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.

Why concrete cracks and why sealing is worthwhile

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The oil tanker Palo Alto is one of several major ships made with concrete hulls.

The oil tanker Palo Alto is one of several major ships made with concrete hulls.

Modern concrete is a wonderful construction material. Major buildings are constructed of it, and major dams, and even some ships. But under the wrong circumstances, concrete has a surprising tendency to crack and fail. I thought I’d explain why that happens and what you can do about it. Concrete does not have to crack easily; ancient concrete didn’t and military or ship concrete doesn’t today. A lot of the fault lies in the use of cheap concrete — concrete with lots of filler — and with the cheap way that concrete is laid. First off, the major components of modern concrete are pretty uniform: sand and rock, Portland cement powder (made from cooked limestone, mostly), water, air, and sometimes ash. The cement component is what holds it all together — cements it together as it were — but it is not the majority of even the strongest concretes. The formula of cement has changed too, but the cement is not generally the problem. It doesn’t necessarily stick well to the rock or sand component of concrete (It sticks far better to itself) but it sticks well enough that spoliation, isn’t usually a problem by itself.

What causes problem is that the strength of concrete is strongly affected (decreased) by having lots of sand, aggregate and water. The concrete used in sidewalks is as cheap as possible, with lots of sand and aggregate. Highway and wall concrete has less sand and aggregate, and is stronger. Military and ship concrete has little sand, and is quite a lot stronger. The lowest grade, used in sidewalks, is M5, a term that refers to its compressive strength: 5 Mega Pascals. Pascals are European (Standard International) units of pressure and of strength. One Pascal is one Newton per square meter (Here’ a joke about Pascal units). In US (English) units, 5 MPa is 50 atm or 750 psi.

Ratios for concrete mixes of different strength.

Ratios for concrete mixes of different strength; the numbers I use are double these because these numbers don’t include water; that’s my “1”.

The ratio of dry ingredients in various concretes is shown at right. For M5, and including water, the ratio is 1 2 10 20. That is to say there is one part water, two parts cement, 10 parts sand, and 20 parts stone-aggregate (all these by weight). Added to this is 2-3% air, by volume, or nearly as much air as water. At least these are the target ratios; it sometimes happens that extra air and water are added to a concrete mix by greedy or rushed contractors. It’s sometimes done to save money, but more often because the job ran late. The more the mixer turns the more air gets added. If it turns too long there is extra air. It the job runs late, workers will have to add extra water too because the concrete starts hardening. I you see workers hosing down wet concrete as it comes from the truck, this is why. As you might expect, extra air and water decrease the strength of the product. M-10 and M-20 concrete have less sand, stone, and water as a proportion to cement. The result is 10 MPa or 20 MPa strength respectively.

A good on-site inspector is needed to keep the crew from adding too much water. Some water is needed for the polymerization (setting) of the concrete. The rest is excess, and when it evaporates, it leaves voids that are similar to the voids created by having air mix in. It is not uncommon to find 6% voids, in commercial concrete. This is to say that, after the water evaporates, the concrete contains about as much void as cement by volume. To get a sense of how much void space is in the normal concrete outside your house, go outside to a piece of old concrete (10 years old at least) on a hot, dry day, and pour out a cup of water. You will hear a hiss as the water absorbs, and you will see bubbles come out as the water goes in. It used to be common for cities to send inspectors to measuring the void content of the wet (and dry) concrete by a technique called “pycnometry” (that’s Greek for density measurement). I’ve not seen a local city do this in years, but don’t know why. An industrial pycnometer is shown below.

Pyncnometer used for concrete. I don't see these in use much any more.

Pycnometer used for concrete. I don’t see these in use much any more.

One of the main reason that concrete fails has to do with differential expansion, thermal stress, a concept I dealt with some years ago when figuring out how cold it had to be to freeze the balls off of a brass monkey. As an example of the temperature change to destroy M5, consider that the thermal expansion of cement is roughly 1 x 10-5/ °F or 1.8 x10-5/°C. This is to say that a 1 meter slab of cement that is heated or cooled by 100°F will expand or shrink by 10-3 m respectively; 100 x 1×10-5 = 10-3. This is a fairly large thermal expansion coefficient, as these things go. It would not cause stress-failure except that sand and rock have a smaller thermal expansion coefficients, about 0.6×10-5 — barely more than half the value for cement. Consider now what happens to concrete that s poured in the summer when it is 80°F out, and where the concrete heats up 100°F on setting (cement setting releases heat). Now lets come back in winter when it’s 0°F. This is a total of 100°F of temperature change. The differential expansion is 0.4 x 10-5/°F x 100°F =  4 x10-4 meter/meter = 4 x10-4 inch/inch.

The force created by this differential expansion is the elastic modulus of the cement times the relative change in expansion. The elastic modulus for typical cement is 20 GPa or, in English units, 3 million psi. This is to say that, if you had a column of cement (not concrete), one psi of force would compress it by 1/3,000,000. The differential expansion we calculated, cement vs sand and stone is 4×10-4 ; this much expansion times the elastic modulus, 3,000,000 = 1200 psi. Now look at the strength of the M-5 cement; it’s only 750 psi. When M-5 concrete is exposed to these conditions it will not survive. M-10 will fail on its own, from the temperature change, without any help needed from heavy traffic. You’d really like to see cities check the concrete, but I’ve seen little evidence that they do.

Water makes things worse, and not only because it creates voids when it evaporates. Water also messes up the polymerization reaction of the cement. Basic, fast setting cement is mostly Ca3SiO5

2Ca3SiO5 + 6 H2O –> 3Ca0SiO2•H2O +3Ca(OH)2•H2O.

The former of these, 3Ca0SiO2•H2O, forms something of a polymer. Monomer units of SiO4 are linked directly or by partially hydrated CaO linkages. Add too much water and the polymeric linkages are weakened or do not form at all. Over time the Ca(OH)2 can drain away or react with  CO2 in the air to form chalk.

concrete strength versus-curing time. Slow curing of damp concrete helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Portland limestone cement strength versus curing time. Slow curing and damp helps; fast dry hurts. Carbonate formation adds little or no strength. Jehan Elsamni 2011.

