Coronavirus and Sunlight

kw: medicine, viruses, coronavirus, ultraviolet, inactivation

I contend that the safest place to see others face-to-face is outside on a sunny, breezy day. Masks are not needed outdoors, only indoors. Here is why.

If someone is ill with the novel coronavirus SARS-Cov-2, the cause of Covid-19 disease, any droplets that leave their body with their breath will contain virus particles, called virions on medical literature. The virions are rather large, some 125 nm in diameter. That's about four times the size of rhinoviruses, the most common cause of the common cold, and a it's a little larger than influenza viruses. However, 125 nm is 1/8,000th of a millimeter. No mask you can afford will capture them, but that is not the point.

Indoors among "the public", the threat is not isolated virions but the droplets released in small amounts by speaking or heavy breathing, in larger amounts by a cough, and in very great amounts by a sneeze. The droplets are mostly between 1,000 and 10,000 times the size of the virions they might contain. Nearly any such droplets that encounter your face covering or mask will be caught in it. So when you wear a mask to the store, when you get home wash it with hand soap and let it dry, or replace it if you have a lot of the disposable kind.

What happens outside? Unless the humidity is very high, the droplets evaporate in a few minutes, or even a few seconds. The virions are now "free". Even before the droplets evaporate, however, if the sun is up, something wonderful happens! Ultraviolet light from the sun destroys the virus genome. The question is, how soon?

I found and downloaded an article, "Predicted Inactivation of Viruses of Relevance to Biodefense by Solar Radiation", by C. David Lytle and Jose-Luis Sagripanti, in Journal of Virology, v79, No. 22, Nov. 2005, p. 14244–14252. The work was supported by DoD and relates to defense against biowarfare agents.

The authors gathered data on solar UV and Hg-vapor UV (such as that used in hospital disinfection lamps), and how quickly different kinds of viruses are destroyed. There are a lot of details, but the relevant conclusions related to coronaviruses are these:

• Sensitivity units are reported two ways, as D37 and as 1-log.
• D37 is the dose of UV needed to destroy all but 37% of the particles. 0.37 is 1/e, and is related to natural logarithms.
• 1-log is the dose of UV needed to destroy 90% (all but 10%) of the particles. It is related to common logarithms, of base 10. This is more understandable and relevant to us.
• The viruses of greatest interest in the article are filoviruses such as Ebola or Marburg. D37 for these is about 7.4 and 1-log is 17. (These data are from Tables 2 and 4)
• The virus of interest today is a coronavirus; the family Coronaviridae has D37 in the range 2.5-3.9 (Table 2), for which I calculate 1-log of 5.7-9.0. Thus SARS-Cov-2 is about twice as sensitive to UV light as the Ebola virus. That's good news.
• The effectiveness of solar radiation depends on the angle of the sun. A specific datum relevant to the DE-PA border area where I live is for Davis, CA, on a typical, sunny July 15. The 1-log level of deactivation for a filovirus occurs in 55 minutes. (If you're lucky enough to live in Hawaii, the sun's UV is twice as strong there, and the relevant time is 21 minutes.)

From these data I calculate that 1-log deactivation (10% remaining viable) takes between 19 and 29 minutes. Let's round these to 20 and 30 minutes. Deactivation is a stochastic matter. If a UV photon passes through the right part of a coronavirus virion, it will damage the RNA. Most of them miss. So let's look at the 20-minute level for a theoretical virus. In 20 minutes, 10% are still viable. In 40 minutes, only 1% are still viable. In an hour, 0.1% are still viable, and so it goes. That is one in a thousand after an hour, and one in a million after two hours, and one in a billion after three hours. For a "tougher" coronavirus, at the 30-minute end of that range, viability after an hour is about 1%, and after three hours it is about one in a million.

So if you're worried that someone emitting viruses is outside, and they blow downwind, two things work in your favor. Firstly, the swirling wind will spread them out so only a few have the chance to reach you, and secondly, if the person is some distance "upwind" from you, sunlight will zap the virions at a steady rate.

There are two further matters I am still researching. 

• How many virions need to enter the body to cause infection? A very infectious virus such as influenza can stably cause infection if around 100 virions are breathed in. This is because many of them are "beaten" by the innate immune system. For more susceptible people, not as many are needed, but I don't know what the normal range of natural resistance is, for people who are not vaccinated. It may not yet be known what the "average infectious load" (my term) is for coronavirus.
• Whether it is sunny or not, oxygen also deactivates virions. How quickly? Whatever I can find out, I'll report.

Why Seven Liberal Arts?

kw: education, philosophy, liberal arts, history

In a compendium of Medieval writing that I have been reading on and off for a few years I came across a summary of liberal education by Hugh of St. Victor. I did not previously know of his master work Didascalicon de Studio Legendi (Didactics on the study of reading), written in about 1135. The excerpts in the compendium (which I will review on a later date) include his exegesis of the liberal arts on the following outline (structure mine; his work is narrative in style):

Philosophy is divided into

1. Theoretical
1. Theology
2. Physics
3. Mathematics
1. Arithmetic
2. Music
3. Geometry
2. Practical
1. Solitary (Ethics)
2. Private (Economics)
3. Public (Politics)
3. Mechanical
1. Spinning
2. Arms-making
3. Navigation (Astronomy)
4. Agriculture
5. Hunting
6. Medicine
7. Theatrical Arts
4. Logical
1. Grammar
2. Expression
1. Probable Demonstration
1. Dialectic
2. Rhetoric
2. Sophistical Demonstration

The number of these, so Hugh says, is twenty-one items. I don't know how that is computed. Then he has this enigmatic statement, "…if you wish to compute stages, you will find there are thirty-eight."

