Deriving Trump’s tariff formula, and correcting it.

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We have a trade imbalance with many countries, it causes a loss of American jobs, and a transfer of currency abroad. This imbalance is not all negative, of course, it provides US consumers with cheaper consumer goods. Trump would like to eliminate the imbalance using tariffs. He hopes that this will create jobs, and that the money raised will help balance the US budget. He’s already moved to end income taxes on tips expecting to replace that tax with tariff income. Trump claims that the tariffs are not inflationary compared to current the tax system that he claims has been hacked by the elites. In past essays, I’ve discussed the pluses and minuses of tariffs here, and here. Now I’d now like to derive the formula Trump uses, see below. The proposed tariff for any country or region, i, he calls ∆τi.

In the equation at left, χi = our exports to country, i. Similarly, mi = our imports from that country. The difference between these two is our trade imbalance, something he’d like to set to zero. There are two other greek terms that I will discuss, ε and φ. These are the elasticity of elasticity of consumption to price, and the elasticity of price to tariffs. Trump uses an asterix here to indicate multiplication. I will use a, more normal, “dot” symbol, •, to the same purpose. For most countries, he takes the two elasticities to cancel to 2, and produces a chart.

Let’s say that the dollar amount we currently buy from some country, i, = mi  = ni • Pi, where ni is the number of items bought from this country, and Pi is the average price. The intended effect of tariffs is to reduce mi  by raising Pi, the price consumers pay for goods from that country. This increase is certainly inflationary in terms of the consumer: a consumer of French wine will pay more per bottle unless he/she switches to US wine. Typically this price rise is not inflationary in terms of the country as a whole, because the producer likely swallows some of the tariff, so for the country as a whole, we pay less per bottle of French wine. The customer does not see that, but it’s worth noting. Trump sees things this way.

Back to the formula, we need to figure out how much the price will go up and how much sales will change. Economists have elasticity numbers for both these relations, denoted φ and ε. We can say that, for any country, I, the rise in the price of the average product is ∆Pi = Pi•∆τi •φ. Where Pi is the original price, ∆τi is the tariff, and φ is the fraction of this tariff that gets passed on to the consumer. A typical value is φ= 1/2 though some claim less. Assuming φ= 1/2 , if we add a 20%=∆τi tariff, as on on French wine, the consumer price will rise by 10%, a change that will cause him/her to buy less.

How much less will the consumer buy? That’s determined by the elasticity of sales, ε. This is the fractional decrease in the number items bought per fractional rise in the price. In math terms, ∆ni /ni = -ε∆Pi/Pi where ε is the elasticity. Now, since ∆Pi = Pi•∆τi •φ, we find that:

∆ni = -ni•ε•∆τi •φ.

There is evidence to suggest that, for the average product, ε equals about 2, and also evidence that it’s 4. Trump prefers 4, and uses it for his calculations. I prefer 2, and will get nearly the same tariffs at the end. Whatever our preferred value for ε, our next step is to use the following approximation, accurate for small ∆(mi);

∆mi  = ∆(ni•Pi) = ∆ni•Pi, +  ni•∆Pi . 

Trump seems to ignore the second term. Perhaps because it can either be positive or negative, as I’d mentioned above, depending on whether you look at things in terms of the customer or of the US as a whole. I’ll keep it in, writing this term in lighter text. In the end I will calculate a fairly similar tariff to Trump:

∆mi = -ni•ε•∆τi •φ•Pi  + ni•Pi•∆τi •φ.

Rearranging the above, and recalling that ni•Pi• =mi, you can find the appropriate tariff to eliminate the trade imbalance.

∆τi =   -∆mi  /(ε • φ• mi  + φ•mi) .

To make the trade imbalance go away, you need -∆mi = χi-mi . Thus,

∆τi =   χi-mi   /(ε • φ • mi  + φ•mi)

This is the Trump formula with an extra term in light text. If you ignore that term and use the values Trump prefers, ε =4 and φ=1/2, you get the exact values of the tariffs he listed on the chart for most countries — those with positive trade imbalances.

