Monday, February 20, 2017

Ranking the Presidents

C-SPAN has just published the 2017 results of their Presidential Historians Survey.

As any good data geek would do, I threw all the data into Excel to see what I could discover. You can download my work here.

I’ve always been interested in these types of studies because, on the one hand they advertise themselves as being totally objective, it’s really hard to squeeze the subjectivity out of them.

After all, any historian — no matter what he claims — brings to the table a certain amount of historical bias. Today’s political climate tends to make that bias even more obvious.

For example, Glen Beck — admittedly nobody’s example of political objectivity — ranks Woodrow Wilson as the most evil man in all of American history. But the survey ranks Wilson a respectable 13th out of 45.

And James Polk — not on the general public’s list of great American Presidents — ranks number 16 — proof that the C-SPAN academic advisors sure know their pre-Civil War history.

To produce the rankings, C-SPAN asked a team from academia to rank all presidents using ten “qualities of presidential leadership”:
  • Public Persuasion
  • Crisis Leadership
  • Economic Management
  • Moral Authority
  • International Relations
  • Administrative Skills
  • Relations with Congress
  • Vision/Setting An Agenda
  • Pursued Equal Justice for All
  • Performance Within the Context of His Times

It’s probably a good idea that such a panel is used and that they don’t ask me or Glen Beck to serve on that panel.

All those categories gave me plenty of data to load into Excel. Let’s see what I discovered.

I thought it would be interesting to measure the presidents on a combination of rank and “consistency”. I measured consistency based on the rank of the standard deviation of the rank in for that president in all the categories.

A consistent president is one who ranks the same in all categories. A president may be consistently good, consistently bad, or consistently mediocre. Is there anything to learn from this?

Here is a scatter plot of the results:


To validate the data, let’s look at a couple of corners. Yep, not only does Abraham Lincoln rank as the number one president, he ranks as the most consistent president. That places him in the lower left corner. A good president all around.

In the other corner are both Lincoln’s predecessor and his successor. Wow. We always knew that James Buchannan did more to cause the Civil War than any other individual. And we know that Andrew Johnson did more to screw up Reconstruction than just about anybody else. Bad presidents all around. Thanks for the legacy, guys.

Here’s another way of looking at things:


This graph color codes the presidents by their rank in each of the ten categories. Since they are ordered by the final score, any place you see “islands” of a different color, that’s an anomaly that’s worthy of discussion.

For example, Lyndon Johnson was a pretty decent president. He ranks at the top for “Relations with Congress” (he had to fight his own Democratic Party to get the Voting Rights Act of 1965 passed; a greater percentage of Republicans voted for the bill than did Democrats). But he rightfully ranks near the bottom for international relations for getting us deeper in the Vietnam war.

Bill Clinton ranks a decent number 15 overall, but comes in near the bottom in for “Moral Authority” because of his fondness for oral activities.

It’s a little harder for me to explain the person that I believe to be the nicest, worst president of them all: Jimmy Carter. A dreadful president who ruined both the American economy and our relations with Iran, I don’t know how he ranked as high as number 26. On the other hand, he’s a decent man in a strong, loving marriage, a Baptist deacon and Sunday School teacher, and a Habitat for Humanity volunteer into his 90s; doesn’t he deserve to be ranked higher than number 14 in “Moral Authority”?

And how did Barack Obama perform in his debut appearance? He came in at number 12, between Woodrow Wilson and James Monroe. That’s probably fair.

He ranked near the bottom in “Relations with Congress”. The only way he got ObamaCare passed was with back-door deals and a “gotta-pass-the-bill-before-you-read-it” mentality, even though his party controlled both houses of Congress at the time.

He also scored pretty low on “International Relations” by touring the world while apologizing for America’s past policies, weakened our position with Russia, and managed to worsen our relationship on both sides of the Middle East — quite an accomplishment!

He scored the highest in the category “Pursued Equal Justice for All”. That sounds about right for somebody who thinks “it’s good for everybody” to “spread the wealth around”.

We’ll have to wait a few years to see what historians think of our Mogul-in-Chief. My guess is his drain-the-swamp and build-the-wall dreams will score high in the “Vision/Setting an Agenda” category.

Fortunately for Mr. Trump, there is no category for “Relationship with the Press”.

Friday, February 17, 2017

On Being a Grammar Nazi

I’ve been conflicted lately over whether I want the reputation of being a Grammar Nazi. There’s no doubt that I am one; I’m just not sure if I want that out there for everybody to see.

I’ve been especially troubled lately over the tendency of people to say “one of the only”.

“He’s one of the only people who can understand this policy.”

“Mary is one of the only people in the office that can program in COBOL.”

Ambiguity is a very bad thing. How many people in the office can program in COBOL? Three? Then Mary is one of the few. But is there really only one? Then Mary is the only one, not one of the only ones.

