We all say we hate it but we all do it

 kw: book reviews, nonfiction, science, mathematics, geometry

…No, my subject is not Sin (but that would be equally true), but Geometry. But before we go on, let me tell a story.

My brother and two close friends took several courses in college together, including a math class that emphasized proofs. I'll conceal identities here, and just represent my brother as Art, and his friends as Bob and Cal. They all did pretty well in their "math proofs" class. Art studied diligently and did well, while Bob struggled mightily to keep a "B" grade, but Cal did the best with the least work. Another fellow student told them one day, "Bob walked into a room and saw a big machine with a large gear on one end. He was told he had to make it run. He looked it over, then put his shoulder against the gear and heaved a great heave, making the gear turn. Art came in next. He nosed around and found a crank that fitted into the gear's shaft. He put it in, and turned the gear. Then Cal came in. He found a cord with a plug, plugged it in, pushed a button, and the machine began to run." When it comes to mathematics courses that require proofs (algebra) or demonstrations (geometry), I am definitely in Bob's league, at best.

Now, when I see a clear geometric demonstration, I can often comprehend it almost instantly. But I could never have produced that demonstration.

These two fellows (one an Arab, one a European), shown in a 15th Century drawing, are having a go at some demonstrations. The Westerner is trying his hand at squaring the circle (which is known to be impossible), while the Arab is, more practically, extending a demonstration of the Pythagorean Theorem.

In a memoir, we read that Abraham Lincoln said of himself that he "nearly mastered the six books of Euclid." In Shape, The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else, by Jordan Ellenberg, we find that Honest Abe struggled for months to square a circle. Of course, he failed, and apparently he never came across a proof or demonstration that doing so is impossible.

All the demonstrations and constructions in Euclid's work must be done with compass and straightedge. The ancient compass was so constructed that once you set the two points you could scribe a circle about one of them, but the two legs collapsed when lifted from the paper; you cannot "set" that kind of compass. Further, the straightedge must have no markings on it; its only use is to draw straight lines through points already marked on the page. It so happens that if you are allowed to make a single mark on the straight edge, effectively turning it into a ruler, you can construct an extended radius, such as what we see in "b" in the illustration above, that has the required length of one side of the square. Otherwise, "No markee, no squaree." This point is not mentioned in Shape, but I suspect that Dr. Ellenberg knows it.

If Euclid were to drop into the office of any modern professor of geometry, he would recognize nearly nothing, except the (probably translated) books on a shelf, nearly out of sight, that he wrote about 2,300 years ago. Much of the "geometry" carried on these days is topology, which isn't about circles, squares or triangles, but about holes. Yes, holes. To a topologist, anything with no holes but with a defined edge is a "circle", including things we'd call squares or triangles. But if you punch a hole in it it's now something else. Most topological work is done in three (or more) dimensions. You may be familiar with the statement, "A topologist has trouble telling the difference between his cup of coffee and the donut he wants to dip into it." Both a cup with a handle, and a donut, are solid shapes with a single hole.

A fun discussion in Chapter 2 involves the title, "How Many Holes Does a Straw Have?" I asked my wife. She said, "One." That is a proper topological answer. If you shorten the straw, and make its wall thicker, it becomes a donut. Distort it some more, also pressing out a cavity (but not a hole!) in one section, and you get a coffee cup. This is easier to do with clay than with paper! But just for fun, the author shows how people defend the answer "Two", because many people would say, "It has a hole in each end"; and even the answer "None", because some would say you started with a flat sheet of paper and rolled it up.

I have to say, I was puzzled that the word "cavity" never appeared in that chapter. Topologically, a cave (source of the word "cavity") has no holes if it has no "other end". In topology, you only have a hole if you can go into one side (or end) and come out the other. So the animal known as Hydra has a cavity, but no holes, while most animals have a single hole called the Alimentary Canal, with a mouth at one end and an anus at the other. So we are donuts. Very lengthy donuts.

Well, that's not where this book is ultimately going. The earlier chapters help us get used to some geometrical ideas, and we soon get to maps. Here are two maps, and they are related:

These maps are the same (but for drawing idiosyncrasies) as on p. 394 of the book. The author calls the second (green) one a "chart", but it is also a map. It is the "first inversion" of the blue map; the green lines represent the relationships between the blue-outlined areas.

Have you ever played Nim? You begin by stacking an arbitrary number of coins in two or more piles. In one version, each player can take either one, two, or three coins, all from one pile. Other versions exist with different "taking" rules. Players alternate taking coins until one coin is left. The player who must then take that last coin loses. The author shows a simple proof that the first player will always lose if the other player makes no mistakes.

These two maps (or "map" and "chart") illustrate something about electoral districts in a state. One method for detecting Gerrymandering (where it isn't obvious, and I'll explain more anon) involves playing Nim with the line segments in the green map until a player can't remove any segment without breaking the map into two pieces. One such game ends after four moves, to look like this:

The green map from before is now a Tree, a connected map with branching but no loops and no holes.

I won't take this further here, except to say this Nim game brings about several possible ways to break up a district made of smaller units into two districts. It is one step in the process of making an electoral map having districts that are "more fair", but then we get into a discussion of what "fair" means.