∆τi =   χi-mi / 2 mi  

Now, I’d like to put back in the missing term, and use the (better) values, values I would trust, ε =2 and φ=1/2. Using those values, I find the tariff should be slightly higher.

∆τi =   χi-mi / 3/2 mi  .

I should note that some countries are creating to these trips by raising their own tariffs, and some are lowering theirs. This will cause a change in the imbalance of trade, and Trump will have to change the tariff schedule periodically to keep up.

Robert Buxbaum, April 10, 2025.

The CPAP, not totally useless.

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CPAP machines (Continuous Positive Airway Pressure machines) are very commonly prescribed to prevent sleep apnea. They were originally prescribed to prevent heart attack, and despite minimal evidence that they help, they are still paid for by most insurance, including medicare. Sleep apnea is associated with snoring and with being overweight. The theory, supported by minimal evidence, was that stopping the apnea would prevent heart attack.

My C-PAP/ APAP. shown with distilled water

Five years ago, I found myself among those prescribed. CPAP, and found no evidence they extended life, or prevented any heart problem. I wrote this blog post, explaining what I thought was going on. I suspected some health risks, and found no obvious sleep benefit; I felt claustrophobic and woke with sniffles. I quickly stopped using the device.

Last month I retried my CPAP, now with a better fitting mask (nose only) and better humidification. I now find sleep benefits and no sniffles, but still see no sign of health benefits. “Even among participants with good CPAP adherence there was no significant reduction in cardiovascular risk in the two largest trials.2,3 ” There also appear to be some bad side effects. If the pressures are too high, the CPAP can cause inflammation and micro-tears in the lung. This is the same problem that killed people on ventilators during COVID. CPAP users show significantly increased inflammation markers, with higher inflammation the higher the pressure used. Lower pressure settings seems to result in fewer heart problems, too, see figure below. The number of cumulative adverse heart-events is lower for patients, randomly selected, who used a pressure below 7 cm H2O (lower than 0.1 psi). Most events happen in the first few months, and don’t know why. The researchers do not comment on this.

From the Lancet, Y. Peter et al, Volume 101, 105015, March 2024, with with results adjusted for age, sex, and BMI. Pressures below ≤7 cmH2O show fewer events. Most CPAPs are set to higher pressures, about 10cmH2O

I suspect that heart attack and stroke are mostly driven by BMI, lack of exercise, and by eating too much of the wrong foods (e.g. waffles, see here). I suspect the CPAP does nothing for this beyond improved sleep, and that, at the current pressure settings, it may be harmful.The health risks might have put me off the machine, except I like getting better sleep.

I figured I could try decreasing the pressure, hoping to get good sleep with fewer lung risks. I can’t reduce usage because healthcare pays for supplies only if you use the device 4+ hours per night, tracking your usage over the internet to make sure. I discovered that my device, an AirSense 10, was set to deliver pressures between 5 and 15 cmH2O resulting in an average delivery pressure of 10.2 cmH2O. I decreased the range to 4.6-12.4 cm, then further, to 5-9 cmH2O. So far, the machine shows no reduction in average pressure(?!) but my sleep is OK.

On a national level, I suspect that this device should not be prescribed as often as it is, and suspect that the set pressures should be lower. There is a replication crisis in science; drug statistics tend to be bogus, and food results too. If it were me I’d look for CPAP research to show real health benefits, I’d use linear regression with an r-squared test for significance, as here.

Robert Buxbaum, March 30, 2025.

Sayings of Zen Judaism

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All of the following bits of Zen-like wisdom are derived from David M. Bader’s book, “Zen Judaism”. Some of these (in italics) have been modified by me. I’ve posted several other examples of zen-wisdom/ humor, e.g this. Most every piece of real wisdom appears as a joke, IMHO.

I bought a copy, then modified some as I saw fit. He’s holding a bagel.

If you meet the Buddha on the road, show him pictures of the grandchildren.

One may take a vow of fasting, or of celibacy, a vow of silence or to avoid sleep is out of the question.

Wherever you go, there you are.  Your luggage is another story.

Be here now, be someplace else later; is that so complicated?

