## Travel blog, May 3-5, 2017

This is going to be a long trip! The original plan was to arrive in Atlanta at 2 pm on Wednesday, May 3, rent a car and drive to Athens, GA to hang out with my friends and attend Hans Parshal’s Ph.D. defense on Thursday. On Friday I was suppose to drive to Atlanta to speak at the analysis conference at the Kennesaw State University, then fly to NYC on Friday evening in order to speak at the AMS Special Session at Hunter College on Saturday morning. On Sunday morning the plan is to fly to Seoul, South Korea, to speak at the conference in honor of Peter Jones. The following Sunday I am due to fly from Seoul to San Francisco to speak at the analysis workshop at MSRI. This is an insane plan and it was certain from the beginning that logistical obstructions are inevitable.

Small problems began on Day 1, namely Wednesday, May 3. My flight out of Rochester was delayed and I did not arrive in Atlanta until after 3 p.m.. The folks at Payless Car Rental, all wearing the unmistakable “I don’t give a fuck” grin on their faces claimed that I arrived too late and economy cars were no longer available. They offer to rent me a slightly more expensive vehicle, which I rejected as a matter of principle. After a short exchange of pleasantries I retreated to a nearby bench and reserved a car at roughly the same price with Alamo on Priceline. Just after 4 p.m. I was finally on the way to Athens, GA.

Since I left after 4 p.m., I was driving into the teeth of the Atlanta rush hour. It was nearly 6.30 p.m. when I finally reached Yorgis and Lenore’s house, tired yet deeply amused by the number of gun shops I passed along the way. Yorgis and Lenore treated me to a wonderful spaghetti carbonara and some very pleasant wine. I followed this experience with a double single malt scotch with Neil and Akos and the nearby bar. There is nothing quite so satisfying as catching up with old friends, especially when mathematical ideas try to penetrate the murky haze induced by sleep deprivation and a light buzz.

In the morning Yorgis and revisited some of our favorite problems that we have been beating our heads against wall over for the past few years. The one problem that has been the absolute bane of my existence is the question of how large $A \subset {\Bbb Z}_p$, $p$ prime, needs to be to ensure that

$|A \cdot A+A \cdot A|>\frac{p}{2}$.

Derrick Hart and I proved almost ten years ago that the conclusion holds if $|A|>p^{\frac{2}{3}}$ and I fully expected the problem to be solved by now. But no such luck! The exponent has not moved below $\frac{2}{3}$ at all, not even by a logarithm. I have not heard a plausible idea to advance this problem in a very long time.

After a very pleasant lunch at the Royal Peasant, Yorgis and I returned to the department, chatted with Neil and Akos and then went downstairs to attend Hans Parschal’s Ph.D. defense. Hans did a fantastic job and the presentation smoothly transitioned to a trip to the local beer garden followed by an excellent dinner at an authentic Central American restaurant.

The plan to speak at the Kennesaw State conference began to unravel on Thursday, though it was not clear until late that day that it was a corpse. Due to weather issues in NYC, my early evening flight from Atlanta to NYC was very likely to materialize, so I was advised to take a 6.45 a.m. flight to NYC instead. This forced me to cancel the Kennesaw State talk and get up at 3 a.m. to drive from Athens, GA to Atlanta, turn in the rental car and fly. AM radio kept me awake during the drive and the shrill voice of our glorious leader woke me up faster than any coffee ever could.

Upon arrival at La Guardia, I took an Uber to Azita Mayeli’s place, dropped off my back, gave little Carla a little stuffed kitty with glasses and took the Long Island Railroad train with Azita to Manhattan. There we met up with Chun-Kit Lai and did a bit of mathematics. Azita went off to teach while Chun-Kit and chatted a while longer. But soon after I collapsed on the couch in the lounge of the CUNY Graduate Center and Chun-Kit went to his hotel room. When I woke up, Azita was done teaching and it was time to listen to an analysis seminar lecture delivered by my Rochester colleague Kazuo Yamazaki. This was truly an excellent talk on the Navier-Stokes equation with lots of background material. But by the end of the talk I understand that I can no longer process anything resembling complicated information until I get a few hours asleep.

