Monthly Archives: April 2018

Map of Italian pasta

 

From the taste atlas of the world, Italy

Fresh from the taste atlas of the world.

As a brief explanation to the above map, Italy has had a troubled history over the last 2000 years. As the Roman Empire fell, the north-east got taken over by Germans. It still speaks German, and drinks beer. Spätzle is an Austrian pasta. The Italian northwest has been under French domination, off and on and it shows in the thick cream sauces. The south was controlled by the Moores for 1000 years, leaving dishes with fennel and olives. And then there is the amazing innovation: the tomato, a gift from Spanish America that seems to have found its home on the eastern seaboard, though Spain controlled the west. I don’t know why. Enjoy.

Robert Buxbaum, May 1, 2018

The worst president was John Adams

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Every now and again a magazine cites a group of historians to pick the best and worst presidents. And there, at the bottom of the scale, I typically find James Buchanan, Franklin Pierce, Andrew Johnson; Warren Harding, and/or Ulysses Grant, none of whom deserve the dishonor, in my opinion. For Pierce and Buchanan, their high crime was to not solve the slavery /succession problem — as if this was a problem that any PhD historian would have been able to solve in a weekend. It was not so simple; the slavery question bedeviled the founding fathers, tormented Daniel Webster and Henry Clay; George Washington and Thomas Jefferson wrestled with it. None could solve it, and all served when the country had relative levels of good feeling. Now, in the 1850s, Pierce and Buchanan inherit this monster, and we blame them for not resolving the slave issue when the nation was at the boiling point and Kansas was burning. They did the best they could in impossible circumstance, buying us time (Pierce also bought us southern Arizona).

Similarly, with Johnson: our historians’ complaint is that he didn’t manage reconstruction well — as if any one of them could have done better. You can’t blame a person for failing in a hopeless situation. Be happy they filled their terms, avoided war with our neighbors, and left the country richer and more populous than they found it.

Moving on to Grant and Harding, their crime was to be president at a time of scandal. But the very essence of this condemnation is that it presents the scandal, a non-issue in the large sweep of America, as if it were the only issue. Both Harding and Grant drank in the white house, and played cards while members of their cabinets stole money. These are major scandals to blue noses, but not so relevant to normal people. Both presidencies were periods of prosperity, employment, and growth. Both presidents paid down the national debt. Harding paid down $2,000,000 of debt, a good chunk of the debt incurred in WWI. Grant paid down a similarly large chunk of the debts of the civil war. Both oversaw times of peace and both signed peace treaties: Harding from WWI, Grant from the civil war and the Indian wars. Both left office with the nation far more prosperous than when they came in. No, these are not bad presidents except in the eyes of puritans who require purity in everyone else, and care little for the needs of the average American.

The worst president, in my opinion, was John Adams, and I would say he set a standard for bad that’s not likely to be beat. How bad was Adams? He oversaw the worst single law ever in American history, the Sedition act. This act, a partner to the Alien act (almost as bad), was pushed though by Adams a mere 8 years after passage of the bill of rights. The act made it illegal to criticize the government in any way. In this, it made a mockery of free expression. Adams put someone in jail for calling him “his rotundancy” — that is, for calling him fat. The supreme court had to step in and undo this unbelievably horrible law, but this was only one of several horrible acts of president Adams.

Another horrible act of president Adams is his decision to pick a war with France, our ally from the revolution. Adams himself had signed the treaty of Paris guaranteeing that we would never go to war with France. So why did Adams do it? He was a puritan, literally. He didn’t like French immorality and hated French Catholicism. He was insulted that French officials had overthrown their king (not that we had done otherwise) that they wore fancy clothes, and that they wanted bribes. He leaked their request for bribes to the press (the XYZ affair) and presented this as the reason for war. So Adams, pure Adams, got us to war with our oldest ally, a war we could not win, and didn’t.

But Adams didn’t stop there. Having decided to go to war, he also decided to stop paying on US debt to the French. He was too pure to pay debt to a nation that overthrew its king and set up a more-egalitarian state than we had. One where slavery was abolished.

Adams, of course, did nothing to address slavery, though he berated others about it. And it’s not like Adams didn’t pay out bribes, just not to the despised Catholics. At the beginning of Adams’s single term a group of Moslems, the Barbary pirates, captured some American ships. Adams agreed to pay bribe after bribe to the Barbary Pirates for return of these US ships. But the more we paid, the more ships the Barbary pirates captured. So Adams, the idiot, just bribed them more. By the end of Adams’s term, 1/4 of the US budget went to pay these pirates. When Jefferson became president, he ended the war with France by the simple solution of buying Louisiana and he sent the US Marines to deal with the pirates of North Africa. Adams could have done these things but didn’t; Jefferson did, and is ranked barely above Adams as a result. So why is it that no historian calls out Addams as an awful president?.I think it’s because Adams wrote beautifully about all the right sentiments, especially to his wife. Historians like writers of high sentiment. According to 170 scholars, the top ten presidents, not counting those on Mount Rushmore are FDR, Truman, Eisenhower, Reagan, Obama, and LBJ.

