Category Archives: Detroit

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.

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.

The main route of lead poisoning is from the soil by way of food, dust, and smoke.

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While several towns have had problems with lead in their water, the main route for lead entering the bloodstream seems to be from the soil. The lead content in the water can be controlled by chemical means that I reviewed recently. Lead in the soil can not be controlled. The average concentration of lead in US water is less than 1 ppb, with 15 ppb as the legal limit. According to the US geological survey, of lead in the soil, 2014., the average concentration of lead in US soil is about 20 ppm. That’s more than 1000 times the legal limit for drinking water, and more than 20,000 times the typical water concentration. Lead is associated with a variety of health problems, including development problems in children, and 20 ppm is certainly a dangerous level. Here are the symtoms of lead poisoning.

Several areas have deadly concentrations of lead and other heavy metals. Central Colorado, Kansas, Washington, and Nevada is particularly indicated. These areas are associated with mining towns with names like Leadville, Telluride, Silverton, Radium, or Galena. If you live in an areas of high lead, you should probably not grow a vegetable garden, nor by produce at the local farmer’s market. Even outside of these towns, it’s a good idea to wash your vegetables to avoid eating the dirt attached. There are hardly any areas of the US where the dust contains less than 1000 times the lead level allowed for water.

Lead content of US soils, from the US geological survey of soils, 2014. Michigan doesn’t look half bad.

Breathing the dust near high-lead towns is a problem too. The soil near Telluride Colorado contains 1010 mg/kg lead, or 0.1%. On a dust-blown day in the area, you could breath several grams of the dust, each containing 1 mg of lead. That’s far more lead than you’d get from 1000 kg of water (1000 liters). Tests of blood lead levels, show they rise significantly in the summer, and drop in the winter. The likely cause is dust: There is more dust in the summer.

Recalled brand of curry powder associated with recent poisoning.

Produce is another route for lead entering the bloodstream. Michigan produce is relatively safe, as the soil contains only about 15 ppm, and levels in produce are generally far smaller than in the soil. Ohio soils contains about three times as much lead, and I’d expect the produce to similarly contain 3 times more lead. That should still be safe if you wash your food before eating. When buying from high-lead states, like Colorado and Washington, you might want to avoid produce that concentrates heavy metals. According Michigan State University’s outreach program, those are leafy and root vegetables including mustard, carrots, radishes, potatoes, lettuce, spices, and collard. Fruits do not concentrate metals, and you should be able to buy them anywhere. (I’d still avoid Leadville, Telluride, Radium, etc.). Spices tend to be particularly bad routes for heavy metal poisoning. Spices imported from India and Soviet Georgia have been observed to have as much as 1-2% lead and heavy metal content; saffron, curry and fenugreek among the worst. A recent outbreak of lead poisoning in Oakland county, MI in 2018 was associated with the brand of curry powder shown at left. It was imported from India.

Marijuana tends to be grown in metal polluted soil because it tolerates soil that is too polluted fro most other produce. The marijuana plant concentrates the lead into the leaves and buds, and smoking sends it to the lungs. While tobacco smoking is bad, tobacco leaves are washed and the tobacco products are regulated and tested for lead and other heavy metals. If you choose to smoke cigarettes, I’d suggest you chose brands that are low in lead. Here is an article comparing the lead levels of various brands. . Better yet, I’s suggest that you vape. There are several advantages of vaping relative to smoking the leaf directly. One of them is that the lead is removed in the process of making concentrate.

Some states test the lead content of marijuana; Michigans and Colorado do not, and even in products that are tested, there have been scandals that the labs under-report metal levels to help keep tainted products on the shelves. There is also a sense that the high cost encourages importers to add lead dust deliberately to increase the apparent density. I would encourage the customer to buy vape or tested products, only.

Here is a little song, “pollution” from Tom Lehrer, to lighten the mood.

Robert Buxbaum, November 24, 2019. I ran for water commissioner in 2016 and lost. I may run again in 2020. Who knows, this time I may win.

Water Towers, usually a good thing.

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Most towns have at least one water tower. Oakland county, Michigan has four. When they are sized right, they serve several valuable purposes. They provide water in case of a power failure; they provide increased pressure in the morning when people use a lot of water showering etc.; and they allow a town to use smaller pumps and to pump with cheaper electricity, e.g. at night. If a town has no tower, all these benefits are gone, but a town can still have water. It’s also possible to have a situation that’s worse than nothing. My plan is to show, at the end of this essay, one of the ways that can happen. It involves thermodynamic properties of state i a situation where there is no expansion headspace or excess drain (most towers have both).

A typical water tower — spheroidal design. A tower of the dimensions shown would contain about 1/2 million gallons of water.

The typical tower stands at the highest point in the town, with the water level about 170 feet above street level. It’s usable volume should be about as much water as the town uses in a typical day. The reason for the height has to do with the operating pressure of most city-level water pipes. It’s about 75 psi and each foot of water “head” gives you about 0.43 psi. You want pressures about 75 psi for fire fighting, and to provide for folks in apartment buildings. If you have significantly higher pressures, you pay a cost in electricity, and you start losing a lot of water to leaks. These leaks should be avoided. They can undermine the roads and swallow houses. Bob Dadow estimates that, for our water system the leakage rate is between 15 and 25%.