This is prefatory to an exhortation to read the best authors in all these fields, but initially to focus on the "Seven Liberal Arts: the Trivium and the Quadrivium". The items bolded and highlighted in color comprise these seven: the trivium in green and the quadrivium in violet. He expected mastery of these to naturally lead to avid reading in all the arts listed (21 or 38).

At first this seemed to me a curious list. But letting it sink in, and thinking more broadly, I realized that the trivium plus the quadrivium still underlie a proper education. What do we care about so much that many universities still require test-taking at a very high level, under the banner of either the SAT or the ACT? A "quantitative section" (mathematical) and a language arts section (reading and writing, which covers logic and grammar at least indirectly), plus science, which hadn't yet been created by Roger Bacon when the Didascalicon was written. 

And what of navigation/astronomy and rhetoric? When I had drivers' training, map-reading was as important as the mechanics of controlling the car. These days, everyone has a GPS unit or Google Maps on their phones, and navigational skills are being lost. Further, hardly anyone uses stellar navigation any more. And while I had public speaking instruction in high school and college, most youngsters today barely have a session or two of "show and tell." So much for logic and rhetoric.

The seven liberal arts, plus instruction in Greek and Latin, constituted a classical education. That, except for the Greek, is what I received during my first few years when I was in a private school. I am glad I had that. And I am sorry that education, in the West at least, has gone downhill since the writing of the Didascalicon some 885 years ago.

Dissatisfiers and Satisfiers

kw: musings, happiness, satisfaction, fulfillment

From time to time I read or hear (radio program) one or another "happiness expert". The article or program will typically include a list of things that do or do not promote happiness. Sometimes I take notes. Collating my notes, I have two composite lists of four items. Here they are, with my thoughts on each:

Things that we think will make us happy, but don't, the Dissatisfiers:

1. Money. You may have heard or read, "Money is the root of all evil." Is it a Bible verse? Not quite. The first phrase of 1 Timothy 6:10 is, "For the love of money is a root of all kinds of evil". "Love of money" is one word in Greek, "philargyria", or literally, "love of the soul for silver". Note that this kind of love is A root, not The root, and that all kinds of evil, not all evils, are the result. We'll see why in a moment. I once had a dispute with a company executive who promoted "passion for profits". I declared that I had built my career on a passion for excellence, and that profits had always followed. His rejoinder was so double-tongued and self-blind that I was glad I already had an exit strategy! Money is useful, but it is a tool. Some say it can become an idol, but it isn't really. In this "modern" age, few believe in material idols, but people might make education, art, love (or lust), or religion an end in themselves, and thus a false god. Money can be a means to obtain one's idol. But its proper use is to secure one's life and comfort, and in anyone with a willing heart, money can be used to help others. Ask a billionaire, "Is it enough?" It is never enough if money is the goal. As a goal it promotes dissatisfaction.
2. Power. The Englishman Lord Acton is credited with saying, "Power tends to corrupt. Absolute power corrupts absolutely." As a lifelong observer of British monarchy in the reign of Victoria and her predecessors, he ought to know. But there is a corollary quote by David Brin, "…it's more true that power attracts the corruptible. The sane are usually attracted by other things than power." In my thirties I said to a supervisor that I was considering aiming for management (I was on a "tech track" at the time). He responded by making me the supervisor of two colleagues. I soon realized that it was all to easy to abuse power, and asked for an end to that experiment. Perhaps that makes me sane, by David Brin's standard, anyway! In the first three centuries of Christianity, nobody would be elevated to be an elder in a church (by a bishop or apostle) if he seemed to greatly desire eldership. Indeed, it was the usual practice to make a "test offer" of temporary eldership, and if the person accepted without protest, the post was temporary indeed, and not followed up with any further offers of responsibility. Augustine wrote that someone had to say, "I don't want it!" three times, on three occasions, before he was eligible to become an elder. "Abuse of power" is much talked about today. Genuine abuse of power is a great source of many evils. Indeed, it matters little how much money you have if someone with power doesn't permit you to use your money as you choose. Liberty is the appropriate power to make your own choices, but confers no right to make choices for anyone else.
3. Pleasure. Here I do not refer to all pleasure, but pleasure as an end to be sought, even by illicit means. Extreme pleasure-seeking leads to addiction. We are motivated by the pleasure/pain principle. However, it is one thing to take pleasure in good work, good relationships, and enjoyable activities, and quite another to seek pleasure to the detriment of others or of one's own well-being. Pleasure can become a false god. When chasing after pleasures disrupts someone's working life, or causes them to fail in school, or to neglect necessary relationships, it is no longer promoting satisfaction, but the opposite.
4. Fame. We all want to be well thought of. We can easily be drawn to wanting to be widely thought of: to have a large number of followers on Twitter or Instagram or whatever; to have the applause from large crowds and so forth. It can be addicting. I accompanied our son to a class camp, with a hundred or so pre-teens. One activity was a campfire. There were several acts and skits, and I sang them a song. They didn't just applaud, the boys cheered and the girls screamed like I was a rock star! I told my son later, "What a rush!! Now I know why rock stars do it." But I'm still glad that, working my way into a music career 50+ years ago, I changed direction and opted for a "day job." I am well enough regarded by the handful of people I really care about. More than that is unnecessary, and leads to dissatisfaction.

