recovery.

Unwarranted Extrapolation?

 kw: analyses, greenhouse effect, climate crisis, carbon dioxide, logistic curve

Introduction

We are daily exhorted to worry about the climate, about "carbon pollution", about the "existential crisis" of "human caused global warming". As I have written elsewhere, before I was a teen I had learned how to analyze the greenhouse effect in the atmosphere of Earth caused by water vapor and carbon dioxide. Decades later I read that if the "windows" in the spectrum between the edges of the absorption bands of carbon dioxide were "closed", the total warming would be less than 4°C (7°F). Still later a series of "official" reports were issued, based primarily on computer modeling, making projections of the warming caused by increased carbon dioxide, with low, moderate, or high estimates of the temperatures that are expected. The reports are dire, the warnings are shrill. They are overdone.

This essay is not a quantitative analysis with lots of math or equations. It is conceptual, but, I hope, not simply "arm waving".

Greenhouse Gases

Let's look first at the two primary gases that affect Earth's temperature by modifying how light from the Sun is reflected and absorbed.

Water Vapor

In the past, one would see in the literature of atmospheric warming by the Sun a statement such as, "Without water in the atmosphere, the average temperature of Earth would be colder by 33°C or 59°F." This makes water vapor by far the most important greenhouse gas. We'll see more in a moment.

Carbon Dioxide

Once the infrared absorption spectrum of carbon dioxide was determined, a few scientists calculated how its concentration in the atmosphere might be adding to the greenhouse effect caused by water vapor. One of these was Svante Arrhenius. Late in the 19th Century he published his calculation that if the amount of carbon dioxide in the atmosphere were doubled (it was at that time about 300 ppm), average temperature of Earth's atmosphere would rise by between 1.5°C and 2°C (that's 2.7°F to 3.6°F).

Infrared Spectra

My first job, by which I worked my way through a couple of years of college, was performing infrared spectroscopy for a project funded by the Department of Defense. I became quite familiar with the way certain gases absorb and, when heated, emit infrared light. This image (one of many similar) shows the infrared absorption spectra of water vapor and carbon dioxide:

These spectra do not include visible light, which would be a little to the left, between 0.4µm and 0.7µm. The abbreviation "µm" means "micrometers", also called "microns", or millionths of a meter. It is immediately evident why water vapor is a strong greenhouse gas. While it doesn't absorb visible light, it absorbs many wide bands of infrared. The next graphic shows why these gases are important:

This chart, from an article in 2010 by Clive Best, shows the balance between solar radiation and terrestrial radiation. This time the wavelength scale starts at zero, so it includes visible and ultraviolet radiation. About 1/3 of the Sun's light is in the visible range; the cream-colored band in the image shows how it is divided up. The surface of the Earth also emits thermal radiation, at longer wavelengths, which we see in the right half. Simply put, if there were no absorption in the atmosphere, the blue "mountain" would mostly fill in under the blue curve of the three. The "blocked" radiation shows the greenhouse effect.

For clarity, three thermal infrared radiation curves are shown for different surface temperatures:

• Black: 210K = -63°C = -145°F, deep winter cold in central Siberia or Antarctica
• Blue: 260K = -13°C = +9°F, a cold winter day in Denver or London
• Lavender: 310K = 37°C = 99°F, just above body temperature, or a hot summer day in NYC

These three curves, and the red curve for the much hotter Sun, show theoretical emission from a "black body", which is a theoretically perfect absorber and perfect emitter. Just for fun, check out the lavender curve: If you get the flu and your temperature is just a couple degrees above normal, a spectrometer pointed at you would record peak radiation from your skin at about 9µm, with significant amounts in the range 5µm-22µm. To a spectroscopist, the range of wavelengths longer than 5µm, out to about 50µm, is longwave infrared, also known as thermal infrared.

Just below the red-blue section we find a combined spectrum for a generalized atmosphere ("Total Absorption and Scattering"), and then spectra for several gases, starting with water vapor and carbon dioxide. These two together produce most of the combined spectrum shown just above water vapor.