Oakland county has four water towers with considerably less volume than the 130 million gallons per day that the county uses. I estimate that the South-east Oakland county tower, located near my home, contains, perhaps 2 million gallons. The other three towers are similar in size. Because our county’s towers are so undersized, we pay a lot for water, and our water pressure is typically quite low in the mornings. We also have regular pressure excursions and that leads to regular water-boil emergencies. In some parts of Oakland county this happens fairly often.

There are other reasons why a system like ours should have water towers with something more like one days’ water. Having a large water reserve means you can benefit from the fact that electric prices are the lowest at night. With a days’ volume, you can avoid running the pumps during high priced, day times. Oakland county loses this advantage. The other advantage to having a large volume is that it gives you more time to correct problems, e.g. in case of an electric outage or a cyber attack. Perhaps Oakland thinks that only one pump can be attacked at one time or that the entire electric grid will not go out at one time, but these are clearly false assumptions. A big system also means you can have pumps powered by solar cells or other renewable power. Renewable power is a good thing for reliability and air pollution avoidance. Given the benefits, you’d expect Oakland county would reward towns that add water towers, but they don’t, as best I can tell.

Here’s one way that a water column can cause problems. You really need those pressure reliefs.

Now for an example of the sort of things that can go wrong in a water tower with no expansion relief. Every stand-pipe is a small water tower, and since water itself is incompressible, it’s easy to see that a small expansion in the system could produce a large pressure rise. The law requires that every apartment hose water system has to have expansion relief to limit these increases; The water tower above had two forms of reliefs, a roof vent, and an overflow pipe, both high up so that pressure could be maintained. But you can easily imagine a plumber making a mistake and installing a stand pipe without an expansion relief. I show a system like that at left, a 1000 foot tall water pipe, within a skyscraper, with a pump at the bottom, and pipes leading off at the sides to various faucets.

Lets assume that the pressure at the top is 20 psi, the pressure at the bottom will be about 450 psi. The difference in pressure (430 psi) equals the weight of the water divided by the area of the pipe. Now let’s imagine that a bubble of air at the bottom of the pipe detaches and rises to the top of the pipe when all of the faucets are closed. Since air is compressible, while water is not, the pressure at the bubble will remain the same as the bubble rises. By the time the bubble reaches the top of the pipe, the pressure there will rise to 450 psi. Since water has weight, 430 psi worth, the pressure at the bottom will rise to 880 psi = 450 + 430. This is enough to damage pump and may blow the pipes as well. A scenario like this likely destroyed the New Horizon oil platform to deadly consequences. You really want those pressure reliefs, and you want a competent plumber / designer for any water system, even a small one.

Robert Buxbaum, September 28- October 6, 2019. I ran for water commissioner is 2016.

Why does water cost what it does?

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Water costs vary greatly about Oakland county, and around the US, and I have struggled in vain to find out why. In part the problem is that each city gets to add as much maintenance and management costs as the city government thinks appropriate. High management and infrastructure fees can increase to the cost of water, but I also not that different cities about Oakland County Michigan get their water at different rates from the multi-county organization that oversees water in South East Michigan: GLWA, The Great Lakes Water Authority.

$112 water bill for zero usage. The base charge is so large that prices are essentially independent of useage.

I’ve attended meetings, both local and multi county and have tried to find out why one town gets its water at a far lower rate than another, near by. Towns get lower rates if they have a water tower, but it is not at all clear what the formula is. It also helps to separate the storm sewage from the sanitary sewage — something that I have proposed for all of Oakland county, but if there is fixed formula of how that affects rates, I’ve not seen it. And I wonder how well communities monitor the amount of storm sewage they generate.

The water itself is free. For the most part, in this county, we pump it from the Detroit river. Some of the rest of the water is pumped from wells. None of this costs anything. There is a pump cost, but it is manicure. Pumping 1 gallon of water up 75 feet, costs about 0.002¢ in pumping cost. The rest of the cost is infrastructure: the cost of the pumps, the pipes, the treatment, the billing and sewage. Among the sewage fees is a pollution penalty, and Oakland county pays plenty of pollution penalties. When it rains, we generate more sewage than the system will handle, and we dump the rest into the rivers and lakes. This results in closed beaches and poisoned fish, and fines too. The county pays the EPA when we do this, and the county passes the cost to the cities. I don’t know what the formula for fee distribution is, and don’t even know what it should be. What I do know is that we do this vastly too often.

Another oddity is that we bill on a per gallon basis. For my home, the bill is about 2¢/ gallon — 100 times the pumping cost. Though the city can claim that we are paying for infrastructure, both clean water infrastructure and sewage infrastructure, it seems odd to bill on a per-gallon used basis, and 1000 times the true per-gallon price. Since most of the price of water is the infrastructure and management cost, it seems like a regressive tax to charge people on the basis of per-gallon used. I also find it odd that cities do a propaganda campaign to tell folks to use less water. Why? I’d much prefer to charge a far lower base charge, and then bill significantly per-gallon. As with much that is socialist, the current system is inefficient, but pleasant for the management.

August 21, 20019, Robert Buxbaum

The electoral college favors small, big, and swing states, punishes Alabama and Massachusetts.