Things that lead to fulfillment and happiness, the Satisfiers:

1. Faith. He that believes only in himself has a fool for a god. We need God, a God who is greater than we are. I speak not of religion, which has to do with what we do. Faith is the belief itself and the object of that belief. Based on what we believe, we may do certain things, and thus be called "religious", but religion without faith is done for fame, and has no useful result. It is said that a faithful person is never entirely satisfied, because we so seldom live up to what we believe in. However, a certain holy yearning to do better is no detriment to the great satisfaction of serving a gracious God as well as we can.
2. Family. Not everyone has a congenial family. If your parents, siblings or other relatives are evil, perhaps it is best to gather a "family of choice." This would be your closest friends (see next item). But in most cases, we are happiest when we spend time with our spouse, children, parents, siblings, and others of our extended family. This is why most people choose to spend holidays with family.
3. Friendship. I knew a youngster during my Freshman year of college who had a huge family. His father had married four times: each of the first three wives had ten or more children and then died, and number four had just had a ninth child and was going strong. He had grandnephews and grandnieces older than he was. Perhaps he didn't need friends. The family farm had forty or more houses on the property, full of his relatives. The rest of us may have only three or four close relatives, or maybe ten or so, but we are built to relate to 100-150 people. We fill the gap with friends and acquaintances. I am not talking about "FaceBook friends" here. Some folks have several thousand of those, but they really have no more than a few dozen actual friends. We cannot be normal if we are entirely solitary.
4. Meaningful Work. I read a book titled Rivethead by Ben Hamper a long time ago. He was a riveter in an auto plant, attaching bumpers to trucks. Stultifying work. He and a couple of others got creative and invented a collective person they named Armand Hammer. By dividing up the work, they had time for other pursuits and a chance to "unwind" (and, I presume, Armand Hammer earned enough to support them all). But it has been truly said, "Love your job and you'll never 'work' a day in your life." I knew someone who strove to excel as a business executive. He was offered a promotion to executive vice president of his company. He was happy where he was, and he felt it was the best fit for him. He didn't think the promotion would be as good a fit, but felt he had to accept it. At the first meeting of the EVP's with the CEO, the CEO began the meeting by saying, "Gentlemen, we have all sold our souls for this." My friend stood and said, "I have not," and left. He resigned and pursued work in a different field, which he soon found was even more satisfying. For many, a job just puts food on the table and pays the rent; they are meaningfully occupied in their church, or volunteering, or carrying on a social hobby. Although just about everyone who writes about this uses the term "meaningful work", it may be better to call it "meaningful occupation" or even "vocation". A Vocation is a calling. When we have a calling we are typically the most satisfied. 

Looking at the second list, I would subsume the first and second points into the third. Firstly to be a Friend of God; secondly, to be a Friend to my family members (as much as that is possible); thirdly, to have Friends to whom I may not be related but who share a mutual love and respect. "A threefold cord is not easily broken" (Ecclesiasted 4:12b). These things lead to satisfaction. The things the foolish pursue lead to dissatisfaction.

Wisdom in Exodus by an heir of its promises

kw: book reviews, commentaries, bible, exodus

I have slowly and carefully read The Rational Bible: Exodus: God, Slavery, and Freedom by Dennis Prager over the past month or so. Having it as an e-book, I can read it at odd times and places. As I mentioned in a review of the volume on Genesis, this volume was published first. This was because, in the author's words, 

"…Exodus contains the Ten Commandments, the most important moral code in world history, and the central moral code of the Torah. If people lived by those ten laws alone, the world would be almost devoid of all man-made suffering." – p.xxii

I would add that this book describes the transition of a family into a nation.

The volume begins with a series of essays, and there are essays throughout, in addition to shorter comments. As I read I made notes; not too many, only 32. However, I will confine myself to the content of just a few of them for this review. To me the most important essay is "The Torah is not Man-Made". In this essay Dr. Prager presents a number of matters that were first presented to the world by the Torah, including:

• A God Who is universal
• A God Who is invisible and incorporeal
• A God Who is moral, and Who judges morally
• A God Who created nature, and therefore is not a part of nature
• A God Who loves and desires to be loved
• Universal human worth
• Universal human rights

Other matters found in the Torah and in no other ancient writings include the importance of kindness to strangers, that women are free agents as men are, and that "slaves" (actually indentured servants with an exception I'll mention anon) are to be treated well and to enjoy a Sabbath rest along with everyone else including strangers (foreign visitors) and working animals.

It is often noted that the Torah doesn't explicitly demand the abolition of slavery. As the author notes in a few places, the relevant Hebrew word can be translated either "slave" or "servant". The difference can only be elicited by noting the context. In principle, a servant works for wages, while a "slave" works not for present wages but to pay off a debt. The way an Israelite became such a slave was by going broke, and then selling himself to another Israelite for certain funds, either to pay of a debt or to feed his family. Such slavery was not permanent; slaves were to be set free at the time of the Sabbatical year. The Torah has stipulations about the price to be paid for a slave's work according to the years remaining until a Sabbatical year.

The exception to temporary slavery (indentured servitude) was if a slave had married during his tenure, and proclaimed to his master, "I love my master, my wife, and my children. I will not go out free." He was taken to the doorpost and had an earlobe pierced through with an awl. He was then to be his master's servant "forever".

To other matters: there is a lovely comment about the daughter of Pharaoh, who took in Moses and raised him. It is very likely that she knew the young girl who offered to find a nursemaid for the infant was related to him, and that the "nursemaid" would be the boy's mother. But she agreed, and paid wages to Moses's mother to care for him until he was weaned. The author comments, "Biology is not destiny; you can be the child of an evil person and be a good person." Also regarding women, the daughter of Pharaoh is one of six prominent women who influenced Moses.