Accept misfortune.  Do not wish for perfect health, or a life without problems. What would you talk about?

Drink tea and nourish life; with the first sip, joy; with the second sip, satisfaction; with the third sip, Danish.

Self abnegation is not easy. It takes much effort, and then what have you got?

The words, “there is no self,” can be terrifying. Still they’re not as bad as, “may you grow like an onion with your head in the ground.”

Bring the Buddha to your table, and on Passover, the prophet Elijah. That’s about as many invisible guests as anyone needs.

If there is no self, whose arthritis is this?

The journey of a thousand miles begins with a single Oy.

The world does not speak. It does not blame or take sides. The world has no expectations, and it demands nothing of others. The world is not Jewish.

Be patient and achieve all things. Be impatient and achieve all things faster.

Be aware of your body. Be aware of your perceptions.  Keep in mind that not every physical sensation is a symptom of a terminal illness.

To find the Buddha, look within. Deep inside you are ten thousand flowers. Each flower blossoms ten thousand times. Each blossom has ten thousand petals.
You might want to see a specialist.

Seek not the outer enticements. Dwell not in the inner strife. Try to find a nice place in the suburbs with good schools.

Practice a livelihood that does not harm yourself or others, choose an occupation furthering love and compassion. Ask about the health plan, too. No freelancing.

Let go of pride, ego, and opinions. Admit your error and forgive those of others. Relinquishment will lead to calm and healing in your relationships. If that doesn’t work, try small claims court.

For the wary Pilgrim, a Zen poem: thousands reach the gateless gate from many paths; once through, they dwell serenely between heaven and earth; enjoying golf, line dancing, Yiddish lessons, and aquacise. Come see our model units at Century Village.

Breathe in. Breathe out. Breathe in. Breathe out. Do this and achieve peace. Forget this and attaining Enlightenment will be the least of your problems.

Go then and wander for the good of the many, for the welfare of the many, out of compassion for the world. Teach what is good in the beginning, good in the middle, and good in the end. Don’t forget to write, and always wear clean underwear. You never know when you could end up in the emergency room.

Robert Buxbaum, March 24, 2025. Other books by David Bader include “Haikus for jews”, “The book of Murray”, and “How to be an extremely Reform Jew”. Bader claims to have achieved complete and perfect emptiness, although two hours later he often feels full again.

The second shortest math paper explained, Fermat’s last theorem conjecture.

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Shown below is the second shortest published math paper; it’s the shortest published math paper, except for this one. This paper relates to an extension to Fermat’s last theorem. That’s well known math, though I think a few words of background would help the educated lay reader.

By way of background, Fermat’s last theorem states that there is no set of integers for which An + Bn = Qn, where n is an integer larger than 2. Thus, there is no set where A3 + B3 = Q3 or A5 + B5 = Q5, etc. This theorem was really a conjecture until recently though Fermat claimed to have proven it in 1695.

The Euler conjecture of the title here, is related to Fermat’s conjecture/theorum: Either conjectured that the smallest collections of A, B, C, D.., whose power to the n, summed, will equal some whole number to the power n, Qn , must have at least as many components (A,B,C,D,..) as the exponent value, n. Thus, while you might find a set of five numbers, A, B, C, D, E where A5 + B5 + C5 + D5 + E5 = Q5, you can’t find a set of four numbers where A5 + B5 + C5 + D5 = Q5. The paper above disproves this conjecture in a most clear way; it shows a counter-example where A5 + B5 + C5 + D5 = Q5.

This is, in a sense, the ideal math paper: clear, short, important, and true. For background to this conjecture, the authors merely reference a page of a math history book.

Robert E. Buxbaum, March 17, 2025. The shortest paper ever is this gem in the journal of psychology.

The shortest published math paper explained, and extended.

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Shown below is the shortest math pater ever published. It appeared in the American Mathematical Monthly, 2004, and would have appeared in a more honored journal if the authors were willing to add more words as an editor requested. You’ll see that the paper itself has only pictures and one sentence with one English word: n2 + 2 can:, I thought I might as well try to explain it because as the editor commented, this is too few words for most readers.