Ca(OH)2 + CO2 → CaCO3 + H2O

Sorry to say, the chalk adds little or no strength, as the graph at right shows. Concrete made with too much water isn’t very strong at all, and it gets no stronger when dried in air. Hardening goes on for some weeks after pouring, and this is the reason you don’t drive on 1 too 2 day old concrete. Driving on weak concrete can cause cracks that would not form if you waited.

You might think to make better concrete by pouring concrete in the cold, but pouring in the cold makes things worse. Cold poured cement will expand the summer and the cement will detach from the sand and stone. Ideally, pouring should be in spring or fall, when the temperature is moderate, 40-60°F. Any crack that develops grows by a mechanism called Rayleigh crack growth, described here. Basically, once a crack starts, it concentrates the fracture forces, and any wiggling of the concrete makes the crack grow faster.

Based on the above, I’ve come to suspect that putting on a surface coat can (could) help strengthen old concrete, even long after it’s hardened. Mostly this would happen by filling in voids and cracks, but also by extending the polymer chains. I imagine it would be especially helpful to apply the surface coat somewhat watery on a dry day in the summer. In that case, I imagine that Ca3SiO5 and Ca(OH)2 from the surface coat will penetrate and fill the pores of the concrete below — the sales pores that hiss when you pour water on them. I imagine this would fill cracks and voids, and extend existing CaOSiO2•H2O chains. The coat should add strength, and should be attractive as well. At least that was my thought.

I should note that, while Portland cement is mostly Ca3SiO5, there is also a fair amount (25%) of Ca2SiO4. This component reacts with water to form the same calcium-silicate polymer as above, but does so at a slower rate using less water per gram. My hope was that this component would be the main one to diffuse into deep pores of the concrete, reacting there to strengthen the concrete long after surface drying had occurred.

Trump tower: 664', concrete and glass. What grade of concrete would you use?

Trump tower: 664′, concrete and glass. What grade of concrete would you use?

As it happened, I had a chance to test my ideas this summer and also about 3 years ago. The city inspector came by to say the concrete flags outside my house were rough, and thus needed replacing, and that I was to pay or do it myself. Not that I understand the need for smooth concrete, quite, but that’s our fair city. I applied for a building permit to apply a surface coat, and applied it watery. I used “Quickrete” brand concrete patch, and so far it’s sticking OK. Pock-holes in the old concrete have been filled in, and so far surface is smooth. We’ll have to see if my patch lasts 10-20 years like fresh cement. Otherwise, no matter how strong the concrete becomes underneath, the city will be upset, and I’ll have to fix it. I’ve noticed that there is already some crumbling at the sides of flags, something I attribute to the extra water. It’s not a problem yet, but hope this is not the beginning of something worse. If I’m wrong here, and the whole seal-coat flakes off, I’ll be stuck replacing the flags, or continuing to re-coat just to preserve my reputation. But that’s the cost of experimentation. I tried something new, and am blogging about it in the hope that you and I benefit. “Education is what you get when you don’t get what you want.” (It’s one of my wise sayings). At the worst, I’ll have spent 90 lb of patching cement to get an education. And, I’m happy to say that some of the relatively new concrete flags that the city put in are already cracked. I attribute this to: too much sand, air, water or air (they don’t look like they have much rock): Poor oversight.

Dr. Robert E. Buxbaum. March 5, 2019. As an aside, the 664 foot Trump Tower, NY is virtually the only skyscraper in the city to be built of concrete and glass. The others are mostly steel and glass. Concrete and glass is supposed to be stiffer and quieter. The engineer overseeing the project was Barbara Res, the first woman to oversee a major, NY building project. Thought question: if you built the Trump Tower, which quality of concrete would you use, and why.

A probability paradox

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Here is a classic math paradox for your amusement, and perhaps your edification: (edification is a fancy word for: beware, I’m trying to learn you something).

You are on a TV game show where you will be asked to choose between two, identical-looking envelopes. All you know about the envelopes is that one of them has twice as much money as the other. The envelopes are shuffled, and you pick one. You peak in and see that your envelope contains $400, and you feel pretty good. But then you are given a choice: you can switch your envelope with the other one; the one you didn’t take. You reason that the other envelope either has $800 or $200 with equal probability. That is, a switch will either net you a $400 gain, or loose you $200. Since $400 is bigger than $200, you switch. Did that decision make sense. It seems that, at this game, every contestant should switch envelopes. Hmm.

The solution follows: The problem with this analysis is an error common in children and politicians — the confusion between your lack of knowledge of a thing, and actual variability in the system. In this case, the contestant is confusing his (or her) lack of knowledge of whether he/she has the big envelope or the smaller, with the fixed fact that the total between the two envelopes has already been set. It is some known total, in this case it is either $600 or $1200. Lets call this unknown sum y. There is a 50% chance that you now are holding 2/3 y and a 50% chance you are holding only 1/3y. therefore, the value of your current envelope is 1/3 y + 1/6y = 1/2 y. Similarly, the other envelope has a value 1/2y; there is no advantage is switching once it is accepted that the total, y had already been set before you got to choose an envelope.

And here, unfortunately is the lesson:The same issue applies in reverse when it comes to government taxation. If you assume that the total amount of goods produced by the economy is always fixed to some amount, then there is no fundamental problem with high taxes. You can print money, or redistribute it to anyone you think is worthy — more worthy than the person who has it now – and you won’t affect the usable wealth of the society. Some will gain others will lose, and likely you’ll find you have more friends than before. On the other hand, if you assume that government redistribution will affect the total: that there is some relationship between reward and the amount produced, then to the extent that you diminish the relation between work and income, or savings and wealth, you diminish the total output and wealth of your society. While some balance is needed, a redistribution that aims at identical outcomes will result in total poverty.

This is a variant of the “two-envelopes problem,” originally posed in 1912 by German, Jewish mathematician, Edmund Landau. It is described, with related problems, by Prakash Gorroochurn, Classic Problems of Probability. Wiley, 314pp. ISBN: 978-1-118-06325-5. Wikipedia article: Two Envelopes Problem.

Robert Buxbaum, February 27, 2019

Great waves, small circles, and the spread of ideas.

