Author Archives: R.E. Buxbaum

About R.E. Buxbaum

Robert Buxbaum is a life-long engineer, a product of New York's Brooklyn Technical High School, New York's Cooper Union to Science and Art, and Princeton University where he got a PhD in Chemical Engineering. From 1981 to 1991 he was a professor of Chemical Engineering at Michigan State, and now runs an engineering shop in Oak Park, outside of Detroit, Michigan. REB Research manufactures and sells hydrogen generation and purification equipment. He's married with 3 wonderful children who, he's told, would prefer to not be mentioned except by way of complete, unadulterated compliments. As of 2016, he's running to be the drain commissioner/ water resources commissioner of Oakland county.

The power of men’s hats

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Here’s a joke from 3rd grade: why do Indians wear feather headdresses? …… To keep their wig warm. One of the main reasons to wear a hat is to keep your head warm. Men generally wear hats outside only, and mainly to keep warm, or to keep the sun off your eyes. We thus show below a delivery boy in a knitted cap (called at torque in Canada), and a boss is a stylish fedora. The two hats keep the head warm, but the fedora protects the eyes too, and the different styles establish who you are in the social chain. It is a good thing when fashion works this way, and uncool, in my mind, when messages are reversed or unclear. It’s equally uncool to see a delivery boy in a fedora as an executive in a wool cap. Either one looks pretentious to me. One is dressing up, the other dressing down or confused. Women’s hats generally look confused to me, in part because there is no such thing as a real business-woman’s hat.

Photo by Andy Barnham.(previously spelled wrong)

Nowadays, many business men don’t wear hats, even outdoors in the sun and cold. This seems like a bad idea, but what would I know? Perhaps the problem is what to do with the hat when you come indoors. You can take it off, but then what. Emily post claims that leaving the hat on indoors is usually considered rude, though not always, and traces this back to medieval knights and to the flag code. Indoors, the delivery boy can stuff his knit hat into his pocket, or roll it into a smaller version on his head, a beanie. The fedora wearer must look for a hat rack, or accept looking rude.

Of course the lack of a hat presents problems too. Without one, you leave your hair to signal your social status and political cultural associations. For a man without a hat there are only three styles of hair: short, medium, or long. Short hair says you are a conventionalist drone, long hair, that you’re a hippy or artist, and with middle-length hair you’re …. uncertain? trans? androgynous? No matter how you slice it, it’s not a good look. Adding a mustache or beard makes it even more awkward, in my opinion, see below. I have previously written about the power of mustaches — that they send a message that you are warrior, and beards — that you are a man of fervor, — or of religious or aristocratic sympathies. But combine a mustache with middle-length hair and you begin to look like another Hitler or Stalin.

Wearing a hat allows for a great variety of social messaging, whether worn with or without facial hair. Some hats are expensive, others cheap; some signal religious affiliation, others are strongly secular, or hip. Some folks wear hats that are suitable only for work or sports, like a hard-hat, bicycle helmet, or a straw boater. They tell folks you’re busy with an activity right now. But most people who wear hats, choose one that’s multidimensional, suitable for sport and work. There is the classic Kangol cap that suggests a certain artsy vibe, or the peak cap or newsboy — that suggests (I imagine) a higher level of worker.

working man in cap

Perhaps the most popular flex-hats in the US are the baseball hat, and its relative the trucker’s hat (you adjust the size on a truckers hat using a band int he back). In the US, you can wear these on the job, or off. I think they work indoors too, but what do I know. The baseball and peaked cap suggests you are higher on the social ladder than the truckers cap, but all of them suggest you draw a paycheck. And they often say a lot more. If your trucker’s hat says, NRA, or John Deere, or Oakland As, there enough information given to start a conversation. Depending on what your cap says, you will be welcome in some societies, not welcome in others. Don’t wear your MAGA hat to a Biden rally.

There is power in hats too. A man in a policeman’s cap is a cop, even if he’s without the rest of his police gear. With no hat, the same man in uniform is a mall security guard. The postal person or UPS delivery person is on the job if wearing his USPS baseball cap or knit. An expensive visor cap, like the kangol suggest artistic status, and an expensive newsboy, or peaked cap. suggests a sort of work-life balance. It was worn by Prince Charles in the 1980s, and by me in 2020.

Although a fedora is a boss-man’s hat, I never wear one since I associate them with mobsters, hipsters, lounge singers, and Jimmy Hoffa. For more formal occasions, when not wearing a peaked cap, I wear a Homburg. Churchill wore a Homburg. In England, there is a level above this, the top-hat, and one slightly between the Homberg and fedora, the derby. In the US, none of these really caught on. The derby is sort of comic, sort of social climber. Chaplin wore one, as did Laurel and Hardy. Derby hats tend to get punched through in old-time comedies. It’s the same with most middle of the road approaches — they appeal to no one.

Robert Buxbaum, March 5, 2020.

Virus and cancer treatment by your immune system

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There are two standard treatments for a disease. One is through a chemical, pill or shot, often using a patented antibiotic or antiviral molecule, sometimes a radioactive chemical or anti-inflammatory. There have been quite a lot of success with these molecules especially against bacterial disease. E.g. penicillin, a molecule found in cheese, was quite effective against infection, syphilis, and even the viral disease, rabies. Still, in surprisingly many cases, a molecule that you’d expect should cure a disease does not. For this reason, recent research has looked into the other approach to a cure — use your own immune system.