The trick to understanding this at all is that most of the background is in the title, which is in the form of a question. The text of the article is in the form of an answer with the diagrams serving as proof. Even with this insight, you’ll likely need more background, but that’s the start.

Here’s the background: Most folks notice that you can make a big equilateral triangle of side-length n, out of n2 unit subtriangles, that is of subtrangles where the side lengths =1. For example, to make an equilateral triangle with length 10, requires 100 unit equilateral triangles, n2.

Now the question in the title involves what happens if all these n2 component triangles are made slightly larger, the sides of each becoming 1+ε/n, where ε is some very small amount. The side of the new big triangle is now n+ε. The question in the title now is can you cover this bigger, super triangle with n2+1 unit triangles. The authors provide two, half answers to this question by their drawings, suggesting two different ways that you can cover the bigger super-triangle with n2+2 unit triangles. That would be 102 for the case where you start with 100 unit triangles and expanded each by ε/n.

The first solution is the bottom of figure 1. This shows what happens if you add two more unit triangles to the bottom row of the old super triangle, and squish a bit from the sides so that the top of the new row matches the bottom of the old row. Doing this leaves you with a row that’s n+ε long at the bottom with wings at the top that expand the sides to n+ε as well. The drawing shows that this new row has effective height, 1+ε.

Now, take every other row and push them together slightly from top-down so that the height becomes (1-ε) but the length expands to n(1+ε). Adding rows like this, you’ll be able to cover the entirety of the bottom space of the new, larger super triangle. Notice that the thickness of each line now 1-ε as shown. Use these longer lines to cover the rest of the bigger super triangle. And that’s the end of the paper. Once again you needed n2+2 unit triangles to cover the bigger super-triangle.

An extension to the above paper was discovered since the original paper. It’s shown in the figure below. Here the original requirement of equilateral triangles is relaxed. For highly elongated triangles, you still find that a normal super-triangle requires n2 sub-triangles. But now, from this figure, you see that an expanded super-triangle (each side expanded by 1+ε/n say) can be covered using only n2+1 of the original size subtriangles.

The proof is clear enough that no words are needed. It’s conceivable that the authors could have published this as an even shorter paper, if it were ever published, but it was not. Instead, I saw this extension as a result from a math competition, here. These insights of geometry come from Princeton University, a top notch place where I was a grad student (in engineering). The school has gone somewhat to seed, IMHO, because of political correctness.

There are shorter published papers, BTW, though this was the shortest published math paper. The shortest technical paper ever is this one from the journal of behavioral sciences.

Robert Buxbaum, March 6, 2025. I’d like to add a joke: To make a long story short, I became an editor.

So long to the SS United States, the fastest ocean liner.

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The SS United States is in the process of being towed to its final resting place, on the sea floor near florida, to be a scuba-diving reef. She is the largest ocean liner to be entirely constructed in the United States and was the fastest ocean liner to cross the Atlantic Ocean in either direction, 36 knots or 41 mph average speed. She won the Blue Riband for this on her first voyage, in 1952, and retained that title till today. There was a faster crossing in June, 1990 by the Hoverspeed Great Britain, 36.6 knots, 42.1 mph average speed, but the Hoverspeed was a 76 meter channel catamaran, not an ocean liner.

The SS United States was half-paid for by the US government. Its purpose was fast passenger transport across the Atlantic. The government contributed because it might be used as a troop ship if needed in times of war. In terms of speed, she handily beat the luxurious British liners, Queen Elizabeth and Queen Ann, but the compromises for speed and military use made the SS United States unsuited for use as a luxury cruise ship.

Designed by William Francis Gibbs, one of the greatest ship designers, the high speed was achieved, in part, by making the ship very light. He used aluminum for the entire superstructure, the stuff above water level, making it the largest aluminum construction when built, 1951. Though larger than the Titanic, the United States is thinner and more pointy. Much lighter than the Queen Elizabeth or Queen Ann, she could go as fast backward as the Titanic could forward. The hull is doubled, with fuel stored between the layers as a protection from collisions and canon; the interior is highly compartmentalized too, to make her fairly unsinkable. This was confirmed when she survived a sea collision shortly after launch. Making the ship light on the top made the SS United States stable in wind and rough seas despite its narrow shape. There were two engine sections, divided into four engine rooms, done to increase the chances that the engines would survive an explosion or torpedo attack.