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As of this month, the District of Columbia has joined 15 states in a pact to would end the electoral college choice of president. These 15 include New York, California, and a growing list of solid-blue (Democratic party) states. They claim the electoral must go as it robed them of the presidency perhaps five times: 2016, 2000, 1888, 1876, and perhaps 1824. They would like to replace the electoral college by plurality of popular vote, as in Mexico and much of South America.

All the big blue states and some small blue states have joined a compact to end the electoral college. As of 2019, they are 70% of the way to achieving this.

As it happens, I had to speak on this topic in High School in New York. I for the merits of the old system beyond the obvious: that it’s historical and works. One merit I found, somewhat historical, is that It was part of a great compromise that allowed the US to form. Smaller states would not have joined the union without it, fearing that the federal government would ignore or plunder them without it. Remove the vote advantage that the electoral college provides them, and the small states might have the right to leave. Federal abuse of the rural provinces is seen, in my opinion in Canada, where the large liberal provinces of Ontario and Quebec plunder and ignore the prairie provinces of oil and mineral wealth.

Several of the founding federalists (Jay, Hamilton, Washington, Madison) noted that this sort of federal republic election might bind “the people” to the president more tightly than a plurality election. The voter, it was noted, might never meet the president nor visit Washington, nor even know all the issues, but he could was represented by an elector who he trusted, he would have more faith in the result. Locals would certainly know who the elector favored, but they would accept a change if he could justify it because of some new information or circumstance, if a candidate died, for example, or if the country was otherwise deadlocked, as in 1800 or 1824.

Historically speaking, most electors vote their states and with their previously stated (or sworn) declaration, but sometimes they switch. In, 2016 ten electors switched from their state’s choice. Sven were Democrats who voted against Hillary Clinton, and three were Republicans. Electors who do this are called either “faithless electors” or “Hamilton electors,” depending on whether they voted for you or against you. Hamilton had argued for electors who would “vote their conscience” in Federalist Paper No. 68.  One might say these electors threw away their shot, as Hamilton did not. Still, they showed that elector voting is not just symbolic.

Federalist theory aside, it seems to me that the current system empowers both large and small states inordinately, and swing states, while disempowering Alabama and Massachussetts. Change the system and might change the outcome in unexpected ways.

That the current system favors Rhode Island is obvious. RI has barely enough population for 1 congressman, and gets three electors. Alabama, with 7 congressmen, gets 9 electors. Rhode Islanders thus get 2.4 times the vote power of Alabamans.

It’s less obvious that Alabama and Massachussetts are disfavored compared to New Yorkers and Californians. But Alabama is solid red, while New York and California are only sort of blue. They are majority Democrat, with enough Republicans to have had Republican governors occasionally in recent history. Because the electoral college awards all of New York’s votes to the winner, a small number Democrat advantage controls many electors.

In 2016, of those who voted for major party candidates in New York, 53% voted for the Democrat, and 47% Republican. This slight difference, 6%, swung all of NY’s 27 electors to Ms Clinton. If a popular vote are to replace the electoral college, New York would only have the net effect of the 6% difference; that’s about 1 million net votes. By contrast, Alabama is about 1/3 the population of New York, but 75% Republican. Currently its impact is only 1/3 of New York’s despite having a net of 2.5 million more R voters. Without the college, Alabama would have 2.5 times the impact of NY. This impact might be balanced by Massachusetts, but at the very least candidates would campaign in these states– states that are currently ignored. Given how red and blue these states are, it is quite possible that the Republican will be more conservative than current, and the Democrat more liberal, and third party candidates would have a field day as is common in Mexico and South America.

Proposed division of California into three states, all Democrat-leaning. Supposedly this will increase the voting power of the state by providing 4 more electors and 4 more senators.

California has petitioned for a different change to the electoral system — one that should empower the Democrats and Californians, or so the theory goes. On the ballot in 2016 was bill that would divide California into three sub-states. Between them, California would have six senators and four more electors. The proposer of the bill claims that he engineered the division, shown at right, so skillful that all three parts would stay Democrat controlled. Some people are worried, though. California is not totally blue. Once you split the state, there is more than three times the chance that one sub-state will go red. If so, the state’s effect would be reduced by 2/3 in a close election. At the last moment of 2016 the resolution was removed from the ballot.

Turning now to voter turnout, it seems to me that a change in the electoral college would change this as well. Currently, about half of all voters stay home, perhaps because their state’s effect on the presidential choice is fore-ordained. Also, a lot of fringe candidates don’t try as they don’t see themselves winning 50+% of the electoral college. If you change how we elect the president we are sure find a new assortment of voters and a much wider assortment of candidates at the final gate, as in Mexico. Democrats seem to believe that more Democrats will show up, and that they’ll vote mainstream D, but I suspect otherwise. I can not even claim the alternatives will be more fair.

In terms of fairness, Marie de Condorcet showed that the plurality system will not be fair if there are more than two candidates. It will be more interesting though. If changes to the electoral college system comes up in your state, be sure to tell your congressperson what you think.

Robert Buxbaum, July 22, 2019.

