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.

Shakespeare’s plays, organized.

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One remarkable thing about Shakespeare’s plays is how varied they are. There are comedies and tragedies; histories of England, and of Rome, musings on religion, and on drink, and lots of cross-dressing. He wrote at least thirty seven plays between 1590 and 1613, alone or as a major collaborator, and the chart below gives a sense of the scope. I have seen less than half of these plays, so I find the chart below both useful and humorous. The humor of the chart is partly that it presents the common man (us) access to the godly (Shakespeare). That access is the root of the best comedy, in my opinion. Shakespeare also has a comic dog, some total idiots, comic violence to women, and a few other cringeworthy laugh-getters, but we’ll not mention those; it’s low comedy. You’ll notice that Merchant of Venice is listed here as a comedy; I think it was seen that way by Shakespeare. The hero of the play in my opinion, is a woman, Portia, who outsmarts all others by her legal genius at the end. Tragedy is when the great individual can not access great things. At least that’s how I see it. As for History; it’s been said, that it starts as tragedy, and ends as comedy. Shakespeare’s histories include some of each. And as for our, US history, Lincoln was tragedy, like LBJ; Truman was comedy, and Andrew Jackson too. And, as for Trump, who knows?

By Myra Gosling, www.goodticklebrain.com
A Shakespeare collaboration. The collaborator, Fletcher, is cited by name.

Ms Gosling’s graphic, wonderful as it is, lists some but not all of Shakespeare’s collaborations. Two listed ones, “Henry VIII,” and “The Two Noble Kinsmen” were with John Fletcher. The cover shown at right, shows Fletcher named as first author. Since Fletcher outlived Shakespeare and took over the company after his death, I’ll assume these are later plays.

“Henry IV, part 1” is thought to be from Shakespeare’s early career, and seems to have been a mass collaboration: something written by a team the way situation comedies are written today. And “Pericles, Prince of Tyre,” listed near the bottom right, seems to have been a mid-career collaboration with George Wilkins. At least four of Shakespeare’s collaborations don’t appear at all in the graphic. “Edward III” and “The Spanish Tragedy”, appear to have been written with Thomas Kyd, likely early in Shakespeare’s career. Perhaps Gosling felt they don’t represent the real Shakespeare, or perhaps she left them off because they are not performed often. Another collaboration, “Sir Thomas More” (an intentional misspelling of Moore?), is well regarded today, and still put on. An existing manuscript includes 300+ lines written in Shakespeare’s hand. Still, Shakespeare’s main contribution seems to have been editing the play to get it past the censors. Finally, “Cardenio,” is a lost play, likely another collaboration with Fletcher. It got good reviews.

The cool thing about Shakespeare’s play writing, in my opinion, is his willingness to let the characters speak for themselves. Even characters who Shakespeare doesn’t like have their say. They speak with passion and clarity; without interruption or mockery. Writing this way is difficult, and most writers can’t avoid putting themselves and their opinions in the forefront. I applaud Ms Gosling for making Shakespeare accessible. Here’s this month’s issue of her blog, GoodTickleBrain.

Robert Buxbaum, June 26, 2019. As a side note, Shakespeare appears to have been born and died on the same date, April 23; in 1564 and 1616, respectively.

Making The City of New Orleans profitable

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The City of New Orleans is the name of the only passenger train between Chicago and New Orleans. It’s also the name of a wonderful song by Steve Goodman, 1971. Hear it, sung by Arlo Guthrie with scenes from a modern ride.

“Riding on the City of New Orleans
Illinois Central Monday morning rail
Fifteen cars and fifteen restless riders
Three conductors and twenty-five sacks of mail
All along the southbound odyssey
The train pulls out at Kankakee
Rolls along past houses, farms and fields
Passin’ trains that have no names
Freight yards full of old black men
And the graveyards of the rusted automobiles…”

Every weekday, this train leaves Chicago at 9:00 PM and gets into New Orleans twenty hours later, at 5:00 PM. It’s a 925 mile trip at a 45 mph average: slow and money-losing, propped up by US taxes. Like much of US passenger rail, it “has the disappearing railroad blues.” It’s a train service that would embarrass the Bulgarians: One train a day?! 45 mph average speed!? It’s little wonder is that there are few riders, and that they are rail-enthusiasts: “the sons of Pullman porters, and the sons of engineers, Ride[ing] their father’s magic carpets made of steel.” The wonder, to me was that there was ever fifteen cars for these, “15 restless riders”.