In the most basic version of this approach, that of Paracelcius, is to give the patient nothing beyond sunshine, a clean dressing, and good food. In surprisingly many cases, this is enough to allow the patient’s own immune system will fight the disease successfully. Currently, this seems like our best option to fight COVID-19, the new Wuhan coronavirus.; antivirals seem to have no particular effect on COVID-19, as with rabies, but patients do get better on their own with time, and there is some indication that sunlight helps too, at least in fighting the disease spread, and perhaps in effecting a cure.

Your immune system is remarkably flexible. When it is up to the task, as in the video below white blood cells multiply enormously around the invader and attack. The white cells do not harm your body cells nor those of friendly bacteria, but rally to kill nearly any invader, even one the cells have never seen before. There is a minimum of side effects (fever, tiredness) but these go away after the invader is gone. The immune system then keeps the memory of the invader alive via “Memory T cells” so that it can attack more quickly if the same invader is seen again. This is what we call immunity, and it’s a type of protection that you generally don’t get from pills.

View post on imgur.com

Unfortunately, not every disease is fought well by the immune system alone. Measles, for example, or smallpox. For several of these diseases we’ve found we can activate the patient’s immune system with a vaccination, even after the patient contacts the disease. An injection of a weaker form of the disease seems to help kick-start the patients own immune system. Vaccination tends to have bad side-effects, but for many diseases, e.g. measles, the bad is outweighed by the good. Interestingly we’ve begun to use this approach on some cancers, too, and it seems to work. Immune therapy, it’s called.

Immune therapy is not generally the first line approach to cancer, but it might be the best for slow cancers, like prostate. Generally, in the fight against cancer, the preferred method is to removes as much of cancer cells as possible, and treat any missed cells using a mix of radiation and chemicals. This works but there are a lot of side-effects. Immune therapy is sort of similar, in a way. Instead of irradiating the bad cells inside the body, one takes the cancer cells outside of the body (or the virus molecules) and uses radiation and chemicals to knock off bits. These bits, a weakened form of the cancer or of the virus, are then cultured and re-injected into the body. Sometimes it works, sometimes not. For melanoma, skin cancer, immune therapy is found to works about 1/4 of the time. Why not more? It seems that sometimes the immune system gets “exhausted” fighting a foe that’s to much for it. And sometimes the activated immune system starts attacking the host body. This is an auto-immune response.

Dr. Robert E. Buxbaum, February 21, 2020

COVID-19 is worse than SARS, especially for China.

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The corona virus, COVID-19 is already a lot worse than SARS, and it’s likely to get even worse. As of today, there are 78,993 known cases and 2,444 deaths. By comparison, from the first appearance of SARS about December 1 2002, there have been a total of 8439 cases and 813 deaths. It seems the first COVID-19 patient was also about December 1, but the COVID-19 infection moved much faster. Both are viral infections, but it seems the COVID virus is infectious for more days, including days when the patient is asymptomatic. Quarantine is being used to stop COVID-19; it was successful with SARS. As shown below, by July 2003 SARS had stopped, essentially. I don’t think COVID-19 will stop so easily.

The process of SARS, worldwide; a dramatic rise and it’s over by July 2003. Source: Int J Health Geogr. 2004; 3: 2. Published online 2004 Jan 28. doi: 10.1186/1476-072X-3-2.

We see that COVID-19 started in November, like SARS, but we already have 10 times more cases than the SARS total, and 150 times more than we had at this time during the SARS epidemic. If the disease stops in July, as with SARS, we should expect to see about a total of 150 times the current number of cases: about 12 million cases by July 2020. Assuming a death rate of 2.5%, that suggests 1/4 million dead. This is a best case scenario, and it’s not good. It’s about as bad as the Hong Kong flu pandemic of 1968-69, a pandemic that killed 60,000 approximately in the US, and which remains with us, somewhat today. By the summer of 69, the spreading rate R° (R-naught) fell below 1 for and the disease began to die out, a process I discussed previously regarding measles and the atom bomb, but the disease re-emerged, less infectious the next winter and the next. A good quarantine is essential to make this best option happen, but I don’t believe the Chinese have a good-enough quarantine.

Several things suggest that the Chinese will not be able to stop this disease, and thus that the spread of COVID-19 will be worse than that of the HK flu and much worse than SARS. For one, both those disease centered in Hong Kong, a free, modern country, with resources to spend, and a willingness to trust its citizens. In fighting SARS, HK passed out germ masks — as many as anyone needed, and posted maps of infection showing places where you can go safely and where you should only go with caution. China is a closed, autocratic country, and it has not treated quarantine this way. Little information is available, and there are not enough masks. The few good masks in China go to the police. Health workers are dying. China has rounded up anyone who talks about the disease, or who they think may have the disease. These infected people are locked up with the uninfected in giant dorms, see below. In rooms like this, most of the uninfected will become infected. And, since the disease is deadly, many people try to hide their exposure to avoid being rounded up. In over 80% of COVID cases the symptoms are mild, and somewhat over 1% are asymptomatic, so a lot of people will be able to hide. The more people do this, the poorer the chance that the quarantine will work. Given this, I believe that over 10% of Hubei province is already infected, some 1.5 million people, not the 79,000 that China reports.

