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Oversee Yes—Impeach No

11/28/2018

Oh, the Democrats are flying high these days. They have taken over the House of Representatives in what was more a blue ripple than a blue wave. But that still represents a significant adjustment to the national stage.

What has a lot of folks salivating is the possibility of impeaching President Trump. That’s because it’s the House of Representatives that initiates such proceedings and then votes to impeach or not.

I understand the desire to save the nation and the world from our president who uses the power of his office to denigrate anyone not agreeing with him and to encourage hatred. He seems to have no sense of duty to all America, only to his America. I think his actions have weakened our land and fostered the destruction of our world.

In spite of this, I believe impeachment to be a terrible idea. I hope with all my heart that the Democrats will not pursue it. There are many reasons.

First, it’s a waste of time and effort that could be applied to actually accomplishing something useful. Suppose the House votes to impeach. Then what happens? At that point the House bows out and it’s up to the Senate to hold a trial and then vote the President’s removal up or down. Last I looked, the Senate will be more Republican than it has been. What are the odds they will choose to remove their party leader? Not bloody likely. Remember, these are the same weak folks who over the last two years have increasingly entered into lockstep with the President.

Second, it would do nothing to reduce the partisan hatred currently racking the country. Just the opposite. We don’t need any more of that. And there is absolutely no reason to take such actions, especially when nothing fruitful would come from it.

Third, if the Democrats really want to increase in strength, they won’t impeach. After all, who are those who yearn for impeachment? They are folks who would endure torture before they would vote Republican. They aren’t the ones who have to be reached in order to build the party. Clearer thinking individuals would be turned off by the senseless impeachment proceedings and the Democratic party would pay for it in the next election.

Now there is an offsetting danger to this last point. Many drooling over impeachment might flip out if the Democrats don’t pursue it. They might, in a juvenile fit of pique, elect to sit out the next election. This is not idle speculation. After all, we’ve seen them do it before. “I’m not going to vote for Hillary because I wanted Bernie.” And look what happened. I hope they’ve learned, but such stupidity is rarely recognized by those exhibiting it.

I do think Congress has the legitimate task of oversight of the president, a task not accepted enough by the former legislators. It’s part of the checks and balances we’re supposed to operate under. So I want the new House and Senate to do that job, although I expect the House to be more attentive. But I don’t want it to be based on a “We’re going to get the President” mindset. I want a reasoned unemotional look at what’s going on.

If, as a result of rational oversight investigations, it is discovered the President truly has committed impeachable offenses, then I might change my mind about it being a bad idea. But only if it’s a true bipartisan effort like it was with Richard Nixon. I doubt such a scenario would ever occur in the current climate, but it is the only one that would succeed, would not tear the country further apart, and would not hurt the Democratic party.

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Paul Erdös

11/21/2018

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The best mathematician I met during my long career was a Hungarian named Paul Erdös. A member of the Hungarian Academy of Sciences, he was gentle, kind, generous. He loved children whom he called epsilons, the Greek letter used to represent mathematically small quantities. He was a little strange.

His life was devoted exclusively to mathematics. He traveled the world, jumping from conference to conference, research institution to research institution. At each location he proposed problems to be solved, informed listeners of problems he’d brought from other locations, and absorbed new problems from those nearby. If a problem went unsolved for a certain length of time, he would attach a monetary value to its solution, increasing as time extended, and pay whomever eventually solved it. Originally winners would not cash the check, instead mounting it on their office wall. With the advent of quality copiers, it became the copy that resides on the wall and the original went to the bank.

He had the money for this because he never had to spend any. A series of mathematicians around the world assumed responsibility for his comfort, providing meals, picking him up at the airport, carting him to conferences, and delivering him to the airport when he left for the next location and the next minder. He often stayed with the minders. When at one couples’ home, both excellent mathematicians, he would walk into their bedroom at 2:00 a.m. and say, “My mind is open.” That meant it was time to rise and do some mathematics.

He showed no hesitation about saying he could devote all of his time to mathematics because he had some condition that removed any interest in sex. He never explained what that condition was.

Once he wanted to ask me about something and suggested we go to lunch. I checked my wallet and found I could handle both our meals. It is the only time in my life I have seen a person do mathematics on a table cloth.

