Saturday, April 03, 2021

Race, Gender and IQ

In modern-day America, anyone arguing that the difference in average IQ between blacks and whites, or the difference in the distribution of IQ between men and women, at least partly explains the difference between average black and white income or between male and female numbers in some academic fields, risks being accused of racism or sexism. Striking examples of the possible consequence of such an accusation are provided by the cases of James Watson and Lawrence Summers. Watson, who received a Nobel prize for his role in the discovery of DNA, arguably the most important biological breakthrough of the century, was so careless as to tell the Times that he was "inherently gloomy about the prospect of Africa" because "all our social policies are based on the fact that their intelligence is the same as ours - whereas all the testing says not really". He was attacked ferociously for the statement, accused of prejudice, stripped of titles and positions.

Prejudice is belief held without evidence. Watson’s view might well have been mistaken —I now think it was, although at the time I did not — but there was evidence to support it, since the average measured IQ in African countries was strikingly below that in European countries. His attackers, so far as I could tell, had no evidence in their support and were acting on pure prejudice.

Summers, then president of Harvard, commenting in an academic talk on the small numbers of women in elite academic positions in fields such as mathematics, offered several possible explanations. One of them was that although the average IQ of men and women was about the same, female IQ had a tighter distribution than male IQ. That would imply fewer women than men far out on the upper tail of the distribution, where Harvard math and physics professors are located. Summers was fiercely attacked for mentioning that possibility, forced out of his position at least in part as a result. Again there was quite a lot of evidence for the claim, no evidence against.

The result of suppressing arguments for an unpopular view is that nobody honestly knows what conclusion would come out of an open debate, hence whether or not the view is true, although many people may find it prudent to pretend to. Until very recently, the only convincing argument I had seen against the claim of lower African genetic IQ was one offered by Thomas Sowell in his Ethnic America. He observed that the average family income of immigrants to the U.S. from the West Indies reached the U.S. average in one generation. West Indians are blacker than Afro-Americans in both their genes and their skin color, so if Afro-Americans did badly because of their African genes, West Indian immigrants should do worse, and similarly if the reason was discrimination. Sowell offered instead an explanation based on the different cultures produced by differences between West Indian and North American slavery.[1]

I have now found more and even better arguments against the hereditarian explanation of racial differences. Chanda Chisala is a Zambian immigrant who appears, like Sowell, happy to engage in arguments on unfashionable subjects. His main topic is not Afro-American IQ but African IQ. He offers several independent lines of evidence to show that its low measured value, variously claimed to be 70 or 80, must be due to African environment not African genes. His evidence is of two sorts: The academic performance of African immigrants in first world countries, where they are exposed to a first world educational environment, and the performance of Africans on two games, checkers and Scrabble.

U.K. data on student performance is available not merely for racial groups conventionally defined but for linguistic subgroups within those populations. Africans on average do not particularly well, but many of the African subgroups, including both the Igbo and the Yoruba, the two largest Nigerian tribes, substantially outperform the native English, in some cases East Asians as well.

His U.S. evidence is more anecdotal. One year, a single college applicant in the U.S. was accepted by all eight Ivy League schools. He was a Nigerian immigrant. Another Nigerian immigrant is a serial entrepreneur who invented a computer application, founded a company, and sold it to Apple for an estimated billion dollars.[2] Black students in elite universities are African or West Indian immigrants or their children in numbers far out of proportion to their share of the population.[3] In a number of cases where data happen to be available, black refugee immigrants, not native speakers of English, substantially outperform in school native Afro-Americans. That is the opposite of the result one would expect if Africans were genetically inferior in intelligence to whites, since Afro-Americans, unlike Africans, have significant white ancestry.

His second line of argument is that African performance in checkers and Scrabble competition would be impossible if African average IQ were anything like as low as the estimates. Both games are, at the high end, heavily g loaded. While success in Scrabble at low levels depends in part on vocabulary, the critical skill in high level plays is the ability to do the mental arithmetic needed to decide which of alternative plays will give the player the most points and his opponent the fewest. Top white players have very high IQ and many of them are mathematicians. Yet a substantial fraction of the world’s top players of checkers, including some at the very highest level, are African, and a substantial fraction of the top players of English language scrabble, including at least one world champion, are from Nigeria.