Bitcoin v cash to avoid Trump’s tariffs or ransom a sailor

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The number and cash value of bitcoin transactions has surged in the last two years, and it seems that a lot of the driving motivation is avoidance of Trump’s tariffs. If you want to avoid Trump’s tariffs, claim that the value of the shipment is less than it really is. Pay part via the normal banking system through the bill of lading (and pay tariffs on that) and pay the rest in bitcoin with no record and no taxes paid. The average bitcoin transaction amount has increased to $33,504, and that seems to be the amount of taxable value being dodged on each shipment. As pointed outAs noted in Cryptopolitan, “smugglers attempting to export Chinese goods to the USA illegally have been found to be among the largest purchasers of Bitcoin.” https://www.cryptopolitan.com/is-us-china-trade-war-fueling-bitcoin-price-rally-to-7500/

Average transaction amount for several crypto currencies. The amount has surged for Bitcoin, blue line.

Bitcoin isn’t the only beneficiary, of course, but it is the largest. The chart at right shows the average transaction value of the major cryptocurrencies. The average for most are in the dollar range that you’d expect for someone evading tariffs in containerized shipments. Someone who wants to import $100,000 worth of Chinese printers will arrange to have them shipped with a lower price bill of lading. The rest of the payment, 1/3 say, would be paid by a bitcoin transfer whose escrow is tied to the legally binding bill of lading.

Number of transactions per day for several cryptocurrencies, data available from Bitinfocharts.com

Bitcoin does not stand out from the other cryptocurrencies so much in the amount of its average transaction, but in the number of transactions per day. As shown at left there are 333,050 bitcoin transactions per day at an average value of $33,504 per transaction. Multiplying these numbers together, we see that Bitcoin is used for some $11.2 billion in transactions per day, or $4.1 trillion dollars worth per year. The legitimate part of the US economy is only $58 billion per day, or $21 trillion per year. The amount will certainly rise if further tariffs are put into effect. 

Most other cryptocurrencies have fewer transactions per day, and the few that have similar (or higher) numbers deal in lower amounts. Etherium is used in 2.5 time more transactions, but the average Etherium transaction is only $679. This suggests that the total Etherium business is only $586 million per day. The dollar amounts of Etherium suggests that it is mostly used for drug trafficking, 

Cash-money is the old fashioned way to avoid tariffs, buy drugs, and do other illegal money transfers. This method isn’t going away any time soon. A suitcase of $100 bills gets handed over and the deal is done. Though it gets annoying as the amounts get large, there is a certain convenience at the other end, when you try to spend your ill-gotten gains. Thus, when Obama wanted to ransom the ten sailors that Iran had captured in 2016, he sent paper bills. According to the LA Times, this was three airplane shipments s of all non-US currency: Euros and Swiss Francs mostly. The first payment was $400 million, delivered as soon as Iran agreed to the release. The rest, $1.3 billion, was sent after the prisoners were released. Assuming that the bundles shown below contained only 100 Euro notes, each bundle would have held about $170 million dollars. We’d have had to send ten bundles of this size to redeem ten US sailors. The US ships, the laptops of sensitive information, and the weapons were granted as gifts to the Iranians. Obama claimed that all this was smart as it was cheaper than a war, and it likely is. The British had 15 sailors captured by Iran in 2009 and paid as well. In the late 1700s, John Adams (an awful president) paid 1/4 of the US budget as ransom to North African pirates. He paid in gold.

These are supposedly the pallets of cash used to ransom our sailors. Obama has justified the need to transfer the cash this way, and indeed a ransom is a lot cheaper than a war.

Obama could have ransomed the sailors with Bitcoin as there was hardly enough Bitcoin in existence, and the Iranians would have had a hard time spending it. In general, it is hard to spend Bitcoin on anything legal. Legitimate sellers want proof that they’ve paid. As a result, a buyer generally has to exchange bitcoin for bank checks — and the financial watchdogs are always sniffing at this step. Things are simpler with paper money, but not totally simple when there is no apparent source.

Iranian released this picture of the US sailors captured. Obama ransomed them for $1.7 billion in Euros.

To get a sense of the amount of paper money used this way, consider that there are $1.1 trillion in hundred dollar bills in circulation. This is four times more money’s worth than the value of all Bitcoin in circulation. Based on the wear on our $100 bills, it seems each bill is used on average 30 times per year. This suggest there are $33 trillion dollars in trade that goes on with $100 bills. Not all of this trade is illegal, but I suspect a good fraction is, and this is eight times the trade in Bitcoin. The cost of transferring cash can be high, but it’s easy to make change for a bundle of $100 bills. There is fee charged to convert Bitcoin to cash; it’s often in excess of 1%, and that adds up when you do billion-dollar kidnappings and billion dollar arms buys. In case you are wondering how German uranium enrichment centrifuges got to Iran when there is an export embargo, I’m guessing it was done through an intermediary country via cash or Bitcoin transactions.

It’s worth speculating on whether Bitcoin prices will rise as its use continues to rise. I think it will but don’t expect a fast rise. Over a year ago, I’d predicted that the price of Bitcoin would be about $10,500 each. I’d based that on Fisher’s monetary equation, that relates the value of a currency to the amount spent and the speed of money. As it happens I got the right dollar value because I’d underestimated the amount of Bitcoin purchases and the speed of the money by the same factor of four. For the price of a Bitcoin to rise, it is not enough for it to be used more. There also has to be no parallel rise in the velocity of transactions (turnovers per year). My sense is that both numbers will rise together and thus that the bitcoin price will level out, long term, with lots of volatility following daily changes in use and velocity.