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Simplified wave motion, GIf by Dan Russel (maybe? I think?).

The scientific method involves looking closely at things. Sometimes we look closely for a purpose — to make a better mouse-trap, say. But sometimes it’s just to understand what’s happening: to satisfy curiosity, to understand the way the world works, or to answer a child. Both motivations bring positive results, but there is a difference in how people honor the product of these motivations. Scientific knowledge developed for curiosity is considered better; it tends to become the model for social understanding, and for art and literature. Meanwhile, science developed for a purpose is considered suspect, and often that suspicion is valid. A surprising amount of our knowledge was developed for war: for the purpose of killing people, destroying things, and occupying lands.

Waves provide a wonderful example of science exploration that was developed mostly for curiosity, and so they have become models of social understanding and culture — far more so than the atom bomb and plague work discussed previously.

Waves appear magical: You poke a pond surface with a stick, and the influence of that poke travels, as if by magic, to all corners of the pond. Apparently the initial poke set off something, and that sets off something else, and we’ve come to use this as a model for cultural ideas. Any major change in music, art, or cultural thought is described as a wave (and not as a disease). The sense of wave is  that a small push occurs, and the impact travels across a continent and across an ocean. The Gifs above and below shows how this happens for the ordinary wave — the one with a peaked top. As shown, the bits of water do not move with the wave. Instead they just circulate in a small circle. The powerful waves that crosses an ocean are composed of many small circles of water rolling in the general direction of the wave. With ideas too, I think, one person can push a second, and that second a third, each acting in his or her own circle, and a powerful transmission of ideas results. Of course, for a big wave, you need a big circle, but maybe not in cases of reflection (reflected waves can add, sometimes very destructively).

simplified wave movement

In the figures I’ve shown, you will notice that the top of the circle always moves in the same direction as the top of the wave. If the wave moves to the right, the circle is clockwise. There are also Rayleigh waves. In these, the top of the wave is not peaked, but broad, with little indents between ripples. For Rayleigh wave the motion is not circular, but elliptical, and the top of the ellipse moves in the opposite direction to that of the wave. These waves go slower than the normal waves, but they are more destructive. Most of the damage of earthquakes is by the late-arriving Rayleigh waves.

If regular waves are related to fast-moving ideas, like rock n roll, Rayleigh waves might be related to slower-traveling, counter-intuitive ideas, paradigm shifts: Religions, chaos, entropy, feminism, or communism. Rayleigh waves are mostly seen in solids, and the destructive power of counter-intuitive ideas is mostly seen in rigid societies.

Then there are also pressure waves, like sound, and wiggle waves (transverse waves). Pressure waves travel the fastest, and work in both solids and liquids. Wiggle waves travel slower (and don’t travel in liquids). Both of these involve no circles at all, but just one bit of material pushing on its neighbor. I think the economy works this way: bouncing springs, for the most part. Life is made up of all of these, and life is good. The alternative to vibration, I should mention, is status. Status is a form of death. There is a certain sort of person who longs for nothing more than an unchanging, no-conflict world: one government and one leadership. Avoid such people.

Robert Buxbaum, February 10, 2019

Why the earth is magnetic with the north pole heading south.

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The magnetic north pole, also known as true north, has begun moving south. It had been moving toward the north pole thought the last century. It moved out of Canadian waters about 15 years ago, heading toward Russia. This year it passed as close to the North pole as it is likely to, and begun heading south (Das Vedanga, old friend). So this might be a good time to ask “why is it moving?” or better yet, “Why does it exist at all?” Sorry to say the Wikipedia page is little help here; what little they say looks very wrong. So I thought I’d do my thing and write an essay.

The motion of the magnetic (true) north pole over the last century; it's nearly at the north pole.

Migration of the magnetic (true) north pole over the last century; it’s at 8°N and just passed the North Pole.

Your first assumption of the cause of the earth’s magnetic field would involve ferromagnetism: the earth’s core is largely iron and nickel, two metals that permanent magnets. Although the earth’s core is very hot, far above the “Curie Temperature” where permanent magnets form, you might imagine that some small degree of magnetizability remains. You’d be sort of right here and sort of wrong; to see why, lets take a diversion into the Curie Temperature (Pierre Curie in this case) before presenting a better explanation.

The reason there is no magnetism above the Curie temperature is similar to the reason that you can’t have a plague outbreak or an atom bomb if R-naught is less than one. Imagine a magnet inside a pot of iron. The surrounding iron will dissipate some of the field because magnets are dipoles and the iron occupies space. Fixed dipole effects dissipate with a distance relation of r-4; induced dipoles with a relation r-6. The iron surrounding the magnet will also be magnetized to an extent that augments the original, but the degree of magnetization decreases with temperature. Above some critical temperature, the surrounding dissipates more than it adds and the effect is that the original magnetic effect will die out if the original magnet is removed. It’s the same way that plagues die out if enough people are immunized, discussed earlier.

The earth rotates, and the earth's surface is negatively charged. There is thus some room for internal currents.

The earth rotates, and the earth’s surface is negatively charged. There is thus some room for internal currents.

It seems that the earth’s magnetic field is electromagnetic; that is, it’s caused by a current of some sort. According to Wikipedia, the magnetic field of the earth is caused by electric currents in the molten iron and nickel of the earth’s core. While there is a likely current within the core, I suspect that the effect is small. Wikipedia provides no mechanism for this current, but the obvious one is based on the negative charge of the earth’s surface. If the charge on the surface is non-uniform, It is possible that the outer part of the earth’s core could become positively charged rather the way a capacitor charges. You’d expect some internal circulation of the liquid the metal of the core, as shown above – it’s similar to the induced flow of tornadoes — and that flow could induce a magnetic field. But internal circulation of the metallic core does not seem to be a likely mechanism of the earth’s field. One problem: the magnitude of the field created this way would be smaller than the one caused by rotation of the negatively charged surface of the earth, and it would be in the opposite direction. Besides, it is not clear that the interior of the planet has any charge at all: The normal expectation is for charge to distribute fairly uniformly on a spherical surface.