In 2015, of the ten top players in the French Scrabble championship, three were from France, three from Gabon, three more from other African countries. Gabon is an ex-French colony with a population of 1.7 million. If one believes Richard Lynn’s figures on its IQ average and standard deviation, there should not be a single person in the country close to the intelligence level required to be a top Scrabble player. Similar arguments make it very nearly impossible that Nigeria could have as many of the world’s top players of English Scrabble as it does if his estimates were close to correct.

Africans do not do nearly as well at chess, although they do not do noticeably worse than other racial groups. Chisala’s explanation is that for chess, unlike Scrabble or checkers, playing at the highest level requires extensive instruction in the literature of the game, so much so that Bobby Fisher found it necessary to learn Russian in order to read the Russian chess literature. Few Africans have the opportunity for that sort of training. Russia has dominated modern chess competition at the highest level not because Russians are smarter than other people but because the Soviet Union chose to put a lot of resources into subsidizing the training of its chess players for purposes of international prestige. They put resources into checkers for the same reason, only to find their dominance challenged by players from Africa.

The evidence Chisala offers does not tell us whether the average African genetic IQ is 95, 100, or 105, but it is clearly not 70 or even 80. That conclusion is one that those skeptical of the hereditarian position will be happy with. Other parts of his argument are not. In the process of arguing that Scrabble performance at the high end requires a high IQ, Chisala  takes on the issue of the effect of differences between the male and female IQ distribution, the same issue that got Lawrence Summers in trouble.

A possible explanation of why top physicists or mathematicians are almost all men is that women are culturally discouraged from entering such fields or discriminated against in them. That does not work for Scrabble, since more women than men play it and nearly half the qualifiers to the North American Scrabble championships are women. Yet only about 5% of the highest rated players are women and no woman yet has won the world championship. As Chisala puts it, “This rising gender disparity as you go higher in expert Scrabble is a big win for the hereditarian corner of the gender-and-intelligence debate.”

He goes on to write:

However, as we have seen many times in this research, a big win for the hereditarian side comes with a hidden pact with the devil: a victory in the gender-and-intelligence debate logically implies a decisive loss in the race-and-intelligence debate (you truly can’t have your cake and eat it in this world). How is it that black Africans, who (on average) are supposed to be about 30 IQ points below white women and supposedly have lower visuospatial or mathematical intelligence and even lower variance in their intelligence distribution, can achieve what has been accepted as statistically impossible for white women – outperforming white men – …

Chisala’s evidence that the genetic IQ of Africans is comparable to that of whites raises the puzzle of why Afro-American IQ apparently is not. One obvious possibility is that, as in the African case, observed lower IQ is due to environment rather than genetics. Chisala rejects that explanation, in part on evidence that the children of wealthy American blacks do less well than the children of poor whites, despite what one would expect to be a more favorable environment, as well as on evidence that African refugees, from a much less favorable environment, outperform American blacks. He offers instead a genetic explanation. His conjecture[5] is that a feature of African genetics makes Africans more vulnerable than whites to unfavorable mutations and that such mutations were imported into the Afro-American gene pool early on by crosses with poor whites. I found his arguments for that conjecture less convincing than his arguments against the genetic inferiority of Africans, which leaves the puzzle of Afro-America IQ, for me, still unsolved.[5]

Part of what I like about Chisala is that he has taught me something I did not know — having read him I am now confident that African genetic IQ is not significantly lower than European. Another thing I like about him is his approach to arguing. He treats Lynn and Jensen, probably the two most prominent of the hereditarian scholars, not as wicked racists but as able scholars who have, for understandable reasons, reached mistaken conclusions. Even when he finds Jensen misstating evidence in a way that makes it appear to support his position, he treats it as a single mistake in the work of a generally careful and competent scholar.

This is connected with a related feature of his work that helps make it more persuasive than other attacks on the hereditarian view of racial IQ — he takes the other side’s arguments seriously. The usual attacks I see on the hereditarian position are ones such as the claim that some races cannot have a lower IQ than others because there is no such thing as race, true in some sense of “race” but irrelevant to questions about the average IQ and average outcomes of races as conventionally defined, or ones that provide some evidence against the position but not very strong evidence, the sort of arguments that might or might not stand up against obvious criticisms.[6]

Each of Chisala’s webbed essays is followed by a long thread of comments, many trying to explain away his evidence. He responds, usually in the next essay, by carefully examining the explanation and showing why it cannot be adequate. It is because he approaches the subject in that way that he does a more convincing job of rebutting hereditarian arguments on race than other critics.