For example, "proportional representation" is often talked about. To get away from R vs D or L vs R (or X vs Y, which could be sexist), I'll refer to the two "interested" parties as H and O (Lionel fans, take note). Consider a state that has ten districts, and having 60% H voters and 40% O voters. Assume they are all pretty evenly spread throughout the state. How would you draw district boundaries to "ensure" that 6 H and 4 O district representatives will be elected? If you could, would that be "fair"? That would simply guarantee that the H's in the legislature would always win every vote, unless the O's could sometimes convince a couple of H's to vote their way. So, effectively, the O citizens in the state would be without representation.

Gerrymandering, so-called because a proposed district map drawn by one Eldridge Gerry included a district shaped like a lizard, is thought of as unfair mapmaking designed to ensure that a certain party will always win. When you know where the voters live, and voter registration is how you know, you can wiggle the boundaries around to get most opponents into the smallest number of districts, and create many more districts that will just barely elect your own members. The illustration below was cropped from an article titled "The most Gerrymandered districts in America":

Even though the author's passion clearly lies in "dealing with Gerrymandering", he acknowledges that while it is often visible, it is dramatically hard to quantify. The more so because we cannot yet clearly define what "fair" means.

I have an idea: a Federal law that requires one election in four to be automatically reversed the day after the poll results are revealed. To reduce the amount of "gaming the system" that would be indulged in, a pair of fair coins would be flipped on the day in question. This ceremony would be conducted in public, with much publicity. If both coins come up Heads, all elections are reversed. Otherwise, their results stand. Of course, that means that sometimes two Reversal Years might occur in a row, and perhaps even three. It would also happen that five, ten, or more years may pass with no Reversal Years. That's OK. The added uncertainty might not make for better legislating, but it would definitely make it more interesting! I have about as much confidence that such a procedure could become law as I have of the Sun setting in the East tomorrow evening.

Now I want to back up to the idea of the Tree. The author has an interesting statement about trees and related graphs in a footnote on p. 106: "…there's a more general notion than a tree, called a directed acyclic graph…a DAG is like a tree where some branches are allowed to fuse together… Think of a particularly aristocratic family where your parents may share a great-grandparent or two." This isn't as rare as he thinks. Inbreeding happens whenever the "breeding pool" gets too small. 

For example, I have an ancestor, a Quaker, whose parents left Nantucket in the fifth generation after its settlement by ten families. Four generations back, her father could have been descended from eight of the ten families if no marriages between cousins or second cousins occurred, as could her mother. However, her father is descended from only seven, and her mother is descended from six. Between the two, going back to the settlers' generation, the Starbuck couple appears three times, the Coffin couple appears three times, and the Garner couple appears twice. And the couple themselves were second cousins (or a little closer than that, considering). First-cousin marriage is legal in seven U.S. states, and second-cousin marriage is legal in all. First-cousin-once-removed marriage is legal in 42 states. Thus, many family "trees" are really "family directed acyclic graphs". Fortunately the software at sites such as Ancestry.com is written to accommodate relationships of all kinds, perhaps even including the one described in the song "I'm My Own Grandpa."

Also, realistically speaking, when you go back more than a dozen generations or so, you'll find all kinds of links between relatives. Anyone living today who is descended from Charlemagne (crowned in the year 800), is a 38th or 39th or 40th generation descendant. Take a "tree" back 38 generations, and there are theoretically almost 275 billion ancestors. But the population of Europe in 800 AD was around 25-30 million. Think that over…

When I started the book, I had no idea it would go in these directions. It is too much fun to think about all these things. This is an author I'll keep in a tickler file.

Heaviest spidering hit yet

 kw: blogs, blogging, spider scanning

A couple of days ago I reported a sufficient number of hits on my blog, over just two days, to download the whole thing. Apparently the incident wasn't even half over. Here is the world view for the past week:

That's 4,897 hits for the USA. The total for the rest of the world is 97, which makes 4,994 overall. Since a typical week without spider activity totals about 300 hits, about 4,700 hits are anomalous.

As it happens, Google Stats notes about 4,700 hits from Safari on a Mac. So again I suspect a single agent on a single machine, but why there are more than twice as many hits on my blog as there are blog pages is mystifying.

Something new among the spiders

 kw: blogs, blogging, spider scanning

Look what I saw when I checked my blog stats:

This is about 350 hits per hour for most of the past nine hours. Almost all from Safari on Mackintosh computer(s). It looks like it was a full-site scan, because that's about all the posts I have, going back to 2005.

I'd be curious to hear from the spider-wrangler, just what is the purpose of all this?

Dual purpose memoir

kw: book reviews, nonfiction, naturalists, natural history, autism, memoirs

I scour the Science shelves at libraries and bookstores. Naturally, once I saw Diary of a Young Naturalist, by Dara McAnulty, I anticipated a good read. I was not disappointed.

The author has been a naturalist as long as he's been able to get out and into nature. The book is taken from his diary starting in Spring 2018, through Winter 2019, just before his 15th birthday. He writes to re-process a day and its experiences. It is a triumph for him to share all that with us.

This is a memoir with two tracks, as his diary has two tracks. He shows us nature as he sees it, and he shows himself to us, as he experiences himself and the world around. This takes some doing because he is autistic, at least according to the modern definition (It wasn't that long ago that "high-functioning" autistic persons were described as having Asperger's Syndrome, but that term has been swallowed up into "the spectrum", which covers a huge range from classical autism—which depicts those who cannot communicate nor even recognize the difference between people and furniture that inexplicably moves about—, to the highest-functioning end of Asperger's, which grades into the hyper-focus of ADHD).