The TV series, NOVA presents a yet more unlikely mechanism: That motion of the liquid metal interior against the magnetic field of the earth increases the magnetic field. The motion of a metal in a magnetic field does indeed produce a field, but sorry to say, it’s in the opposing direction, something that should be obvious from conservation of energy.

The true cause of the earth’s magnet field, in my opinion, is the negative charge of the earth and its rotation. There is a near-equal and opposite charge of the atmosphere, and its rotation should produce a near-opposite magnetic field, but there appears to be enough difference to provide for the field we see. The cause for the charge on the planet might be due to solar wind or the ionization of cosmic rays. And I notice that the average speed of parts of the atmosphere exceeds that of the surface —  the jet-stream, but it seems clear to me that the magnetic field is not due to rotation of the jet stream because, if that were the cause, magnetic north would be magnetic south. (When positive charges rotate from west to east, as in the jet stream, the magnetic field created in a North magnetic pole a the North pole. But in fact the North magnetic pole is the South pole of a magnet — that’s why the N-side of compasses are attracted to it, so … the cause must be negative charge rotation. Or so it seems to me.  Supporting this view, I note that the magnet pole sometimes flips, north for south, but this is only following a slow decline in magnetic strength, and it never points toward a spot on the equator. I’m going to speculate that the flip occurs when the net charge reverses, thought it could also come when the speed or charge of the jet stream picks up. I note that the magnetic field of the earth varies through the 24 hour day, below.

The earth's magnetic strength varies regularly through the day.

The earth’s magnetic strength varies regularly through the day.

Although magnetic north is now heading south, I don’t expect it to flip any time soon. The magnetic strength has been decreasing by about 6.3% per century. If it continues at that rate (unlikely) it will be some 1600 years to the flip, and I expect that the decrease will probably slow. It would probably take a massive change in climate to change the charge or speed of the jet stream enough to reverse the magnetic poles. Interestingly though, the frequency of magnetic strength variation is 41,000 years, the same frequency as the changes in the planet’s tilt. And the 41,000 year cycle of changes in the planet’s tilt, as I’ve described, is related to ice ages.

Now for a little math. Assume there are 1 mol of excess electrons on a large sphere of the earth. That’s 96500 Coulombs of electrons, and the effective current caused by the earth’s rotation equals 96500/(24 x3600) = 1.1 Amp = i. The magnetic field strength, H =  i N µ/L where H is magnetizability field in oersteds, N is the number of turns, in this case 1, µ is the magnetizability. The magnetizability of air is 0.0125 meter-oersteds/ per ampere-turn, and that of a system with an iron core is about 200 times more, 2.5 meter-tesla/ampere-turn. L is a characteristic length of the electromagnet, and I’ll say that’s 10,000 km or 107 meters. As a net result, I calculate a magnetic strength of 2.75×10-7 Tesla, or .00275 Gauss. The magnet field of the earth is about 0.3 gauss, suggesting that about 100 mols of excess charge are involved in the earth’s field, assuming that my explanation and my math are correct.

At this point, I should mention that Venus has about 1/100 the magnetic field of the earth despite having a molten metallic core like the earth. It’s rotation time is 243 days. Jupiter, Saturn and Uranus have greater magnetic fields despite having no metallic cores — certainly no molten metallic cores (some theorize a core of solid, metallic hydrogen). The rotation time of all of these is faster than the earth’s.

Robert E. Buxbaum, February 3, 2019. I have two pet peeves here. One is that none of the popular science articles on the earth’s magnetic field bother to show math to back their claims. This is a growing problem in the literature; it robs science of science, and makes it into a political-correctness exercise where you are made to appreciate the political fashion of the writer. The other peeve, related to the above concerns the game it’s thoroughly confusing, and politically ego-driven. The gauss is the cgs unit of magnetic flux density, this unit is called G in Europe but B in the US or England. In the US we like to use the tesla T as an SI – mks units. One tesla equals 104 gauss. The oersted, H is the unit of magnetizing field. The unit is H and not O because the English call this unit the henry because Henry did important work in magnetism.  One ampere-turn per meter is equal to 4π x 10−3 oersted, a number I approximated to 0.125 above. But the above only refers to flux density; what about flux itself? The unit for magnetic flux is the weber, Wb in SI, or the maxwell, Mx in cgs. Of course, magnetic flux is nothing more than the integral of flux density over an area, so why not describe flux in ampere-meters or gauss-acres? It’s because Ampere was French and Gauss was German, I think.

Harvard Eunuchs

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Success is measured in different ways in different cultures. Among US academics, the first mark of success is going to a great college. If you graduate from Eureka college, as Ronald Reagan did, you are pretty-well assumed to be an idiot; if you went to Harvard and Princeton, as John Kennedy did, you’re off on a good start to popular acclaim, even if your entry essay was poor, and you got thrown out of one because of cheating. Graduation from a top college does not guarantee being seen as a success forever, though. You have to continue in the Harvard way: use big words — something that puts-off the less-educated; you have to win awards, write books or articles; have the right politics; work at a high power job and money, meet the right people, exercise regularly, etc. It’s hard work being successful; disposable income is tight, and one rarely has time for kids.

Fertility rates, 1950 and now

Fertility rates compared, world-wide, 1970 vs 2014.

By contrast, in ancient societies, success included food, leisure, land, and general respect. A successful person is seated at the front of the church, and consulted as few academics are. And there is another great measure: children. In traditional societies, children are valued, They are seen as a joy in your youth, and a comfort in your old age. They are you and your wife reborn, with reborn wonder. They are your future, and the defenders of your legacy; ready to take on the world with an outlook of their own, but one that you had a unique chance to mold. In the Bible, children are a sign of blessing, and the opposite is explicitly stated as a punishment for violating God’s commands.

I have come to wonder why rich countries have so few children, and why successful people in rich countries have yet fewer than the average. These people and countries are no worse than others, yet they are common. Harvard produces a surprising number of “Legal Eunuchs” — people with a refined place in society, but no time or children; people who work tirelessly for the pleasure and success of others. Harvard couples marry late, or not at all. If they marry, they usually produce childless households, DINKs — Double Income No Kids.