As a political thought, I expect is that Bitcoin traders will mostly support Trump. My expectation here is for the classic alliance of bootleggers and prohibition police during prohibition. The police salaries and bonuses depended on liquor being illegal, and bootleggers knew that their high prices and profits depended on the same thing. I thus expect Bitcoin dealers will support Trump as a way of protecting Bitcoin profits and value. Amazon’s owner, Jeff Bezos is strongly anti-Trump, I suspect, because Amazon profits from no-tariff imports.

Robert Buxbaum,  July 10, 2019. Here are my thoughts about tariffs and free trade, and here is Satochi’s original article proposing Bitcoin and explaining how it would work. As for Iran, they’ve announced a fee for any ship in the Gulf of Hormuz. If you don’t pay, you might get attacked as a Japanese tanker recently was. My guess is payments are made in cash or Bitcoin to avoid embarrassing the payer.

How to avoid wet basements

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My house is surrounded my mulch — it absorbs enough rainwater that I rarely have to water.

Generally speaking water gets to your basement from rain, and the basic way you avoid wet basements is by providing some more attractive spot for the rainwater to go to. There are two main options here: divert the water to a lake or mulch-filled spot at least 8 feet away from your home, or divert it to a well-operated street or storm drain. My personal preference is a combination of both.

At right I show a picture of my home taken on a particularly nice day in the spring. Out front is a mulch-filled garden and some grass. On the side, not shown is a driveway. Most of the rain that hits our lawn and gardens is retained in 4 inches of mulch, and waters the plants. Four inches of mulch-covered ground will hold at least four inches of rainwater. Most of the rain that hits the house is diverted to downspouts and flows down the driveway to the street. Keeping some rainwater in the mulch means you don’t have to pay so much to water the trees and shrubs. The tree at the center here is an apple tree. I like fruit trees like this, they really suck up water, and I like the apples. We also have blueberries and roses, and a decorative pear (I like pears too, but they are messy).

In my opinion, you want some slope even in the lawn area, so excess rainwater will run to the sewers and not form a yard-lake, but that’s a professional preferences; it’s not always practical and some prefer a brief (vernal ) lake. A vernal lake is one that forms only in the spring. If you’ve got one, you may want to fill it with mulch or add trees that are more water tolerant than the apple, e.g. swamp oak or red cedar. Trees remove excess water via transpiration (enhanced evaporation). Red Cedars grow “knees” allowing them to survive with their roots completely submerged.

For many homes, the trick to avoiding a flooded basement is to get the water away from your home and to the street or a retention area.

When it comes to rain that falls on your hose, one option is to send it to a vernal lake, the other option is to sent it to the street. If neither is working, and you find water in your basement, your first step is to try to figure out where your rainwater goes and how it got there. Follow the water when it’s raining or right after and see where it goes. Very often, you’ll discover that your downspouts or your driveway drain into unfortunate spots: spots that drain to your basement. To the extent possible, don’t let downspout water congregate in a porous spot near your house. One simple correction is to add extenders on the downspouts so that the water goes further away, and not right next to your wall. At left, I show a simple, cheap extender. It’s for sale in most hardware stores. Plastic or concrete downspout pans work too, and provide a good, first line of defense agains a flood basement. I use several to get water draining down my driveway and away from the house.

Sometimes, despite your best efforts, your driveway or patio slopes to your house. If this is the case, and if you are not quite ready to replace your driveway or patio, you might want to calk around your house where it meets the driveway or patio. If the slope isn’t too great, this will keep rainwater out for a while — perhaps long enough for it to dry off, or for most of the rainwater to go elsewhere. When my driveway was put in, I made sure that it sloped away from the house, but then the ground settled, and now it doesn’t quite. I’ve put in caulk and a dirt-dam at the edge of the house. It keeps the water out long enough that it (mostly) drains to the street or evaporates.

A drain valve. Use this to keep other people’s sewer water out of your basement.

There is one more source of wet basement water, one that hits the houses in my area once a year or so. In our area of Oakland county, Michigan, we have combined storm and sanitary sewers. Every so often, after a big rain, other people’s rainwater and sanitary sewage will come up through the basement drains. This is really a 3rd world sewer system, but we have it this way because when it was put in, in the 1900s, it was first world. One option if you have this is to put in a one-way drain valve. There are various options, and I suggest a relatively cheap one. The one shown at right costs about $15 at Ace hardware. It will keep out enough water, long enough to protect the important things in your home. The other option, cheaper and far more hill-billy, is to stuff rags over your basement drains, and put a brick over the rags. I’ll let you guess what I have in my basement.

Robert Buxbaum, June 13, 2019

How tall could you make a skyscraper?