A sack of mail being picked up on the fly.

I would be happy to see more trips and a faster speed, at an average speed of at least 60 mph. This would require 85 mph or higher between stops, but it would save on salaries, and it would bring in some new customers. But even if these higher speeds cost nothing extra, in net, you’d still need something more to make the trip profitable; a lot more if the goal is to add another train. Air-traffic will always be faster, and the automobile, more convenient. I find a clue to profitability in the fifteen cars of the song and in the sacks of mail.

Unless I’m mistaken, mail traffic was at least as profitable as passenger traffic, and those “twenty-five sacks of mail” were either very large, or just the number on-loaded at Kankakee. Passenger trains like ‘the city of New Orleans’ were the main mail carriers till the late 1970s, a situation that ended when union disputes made it unprofitable. Still, I suspect that mail might be profitable again if we used passenger trains only for fast mail — priority and first class — and if we had real fast mail again. We currently use trucks and freight trans for virtually all US mail, we do not have a direct distribution system. The result is that US mail is vastly slower than it had been. First class mail used to arrive in a day or two, like UPS now. But these days the post office claims 2 to 4 business days for “priority mail,” and ebay guarantees priority delivery time “within eight business days”. That’s two weeks in normal language. Surely there is room for a faster version. It costs $7.35 for a priority envelope and $12.80 for a priority package (medium box, fixed price). That’s hardly less than UPS charges.

Last day of rail post service New York to Washington, DC. .June 30, 1977.

Passenger trains could speed our slow mail a lot, if it were used for this, even with these slow speeds. The City of New Orleans makes this trip in less than a day, with connections available to major cities across the US. If priority mail went north-south in under one day, people would use it more, and that could make the whole operation profitable. Trains are far cheaper than trucks when you are dealing with large volumes; there are fewer drivers per weight, and less energy use per weight. Still there are logistical issues to making this work, and you want to move away from having many post men handling individual sacks, I think. There are logistical advantages to on-loading and off-loading much larger packages and to the use of a system of standard sizes on a moving conveyor.

How would a revised mail service work? I’d suggest using a version of intermodal logistics. Currently this route consists of 20 stops including the first and last, Chicago and New Orleans. This suggests an average distance between stops of 49 Miles. Until the mid 70s, , mail would be dropped off and picked up at every stop, with hand sorting onboard and some additional on-off done on-the-fly using sacks and hooks, see picture above. For a modern version, I would suggest the same number of passenger stops, but fewer mail pick ups and drop offs, perhaps only 1/3 as many. These would be larger weight, a ton or more, with no hand sorting. I’d suggest mail drop offs and pick ups every 155 miles or so, and only of intermodal containers or pods: ten to 40 foot lengths. These containers plus their contents would weigh between 2,500 and 25,000 pounds each. They would travel on flatcars at the rear of the passenger cars, and contain first class and priority mail only. Otherwise, what are you getting for the extra cost?

The city of New Orleans would still leave Chicago with six passenger cars, but now these would be followed by eight to ten flatcars holding six or more containers. They’d drop off one of the containers at a stop around the 150 mile mark, likely Champaign Urbana, and pick up five or so more (they’d now have ten). Champaign Urbana is a major east-west intermodal stop, by the way. I’d suggest the use of six or more heavy forklifts to speed the process. At the next mail-stop, Centralia, two containers might come off and four or more might come on. Centralia is near St. Louis, itself a major rail hub for trains going west. See map below. The next mail stop might be Memphis. Though it’s not shown as such, Memphis is a major east-west rail hub; it’s a hub for freight. A stripped down mail-stop version of passenger train mail like this seems quite do-able — to me at least. It could be quite profitable, too.