The rest of the day and evening was a blur. Azita and I picked up some groceries and I made an eggplant, garlic and tomato pasta which Reza, Azita and I proceeded to consume with great vigor along with several glasses of nice red wine. I am now on the couch typing away and thinking that I should be sleeping instead. But writing is a real pleasure, so I continue even though my eyelids are getting droopy and my thought processes have long passed the state of coherence.

Tomorrow I am supposed to be speaking the AMS Special Session at Hunter College and after that I am getting together with Sinan Gunturk for lunch followed by some beer drinking with David Karapetyan later in the evening. This is the plan anyways and in my next blog entry I will describe how closely the reality followed it in the end.

## The creeping feeling of dread

I feel a bittersweet connection to my ancestors. A haunting story is described in a wonderful documentary about the Vilna Ghetto, entitled “Partisans of Vilna”. An injured woman sneaked into the Jewish ghetto in Vilna in 1941 and told the people there about mass shootings of Jews in the Ponar Forest. The Jews listened to her and did not know what to make of it, so they had her examined by a very respected doctor, one of the pillars of the community. After a long and thorough examination, he concluded that the woman was crazy and the story a figment of her imagination.

We are not at the Ponar Forest stage of the current crisis yet, but all the major ingredients are there. We have a depraved degenerate megalomaniac as a leader who surrounds himself with sycophants, bigots, thieves, obscurantists and homicidal lunatics. We have a Congress so obsessed with the opportunity to impose its draconian agenda, that they seem willing to look the other way while the delirious vision of the glorified slum lord overrides decades of progress by Democrats and Republicans alike.

Just like the infamous election of 83 years ago in Germany, the recent American election resulted in the existence of alternate realities where one group is deliriously happy and hopeful, another is living in fear and the rest squirming to adjust to the changing landscape and convince themselves that everything is fine. This forebodes the struggle within our country the likes of which we have not seen since the Civil War.

We are still waiting for the proverbial other shoe to drop. The revolt of the masses on the Right that cocked a snook at the Republican establishment and brought a certified creep to the White House will be followed by an analogous movement on the Left, led by Bernie Sanders and even more extreme members of his religion. Both Trumpistan and Bernistan inhabitants believe that blue collar jobs left this country because the elites sold them out. Both groups are on a collision course with reality and will eventually need to unite to perpetuate their delusions. The resulting two-headed monster will be even scarier and more insidious than the one we will face on January 21.

I implore every decent person out there to work hard against the overwhelming tendency to normalize the incoming wave of ignorance and totalitarianism. When we are old and grey, if we live that long, we need to be able to tell our children and our grandchildren that when fascism came, we did not lie to ourselves and did not hide under our beds. Everything we hold dear is at stake.

## A comment on liberal arrogance

I am reading with very mixed feelings the articles that are springing up all over the place about how liberal arrogance caused the working class to turn against us. There is certainly much truth to this claim and I have expressed thoughts of this type going back to 2001, as my friend Dimitry Ryabogin pointed out to me this morning. Nevertheless, there is an aspect of this dilemma that does not get nearly enough attention. Out of disgust for liberal arrogance, the working class is also rejecting left of center policies and doing so to its own detriment.

The liberal elites that the Right talks about so much are mostly highly educated upper middle class folks with relatively secure jobs in high demand professions. They are going to survive the Trump presidency just fine, at least in terms of economic considerations. But the working class and rural folks who are languishing in jobs that are rapidly getting phased out or moved to the Third World countries badly need the government intervention to provide healthcare, modern education system and training programs to succeed in the 21st century. Instead, they continue voting for people, both on the local and federal levels that are hell bent on destroying their children’s futures.

These observations do not imply that the liberal elites can simply abandon the rural and working class segment of the former great liberal coalition. This would be both irresponsible and impractical. We care about the future of this country as a whole and we understand very well that if the Right wing agenda succeeds, none of us have a future to look forward to. But this does not take the responsibility off the working class folks to think carefully about their future and not let the obscurantist gun-totting lunatic agenda to blind them to both their immediate needs and the future of their children.

## Some random thoughts on elementary calculus

Here is a quick and very simple observation about elementary sums and integrals, summation by parts and Fubini.

Let us compare

$\sum_{n=1}^{\infty} \frac{n}{2^n}$ and

$\int_1^{\infty} \frac{x}{2^k} dx$.

There are many ways to handle the sum above, but perhaps the most straightforward is the following. Rewrite the sum in the form

$\sum_{n=1}^{\infty} 2^{-n} \left\{ \sum_{k=1}^n 1 \right\}$.