The interior design was American modern, and fire-proof, with few weighty decorations. Furnishings were fiberglass, steel or aluminum, for the most part, see picture below. The red, white, and blue stacks added to the American look. Both are used (recall that there are two engine rooms), and both have aluminum wings. These shield the deck from any sparks that might come out the stacks.

In the end, it was the crossing speed not the comfort level that doomed the SS United States. Even at a top speed of 44.1 mph, crossing the Atlantic took 3+ days. That could not compete with jet planes that travelled at 500 mph. I’ve argued that long range, “high speed” passenger trains make little sense for the same reason. Even at 100+ mph, few Americans will be willing to spend 36 hours traveling from Chicago to Seattle. Fast boats are useful, I think, but only in smaller size foreshorten trips, similar to the Hoverspeed.

5 blade propeller on display at Throg’s neck. Paired with a 4 blade propeller it reduced vibration and wear at high speed.

Also helping it reach the speeds it did, the SS United States benefitted from innovations in the engines and in the propellers. There were four engines, in two engine sections. These were modern, light weight, compact, steam turbines running at high pressures and temperatures: 975°F and 925 psi. Each turbine delivered 60,000 shaft hp to a variable-speed, geared shaft. The inboard propellers had 5 blades and the outboard (end of ship) had four. This difference in blade number was a secret, design innovation that allowed faster speed, without vibration and cavitation. The 5 blade propeller shown on display at left, accelerated the water, while the 4 blade accelerated it faster. At the time, this was secret technology. We now have some better propellers, though no faster ocean liners. The Hoverspeed uses water jet for propulsion, by the way.

Leaving the Delaware River heading to the Gulf of X

On its way to the bottom of the sea, the ship will first stop at MARS. That is not the planet Mars, but at an engineering firm, “Modern American Recycling Services” in Mobile Alabama, on The Gulf of X. There the MARS folks will prepare the ship to sink in an even way, where its supposed to; a way that works for scuba divers.

Robert Buxbaum, February 28, 2025. My sense is there is still room for steam power. I also think the US government should return to investing in US ship-building, especially for double-use, military and commercial, like this one. A new favorite phrase, from Ovid, Metamorphosis: “Omnia mutantur, nihil interit”. Everything changes, but nothing passes away. RIP, old friend.

Waffle house life and cardiac death

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Cardiac death rates vary by a factor of six or more across regions of the US, from very low rates in Arizona, Utah, Washington, about 1/1000/year, to well over 6/1000/year in the US southeast. This is shown in the map below based on CDC data from 2013, mapped by Dr. Robert-J using ArcGIS Pro in 2015, Source here.

The author of this graph humorously(?) overlayed the cardiac death data with yellow dots showing the location of all US waffle houses. I infer from this something that Dr. J. denies: that waffle houses, or waffle eating is a significant contributor to these cardiac deaths. Other possibilities (my own list) include opioids, pollution, low exercise, depression, and poor healthcare. Still, I can’t help thinking that diet is a big contributor.

Here is a more up-to-date map, by county, showing that cardiac deaths still concentrate in the southeast, but now they are joined by Nevada and eastern California. I downloaded this map directly from the CDC, but this time, the map is in terms of Age Adjusted Mortality Rates, that is lives lost per 100,000 persons, relative to some ideal, people living in Minnesota, Colorado, and Massachusetts, I suppose. As before, the red areas are those with a higher cardiac death rates. Why are West Californians healthier and folks in Minnesota and Colorado, perhaps because they exercise more, and exercise is a good thing, but these could also be areas with better healthcare, or fewer opioids. Some cities are healthier, some are worse. Why?.