The rebuttals are sometimes entertaining as well as convincing. Responding to the argument that Africans who decide to migrate to the U.K. are a select group, much more intelligent than the African average, he offers statistics showing that many are poor, few have high end careers. He also writes, responding to one critic:

I do not really know how it works in Jamaica, but I am quite confident that realizing that life is better in a very rich country than in your poor country is never exactly the most g-loaded epiphany among Africans.


[1] I gather that Sowell later modified the theory, still attributing the result to culture but with a different explanation of its origin.

[2] Chinedu Echureo, the inventor of HopStop.

[3] “While about 8 percent, or about 530, of Harvard's undergraduates were black, Lani Guinier, a Harvard law professor, and Henry Louis Gates Jr., the chairman of Harvard's African and African-American studies department, pointed out that the majority of them -- perhaps as many as two-thirds -- were West Indian and African immigrants or their children, or to a lesser extent, children of biracial couples.” (Top Colleges Take More Blacks, but Which Ones?, NYT June 24, 2004)

[4] The series starts with https://www.unz.com/article/the-iq-gap-is-no-longer-a-black-and-white-issue/ and goes on through eight more essays.[5] One tempting explanation for part of it is vitamin D deficiency. The same adaptation to a high sunlight environment by which blacks are commonly recognized, dark skin, also results in less conversion of sunlight to vitamin D, and there is evidence  linking vitamin D deficiency in pregnant women, to lower IQ of the children. I suspect that if the answer were that simple we would already know it, but it could be a partial explanation.

How might one combine that speculation with Chisala’s evidence on the academic performance of African immigrants to the U.K.? The answer may be that a large fraction of the immigrants were born in Africa in an environment where their mothers were exposed to the level of sunlight they were adapted to. If that is the whole story, it implies that the next generation may not do as well. The British diet appears to compare poorly with the American in that respect: “Unlike most other high latitude western countries, the UK does not fortify any staple food items with vitamin D, aside from a small amount added to margarine.”


[6] One used data on the illegitimate children of Afro-American servicemen stationed in Germany after the end of WWII — ignoring the fact that the fathers were not a random sample of Afro-American males. The other observed that differences in school performance between white and black students could be eliminated by a regression that controlled for differences in parental income, home environment, and the like — all of which are to some degree proxies for parental IQ.

Friday, March 19, 2021

Case Rates, Death Rates, and Vaccination: A Puzzle

I have been following Covid figures for the U.S., for Israel, and for Santa Clara County, where I live.  In all three vaccination has been largely of the elderly, which one would expect to bring death rates down much faster than case rates. The only place where that seems to have happened is Israel. Even there, the effect does not seem to be as large as one would expect.

For each of the three I calculated the ratio between the most recent 7 day average of death rates that I could find and the earlier peak 7 day average, then calculated the corresponding ratio for case rates, assuming a 9 day lag between cases and deaths, and compared the two ratios. I chose a nine day lag because it let me match a death rate peak to a case rate peak. A longer lag might be more plausible, but I do not think it would change my results by much.

The U.S. and Israel give the death rate figures up to yesterday, while the county gives them only up to two and a half weeks ago on the theory that the more recent death figures are not reliable, so the interval for the county was shorter than for the countries. Since what I was comparing was not county to country but fall in death rate in the county to fall of case rate in the county and similarly for each country, that should not be a problem.

 

The results:

 

In Santa Clara County, case rates fell by a factor of 6.5 while death rates fell by a factor of 3.9.

 

For the U.S., case rates fell by a factor of 4 while death rates fell by a factor of 2.6

 

For Israel, case rates fell by a factor of 2.95 while death rates fell by a factor of 4.3

 

Only in Israel did death rates fall faster than case rates. I do not know if recent death rate figures for Israel are reliable, so redid the calculation using the same dates I used for Santa Clara County. That gave me ratios of 2.3 for cases, 2.6 for deaths. Deaths were still falling faster than cases, but not by very much.