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Built in 1931, the highest usable floor space of the Empire State building is 1250 feet (381m) above the ground. In 1973, that record was beaten by the World Trade Center building 1, 1,368 feet (417 m, building 2 was eight feet shorter). The Willis Tower followed 1974, and by 2004, the tallest building was the Taipei Tower, 1471 feet. Building heights had grown by 221 feet since 1931, and then the Burj Khalifa in Dubai, 2,426 ft ( 739.44m):. This is over 1000 feet taller than the new freedom tower, and nearly as much taller than the previous record holder. With the Saudi’s beginning work on a building even taller, it’s worthwhile asking how tall you could go, if your only  limitations were ego and materials’ strength.

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

Having written about how long you could make a (steel) suspension bridge, the maximum height of a skyscraper seems like a logical next step. At first glance this would seem like a ridiculously easy calculation based on the math used to calculate the maximum length of a suspension bridge. As with the bridge, we’d make the structure from the strongest normal material: T1, low carbon, vanadium steel, and we’d determine the height by balancing this material’s  yield strength, 100,000 psi (pounds per square inch), against its density, .2833 pounds per cubic inch.

If you balance these numbers, you calculate a height: 353,000 inches, 5.57 miles, but this is the maximum only for a certain structure, a wide flag-pole of T1 steel in the absent of wind. A more realistic height assumes a building where half the volume is empty space, used for living and otherwise, where 40% of the interior space contains vertical columns of T1 steel, and where there’s a significant amount of dead-weight from floors, windows, people, furniture, etc. Assume the dead weight is the equivalent of filling 10% of the volume with T1 steel that provides no structural support. The resulting building has an average density = (1/2 x 0.2833 pound/in3), and the average strength= (0.4 x 100,000 pound/in2). Dividing these numbers we get a maximum height, but only for a cylindrical building with no safety margin, and no allowance for wind.

H’max-cylinder = 0.4 x 100,000 pound/in2/ (.5 x 0.2833 pound/in3) = 282,400 inches = 23,532 ft = 4.46 miles.

This is more than ten times the Burj Khalifa, but it likely underestimates the maximum for a steel building, or even a concrete building because a cylinder is not the optimum shape for maximum height. If the towers were constructed conical or pyramidal, the height could be much greater: three times greater because the volume of a cone and thus its weight is 1/3 that of a cylinder for the same base and height. Using the same materials and assumptions,

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

H’max-cone = 3 H’max-cylinder =  13.37 miles.

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 we’ll see, is something like the Eiffel tower.

Before speaking about this shape, I’d like to speak about building materials. At the heights we’re discussing, it becomes fairly ridiculous to talk about a steel and glass building. Tall steel buildings have serious vibration problems. Even at heights far before they are destroyed by wind and vibration , the people at the top will begin to feel quite sea-sick. Because of this, the tallest buildings have been constructed out of concrete and glass. Concrete is not practical for bridges since concrete is poor in tension, but concrete can be quite strong in compression, as I discussed here.  And concrete is fire resistant, sound-deadening, and vibration dampening. It is also far cheaper than steel when you consider the ease of construction. The Trump Tower in New York and Chicago was the first major building here to be made this way. It, and it’s brother building in Chicago were considered aesthetic marvels until Trump became president. Since then, everything he’s done is ridiculed. Like the Trump tower, the Burj Khalifa is concrete and glass, and I’ll assume this construction from here on.

let’s choose to build out of high-silica, low aggregate, UHPC-3, the strongest concrete in normal construction use. It has a compressive strength of 135 MPa (about 19,500 psi). and a density of 2400 kg/m3 or about 0.0866 lb/in3. Its cost is around $600/m3 today (2019); this is about 4 times the cost of normal highway concrete, but it provides about 8 times the compressive strength. As with the steel building above, I will assume that, at every floor, half of the volume is living space; that 40% is support structure, UHPC-3, and that the other 10% is other dead weight, plumbing, glass, stairs, furniture, and people. Calculating in SI units,

H’max-cylinder-concrete = .4 x 135,000,000 Pa/(.5 x 2400 kg/m3 x 9.8 m/s2) = 4591 m = 2.85 miles.

The factor 9.8 m/s2 is necessary when using SI units to account for the acceleration of gravity; it converts convert kg-weights to Newtons. Pascals, by the way, are Newtons divided by square meters, as in this joke. We get the same answer with less difficulty using inches.

H’max-cylinder-concrete = .4 x 19,500 psi/(.5 x.0866  lb/in3) = 180,138″ = 15,012 ft = 2.84 miles

These maximum heights are not as great as for a steel construction, but there are a few advantages; the price per square foot is generally less. Also, you have fewer problems with noise, sway, and fire: all very important for a large building. The maximum height for a conical concrete building is three times that of a cylindrical building of the same design:

H’max–cone-concrete = 3 x H’max-cylinder-concrete = 3 x 2.84 miles = 8.53 miles.

Mount Everest, picture from the Encyclopedia Britannica, a stone cone, 5.5 miles high.

That this is a reasonable number can be seen from the height of Mount Everest. Everest is rough cone , 5.498 miles high. This is not much less than what we calculate above. To reach this height with a building that withstands winds, you have to make the base quite wide, as with Everest. In the absence of wind the base of the cone could be much narrower, but the maximum height would be the same, 8.53 miles, but a cone is not the optimal shape for a very tall building.