Look carefully at the rightmost absorption band for carbon dioxide. It mostly overlaps the major band for water vapor. This shows that the two gases do not act independently. When humidity is high, the differential effect of carbon dioxide is small, but in dry air, carbon dioxide has a stronger effect.

The other major absorption band for carbon dioxide, between 4µm and 5µm, is near the edges of the thermal radiation bands, so it has even less effect. It is little affected by the nearby band for water vapor.

Let's look briefly at the rest of the gases. I am disappointed that the creator of this chart chose to combine oxygen and ozone. Perhaps it was out of trust that most who read the article would know that the broad absorption at the far left, in the ultraviolet range, is for ozone, and the others are for oxygen. Anyway, it shows that oxygen, which makes up 21% of the atmosphere, is a mild greenhouse gas, while ozone, which is nearly all in the stratosphere, is a strong greenhouse gas, but only at high altitudes. Ozone's absorption of solar UV is the major reason that the upper stratosphere is warmer than the lower stratosphere. 

Methane is next. It looks like a poor absorber, but that is because it occurs in very low concentration, less than two parts per billion (or less than 200,000 times the concentration of carbon dioxide). The fact that it shows up at all warns us that it will be a strong absorber if its concentration rises much. If an atmospheric sample had equal amounts of carbon dioxide and methane, the greenhouse warming by methane would be more than 80 times as much!

Nitrous oxide is also a strong greenhouse gas, but is present at very low concentration, about 300 parts per billion, or less than 1/1,000th the concentration of carbon dioxide.

Rayleigh scattering is a physical effect; the "gas" for this part is the combination of nitrogen and oxygen. A small proportion of light is scattered off the molecules of these gases, and the scattering is stronger for shorter wavelengths. It is the shorter wavelength visible light (blue), scattered from sunlight, that makes the sky blue. As a matter of fact, for any planet with an atmosphere, anywhere in the universe, unless the air is very dusty, the sky will be more blue than the star that is that planet's "sun".

What a Greenhouse Gas Does

Let us consider, for the moment, only water vapor in an otherwise "pure" atmosphere of nitrogen and oxygen. Sunlight heats the surface, which radiates thermal infrared. Much of this is absorbed by the water vapor, which heats the atmosphere. This heat also produces thermal infrared radiation, and to a first approximation, half is aimed downward and half is aimed upward, to eventually escape into space. What goes down heats the ground, so more up-going radiation ensues. This feedback process raises the temperature of everything until the amount of radiation escaping is equal to the amount that descended from the Sun. In short: Sunlight in, IR out, with a "hang up" as some, or most, of the IR cycles between the surface and the atmosphere. The "greenhouse effect" is the "hang up".

According to Clive Best in his article, most of the possible absorption by carbon dioxide was already occurring before the Industrial Revolution. This is expressed in the diagrams above by the portions of the curves that have already reached 100%. Let's look closer at one of the diagrams:

When a portion of the spectrum is below 100% absorption, and the concentration of the gas being investigated is increased, the wings of the absorption band rise, and the area that absorbs 100% increases. The "Area of Interest" in this image is between about 12µm and 14µm, and the absorption by water vapor is usually less than 50% in this range. This is where almost all the action is; this is the source of "global warming" by carbon dioxide! In order to pull the left side of the curve upward until nearly all of it reaches 100% would require increasing the gas concentration by a factor of ten or more.

While we are here, let us take a side trip to Venus. There, the atmosphere is almost all carbon dioxide, at a pressure of 92 atmospheres, or 1,334 psi. That is 220,000 times as much carbon dioxide as Earth's atmosphere. The tapered bands, and the smaller peaks shown, will all be at 100%, and even the little bits of hash near 10µm and elsewhere, plus others not shown here, will be at 100%. The spectrum will be a bunch of rectangles, filling much more of the total space. No wonder the temperature on Venus is above 460°C (860°F)! Of course, it "helps" that Venus gets sunlight twice as intense as that on Earth.

All these details about absorption, and the interactions between the absorption profiles of carbon dioxide, water vapor, and other gases, result in a very complex system. I hope it is evident that, in the range of a few hundred parts per million, up to one or two thousand parts per million, the extra effect of the growing margins of the absorption bands is less and less as concentration increases. There is a point of diminishing returns. Let us discuss the Logistic Curve.

