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.

A hydrogen permeation tester

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Over the years I’ve done a fair amount of research on hydrogen permeation in metals — this is the process of the gas dissolving in the metal and diffusing to the other side. I’ve described some of that, but never the devices that measure the permeation rate. Besides, my company, REB Research, sells permeation testing devices, though they are not listed on our site. We recently shipped one designed to test hydrogen permeation through plastics for use in light weight hydrogen tanks, for operation at temperatures from -40°C to 85°C. Shortly thereafter we got another order for a permeation tester. With all the orders, I thought I’d describe the device a bit — this is the device for low permeation materials. We have a similar, but less complex design for high permeation rate material.

Shown below is the central part of the device. It is a small volume that can be connected to a high vacuum, or disconnected by a valve. There is an accurate pressure sensor, accurate to 0.01 Torr, and so configured that you do not get H2 + O2 reactions (something that would severely throw off results). There is also a chamber for holding a membrane so one side is help in vacuum, in connection to the gauge, and the other is exposed to hydrogen, or other gas at pressures up to 100 psig (∆P =115 psia). I’d tested to 200 psig, but currently feel like sticking to 100 psig or less. This device gives amazingly fast readings for plastics with permeabilities as low as 0.01 Barrer.

REB Research hydrogen permeation tester cell with valve and pressure sensor.

REB Research hydrogen permeation tester cell with valve and pressure sensor.

To control the temperature in this range of interest, the core device shown in the picture is put inside an environmental chamber, set up as shown below, with he control box outside the chamber. I include a nitrogen flush device as a safety measure so that any hydrogen that leaks from the high pressure chamber will not build up to reach explosive limits within the environmental chamber. If this device is used to measure permeation of a non-flammable gas, you won’t need to flush the environmental chamber.

I suggest one set up the vacuum pump right next to the entrance of the chamber; in the case of the chamber provided, that’s on the left as shown with the hydrogen tank and a nitrogen tank to the left of the pump. I’ve decided to provide a pressure sensor for the N2 (nitrogen) and a solenoidal shutoff valve for the H2 (hydrogen) line. These work together as a safety feature for long experiments. Their purpose is to automatically turn off the hydrogen if the nitrogen runs out. The nitrogen flush part of this process is a small gauge copper line that goes from the sensor into the environmental chamber with a small, N2 flow bleed valve at the end. I suggest setting the N2 pressure to 25-35 psig. This should give a good inert flow into the environmental chamber. You’ll want a nitrogen flush, even for short experiments, and most experiments will be short. You may not need an automatic N2 sensor, but you’ll be able to do this visually.

Basic setup for REB permeation tester and environmental chamber

Basic setup for REB permeation tester and environmental chamber

I shipped the permeation cell comes with some test, rubbery plastic. I’d recommend the customer leave it in for now, so he/she can use it for some basic testing. For actual experiments, you replace mutest plastic with the sample you want to check. Connect the permeation cell as shown above, using VCR gaskets (included), and connect the far end to the multi-temperature vacuum hose, provided. Do this outside of the chamber first, as a preliminary test to see if everything is working.

For a first test live the connections to the high pressure top section unconnected. The pressure then will be 1 atm, and the chamber will be full of air. eave the top, Connect the power to the vacuum pressure gauge reader and connect the gauge reader to the gauge head. Open the valve and turn on the pump. If there are no leaks the pressure should fall precipitously, and you should see little to no vapor coming out the out port on the vacuum pump. If there is vapor, you’ve got a leak, and you should find it; perhaps you didn’t tighten a VCR connection, or you didn’t do a good job with the vacuum hose. When things are going well, you should see the pressure drop to the single-digit, milliTorr range. If you close the valve, you’ll see the pressure rise in the gauge. This is mostly water and air degassing from the plastic sample. After 30 minutes, the rate of degassing should slow and you should be able to measure the rate of gas permeation in the polymer. With my test plastic, it took a minute or so for the pressure to rise by 10 milliTorr after I closed the valve.

If you like, you can now repeat this preliminary experiment with hydrogen connect the hydrogen line to one of the two ports on the top of the permeation cell and connect the other port to the rest of the copper tubing. Attach the H2 bleed restrictor (provided) at the end of this tubing. Now turn on the H2 pressure to some reasonable value — 45 psig, say. With 45 psi (3 barg upstream) you will have a ∆P of 60 psia or 4 atm across the membrane; vacuum equals -15 psig. Repeat the experiment above; pump everything down, close the valve and note that the pressure rises faster. The restrictor allows you to maintain a H2 pressure with a small, cleansing flow of gas through the cell.