Both Dara and his brother Lorcan are "on the spectrum," though they experience it differently and behave differently. I'm not certain that his sister Bláthnaid is also autistic, but once or twice he writes of her as though she might be so. Whatever their status, all three children are very, very lucky in having a mother who knows how to nurture them and provides a safe haven for them, and a father who is equally accepting and nurturing. This family picture is from Irish News. Dara is wearing blue.

Dara, in particular, is easily overwhelmed by business/busyness in the human world. It is time-consuming and difficult for him to recover from attending a public function or giving a speech, something he is called on to do more and more often, particularly as his blog has gained popularity and he's become better known among naturalists and environmentalists. Just attending school takes its toll, all the more when he is bullied, as autistic youngsters frequently are. However, the school in their new neighborhood is quite different, he's bullied far less often, and he writes of gathering a number of students to form a club for environmental activism.

In spite of all the troubles he's had, Dara writes with open-hearted charm. There's a freshness akin to what I've enjoyed during conversations with young friends "on the spectrum." Describing his family's last leave-taking of Rathlin Island, which he describes as shaped like a mermaid's tail—they were soon to move farther away from the northern coast—, he says, "There's a Rathlin space inside me, mermaid-shaped, and it needs to be filled again." In this picture, perhaps you can almost see the mermaid, off the picture to the upper right, taking her leave. (Picture from Wikimedia).

Later on, writing of a walk in late September: "The beach is invigorating today. I haven't stretched my legs properly in a few days, and the comfort of walking unloads a little more weight. With every passing day, a little more joy sneaks in – is there a peak, a maximum amount of joy that we're allowed to feel?"

I see I have dwelt mostly on autism. The book is filled with bits of knowledge about birds and other animals. I don't know if I can easily recognize more than a handful of bird species. Dara seems to know dozens, perhaps hundreds, by sight, sound, or even from a single fallen feather. He's much more than a bird watcher, however. He writes of insects, particularly those that inhabit streams and ponds, toads and frogs, and numerous other creatures whose habitats we have, quite frankly, invaded and often ruined.

He has a visceral reaction to things. He feels with his whole body. This can cause surprise at times: he writes of finding a jay feather and handing it to a girl standing nearby. Her mother snatched it away, saying, "Dirty!", at which point Dara screamed. He screamed loud and long, and it took much of his mother's care to calm him down. This was probably when he was younger than ten. He also writes of a later incident: seeing a boy pick up a chestnut, followed by a similar reaction from that boy's mother. But Dara held back and waited. When the mother was distracted, he found a bigger chestnut, sidled up to the boy, told him a bit about chestnut trees, and let the boy whisk the nut into his pocket before the mother could see. That's one-on-one activism, and I hope the youngster keeps his love of nature.

At about 200 pages, the book is just right. Not every day is detailed, perhaps a quarter of them or less. What we do have produces a comforting feeling that at least some young people are "getting it", that they realize we cannot continue to devour the earth, heedless of those with whom we share it.

Back door astronaut

 kw: book reviews, nonfiction, space flight, test pilots, commercial space flight, biographies

Let's cut to the chase. Test Gods: Virgin Galactic and the Making of a Modern Astronaut, by Nicholas Schmidle, is deep and complex, though very readable, bringing to us the story of an extraordinary test pilot, warts and all, and some of the author's story, also warts and all, interwoven with the history of an extraordinary spaceship company.

Marines Pilot Mark Stucky found his way to becoming an astronaut at NASA blocked at every turn, and eventually found his way to the company Scaled Composites, where he test-flew the prototype of SpaceShip Two, an improved replacement for SpaceShip One, being built for Virgin Galactic.

SpaceShip Two crashed in 2014, which set back Virgin's plans by a couple of years. A second version of SpaceShip Two was built. The book opens with a test flight in in 2016 in which SS2 spun out at altitude. The episodes ends with Mark Stucky about to try something. We know it worked because he is still with us, but it isn't until a later chapter that we learn the trick Stucky used to bring the craft under control.

The narrative carries us through the test flight of Dec. 13, 2018, when Stucky and co-pilot Frederick Sturckow flew the craft to an altitude of 51.4 miles, above the 50-mile criterion used in the US for "the edge of space." At that point the two men joined the elect number of astronauts, and also became the first persons to reach this altitude in a piloted craft since the Space Shuttle program was shut down in 2011.

The author was "embedded" in Virgin Galactic from 2014-2018, and his unusual level of access allowed him to write such a book about Mark Stucky, Virgin Galactic, and provide close-up-and-personal insight into Richard Branson, the founder (and main funder) of Virgin Galactic, other company figures, and some of the test pilots. This photo shows Mark Stucky and David Mackay after they piloted SS2 on its first flight past Mach 1 (the December 2018 flight reached Mach 3, and it takes Mach 25 to achieve orbit).

When Stucky and the author met, as I understand from the text, they learned that Stucky had known, and been trained by, the author's father Robert Schmidle, a test pilot and fighter pilot for the Air Force. It turned out that the several of the test pilots at either Scaled or Virgin had known the elder Schmidle and some had been trained by him. Thus, the book is in part about the author himself, learning more of the test pilots' life that his father seldom spoke about.

Test pilots are a special breed. They think their way through crises that make most people freeze. My father knew a fighter pilot during WWII; they are of similar stock. This man in particular had a gunfighter's reflexes; Dad called him "twitchy". Such men do things so far beyond most of us, that the book's title Test Gods is warranted, at least on a secular level.