Amtrak Passenger rail map. The city of New Orleans is the dark blue line going north-south in the middle of the map.

Intermodal, flat-bed trucks would take the mail to sorting locations, and from there to distribution points. To speed things, the containers might hold pre-sorted sacks of mail. Intermodal trucks might also carry some full containers east and west e.g. from Centralia to St. Louis, and some full flatcars could be switched on and off too. Full cars could be switched at the end, in New Orleans for travel east and west, or in the middle. There is a line about “Changing cars in Memphis Tennessee.” I imagine this relates to full carloads of mail joining or leaving the train in Memphis. Some of these full intermodal containers could take priority mail east and west. One day mail to Atlanta, and Houston would be nice. California in two days. That could be a money maker.

At this point, I would like to mention “super-fast” rail. The top speeds of these TGV’s “Transports of Grande Vitess” are in the range of 160 mph (265 km/hr) but the average speeds are lower because of curves and the need to stop. The average speeds are roughly 125 mph on the major routes in Europe, but they require special rails and rail beds. My sense is that this sort of special-use improvement is not worth the cost for US rail traffic. While 60 -90 mph can be handled on the same rails that carry freight, the need for dedicated track comes with a doubling of land and maintenance costs. And what do you have when you have it? The bullet rail is still less than half as fast as air travel. At an average speed of 125 mph, the trip between Chicago and New Orleans would take seven hours. For business travelers, this is not an attractive alternative to a two hour flight, and it is not well suited for intermodal mail. The fuel costs are unlikely to be lower than air travel, and there is no easy way to put mail on or off a TGV. Mail en-route would slow the 125 mph speed further, and the use of intermodal containers would dramatically increase the drag and fuel cost. Air travel has less drag because air density is lower at high altitude.

Meanwhile, at 60 mph average speeds, train travel can be quite profitable. Energy use is 1/4 as high at 60 mph average as at 120 mph. An increase of average speed to 60 mph would barely raise the energy use compared to TGV, but it would shorten the trip by five hours. The new, 15 hour version of “The City of New Orleans” would not be competitive for business travel, but it would be attractive for tourists, and certainly for mail. Having fewer hours of conductor/ engineer time would save personnel costs, and the extra ridership should allow the price to stay as it is, $135 one-way. A tourist might easily spend $135 for this overnight trip: leaving Chicago after dinner and arriving at noon the next day. This is far nicer than arriving at 5:00 PM, “when the day is done.”

Robert Buxbaum, June 21, 2019. One summer during graduate school, I worked in the mail room of a bank, stamping envelopes and sorting them by zip code into rubber-band tied bundles. The system I propose here is a larger-scale version of that, with pre-sorted mail bags replacing the rubber bands, and intermodal containers replacing the sacks we put them in.

How to avoid wet basements

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

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

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

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

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

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

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

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

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

Robert Buxbaum, June 13, 2019

How tall could you make a skyscraper?

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

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

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

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

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

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

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

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

A cone is a better shape for a very tall tower, and it is the shape chosen for “the shard”, the second tallest building in Europe, but it’s not the ideal shape. The ideal, as we’ll see, is something like the Eiffel tower.

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

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

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

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

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

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

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

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

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

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

dA/dΗ = 1/σ dW/dH.

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

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

dA/A = 5.55 x 10-6 dH,

∫dA/A = ∫5.55 x 10-6 dH,

ln (Abase/Atop) = 5.55 x 10-6 ∆H,

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

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

dA/dH = 4√Abase.  But since

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

5.55 x 10-6 √Abase = 4.

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

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

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

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

Nimrod examining the tower, Peter Breugel

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

Robert Buxbaum, June 3, 2019.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

How long could you make a suspension bridge?

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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.

The Japanese diet, a recipe for stomach cancer.