The Logistic Curve

Here is one familiar situation. A weakling wants to get stronger (usually this is a guy, so I'll use male pronouns). He goes to a gym and engages a trainer. He is tested with several weights; let us assume that, for starters, he can bench press 50 pounds. That means he can't even do one pushup. He trains three times weekly, with much grit and determination. After a few months he can "bench" 80 pounds, and in a few more, he attains 100 pounds, and can now do one or two pushups. In another year he finds his one-rep bench press is approaching 200 pounds! He has quadrupled his strength, and he looks a lot better also, more filled out. Question: Can he quadruple it again? 800 pounds? Men who have trained for decades seldom exceed 500 pounds; the record for someone who never took steroids is less than 1,000. Well, then, can he attain 400 pounds? Possibly, but at that point he is likely to have joint or tendon problems. The bones and tendons he started with can't increase as much as the muscles that attach to them. Somewhere in the 200-400 pound range he has a limit.

Let's consider this graph:

The blue line is a much-studied relationship that is not well known outside mathematics and statistics departments. It is called the Logistic Curve. The red curve is an Exponential Curve, such as compound interest. The units of this graph don't matter. Many natural phenomena can be described by setting this curve in appropriate units. For example, if the red curve shows the natural ability of locusts to multiply (let's say the units along X are weeks), the blue curve shows what will happen when they eat everything nearby and must begin to migrate to find more food. They may carry along for a while and reach the "carrying capacity", or "saturation", but somewhere off the right end of the graph, the curve will fall again when the locusts have eaten everything they can reach. Or, consider our ambitious weightlifter. Let's assume "10" represents the point where he started concentrated training. His strength doubles, doubles again, and then he finds it hard to make such great gains. Eventually, he "tops out". If he's lucky, he has done this without pulling any tendons or breaking any bones. That's why he has a trainer…

How does this relate to the greenhouse effect and carbon dioxide? For the next graph I've recast the axes to make a useful analysis, at least in a general way.

The amount of absorption by carbon dioxide as its concentration increases, and the level of added heat that this causes, is also a logistic curve. If we want to make predictions about what might happen with increasing gas concentration, we need to know where we are on the curve. NOTE: The temperature scale is not intended to be highly accurate, but to show relative relationships.

Depending on which horizontal scale we use, the baseline, "pre-industrial" amount, is either the lower black circle or the lower blue circle. We don't know for sure just how much heating was already in place in pre-industrial times, compared to a situation with zero carbon dioxide. Such a "zero situation" has never occurred on Earth. But we can compare two scenarios, one using the black circles and the black scale, and one using the blue circles and the blue scale; both follow the blue curve. The implication of the dotted black curve will also be considered.

The "We are in the early stages" scenario (black scale)

Temperature has risen, as gas concentration went from 280 ppm to 420 ppm over the past 175 years, and we find ourselves a bit beyond halfway along the rising portion of the curve. The amount the curve can rise until saturation is about equal to what has already occurred.

The "We are in a later stage" scenario (blue scale)

The upper blue circle shows that we are near the top of the curve. There is a little ways to go, but even doubling or tripling the gas concentration will not push us much further.

I have not been able to discover whether the climate modeling community has picked a spot on a logistic curve, or if they are even using one.

The "This could destroy everything" scenario (black scale, black dashed line)

If the climate disaster prophets are using predictive curves at all, they are probably using one that doesn't peel over at some saturation level, but goes up forever. The portion of the blue curve between the black circles looks pretty straight, straight enough that many folks, not seeing the whole picture, will project a straight line to forever. I am pretty sure that the "impending disaster" predictions that get all the press these days (at least since the first IPCC Assessment Report in 1990) are following a linear extrapolation, such as the dashed black line.

I favor the blue circles, which imply that most of what could happen has happened already. The global climate system may gain another half degree or one degree, but not more.

That is my conclusion, dear readers. I believe we are being bullied into making drastic changes based on a nonsensical extrapolation.