I really can't say more. It seems that authors like Nick Schmidle are also a special sort, able to take firm grip on our heart strings and make us see through their eyes and feel in our own guts, what they are feeling.

I understand from some searching around that the publication of Test Gods precipitated a falling out between Mark Stucky and Virgin Galactic. Perhaps the book exposed too much. But the cracks were beginning to show long before. When you corral too many alpha males together, fireworks are guaranteed. I credit Mark Stucky's unusual tact with holding things together as long as they held.

A little over a year ago the Virgin Galactic's craft, piloted by a new set of pilots, "reached space" for the fourth time, the first with a full crew of four, including Richard Branson, attaining an altitude of 53.5 miles. Perhaps Branson's dream of taking tourists to the edge of space is soon to be achieved, at a little less than half a million per ticket.

Technical note: SS2, officially named VSS Unity, is launched from a dual-fuselage "mother ship" called White Knight Two, now officially named VSS Eve. The launching craft brings the spaceship to an elevation of about 48,000 feet (nearly 24 miles, almost halfway to the 50-mile criterion), and then releases it to power its way upward to space.

Give it to me straight, Doc

 kw: book reviews, nonfiction, science, publications, research, fraud, bias, negligence, hype, polemics

When I was a chemistry major, taking organic chemistry, we had a lab exercise called The Martius Yellow Competition. It's a famous experiment, designed at Harvard, in which we had to produce seven compounds, one of which was the famous dye Martius Yellow. The dye is protein-specific, making it useful for staining certain cell preparations for microscopy. That also makes it problematic if you get it on you. It stains your skin bright yellow, and the stained skin takes about a month to grow out. A few of my fellow students finished that lab day with big yellow blotches on their hands and even faces.

What is of interest here is that two of the compounds—all are crystalline solids at room temperature—are hard to crystallize. To get one of them to precipitate out of solution, we had to cool the solution on an ice bath and then scratch the bottom of the flask, carefully, with a metal spatula. The other needed exposure to UV light, which we accomplished by putting the flask on a window sill for an hour or so.

Of course, if you already have a little bit of the target material on hand, in crystalline form, you can get a solution to crystallize quickly by seeding it with a bit of dust from crushing a tiny crystal of the same stuff. And here the professor told us a story. One of his mentors was an elderly chemist who had a beard. Once in a while one of his students would be having a hard time getting a solution to crystallize. He would call the professor over for advice or help. The professor would look at the flask, scratching his beard, and then the desired crystals would begin to form! As we heard the story we first thought the old professor must have poor hygiene habits. But No: Then he told us the old fellow knew what to anticipate, and early in the morning of such a day, he would put a bit of solution on his beard and let it dry. The scratching would release a few seed crystals into the air. When any of them fell into the flask in question, it would start the crystallization!

Such playful tricks aside, during my extended education (14 years at four universities and colleges), I learned that some scientists play fast and loose with their "science." Not all published "science" is genuine, and some of it is downright dangerous. I knew professors who were, quite simply, frauds. I don't wish to mention any names, because others have already exposed the worst of them, or their "work" has been superseded anyway. But I learned that there are several ways to get results into print even if you have no useful results to report. It's the fruit of the perverse motivation system called "Publish or Perish".

Thankfully, I don't need to get into detail, because a real scientist, Dr. Stuart Ritchie, has written a great book about how science goes wrong: Science Fictions: How Fraud, Bias, Negligence and Hype Undermine the Search for Truth. Dr. Ritchie is a real scientist, in contrast to myself: I got the degrees, but spent almost half a century writing software for scientists, without doing any science. Much of my value was making sure they got their math right, because I remembered all the calculus they had forgotten. I am particularly adept at statistics, so I know deeply how easily they can be misused to cook up a result almost out of thin air.

As an illustrative aside: I am an amateur radio operator (a Ham). On one occasion the members of a radio club I was part of visited an amateur who specialized in moon-bounce communication. He had a steerable antenna the size of a barn door, fed by a thousand-watt transmitter. It was just barely capable of getting a signal to the Moon and hearing it when it came back. The signal was noisy and barely discernable above background noise. Sometimes a Morse code "dah" would be broken up and sound like two "dits". (The dah is three times as long as the dit). Our host told us that sometimes the signal is so buried in the noise, and you listen so hard, that you can imagine an entire conversation out of random noise.

This is relevant. Many, many published results are based on something called "statistical significance", which has a criterion called the p value, with a "significance threshold" of 0.05. As long as the p value is less than 0.05, the result is considered "significant". It requires backward thinking to understand a p value. It is the probability that the "result" you obtained could have happened completely at random. Sometimes you will hear it said that there's only one chance in twenty, or less, that the conclusion you have drawn is incorrect.

That is not a very strict criterion. If you peruse scientific literature that includes statistical analysis, you are likely to find that most of the papers show results with a p value only a little below the threshold: 0.048, 0.04, 0.045, and so forth. Sometimes a "more robust" result will be reported, with a p value of 0.01 or even 0.005. To me, that is more like it. Because if you have thirty or so publications, all touting a p value just below 0.05, you have to say to yourself, "At least one of these is likely to be false. Maybe more than one." Then you should ask, "How can I find out which?"