Changing the order of summation we obtain

$\sum_{k=1}^{\infty} \sum_{n=k}^{\infty} 2^{-n}$ and the result is easily obtained by summing up the geometric series twice.

We just applied the summation by parts principle. Nevertheless, we get an interesting perspective on things when we apply the same idea to the integral. To make things a bit clear, let’s replace $2^{-x}$ by $e^{-x}$. We have

$\int_1^{\infty} \frac{x}{e^x} dx$

$\int_1^{\infty} e^{-x} \int_0^x dy dx$.

Reversing the order of integration we obtain

$\int_1^{\infty} \left\{ \int_y^{\infty} e^{-x} dx \right\} dy$

$=\int_1^{\infty} e^{-y} dy=e^{-1}$.

This process is, of course, equivalent to the integration by parts, but it is amusing nevertheless. In general, consider

$\int_a^b f'(x)g(x)dx$

$\int_a^b f'(x) \left\{ \int_a^x g'(y)dy+g(a) \right\} dx$

$=(f(b)-f(a))g(a)$

$+\int_a^b \int_a^x f'(x)g'(y) dydx$

$=(f(b)-f(a))g(a)+\int_a^b \left\{ \int_y^b f'(x) dx \right\} g'(y)dy$

$(f(b)-f(a))g(a)+\int_a^b (f(b)-f(y))g'(y)dy$

$(f(b)-f(a))g(a)+(g(b)-g(a))f(b)-\int_a^b f(y)g'(y)dy$

$=g(b)f(b)-g(a)f(a)-\int_a^b f(y)g'(y)dy$, which is just the classical integration by parts formula derived using the fundamental theorem of calculus and Fubini.

## Princeton and President Wilson

Reuters is reporting that Princeton may scrub U.S. President Wilson’s name for racist ties. There is absolutely no doubt that President Wilson was a racist. He reintroduced segregation for Federal workers. He also told a group of visiting African American leaders that segregation is a good thing and then kicked them out. There is a long list of other actions of this type, but they only serve to reinforce and already obvious point. And yet, several interesting questions immediately arise. How far are we prepared to go to condemn offensive views of our ancestors? Just as importantly, are we truly prepared to be consistent in this process?

Let us begin by going further back in time to 1958, when Abraham Lincoln addressed a crowd in Springfield, Illinois, in the last speech of the 1858 Senate campaign. Here is the part of speech I find most interesting: ” … Through all, I have neither assailed , nor wrestled with any part of the Constitution. The legal right of the Southern people to reclaim their fugitives I have constantly admitted. The legal right of Congress to interfere with their institution in the states, I have constantly denied. In resisting the spread of slavery to new teritory, and with that, what appears to me to be a tendency to subvert the first principle of free government itself my whole effort has consisted. To the best of my judgment I have labored for, and not against the Union. As I have not felt, so I have not expressed any harsh sentiment towards our Southern bretheren. I have constantly declared, as I really believed, the only difference between them and us, is the difference of circumstances.”

There is no real comparison between Lincoln’s position and that of Wilson, and yet it is difficult to stomach the words “The legal right of the Southern people to reclaim their fugitives I have constantly admitted”, or “…the only difference between them and us, is the difference of circumstances.” Would Lincoln really phrase things in this way if the South had enslaved white Methodists? And there are many other quotes by Lincoln that raise serious questions as well. He once said, ““My paramount object in this struggle is to save the Union, and is not either to save or destroy slavery.”

He also said, ““…I will say in addition to this that there is a physical difference between the white and black races which I believe will forever forbid the two races living together on terms of social and political equality.” There is more, but the point is clear enough. Are we prepared to take down the Lincoln memorial in view of these horrific and morally repugnant statements?

The question of consistency brings us back to the modern times. President Obama, widely acknowledged as an enlightened and progressive President, sat through numerous anti-Semitic sermons by Reverend Jeremiah Wright and, to the best of my knowledge, never complained. Obama has frequently said that Reverend Wright is one of the major influences in his life. Reverend Wright continued making blatantly anti-Semitic statements throughout Obama’s presidency and Obama did not choose to comment on any of them. Can future generations, in good conscience, put Obama’s names on college campus buildings?