 

Israel has had the highest vaccination rate of the three, so it makes sense that it would look better on the deaths vs cases comparison. But at this point, 11% of the U.S. population has been fully vaccinated, another 12% have received one dose. Vaccination has been largely, although not entirely, of the elderly. People 65 and over are  about 20% of the population and about 80% of all deaths from Covid, so one would expect vaccination alone to have cut deaths roughly in half. For Israel, 80% of adults over 60 have received two doses of the vaccine, which should have cut deaths relative to cases more than in half, a larger effect than my calculations show.

 

I  see two possible explanations for the pattern. One is that older people are not only much more likely to die if infected, they are also much more likely to show symptoms if infected; people who are infected but don’t show symptoms are unlikely to be tested and so don’t go into the count of cases. That would explain why deaths don’t fall faster than cases but not why, in two of my three areas, they fell substantially slower. And it requires that older people are not only more likely to show symptoms but as much more likely to show symptoms as to die. That does not seem to be the case, according to a source I found online.

 

The other possible explanation is that many of what are counted as deaths due to Covid are actually deaths while having Covid, people who die from some other cause but are tested and found to be infected. We would expect the number of those to be proportional to the number of cases.

 

If the first explanation is correct, figures on the number of cases overstate how fast it is falling, since symptomatic cases are falling faster than asymptomatic ones. Since asymptomatic cases are apparently still contagious, although less contagious than symptomatic cases, that implies that the risk of getting Covid from a random stranger has not fallen as fast as the decline in cases would imply.

 

If the second explanation is correct we have badly overestimated how deadly Covid is, hence probably over reacted to it.


P.S. (3/22): I now have a third and more plausible explanation of my puzzle. I was using a 9 day lag between case and death because that was the lag in the peaks. But even if, on average, it takes nine days from detecting a case to a death, the actual lag is a range, say sixteen days to two days (actually longer, but that will do for my example). I was starting my calculation with the date when cases were at their peak, and nine days later for deaths. That meant that I was including in deaths ones from cases well before the peak, when the case rate was lower, which pulled down the death rate, making the drop from then until now smaller.
To test this conjecture, I redid my calculation starting two weeks later. Now I got the expected result. For all three cases — Santa Clara County, the U.S., and Israel, death rates fell faster, not slower, than case rates nine days earlier.

Friday, February 26, 2021

The CDC gets life expectancy wildly wrong

According to a CDC spokesman, U.S. life expectancy has fallen by a year as a result of Covid. A little arithmetic shows that that cannot be close to correct. 

Total deaths so far are about 500,000 out of a population of about 330,000,000. The average death cost 12 years of life. Multiply that out and the average person lost not one year but .018 year of life.That's an error of almost two orders of magnitude. Including deaths indirectly caused and additional deaths over the next few months might increase it a little, but there is no way it can be one year or even close.

Dr. Peter Bach explains the error on his blog. What the CDC apparently did was to calculate what the effect on life expectancy would be if mortality rates stayed at their 2020 level,  how much Covid would reduce life expectancy if the pandemic was repeated every year forever.

After an error of that magnitude, it is difficult to take seriously any factual claim they make. It will be interesting to see if they admit the error.

P.S. To be fair, I have not found the claim on the CDC web site, only in media reports that attribute it to "Robert Anderson, who oversees the numbers for the CDC." 

P.P.S. I have now found it on the CDC web site in the form of an interview with Elizabeth Arias, who apparently produced the number:
 
I posted a version of this to FaceBook. Some people defended the CDC on the grounds that the usual way of calculating life expectancy is by measuring the current mortality rate as a function of age and projecting it it into the future. The problem is that, as you can see by the interview, Elizabeth Arias makes no attempt to explain that what she is describing is a measure that she knows, in this case, badly misrepresents what it is supposed to be measuring. 

Sunday, February 14, 2021

Have We Reached Herd Immunity?

I have been looking at the number of new cases per day, both for Santa Clara County and for the U.S., and the pattern is striking. Over the past month, number of new cases per day in the U.S. has gone down by a factor of about 2.4, for the county by a factor of about 3.5. Death rates are also down, although by much less, but one would expect death rates to lag case rates by a few weeks. I don't think the explanation can be the weather, since it's still winter.  I don't think it can be vaccination because there has not yet been enough of it to substantially affect the case rate.

The other obvious explanation is that the previous high was created by a lower level of precaution due to XMas and New Years. But that explains only a reduction in the rate of increase, not a reduction in the level, since all those people infected during the holidays were then around to infect other people. The fact that the level is falling means that each infected person is passing the infection on to fewer than one person, which is the definition of herd immunity.