The bottom ten presidents. And there's Trump at the very bottom, with the usual suspects. Harrison was only president for a month.

The bottom ten presidents. And there’s Trump at the very bottom, with the usual suspects. Harrison was only president for a month.

And that brings us to the new poll. It includes William Henry Harrison among the worst. Harrison took office, became sick almost immediately, and died of Typhoid 31 days after taking office. The white house water supply was just down river from the sewage outlet, something you find in Detroit as well. He did nothing to deserve the dishonor except drinking the water after running a great presidential campaign. His campaign song, Tippecanoe and Tyler too is wonderful listening, even today.

And that brings us to the historian’s worst of the worst. The current president, Donald J. Trump. This is remarkable since it’s only a year into Trumps term, and since he’s done a variety of potentially good things: He ended a few trade deals and regulations that most people agree were bad. The result is that the stock market is up, employment is up, people are back at work, and historians are unhappy. What they want is another FDR, someone who’ll tell us: “We have nothing to fear, but fear itself.” whatever that means. By historian polls FDR is the second or third best president ever.

Robert Buxbaum. April 25, 2018. Semi-irrelevant: here’s a humorous song about Harrison. 

Alkaline batteries have second lives

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Most people assume that alkaline batteries are one-time only, throwaway items. Some have used rechargeable cells, but these are Ni-metal hydride, or Ni-Cads, expensive variants that have lower power densities than normal alkaline batteries, and almost impossible to find in stores. It would be nice to be able to recharge ordinary alkaline batteries, e.g. when a smoke alarm goes off in the middle of the night and you find you’re out, but people assume this is impossible. People assume incorrectly.

Modern alkaline batteries are highly efficient: more efficient than even a few years ago, and that always suggests reversibility. Unlike the acid batteries you learned about in highschool chemistry class (basic chemistry due to Volta) the chemistry of modern alkaline batteries is based on Edison’s alkaline car batteries. They have been tweaked to an extent that even the non-rechargeable versions can be recharged. I’ve found I can reliably recharge an ordinary alkaline cell, 9V, at least once using the crude means of a standard 12 V car battery charger by watching the amperage closely. It only took 10 minutes. I suspect I can get nine lives out of these batteries, but have not tried.

To do this experiment, I took a 9 V alkaline that had recently died, and finding I had no replacement, I attached it to a 6 Amp, 12 V, car battery charger that I had on hand. I would have preferred to use a 2 A charger and ideally a charger designed to output 9-10 V, but a 12 V charger is what I had available, and it worked. I only let it charge for 10 minutes because, at that amperage, I calculated that I’d recharged to the full 1 Amp-hr capacity. Since the new alkaline batteries only claimed 1 amp hr, I figured that more charge would likely do bad things, even perhaps cause the thing to blow up.  After 5 minutes, I found that the voltage had returned to normal and the battery worked fine with no bad effects, but went for the full 10 minutes. Perhaps stopping at 5 would have been safer.

I changed for 10 minutes (1/6 hour) because the battery claimed a capacity of 1 Amp-hour when new. My thought was 1 amp-hour = 1 Amp for 1 hour, = 6 Amps for 1/6 hour = ten minutes. That’s engineering math for you, the reason engineers earn so much. I figured that watching the recharge for ten minutes was less work and quicker than running to the store (20 minutes). I used this battery in my firm alarm, and have tested it twice since then to see that it works. After a few days in my fire alarm, I took it out and checked that the voltage was still 9 V, just like when the battery was new. Confirming experiments like this are a good idea. Another confirmation occurred when I overcooked some eggs and the alarm went off from the smoke.

If you want to experiment, you can try a 9V as I did, or try putting a 1.5 volt AA or AAA battery in a charger designed for rechargeables. Another thought is to see what happens when you overcharge. Keep safe: do this in a wood box outside at a distance, but I’d like to know how close I got to having an exploding energizer. Also, it would be worthwhile to try several charge/ discharge cycles to see how the energy content degrades. I expect you can get ~9 recharges with a “non-rechargeable” alkaline battery because the label says: “9 lives,” but even getting a second life from each battery is a significant savings. Try using a charger that’s made for rechargeables. One last experiment: If you’ve got a cell phone charger that works on a car battery, and you get the polarity right, you’ll find you can use a 9V alkaline to recharge your iPhone or Android. How do I know? I judged a science fair not long ago, and a 4th grader did this for her science fair project.

Robert Buxbaum, April 19, 2018. For more, semi-dangerous electrochemistry and biology experiments.

Calculating π as a fraction

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Pi is a wonderful number, π = 3.14159265…. It’s very useful, ratio of the circumference of a circle to its diameter, or the ratio of area of a circle to the square of its radius, but it is irrational: one can show that it can not be described as an exact fraction. When I was in middle school, I thought to calculate Pi by approximations of the circumference or area, but found that, as soon as I got past some simple techniques, I was left with massive sums involving lots of square-roots. Even with a computer, I found this slow, annoying, and aesthetically unpleasing: I was calculating one irrational number from the sum of many other irrational numbers.

At some point, I moved to try solving via the following fractional sum (Gregory and Leibniz).