If you like to do these experiments with a computer record, this might be a good time to connect your computer to the vacuum reader/ controller, and to the thermocouple, and to the N2 pressure sensor. 

Here’s how I calculate the permeability of the test polymer from the time it takes for a pressure rise assuming air as the permeating gas. The volume of the vacuumed out area after the valve is 32 cc; there is an open area in the cell of 13.0 cm2 and, as it happens, the  thickness of the test plastic is 2 mm. To calculate the permeation rate, measure the time to rise 10 millitorr. Next calculate the millitorr per hour: that’s 360 divided by the time to rise ten milliTorr. To calculate ncc/day, multiply the millitorr/hour by 24 and by the volume of the chamber, 32 cc, and divide by 760,000, the number of milliTorr in an atmosphere. I found that, for air permeation at ∆P = one atm, I was getting 1 minute per milliTorr, which translates to about 0.5 ncc/day of permeation through my test polymer sheet. To find the specific permeability in cc.mm/m2.day.atm, I multiply this last number by the thickness of the plastic (2 mm in this case), divide by the area, 0.0013 m2, and divide by ∆P, 1 atm, for this first test. Calculated this way, I got an air permeance of 771 cc.mm/m2.day.atm.

The complete setup for permeation testing.

The complete setup for permeation testing.

Now repeat the experiment with hydrogen and your own plastic. Disconnect the cell from both the vacuum line and from the hydrogen in line. Open the cell; take out my test plastic and replace it with your own sample, 1.87” diameter, or so. Replace the gasket, or reuse it. Center the top on the bottom and retighten the bolts. I used 25 Nt-m of torque, but part of that was using a very soft rubbery plastic. You might want to use a little more — perhaps 40-50 Nt-m. Seal everything up. Check that it is leak tight, and you are good to go.

The experimental method is the same as before and the only signficant change when working with hydrogen, besides the need for a nitrogen flush, is that you should multiply the time to reach 10 milliTorr by the square-root of seven, 2.646. Alternatively, you can multiply the calculated permeability by 0.378. The pressure sensor provided measures heat transfer and hydrogen is a better heat transfer material than nitrogen by a factor of √7. The vacuum gauge is thus more sensitive to H2 than to N2. When the gauge says that a pressure change of 10 milliTorr has occurred, in actuality, it’s only 3.78 milliTorr.  The pressure gauge reads 3.78 milliTorr oh hydrogen as 10 milliTorr.

You can speed experiments by a factor of ten, by testing the time to rise 1 millitorr instead of ten. At these low pressures, the gauge I provided reads in hundredths of a milliTorr. Alternately, for higher permeation plastics (or metals) you want to test the time to rise 100 milliTorr or more, otherwise the experiment is over too fast. Even at a ten millTorr change, this device gives good accuracy in under 1 hour with even the most permeation-resistant polymers.

Dr. Robert E. Buxbaum, March 27, 2019; If you’d like one of these, just ask. Here’s a link to our web site, REB Research,

Statistics for psychologists, sociologists, and political scientists

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In terms of mathematical structure, psychologists, sociologists, and poly-sci folks all do the same experiment, over and over, and all use the same simple statistical calculation, the ANOVA, to determine its significance. I thought I’d explain that experiment and the calculation below, walking you through an actual paper (one I find interesting) in psychology / poly-sci. The results are true at the 95% level (that’s the same as saying p >0.05) — a significant achievement in poly-sci, but that doesn’t mean the experiment means what the researchers think. I’ll then suggest another statistic measure, r-squared, that deserves to be used along with ANOVA.

The standard psychological or poly-sci research experiments involves taking a group of people (often students) and giving them a questionnaire or test to measure their feelings about something — the war in Iraq, their fear of flying, their degree of racism, etc. This is scored on some scale to get an average. Another, near-identical group of subjects is now brought in and given a prompt: shown a movie, or a picture, or asked to visualize something, and then given the same questionnaire or test as the first group. The prompt is shown to have changed to average score, up or down, an ANOVA (analysis of variation) is used to show if this change is one the researcher can have confidence in. If the confidence exceeds 95% the researcher goes on to discuss the significance, and submits the study for publication. I’ll now walk you through the analysis the old fashioned way: the way it would have been done in the days of hand calculators and slide-rules so you understand it. Even when done this way, it only takes 20 minutes or so: far less time than the experiment.