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Japan has the highest life expectancy in the world, an average about 84.1 years, compared to 78.6 years for the US. That difference is used to suggest that the Japanese diet must be far healthier than the American. We should all drink green tea and eat such: rice with seaweed and raw or smoked fish. Let me begin by saying that correlation does not imply causation, and go further to say that, to the extent that correlation suggests causation, the Japanese diet seems worse. It seems to me that the quantity of food (and some other things) are responsible for Americans have a shorter life-span than Japanese, the quality our diet does not appear to be the problem. That is, Americans eat too much, but what we eat is actually healthier than what the Japanese eat.

Top 15 causes of death in Japan and the US in order of Japanese relevance.

Top 15 causes of death in Japan and the US in order of Japanese relevance.

Let’s look at top 15 causes of deaths in Japan and the US in order of significance for Japan (2016). The top cause of disease death is the same for Japan and the US: it’s heart disease. Per-capita, 14.5% of Japanese people die of this, and 20.9% of Americans. I suspect the reason that we have more heart disease is that we are more overweight, but the difference is not by that much currently. The Japanese are getting fatter. Similarly, we exceed the Japanese in lung cancer deaths (not by that much) a hold-over of smoking, and by liver disease (not by that much either), a holdover of drinking, I suspect.

Japan exceeds the US in Stroke death (emotional pressure?) and suicide (emotional pressure?) and influenza deaths (climate-related?). The emotional pressure is not something we’d want to emulate. The Japanese work long hours, and face enormous social pressure to look prosperous, even when they are not. There is a male-female imbalance in Japan that is a likely part of the emotional pressure. There is a similar imbalance in China, and a worse one in Qatar. I would expect to see social problems in both in the near future. So far, the Japanese deal with this by alcoholism, something that shows up as liver cancer and cirrhosis. I expect the same in China and Qatar, but have little direct data.

Returning to diet, Japan has more far more stomach cancer deaths than the US; it’s a margin of nine to one. It’s the number 5 killer in Japan, taking 5.08% of Japanese, but only 0.57% of Americans. I suspect the difference is the Japanese love of smoked and raw fish. Other diet-related diseases tell the same story. Japan has double our rate of Colon-rectal cancers, and higher rates of kidney disease, pancreatic cancer, and liver cancer. The conclusion that I draw is that green tea and sushi are not as healthy as you might think. The Japanese would do well to switch the Trump staples of burgers, pizza, fries, and diet coke.

The three horsemen of the US death-toll: Automobiles, firearms, and poisoning (drugs). 2008 data.

The three horsemen of the US death-toll: Automobiles, firearms, and poisoning (drugs). 2008 data.

At this point you can ask why our lives are so much shorter than the Japanese, on average. The difference in smoking and weight-related diseases are significant but explain only part of the story. There is also guns. About 0.7% of Americans are killed by guns, compared to 0.07% of Japanese. Still, guns give Americans a not-unjustified sense of safety from worse crime. Then there is traffic death, 1.5% in the US vs 0.5% in Japan. But the biggest single reason that Americans live shorter lives  is drugs. Drugs kill about 1.5% of Americans, but mostly the young and middle ages. They show up in US death statistics mostly as over-dose and unintentional poisoning (overdose deaths), but also contribute to many other problems like dementia in the old. Drugs and poisoning do not shown on the chart above, because the rate of both is insignificant in Japan, but it is the single main cause of US death in middle age Americans.

The king of the killer drugs are the opioids, a problem that was bad in the 60s, the days of Mother’s Little helper, but that have gotten dramatically worse in the last 20 years as the chart above shows. Often it is a doctor who gets us hooked on the opioids. The doctor may think it’s a favor to us to keep us from pain, but it’s also a favor to him since the drug companies give kickbacks. Often people manage to become un-hooked, but then some doctor comes by and re-hooks us up. Unlike LSD or cocaine, opioid drugs strike women and men equally. It is the single major reason we live 5 1/2 years shorter than the Japanese, with a life-span that is shrinking.

Drug overuse seems like the most serious health problem Americans face, and we seem intent on ignoring it. The other major causes of death are declining, but drug-death numbers keep rising. By 2007, more people died of drugs than guns, and nearly as many as from automobile accidents. It’s passed automobile accidents since then. A first suggestion here: do not elect any politician who has taken significant money from the drug companies. A second suggestion: avoid the Japanese diet.