He rarely became angry. I was told, though, during the cold war when he was visiting this country, a “clever” reporter asked if he wasn’t happy to be in this free country. He blasted the reporter and said Hungary was his homeland and he loved it.

I first met him when he visited my university where a colleague and I had spent six months trying to prove a theorem that said, “If condition A was true, then condition B was.” Professor Erdös was prowling the halls and I invited him into my office, shaking. I explained the problem. He said nothing, then his head slumped and I thought the mathematical world was going to know me as the mathematician in whose office Paul Erdös died. Fortunately, he raised his head and said, “That may not be trivial. I will think about it.” The next morning he called me to say he had proven that what we wanted to show was almost never true!

He sent me a letter containing his proof. This was one of over 1500 letters he wrote that year, a number he authored every year! I am the lucky recipient of three, and I have them preserved in a special place.

At one conference I learned that this gentle man had one area of aggressive behavior. I foolishly stood between him and a buffet table. When they announced the food was ready, I was run over as he raced to get his fill.

He phoned me occasionally. He always called the office phone, never my own, and asked for me. The administrative assistant would run to my office to tell me, in awe, who was on the phone. It always terrified me. Would I be able to answer whatever he wanted or would I be exposed for the incompetent idiot I was? One time I couldn’t imagine what was the purpose of the call. When I picked up the phone he said, “Are you going to the conference next week?” and he mentioned a city. I admitted I was. He said, “I am too,” and he hung up. Weird, huh?

There’s something called an Erdös number. Erdös is the only one with Erdös number 0. If you have published a joint paper with Erdös your number is 1. If it isn’t 1 but you’ve published a paper with someone whose number is 1, then your number is 2. If it isn’t 1 or 2 but you’ve published a paper with someone whose number is 2, then your number is 3. And so forth. Mathematicians are proud of their Erdös numbers. Mine is 2.

Professor Paul Erdös died in 1996. I am so fortunate to have had a slight connection to this great man who never failed to ask about and show interest in my research.

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Compromise

11/14/2018

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There used to be an English word called “compromise.”

It was a noun meaning “an agreement or a settlement of a dispute that is reached by each side making concessions.”

It also was a verb with the definition “settle a dispute by mutual concession” or “accept standards that are lower than is desirable.”

The United States Senate used to pride itself as a chamber of compromise.

“Compromise” used to be considered a good word.

Not so now.

You see, the only important words these days are “win” and “lose.” If you don’t win, you lose, and that is unacceptable.

President Trump and Bernie Sanders are proponents of this philosophy. Each has a strong following of devotees. By osmosis their non-thinking worshipers adopt the all or nothing view of their saint. And partisan politics is the result.

“Compromise” no longer has meaning. Because compromise implies both the words win and lose apply to everyone effecting the compromise. In other words, nobody gets everything they want, but everybody gets something they want. That’s how civilized societies survive.

It’s not unreasonable to surmise that our “civilized” society will not survive as long as the word remains taboo.

I was at a candidate forum recently and a couple of the office seekers said bipartisan approaches work for 60% of the problems dealt with in our national legislature. That sounds good. Until you realize that 40% of the time it doesn’t work and that is the situation with most of our major problems.

Those problems either will not be solved, or a solution will be imposed by one political party, alienating about half the citizenry. Is that what we want? Do we want to wait for our team to be in control and then force our views on everybody else? Is it really better to not give an inch and get nothing of what we want?

I believe no acceptable solutions will occur unless we remove “compromise” from the list of words you teach your children not to say.

I have no insights on how to deal with the difficult problems our nation faces. But I feel the most hope would come from input from a variety of views and a willingness to bring back that word compromise. Let’s look at one of the problems through my highly non-expert eyes.

Social Security! The funds to support it are running out. That’s a fact. So to get somewhere we have to start by not ignoring facts. Is it so unreasonable for one side to consider delaying the age at which Social Security can be received, as long as protections exist for those whose health precludes working longer? Is it so hard for the other side to accept an increased wage cap so those earning large incomes contribute more to the Social Security pool? If we want solutions, we have to ask and answer the difficult questions and recognize we can’t have everything we want.

There are so many other areas that scream for compromise. Any solutions will be difficult to achieve, and I certainly don’t have the smarts to know how to accomplish them. But I know nothing will happen if compromise doesn’t occur. These areas include spending, healthcare, national defense and education, among many others.