The "how" is to replicate the experiment. Some experiments aren't too hard to replicate. What if the new experiment gets a different result? You can't stop there and say "It was wrong." It requires digging deeper, and nailing it down, then finding a journal to publish your counter-article (which can be remarkably hard; see the author's first story). In Science Fictions you'll read about some of the ways one can follow up.

What is more serious is the practice of hiding results that didn't work out, often called Null results. This is called the File Drawer Bias. For some kinds of experiments, particularly in psychology and medicine, there may be five or ten times as many "results" in the file drawer as the ones that were published. Automatically, we have to realize that a quarter to a half of the published reports are probably incorrect. Again, replication might be able to clear the matter up. However, doing experiments takes time and money. Our author reports a partial solution that is being implemented by many funding bodies, both governmental and private: They will only support the experiment if it is pre-registered and the results are guaranteed to be published. Such as system can still be gamed, but it is harder.

All this shows up close to halfway into the book, where the author tackles the issue of Publication Bias. Earlier, he takes on Fraud, as the most dangerous, and paradoxically, often the hardest to deal with in any timely way. A few heartbreaking stories are told, such as a surgeon who claimed he had perfected an artificial trachea to replace one damaged by accident or cancer. All of his patients died, usually after only a few months. Yet he was protected by the institution where he worked because of his fame. But eventually it all blew up. Far too many charlatans get famous enough (based on little substance!), that they are protected this way. And let us not forget the "accepted science" of the late 1700's, which resulted in the physicians for retired President George Washington bleeding him nearly dry because of a bad cold, such that he died.

Fortunately, we are more likely to encounter various kinds of bias. We are all biased. I was fortunate enough to take a class in literary discernment (I don't recall its actual title). We read articles from a great many publications. Some journals that I remember were The Wall Street Journal, Commonweal, National Review, The New Republic, The London Times, and The New York Times. We learned that every writer is biased, as is every editor. We learned to determine the bias of each writer and, from multiple articles, the likely bias of the editorial board for some of the publications. We also learned how to tell if a writer or editor is aware of the bias and has tried to mitigate it to any degree. Hint: Look for the number of modifiers (adjectives and adverbs) and their "flavor" (for example, "The company reached a compromise with the plaintiff" compared to "…reached a risky compromise…" or "…reached a satisfactory compromise…", and also compare to "…barely reached…"). Honest editors remove as many modifiers as possible, keeping only those that bear their weight in meaning.

I don't know how much Negligence is a problem. The stories didn't stick with me. Hype was of greater interest. Who remembers (from 1989) Cold Fusion? Lots of hype. Eventually, a total fizzle. The first story in the "Hype" chapter of Science Fictions tells of a supposed bacterium that used arsenic instead of phosphorus in its biochemistry. It turned out to be a story of contamination in the lab, not novel biochem in the field. It seems to be accepted today for a scientist with any kind of result to issue a press release long before submitting an article for peer review and publication. Perhaps the Snake Oil guy above would fit better alongside this paragraph!

But, seriously, what, oh what, can be done about it? Dr. Ritchie knows science from the inside. His last two chapters plus the Epilogue have suggestions that look workable to me. They primarily deal with incentives. Some of the current incentives seem designed to reward bad science. The simplest example is the Publish or Perish atmosphere in which tenure is only to be had by publishing at a superhuman level. This rewards "salami slicing", in which work that has several results will be published as several small papers rather than one that links them all together.

A family proverb is the "Moses method": To change the system, get everyone into the wilderness and wait 40 years for the older generation to die off. I hope the suggestions of Dr. Ritchie can make great inroads into the mess we are presently in, a lot quicker than 40 years.

Special bonus feature:

I sometimes tell scientists I know my suggestion for getting lots of good science done:

• Do a sketchy experiment to test an outlandish hypothesis. Drag it out until you get some kind of publishable result.
• Publish, with much fanfare.
• Based on the publication, trawl for funding to do more experiments to "confirm" your finding.
• Publish again; two papers if possible. Many more, if you can.
• Produce plenty of fanfare, including "stick in your eye" statements to rile up the establishment.
• Repeat as much as possible or until you can't get more funding.
• Some angered scientists will publish rebuttals. Some may even try to replicate your result.
• Answer every rebuttal, vociferously, in multiple venues if possible.
• Publish a "synthesis" of the entire matter. Be sure to cite all your prior work. Your "citation index" gets you noticed more.

This will get a lot of scientists to work their butts off to prove you wrong. One side effect is likely to be some unexpected, good science. Then, if you want to retain a shred of reputation, publish again, "de-biasing" your results, with more modest conclusions and a bit of mea culpa about the "little bit of overreach" in which you formerly indulged.

And now, back to our regularly scheduled program. It's a great book!

Today's spiders, Russian style

 kw: blogs, blogging, spider scanning

I posted a book review a few hours ago. I just looked at the stats and saw a big spike. Here we see the national "interest" over the past 24 hours (as of 9pm EDT):

Eight arms and nine brains

 kw: book reviews, nonfiction, octopuses, intelligence, philosophy

After reading (and reviewing) Metazoa by Peter Godfrey-Smith, I just had to get his earlier book Other Minds: The Octopus, the Sea, and the Deep Origins of Consciousness.