Robert Buxbaum, April 28, 2019.

Qatar, unbalanced but stable

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Doha Airport, Qatar.

Doha Airport, Qatar.

I visited Qatar twice this month, just passing through and only visited in the airport, but there were several things that so impressed me that I had to write. What impressed me most was not so much the size and richness of the airport, but the clothes of the locals. All of the local men wore the same, very sharp robes: blindingly white, long sleeved, and floor-length. They’re called Thobes. While other nations wear something similar. Here, every one was unwrinkled, and unstained. They all looked new, with no signs they’d ever been washed. Some were worn with cuff-links (gold), and most had a pen sticking out of the breast pocket (gold). White pants peak from underneath and a headress usually sits on the head. It’s a really dramatic look, like seeing dozens of Ricardo Montaubans of Fantasy Island in one place. Local women and children were these too, but I found the thobes so dramatic that the women and children disappeared from my mind-space almost immediately. There is a local woman in the picture above, but you hardly notice.

Not everyone wears the thobes. There are lots of stores filled with gold and technology, beer and coffee, and these are maned by non-locals, Moslems mostly, almost all men. The non-locals wear western garb, not particularly sharp; none wear thobes of any sort. Some months ago, I wrote that China had severe imbalance and speculated that it was ripe for revolution. As it happens the large number of foreign worker means that Qatar is far more unbalanced. To some extent this is shown by the male-female population pyramid below.

Qatar demographic pyramid. Vastly more males than females, mostly foreign workers.

Qatar demographic pyramid. The imbalance is caused by the presence of vastly more male than female foreign workers.

Qatar is a country of 2,500,000 residents, of whom 310,000 are locals — citizens and permanent residents. The rest are foreign workers; long term inhabitants without permanent residency or citizenship. They make up 85% of the population. They are  recruited from poor, English-speaking Muslim countries mostly: Egypt, Malaysia, Tunisia. They do all the work, as best I could tell. I saw no one who looked like a local working, male or female.

Foreign workers have very few rights, but don’t seem unhappy. There is no right to unionize, and not even the right to roam around the country. For the most part, they live in employer-owned housing, and are transported back and forth to work in employer vans. They sign up for year-long contracts, and at the end of the year, they have the choice to re-up or leave. Up a year ago, foreign workers could not become permanent residents. As of last year, the Emir’s order 10 authorized permanent residency status for as many as 100 foreign workers who had sufficient means, had been in Qatar for 10 to 20 years (depending on whether they were born there), had stayed out of trouble, and who otherwise were considered desirable. It’s a step.

I suspect that the foreign workers feel lucky to have good pay, decent hours, and a clean bed. Then again, the workers are recruited for positive outlook. And the ones I saw might have had more rights than most. The airport is part of the Umm Al Houl, free enterprise zone. These are areas of Qatar where westerners and their vices like alcohol are tolerated and welcome.

Qatar natural gas production. Natural gas provides 90% of the country's income as best I can tell.

Qatar natural gas production. Natural gas provides 90% of the country’s income as best I can tell. That’s half the GDP almost, the rest of the GDP is Qataris spending the money

There are three “free enterprise zones” in Qatar; the name for the one near the airport, “Al Houl” interestingly enough means “bird trap”. What’s going on with them, as best I can tell, is diversification. Qatar is the worlds second largest exporter of natural gas, with most going to Europe, and a significant portion to India and China. But the gas will run out eventually. They are trying to supplant this income with tourism, industry and transport: running a major airline, a bustling, air hub, and tourist hotels. The airline is only marginally profitable, and though I didn’t see the hotels, I imagine they are luxurious and marginally profitable too. Saudi Arabia, next door, is trying to diversify the same ways, aiming to control west-east, air-traffic via Emirates air.