Wuhan quarantine “living room”. It’s guaranteed to spread the disease as much as it protects the neighbors.

Also making me think that quarantine will not work as well here as with SARS, there is a big difference in R°, the transmission rate. SARS infected some 2000 people over the first 120 days, Dec. 1 to April 1. Assuming a typical infection time of 15 days, that’s 8 cycles. We calculate R° for this stage as the 8th root of 2000, 8√2000 = 2.58. This is, more or less the number in the literature, and it is not that far above 1. To be successful, the SARS quarantine had to reduce the person’s contacts by a factor of 3. With COVID-19, it’s clear that the transmission rate is higher. Assuming the first case was December 1, we see that there were 73,437 cases in only 80. R° is calculated as the 5 1/3 root of 73,437. Based on this, R° = 8.17. It will take a far higher level of quarantine to decrease R° below 1. The only good news here is that COVID-19 appears to be less deadly than SARS. Based on Chinese numbers the death rate appears to be about 2000/73,437, or about 3%, varying with age (see table), but these numbers are overly high. I believe there are a lot more cases. Meanwhile the death rate for SARS was over 9%. For most people infected with COVID-19, the symptoms are mild, like a cold; for another 18% it’s like the flu. A better estimate for the death rate of COVID-19 is 0.5-1%, less deadly than the Spanish flu of 1918. The death rate on the Diamond Princess was 3/600 = 0.5%, with 24% infected.

The elderly are particularly vulnerable. It’s not clear why.

Backing up my value of R°, consider the case of the first Briton to contact the disease. As reported by CNN, he got it at conference in Singapore in late January. He left the conference, asymptomatic on January 24, and spent the next 4 days at a French ski resort where he infected one person, a child. On January 28, he flew to England where he infected 8 more before checking himself into a hospital with mild symptoms. That’s nine people infected over 3 weeks. We can expect that schools, factories, and prisons will be even more hospitable to transmission since everyone sits together and eats together. As a worst case extrapolation, assume that 20% of the world population gets this disease. That’s 1.5 billion people including 70 million Americans. A 1% death rate suggests we’ll see 700,000 US deaths, and 15 million world-wide this year. That’s almost as bad as the Spanish flu of 1918. I don’t think things will be that bad, but it might be. The again, it could be worse.

If COVID-19 follows the 1918 flu model, the disease will go into semi-remission in the summer, and will re-emerge in the fall to kill another few hundred thousand Americans in the next fall and winter, and the next after that. Woodrow Wilson got the Spanish Flu in the fall of 1918, after it had passed through much of the US, and it nearly killed him. COVID-19 could continue to rampage every year until a sufficient fraction of the population is immune or a vaccine is developed. In this scenario, quarantine will have no long-term effect. My sense is that quarantine and vaccine will work enough in the US to reduce the effect of COVID-19 to that of the Hong Kong flu (1968), so that the death rate will be only 0.1 – 0.2%. In this scenario, the one I think most likely, the US will experience some 100,000 deaths, that is 0.15% of 20% of the population, mostly among the elderly. Without good quarantine or vaccines, China will lose at least 1% of 20% = about 3 million people. In terms of economics, I expect a slowdown in the US and a major problem in China, North Korea, and related closed societies.

Robert Buxbaum, February 18, 2020. (Updated, Feb. 23, I raised the US death totals, and lowered the totals for China).

Italian Engineering and the Kennedy assassination.

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There are several unbelievable assertions surrounding the Kennedy assassination, leading many to conclude that Oswald could not have killed Kennedy alone. I believe that many of these can be answered once you realize that Oswald used an Italian gun, and not a US gun. Italian engineering differs from our in several respects that derive from the aesthetic traditions of the countries. It’s not that our engineers are better or worse, but our engineers have a different idea of what good engineering is and thus we produce designs that, to an Italian engineer, are big, fat, slow, and ugly. In our eyes Italian designs are light, fast, pretty, low-power, and unreliable. In the movie, Ford vs Ferrari, the American designer, Shelby says that, “If races were beauty contests, the Ferrari would win.” It’s an American, can-do, attitude that rings hollow to an Italian engineer. 

Three outstanding questions regarding the Kennedy assassination include: How did Oswald fire three bullets, reasonably accurately in 5 to 8 seconds. How did he miss the limousine completely on the first, closest shot, then hit Kennedy twice on the next two, after previously missing on a close shot at retired general, Edwin Walker. And how could the second shot have gone through Kennedy’s neck, then through his wrist, and through Connolly twice, emerging nearly pristine. I will try to answer by describing something of the uniquenesses of the gun and bullets, and of Italian engineering, in general. 

Oswald cartridge.

The rifle Oswald used was a Modello 91/38, Carcano (1938 model of a design originally used in 1891) with an extra-long, 20.9″ barrel, bought for only $19.95 including a 4x sight. That’s $12.50 for the gun, the equivalent of $100 in 2020). The gun may have been cheep, but it was a fine Italian weapon: it was small, fast, pretty, manual, and unreliable. The small size allowed Oswald to get the gun into the book depository without arousing suspicion. He claimed his package held curtain rods, and the small, narrow shape of the gun made the claim believable.