So I arrogantly proclaimed my Nazi-ness to the world, eager to rid it of this literary travesty.

Until I read on the Google-nets that it’s actually okay to say “one of the only”.

Rats.

My career as a Grammar Nazi can be traced to an episode of “All in the Family” (Honest, I looked for a YouTube clip and couldn’t find one; so you’ll have to trust me on this one.) where Michael told Gloria that he couldn’t “loan” her any money, he had to “lend” her money because “loan” is a noun and “lend” is a verb.

Yea for Meathead, I thought. Way to put your wife in her place! (As I recall, she was not impressed and she slugged him. Our grammatical skills are so underappreciated.)

That is, until I discovered that Merriam-Webster — and who can argue with them? — says that “loan” has been a verb for 700 years — and still is.

The famous dictionary site has been wrong before. In my opinion, they completely missed the mark with the whole “try and” vs. “try to” argument.

On the other hand, they totally understand the concept of the extended meaning of the word “Nazi”. (You have no right to be offended if I use the word to describe myself.)

Being a Grammar Nazi is bad enough. Being a Closet Grammar Nazi is a fate I have chosen for myself, to avoid the slings and arrows of outrageous ostracism.

I think I need somebody to pat me on the head and say “there”, “their”, and “they’re”.

Monday, February 06, 2017

Citizen-in-Chief

Bill O’Reilly’s Super Bowl interview with Donald Trump gave us the famous quote: “There are a lot of killers. You think our country is so innocent?” Everybody’s talking about it.

So many people are talking about it, I have nothing further to say about it.

Instead, I’m going to analyze an exchange near the end of the interview.

Attempting to humanize the President, O’Reilly asked: “Do you ever say to yourself, ‘I can’t believe I’m here’?”

The President gave a typical Trump-esque ramble:
“The other day, I walked into the main entrance of the White House, and I said to myself, this is sort of amazing. Or you walk into Air Force One, it’s like a surreal experience in a certain way. But you have to get over it because there’s so much work to be done, whether it’s jobs or other nations that truly hate us; you have to get over it.”

I think he missed the chance to make a good point so I guess I’ll have to make it for him.

Much has been made of the fact that Donald Trump is our first President with neither previous political or military experience. Heck, most of our presidents had an abundance of both.

The fact that can even happen is a testament to the genius of our representative form of government.

In many countries, the head of state is actually required to be a member of Parliament, because the office is elected from their ranks.

In other countries, you have to be a member of a particular family or blood line to be King.

And in still others, the General of the victorious army becomes the de facto leader.

But in America, we can actually elect a Citizen-in-Chief. And that’s exactly what we’ve done this time. It’s amazing that it took us this long.

George Washington literally came out of retirement to become President. And he immediately returned to retirement at the end of his service. His concept of a perfect country was a party-less system run by a citizen administration.

Thomas Jefferson and John Adams screwed that up. They started a string of professional politicians in the form of diplomats, governors, senators, and congressmen to become President. Even in their private life, more than half of our presidents have been lawyers. Very few were successful businessmen (both Bushes, Carter, and Truman). One was even an actor.

Maybe this is the start of a trend. Maybe it’s a good idea to let our lawmakers be professional lawmakers, but demand our Presidents be professional administrators. Maybe that’s the kind of division in power the Founding Fathers had in mind.

So if I had been the President, and O’Reilly had asked me “Can you believe it?”, my response would have been:
“Bill, it’s an honor to be here. I am humbled that the voters of this great country put their trust in me. But yeah, I can believe it. Because this is what is meant to be. It’s the very nature of a Republic. The citizens hiring a fellow citizen to go to Washington and make sure that the government is administered in a fair and equitable way and that laws are enforced and that their money is well-spent. That’s what this office is about; and that’s why I’m here.”

Maybe some day Donald will hire me as his speech writer.

Tuesday, January 31, 2017

Exoplanets Obey Kepler

Many years ago, this young, budding astronomy geek was just a naïve 10-year-old kid, marveling at the wonders of spaceflight, living the history of Mercury, Gemini, and Apollo literally as it happened.

Even as we reached for the Moon, we stretched toward the stars. There were a few scientific dogmas that we learned, and we were taught that these truths were pretty much established as fact for all eternity.

First, in spite of the fact that we were reaching the Moon in about three days, other inter-planetary travel was expected to be much, much more difficult. Mars could take a year to reach. Other planets even much longer. And inter-stellar travel? Captain Kirk might be able to put the Enterprise into warp drive, and the Space Family Robinson could reach Alpha Centauri after a few years in suspended animation, but we shouldn’t expect it soon.

No, it would take hundreds or thousands of years to reach the closest stars given the technology available. Space is very large and very, very empty. That’s why they call it “space”.