The author has spent much time at a place near Australia called Octopolis, where as many as a dozen or more octopuses, which are usually solitary, live in rather close association. Near the end of the book he muses about how Octopolis came to be, and mentions in a glancing way a few other reports of these animals living near one another. He has also spent much time "visiting" giant cuttlefish (up to a meter in size) that frequent other areas, also near Australia. These experiences inform his thoughts about "What is it like to be an octopus" and about consciousness in general.

Theories of why we have large brains and consciousness tend to revolve around our sociability. At least among apes, brain size correlates with social environment. So why do octopuses have such large brains? Currently, only at Octopolis are they seen to associate socially, although much of that is fighting. I suppose society has to start somewhere.

The book opens with a quote from William James, which I reproduce here in full:

The demand for continuity has, over large tracts of science, proved itself to possess true prophetic power. We ought therefore ourselves sincerely to try every possible mode of conceiving the dawn of consciousness so that it may not appear equivalent to the irruption into the universe of a new nature, not-existent until then. —William James, The Principles of Psychology, 1890

This exactly accords with my understanding. René Descartes thought that only humans were conscious, leaving him free to unflinchingly torture a dog, claiming the animal's screams were robotic utterances. I titled my review of Metazoa "Is 1% of a mind still a mind?" Let's see if we can figure what proportion of a mind as we know it might reside in the common octopus, Octopus vulgaris.

The nervous system of the common octopus includes half a billion neurons. However, 60% of these reside in eight sub-brains, one near the base of each arm, and the other 40% are in a torus (a donut-shaped mass) that surrounds the esophagus. Thus, the main brain has about 200 million neurons, while each arm's sub-brain has about 37.5 million. We should probably consider the main torus as equivalent to the cortex in vertebrate brains, and the 8 sub-brains, taken together, as equivalent to the cerebellum, which runs the body and, so far as we know, does not contribute to consciousness. The size of the main torus is equivalent to the entire brain of a Norway rat. But if we consider the octopus torus-brain equivalent to the vertebrate cortex, it more closely matches that of an average house cat (250 million) or a less-familiar animal, the rock hyrax (200 million).

Octopuses are mollusks. Of mollusks, octopuses, squids, cuttlefish, and scarcer animals such as the nautilus and sepiolid ("Dumbo octopus") make up the order of cephalopods, which means "head-foot". Among mollusks, all the brains are found among the cephalopods. The largest snails and clams (members of two other orders of mollusks) have brains containing ten to twenty thousand neurons, not millions.

What is the size of the human cortex? We've all heard that we have "about 100 billion nerve cells". The actual number is close to 85 billion, but only 16 billion make up the cortex, where we think consciousness is created, the feeling of what it is to "be a person." Most of the rest are in the cerebellum, which runs the mechanics of our body. If there is a linear relationship at work here, 16÷0.5 = 32: our cortex is 32 times as large as that of an octopus. Does that mean we are 32 times as conscious? Maybe so! Or perhaps self-awareness (which may or may not be the same thing) is a less-than-linear function of brain size, such as a square root. Then we could say we are about 5.5 times as self-aware as an octopus. 

Let's speculate for a moment what it might "be like" to be a honeybee, which has a million neurons. Estimating that half are involved in its sense of self, the little bee may be 1/32,000th as conscious as we are, or perhaps as much as 1/180th. Whatever they think about, it's sure to be a lot slower, and less profound. Beyond that I dare not tread!

Regardless, it is pretty clear from the stories and analyses by Dr. Godfrey-Smith that octopuses are quite self-aware. He tells one story that touched me, of a SCUBA diver who saw an octopus in its den and reached his hand toward it. The octopus reached back and grasped his hand, then came out of the den and began "walking" (they do this on two or four of their arms, with the others coiled or held upward), leading the man on a "tour" of the area that lasted ten minutes. That incident may be the closest a person and an octopus have come to communication on any meaningful level. Far too frequently, the animals are brought into a lab and "tested" with mazes or food choices and so forth. Frequently, they express their frustration by squirting water on the experimenters. Perhaps they prefer not to be treated like the village idiot.

A side thought just occurred to me. The brains of birds and mammals are differently arranged, and the neurons of birds seem to be more efficiently packed and connected. Thus an African gray parrot, with a walnut-sized brain, nonetheless has about 2.5 billion neurons, and can learn to speak and hold conversations with humans. Rather simple conversations, true, but none of us has learned even a single word of "parrot".

As we ponder now we might communicate with residents of a different planet around some other star, we would do well to consider how we can better communicate with parrots, octopuses, and other critters among which we live. 

Do octopuses have a visual language? Their skin is akin to a video screen, and sometimes seems to reflect their thinking. Perhaps much of the time their skin patterns are akin to a visual EEG! I wonder what is on this one's mind.

I really like this author's writing. I've riffed on what he wrote more than reported about it. The best authors stimulate thought!

Who's afraid of the big bad COVID?

 kw: analysis, epidemiology, immune system, vaccination, herd immunity

The magic number is 7. We'll get back to this. 

The first thing to understand about a pandemic disease is the ratio of infection to symptomatic illness. Only then can you understand the progress of the disease through time in a population. This ratio is the first thing a national disease-monitoring organization such as CDC should determine. However, they have not, or if they did, they are not telling. I have sought other sources.