The GDP of Qatar is $191 B as of last year at the going exchange, and over $450 B at price parity. That suggests a few things. For one that the Qatari currency is undervalued. It also suggests a per-capita GDP of at least $76,400, or perhaps of $616,000 or higher depending on how you count buying power and foreign workers. This money buys a nice lifestyle, if not republican freedoms.  In terms of government, Qatar is a real monarchy, Emir Hamad bin Khalifa al-Thani’s is an absolute ruler who came to power the traditional way: he overthrew his father. Similar to this, his father, Khalifa al-Thani, came to power by overthrowing his cousin. Supporting the Emir’s rule, there is an Advisory Council. The 35 ministers are mostly relatives, and as in North Korea, it has only advisory power. The Prime Minister and Minister of Foreign Affairs is Sheikh Hamad bin Jasim bin Jabir al-Thani; the Deputy Prime Minister is Abdallah Al-Thani. The Economy and Commerce minister is Fahd Al-Thani, and the Communications and Transport minister is Ahmad Al-Thani. Nasir al-Thani heads Cabinet Affairs; Hamad al-Thani is the Secretary of State, and the Governor of the Central Bank is Abdallah bin Saud al-Thani.

Qatar main mosque. Residents stand out from the foreign workers.

Qatar main mosque. Residents stand out from the foreign workers.

My sense was that Qatar was the Disneyland version of Islam. Life in the Qatari free zones resembled normal Islamic life the way that Main Street of Disneyland resembles an actual main street in the US. Every citizen is well dress and rich without having to work. Western visitors are welcome, and not forced to follow the local customs with vices in their own zones. And the state supports all ecological and left-wing causes except for unionization. It’s anti Israel, pro revolution (elsewhere of course) and virulently against petroleum production in all counties outside of Qatar. Al Jazeera, the Emir’s left-leaning news agency, spreads money and influence world-wide. Left-flavored news is presented with high-quality graphics, and different versions of the news story published in different languages. The Emir acknowledges that Al Jazeera is a money-losing propaganda agency, but as with Disneyland, most people seem happy to live the fiction.

Qatari woman and shop. They blend into the scenery compared to the resplendent men

Qatari woman and shop. They blend into the scenery compared to the resplendent men

The local Qataris seem happy with their lot, as best I can tell. The next world soccer tournament will be held in Qatar, 2022, and Qatari’s are excited, as best I can tell. There is a lot of building going on, some for the world cup, the rest for general tourism and the free enterprise zones. The free enterprise zones may catch on, but there is a cold war going on with Saudi Arabia, and the Saudi’s are doing what they can to pour cold water on the programs. So far Qatar seems to be winning the propaganda war at home and abroad. Its people are happy, it shows a beautiful, progressive face to the west, and it seems to have the majority of the middle east travel. Stable but for how long?

Robert Buxbaum April 15, 2019. As I side note, I just bought a Qatari Thobe.

Speed traps penalize the poor

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On a street corner about 1/4 mile from my house, at the intersection of the two busiest of the local streets, in the center-median of the street, is parked a police car. He’s there, about 18 hours a day, looking to give out tickets. The cross-street that this officer watches is where drivers get off the highway. In theory, they should instantly go from 65 mph on the highway to 35 mph now. Very few people do. The officer does not ticket every car, by the way, but seems to target those of poor people from outside the city limits. The only time ai was ticketed, I was driving a broken-down car while mine was in the shop. As best I can tell, he choose cars for revenue, not for safety. It’s a speed trap. It’s appalling. And our city isn’t alone in having one.

Speed traps are an annoyance to rich, local folk who sometimes get ticketed, but they’re a disaster for the poor. Poor people are targeted, and these people don’t have any savings. They don’t have the means to pay a suddenly imposed bill of $150 or more. Meanwhile, the speed-trap officer is incentivized to increase revenue and look for other violations: expired registrations or insurance, seat-belt violations, open alcohol, unpaid tickets. Double and triple fines are handed out, and sometimes the car is impounded. A poor driver is often left without any legal way to get to work, to earn money to pay the fines. Police officers behave this way because they are evaluated based on the revenue they generate, based on the number of tickets they write. It’s a horrible situation, especially for the poor

Speed traps to little and cost much.