I am a little puzzled about a statement I found in a couple of places that "Abraham was the first Jew." Also, in one place it states that Abram was "not born a Jew but became one late in life". This is in contrast to several instances in which Abram/Abraham violated kashrut (Kosher laws), such as when he served meat and milk together to the three visitors, who turned out to be God and two angels. In this and other instances, the author properly notes that the patriarchs who lived before the giving of the Law cannot be expected to follow its precepts. A relevant and more accurate comment is found with Exodus 1:7, about Abraham's descendants:

"This group was first known as Hebrews, then as Israelites, then as Jews"

The first mention of the term "Jews" is in 2 Kings 16:6, "At that time Rezin king of Syria … drove the Jews from Elath…" This was an aftermath of a battle between Ahaz king of Judah and Pekah king of Israel, which occurred about 732 BC. This was 200 years after the division of the kingdom of Israel and between eleven and thirteen centuries after the death of Abraham, depending on which chronology of ancient history you accept. My own study of the usage of the three ethnic terms indicates:

1. Abraham was called "the Hebrew". His descendants are Hebrews, and the descendants of Jacob/Israel in Egypt were usually called Hebrews.
2. Jacob's descendants were called "children of Israel" (first mention Genesis 32:32) and later "Israelites" (Exodus 9:7).
3. After the division of the kingdom between Solomon's son Rehoboam, who became king of the Judah, the southern kingdom, and Jereboam, who became king of Israel, the northern kingdom, over time the "southerners" became known as Jews.

Perhaps these distinctions are more important to a Christian than to a Jew. It is clear from statements made in the first five books of the New Testament, and statements by Paul in two of his letters, that descent from Abraham was very important to the Jews of the First Century. For Jews to count Abraham as "the first Jew" makes sense in this context.

I was very affected by the explanation of "taking the name of the Lord in vain." The author explains that "take" in this verse really means to "carry" or even "bear". Those who affirm their belief in God "bear" His name; they represent God to the world. If anyone, in the name of God, does evil, so that the name of God is impugned, that is to "take" His name in vain. The last phrase of the verse is, "…the Lord will not hold guiltless him who takes His name in vain." This is the only one of the Ten Commandments with an explicit penalty. To misrepresent God is utterly serious!

Those who claim to follow God, the God of the Torah, whether Jews or Christians, represent Him. The world sees them as His representatives. To a Christian a relevant term is "ambassadors for Christ" (2 Corinthians 5:20). To a Jew it is "a people called by the name of the Lord" (Deuternomy 28:10). Among world religions, none claim that their god is the God of the Torah, though the Muslims imply that Allah is the God of Jews and Christians (it is not so!). The author doesn't mention Islam or Allah in this book, but it is clear he has them in mind in his discussion of Exodus 20:7, decrying those who kill innocent people in the name of their god.

I will mention one more matter, Theodicy, or "vindication of God." Specifically, it is a common question: "Why does God permit unjust suffering?" In the two volumes of The Rational Bible so far published, Dr. Prager turns this question into a proof of the afterlife. Along with statements of this or that Biblical figure being "gathered to his fathers," we have also Exodus 23:7, "…do not kill the innocent and righteous; for I will not justify the wicked man." Since we see that the wicked frequently seem to "get away with it," such a passage can only mean that God reserves some to future punishment in the afterlife. We also read,

"The believer has to account for the existence of one thing—unjust suffering; the atheist has to account for the existence of everything else." – commentary on Exodus 2:24

Whereas most books I read are from the library, I am glad to own e-book copies of this volume and its companion, so I can re-read them, and I eagerly await publication of the other three! Considering the time and work involved, I thus wish Dennis Prager a long and fruitful and fulfilling life.

Whether you are a believer or not, The Rational Bible has wisdom for you, in a generation in which wisdom is very scarce.

Spiders from all directions

kw: blogs, blogging, spider scanning

I checked the stats just now, and imagine my surprise at the big spike about two days ago, or two and a half. The map shows that the biggest "customer" has been Turkmenistan. Who knows what they are up to?

Here is the Audience list, the top ten:

The single big spike is probably Indonesia. The US provides background "clutter" of about 40 hits daily, at a steady rate, only visible here on May 7-9. The visible "grass" is a five-day run, with Turkmenistan providing the little spikes from May 9-12, and Russia the "rough hump" over the past day and a half.

I have noticed a time or two that my post "The largest homophone set" is a heavy favorite of spiders. I wonder if the Turkmen and the Russians know that "homophone" is a grammatical term…

A new focus of spider activity?

kw: blogs, blogging, spider scanning

Just after posting the prior item, I checked Stats, and saw this. The five spikes during the past several days represent 95 hits from Turkmenistan.

Am I right to conclude this is spidering activity?

The usual is less usual than we think

kw: analysis, statistics, black swans, statistical distributions

Alternative Title: Thousand-year Floods Occur Too Often

Just to set expectations ahead of time: The aim of this article is to analyze activity for a stock in the U.S. stock market. However, the phenomena of interest here apply in numerous areas, including flood control, a fun place to begin.

This picture shows the Sorlie Bridge linking Grand Forks, ND with East Grand Forks, MN, during the flood of 1997. It's what happens when you design for a 100-year flood, and it has been 170 years since the last big flood. The peak flow was only 5% greater than the design criterion.

What would a 1,000-year flood look like? Sooner or later it'll happen. Some interesting statistics are involved.

Here we have a log-Pearson plot of gauged "floods" on a river in Australia. AEP is "Annual Exceedance Probability". I was taught how to make such plots during a summer project in graduate school. The data are the highest flow recorded every time the river overflows its inner banks. There are 46 such events charted here. I infer from the rightmost datum that the record goes back about 80 years. A "flood" as thus defined will happen every year or two.