π/4 = 1/1 -1/3 +1/5 -1/7 …

This was an appealing approach, but I found the series converges amazingly slowly. I tried to make it converge faster by combining terms, but that just made the terms more complex; it didn’t speed convergence. Next to try was Euler’s formula:

π2/6 = 1/1 + 1/4 + 1/9 + ….

This series converges barely faster than the Gregory/Leibniz series, and now I’ve got a square-root to deal with. And that brings us to my latest attempt, one I’m pretty happy with discovering (I’m probably not the first). I start with the Taylor series for sin x. If x is measured in radians: 180° = π radians; 30° = π/6 radians. With the angle x measured in radians, can show that

sin x = x – x3/6 + x5/120 – x7/5040 + …

Notice that the series is fractional and that the denominators get large fast. That suggests that the series will converge fast (2 to 3 terms?). To speed things up further, I chose to solve the above for sin 30° = 1/2 = sin π/6. Truncating the series to the first term gives us the following approximation for pi.

1/2 = sin (π/6) ≈ π/6.

Rearrange this and you find π ≈ 6/2 = 3.

That’s not bad for a first order solution. The Gregory/ Leibniz series would have gotten me π ≈ 4, and the Euler series π ≈ √6 = 2.45…: I’m ahead of the game already. Now, lets truncate to the second term.

1/2 ≈ π/6 – (π/6)3/6.

In theory, I could solve this via the cubic equation formula, but that would leave me with two square roots, something I’d like to avoid. Instead, and here’s my innovation, I’ll substitute 3 + ∂ for π . I’ll then use the binomial theorem to claim that (π)3 ≈ 27 + 27∂ = 27(1+∂). Put this into the equation above and we find:

1/2 = (3+∂)/6 – 27(1+∂)/1296

Rearranging and solving for ∂, I find that

27/216 = ∂ (1- 27/216) = ∂ (189/216)

∂ = 27/189 = 1/7 = .1428…

If π ≈ 3 + ∂, I’ve just calculated π ≈ 22/7. This is not bad for an approximation based on just the second term in the series.

Where to go from here? One thought was to revisit the second term, and now say that π = 22/7 + ∂, but it seemed wrong to ignore the third term. Instead, I’ll include the 3rd term, and say that π/6 = 11/21 + ∂. Extending the derivative approximations I used above, (π/6)3 ≈ (11/21)3 + 3∂(11/21)2, etc., I find:

1/2 ≈ (11/21 + ∂) -(11/21)3/6 – 3∂(11/21)2/6 + (11/21)5/120 + 5∂(11/21)4/120.

For a while I tried to solve this for ∂ as fraction using long-hand algebra, but I kept making mistakes. Thus, I’ve chosen to use two faster options: decimals or wolfram alpha. Using decimals is simpler, I find: 11/21 ≈ .523810, (11/21)2 =  .274376; (11/21)3 = .143721; (11/21)4 = .075282, and (11/21)5 = .039434.

Put these numbers into the original equation and I find:

1/2 – .52381 +.143721/6 -.039434/120 = ∂ (1-.274376/2 + .075282/24),

∂ = -.000185/.86595 ≈ -.000214. Based on this,

π ≈ 6 (11/21  -.000214) = 3,141573… Not half bad.

Alternately, using Wolfram alpha to reduce the fractions,

1/2 – 11/21+ 113/6•213 -115/(120•215) = ∂ (24(21)4/24(21)4 – 12•112212/24•214+ (11)4/24•214)

∂ = -90491/424394565 ≈ -.000213618. This is a more exact solution, but it gives a result that’s no more accurate since it is based on a 3 -term approximation of the infinite series.

We find that π/6 ≈ .523596, or, in fractional form, that π ≈ 444422848 / 141464855 = 3.14158.

Either approach seems OK in terms of accuracy: I can’t imagine needing more (I’m just an engineer). I like that I’ve got a fraction, but find the fraction quite ugly, as fractions go. It’s too big. Working with decimals gets me the same accuracy with less work — I avoided needing square roots, and avoided having to resort to Wolfram.

As an experiment, I’ll see if I get a nicer fraction if I drop the last term (11)4/24•214: it is a small correction to a small number, ∂. The equation is now:

1/2 – 11/21+ 113/6•213 -115/(120•215) = ∂ (24(21)4/24(21)4 – 12(11221)2/24•214).

I’ll multiply both sides by 24•214 and then by (5•21) to find that:

12•214 – 24•11•213+ 4•21•113 -115/(5•21) = ∂ (24(21)4 – 12•112212),

60•215 – 120•11•214+ 20•21^2•113 -115 = ∂ (120(21)5 – 60•112213).

Solving for π, I now get, 221406169/70476210 = 3.1415731

It’s still an ugly fraction, about as accurate as before. As with the digital version, I got to 5-decimal accuracy without having to deal with square roots, but I still had to go to Wolfram. If I were to go further, I’d start with the pi value above in digital form, π = 3.141573 + ∂; I’d add the 7th power term, and I’d stick to decimals for the solution. I imagine I’d add 4-5 more decimals that way.

Robert Buxbaum, April 2, 2018