Dr. Anthony Fauci, without citing sources, claimed a few times that of the total number infected with SARS-CoV-2 virus, about 40% have no symptoms. An estimate out of South Korea claims 30%. But both of these are actually talking about asymptomatic carriers, those who have no overt symptoms but can still spread the disease. A few test surveys that I have been able to find showed a different picture. In a test survey, everyone in some population is tested, such as residents in a dormitory. Reports popped up, were public for a few weeks or less, and then vanished. They had a narrow range of numbers of the ratio of infection to illness. From these I got the magic number above. Stated a better way:

For every 7 persons whose test showed they were infected, one was ill and the rest had no symptoms.

 The range of magic numbers was between 5 and 9. For one test survey it was 10. Therefore, in the earlier stages of the COVID-19 pandemic, when there were no accurate tests, the numbers of known cases was only 1/7th of the actual number of infections.

If we combine that with the 30%-40% "claimed asymptomatic carrier" rate, we can surmise the following, for a total of 1,000 infected persons:

• 143 will be ill at some point (we're not counting deaths yet; some of these will die).
• Between 61 and 95 will be "carriers" who have no symptoms, for a total of 204 to 238 who can infect others.
• The remaining 762 to 796 who are infected will recover without consequence, for themselves or for others.

Now to re-examine the first bullet point above: How many of the 143 will die? Spoiler: less than 2, and maybe much less than that.

I am going to use data from the charts supplied at Worldometer, as faulty as it is. The definition of a "Case" has changed over time. Early on, people with certain symptoms were "presumed positive". Later, testing was implemented. To date, in the U.S. about twice as many tests have been performed as there are persons in the country. However, there are those who get a test every week, some (like myself and my wife) who have been tested 3-4 times, and well over half of U.S. residents have never been tested. At the present time, the number of "cases" includes test results, which depends on the accuracy of record-keeping (We all have heard stories of people who were in line to get a test, had "signed in at the door", and then before getting tested, opted out and left; later they got a letter in the mail stating that they had tested Positive. Maybe the person in back of them in line was the one really tested, or something. We'll never know).

There is the further problem with "no Flu season in 2020-21". Really? Is that believable? Reasonably accurate tests for SARS-CoV-2 were just coming into use during the winter of 2020. COVID "cases" were among the "presumed positive". I contend that between 30,000 and 60,000 U.S. residents who are counted as "COVID deaths" actually died of Influenza. There are also those who died while they were infected with the virus, but they did not die OF the virus (car accidents, suicide, etc.). News of such events is being suppressed, so it is hard to gather statistics. Let's hope the number is small. With all those disclaimers, let's look at this chart, taking it (mostly) at face value.

The blue and brown curves are 7-day averages, as calculated at Worldometer. Blue is cases reported each day, however such cases were determined. This is for the U.S., and the axis to use is labeled "100k" and so forth. Five waves of infection can be seen; they peaked in April 2020, late August 2020, January 2021, April 2021 and late August 2021.

Each peak has a corresponding peak in daily deaths, the brown curve. The axis is labeled "2k" and so forth. These curves are scaled to have visible parity during the third wave. Note that the peaks in deaths and the curves for daily deaths are offset from the peaks and curves for cases…except for the first wave. At the beginning, people didn't get help until they were at death's door, so many of those who died did so within a day of being admitted to a hospital, and they had been reported as a "case" on the day of admittance. Thus, let's look at the same chart, with cases shifted 15 days back, which makes the third wave overlap as well as possible. 

This presentation makes the dates harder to discern. I presented a similar chart on August 1, just 2 months ago, when the fifth wave was just beginning, stating "Herd immunity has arrived." This conclusion was based on the anomaly about Wave 4: there was no peak in the death rate, and during the summer of 2021 case rates were lower than at any time since mid-March 2020.

The 5th wave is the Delta wave. It is smaller than Wave 3 because it is occurring primarily among the unvaccinated (in which I count those formerly infected: "vaccinated by God"). It also appears to have about a 15-day delay between discovery and death. However, look at the subtle vertical shift over time. The death rate is lower in proportion during Wave 5 than it was previously. And the gorilla in the room is the very high death rate during Wave 1.

What happened during Wave 1? Firstly, we had no clue what was going on. There were no effective treatments. President Trump ordered certain companies to ramp up the production of ventilators. It turned out that ventilators caused more deaths than they prevented. They aren't supposed to be used for weeks at a time. But even more, many of these deaths occurred in nursing homes where the virus ran rampant. This was aggravated in five states whose Governors ordered COVID patients moved from hospitals back to the nursing homes they came from, creating the first super-spreader events. 

Secondly, there were no effective medicinal interventions yet. Now there are two for early use (coded IVM and HCQS), and also monoclonal antibody treatments such as Regeneron, which was used to treat President Trump. Thus, the blast of early deaths represented the "low hanging fruit". A large proportion of the most vulnerable Americans died in Wave 1. Most variants of the virus that have arisen later cause fewer deaths, and we have medicines that work better. So let's look at another couple of charts.

For these I used the 7-day averaged number of cases or deaths at the peak of each wave. These are not totals for each wave, be clear on that. For a few cases in one state or another, and in the U.S. during Wave 4, where there was no peak in the death rate, I used a date 15 days delayed from the peak in cases.

The chart on the left has the data for the U.S. along with the five states whose governors forced COVID patients into nursing homes. Each bar represents the ratio of peak death rate divided by peak case rate, in each wave. The chart on the right has data for seven states I found of interest, including some in which I have lived. The one I find of particular interest is South Dakota (I lived there 8 years), which seems to have had a better handle on this disease than the rest, particularly in Waves 1 and 5.