Extending the coordinates of this chart I estimate that a 1,000-year flood would have a peak flow of between 350 and 400 on the scale shown (I infer m³/s; in ft³/s: 12,000-14,000), not quite twice the flow of a 100-year flood.

Quantitative hydrology doesn't extend back even 200 years. How can we validate the use of log-Pearson analysis in extrapolating for 1,000-year floods? There are also at least two other analysis methods in use. How could we validate any of them?

Nearly forty years ago, a fellow student of mine in graduate school worked out such a validation, for at least one "creek" in the Black Hills area. In this view from Google Maps, the creek mouth is off the left. The image width is about a quarter mile.

The boulders seen here are not glacial erratics. The student, Bill, measured lichen patches on hundreds of the boulders, choosing only those larger than he was. He was able to discern, by the size of the largest patch of a certain kind of lichen on each boulder, when they were last tumbled down the creek and washed out onto the plain, sometimes as far as a couple of miles. He determined the outwash area for twenty large floods from that creek. I saw a map he made of those outwash areas.

References on lichenometry helped him obtain approximate dates for the floods. All had occurred in the past 5,000 years. As a student of hydrology, he was able to determine the flow volume needed to move a car-size boulder a half mile to a mile from the creek mouth. Here's the kicker: a chart of historical hydrology measurements on that creek indicate that every one of the twenty floods was at least a 1,000-year flood. But they were actually something like 250-year floods! (or, actually, scattered out from 250 years and upward.) Such data didn't fit into the historical analysis. To be clear about what follows, the log-Pearson analysis is not related to the Normal Distribution, nor to Lognormal statistics.

Statistical analysis in many areas depends heavily on the Normal Distribution, AKA Gaussian. As it happens, this is frequently a very good model. However, even the textbook example, human height, isn't as "normal" as it might seem. In this blog post by John D. Cook, he shows that extremes of height and of shortness are not well predicted by a normal distribution with a standard deviation of 2.5 inches, the criterion that fits well for about 95% of the data for men and for women (which must be analyzed separately). By that measure, there should be no more than one man taller than seven feet, or shorter than 4'-5", nor one woman taller than 6'-9", or shorter than 4'-1", among our entire world population of more than 7 billion. But the NBA is full of seven-footers (more than 40, as counted in 2018), and there are numerous "little people", particularly in entertainment, ranging from four feet down to just above two feet tall. The shortest adult woman on record measured nineteen inches. Data such as these fit better a "fat tailed" distribution, for which more extreme values are more frequent than a Normal analysis would predict.

For events such as floods, it is likely that the excess frequency of extra-large floods is due to a different climate regime from the usual. For height measurements on people, different populations with distributions account for some of the "excess" variation, while medical issues such as glandular gigantism or dwarfism also account for some. These kinds of considerations indicate that we need to study a broader scope of phenomena. If an analysis doesn't include everything relevant, our model is incomplete. But what of "surprises" in a data set that is thought to be well-behaved?

These are examples of black swans. I reviewed The Black Swan by N.N. Taleb thirteen years ago. The book's theme is that "uncommon" events aren't so uncommon. He applied findings such as these to investing. You may recall there had been a significant bear market a few years earlier, starting in 2000. The one that followed the book by a year (2008-09) made Taleb look like a prophet. Now we are in the middle of another one.

One claim in The Black Swan is that daily moves on stock issues follow a Cauchy distribution. It is described as the ratio of the sine of one uniform random variable divided by the cosine of another. Mathematically, that is the tangent of a uniform random variable over the interval [-π/2, π/2], but not including the end points, for which its value is infinite. The Cauchy distribution is typically described as a tangent function over the half circle.

That was something I could test. The Cauchy distribution is very fat-tailed or, viewed another way, it middle part very skinny compared to a normal distribution. It looks like this. We'll see how a normal curve looks in a moment.

Does the distribution of daily closing values of stocks in the market look like this? I chose the most stable stock in America, AT and T, to test this. I used data for the past 37 years (everything available through Yahoo! Finance). I used what they call "Adjusted Close", which factors in the values of stock splits and dividends. I analyzed the entire period, and two sub-periods, the ten years from 1/1/1984 to 12/31/1993 and the two years from 1/1/2018 to 12/31/2019. Note: I'll call this company "ATT" to avoid the ampersand, which is not well behaved in HTML text.

This is the shape of the distribution of daily moves, expressed in percent, and two normal distribution curves. As the legend indicates, the blue curve shows the recent two years, the green curve shows the early ten years (which includes the crash of 1987), and the red curve shows all 37 years. The dashed magenta line is a normal curve with the same standard deviation as the 37-year curve, and the thin black line is a normal curve that fits the bulk of the data, but not the tails. I hope you can see that a normal curve looks broader than the Cauchy curve in the chart just above. The range -10% to +10% doesn't quite encompass all the data; there are three data points further to the right and one further to the left…out of nearly 9,200 daily motions.

It may take some peering, but it is also visible that the black curve outside the range [-2%,+2%] lies below the red, green, and blue curves. Those small amounts are the "fat" in the fat tails of those three distributions. Their very similar shapes also illustrate why I call ATT so stable. Through thick and thin it preserves a certain character of daily responses to market pressures. I do not intend to compare ATT to another stock here; that is for another day, another post.

It will perhaps be easier to see the implications of these data by looking at cumulative distribution functions (CDF's).

The x-axis of this chart is in units of standard deviation. The straight, black dashed line shows how a normal distribution would plot as a straight line. The ATT data going above at the left and below at the right are the fat tails of their distribution.

Looking at the two charts above, one may suspect that the ATT CDF is not as fat-tailed as a Cauchy distribution. The next chart shows this:

The x- and y- axes are in different units because I didn't normalize them. However, the very flat shape of the curve between -2 and +2 standard deviation units shows that the tails are much fatter than those for the ATT data.