The first question, the fast shooting, is answered in part by the fact that loading the 91/38 Carcano rifle takes practice. Three American marksmen who tried to duplicate the shots for the Warren commission didn’t succeed, but they didn’t have the practice with this type of gun that Oswald had. The Carcano rifle used a bolt and clip loading system that had gone out of style in the US before WWI. To put in a new shell, you manually unlock and pull back the bolt. The old casing then flies out, and the spring–clip loads a new shell. You then have to slam the bolt forward and lock it before you can fire again. For someone practiced, loading this way is faster than with a semi-automatic. To someone without practice it is impossibly slow, like driving a stick shift car for the first time. Even with practice, Americans avoid stick shift cars, but Italians prefer them. Some time after the Warren report came out, Howard Donahue, an American with experience on this type of rifle, was able to hit three moving targets at the distance in 4.8 seconds. That’s less than the shortest estimate of the time it took Oswald to hit twice. Penn of Penn and Teller recreates this on TV, and shows here that Kennedy’s head would indeed have moved backward.

Oswald’s magic bullet, shot two.

That Oswald was so accurate is explained, to great extent by the way the sight was mounted and by the unusual bullets. The model 38 Carcano that Oswald bought fired light, hollow, 6.5×52mm cartridges. This is a 6.5 mm diameter bullet, with a 52 mm long casing. The cartridge was adopted by the Italians in 1940, and dropped by 1941. These bullets are uncommonly bullet is unusually long and narrow (6.5 mm = .26 caliber), round-nosed and hollow from the back to nearly the front. In theory a cartridge like this gives for greater alignment with the barrel., and provides a degree of rocket power acceleration after it leaves the muzzle. Bullets like this were developed in the US, then dropped by the late 1800s. The Italians dropped this bullet for a 7.5 mm diameter version in 1941. The 6.5 mm version can go through two or three people without too much damage, and they can behave erratically. The small diameter and fast speed likely explains how Oswald’s second shot went through Kennedy and Connolly twice without dong much. An American bullet would have done a lot more damage.

Because of the light weight and the extra powder, the 6.5 mm hollow bullet travels uncommonly fast, about 700 m/s at the muzzle with some acceleration afterwards, ideally. Extra powder packs into the hollow part by the force of firing, providing, in theory, low recoil, rocket power. Unfortunately these bullets are structurally weak. They can break apart or bend and going off-direction. By comparison the main US rifle of WWII, the M1, was semi-automatic, with bullets that are shorter, heavier, and slower, going about 585 m/s. Some of our bullets had steel cores too to provide a better combination of penetration and “stopping power”. Only Oswald second shot stayed pristine. It could be that his third shot — the one that made Kennedy’s head explode — flattened or bent in flight.

Oswald fragment of third bullet. It’s hollow and seems to have come apart in a way a US bullet would not.

The extra speed of Oswald’s bullets and the alignment of his gun would have given Oswald a great advantage in accuracy. At 100 yards (91 m), test shots with the rifle landed 2 1⁄2 to 5 inches high, within a 3-to-5-inch circle. Good accuracy with a sight that was set to high for close shot accuracy. The funky sight, in my opinion , explains how Oswald managed to miss Walker, but explains how he hit Kennedy accurately especially on the last, longest shot, 81 m to Kennedy’s head

Given the unusually speed of the bullets (I will assume 750 m/s) Oswald’s third shot would have taken 0.108 s to reach the target. If the sight were aligned string and if Kennedy were not moving, the bullet would have been expected to fall 2.24″ low at this range, but given the sight alignment we’d expect him to shoot 3-6″ high on a stationary target, and dead on, on the president in his moving vehicle. Kennedy was moving at 5 m/sand Oswald had a 17° downward shot. The result was a dead on hit to the moving president assuming Oswald didn’t “lead the shot”. The peculiarities of the gun and bullets made Oswald more accurate here than he’d been in the army, while causing him to miss Walker completely at close range.

comparison of the actual, second shot, “magic bullet,” left, with four test-shot bullets. Note that one of the test bullets collapsed, two bent, and one exploded. This is not a reliable bullet design.

We now get to the missed, first shot: How did he miss the car completely firing at the closest range. The answer, might have to do with deformation of the bullets. A hollow base bullet can explode, or got dented and fly off to the side. More prosaically, it could be that he hit a tree branch or a light pole. The Warren commission blamed a tree that was in the way, and there was also a light pole that was never examined. For all we know the bullet is in a branch today, or deflected. US bullets would have a greater chance to barrel on through to at least hit the car. This is an aspect of Italian engineering — when things are light, fast, and flexible, unusual things happen that do not expect to happen with slow, ugly, US products. It’s a price of excellence, Italian style.

Another question appears: Why wasn’t Oswald stopped when the FBI knew he’d threatened Kennedy, and was suspected of shooting at Walker. The simple answer, I think, is that the FBI was slow, and plodding. Beyond this, neither the FBI nor the CIA seem to have worried much about Kennedy’s safety. Even if Kennedy had used the bubble top, Oswald would likely have killed him. Kennedy didn’t care much for the FBI and didn’t trust Texas. Kennedy had a long-running spat with the FBI involving his involvement with organized crime, and perhaps running back to the days when Kennedy’s father was a bootlegger. His relation with the CIA was similar.