An article on the effect of speed traps. It appears they do little good and cause much pain, especially to the poor. Here is a link to the whole article.

The article above looks at the impact of speed traps on poor people. The damage is extreme. The folks targeted are often black, barely holding it together financially. They are generally not in a position to pay $150 for “impeding traffic,” and even less in a position to deal with having their car impounded. How are they supposed to pay the bill? And yet they are told they are lucky to have been given this ticket — impeding traffic, a ticket with no “points.” But they are not lucky. They are victims. Tickets with no points is are money generators, and many poor people realize it. If they were to get a speeding ticket, they would have the opportunity to void the penalty by going to traffic school. With a ticket for impeding traffic, there is no school option. Revenue stays local, mostly in that police precinct. Poor people know it, and they don’t like it. I don’t either. After a while, poor people cease to trust the police, or to even speak to them.

In what world should you pay $150 for impeding traffic, by the way? In what world should the police be taken from their main job protecting the people and turned into a revenue arm for the city? I’d like to see this crazy cycle ended. The first steps, I think, are to end speed traps, and to limit the incentive for giving minor tickets, like impeding traffic. As it is we have too many people in jail and too many harsh penalties. 

Robert Buxbaum, April 10, 2019. I ran for water commissioner in 2016, and may run again in 2020.

Let’s visit an earth-like planet: Trappist-1d

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According to Star Trek, Vulcans and Humans meet for the first time on April 5, 2063, near the town of Bozeman, Montana. It seems that Vulcan is a relatively nearby, earth-like planet with strongly humanoid inhabitants. It’s worthwhile to speculate why they are humanoid (alternatively, how likely is it that they are), and also worthwhile to figure out which planets we’d like to visit assuming we’re the ones who do the visiting.

First things first: It’s always assumed that life evolved on earth from scratch, as it were, but it is reasonably plausible that life was seeded here by some space-traveling species. Perhaps they came, looked around and left behind (intentionally or not) some blue-green algae, or perhaps some more advanced cells, or an insect or two. A billion or so years later, we’ve evolved into something that is reasonably similar to the visiting life-form. Alternately, perhaps we’d like to do the exploring, and even perhaps the settling. The Israelis are in the process of showing that low-cost space travel is a thing. Where do we want to go this century?

As it happens we know there are thousands of stars with planets nearby, but only one that we know that has reasonably earth-like planets reasonably near. This one planet circling star is Trappist-1, or more properly Trappist 1A. We don’t know which of the seven planets that orbit Trappist-1A is most earth-like, but we do know that there are at least seven planets, that they are all roughly earth size, that several have earth-like temperatures, and that all of these have water. We know all of this because the planetary paths of this star are aligned so that seven planets cross the star as seen from earth. We know their distances from their orbital times, and we know the latter from the shadows made as the planets transit. The radiation spectrum tells us there is water.

Trappist 1A is smaller than the sun, and colder than the sun, and 1 billion years older. It’s what is known as an ultra-cool dwarf. I’d be an ultra cool dwarf too, but I’m too tall. We can estimate the mass of the star and can measure its brightness. We then can calculate the temperatures on the planets based their distance from the star, something we determine as follows:

The gravitational force of a star, mass M, on a planet of mass, m,  is MmG/r2, where G is the gravitational constant, and r is the distance from the star to the planet. Since force = mass times acceleration, and the acceleration of a circular orbit is v2/r, we can say that, for these orbits (they look circular),

MmG/r2 = mv2/r = mω2r.

Here, v is the velocity of the planet and ω is its rotational velocity, ω = v/r. Eliminating m, we find that

r3 = MG/ω2.

Since we know G and ω, and we can estimate M (it’s 0.006 solar masses, we think), we have a can make good estimates of the distances of all seven planets from their various rotation speeds around the star, ω. We find that all of these planets are much closer to their star than we are to ours, so the their years are only a few days or weeks long.