The same pattern is seen in Europe, UK, Japan, Canada, Russia, and China, as the map above shows. Particularly among the élite, the great works are being created for the deplorables and their children. Could anything be more depressing?

The seven things include that Eunuchs can be trusted, that they love to serve, that they are compassionate, that they are passionate (for excellence) and that they have fewer distractions.

There’s and organization for everything these days. In this case, the seven things you didn’t know include that Eunuchs can be trusted, that they love to serve, that they are compassionate, that they are passionate for excellence, and that they have fewer distractions. This is the opposite of toxic masculinity, but it comes at a cost. 

I think one reason for the growing ranks of Harvard Eunuchs is a dislike of masculinity; masculinity is sort-of toxic,  associated with war, revolution, and selfishness. In the 1800s, only Republicans and Communists had beards; the more-refined gentleman did not. The eunuch qualities listed above, are considered noble, charitable, and selfless. Clearly it helps others if you are selfless, but why do it? I think the answer is self-doubt about ones worthiness to enjoy the fruits of your labor. To get to Harvard takes striving, and that relates to a degree of self-doubt and loathing about your worthiness today.

I graduated from Cooper Union, and went to Princeton for graduate school. It was a magical place, I became machines chairman, then chairman of the Graduate College House Committee. I dealt with a lot of very bright, accomplished people, and a pattern I saw often was self-doubt and loathing. And the most accomplished students were the ones with the most self-loathing. It made them strive to be better; it drove the innovative research and the grant writing. It motivated graduates to try to become professors (only a few would succeed) or judges, or financiers, or politicians. All that takes time, striving, and putting off your wants in the here-and-now, for a reward to the future you that is worthy. It’s a system that produces greatness, but at great personal cost.

So what’s to be done? How do you help yourself, or some other, the bright, educated fellow see that he or she is good enough. Unfortunately, for those in the system, good enough equals bad. I found it helped to say, in my own words, the words or Solomon:”Eat, drink, and enjoy yourself.” “It is not good to be over-wise… Why wear yourself out?” Not that these words changed them, but they did seem to give comfort. I’d suggest the write things that were honest; that people understand, and that they take time for themselves. “May your fountain be blessed, and enjoy the wife of your youth.” (Ps.127:3-4, Ecc.8:15, Pr.5:18…) It suffices to retell old truths and raise a new generation. Only make sure that what you have to say is honest and logical, and trust your own value. As for toxic masculinity, it can have its own charm.

Robert E. Buxbaum, January 29, 2019. I got the title for this article, and the idea, from the phrase, “Legal Eunuchs” in this wonderful book review (2005) by Alan Dershowitz.

Disease, atom bombs, and R-naught

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A key indicator of the speed and likelihood of a major disease outbreak is the number of people that each infected person is likely to infect. This infection number is called R-naught, or Ro; it is shown in the table below for several major plague diseases.

R-naught - communicability for several contagious diseases, CDC.

R-naught – infect-ability for several contagious diseases, CDC.

Of the diseases shown, measles is the most communicable, with an Ro of 12 to 18. In an unvaccinated population, one measles-infected person will infect 12- 18 others: his/her whole family and/ or most of his/her friends. After two weeks or so of incubation, each of the newly infected will infect another 12-18. Traveling this way, measles wiped out swaths of the American Indian population in just a few months. It was one of the major plagues that made America white.

While Measles is virtually gone today, Ebola, SARS, HIV, and Leprosy remain. They are far less communicable, and far less deadly, but there is no vaccine. Because they have a low Ro, outbreaks of these diseases move only slowly through a population with outbreaks that can last for years or decades.

To estimate of the total number of people infected, you can use R-naught and the incubation-transmission time as follows:

Ni = Row/wt

where Ni is the total number of people infected at any time after the initial outbreak, w is the number of weeks since the outbreak began, and wt is the average infection to transmission time in weeks.

For measles, wt is approximately 2 weeks. In the days before vaccine, Ro was about 15, as on the table, and

Ni = 15w/2.

In 2 weeks, there will be 15 measles infected people, in 4 weeks there will be 152, or 225, and in 6 generations, or 12 weeks, you’d expect to have 11.39 million. This is a real plague. The spread of measles would slow somewhat after a few weeks, as the infected more and more run into folks who are already infected or already immune. But even when the measles slowed, it still infected quite a lot faster than HIV, Leprosy, or SARS (SARS is a form of Influenza). Leprosy is particularly slow, having a low R-naught, and an infection-transmission time of about 20 years (10 years without symptoms!).

In America, more or less everyone is vaccinated for measles. Measles vaccine works, even if the benefits are oversold, mainly by reducing the effective value of Ro. The measles vaccine is claimed to be 93% effective, suggesting that only 7% of the people that an infected person meets are not immune. If the original value of Ro is 15, as above, the effect of immunization is to reduce the value Ro in the US today to effectively 15 x 0.07 = 1.05. We can still  have measles outbreaks, but only on a small-scale, with slow-moving outbreaks going through pockets of the less-immunized. The average measles-infected person will infect only one other person, if that. The expectation is that an outbreak will be captured by the CDC before it can do much harm.

Short of a vaccine, the best we can do to stop droplet-spread diseases, like SARS, Leprosy, or Ebola is by way of a face mask. Those are worn in Hong Kong and Singapore, but have yet to become acceptable in the USA. It is a low-tech way to reduce Ro to a value below 1.0, — if R-naught is below 1.0, the disease dies out on its own. With HIV, the main way the spread was stopped was by condoms — the same, low tech solution, applied to sexually transmitted disease.

Image from VCE Physics, https://sites.google.com/site/coyleysvcephysics/home/unit-2/optional-studies/26-how-do-fusion-and-fission-compare-as-viable-nuclear-energy-power-sources/fission-and-fusion---lesson-2/chain-reactions-with-dominoes

Progress of an Atom bomb going off. Image from VCE Physics, visit here

As it happens, the explosion of an atom bomb follows the same path as the spread of disease. One neutron appears out of somewhere, and splits a uranium or plutonium atom. Each atom produces two or three more neutrons, so that we might think that R-naught = 2.5, approximately. For a bomb, Ro is found to be a bit lower because we are only interested in fast-released neutrons, and because some neutrons are lost. For a well-designed bomb, it’s OK to say that Ro is about 2.