As science fiction and science approach one another

 kw: book reviews, nonfiction, popular culture, films, television, science fiction and science

For many of us, when we are not thinking about food, work, or sex, we're thinking about space. Those who are lucky enough to work in the field think about, in order, space (work), space (dreams), and then the others. One such is Ariel Waldman, who has gathered the content of conversations and interviews about her favorite subject into her new book Out There: The Science Behind Sci-fi Film and TV.

The book's 19 chapters introduce subjects ranging from escaping Earth gravity to loneliness, from spacesuit design to starship speculations, and from what alien creatures and their languages might be. I'll touch on a couple of items that I found interesting.

Chapter 5 is titled "Artificial Intelligence – Should spaceships be sentient?", and is headed by this evocative illustration. Some of us remember HAL, the conflicted, eventually homicidal shipmind in 2001: A Space Odyssey. In science fiction, intelligent machines are most frequently presented as risky or downright dangerous. Not all, though; at the end of Isaac Asimov's Foundation/I Robot series of intertwined stories, R Daneel Olivaw has attained near-deity and is quite benevolent, but such depictions are rare.

I've read stories in which the shipmind is a brain grafted to machinery (the best is "The Ship Who Sang" by Anne McCaffrey), others with human minds downloaded into computers, others with purpose-built AGI's, and many more with no technology indicated.

Here's my take on conferring all power upon a mechanism: If it is based on biological neuroanatomy, it will not be any more reliable than are we, or pigeons, or whatever bio-brain is modeled. If it is based on familiar multi-CPU/GPU-OS architecture, it has a better chance of being reliable, but it will be less relatable. I suggest that command-and-control be based on utterly reliable hardware, and that the "ship shrink" and other artificial companions be separate from it.

Chapter 9 is titled "Asteroids – What's so interesting about a bunch of space rocks?" So far, all the asteroids that have been visited by spacecraft are more akin to rubble piles. The idea of hollowing out an asteroid to make a habitat must await our finding some that are more solid. 

Metallic asteroids such as Psyche (the target of a spacecraft, also named Psyche, that will arrive in 2029) are thought to be quite solid, with little surface rubble. Others may have a large-ish solid core, with "shells" of rubble up to several or many meters thick. Psyche's size is about 278km×238km×171km; it is one of the largest asteroids. Good targets for mining or other uses will be less than a kilometer in size.

A quote by the author is apropos: "The idea of asteroids as human habitats might not be as alluring as the fantasy of living on the Moon or Mars, which would be unbelievably challenging environments to make a home out of, but they are an interesting option." I am not sure if the phrase "unbelievably challenging" was intended by the author to refer to the Moon and Mars, or to the asteroids. I'd put it this way, that if it is 100 times as hard to make a livable habitat in or on Mars or the Moon as on Earth, an asteroid habitat would be a further 100 times as hard as the Moon to live on or in.

Also, the people who advised the author put to rest the idea that the "asteroid belt" is awash with dangerous rocks that one must dodge when attempting to traverse it. Many spacecraft have zoomed through the whole depth of "the Belt" at speeds of thousands of km per hour, without mishap. Not so much as a grain of sand, so far as we know, has hit any of them. 

Think of it like this: The total mass of the main belt between Mars and Jupiter is about 3% of the mass of the Moon, which is 7.348 × 10²² kg (Wikipedia article is here), and the four largest asteroids make up about 60% of that. The next million known asteroids bring the total mass of "bigger pieces" up to about 99% of the expected total mass.

Suppose that all the rest of the total mass were grains of sand with a size of about 1mm, weighing 2.5 mg each. Divide that into 0.012% of the mass of the Moon; it comes to a lot of grains (it's a 25-digit number). Then, the belt itself can be treated as a torus with an inner radius of 290 million km and an outer radius of 500 million km, which is halfway to Jupiter from Mars, so its volume is, very roughly, a 9 followed by 24 digits, in kilometers...I'll forego putting the calculations here. Dividing the volume by the number of grains I find 24. Each virtual grain has 24 cubic kilometers to itself, on average. Calculating the "expected impact cross section", the number of grains a square meter of spacecraft is likely to encounter passing through the 310-million-km thickness of the belt, I find 0.32 expected impacts.