If behavior is held constant, herd immunity ought to first appear as a constant rate of infection, each person passing the disease on to one other, then gradually become a shrinking rate. It looks as though we reached herd immunity under non-holiday behavior something close to two months ago, infection rates kept going up due to the holiday bump, and by the time that ended we were far enough into herd immunity (with non-holiday behavior) so that rates were falling. 

I was still surprised that they were falling so fast until I looked at how many cases had occurred recently. I haven't made an exact calculation, but it looks as though, for both the county and the country as a whole, the surge in cases over the two months of the peak  roughly doubled the cumulative total. It wouldn't be that surprising if that had pushed us well past the start of herd immunity.

There are two qualification to be made to the optimistic conclusion that the pandemic is almost over. One is that the requirement for herd immunity depends, among other things, on how people behave. If everyone concludes the pandemic is over and drops all precautions against passing on Covid, cases might start increasing again. The other is that there are at least two new variants of Covid now spreading through the U.S., and we cannot be sure that people immune to the old variant will be equally immune to the new. If, to take the most pessimistic possibility, the protection provided by having had Covid turns out to have no effect one of the variants, we are back to ground zero and in trouble.

My guess, however, is that neither will happen, and that in another few months the case rate will be back to last spring's lows. And falling.

Sunday, January 17, 2021

Why Trump Shouldn't be Impeached

As best I can tell, while Trump is morally responsible for the recent riot he is not legally responsible, since everything he did that contributed to it was something he had a legal right to do. But requirements for impeachment, other than a majority vote in the House to impeach and two-thirds in the Senate to convict, are unclear, so that is not, in my view, the fundamental issue.

Our legal system has so far been pretty stable. One reason is an implicit rule: When power shifts, the winners don't punish the losers. Impeaching Trump after he has left office, as a punishment not a way of removing him from power, violates that rule. That would be a  dangerous precedent, one step further towards making political conflict something closer to a civil war. 

People will, of course, argue that this is a special case, that Trump is uniquely guilty. But once the precedent is established other people, in a polity already sharply divided, will find other special cases.

For the same reason I am bothered by people who gloat over the prospect that Trump, once out of office, will be prosecuted for things he did in business before he was president. Obviously having been president doesn't give legal immunity — anyone who wants to sue him will be, and should be, free to do so. But criminal prosecution is at the discretion of the prosecutor; Obama protected illegal immigrants who he didn't want arrested by instructing law enforcement not to arrest them. If Trump gets prosecuted by officials who are his political enemies for business dealings he did not get prosecuted for when they happened, it will be pretty clear that it isn't the dealings he is being prosecuted for. 

That again would be an unfortunate precedent.

Monday, January 04, 2021

Fauci, Lying, Greyhound Racing, and Trump

“When polls said only about half of all Americans would take a vaccine, I was saying herd immunity would take 70 to 75 percent,” Dr. Fauci said. “Then, when newer surveys said 60 percent or more would take it, I thought, ‘I can nudge this up a bit,’ so I went to 80, 85.”

“We need to have some humility here,” he added. “We really don’t know what the real number is. I think the real range is somewhere between 70 to 90 percent. But, I’m not going to say 90 percent.”

Doing so might be discouraging to Americans, he said, because he is not sure there will be enough voluntary acceptance of vaccines to reach that goal.

(NY Times, Dec. 24, 2020, “How Much Herd Immunity is Enough.”)

Poll information about how many Americans would take a vaccine is not evidence about how many people must be immune to achieve herd immunity. By Fauci’s own account, his changed statement reflected not what the scientific evidence showed but what he thought it prudent to tell people it did. He had just publicly admitted, in the New York Times, that he was a liar.

If he is not telling the truth, what is he doing?

Greyhound racing uses a mechanical rabbit, kept moving ahead of the dogs to give them something to chase. Too close and they might catch it, too far ahead and they might lose interest. The most plausible conjecture I can come up with to explain Fauci’s account of what he is doing is that he is following the same approach. In order to get people to do what he wants, whether that is getting vaccinated or wearing masks, he has to persuade them that it will do some good. If they believe the problem is almost solved, each individual may figure that others will solve it and he can slack off, or may decide to maintain precautions for a little while longer, at which point the pandemic will disappear and he can stop. If, on the other hand, people believe the solution is very far away, it is tempting to give up on it.