The progress of a bomb going off will follow the same math as above:

Nn = Rot/nt

where Nn is the total number of neutrons at any time, t is the average number of nanoseconds since the first neutron hit, and nt is the transmission time — the time it takes between when a neuron is given off and absorbed, in nanoseconds.

Assuming an average neutron speed of 13 million m/s, and an average travel distance for neutrons of about 0.1 m, the time between interactions comes out to about 8 billionths of a second — 8 ns. From this, we find the number of neutrons is:

Nn = 2t/8, where t is time measured in nanoseconds (billionths of a second). Since 1 kg of uranium contains about 2 x 1024 atoms, a well-designed A-bomb that contains 1 kg, should take about 83 generations (283 = 1024). If each generation is 8 ns, as above, the explosion should take about 0.664 milliseconds to consume 100% of the fuel. The fission power of each Uranium atom is about 210 MeV, suggesting that this 1 kg bomb could release 16 billion Kcal, or as much explosive energy as 16 kTons of TNT, about the explosive power of the Nagasaki bomb (There are about 38 x10-24 Kcal/eV).

As with disease, this calculation is a bit misleading about the ease of designing a working atomic bomb. Ro starts to get lower after a significant faction of the atoms are split. The atoms begin to move away from each other, and some of the atoms become immune. Once split, the daughter nuclei continue to absorb neutrons without giving off either neutrons or energy. The net result is that an increased fraction of neutrons that are lost to space, and the explosion dies off long before the full power is released.

Computers are very helpful in the analysis of bombs and plagues, as are smart people. The Manhattan project scientists got it right on the first try. They had only rudimentary computers but lots of smart people. Even so, they seem to have gotten an efficiency of about 15%. The North Koreans, with better computers and fewer smart people took 5 tries to reach this level of competence (analyzed here). They are now in the process of developing germ-warfare — directed plagues. As a warning to them, just as it’s very hard to get things right with A-bombs, it’s very hard to get it right with disease; people might start wearing masks, or drinking bottled water, or the CDC could develop a vaccine. The danger, if you get it wrong is the same as with atom bombs: the US will not take this sort of attack lying down.

Robert Buxbaum, January 18, 2019. One of my favorite authors, Issac Asimov, died of AIDS; a slow-moving plague that he contacted from a transfusion. I benefitted vastly from Isaac Asimov’s science and science fiction, but he wrote on virtually every topic. My aim is essays that are sort-of like his, but more mathematical.

Google+ vs Facebook and Twitter; of virtue and sin

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Google has just announced the end of support for Google+; I’m sorry to see it go. It was supposed to be the better version of Facebook killer. It was, and I suspect that’s why it died. Unlike Facebook, Google+ allowed me to decide which group of friends I would get to see which group of my posts. I thought that was a good thing. I only shared political posts with some folks — those who I thought would not mind; and only shared jokes with other folks; family photos with yet others; religion thoughts with others, and technical thoughts with other folks still.

Google+ called the different groups in your life, “rings of friendship,” and it seemed to me that such rings were an important part of being able to live in a polite society. Any normal person shares different things with different people. There will be some overlap, of course, but rings of friendship allowed you to shield your friends from your religious and political views, and allowed you to shield technical colleagues from family photos that would bore them. Behaving this way is common sense and simple politeness.

Google+ died, in part I think, because maintaining rings of friendship requires forethought. It also requires that your friends honor your privacy, and accept that they will not be a complete part of your life and confidence. But such activity requires work, both on the part of the poster, and on the part of the recipient. Besides, posting this way tends to make your posts dull. It reduced the number of eye-ball-grabbing rants that get seen by people who are highly offended by seeing the rant. Facebook, by contrast, uses and algorithm to decide who sees what. It requires no work from us, and I suspect the algorithm makes posts more interesting as it seems to favor the sensational, salacious, and inappropriate.

Facebook spreads the most salacious posts, I think, to increase the amount of time people spend on FB. That would be entirely self-serving, but it also gives the user a thrill as you see how many likes and followers, Facebook suggests “friends” that you never knew, who your other friends know, or who have similar interests. People friend these folks they hardly know, and post the most controversial of things in hope of getting followers and “likes.” It’s destructive to privacy, but it’s a dopamine rush in having people think you are a more interesting and exciting person than you are. The graphic below associates FB with the deadly sin of Envy — the desire to have what you don’t have.

An interesting take on social media

An interesting take on social media — the main platforms are the seven deadly sins.

There are six other deadly sins, and six of the other major social platforms seem designed to target one each. LinkedIn seems to target greed; Tinder targets Lust and Yelp targets gluttony. Instagram targets pride, the greatest of the deadly sins. It was natural that Facebook would acquire Instagram as Facebook had the most money, and pride is the strongest draw among the sins. In the graphic above Netflix is associated with sloth; I’m not sure that’s entirely fair: Netflix is passive, but no more passive than YouTube (owned by Google).

Twitter deserves a special mention. It was designed to be more immediate than FB, and I find it’s even more tipped to the salacious. When you post to Twitter, you have no control over who sees it; your only control is over what you see, and most people like to see salacious. President Donald Trump’s presidency is largely built on his Twitter posts. He claims he’s the Hemingway of 140 characters, and he certainly is good at grabbing eyeballs with outrageous comments and short simplifications of difficult matters. Last week his Twitter insult of Congressman Adam Schiff caught the news services all about. Similarly several congressmen calling Trump a mother***ker made news, Trump’s insult was more amusing, IMHO, if you read the name Adam a variant pronunciation. Facebook can tolerate the salacious like this, but it still limits the number of eyeballs to friends and acquaintances. Twitter is the home of wrath, and so far it seems a lot more successful than Google+.

Google+ was a reminder that world of social media is not all darkness and deadly sins. To my mind, Google+ was supposed to contract the evils of envy and intemperance with the virtue of temperance. That is Google+ was one of the cardinal virtues: Temperance in this case amounted to giving the appropriate amount of information to each of your friends, and not being excessive with any. It’s possible that the failure of Google+ was that it did not directly go after the audience for LinkedIn, but instead tried to mimic Facebook. Linked In (Greed) is almost exactly the opposite of Temperance.