The second fact we learned was that stars could never be imaged as a disk. We really don’t see the stars; we see the light emitting from the stars. There’s a difference. Remember that first rule about space being really big and really empty? Stars will never be anything more than a point of light.

And planets around other stars? (We now call them exoplanets.) Well, the Enterprise and the Jupiter 2 seemed to bump into them all the time. But their existence was only hypothesized.

Yeah, stars probably had planets orbiting around them — why should Sol be the only lucky one? But — remember the first rule about space being really big and really empty? — we would probably never see them. After all, the start were too bright and the planets too small. Stars generated their own light, but planets only reflected back a tiny part of that light into space. Our lifetime could only hope for the possibility of planets, not the reality of them.

The first rule still holds; space is still really big and really empty. But the ability to see stars and planets beyond our Solar System’s influence has been greatly improved over the last few years. We can now "see" exoplanets, but most are observed indirectly; we can see them only as the brief dimming of a star if their orbit lines up exactly with the Earth. Consider watching a mosquito fly in front of a searchlight a hundred miles away. It’s like that.

But since 2008, we have been able to spot a few planets directly. New advances in things like adaptive optics and the ability to block out the disk of the star are just a couple of tools that can now be used to directly observe planets. Yes, they are real!

It’s easiest to spot exoplanets directly when three conditions are true:
  1.  The planet is very large in relation to its host star -- dozens of times larger than Jupiter helps.
  2.  The planet orbits far enough from the host star that it doesn’t get washed out in the star’s light.
  3.  The plane of the orbit is close to a right angle to the plane of the Earth and the host star. Observing planets by transit is only possible when the planet is in the same plan. Observing directly is easiest when it’s in a 90-degree angle. It’s a three-dimensional geometry thing. Work it out for yourself.

Fortunately, all those factors have come together to give us one of the most remarkable astronomical movies ever filmed. Seven years in the making. But worth the time and effort. It’s a thing of beauty:



Check the original article to see the picture in motion.

There they are: four beautiful planets, just as hypothesized. Each orbit obeying Kepler’s laws of planetary motion exactly as they should.

It’s been a long time coming. I haven’t yet seen flying cars or hoverboards. My Roomba is the closest thing I have to Rosie the robot maid. And I’m still looking for my personal jet pack!

But, hey, I’ve seen a movie of a remote planetary system. My life is now complete.

Friday, January 27, 2017

Taxi Cab Numbers

The number 1729 is very dear to the hearts of mathematicians.

The story goes back to a 1919 conversation between the famous British mathematician G. H. Hardy and the Indian genius mathematician Srinivasa Ramanujan. Ramanujan asked the taxi number that Hardy had ridden in on the way. Hardy replied that it was number 1729 and mentioned that the number “seemed to be rather a dull one”.

“No”, Ramanujan replied, “it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.”

And it’s true. The number 1729 can be expressed as 13 + 123 and also as 93 + 103 and is the smallest number for which that is true.

In the world of recreational mathematics — yes, there is such a thing — such numbers are now known as Taxi Cab Numbers. They even have their own web site.

The next number in the sequence is 4,104 = 23 + 163 = 9 3 + 15 3, then 13,832 = 23 + 243 = 183 + 203, then 20,683 = 103 + 273 = 193 + 243 and so on.

This gives rise to a variety interesting math problems. For example, can you write a computer program that calculates such numbers? Sure. In fact, here are 25 of them.

The series is infinite. In other words, given enough computing power, you will always be able to find a next-higher number. Always.

And this why stop at two different ways? For example, what’s the smallest number that can be expressed as the sum of two cubes in three different ways? That number is 87,539,319 which is 2283 + 4233 and 1673 + 4363 AND 2553 + 4143

How about in four ways? It’s 6,963,472,309,248, which is 13,3223 + 16,6303 and 10,2003 + 18,0723 and 5,4363 + 18,9483 and 2,4213 + 19,0833 .

You can imagine, they get crazy-big after that.

Oh, why stop with just adding two numbers together? What about adding three numbers? Why not include negative numbers? And exponents other than cubes?

In other words, the sum of A numbers raised to the power of B, C different ways.

Yep. There are an infinite number of all these variations. I didn’t even get into the possibility of subtracting numbers, not just adding them.

That’s the cool thing about math. Almost everything in math is infinite. No matter what cool thing you find, somebody with enough imagination — and perhaps enough computer power — will be able to figure out the next thing one bigger.

Want a billion digits of pi? Okay. Heck, how about five billion?

How about ten million digits of the square root of two?

I could do this all day.

Numbers extend forever. And since numbers are really just a construct of our mind, you could argue that the mind could extend forever.

And only you can decide if that’s a comforting thought ... or a scary one.