Things have been getting worse in recent years. From 2019 to 2022, the national Cardio-vascular disease caused AAMR increased by 9.3%. Some of this may be COVID or the COVID vaccine, I suppose, or depression. Men seem to be hit harder than women, with the same regional differences. As shown in the map at right, southeast rural men have a lifespan more than 4 years shorter than the national average, or about 7 years shorter than that for women. And this is on top of their already significantly shorter lifespan compared to other developed countries. There’s no obvious reason.

As a marketing thought, assuming that the cause of cardiac death is that people eat high-carb, high fat meals, then the owners of Waffle House might have noticed, and chosen to build there. If so this would be a case where apparent causation is reversed: the relationship between Waffle houses and death is that Waffle houses were built where people were dying of heart disease. It’s a scary thought, but not unlikely. I’d expect new Waffle houses would appear in mid-Michigan, mid Georgia, northern New Jersey, and NW Indiana. These are places where people will likely like the food and ambiance. I’ve taken a light hearted view here because the alternative is too depressing. These rates are dramatic and horrible. I hope RFK Jr. will help increase US lifespans, but have no great faith in him. Trump gave him two years to show significant improvements.

Robert Buxbaum, February 24, 2025.

Coal and nuclear power, the secret to China’s cheap products

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We’ve become accustomed to buying cheap products from China: items made of glass, plastic, and metal come to the US by the ship-load, approximately $600 B worth last year, the highest from any country. Labor isn’t cheaper in China, certainly not when compared to Mexico or India, nor are the machines that make the products more advanced. What’s behind China’s ability to produce at their low prices is cheap energy—specifically, coal and nuclear-based electricity. While the US and most western countries have shut down coal plants to stop global warming, and have even shut working nuclear reactors for no obvious reason, China has aggressively expanded coal and nuclear energy production. The result? They are the largest single source of CO2, and have some of the lowest electricity prices in the world, Chinese electricity prices are about 1/4 of European, and 2/3 of U.S.

In recent years, the U.S. and Europe have increasingly relied on renewable energy sources like wind and solar. While these can work in certain areas, they require far more land than nuclear or coal, and expensive infrastructure because the power is intermittent, and generally not located close to the customer. The UK and Germany, countries with long periods of cloudy, windless conditions, have switched to solar and wind, leading to soaring electricity prices and a moribund industrial sector. Germany shut down all of its nuclear plants, 17 of them, largely to rely on electricity imported from its neighbors, and coal-fired sources that are far more polluting and unsafe than the nuclear plants they shut. The UK shut 5 nuclear reactors since 2012.

Meanwhile, China continues to build nuclear and coal plants. China is the largest user of coal power, and is planning to build 100 more coal-fired plants this year. Beyond this, China is building nuclear power rectors, including the world’s first 4th generation reactor (a pebble bed design). China has built 20 nuclear plants since 2016, and has 21 under construction. With this massive energy advantage, China produces things at low price for export: appliances, clothes, furniture, metal and plastic goods, all at a fraction of our cost. By selling us the things we used to make, China imports our jobs and exports pollution from their coal plants.

Many people instinctively understand that outsourcing production to China is harmful to both US employment and world pollution. Yet, until recently, US politicians encouraged this transfer through trade agreements like the TPP. Politicians bow to high-spending importers, and to environmental activists. It seems we prefer cheap goods to employment, and we’re OK with pollution so long as we don’t see the pollution being made. But, by outsourcing production, we’ve also outsourced control over critical industries, we’ve limited out ability to innovate, and we make ourselves dependent on China. Likely, that was part of China’s intent.

Russia has followed a similar path, keeping electricity costs mostly through low through coal, but also nuclear power, exporting their goods mostly to the EU. Before the Ukraine war, Germany in particular, relied on Russian gas, electricity, and fertilizer, products of Russian cheap power. By cutting off those energy, Germany has dealt a severe blow to its economy. Not everyone is happy.

Transfer of electricity, GWh, between European countries, 2023. Energy is most expensive in importer-nations, and GDP growth is slowest.

The incoming Trump administration has decide that, to compete with China’s manufacturing power, we need to develop our own through tariffs, and we need to increase our energy production. Tariffs can help balance the budget, and bring production back home, but without more energy, our industries will struggle to produce. I’m generally in support of this.