The seven godly virtues are listed below, as set out by Pope Gregory, based on Paul. The first three are considered Godly, the other four Cardinal.

  1. Faith: belief in the right things (including the virtues!).
  2. Hope: taking a positive future view, that good will prevail.
  3. Charity: concern for, and active helping of, others.
  4. Fortitude: never giving up.
  5. Justice: being fair and equitable with others.
  6. Prudence: care of and moderation with money.
  7. Temperance: moderation of needed things and abstinence from things which are not needed.

Looking at this list it strikes me that the first three virtues are already present in social media. I associate Wikipedia with Faith, I associate it with a belief in knowledge itself, and in the ability of people to self govern. I associate Google, before it decided to be political, with Hope. It was based on a positive view of nature and people: that given free access to organized information they will come to the right conclusions. I liked that originally, ranking was decided based on people’s common choice. It was anti-FB, and humbling: there was no way that you could proclaim yourself greater than your neighbor if others didn’t see you that way. Currently Google allows paid customers to promote themselves, and conforms search for political patrons, eg China. In this way, it has become more like FB.

I associate “Go fund me,” with the virtue of Charity, and would like to propose that perhaps Prudence is Consumer Reports, or maybe e-bay. This leaves room for Fortitude, Justice, and Temperance (now that Google+ is dead). I leave it to you to fill in the gap.

Robert Buxbaum, January 8, 2019. There is a great manga fiction involving the seven deadly sins; Full Metal Alchemist. Also I should note that there are many versions of the seven virtues including the seven virtues of Buddhism: Right decisions, Valor, Benevolence, Respect, Honesty, Honor, and Loyalty.

Water Conservation for Michigan – Why?

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The Michigan Association of Planners is big on water conservation, joining several environmental groups to demand legislation requiring water conservation:

POLICY 4. Water Conservation: The Michigan Association of Planning supports state legislation requiring water conservation for public, and private users.

Among the classic legislation passed so far are laws requiring low flush toilets, and prohibiting high-volume shower heads as in this Seinfeld episode. I suppose I should go along: I’m running for water commissioner, and consider myself a conservationist. The problem is, I can’t see a good argument for these laws for most people here in Oakland County, or in neighboring Macomb and Wayne Counties. The water can’t run out because most users take it from the river and return it to the river, cleaned after it’s used; it’s all recycled.

Map of the main drinking-water pipes serving south-east Michigan

Map of the main drinking-water pipes serving south-east Michigan

The map above shows the clean water system for south-east Michigan. The high-population areas, the ones that are colored in the map, get their water from the Detroit River or from Lake Huron. It’s cleaned, pumped, and carried to your home along the pipes shown. Then after you’ve used the water, it travels back along another set of pipes to the water treatment plant and into the Detroit River.

Three-position shower head -- a wonderful home improvement I got it at universal plumbing.

Three-position shower head — a wonderful home improvement. I got it at universal plumbing.

When the system is working well, the water we return to the Detroit River is cleaner than the water we took in. So why legislate against personal use? If a customer wants to enjoy a good shower, and is willing to pay for the water at 1.5¢ per gallon, who cares how much water that customer uses? I can understand education efforts, sort-of, but find it hard to push legislation like we have against a high-volume shower head. We can not run out, and the more you use, the less everyone pays per gallon. A great shower head is a great gift idea, in my opinion.

The water department does not always work well, by the way, and these problems should be solved by legislation. We give away, for $200/year, high value clean water to Nestle company and then buy it back for $100,000,000. That’s a problem. Non-flushable toilet wipes are marketed as flushable; this causes sewer blockades. Our combined sewers regularly dump contaminated water into our rivers, lakes, and basements. These problems can be solved with legislation and engineering. It’s these problems that I’m running to solve.

Robert Buxbaum, January 6, 2019. If you want to save water, either to save the earth, or because you are cheep, here are some conservation ideas that make sense (to me).

The hard scrabble dictionary

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The rules or Scrabble are unchanging and always changing. The general rule is that Scrabble allows the use of every common word in the English language. In practice, there are two or more dictionaries of words. One of these has virtually no abbreviations, only a few foreign-derived words, and only a select few offensive terms. It is this one, “The Official Scrabble Players Dictionary,” that determines play. You’ll need the other dictionary to look up swear words or secondary meanings, or find common abbreviations.

Words get removed from the scrabble dictionary when someone -- anyone might find them offensive.

Words get removed from the scrabble dictionary when someone — anyone might find them offensive.

Both of these dictionaries change on a regular basis, by the way. And this is as it should be, and both exist in both English and American versions. The common dictionary adds words slowly, as they come into use and drops them slowly as they fall out. The Scrabble dictionary changes fast and for no obvious reason, adding and removing words for political and social aspect and for improved playability (whatever that is). Thus there is little rhyme or reason to the additions or deletions. Four years ago some ten 4000 words were added, mostly unusual words, and many insult words were removed. When the dictionary was changed again in September of this year, players are not told of some changes, but for the most part, there no obvious way to guess. Several words that were offensive in the last version, now are not. Other words that were OK then are now removed as offensive. You’ll play a word you’ve used for years and be told that it is no longer valid. Or someone will use a word you’ve never seen, and never will see otherwise, and you’ll find it is valid. Words added this year include: OK (previously an abbreviation), zen (previously a foreign word), and sheeple (previously a portmanteau, non-word). Also, I’m happy to say, fuck (a welcome addition). I looked up a bunch of previously removed insult words, and find that goy and spic are back, but i find that negro is not.  There is no list in print that tells you what’s been added, and that’s not right. Some articles have a few examples of new words, and some claim to have a list, but clearly it’s only a small fraction of the real list. There is nothing like a full addition list that I could find.

I’ve a bigger gripe though against removed words, especially when they are common words made to disappear for political effect. The previous dictionary, 2014, removed spic, goy, goyim, and negro; that was not right. The current dictionary added back all but negro (check for yourself, here). The word is still in use, both verbally and in literature, and not particularly offensive, less offensive than spic, IMHO. The American Negro College Fund doesn’t seem to mind the word negro. Malcolm X didn’t either. No one tells you these words are gone; they just disappear in the night.

