Monthly Archives: May 2019

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How long could you make a suspension bridge?

The above is one of the engineering questions that puzzled me as a student engineer at Brooklyn Technical High School and at Cooper Union in New York. The Brooklyn Bridge stood as a wonder of late 1800s engineering, and it had recently been eclipsed by the Verrazano bridge, a pure suspension bridge. At the time it was the longest and heaviest in the world. How long could a bridge be made, and why did Brooklyn bridge have those catenary cables, when the Verrazano didn’t? (Sometimes I’d imagine a Chinese engineer being asked the top question, and answering “Certainly, but How Long is my cousin.”)

I found the above problem unsolvable with the basic calculus at my disposal. because it was clear that both the angle of the main cable and its tension varied significantly along the length of the cable. Eventually I solved this problem using a big dose of geometry and vectors, as I’ll show.

Vector diagram of forces on the cable at the center-left of the bridge.

Vector diagram of forces on the cable at the center-left of the bridge.

Consider the above vector diagram (above) of forces on a section of the main cable near the center of the bridge. At the right, the center of the bridge, the cable is horizontal, and has a significant tension. Let’s call that T°. Away from the center of the bridge, there is a vertical cable supporting a fraction of  roadway. Lets call the force on this point w. It equals the weight of this section of cable and this section of roadway. Because of this weight, the main cable bends upward to the left and carries more tension than T°. The tangent (slope) of the upward curve will equal w/T°, and the new tension will be the vector sum along the new slope. From geometry, T= √(w2 +T°2).

Vector diagram of forces on the cable further from the center of the bridge.

Vector diagram of forces on the cable further from the center of the bridge.

As we continue from the center, there are more and more verticals, each supporting approximately the same weight, w. From geometry, if w weight is added at each vertical, the change in slope is always w/T° as shown. When you reach the towers, the weight of the bridge must equal 2T Sin Θ, where Θ is the angle of the bridge cable at the tower and T is the tension in the cable at the tower.

The limit to the weight of a bridge, and thus its length, is the maximum tension in the main cable, T, and the maximum angle, that at the towers. Θ. I assumed that the maximum bridge would be made of T1 bridge steel, the strongest material I could think of, with a tensile strength of 100,000 psi, and I imagined a maximum angle at the towers of 30°. Since there are two towers and sin 30° = 1/2, it becomes clear that, with this 30° angle cable, the tension at the tower must equal the total weight of the bridge. Interesting.

Now, to find the length of the bridge, note that the weight of the bridge is proportional to its length times the density and cross section of the metal. I imagined a bridge where the half of the weight was in the main cable, and the rest was in the roadway, cars and verticals. If the main cable is made of T1 “bridge steel”, the density of the cable is 0.2833 lb/in3, and the density of the bridge is twice this. If the bridge cable is at its yield strength, 100,000 psi, at the towers, it must be that each square inch of cable supports 50,000 pounds of cable and 50,000 lbs of cars, roadway and verticals. The maximum length (with no allowance for wind or a safety factor) is thus

L(max) = 100,000 psi / 2 x 0.2833 pounds/in3 = 176,500 inches = 14,700 feet = 2.79 miles.

This was more than three times the length of the Verrazano bridge, whose main span is ‎4,260 ft. I attributed the difference to safety factors, wind, price, etc. I then set out to calculate the height of the towers, and the only rational approach I could think of involved calculus. Fortunately, I could integrate for the curve now that I knew the slope changed linearly with distance from the center. That is for every length between verticals, the slope changes by the same amount, w/T°. This was to say that d2y/dx2 = w/T° and the curve this described was a parabola.

Rather than solving with heavy calculus, I noticed that the slope, dy/dx increases in proportion to x, and since the slope at the end, at L/2, was that of a 30° triangle, 1/√3, it was clear to me that

dy/dx = (x/(L/2))/√3

where x is the distance from the center of the bridge, and L is the length of the bridge, 14,700 ft. dy/dx = 2x/L√3.

We find that:
H = ∫dy = ∫ 2x/L√3 dx = L/4√3 = 2122 ft,

where H is the height of the towers. Calculated this way, the towers were quite tall, higher than that of any building then standing, but not impossibly high (the Dubai tower is higher). It was fairly clear that you didn’t want a tower much higher than this, though, suggesting that you didn’t want to go any higher than a 30° angle for the main cable.

I decided that suspension bridges had some advantages over other designs in that they avoid the problem of beam “buckling.’ Further, they readjust their shape somewhat to accommodate heavy point loads. Arch and truss bridges don’t do this, quite. Since the towers were quite a lot taller than any building then in existence, I came to I decide that this length, 2.79 miles, was about as long as you could make the main span of a bridge.

I later came to discover materials with a higher strength per weight (titanium, fiber glass, aramid, carbon fiber…) and came to think you could go longer, but the calculation is the same, and any practical bridge would be shorter, if only because of the need for a safety factor. I also came to recalculate the height of the towers without calculus, and got an answer that was shorter, for some versions, a hundred feet shorter, as shown here. In terms of wind, I note that you could make the bridge so heavy that you don’t have to worry about wind except for resonance effects. Those are the effects are significant, but were not my concern at the moment.

The Brooklyn Bridge showing its main cable suspension structure and its catenaries.

Now to discuss catenaries, the diagonal wires that support many modern bridges and that, on the Brooklyn bridge, provide  support at the ends of the spans only. Since the catenaries support some weight of the Brooklyn bridge, they decrease the need for very thick cables and very high towers. The benefit goes down as the catenary angle goes to the horizontal, though as the lower the angle the longer the catenary, and the lower the fraction of the force goes into lift. I suspect this is why Roebling used catenaries only near the Brooklyn bridge towers, for angles no more than about 45°. I was very proud of all this when I thought it through and explained it to a friend. It still gives me joy to explain it here.

Robert Buxbaum, May 16, 2019.  I’ve wondered about adding vibration dampers to very long bridges to decrease resonance problems. It seems like a good idea. Though I have never gone so far as to do calculations along these lines, I note that several of the world’s tallest buildings were made of concrete, not steel, because concrete provides natural vibration damping.