The Mateba, Italian semi-automatic revolver, $3000, available only in 357 Magnum and 44 magnum.

I should mention that the engineering styles and attitudes of a country far outlast the particular engineer.We still make big, fat, slow, ugly cars — that are durable and reasonably priced. Germans still overbuild, and Italian cars and guns are as they ever were: beautiful, fast, expensive, and unreliable. The fastest production car is Italian, a Bugatti with a top speed of 245 mph; the fastest rollercoaster is at Ferrari gardens, 149 mph, and in terms of guns, let me suggest you look at the Mateba, left, a $3000 beautiful super fast semi-automatic revolver (really), produced in Italy, and available in 357 magnum and .44 magnum only . It’s a magnificent piece of Italian engineering beautiful, accurate, powerful, and my guess is it’s unreliable as all get out. Our, US pistols typically cost 1/5 to 1/10 as much. A country’s cars, planes, and guns represent the country’s aesthetics. The aesthetics of a county changes only slowly, and I think the world is better off because of it

Robert Buxbaum, February 14, 2020. One of my favorite courses in engineering school, Cooper Union, was in Engineering Aesthetics and design.

Affirmative action for Elizabeth Warren, 1/1000 Indian

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The following is Elizabeth Warren’s law registration for the state of Texas, 1986 claiming she is an American Indian. There was very little evidence for it and an genetic test showed she was somewhere between 1/256 and 1/1000 Indian. My son was determined to have 1/1000 Indian blood in a similar test, and we have no Indian ancestors at all, as best as I can tell. Still, as an Indian Ms. Warren is entitled to affirmative action; she’s to get preferential hiring financial, and educational treatment over someone more qualified, but without Indian blood. Affirmative action was institute as a way to redress the suffering of Indians and other minorities, but it is not clear that is serves this purpose when someone with so little, or no blood can take the advantage. There is no requirement of proof that you are at all Indian by blood, and even if you are 1/1000 Indian, what about the other 999/1000? Why don’t they count to give yo lower standing than someone who is 1/10 Indian, say. How indian should you have to be to get benefits.

Related to the question of how much Indian blood you should have to have to get benefits is the question of making other folks suffer to provide this benefit. Many of the people who suffer because of affirmative action are dependents of immigrant minorities, Jews, Italians, and Chinese, and these folks have not had it that well. The Italians were discriminated against in hiring, as mandated by the city council, see announcement below, and Chinese immigrants had very limited migration and work rights, as specified under The Chinese Exclusion Act of 1882. This act was not repealed until 1943 as part of our war against Japan.

In the late 1800s anti Italian discrimination was common. In part this was the Tammany Hall Irish doing their best to keep out an upstart immigrant group. Should Italians have affirmative action preferences?

At maximum Ms. Warren is less than 1% indians and thus over 99% Texan. This is to suggest that the majority of her bloodline is descent is from those who displaced the Indians, but her preferential hiring was likely in preference to other minorities who suffered too, and who likely have a purer bloodline to that suffering and exclusion than Ms Warren has. Is this what we want from affirmative action? The form we’ve got benefits, for the most part, only the most crooked, connected members of society. People like Ms Warren. I think this has to change.

Robert Buxbaum, January 23, 2020

A series solution to the fussy suitor/ secretary problem

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One way to look at dating and other life choices is to consider them as decision-time problems. Imagine, for example that have a number of candidates for a job, and all can be expected to say yes. You want a recipe that maximizes your chance to pick the best. This might apply to a fabulously wealthy individual picking a secretary or a husband (Mr Right) in a situation where there are 50 male choices. We’ll assume that you have the ability to recognize who is better than whom, but that your pool has enough ego that you can’t go back to anyone once you’ve rejected the person.

Under the above restrictions, I mentioned in this previous post that you maximize your chance of finding Mr Right by dating without intent to marry 36.8% of the fellows. After that, you marry the first fellow who is better than any of the previous. My previous post had a link to a solution using Riemann integrals, but I will now show how to do it with more prosaic math — a series. One reason for doing this by series is that it allows you to modify your strategy for a situation where you can not be guaranteed a yes, or where you’re OK with number 2, but you don’t like the high odds of the other method, 36.8%, that you’ll marry no one.

I present this, not only for the math interest, but because the above recipe is sometimes presented as good advice for real-life dating, e.g. in a recent Washington Post article. With the series solution, you’re in a position to modify the method for more realistic dating, and for another related situation, options cashing. Let’s assume you have stock options in a volatile stock company, if the options are good for 10 years, how do you pick when to cash in. This problem is similar to the fussy suitor, but the penalty for second best is small.

The solution to all of these problems is to pick a stopping point between the research phase and the decision phase. We will assume you can’t un-cash in an option, or continue dating after marriage. We will optimize for this fractional stopping point between phases, a point we will call x. This is the fraction of guys dated without intent of marriage, or the fraction of years you develop your formula before you look to cash in.

Let’s consider various ways you might find Mr Right given some fractional value X. One way this might work, perhaps the most likely way you’ll find Mr. Right, is if the #2 person is in the first, rejected group, and Mr. Right is in the group after the cut off, x. We’ll call chance of of finding Mr Right through this arrangement C1, where

C1 = x (1-x) = x – x2.