We know that three planets have a temperatures reasonably close to earths, and we know that these three also have water based on observation of the absorption of light from their atmosphere as they pass in front of their star. To tell the temperature, we use our knowledge of how bright the star is (0.0052 times Sol), and our knowledge of the distance. As best we can tell, the following three of the Trappist-1 planets should have liquid surface water: Trappist 1c, d and e, the 2nd, 3rd and 4th planets from the star. With three planets to choose from, we can be fairly sure that at least one will be inhabitable by man somewhere in the planet.

The seven orbital times are in small-number ratios, suggesting that the orbits are linked into a so-called Laplace resonance-chain. For every two orbits of the outermost planet, the next one in completes three orbits, the next one completes four, followed by 6, 9 ,15, and 24. The simple whole number relationships between the periods are similar to the ratios between musical notes that produce pleasant and harmonic sounds as I discussed here. In the case of planets, resonant ratios keep the system stable. The most earth-like of the Trappist-1 planets is likely Trappist-1d, the third planet from the star. It’s iron-core, like earth, with water and a radius 1.043 times earth’s. It has an estimated average temperature of 19°C or 66°F. If there is oxygen, and if there is life there could well be, this planet will be very, very earth-like.

The temperature of the planet one in from this, Trappist-1c, is much warmer, we think on average, 62°C (143°F). Still, this is cool enough to have liquid water, and some plants live in volcanic pools on earth that are warmer than this. Besides this is an average, and we might the planet quite comfortable at the poles. The average temperature of the planet one out from this, Trappist-1e, is ice cold, -27°C (-17°F), an ice planet, it seems. Still, life can find a way. There is life on the poles of earth, and perhaps the plant was once warmer. Thus, any of these three might be the home to life, even humanoid life, or three-eyed, green men.

Visiting Trappist-1A won’t be easy, but it won’t be out-of hand impossible. The system is located about 39 light years away, which is far, but we already have a space ship heading out of the solar system, and we are developing better, and cheaper options all the time. The Israeli’s have a low cost, rocket heading to the moon. That is part of the minimal technology we’d want to visit a nearby star. You’d want to add enough rocket power to reach relativistic speeds. For a typical rocket this requires a fuel whose latent energy is on the order mc2. That turns out to be about 1 GeV/atomic mass. The only fuel that has such high power density is matter-antimatter annihilation, a propulsion system that might have time-reversal issues. A better option, I’d suggest is ion-propulsion with hydrogen atoms taken in during the journey, and ejected behind the rocket at 100 MeV energies by a cyclotron or bevatron. This system should work if the energy for the cyclotron comes from solar power. Perhaps this is the ion-drive of Star-Trek fame. To meet the Star-Trek’s made-up history, we’d have to meet up by April, 2063: forty-four years from now. If we leave today and reach near light speed by constant acceleration for a few of years, we could get there by then, but only as time is measured on the space-ship. At high speeds, time moves slower and space shrinks.

This planetary system is named Trappist-1 after the telescope used to discover it. It was the first system discovered by the 24 inch, 60 cm aperture, TRAnsiting Planets and PlanetesImals Small Telescope. This telescope is operated by The University of Liége, Belgium, and is located in Morocco. The reason most people have not heard of this work, I think, has to do with it being European science. Our news media does an awful job covering science, in my opinion, and a worse job covering Europe, or most anything outside the US. Finally, like the Israeli moon shot, this is a low-budget project, the work to date cost less than €2 million, or about US $2.3 million. Our media seems committed to the idea that only billions of dollars (or trillions) will do anything, and that the only people worth discussing are politicians. NASA’s budget today is about $6 billion, and its existence is barely mentioned.

The Trappist system appears to be about 1 billion years older than ours, by the way, so life there might be more advanced than ours, or it might have died out. And, for all we know, we’ll discover that the Trappist folks discover space travel, went on to colonize earth, and then died out. The star is located, just about exactly on the ecliptic, in the constellation Aquarius. This is an astrological sign associated with an expansion of human consciousness, and a revelation of truths. Let us hope that, in visiting Trappist, “peace will guide the planets and love will steer the stars”.

Robert Buxbaum, April 3, 2019. Science sources are: http://www.trappist.one. I was alerted to this star’s existence by an article in the Irish Times.