It is also important to address the issue of hypocrisy from a slightly different point of view. I do not have specific data on the folks who occupied the office of the Princeton President in order to address the issue of President Wilson, but I wonder how they feel about the well-documented rise in anti-Semitism the Harvard campus. The problem was identified back in 2002 by Larry Somners (http://www.nytimes.com/2002/09/21/us/harvard-president-sees-rise-in-anti-semitism-on-campus.html) and things have only gotten worse since then. What do these protesters think about schools like Columbia providing a forum for President Ahmadinejad, a virulent anti-Semite, and yet violently protesting speeches by Alan Dershowitz, a life-long supporter of human rights?

In short, I am of two minds on the topic of removing President Wilson’s name from Princeton’s buildings. On one hand, I am happy to see a serious examination of racism, misogyny and homophobia in our nation’s past and present. On the other hand, this process can quickly degenerate into an indiscriminate witch hunt where a balanced and critical understanding of the past will not prevail. Moreover, too often this mission is led by hypocritical activists who are trying to establish the hegemony of a rather narrow spectrum of views under the cover of progressive and inclusive ideology.

## The Tsarnaev verdict: bloodlust and excuses

The federal jury decided yesterday that the proper way to mete out justice in the Dzhokhar Tsarnaev case is to execute the 21 year old who, along with his brother, Tamerlan, was the junior member of the duo that set off a bomb that killed three people and injured many others during the Boston Marathon on April 15, 2013. Dzhokhar tried to kill himself during the stand-off with the police by shooting himself threw the jaw. After a lengthy hospital stay, he was put on trial and easily convicted of multiple homicides among other charges. A life sentence without a possibility of parole could have followed and Dzhokhar Tsarnaev would have joined the large and rather stinky proverbial trash bin of history. But the jurors in perhaps the most progressive State of the Union, Massachusetts, decided to impersonate a lynch mob from a 19th century Old West town of your choosing and convicted Dzhokhar to death, citing his lack of remorse and a heinous nature of his crimes.

Reasonable people are going to tell me that calling the federal jury a lynch mob is a hyperbole designed to stir up emotions and fears. I disagree. The feature of the lynch mob that people typically focus on is its extra-judicial nature. But this does not go nearly far enough, especially in the day and age when even the most oppressive and dictatorial regimes in the world figured out how to use officially setup courts as fig leaves for their activities. There is no evidence that the Tsarnaev jury was manipulated by the government, but it was certainly influenced by the public opinion. It turns out that liberalism in Massachusetts quickly reaches its limitations when the inhabitants of Boston are threatened on their own streets. What is far more disturbing is that the blood lust did not stop long after it became clear that the Boston Marathon bombing was an isolated event and not a part of a systematic campaign to terrorize our nation. What makes the Tsarnaev jury a lynch mob is that it made the decision to execute Dzhokhar based on fear and mass hysteria, not on reason and fundamental interests of our society.

Let us take a few steps back in time and think back to World Trade Center attack on September 9, 2001. I remember very clearly discussing the events with friends and family and noting that the degree of success of this outrageous crime will be determined by our reaction. As terrible as the attack was, the overall cost, both interns of human casualties and infrastructure damage was relatively small compared to what happened after. I do not believe for a moment that Bin Laden and his goons would have been satisfied if the story of 9/11 ended on that day. What made it the most successful terrorist attack in history is the subsequent invasion of Iraq and Afghanistan which undermined American standing in the world, damaged our financial infrastructure and endangered our national security for generations to come.

This essay is not written by a pacifist. I am all for the use of force when terrorists pose a clear and present danger. But in the case of Tsarnaev, execution does nothing more than fulfill our carnal need for vengeance. It will do nothing to deter other terrorists. Does anybody really believe that life imprisonment is preferable to a typical jihadist who is seeking glory in afterlife? Putting this guy away for life quietly and without fanfare would have been much more effective.

As the impact of the Tsarnaev death verdict is slowly sinking in, excuses abound. Every possible explanation for the verdict has been tried. Some have argued that death penalty is a statement that our society does not tolerate terrorism. Others have pointed out that dead Tsarnaev cannot be traded for kidnapped hostages. Historical precedents where massive use of the death penalty allegedly deterred terror have been brought up as well. I do not necessarily doubt the motivation of the authors of these arguments. But the fundamental reason we are going to kill Tsarnaev is that he injured us and we want revenge. The rest is simply window dressing.

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