I’ll call the “off the street score” for the ith subject, Xi°. It would be nice if papers would publish these, but usually they do not. Instead, researchers publish the survey and the average score, something I’ll call X°-bar, or X°. they also publish a standard deviation, calculated from the above, something I’ll call, SD°. In older papers, it’s called sigma, σ. Sigma and SD are the same thing. Now, moving to the group that’s been given the prompt, I’ll call the score for the ith subject, Xi*. Similar to the above, the average for this prompted group is X*, or X°-bar, and the standard deviation SD*.

I have assumed that there is only one prompt, identified by an asterix, *, one particular movie, picture, or challenge. For some studies there will be different concentrations of the prompt (show half the movie, for example), and some researchers throw in completely different prompts. The more prompts, the more likely you get false positives with an ANOVA, and the more likely you are to need to go to r-squared. Warning: very few researchers do this, intentionally (and crookedly) or by complete obliviousness to the math. Either way, if you have a study with ten prompt variations, and you are testing to 95% confidence your result is meaningless. Random variation will give you this result 50% of the time. A crooked researcher used ANOVA and 20 prompt variations “to prove to 95% confidence” that genetic modified food caused cancer; I’ll assume (trust) you won’t fall into that mistake, and that you won’t use the ANOVA knowledge I provide to get notoriety and easy publication of total, un-reproducible nonsense. If you have more than one or two prompts, you’ve got to add r-squared (and it’s probably a good idea with one or two). I’d discuss r-squared at the end.

I’ll now show how you calculate X°-bar the old-fashioned way, as would be done with a hand calculator. I do this, not because I think social-scientists can’t calculate an average, nor because I don’t trust the ANOVA function on your laptop or calculator, but because this is a good way to familiarize yourself with the notation:

X°-bar = X° = 1/n° ∑ Xi°.

Here, n° is the total number of subjects who take the test but who have not seen the prompt. Typically, for professional studies, there are 30 to 50 of these. ∑ means sum, and Xi° is the score of the ith subject, as I’d mentioned. Thus, ∑ Xi° indicates the sum of all the scores in this group, and 1/n° is the average, X°-bar. Convince yourself that this is, indeed the formula. The same formula is used for X*-bar. For a hand calculation, you’d write numbers 1 to n° on the left column of some paper, and each Xi° value next to its number, leaving room for more work to follow. This used to be done in a note-book, nowadays a spreadsheet will make that easier. Write the value of X°-bar on a separate line on the bottom.

T-table

T-table

In virtually all cases you’ll find that X°-bar is different from X*-bar, but there will be a lot of variation among the scores in both groups. The ANOVA (analysis of variation) is a simple way to determine whether the difference is significant enough to mean anything. Statistics books make this calculation seem far too complicated — they go into too much math-theory, or consider too many types of ANOVA tests, most of which make no sense in psychology or poly-sci but were developed for ball-bearings and cement. The only ANOVA approach used involves the T-table shown and the 95% confidence (column this is the same as two-tailed p<0.05 column). Though 99% is nice, it isn’t necessary. Other significances are on the chart, but they’re not really useful for publication. If you do this on a calculator, the table is buried in there someplace. The confidence level is written across the bottom line of the cart. 95% here is seen to be the same as a two-tailed P value of 0.05 = 5% seen on the third from the top line of the chart. For about 60 subjects (two groups of 30, say) and 95% certainty, T= 2.000. This is a very useful number to carry about in your head. It allows you to eyeball your results.

In order to use this T value, you will have to calculate the standard deviation, SD for both groups and the standard variation between them, SV. Typically, the SDs will be similar, but large, and the SV will be much smaller. First lets calculate SD° by hand. To do this, you first calculate its square, SD°2; once you have that, you’ll take the square-root. Take each of the X°i scores, each of the scores of the first group, and calculate the difference between each score and the average, X°-bar. Square each number and divide by (n°-1). These numbers go into their own column, each in line with its own Xi. The sum of this column will be SD°2. Put in mathematical terms, for the original group (the ones that didn’t see the movie),

SD°2 = 1/(n°-1) ∑ (Xi°- X°)2

SD° = √SD°2.

Similarly for the group that saw the movie, SD*2 = 1/(n*-1) ∑ (Xi*- X*)2

SD* = √SD*2.