That is interesting. It is larger than I would expect, considering that no spacecraft have been damaged while traversing the asteroid belt. It also emphasizes that some of the estimates in the prior paragraph could be very far off. At any rate, it is unlikely that anyone aboard a spacecraft on its way through the belt will ever see anything, unless they purposely pass by a known asteroid.

The subjects are all interesting, and I could write about my reactions to all of them. But this is a review, not a synopsis! It is a small book, in its own way, but well worth reading. Small: the pages are large, but the paper is thick so there are only 134. Each chapter has a full-page illustration like those shown above, and a full-page title, plus a page of some halftone-dot pattern; all that subtracts 57 pages from the total. It is still worthwhile.

I must also applaud the artwork of Phil Wheeler (this is his agent's website). I've included just two of his illustrations for this book, but I was strongly tempted to provide thumbnails of them all.

We all do it but we think we are bad at it

 kw: book reviews, nonfiction, mathematics, geometry

The book is Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else, by Jordan Ellenberg, a professor of mathematics who happens to write very well, who has also advised in the production of several films. Thinking about what kind of image to use to illustrate this review, I tried a few prompts with DALL-E3, and settled on this one:

The old geometer in his workroom, surrounded by the tools of his craft, clip art

After several trials, this image in dark sepia appealed to me the most.

The term Geometry means "measuring the Earth", but in practical terms it means to measure earthly things. That's something we all do frequently. For example, my wife and I are in the process of getting a bathroom remodeled, because ancient pipes have given out and the walls and floor need to be destroyed to get at them. We need to buy tile and supplies for the new floor, and a different kind of tile (or other covering) for the walls. What do we do? We take measurements and calculate areas. That's a geometrical task.

When we were in seventh and eighth grade, most of us had Geometry one year and Algebra the next. However, I suspect few of us had an Algebra teacher who showed us that geometry and algebra tackle the same problems from different directions; they are equivalent. What made geometry class so hard for me was the proofs. The Proofs! One needs a certain kind of mind to formulate a Proof. I don't have it. With a lot of painful study, I can figure out all the steps in a proof I have been shown, but I could never have produced it myself, and I soon forget it.

This book is not about proofs (but a few simple ones are shown, perhaps as a kind of inoculation: "See, that isn't so bad, is it?" To which I answer, "Yup, it's bad."). No, it is about geometrical thinking. For example, about trees. Biologically, a tree is a branching structure with a root, trunk, branches, twigs, and leaves. Conceptually, a biological tree is a metaphor for a way of arranging information, such as a family tree, a categorization of machine tools, or the districts and blocks and buildings in a neighborhood. A tree has one specific, critical characteristic: branches don't join back to branches. Otherwise, you have a network.

In a chapter on genealogy (#8, You are your own negative-first cousin, and other maps) the author states that your parents "don't share a known ancestor (unless you are from a truly aristocratic clan)." Not so fast, Dr. Ellenberg. Generally, we consider that a "family tree" is a genuine tree. With you as the root, your parents as the first two branches, your grandparents as the next, and so forth, the tree branches and branches but branches don't re-combine. However, sooner or later, they have to, as author notes in passing. If we look deeper into the situation we can go one better than that. 

In most jurisdictions, it is legal for first cousins to marry. In some, only certain first cousins can marry: they can have a common grandparent as long as the siblings in their parents' generation are of opposite sex. Thus, my mother had a sister and a brother. It would not be legal to marry the daughter of my mother's sister, but is quite legal to marry the daughter of my mother's brother. Such "available" cousins are called "kissing cousins".

Among my ancestors is a certain Joseph Macy, born on Nantucket Island in 1765, son of Joseph Macy and Mary Starbuck. Among his great-great grandparents—there are 16 of them—the surname Coffin appears three times and the name Starbuck appears twice. So he was his own third cousin three different ways. There were ten families that settled Nantucket in the 1600's. Within just a couple of generations, marriages between second or third cousins became necessary, and marriages between first cousins were getting common. So the genealogy of the Nantucket settlers is a bit of a treelike network. There are other interesting cross-links elsewhere in my family "tree", but I'll leave them for a later discussion. I'll just leave you with this thought. Joseph Macy was descended from Charlemagne; and so, of course, am I. The relationship is distant: 39 generations. That many generations ago, I had, formally speaking, 549,755,813,764 ancestors. It's about 550 billion. That implies a lot of cross-linkages in everyone's family tree, once you get back one or two dozen generations. As it happens, according to the data I have at present, I have five ancestors descended from Charlemagne.