US production is more energy efficient than Chinese production, and thus less polluting. Besides, making things here saves on transport, provides jobs, and helps to build US technology for the future. I’m happy to see us start to build more nuclear power reactors, and restart some old plants. Solar and wind is good too, but is suited to only in some areas, windy and sunny ones, and even there, they need battery storage so that the power is available when needed.

Robert Buxbaum, January 21, 2025

The elite colleges, academic writing, and the Journal of Universal Rejection.

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What makes something elite? For elite colleges and academic journals, a large part is selectivity, the lower fraction of people who can go to your college or publish in your journal, or earn your credential, the more selective, thus the most elite. Harvard, boasts that “the best” apply, and of these, only 3% get in. Thus Harvard selects for the top 1%, or so they claim. These are not selected as the brightest, or most moral or motivated, but by a combination: they are the most Harvardian.

The top 20 most selective US colleges, 2022-23 according to Nathan Yau, FlowingData.com

Selectivity is viewed as good. That this 1% can get into Harvard makes the students elite and makes Harvard desirable. Some lower-class Ivy colleges (Columbia, for example) have been found to cheat to pretend higher selectivity; they’ve exaggerated the number of people who apply so they can inflate their rejection rate, and justify a high tuition, and presumably a high salary for their graduates. And it’s self-sustaining. Generally speaking, college professors and high-powered executives are drawn from elite institutions. Elite grads pick other elite grads as their way to get the best material, with the best education.

By this measure, selectivity, The Journal of Universal Rejection is the most elite and best. It’s the journal you should definitely get. The reject every article submitted on every subject. They are thus more elite than Harvard or Cal Tech, and more select than the quorum of US presidents, or Olympic gold winners, or living Chess champions, and they got there by just saying no. Many people send their articles, by the way, all rejected.

My lesson from this, is that selectivity is a poor metric for quality. Just because an institution or journal that is select in some one aspect does not mean that it will be select in another. Top swimmers and footballers rarely go to Harvard, so they have to pick from a lower tear of applicants for their swimming and football teams. It’s the same with the top in math or science, they apply to Cal Tech, with the rejects going to Stanford or Princeton. As for top chess players or US Navy Seals, a Harvard degree does nothing for them; few seals go to Harvard, and few Harvard students could be Seals. Each elite exists in its own bubble, and each bubble has its own rules. Thus, if you want to be hired as a professor, you have to go to the appropriate institution, though not necessarily from the top most selective.

From Nature, 2024. 20% of all academics come from just 8 schools, 40% come from the top 21.

As for journals to read or write in, an elevated reader like you should publish where you can be read, and understood, and perhaps to change things for the better, I think. Some money would be nice too, but few scientific journals offer that. Based on this, I have a hard time recommending scientific journals, or conferences. More and more, they charge the writer to publish or present, and offer minimal exposure of your ideas. They charge the readers and attendees such high fees that very few will see your work; university libraries subscribe, but often on condition that not everyone can read for free. Journal often change your writing too, sometimes for the better, but often to match the journal outlook or style, or just to suggest (demand) that you cite some connected editor. JofUR is better in a way, no charge to the author, and no editorial changes.

Typically, journals limit your ability to read or share your work, assuming they accept it, then they expect you to review for them, for free. So why do academics write for these journals? They’re considered the only legitimate way to get your findings out; worse, that’s how universities evaluate your work. University administrators are chosen with no idea of your research quality, and a requirement of number-based evaluation, so they evaluate professors by counting publications, particularly in elite (selective) journals, and based on the elite (selective) school you come from. It’s an insane metric that results in awful research and writing, and bad professors too. I’ve come to think that anyone, outside of academia, who writes in a scientific journal is a blockhead. If you have something worthwhile to say, write a blog, or maybe a book, or find a free, open access journal. In my field, hydrogen, the only free, open access journals are published in Russia and Iran.

And just for laughs, if you don’t mind the futility of universal rejection, there’s JoUR. Mail your article, with a self addressed return, or email it to j.universal.rejection@gmail.com. You’ll get a rejection notice and you’ll join an un-elite group: rejected, self effacing academics with time on their hands.