We could used derivatives to solve for the optimum value of x, but there are other ways of finding Mr Right. What if Guy #3 is in the first group and both Guys 1 and 2 are in the second group, and Guy #1 is earlier in the second line-up. You’d still marry Mr Right. We’ll call the chance of finding Mr Right this way C2. The odds of this are

C2 = x (1-x)2/2

= x/2 – x2 + x3/2

There is also a C3 and a C4 etc. Your C3 chance of Mr Right occurs when guy number 4 is in the first group, while #1, 2, and 3 are in the latter group, but guy number one is the first.

C3 = x (1-x)3/4 = x/4 – 3x2/4 + 3x3/4 – x4/4.

I could try to sum the series, but lets say I decide to truncate here. I’ll ignore C4, C5 etc, and I’ll further throw out any term bigger than x^2. Adding all smaller terms together, I get ∑C = C, where

C ~ 1.75 x – 2.75 x2.

To find the optimal x, take the derivative and set it to zero:

dC/dx = 0 ~ 1.75 -5.5 x

x ~ 1.75/5.5 = 31.8%.

That’s not an optimal answer, but it’s close. Based on this, C1 = 21.4%, C2 = 14.8%, C3 =10.2%, and C4= 7.0% C5= 4.8%Your chance of finding Mr Right using this stopping point is at least 33.4%. This may not be ideal, but you’re clearly going to very close to it.

The nice thing about this solution is that it makes it easy to modify your model. Let’s say you decide to add a negative value to not ever getting married. That’s easily done using the series method. Let’s say you choose to optimize your chance for either Mr 1 or 2 on the chance that both will be pretty similar and one of them may say no. You can modify your model for that too. You can also use series methods for the possibility that the house you seek is not at the last exit in Brooklyn. For the dating cases, you will find that it makes sense to stop your test-dating earlier, for the parking problem, you’l find that it’s Ok to wait til you’re less than 1 mile away before you settle on a spot. I’ll talk more about this latter, but wanted to note that the popular press seems overly impressed by math that they don’t understand, and that they have a willingness to accept assumptions that bear only the flimsiest relationship to relaity.

Robert Buxbaum, January 20, 2020

Samuel Johnson: “No man but a blockhead ever wrote except for money.”

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Some days, I spend hours at a time on facebook, and when I’m done, I often feel it was a complete waste of time. I do not make friends this way, and I have little evidence that I’ve convinced anyone. Still, for some reason, I can’t seem to stay off for long, so I figure I might as well look for the attraction.

One positive thing I do (did) with FB was to run for office. I lost, but I was able to speak to more people using FB in a day than I could have otherwise. Another thing I do is to spread articles — those I find interesting, and my own writing, blog posts, mostly. I write these posts for free, and while I imagine my blog posts do some good. I sometimes get nice comments suggesting people read the blogs and think about what I say. Still, it does not make money, and takes a fair amount of effort.

I can imagine I help mankind in some subtle, long range way, or perhaps gain some long-range fame. But who cares about long-range fame? And, as for helping people, it is also possible I will hurt them too. Computers sit analyzing my words, and everyone’s, tracking their views and using the data for what. I’m just feeding the computer, and that makes me think my writing may harm more than help. What I write on FB is owned by FB. It’s free content for the owners of FB to re-use to sell: my personality, capsulated, my friends likes and dislikes, for sale at a price. My posts turn me and my friends into commodities — and there isn’t even remuneration.

It is claimed that, in the 2016 election, Trump was able to win, at low cost, through a Russian-managed facebook campaign. The educated elites of politics were not able to come with the wiley Russians, for all their brain-power, and despite help from the FBI, or so the theory goes. If so, it’s a warning that all the information I provide to facebook is available to Trump and the Russians to use against me. The management of facebook was committed to Ms Clinton in 2016, and is completely committed to Trump’s removal as best I can tell. If they are not able to beat the Russians, maybe I should not try. Then again, maybe they’re not as elite as they think.

Sometimes I imagine that the alternative of not-posting is worse; it is to have no voice at all, and to have no information of the common discussion. The newspapers seem no less biassed than those on my FB. I write then in a bizarre chasm between hope for posterity, and a better world, and out of desperation that to be an unheard, quiet one, is to be dead. I suspect I’m not unique here.

Robert E. Buxbaum, January 27, 2020.

If the test of free will is that no one can tell what I will do….

Free will is generally considered a good thing — perhaps a unique gift from the creator to man-kind. Legal philosophers contend that it is free will that makes us liable to legal punishment for our crimes. while piranhas and machines are not. We would never think of jailing a gun or a piranha even it harmed a child.

It’s not totally clear that we have free will, though, nor is it totally clear what free will is. The common test is that no one can tell what I will do. If this is the only requirement, though, it seems a random number generator should be found to have free will. One might want to add some degree of artificial intelligence so that the random numbers are used to make decisions that are rational in some sense, say choosing between tea and coffee, for example, and not tea and covfefe, but this should not be difficult. With that modification, we should find that the random device would make free decisions as boldly or conservatively as any person.