The "easy take-away" is this: During Wave 1, D/C was about 7% nationwide, ranging from 4.5% to 9.5% for the five states shown on the left, and (except for NH) between 1.7% and 4.5% for the seven states shown on the right. The death rate has continued downward since then.

While state numbers hop around a bit, the national averages for the five waves are

7%, 1.7%, 1.4%, 1.0%, 1.1%

Let us return to the magic number, 7. On average, for 7 infections, there is one illness. Is all the testing finding every infection, whether ill or not? Not really. The vast majority of tests are done by those who either think they are sick, are feeling sick, or fear/think they have been exposed. So, if there are 6 people out there with no symptoms for everyone who has symptoms, and very few of those 6 are getting tested, they are still not known.

We were told that we needed to achieve 70% "fully vaccinated" to gain herd immunity. That was based on an infectivity rate for the Alpha variant, which is pretty much out of the picture by now. Back to variants in a moment. To date (Oct 1, 2021), just over 185.25 million Americans are recorded as fully vaccinated. This is called 56.1% of the population in news reports, but of course no children under age 12 have been vaccinated, and it isn't certain that they ever ought to be, at least with today's vaccines. That's 48 million, or 14.4% of the population. So the proportion of those12 and older who are fully vaccinated is about 65%. Getting close! But let's remember, the 2-shot "vaccines" are claimed to be 95% effective, while the one-shot version is 65% effective. We can expect about 90% overall effectiveness, so the "actually immune" adults in the U.S. total about 58.5%. One more factor must be considered.

The number of past infections that have resulted in recovery is 33.7 million, or 11.8% of persons 12 and older. 58.5+11.8 = 70.3%. By the criterion set by the CDC, we have achieved herd immunity. More vaccinations and more recoveries happen every day, so we are moving farther and farther into "herd immunity" territory.

So what's with Wave 5? I call it the Delta Wave. A word on variants.

There are many "serotypes" of the SARS-CoV-2 virus. A year ago it was reported that about 30 were circulating in the U.S., and more than 100 were known in China. It's practically impossible to get useful data out of China any more, so we don't know how many serotypes exist. A Serotype is a minor variation in the RNA of the virus. Not all have any practical effect. But a few do. The serotypes are grouped into families by RNA similarity and by clinical measures including infectivity and virulence. So far, there are 12 such Variants.

Infectivity is a measure of how many virus particles one must ingest to cause an active infection, for a person of "average immunity" (a quantity that has never been quantified). Those 5%-10% of vaccinated persons for whom the vaccine "didn't take" have lower immunity, didn't respond strongly enough to the mRNA agent in the vaccine, and so didn't develop a useful antibody defense. They were easier to infect before, and remain easier to infect. For most of us, there is some number, perhaps 1,000 particles, that are sufficient to swamp our early immune response and trigger active infection (whether we ever get symptoms or not, and I picked 1,000 "out of the hat"). We may be exposed to 100 particles several times, and out body fights them off, all the while getting more "wise" to the virus. That produces natural immunity without infection.

Reversing the logic, we have the case spreading rate. For a virus of average infectivity, someone who is infected might infect two other persons during his or her period of active infection. The 70% figure for achieving herd immunity was based on a case spreading rate of 3. I have read claims that the Delta variant is more infective (a smaller number of particles are sufficient to cause active infection), such that the case spreading rate is 6. 

Some claim that if this rate is greater than 5, herd immunity is no longer possible. That is nonsense. Those who state such things have their math wrong. They are using a simple ratio, but the math actually requires inverting a Weibull distribution, and never goes to 100%, meaning that herd immunity is always possible. However, it does get harder to achieve when infectivity is greater. For example, polio has a very high infectivity, as does measles, but we rely on herd immunity in both cases by striving for vaccination rates of 95% of the population, primarily by requiring all school children to be vaccinated for measles and polio (and a bunch of others).

Virulence refers to the likelihood of serious illness or death. If we look at Wave 1 above, it appears that virulence was such as to cause a 5% death rate, before we found effective treatments, and now it is about 1%. Untreated, AIDS and Ebola have a near-100% death rate. Influenza has a virulence about 1/10th as great as SARS-CoV-2, with a great range depending on the yearly variant.

So, although there are hundreds of serotypes out there, we hear of only Variants ranging from Alpha to Mu, the 1st and 12th letters of the Greek alphabet. Waves 1 through 5 were due to Variants Alpha and Lambda (11th). A Variant is a collection of similar serotypes. Delta was the fourth variant identified, but was kept out of the U.S. until late this summer. Now it is dominant.

If the Delta variant were to arrive in a totally naïve population, a big, big Wave of infections would occur. The comparatively smaller size of Wave 5 shows that it is occurring among the non-immune, which presently comprise 30% of adults in the U.S. All the variants so far known cause only mild infection in the vaccinated. Yes, there have been a number of vaccinated people who caught the disease and died. They are among the 5%-10% identified earlier. The mRNA vaccine didn't produce a useful response in them.

Now, a final word about the magic number, 7. For at least Waves 1 through 4, reduce the death rate by a factor of 7 to get a true death/case ratio. It is likely also true for Delta, so we find that actual death rates for the five waves are:

1.0%, 0.25%, 0.2%, 0.14%, 0.16%

That's a low death rate, and I repeat, we have achieved herd immunity for Alpha and Lambda, and we're on the way to achieving it for Delta.