As before, n° and n* are the number of subjects in each of the two groups. Usually you’ll aim for these to be the same, but often they’ll be different. Some students will end up only seeing half the move, some will see it twice, even if you don’t plan it that way; these students’ scares can not be used with the above, but be sure to write them down; save them. They might have tremendous value later on.

Write down the standard deviations, SD for each group calculated above, and check that the SDs are similar, differing by less than a factor of 2. If so, you can take a weighted average and call it SD-bar, and move on with your work. There are formulas for this average, and in some cases you’ll need an F-table to help choose the formula, but for my purposes, I’ll assume that the SDs are similar enough that any weighted average will do. If they are not, it’s likely a sign that something very significant is going on, and you may want to re-think your study.

Once you calculate SD-bar, the weighted average of the SD’s above, you can move on to calculate the standard variation, the SV between the two groups. This is the average difference that you’d expect to see if there were no real differences. That is, if there were no movie, no prompt, no nothing, just random chance of who showed up for the test. SV is calculated as:

SV = SD-bar √(1/n° + 1/n*).

Now, go to your T-table and look up the T value for two tailed tests at 95% certainty and N = n° + n*. You probably learned that you should be using degrees of freedom where, in this case, df = N-2, but for normal group sizes used, the T value will be nearly the same. As an example, I’ll assume that N is 80, two groups of 40 subjects the degrees of freedom is N-2, or 78. I you look at the T-table for 95% confidence, you’ll notice that the T value for 80 df is 1.99. You can use this. The value for  62 subjects would be 2.000, and the true value for 80 is 1.991; the least of your problems is the difference between 1.991 and 1.990; it’s unlikely your test is ideal, or your data is normally distributed. Such things cause far more problems for your results. If you want to see how to deal with these, go here.

Assuming random variation, and 80 subjects tested, we can say that, so long as X°-bar differs from X*-bar by at least 1.99 times the SV calculated above, you’ve demonstrated a difference with enough confidence that you can go for a publication. In math terms, you can publish if and only if: |X°-X*| ≥ 1.99 SV where the vertical lines represent absolute value. This is all the statistics you need. Do the above, and you’re good to publish. The reviewers will look at your average score values, and your value for SV. If the difference between the two averages is more than 2 times the SV, most people will accept that you’ve found something.

If you want any of this to sink in, you should now do a worked problem with actual numbers, in this case two groups, 11 and 10 students. It’s not difficult, but you should try at least with these real numbers. When you are done, go here. I will grind through to the answer. I’ll also introduce r-squared.

The worked problem: Assume you have two groups of people tested for racism, or political views, or some allergic reaction. One group was given nothing more than the test, the other group is given some prompt: an advertisement, a drug, a lecture… We want to know if we had a significant effect at 95% confidence. Here are the test scores for both groups assuming a scale from 0 to 3.

Control group: 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3.  These are the Xi° s; there are 11 of them

Prompted group: 0, 1, 1, 1, 2, 2, 2, 2, 3, 3.  These are the Xi* s; there are 10 of them.

On a semi-humorous side: Here is the relationship between marriage and a PhD.

Robert Buxbaum, March 18, 2019. I also have an explanation of loaded dice and flipped coins; statistics for high school students.

C-Pap and Apnea

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A month of so ago, I went to see a sleep doctor for my snoring. I got a take-home breathing test that gave me the worst night’s sleep in recent memory. A few days later, I got a somber diagnosis: “You are a walking zombie.” Apparently, I hold my breath for ten seconds or more every minute and a half while sleeping. Normal is supposed to be every 4 to 10 minutes. But by this standard, more than half of all middle-aged men are sub-normal (how is this possible?). As a result of my breath-holding, the wrinkled, unsmiling DO claimed I’m brain-dead now and will soon be physically dead unless I change my ways. Without spending 3 minutes with me, the sleep expert told me that I need to lose weight, and that I need a C-Pap (continuous positive airway pressure) device as soon as possible. It’s supposed to help me lose that weight and get back the energy. With that he was gone. The office staff gave me the rest of the dope: I was prescribed  a “ResMed” brand C-Pap, supplied by a distributor right across the hall from the doctor (how convenient).