My opinion, such as it is. I’m asking Mattel, Hasbro, Colliers, and/or Merriam-Webster: allow in all normal words, despite the fact that several have implied insults, or real ones. AND PUBLISH A COMPLETE CORRECTIONS PAGE, you [non recognized word]. Thank you.

Robert Buxbaum, December 27, 2018.

We don’t need no stinking primary clarifier

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Virtually every sewage plant of Oakland County uses the activated sludge process, shown in the layout below. Raw sewage comes in, and goes through physical separation — screening, grit removal, and a first clarifier – settling tank before moving to the activated sludge oxidation reactor. The 1st clarifier, shown at left below, removes about half of the incoming organics, but it often stinks and sometimes it “pops” bubbles of fart. This is usually during periods of low flow, like at night. When the flow is slow, it arrives at the plant as a rotting smelly mess; it’s often hard to keep the bubbles of smell down.

Typical Oakland Sewage plant, activated sludge process with a primary clarifier.

Typical Oakland County Sewage treatment plant, activated sludge process with a primary clarifier.

The smell is much improved in the oxidation reactor, analyzed here, and in the 2nd clarifier, shown above at right. Following that is a filter, an ultraviolet cleanup stage, and the liquids are discharged to a local river. In Oakland county, the solids from the two clarifiers are hauled off to a farm, or buried in a landfill. Burial in a landfill is a costly waste, as I discuss here. The throughputs for most of these treatment plants is only about 2-3 million gallons of sewage per day. But Oakland county can produce 500 million gallons of sewage per day. The majority of this goes to Detroit for treatment, and sometimes the overflow is dumped rotting and smelly, in the rivers.

A few months ago, I visited the Sycamore Creek Wastewater facility outside of Cincinnati. This is an 8 million gallon per day plant that uses the “extended aeration process”, shown in the sketch below. I noticed several things I liked: the high throughput (the plant looks no bigger than our 2-3 million gallon plants) and the lack of a bad smell, primarily. The Sycamore Creek plant had an empty hole where the primary clarifier had once been. Lacking this clarifier, the screened sewage could not sit and pop. Instead it goes directly from grit removal to the oxidation reactor, a reactor that looks no bigger than in our plants. This reactor manages a four times higher throughput, I think, because of a higher concentration of cellular catalyst. Consider the following equation derived in a previous post:

ln C°/C = kV/Q.

Here, C° and C are the incoming and exit concentrations of soluble organic; k is the reaction rate, proportional to cellular concentration, V is the volume of the reactor, Q is the flow, and ln is natural log. The higher cellular concentration in the extended aeration plant results in an increased reaction rate, k. The higher the value of k, the higher the allowed flow, Q, per reactor volume, V.

The single clarifier at the end of the Sycamore Creek plant does not look particularly big. My sense is that it deals with a lot more sludge and flow than is seen in our 2nd clarifiers because (I imaging) the sludge is higher density, thus faster settling. I expect that, without the 1 clarifier, there is extra iron and sulfate in the sludge, and more large particles too. In our plants, a lot of these things are removed in the primary clarifier. Sludge density is also increased, I think, because the Cincinnati plant recycle a greater percentage of the sludge (I list it as 90% in the diagram). Extra iron in the reactor also helps to remove phosphates from the water effluent that flows back to the river, an important pollution concern. Iron phosphates are insoluble, and thus leave with the sludge. In Oakland county’s activated sludge plants, it is typical to add iron to the reactor or clarifier. In Cincinnati’s extended aeration plant, I’m told, iron addition is generally not needed.

Typical Oakland Sewage plant, activated sludge process with a primary clarifier.

Cincinnati sewage treatment plant, extended aeration process with no primary clarifier.

The extended aeration part of the above process refers to the secondary sludge oxidizer, the continuously stirred tank reactor, or CSTR shown at lower right above. The “CSTR” is about 1/5 the volume of the main oxidation reactor and about the size of a clarifier. Oxidation in the CSTR compliments that in the main oxidizer removing organics, making bio-polymer, and improving (I think) the quality of the sludge that goes to the farms. Oxidation in the CSTR reduces the amount of sludge that goes to the farms. The sludge that does go, is  less-toxic and more concentrated in organics and minerals. I’m not sure if the CSTR product is as good as the product from an anaerobic digester, or if the CSTR is cheaper to operate, but it looks cheaper since there is no roof, and no (or minimal) heating. This secondary oxidizer is very efficient at removing organics because the cellular catalyst concentration is very high – much higher than in the main oxidizer.

During periods of high load, early morning, the CSTR seems to serve as a holding tank so that sludge does not build up in the clarifier. Too much sludge in the clarifier can start to rot, and ruin the effluent quality. The way you tell if there is too much sludge, by the way, is through a device called the “sludge judge.” I love that name. The Cincinnati plant used a centrifugal drier; none of our plants do. The Cincinnati plant had gap the bubble spots of the main oxidizer. This is good for denitrification, I’m told, an important process that I discuss elsewhere.

The liquid output of their clarifier (or ours) is not pure enough to be sent directly to the river. In this plant, the near-pure water from the clarifier is sent to a trickling filter, a bed of sand and anthracite that removes colloidal remnants. Some of our plants do the same. I suspect that the large surface area in this filter is also home to some catalysis: last stage oxidation of remaining bio-organics. On a regular basis, the filter bed is reverse-flushed to remove cellular buildup, slime, and send it to the beginning of the process. The trickling filter output is then sent to an ultraviolet, bacteria-killing step before being released to the rivers. All in all, I suspect that an extended aeration process like this is worth looking into for Oakland County, especially for our North Pontiac sewage treatment facility. That plant is particularly bad smelling, and clearly too small to treat all its sewage. Perhaps we can increase the throughput and decrease the smell at a minimal cost.

Dr. Robert E. Buxbaum, December 18, 2018. I’m running for water commissioner of Oakland county, MI. If you like, visit my campaign site. Here are some sludge jokes and my campaign song.