I will now calculate the optimal shape for a tall building in the absence of wind. I will start at the top, but I will aim for high rent space. I thus choose to make the top section 31 feet on a side, 1,000 ft2, or 100 m2. As before, I’ll make 50% of this area living space. Thus, each apartment provides 500 ft2 of living space. My reason for choosing this size is the sense that this is the smallest apartment you could sell for a high premium price. Assuming no wind, I can make this part of the building a rectangular cylinder, 2.84 miles tall, but this is just the upper tower. Below this, the building must widen at every floor to withstand the weight of the tower and the floors above. The necessary area increases for every increase in height as follows:

dA/dΗ = 1/σ dW/dH.

Here, A is the cross-sectional area of the building (square inches), H is height (inches), σ is the strength of the building material per area of building (0.4 x 19,500 as above), and dW/dH is the weight of building per inch of height. dW/dH equals  A x (.5 x.0866  lb/in3), and

dA/dΗ = 1/ ( .4 x 19,500 psi) x A x (.5 x.0866  lb/in3).

dA/A = 5.55 x 10-6 dH,

∫dA/A = ∫5.55 x 10-6 dH,

ln (Abase/Atop) = 5.55 x 10-6 ∆H,

Here, (Abase/Atop) = Abase sq feet /1000, and ∆H is the height of the curvy part of the tower, the part between the ground and the 2.84 mile-tall, rectangular tower at the top.

Since there is no real limit to how big the base can be, there is hardly a limit to how tall the tower can be. Still, aesthetics place a limit, even in the absence of wind. It can be shown from the last equation above that stability requires that the area of the curved part of the tower has to double for every 1.98 miles of height: 1.98 miles = ln(2) /5.55 x 10-6 inches, but the rate of area expansion also keeps getting bigger as the tower gets heavier.  I’m going to speculate that, because of artistic ego, no builder will want a tower that slants more than 45° at the ground level (the Eiffel tower slants at 51°). For the building above, it can be shown that this occurs when:

dA/dH = 4√Abase.  But since

dA/dH = A 5.55 x 10-6 , we find that, at the base,

5.55 x 10-6 √Abase = 4.

At the base, the length of a building side is Lbase = √Abase=  4 /5.55 x 10-6 inches = 60060 ft = 11.4  miles. Artistic ego thus limits the area of the building to slightly over 11 miles wide of 129.4 square miles. This is about the area of Detroit. From the above, we calculate the additional height of the tower as

∆H = ln (Abase/Atop)/ 5.55 x 10-6 inches =  15.1/ 5.55 x 10-6 inches = 2,720,400 inches = 226,700 feet = 42.94 miles.

Hmax-concrete =  2.84 miles + ∆H = 45.78 miles. This is eight times the height of Everest, and while air pressure is pretty low at this altitude, it’s not so low that wind could be ignored. One of these days, I plan to show how you redo this calculation without the need for calculus, but with the inclusion of wind. I did the former here, for a bridge, and treated wind here. Anyone wishing to do this calculation for a basic maximum wind speed (100 mph?) will get a mention here.

From the above, it’s clear that our present buildings are nowhere near the maximum achievable, even for construction with normal materials. We should be able to make buildings several times the height of Everest. Such Buildings are worthy of Nimrod (Gen 10:10, etc.) for several reasons. Not only because of the lack of a safety factor, but because the height far exceeds that of the highest mountain. Also, as with Nimrod’s construction, there is a likely social problem. Let’s assume that floors are 16.5 feet apart (1 rod). The first 1.98 miles of tower will have 634 floors with each being about the size of Detroit. Lets then assume the population per floor will be about 1 million; the population of Detroit was about 2 million in 1950 (it’s 0.65 million today, a result of bad government). At this density, the first 1.98 miles will have a population of 634 million, about double that of the United States, and the rest of the tower will have the same population because the tower area contracts by half every 1.98 miles, and 1/2 + 1/4 + 1/8 + 1/16 … = 1.

Nimrod examining the tower, Peter Breugel

We thus expect the tower to hold 1.28 Billion people. With a population this size, the tower will develop different cultures, and will begin to speak different languages. They may well go to war too — a real problem in a confined space. I assume there is a moral in there somewhere, like that too much unity is not good. For what it’s worth, I even doubt the sanity of having a single government for 1.28 billion, even when spread out (e.g. China).

Robert Buxbaum, June 3, 2019.

Vitamin A and E, killer supplements; B, C, and D are meh.

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It’s often assumed that vitamins and minerals are good for you, so good for you that people buy all sorts of supplements providing more than the normal does in hopes of curing disease. Extra doses are a mistake unless you really have a mis-balanced diet. I know of no material that is good in small does that is not toxic in large doses. This has been shown to be so for water, exercise, weight loss, and it’s true for vitamins, too. That’s why there is an RDA (a Recommended Daily Allowance). 

Lets begin with Vitamin A. That’s beta carotene and its relatives, a vitamin found in green and orange fruits and vegetables. In small doses it’s good. It prevents night blindness, and is an anti-oxidant. It was hoped that Vitamin A would turn out to cure cancer too. It didn’t. In fact, it seems to make cancer worse. A study was preformed with 1029 men and women chosen random from a pool that was considered high risk for cancer: smokers, former smokers, and people exposed to asbestos. They were given either15 mg of beta carotene and 25,000 IU of vitamin A (5 times the RDA) or a placebo. Those taking the placebo did better than those taking the vitamin A. The results were presented in the New England Journal of Medicine, read it here, with some key findings summarized in the graph below.