ROBERT BUXBAUM, January 16, 2025. If, for some reason, you want to get your progeny into an elite college, my niece, a Harvard grad., has a company that does just that, International College Counselors, they help with essays, testing, and references, and nudge your progeny to submit on time.

Golfball dimples on a car for improved mpg.

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The Mythbusters dimpled Taurus, and a diagram meant to show how drag is reduced. On a golf ball, at low NRE, vortex separation is moved back to 110°, the mechanism on a car is different, I suspect.

The dimples on a golf ball reduce air-drag resistance, so why don’t we put dimples on planes or cars? Perhaps because it’s ugly, or that cars are much bigger and than golf-balls, so we expect the effect of skin effects to be smaller. Finally, a Reynolds number analysis suggests that dimples on cars should increase drag, not reduce it.

In 2009, the Mythbusters decided to test the conjecture. Hosts Jamie Hyneman and Adam Savage ran careful gas usage tests on a Ford Taurus that was first covered with smooth clay. They drove the car repeatedly (5X) on a track at 65 mph (about 100 km/h), and measured “slightly over 26 mpg,” 9.047 l/100km, a respectable value. They then carved dimples into the clay to simulate the surface of a golf ball. See picture at right, and put the removed clay into the trunk so there would be no decrease in weight.

Underneath a Porche GT4, smallish dimples.

They then drove the dimpled car over the same course, five times as before at exactly 65 mph, and found the car got 14% more mpg, 29.6 mpg, or 7.946 l/100 km. See video excerpt here. They considered it their most surprising Mythbuster episode.

As it happens, dimples had been put on some production cars, even before the episode. They are just located underneath where most people don’t see them. The VW “Golf” had dimples even before the episode, and the Porsche Cayman GT4 does today, see picture above left, but most experiments find little or nothing. Car dimples are typically smaller than those used on Mythbusters, so that may be an explanation. Dimples have been found to help on soccer balls (the stitching acts as the dimples), and bicycle wheels (less advantage).

PHYSICS OF FLUIDS 18, 041702 (2006) Mechanism of drag reduction by dimples on a sphere, Jin Choi, Woo-Pyung Jeon, and Haecheon Choia.

The graph at right shows the source of confusion for cars and the great advantage for golf balls. It’s a plot of the drag coefficient for smooth and dimpled golf balls, as a function of the Reynolds Number, where NRE = Vdρ/µ. In this formula, V is velocity, d is the diameter of the car, ball or whatever, ρ is the density of the fluid, and µ is viscosity. NRE can be thought of as the ratio of the inertial to viscous forces acting on the object. It’s a way of describing the combined effects of speed and size for different objects in motion.

We see, above, that dimples reduce golf-ball drag by more than 50%, but only at speeds/ Reynolds numbers that are much lower than for normal cars, NRE between about 4×104 and 3.5×105, as are typical of golf balls during play. A typical car at 65mph will have a NRE.CAR = 3×106, suggesting that there should be no advantage for dimples, or possibility a disadvantage, that dimples should increase drag. A side note one sees, above, is that it is only the dimples on the front of the golf-ball that reduce drag: other dimples do nothing. If one were to add dimples to high-speed trains and airplanes I’d suggest them only on the front, so far I have not seen them.

I think that the Mythbusters did a good job with their experiments, and find their 14% improvement significant. So why do so few other cars see and advantage. One thought I had was to note that the Ford Taurus is a remarkably round car, providing ample space for front dimples to help, most cars today are more angular. I also note that the production cars have smaller dimples, as on the Porsche, above. Then again, the Mythbusters folks may have made some non-obvious experimental error.

Robert Buxbaum, January 4, 2024. An important side issue in this is that Google’s AI was awful, a handicap in researching this article. It lies continuously and convincingly, and did so here. I’d asked it for the year of the episode, and the AI lied, and said 2012. I asked for the type of car, the AI said an SUV, and it gave a misdescription of the tests. Lying AIs appear as villains in science fiction, e.g. HAL of 2001 A Space Odyssey, now in real life.