Dr. Ellenberg likes long chapter titles. One of the shorter titles is "His style was invincibility" (Ch 5), in which we are introduced to an unbeatable Checkers player named Marion Franklin Tinsley. His story is the backdrop to investigating combinatorial math, using games. Tic Tac Toe is a simple game with a simple strategy, and is a "known game" because of its simplicity. There are 765 possible positions (the "state space"), and about 27,000 possible games, or ways to pass through a series of states in the state space. If two players play perfectly, every game is a draw. What about Checkers? The state space of Checkers is about 500 billion billion, or a 5 followed by 20 other digits. With a state space this large, nobody can learn the whole of it, and neither can any computer so far produced. Just for the record, the state space of the positions in Chess is a 2 followed by 46 other digits. This means that it is possible for a human player to still win either Chess or Checkers against a computer program, but it is very hard, because there are various heuristics (rules of thumb based on experience) that measure the strength of one position relative to another, and a machine can check millions of possibilities while a human player is thinking over five or ten. Then there is Go, for which the number of legal board positions is a number with more than 170 digits; this is an estimate! Considering that the number of atoms in the Universe is a 100-digit number, you would need billions of billions of billions (string out four more "billions") of Universes to contain a computer memory big enough to encompass the state space of Go.

But the process of analyzing any of these games is to build a tree! The starting position of the game is the root of the tree. In a game of Checkers, the number of possible starting moves by the first player is 14. Similarly for the initial moves of the second player, so the two-move state space is 14x14 = 196. These moves vary in how "strong" they are, how likely to lead to a Win. If you have a way to evaluate the strength of each move, you can label the nodes in the tree accordingly.

With each move the state space for that move is another factor that's usually between 12 and 16, until pieces start getting captured (which reduces the branching), and it can exceed 16 when some pieces get longer multi-jump options. It doesn't take long for the number of twigs on this tree to become millions, billions, etc.

The last chapter has the title "How math broke democracy (and might still save it)". It is about Gerrymandering, the practice of setting up voting districts in a state or county so as to favor one political party. This graphic from Statista shows examples from 2020. Redistricting, and thus Gerrymandering, follows each census; it's in the Constitution (the redistricting part!). 

There are many definitions of "fair", and none of them is "fair enough" to satisfy everyone involved. There are many proposals for rules or laws to produce a more "fair" outcome, but again, every such proposal generates lots of heat but hardly any light. 

In 2019 the Supreme Court punted on a possible method to ameliorate the problem. The author was involved, as a co-creator of an Amicus brief. Gerrymandering cannot be eliminated, not so long as people have emotions and a lust for power. The chapter does not end with a conclusion, but with a few tantalizing possibilities. None of them is likely to receive the support of a large enough majority to become embalmed in law. It is clear from the passionate tone of the chapter that this matter is of great importance to the author. Here, Geometry is Power.

Geometry is all around us. We all do it. We all think we are bad at it. It takes a peculiar kind of mind to revel in the proofing process, but just as very few people design the cars that millions of us drive, or the phones we consult so compulsively, we know what we need to know, and as this book shows, we know more than we think we do.

The most divisive amendment

 kw: book reviews, nonfiction, firearms, weapons training, second amendment

Dan Baum is an unlikely gun guy. As he describes himself in Gun Guys: A Road Trip, he is a liberal Democrat, a Jew, and a bemused spectator caught in the middle of the gun rights debate. Were it not for a chance occurrence when he was seven, at a summer camp, he might never have discovered his inner Gun Guy. The campers were taken to a gun range and taught basic gun etiquette, and then each had a chance to shoot five .22 rifle bullets at a target. The other boys' targets showed a wide scatter of shots; some targets were untouched. All of Dan's shots were in the central "black", including a couple at dead center. The instructor breathed a far-from-grudging, "Nice shootin', Tex."