We now have a divided government, a sure recipe for stagnation. Unless the word compromise reappears. I have heard it bandied about since the recent election, saying maybe we can find common ground on infrastructure. That’s good, but I also hear both sides say they won’t give an inch on the problems important to them. In other words, they are saying they support no steps to solve problems if it means not getting everything. This is despicable on all sides.

Each of us has to ask where we stand. Are we among those who say all or nothing; only a win is acceptable? Or are we willing to give something in order to get something?

And are there enough good hearted and practical people left to reinstate the word “compromise?”

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It's Not Bad to Be Bad at Math

11/7/2018

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I’ve always done well at math. Probably a good thing because I’ve spent two-thirds of my life plying the trade. A bit of that time was in industry, but mostly I’ve been involved in teaching and research.

I love math. And I have great admiration for its practitioners, even if I can’t understand the particular branch of the subject in which they work (and yes, that happens). I’ve written before of the thrill of developing results no one else in the world knows.

I’m sure it will come as a big surprise, but not everyone feels the same way. And why should they?

After all, few of us need to determine when two boats will meet if one begins at point A heading west at 10 miles per hour, the second from point B 100 miles to the west of A heading east at 7 miles per hour, with a current of 2 miles per hour going northeast. Whew, just reading the problem blows my mind! Furthermore, only technical folk need to know how to take the derivative of the cosine of two times x squared.

What’s different about math as opposed to some other subject such as, oh, let’s say embalming?

My guess is more people would dislike studying embalming than dislike studying math. But no one discusses embalming anxiety and I doubt attention has been given to that possible disorder while math anxiety has been the subject of much research and suggestions of therapeutic ways to treat it.

The problem is that, unlike embalming, everyone has to take math at some point in their lives. Even if it’s nothing more than learning to multiply and divide, although I suppose there’s an argument, not shared by me, even that is unnecessary with all phones having calculator apps. Back in my day we learned some esoteric hand method for taking the square root of a number. Not once in my life since have I used it. (If you haven’t ever seen this and have a sick need to check it out, take a look at https://xlinux.nist.gov/dads/HTML/squareRoot.html)

It seems everyone is an expert about education, especially legislators. After all, they’ve all gone to school, right? Although sometimes I wonder. At any rate, they are very good at increasing math anxiety for many. For example, until recently in my state, it was dictated that every high school student had to pass Algebra Two in order to graduate. I can’t think of a single reason why that should be a universal requirement. I’m pleased to say it has been scaled back to Algebra One which, I suppose, is an improvement. I believe, though, a far better required course, and such courses do exist, would concentrate on balancing checkbooks, determining the best deal among many, and seeing through the statistical lies foisted on us by those with self-serving goals.

Of course, if you teach math at a university, you tend to have to deal with students who take math, and not all of them want to. I’m sure the number of my students admitting to this lack of interest tallies in the hundreds. They are taking the math because of general education requirements or the needs of their majors.

What is heartbreaking is, because they are experiencing difficulties with the mathematics, many feel there is something basically wrong with them. This sometimes is fostered, I’m sorry to say, by parents.

How to handle such a situation. Usually I respond with something like, “Why should you like it? Or be good at it?” Then I ask the student what she does well.

I might be told she plays the piano, and I’m filled with envy. I would love to play any instrument, but, unfortunately, I have negative musical ability. And I tell her that. I emphasize the similarity we find ourselves in; it’s only the particular area of expertise that differs.

I tell the student I’ve tried hard, took piano lessons both as a child and an adult, each time eventually giving up to the great relief of the poor folk trying to advance me beyond Chopsticks.

Of course, it’s a nice philosophical conversation, and I think in general the student feels better as a result. But there’s no getting around reality and at some point she’ll say, “But I need to pass the course or I won’t graduate.”

Then it’s time to tackle the major problem, getting the student through and trying to make the experience as least unpleasant as possible. Usually, working together, we’re successful.

I think the biggest success, though, is when the student winds up recognizing that doing poorly in math does not imply unworthiness or doing poorly in life.

One of the best letters I have ever received from a former student said, “You gave me a D, but you told me I had great potential and to believe in myself. I’ve had a good and successful life.”

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Oversee Yes—Impeach No

Paul Erdös

Compromise

It's Not Bad to Be Bad at Math

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