Stock market motions, at least for this stock, are thus not as extremely variable as a Cauchy-distributed function.

I must at this point make an aside regarding lognormal distributions. My geologic background as an undergraduate emphasized sedimentology. One tool used to study sediments such as a sandy soil is to shake a sample through a stack of sieves and make a frequency distribution of the result, by weight. The sieves are carefully crafted to separate particles, at each step, that are 1.414 (i.e., √2) smaller in diameter. The frequency distribution so produced is a lognormal analysis. A frequency plot for a well-developed sediment from a single source will look like a normal curve, except that the x-axis is the logarithm of particle diameter. Over the years I found that many natural phenomena that have a wide range are lognormally distributed. We can check for lognormality by charting on log-probability coordinates.

I decided to see if the distribution of stock price daily moves might be related to a lognormal distribution. I squared the ATT data; thus all the results are positive, no longer both up and down. This is a CDF of the result, with the vertical axis logarithmic.

If the data closely followed the black dashed line, they would be lognormally distributed. The data charted at 1E-08 were actually zero, but that cannot be shown on a log-probability chart. What is the big dip leading up to them? This is a consequence of the size of a penny! I call it the "penny effect". During part of the interval stocks were traded only in increments of 1/16 of a dollar, then in increments of certain fractions of a penny, and since then in whole cents.

If the stock is trading for $10, and the next day the closing price is $10.01, the difference between the two is 0.1%, or 0.001 (10.01/10.00 - 1). Squaring this produces 0.000001. When the adjusted closing price is closer to $5, as it was in the early 1980's, a penny difference is 0.002, which squares to 0.000004. This, and a psychological effect that many people avoid prices so close to a prior day's price all led to the drop-off seen here. Since this is a pretty good fit to lognormality, other than the "penny effect", I call the distribution of stock price moves "Square Root of Lognormal."

Let's look at the squared Cauchy data. It is a continuous distribution with no pennies to worry about, so there is no drop-off. But the data are not lognormal either. The black dashed line is lognormal. The tails of this distribution are fatter than the tails of a lognormal distribution, much fatter. From experience I can tell you, that's pretty hard to do!

It so happens that this distribution is ill-behaved no matter how you transform it. In terms only a statistician could love, the Cauchy distribution has no "moments". That means that trying to measure anything other than its average value is meaningless. You can calculate a standard deviation for it, for example, but it has no meaning.

How does this relate to black swans? In stock market terms, if the daily moves were truly distributed according to Cauchy statistics, huge moves would be even more common than they are. However, the Square Root of Lognormal function that daily prices do seem to follow is not nearly so extreme, but it does have many more large moves, up or down, than a normal model would lead someone to believe. The standard deviation of the ATT data is about 1.5%. That means that, as seen in the chart above titled "Daily Change, all", none of the daily price moves should have been outside the bounds of [-4%, +4%]. However, on 250 occasions, a daily move was outside this range. That's only 2.7% of all the data. However, 250 times in 37 years means that six or seven times yearly, ATT's stock price moved by more than a normal model would predict is even possible during a run of nearly 9,200 market days.

Conclusion? To better predict the range of variation for a particular stock, list the daily moves over a period of a few years, square them, and plot as a CDF. From this you can determine a log-standard deviation, and its square root will yield a much better parameter of variation for the stock's behavior.

This last chart is a frequency diagram of the squared data for ATT, and the horizontal axis is logarithmic. The blip at the left is the "penny effect". Other than that, and a bit of skew, it looks a lot like a normal distribution; the choice of axis shows its affinity to a lognormal distribution.

Whether this will lead to a more robust way to set an investment strategy is anyone's guess!

More on continued human evolution

kw: book reviews, nonfiction, anthropology, paleoanthropology, evolution, human evolution

In March I reviewed The 10,000 Year Explosion, by Gregory Cochran and Henry Harpending, which presents convincing evidence and discussion about how the human species continues to evolve. In one chapter they refer to a colleague's work and his book, Before the Dawn: Recovering the Lost History of Our Ancestors by Nicholas Wade. Naturally, I obtained the book and read it carefully.

To be up front here: Though I am a Christian, of a very evangelical and Biblical tradition, I am also a scientist, with perhaps way too much education in all the physical sciences; I finished my formal education at age 37. I wrote software for scientists for forty years. In retirement, I work for a natural history museum part time, both as a computer scientist and a biologist. At a young age I learned the "Gap theory" of interpreting Genesis and other parts of the Bible that refer to prehistory such as Job 38:4-7, Zechariah 12:1, and Isaiah 45:18. By careful study I determined that cosmology and deep time (13+ billion years of it), plus the facts of evolution and the theory of natural selection that describes how it operates, are no threat to Biblical faith nor to any revelation in the Bible.

Therefore, concerning people, the extreme Biblical literalist view is that humans (and all other living species) were created ex nihilo less than 10,000 years ago, and are the same now as they were then, barring various kinds of catastrophe and degeneration. Their creation was very shortly after that of the universe and Earth.

The scientific view is that once life on Earth began, natural selection operated for about two billion years to produce multicellular life from unicellular life, then the multicellular creatures continued evolving until all living forms we see today were produced, along with some ten, to 100, to even 1,000 times as many species that went extinct in past eons; then among the tiny twig on the "tree of life" known as Great Apes, one ape species split into three species, which continued to evolve and adapt to different environments to become humans, chimpanzees, and bonobos; along the way other species such as H. erectus and Neanderthals arose and later became extinct.