This was 1961. Things were about the same as they had been in 1955, when I first shot a .22 rifle at a YMCA camp. As I recall, all my shots were on the paper target, but none were near the center. Still, I was a better shot than many of the boys. In my case, that was as far as it went. In Dan's case, the camp was long, and he was able to continue to learn shooting.

Away from camp, he led the ordinary life of a middle-class Jew. Year after year at the camp, his marksmanship skills grew, as did his general love for handling guns and enjoying caring for them. At home, he had to be satisfied with toy guns and friends who would play military or police games. He was in college when he bought a "real gun".

Fast-forward a number of years. Dan decided to get into gun culture, to learn how people with various backgrounds relate to guns and gun use. His interest was a mingling of personal curiosity and journalistic interest. He performed open carry for a time, then obtained a concealed carry permit (in his state at the time, reciprocal agreements meant he could carry his concealed handgun in a number of other states). He visited gun shows, gun shops (a great many of those were out of business), and participated in NRA and other online forums and in-person conferences.

He reports that he was well received almost everywhere. People were often puzzled that a Jewish Democrat could be a "gun nut", but were typically willing to impart knowledge and expertise. The big exception was the "cachers", as he calls them: the men (and the occasional woman) who expect anarchy to break out (some are licking their lips over the prospect), who buy large amounts of firearms and ammunition and bury them here and there, to make it harder for "someone" to steal the artillery or rob them of it. They hated Dan from the instant any of them became aware of him, and vilified him at every opportunity, nearly always behind the screen of an online avatar or anonymous account.

I'll leave it to you to read the rest. He had many good experiences, some awkward ones, and a few that terrified him. Guns and gun rights are the second-most polarizing issue in America today.

I have a few thoughts I'll pass along. Firstly, while it is true that the Second Amendment does not limit the right of American citizens to own firearms (even military weapons including a great many the Founding Fathers had no idea would be invented); it does begin with that pesky "militia" clause. Here is the text, in its entirety:

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

I find it interesting that there are several slight versions of this that were ratified by various US states in 1791. The above version was ratified by Delaware. The different versions have variations in presence or absence of the commas, and in capitalization, but the words are all exactly the same. The number of words written about these 27 words is comparable to the number of words written about the doctrine of the Trinity. I'll just add my two sen worth (a sen is 1/100 of a Japanese yen) thus: What part of "well regulated militia" do you not understand? People such as the "cachers", in particular, are the opposite of well regulated.

Further, it has been said, "The Second Amendment is there in case the government violates the First Amendment." There is a little ground to reach this conclusion based on some things written by the Founders, but the breadth of opinion on such an idea among them was very great, and I think this fact is expressed in the very ambiguity of the Second Amendment. 

Let's chase a rabbit, just a bit: Your rights to free speech are being stomped on, right now, by a coalition (conspiracy, to some) of Left-wing politicians, social media companies, and the "mainstream media". It doesn't matter whether you favor the Donkey or the Elephant. Can anything you might do because of the existence of the Second Amendment correct the situation? This coalition/conspiracy consists of a few hundred thousand people. Y'gonna kill 'em all? If you do shoot someone while "defending your rights", and police are sent to arrest you, will you continue the killing? 

Have you learned the lessons of Waco and Ruby Ridge? The futility of taking on an army that is able and willing to spend millions, or if need be, billions, to overcome you? How big a private militia can your raise, in order to destroy the "tyrants"? Take a look at the Wagner Group. They had a better chance than most to take on the army of Russia. They were driven into exile and their leader was assassinated. Ho Hum. Putin enjoys another serving of caviar. And the US Army is several times as powerful as the Russian Army.

I have never owned a gun. I prefer archery. I am a Christian, but not an anti-gun Christian (see Luke 22:36). Should anarchy increase, I may find a compelling reason to obtain one or more firearms, and to make sure my wife and I are properly trained to use them. But I like coalition-building, forging strong friendships, numerous friendships, meaningful and useful friendships. I'll leave it there.