The numbers should be truly random, but even if they are not quite, this should not be a barrier. We generally take statistical things to be random, the speed of the wind tomorrow at 3:00 PM for example even though there is a likely average, and 500 mph is exceedingly unlikely. And, if that isn’t quite random enough, one could use quantum mechanics. One could devise a system that measures the time between the next two radioactive decays to an accuracy many times greater than the likely time between. If the sample has a decay every 100 seconds or so, the second and third digit of this time after the decimal is random to an extent that most would accept, and that one can predict it at all — or so we understand it. (God might be an exception here, but since He is outside of time, prediction becomes an oxymoron). Using these quantum mechanic random numbers, one should be able to make decisions showing as much free will as any person shows, and likely more . Most folks are fairly predictable.

Since God is considered to be outside of time, any mention of his fore-knowledge or pre-determination is an oxymoron. There is no pre or fore if you’re outside of time, as I’d understand things

 I notice that few people would say that a radioactive atom has free will, though, and that many doubt that people have free will. Still no one seems interested in handing major issues to a computer, or holding the machine liable if things turn out poorly. And if one wants to argue that people have no free will, it seems to me that the argument for punishment would get rather weak. Without free will, shy would it be more wrong to kill a person than a piranha, or a plant.

Robert Buxbaum, January 19, 2020. Just some random thoughts on random number generators. I’ve also had thoughts about punishments, and about job choices.

Sewage reactor engineering, Stirred tank designs

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Over the past few years, I’ve devoted several of these essays to analysis of first-stage sewage treatment reactors. I described and analyzed the rotating disc reactor found at the plant is Holly here, and described the racetrack,“activated sludge” plug reactor found most everywhere else here. I also described a system without a primary clarifier found near Cincinatti. All of these were effective for primary treatment; soluble organics are removed by bio-catalyzed oxidation:

2 H-C-O-H + O2 –> CO2 + H2O.

A typical plant in Oakland county treats 2,000,000 gallons per day of this stuff, with the bio-reactor receiving liquid waste containing about 200 ppm of soluble and colloidal biomass. That’s 400 dry gallons for those interested, or about 3200 dry lbs./day. About half of this will be oxidized to CO2 and water. The rest (cell bodies) are removed with insoluble components, and applied to farmers fields or buried, or burnt in an incinerator.

There is another type of reactor used in Oakland County. It’s mostly used for secondary treatment, converting consolidated sludge to higher-quality sludge that can be sold or used on farms with less restriction, but it is a type of reactor used at the South Lyon treatment plant, for primary treatment. It is a Continually stirred tank reactor, or CSTR, a design that is shown in schematic below.

As of some years ago, the South Lyon system involved a single largish pond lined with plastic with a volume about 2,000,000 gallons total. About 700,000 gallons per day of sewage liquids went into the lagoon, at 200 ppm soluble organics. Air was bubbled through the liquid providing a necessary reactant, and causing near-perfect mixing of the contents. The aim of the plant managers is to keep the soluble output to the, then-acceptable level of 10 ppm; it’s something they only barely managed, and things got worse as the flow increased. Assume as before, a value V and a flow Q.

We will call the concentration of soluble organics C, and call the initial concentration, the concentration that enters,  Ci. It’s about 200 ppm. We’ll call the output concentration Co, and for this type of reactors, Co = C.  The reaction is first order, approximately, so that, if there were no flow into or out of the reactor, the concentration of organics would decrease at the rate of

dC/dt = -kC.

Here k is a reaction constant, dependent on temperature oxygen and cell content. It’s typically about 0.5/hour. For a given volume of tank the rate of organic removal is VkC. We can now do a mass balance on soluble organics. Since the rate of organic entry is QCi and the rate leaving by flow is QC. The difference must be the amount that is reacted away:

QCi – QC = VkC.

We now use algebra, to find that

Co = Ci/(1 + kV/Q).

V/Q is sometimes called a residence time; for the system. At normal flow, the residence time of the South Lyon system is about 2.8 days or 68.6 hours. Plugging these numbers in, we find that the effluent from the reactor leaves at 1/35 of the input concentration, or 5.7 ppm, on average. This would be fine except that sometimes the temperature drops, or the flow increases, and we start violating the standard. A yet bigger problem was that the population increased by 50% while the EPA standard got more stringent to 2 ppm. This was solved by adding another, smaller reactor, volume = V2. Using the same algebraic analysis, as above you can show that, with two reactors,

Co = Ci/ [(1 + kV/Q)(1+kV2/Q)].

It’s a touchy system, but it meets government targets, just barely, most of the time. I think it is time to switch to a plug-flow reactor system, as used in much of Oakland county. In these, the fluid enters a channel and is reacted as it flows along. Each gallon of fluid, in a sense moves by itself as if it were its own reactor. In each gallon, we can say that dC/dt = -kC. We can thus solve for Co in terms of the total residence time, where t again is V/Q. We can rearrange this equation and integrate: ∫dC/C = – ∫kdt. We then find that, 

      ln(Ci/Co) = kt = kV/Q

To convert 200 ppm sewage to 2 ppm we note that Ci/Co = 100 and that V = Q ln(100)/k = Q (4.605/.5) hours. An inflow of 1000,000 gallons per day = 41,667 gal/ hour, and we find the volume of tank is 41,667 x 9.21 = 383,750 gallons. This is quite a lot smaller than the CSTR tanks at South Lyon. If we converted the South Lyon tanks to a plug-flow, race-track design, it would allow it to serve a massively increased population, discharging far cleaner sewage. 