Comparison of cumulative mortality and cardiovascular disease between those receiving Vitamin A (5 times RDA) and those receiving a placebo. From Omenn et. al, Clearly, this much vitamin A does more harm than good.

The main causes of death were, as typical, cardiovascular disease and cancer. As the graph shows, the rates of death were higher among people getting the Vitamin A than among those getting nothing, the placebo. Why that is so is not totally clear, but I have a theory that I presented in a paper at Michigan state. The theory is that your body uses oxidation to fight cancer. The theory might be right, or wrong, but what is always noticed is that too much of a good thing is never a good thing. The excess deaths from vitamin A were so significant that the study had to be cancelled after 5 1/2 years. There was no responsible way to continue. 

Vitamin E is another popular vitamin, an anti-oxidant, proposed to cure cancer. As with the vitamin A study, a large number of people who were at high risk  were selected and given either a large dose  of vitamin or a placebo. In this case, 35,000 men over 50 years old were given either vitamin E (400 to 660 IU, about 20 times the RDA) and/or selenium or a placebo. Selenium was added to the test because, while it isn’t an antioxidant, it is associated with elevated levels of an anti-oxidant enzyme. The hope was that these supplements would prevent cancer and perhaps ward off Alzheimer’s too. The full results are presented here, and the key data is summarized in the figure below. As with vitamin A, it turns out that high doses of vitamin E did more harm than good. It dramatically increased the rate of cancer and promoted some other problems too, including diabetes.  This study had to be cut short, to only 7 years, because  of the health damage observed. The long term effects were tracked for another two years; the negative effects are seen to level out, but there is still significant excess mortality among the vitamin takers. 

Cumulative incidence of prostate cancer with supplements of selenium and/or vitamin E compared to placebo.

Cumulative incidence of prostate cancer with supplements of selenium and/or vitamin E compared to placebo.

Selenium did not show any harmful or particularly beneficial effects in these tests, by the way, and it may have reduced the deadliness of the Vitamin A.. 

My theory, that the body fights cancer and other disease by oxidation, by rusting it away, would explain why too much antioxidant will kill you. It laves you defenseless against disease As for why selenium didn’t cause excess deaths, perhaps there are other mechanisms in play when the body sees excess selenium when already pumped with other anti oxidant. We studied antioxidant health foods (on rats) at Michigan State and found the same negative effects. The above studies are among the few done with humans. Meanwhile, as I’ve noted, small doses of radiation seem to do some good, as do small doses of chocolate, alcohol, and caffeine. The key words here are “small doses.” Alcoholics do die young. Exercise helps too, but only in moderation, and since bicycle helmets discourage bicycling, the net result of bicycle helmet laws may be to decrease life-span. 

What about vitamins B, C, and D? In normal doses, they’re OK, but as with vitamin A and E you start to see medical problems as soon as you start taking more– about  12 times the RDA. Large does of vitamin B are sometimes recommended by ‘health experts’ for headaches and sleeplessness. Instead they are known to produce skin problems, headaches and memory problems; fatigue, numbness, bowel problems, sensitivity to light, and in yet-larger doses, twitching nerves. That’s not as bad as cancer, but it’s enough that you might want to take something else for headaches and sleeplessness. Large does of Vitamin C and D are not known to provide any health benefits, but result in depression, stomach problems, bowel problems, frequent urination, and kidney stones. Vitamin C degrades to uric acid and oxalic acid, key components of kidney stones. Vitamin D produces kidney stones too, in this case by increasing calcium uptake and excretion. A recent report on vitamin D from the Mayo clinic is titled: Vitamin D, not as toxic as first thought. (see it here). The danger level is 12 times of the RDA, but many pills contain that much, or more. And some put the mega does in a form, like gummy vitamins” that is just asking to be abused by a child. The pills positively scream, “Take too many of me and be super healthy.”

It strikes me that the stomach, bowel, and skin problems that result from excess vitamins are just the problems that supplement sellers claim to cure: headaches, tiredness, problems of the nerves, stomach, and skin.  I’d suggest not taking vitamins in excess of the RDA — especially if you have skin, stomach or nerve problems. For stomach problems; try some peniiiain cheese. If you have a headache, try an aspirin or an advil. 

In case you should want to know what I do for myself, every other day or so, I take 1/2 of a multivitamin, a “One-A-Day Men’s Health Formula.” This 1/2 pill provides 35% of the RDA of Vitamin A, 37% of the RDA of Vitamin E, and 78% of the RDA of selenium, etc. I figure these are good amounts and that I’ll get the rest of my vitamins and minerals from food. I don’t take any other herbs, oils, or spices, either, but do take a baby aspirin daily for my heart. 

Robert Buxbaum, May 23, 2019. I was responsible for the statistics on several health studies while at MichiganState University (the test subjects were rats), and I did work on nerves, and on hydrogen in metals, and nuclear stuff.  I’ve written about statistics too, like here, talking about abnormal distributions. They’re common in health studies. If you don’t do this analysis, it will mess up the validity of your ANOVA tests. That said,  here’s how you do an anova test.