The combined view I have (following G.H. Pember and others) is that Genesis 1:1 occurred "in the dateless past", to quote C.I. Scofield, and that the first verb in Genesis 1:2 is "became": "The earth became waste and empty", where Isaiah 45:18 tells us the original formation of the planet was "not waste". Prior to historical time, "anatomical" humans, that were not "behaviorally modern", experienced a big change. Their worldwide spreading from a homeland in Africa began during a warm spell between ice ages about 50,000 years ago. That behavioral change probably marks a point in time that God intervened, as recorded in Genesis 2:7, "And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul." (King James Version). The grammatical emphasis is on the word "living". This does not describe a creation ex nihilo. "Dust of the ground", a metaphor for humanity, existed already, but when God breathed a spirit into "the man", the animal soul became a "living soul," a soul that is now able to contact God. The rest of the Bible describes contact after contact between God and various people. The Septuagint translates "living soul" as ψυχὴν ζῶσαν , "psuchen zosan", which refers to divine life, not biological life. 

With all that in mind, I consider two questions:

1. Do the mechanisms of natural selection still operate on humans?
2. Do any changes thus wrought continue to improve our adaptation to modern environments, or are they only degradations from a formerly more perfect humanity? (as many Christians believe)

I look for well-researched books like Before the Dawn and The 10,000 Year Explosion to find answers to those two questions. With new genetic tools made available in the past twenty years, there is evidence aplenty that humans are still evolving, and that we continue to become better suited to the environments into which our travels have taken us. Further, genetics has led anthropologists and archaeologists to look more keenly at their own studies for things that were overlooked under an older paradigm that stated, "once humans developed culture, physical evolution came to a halt." It most assuredly did not!

I'll begin by discussing a few items I bookmarked. I can tell which chapter these are in, but the "page" numbers of the eBook don't correspond to printed pages. In the first chapter, after defining two periods of prehistory, the 5 million years since pre-humans split from other apes, and the 45,000 years between the time some left Africa and the development of writing, they ask,

"Why should the human genome, specifically shaped for survival in the present, have so much to say about the past?" (early in Chapter 1, "Genetics & Genesis")

I immediately thought, "Only if 'the present' means 'the past 500-1000 years' can this question be meaningful." Actually, as the author goes on to discuss, our genome contains material that supported survival over the entire span, including some important genes that have been kept nearly unchanged for tens or hundreds of millions of years; also others that arose in the past few thousand and even the past few hundred years, and some that are "works in progress" right now.

More to the point, an allele (a specific form of a gene) that arose and became frequent long ago will contain "silent mutations" that can inform us of our history. Time for a side trip.

The Central Dogma of Genetics states that DNA is copied to RNA, and RNA is transcribed to chains of amino acids, which are peptides and proteins. Transcription takes place in a molecular machine called a ribosome. There are 64 3-letter codons of DNA or RNA. There are 20 amino acids. Thus, the "translation table" to convert an RNA codon into an amino acid has multiple entries for each amino acid. Only one amino acid, methionine, has a single code. The other 19 have two, three, or four codons that "mean" them. Thus, the codons GGU, GGA, GGC, and GGG all code for glycine. If something changes a GGG in your DNA to GGA, it won't change the amino acid that results. That is an example of a silent mutation. 

We won't get into any of the many things that can cause such a change, but we all accumulate many in each of our cells in our lifetime. There are also other kinds of mutations, and some lead to new proteins. A mutation that is helpful in any way will be kept; one that is harmful will usually cause the death of the cell. Mutations that wind up in our gametes (sex cells), that didn't cause them to die already, can get into our children. We typically pass on about 50 mutations to each child. In a genome of a billion codons, 50 is not many.

The studies of what might have happened in the past depend on the rate at which silent mutations accumulate. Of course, it is possible for a silent mutation to re-mutate back the way it was, but the number of these will be very small, since point mutations are rare to start with (50 out of a billion per generation, per person). This principle is brought out numerous times in the book. End of side trip.

If we first look back 5,000,000 years or so, to the ancestor of humans, chimps, and bonobos, what would we see? There is scant fossil evidence. Central and east-central Africa were warm and humid then as they are now; there were no ice ages yet. In conditions like that, even teeth rot too quickly to leave fossils for us to find today. What little we know matches what we can infer by taking an "average hominin": the size of a chimp or smaller (males 50-100 kg, females 30-60 kg), furry like modern chimps, brain size similar to a chimp (450 cc) or maybe a bit smaller, promiscuous in sexual habits, possibly patriarchal but maybe not, and probably violently territorial and xenophobic. Today, bonobos are a little smaller than chimpanzees, equally furry, with a brain the same size, even more promiscuous, matriarchal, but less xenophobic and much less violent. Humans have become a little larger overall, and a foot or two taller, mostly hairless, but with much larger brains (1,400-1,600 cc), sexually more private but not necessarily less promiscuous, usually patriarchal (sorry, feminists), and with a great range of xenophobia and territorial aggression.

While chimps and bonobos are so physically similar that they were thought to be the same species until a generation ago, they are behaviorally very different. Further, humans are very, very different from both in many ways, but we can see our behavior reflected in theirs. It is almost as if we have a range of cultural expressions that encompasses all the variations found in bonobos and chimps.

Now look back 50,000 years, to the "behaviorally modern humans" (BMH) who left Africa to spread the world over. The archaic human species they encountered and what happened as a result are stories for another day. What were these "moderns" like? Between 100,000 (maybe 150,000) years ago and 50,000 years ago, the species (still called Homo sapiens) is called "anatomically modern humans" (AMH), and is physically very similar to "us, today", but with more archaic behavior. We will set aside for the moment the theological implication I made earlier about what may have happened 50,000 years ago. What is the difference between AMH and BMH? As I found upon reading later chapters, it's probably best to not consider us, today as BMH, but just "modern humans", MH, after another transition between 15,000 and 10,000 years ago. Both behavior and anatomy changed after that.