The solution, as for the greyhound race, is to keep adjusting the estimate, subject to what you can get people to believe and how close the rabbit has to be to motivate the dog to run.

In the short run this approach, like other versions of lying to people for their own good — telling them, early in the pandemic, that masks were useless to them, in order to save masks for medical personnel, or that a lockdown would be only for a few weeks, in order to get people to go along with it — looks attractive, a way of saving lives. In the longer run, it risks persuading an increasing number of people that they should not believe what authority figures tell them.

That is not a wholly bad thing, given that elite opinion, as filtered through the media, is frequently unreliable, sometimes, as in this case, deliberately dishonest. But there is a problem, currently illustrated by the number of Americans who believe Trump’s claim that he really won the election. The more people who distrust elite sources of opinion, the harder it is to get people to coordinate on a common view of reality. If you cannot trust the President’s advisor on the epidemic or, in other contexts, the New York Times, to tell you the truth, why should you trust the people who tell you that the election was, on the whole, honest, that although there were probably, as in most elections, a few glitches here and there, there was nothing nearly large enough to reverse the result?

If there are no elite information sources that you trust, you might as well believe what you want to believe, as people are very much inclined to do.

Postscripts on the Pandemic:

Fauci's quoted statements provide further evidence that what he says reflects what he wants to tell people, not his scientific opinion.

“If you really want true herd immunity, where you get a blanket of protection over the country ... you want about 75 to 85 percent of the country to get vaccinated,” Fauci, the longtime head of the National Institute for Allergy and Infectious Diseases, said in a live-recorded interview with Rameswaram, the host of Today, Explained. “I would say even closer to 85 percent.” (Vox, 12/15/20)

Current estimates imply that more than 100 million Americans have had the disease already (91 million as of September, according to the CDC). The same mechanisms that make vaccines work also imply that those people are immune to the disease, at least for a while. If those people are put at the back of the queue for vaccines, vaccinating 70% of the population will make 100% immune, at least if immunity does not turn out to expire in less than a year. If we make no attempt to avoid vaccinating those who have had the disease, 70% vaccinated should mean about 80% immune. Fauci is  ignoring that, presumably because taking account of it reduces the percent vaccinated that he can claim we need.

There is, however, a reason to raise our estimate of the requirement for herd immunity, having nothing to do with changes in what people will believe. There are now two new and more contagious variants of the disease, one first detected in the UK, one in South Africa. The more contagious the disease, the larger the number of people who must be immune for herd immunity.

Wednesday, December 30, 2020

Defamation Law vs Censorship

Mac Isaac, the laptop repairman with whom Hunter Biden apparently left a laptop, has sued Twitter. His complaint is not that Twitter locked the New York Post account of the contents of the laptop's hard drive. It is that their explanation for locking it was the claim that the account was in violation of Twitter's hacked material rules, and that Twitter, in explaining that policy, defines a hack as

an intrusion or access of a computer, network, or electronic device that was unauthorized or exceeded authorized access.

By Isaac's account of what happened, his access to a laptop that had been dropped off at his shop for repair and then abandoned was authorized, hence not a hack. It followed that Twitter was making false statements which, according to Isaac, have had large negative effects on him. On the face of it, it looks like a legitimate case.

What made the story of particular interest to me was that Isaac is doing something I had thought about doing, decided not to do, and suggested to a law firm that they might do in similar cases — with regard to Facebook, not Twitter. 

About a year ago, I discovered that Facebook was blocking all links to my web page. Anyone who attempted to put up such a link got a message saying that the page violated Facebook's community standards. I went through the procedures on Facebook to object, never got any response. Eventually they stopped blocking it, still with no explanation.

Facebook is a private firm, and as such has a legal right to decide what messages they will or will not publish. They do not have a legal right to defame me, which, assuming that nothing on my page actually violated their community standards, they were doing. The problem had been solved when they stopped blocking the page, and in any case was never a large enough problem to justify the trouble of a court case. But it occurred to me that it might justify a class action by someone else, so I emailed a law firm that seemed appropriate with the suggestion.

Mac Isaac, or his attorney, apparently had the same idea in a much larger case, and has now acted on it. I wish him well.