I picked up the C-Pap three months later. Though I was diagnosed as needing one “as soon as possible,” no one would release the device until they were sure it was covered by my insurance company. The device when I got it, was something of a horror. The first version I tried fit over the whole face and forces air into my mouth and nose simultaneously, supposedly making it easier to inhale, but harder to exhale. I found it more than a bit uncomfortable. The next version was nose only and marginally more comfortable. I found there was a major air-flow restriction when I breath in and a similar pressure penalty when I breathed out. And it’s loud. And, if you open your mouth, there is a wind blowing through. As for what happens if the pump fails or the poor goes out, I notice that there are the tiniest of air-holes to prevent me from suffocating, barely. A far better design would have given me a 0-psi flapper valve for breathing in, and a 1/10 psi flapper for breathing out. That would also reduce the pressure restriction I was feeling every time I took a deep breath. One of my first blog essays was about engineering design aesthetics; you want your designs to improve things under normal conditions and fail safe, not like here. Using this device while awake was anything but pleasant, and I found I still hold my breath, even while awake, about every 5 minutes.

Since I have a lab, and the ability to test these things, I checked the pressure of the delivered air, and found it was 3 cm of water, about 1/20 psi. The prescription was for 5 cm or water (1/14 psi). The machine registers this, but it is wrong. I used a very simple water manometer, a column of water, similar to the one I used to check the pressure drop in furnace air filters. Is 1/20 psi enough?How did he decide on 1/14 psi by the way? I’ve no idea. !/14 psi is about 1/200 atm. Is this enough to do anything? While the C-Pap should get me to breathe more, I guess, about half of all users stop after a few tries, and my guess is that they find it as uncomfortable as I have. There is no research evidence that treatment with it reduces stroke or heart attack, or extends life, or helps with weight loss. The assumption is that, if you force middle-aged men to hold their breath less, they will be healthier, but I’ve no clear logic or evidence to back the assumption. At best, anything you gain on the ease of breathing in, you lose on the difficulty of breathing out. The majority of middle-aged men are prescribed a C-Pap, if they go for a sleep study, and it’s virtually 100% for overweight men with an apple-shaped body.

I’d have asked my doctor about alternatives or for a second opinion but he was out the door too fast. Besides, I was afraid I’d get the same answer that Rodney Dangerfield got: “You want a second opinion? OK. You’re ugly, too.” Mr. Dangerfield was not a skinny comic, by the way, but he was funny, and I assume he’d have been prescribed a C-Pap (maybe he was). He died at 82, considerably older than Jim Fixx, “the running doctor,” Adelle Davis, the “eat right for health” doctor, Euell Gibbons “in search of the wild asparagus,” or Ethan Pritkin, the diet doctor. God seems to prefer fat comedians to diet experts; I expect that most-everyone does.

Benjamin Franklin and his apple-shaped body

Benjamin Franklin and his apple-shaped body; I don’t think of him as a zombie.

What really got my goat, besides my dislike of the C-Pap, is that I object to being called a walking zombie. True, I’m not as energetic as I used to be, but I manage to run a company, and to write research papers, and I get patents (this one was approved just today). And I write these blogs — I trust that any of you who’ve read this far find them amusing. Pretty good for a zombie — and I ran for water commissioner. People who use the C-Pap self-report that they have more energy, but self-reporting is poor evidence. A significant fraction of those people who start with the C-Pap, stop, and those people, presumably were not happy. Besides, a review of the internet suggests that a similarly large fraction of those who buy a “MyPillow.com” claim they have more energy. And I’ve seen the same claims from people who take a daily run, or who pray, or smoke medical marijuana (available for sleep apnea, but not from this fellow), or Mirtazapine (study results here), or  for electro-shock therapy, a device called “Inspire.” With so many different products providing the same self-reported results, I wonder if there isn’t something more fundamental going on. I’d wish the doc had spent a minute or two to speak to this, or to the alternatives.

As for weight loss, statistical analysis of lifespan suggests that there is a health advantage to being medium weight: not obese, but not skinny. I present some of this evidence here, along with evidence that extra weight helps ward off Alzheimer’s. For all I know this protection is caused by holding your breath every few minutes. It helps to do light exercise, but not necessary for mental health. In terms of mental health, the evidence suggests that weight loss is worse than nothing.

Jared Gray, author of the Alien movies, was diagnosed with apnea, so he designed his own sleep-mask.

Jared Gray, author of the Alien movies, was diagnosed with apnea, so he designed his own sleep-mask.