Robert Buxbaum, November 17, 2019

Maximum height of an NYC skyscraper, including wind.

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Some months ago, I demonstrated that the maximum height of a concrete skyscraper was 45.8 miles, but there were many unrealistic assumptions. The size of the base was 100 mi2, about that of Sacramento, California; the shape was similar to that of the Eiffel tower, and there was no wind. This height is semi-reasonable; it’s about that of the mountains on Mars where there is a yellow sky and no wind, but it is 100 times taller than the tallest skyscraper on earth. the Burj Khalifa in Dubai, 2,426 ft., shown below. Now I’d like to include wind, and limit the skyscraper to a straight tower of a more normal size, a city-block square of manhattan, New York real-estate. That’s 198 feet on a side; this is three times the length of Gunther’s surveying chain, the standard for surveying in 1800.

Burj Khalifa, the world’s tallest building, Concrete + glass structure. Dubai tourism image.

As in our previous calculation, we can find the maximum height in the absence of windby balancing the skyscrapers likely strength agains its likely density. We’ll assume the structure is made from T1 steel, a low carbon, vanadium steel used in bridges, further assume that the structure occupies 1/10 of the floor area. Because the structure is only 1/10 of the area, the average yield strengthener the floor area is 1/10 that of T1 steel. This is 1/10 x 100,000 psi (pounds per square inch) = 10,000 psi. The density of T1 steel is 0.2833 pounds per cubic inch, but we’ll assume that the density of the skyscraper is about 1/4 this; (a skyscraper is mostly empty space). We find the average is 0.07 pounds per cubic inch. The height, is the strength divided by the density, thus

H’max-tower = 10,000psi / 0.07 p/in3 = 142, 857 inches = 11, 905 feet = 3629 m,

This is 4 1/4 times higher than the Burj Khalifa. The weight of this structure found from the volume of the structure times its average density, or 0.07 pounds per cubic inch x 123 x 1982x 11,905 = 56.45 billion pounds, or, in SI units, a weight of 251 GNt.

Lets compare this to the force of a steady wind. A steady wind can either either tip over the building by removing stress on the upwind side, or add so much extra stress to the down-wind side that the wall fails. The force of the wind is proportionals to the wind’s energy dissipation rate. I’ll assume a maximum wind speed of 120 mph, or 53.5 m/s. The force of the wind equals the area of the building, times a form factor, ƒ, times the rate of kinetic energy dissipation, 1/2ρv2. Thus,

F= (Area)*ƒ* 1/2ρv2, where ρ is the density of air, 1.29kg/m3.

The form factor, ƒ, is found to be 1.15 for a flat plane. I’ll presume that’s also the form factor for a skyscraper. I’ll take the wind area as

Area = W x H,

where W is the width of the tower, 60.35 m in SI, and the height, H, is what we wish to determine. It will be somewhat less than H’max-tower, =3629 m, the non-wind height. As an estimate for how much less, assume H = H’max-tower, =3629 m.
For this height tower, the force of the wind is found to be:

F = 3629 * 60.35* 2123 = 465 MNt.

This is 1/500 the weight of the building, but we still have to include the lever effect. The building is about 60.1 times taller than it is wide, and as a result the 465 MNt sideways force produces an additional 28.0 GNt force on the down-wind side, plus and a reduction of the same amount upwind. This is significant, but still only 1/9 the weight of the building. The effect of the wind therefore is to reduce the maximum height of this New York building by about 9 %, to a maximum height of 2.05 miles or 3300 m.

The tallest building of Europe is the Shard; it’s a cone. The Eiffel tower, built in the 1800s, is taller.

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as before, is something like the Eiffel tower. You can show, though I will not, that even with wind, the maximum height of a conical building is three times as high as that of a straight building of the same base-area and construction. That is to say that the maximal height of a conical building is about 6 miles.

In the old days, one could say that a 2 or 6 mile building was inconceivable because of wind vibration, but we’ve found ways to deal with vibration, e.g. by using active damping. A somewhat bigger problem is elevators. A very tall building needs to have elevators in stages, perhaps 1/2 mile stages with exchanges (and shopping) in-between. Yet another problem is fire. To some extent you eliminate these problems by use of pre-mixed concrete, as was used in the Trump tower in New York, and later in the Burj Khalifa in Dubai.

The compressive strength of high-silica, low aggregate, UHPC-3 concrete is 135 MPa (about 19,500 psi), and the density is 2400 kg/m3 or about 0.0866 lb/in3. I will assume that 60% of the volume is empty and that 20% of the weight is support structure (For the steel building, above, I’d assumed 3/4 and 10%). In the absence of wind,

H’max-cylinder-concrete = .2 x 19,500 psi/(0.4 x.0866  lb/in3) = 112,587″ = 9,382 ft = 1.77 miles. This building is 79% the height of the previous, steel building, but less than half the weight, about 22,000,000,000 pounds. The effect of the wind will be to reduce the above height by about 14%, to 1.52 miles. I’m not sure that’s a fire-safe height, but it is an ego-boost height.

Robert Buxbaum. December 29, 2019.