So, to get a BMH person, start with a very well-conditioned person, not quite an Olympic athlete, perhaps…or, what the heck, let's go with a couple of Olympians. We can pick the runner Usain Bolt (6' 5", 207 lb/195 cm, 94 kg) for the male, and gymnast Kylie Dickson (5' 6", 110 lb/167 cm, 50 kg) for the female. The BMH's were bare-skinned and lived in Africa, so the skin would be black. Shorten the male by several inches while leaving his weight the same. Double the strength of his muscles and bones, and add 20% to the thickness of his skull. Add 10-20 kg to the weight of the female, and make her bones and muscle proportionally greater. Both this man and this woman would look like modern weightlifters (the ones who don't use steroids). You wouldn't want to meet either one in a dark alley, unless perhaps you had a 5th degree Black Belt in Aikido. I have a Korean friend who is a 4th degree black belt; he doesn't need a weapon, he is a weapon. But he might not prevail against an average BMH male.

What else might be different? "Modern" behavior, to an anthropologist, is the more sophisticated late paleolithic toolkit that showed up about 50,000 years ago, along with sophisticated art (cave paintings being a stellar example), and more group interaction, including some tolerance of strangers so trading could be carried out. The story told by their bones, however, is of frequent and persistent combat and warfare. Although the women were also stronger than we'd find usual today, they didn't engage in combat, but had harder domestic work (like pulling hides off animals), than would have been usual later on.

So, back to, what differed between AMH and BMH? Not the anatomy, except perhaps in fine details. From 100,000 (or so) years ago until 15,000 years ago, the anatomy remained very similar. But better group dynamics, probably fostered by the development of language, seems to be a crucial step. It seems to me that sophisticated art had to follow language; once symbolic representation of thought was possible, other symbolisms including artistic artifacts could follow. The 10th chapter "Language" goes into this very comprehensively. Language seems to have appeared shortly before 50,000 years ago, and much else followed.

Chapter 7, "Settlement", brought out something that surprised me: the author's contention (he is far from alone in this) that people began to settle down into communities as much as 5,000 years before agriculture. I'd thought it was the other way around, and I've read that numerous times. I can't debate the point, so I'll leave it to you to read what the author has to say. But it convinced me. Starting before 15,000 years ago, a few thousand years of warming were followed by more cold, that broke about 11,500 years ago. The coldest bit was the Younger Dryas period, which lasted 800 years. Settling down apparently marks the major psychological transition between BMH and MH. People had to learn to tolerate the presence of unrelated strangers, and not try to kill them on sight; some cultures today are still prone to do that! They could then engage in long-range trading.

Midway in the chapter I find the statement, "Specialization in roles may have occurred for the first time." I think not. Even in a kinship group of 50-150 persons, someone will be a little better than most at making tools, and another will be a little better than most at accurate throwing of weapons, or at climbing of trees. One woman's more nimble fingers might weave a better, stronger basket more quickly than others'. So intrafamily trading probably began way, way back. Once you are able to converse peaceably with people in the family nearby, interfamily trading can get rolling, and that will naturally grow into trade networks that span continents.

Looking through my notes, I find a number of interesting items about settlement and socialization. But I'll skip a few to get to the critical point. How much of all this has genetic underpinnings? The author thinks, quite a lot. We can see in our more slender skeletons, compared with "Cro-Magnon" of 10-12,000 years ago, that MH's have changed over that time. We aren't quite as likely to club one another over the head. It makes me wonder, how warlike were BMH's? The Dani in New Guinea and the Yanomami in Brazil, until the past few decades, were used to losses of around 30% of each generation to inter-village warfare. What was warfare like 40,000 years ago, when skulls were thicker and bones twice as robust (muscles also, one must presume)? Shudder!

But what is happening now? Human skin changed from pale to black after hair was lost from the body. [Just by the way, my personal notion is that hair loss had to soon follow the domestication of fire. Think of a furry month-old baby falling into the fire, or an ember blowing onto it. In my twenties I had a beard; it caught fire once, and only very quick thinking by my father kept me from suffering disfiguring burns (I still have a couple of tiny scars). I have read that the most popular theory for hair loss is running. Humans can run down anything except a thoroughbred horse; and maybe over a day or two, the horse would also get too tired to keep going. Perhaps both influences played a part.] The people that made their way from Africa to northern Europe and northern Asia became pale again. This seems to have happened primarily in the past 5,000 years. Europeans and north Asians have different genetic mechanisms for skin coloration, so paler skin evolved at least twice. Lactose tolerance evolved at least four times, at different times in different places. Our jaws are smaller than was average for earlier MH's, which is why so many of us have to have our wisdom teeth pulled. Suffice it to say, the sore back many of us wake up with is also evidence that 2-3 million years has not been enough for a truly functional and robust erect spine to finish evolving.

The author has numerous added examples. Physically we are still evolving, and those of our behaviors that have a strong genetic element are evolving also. Where will it all take us? The presence of five "races" (we need a better word now; this one is too political) indicates that the human species is partway along a path toward splitting into multiple species. If sea-spanning ships and jet planes had never been invented, in another 50,000 years, would there be three or four or five species of human? It's possible. If we plant a colony on (better, underground) Mars, how long will they remain the same species? Since there would be a much smaller number of them, genetic drift, along with a very few novel genetic alterations (mutations), could render them genetically incompatible with "the folks back home"; that is, a new species of human. Homo arensis?