Benjamin Franklin was over-weight and apple-shaped, and no zombie, The same is true of John Adams, Otto Von Bismarck, and Alfred Hitchcock. All lived long, productive lives. Hitchcock was sort of morbid, it will be admitted, but I would not want him otherwise. Ed McMahon, Johnny Carson’s side-kick, apologized to America for being overweight and smoking, bu the outlived Johnny Carson by nine years, dying at 89. Henry Kissinger is still alive and writing at 95. He was always fatter than any of the people he served. He almost certainly had sleep apnea, back in the day, and still has more on the ball, in my opinion, than most of the talking-head on TV. The claim that overweight, middle-aged men are all zombies without a breath assisting machine doesn’t make no sense to me. But then, I’m not a sleep doctor. (Do sleep doctors get commissions? Why did he choose, this supplier or this brand device? With so little care about patients, I wonder who runs the doctor’s office.)

I looked up my doctor on this list provided by the American Board of Sleep Medicine. I found my doctor was not certified in sleep medicine. I suppose certified doctors would prescribe something similar  but was disappointed that you don’t need sleep certification to operate as a sleep specialist. In terms of masks, I figure, if you’ve got to wear something, you might as well wear something cool. Author Jared Gray, shown above (not the author of the Alien) was diagnosed with Apnea 6 months ago and made his own C-Pap mask to make it look like the alien was attacking him. Very cool for an ex-zombie, but I’m waiting to see a burst of creative energy.

What do we zombies want? Brains.

When do we want them? Brains.

What do vegetarian zombies want? Grains.

Robert Buxbaum, March 15, 2019. In case real zombies should attack, here’s what to do.  An odd legal/insurance issue: in order to get the device, I had to sign that, if I didn’t use it for 20 days in the first month of 4 hours per night, and thus if the insurance did not pay, I would be stuck with the full fee. I signed. This might cost me $1000 though normally in US law, companies can only charge a reasonable restock fee, but it can’t be unreasonable, like the full  price. I also had to sign that I would go back to the same, quick-take doctor, but again there has to be limits. We’ll see how the machine pans out, but one difference I see already: unlike my pillow.com, there is no money back guarantee with the C-Pap treatment.

Seize the day

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It is forbidden knowledge what our term of years, mine and yours.
Don’t scan the tables of your Babylonian seers.
Better far to bear the future, my Leuconoe, like the past.
Whether Jupiter has many years yet to give,
Or this one is our last:

This, that makes the Tyrrhene waves spent against the shore.
Strain your wine and strain your wisdom.
Life is short; should we hope for long?
In the moment of our talking, precious time has slipped away.
Seize the moment. Trust tomorrow little as you may.

by Horace (23 BC Roman poet) Odes, 1.11

This poem by Horace, in 23 BC is the first appearance of the phrase “carpe diem,” translated as seize he day. I’d decided to look over the translation from Wikipedia, and to correct and update the translation as I saw fit, to some extent to extract the meanings better, to some extent to make the grammar less-clunky, and to some extent to make it rhyme. Seen in context, the whole poem looks  romantic, and the intent of the famous phrase seems more like ‘seize the moment’ when read in context. Either translation is acceptable from the Latin, as I understand it.

The phrase, “seize the day” appears in several important movies. Robin Williams speaks it to a class of literature students in the sense that I read it here — seize the moment — in this scene of “The Dead Poets Society,” He’s trying to get the boys to appreciate the purpose of poetry, and the preciousness of their years in prep-school. A well-done movie, IMHO. The newspaper sellers sing the phrase for different intent in this song in “Newsies.” For them, the intent is more like seize the opportunity, or maybe even seize power. It’s not Horace’s intent, but it’s sung in front of the statue of Horace Greeley, and it works.

In either context, there is a certain young masculinity about this phrase. In both movie, the cast experiencing the idea is male and young. I don’t think either movie would work as well with women dancing or singing to this idea.

Robert E. Buxbaum, March 9, 2019. In case you should wonder what happens to Frank Kelly (Sullivan) after the movie ends, I’ve written about that.  Also, a friend of mine notes that the grammar used in these movies is wrong:  “Carpe diem” is singular, for this 3rd declension noun. The equivalent Latin plural is “Carpite diem:” That’s the equivalent of you-all, should seize the moment. Unlike in the movies, much of classic education is spent on pedantic, uninspiring, minutia, like Latin grammar, but that’s what’s necessary to permit distinction of meaning. Thank you, David Hoenig for grammar help.

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.