“Beating the drum for justice”

I’m going to quote a few pages from Just Mercy by Bryan Stevenson here, because I think they’re really important. It’s pretty crazy how no matter how many times I read them, a little lump in my throat never fails to develop.

I want to let the quote sit by itself without added commentary, so let me just say that I think this is a book that every person should read.

After making the three-hour drive back from Gadsden earlier in the day and heading straight to the office, it was once again approaching midnight as I left the office for home. I got in my car, and to my delight the radio came on as soon as I turned the ignition. In just over three years of law practice I had become one of those people for whom such small events could make a big difference in my joy quotient. On this late night, not only was my radio working but the station was also hosting a retrospective on the music of Sly and the Family Stone. I’d grown up listening to Sly and found myself rolling joyfully through the streets of Atlanta to tunes like “Dance to the Music,” “Everybody Is a Star,” and “Family Affair.”

Our Midtown Atlanta apartment was on a dense residential street. Some nights I had to park halfway down the block or even around the corner to find a space. But tonight I was lucky: I parked my rattling Civic just steps from our new front door just as Sly was starting “Hot Fun in the Summertime.” It was late, and I needed to get to bed, but the moment was too good to let pass, so I remained in the car listening to the music. Each time a tune ended I told myself to go inside, but then another irresistible song would begin, and I would find myself unable to leave. I was singing along to “Stand!” the soaring Sly anthem with the great gospel-themed ending, when I saw a flashing police light approaching. I was parked a few doors up from our apartment, so I assumed that the officers would drive by in pursuit of some urgent mission. When they came to a stop twenty feet in front of me, I wondered what was going on.

Our section of the street only ran one way. My parked car was facing in the proper direction; the police car had come down the street in the wrong direction. I noticed for the first time that it wasn’t an ordinary police cruiser but one of the special Atlanta SWAT cars. The officers had a spotlight attached to their vehicle, and they directed it at me sitting in my car. Only then did it occur to me that they might be there for me, but I couldn’t imagine why. I had been parked on the street for about fifteen minutes listening to Sly. Only one of my car speakers worked and not very well. I knew the music couldn’t be heard outside the car.

The officers sat there with their light pointed at me for a minute or so. I turned off the radio before “Stand!” was over. I had case files on my car seat about Lourida Ruffin and the young man who had been shot in Gadsden. Eventually two police officers got out of their vehicle. I noticed immediately that they weren’t wearing the standard Atlanta police uniform. Instead they were ominously dressed in military style, black boots with black pants and vests.

I decided to get out of my car and go home. Even though they were intensely staring at me in my car, I was still hoping that they were in the area for something unrelated to me. Or if they were concerned that something was wrong with me, I figured I would let them know that everything was okay. It certainly never occurred to me that getting out of my car was wrong or dangerous.

As soon as I opened my car door and got out, the police officer who had started walking toward my vehicle drew his weapon and pointed it at me. I must have looked completely bewildered.

My first instinct was to run. I quickly decided that wouldn’t be smart. Then I thought for an instant that maybe these weren’t real police officers.

“Move and I’ll blow your head off!” The officer shouted the words, but I couldn’t make any sense of what he meant. I tried to stay calm; it was the first time in my life anyone had ever pointed a gun at me.

“Put your hands up!” The officer was a white man about my height. In the darkness I could only make out his black uniform and his pointed weapon.

I put my hands up and noticed that he seemed nervous. I don’t remember deciding to speak, I just remember the words coming out: “It’s all right. It’s okay.”

I’m sure I sounded afraid because I was terrified.

I kept saying the words over and over again. “It’s okay, it’s okay.” Finally I said, “I live here, this is my apartment.”

I looked at the officer who was pointing the gun at my head less than fifteen feet away. I thought I saw his hands shaking.

I kept saying as calmly as I could: “It’s okay, it’s okay.”

The second officer, who had not drawn his weapon, inched cautiously toward me. He stepped on the sidewalk, circled behind my parked car, and came up behind me while the other officer continued to point the gun at me. He grabbed me by the arms and pushed me up against the back of my car. The other officer then lowered his weapon.

“What are you doing out here?” said the second officer, who seemed older than the one who had drawn his weapon. He sounded angry.

“I live here. I moved into that house down the street just a few months ago. My roommate is inside. You can go ask him.” I hated how afraid I sounded and the way my voice was shaking.

“What are you doing out in the street?”

“I was just listening to the radio.” He placed my hands on the car and bent me over the back of the vehicle. The SWAT car’s bright spotlight was still focused on me. I noticed people up the block turning on their lights and peering out of their front doors. The house next to ours came to life, and a middle-aged white man and woman walked outside and stared at me as I was leaned over the vehicle.

The officer holding me asked me for my driver’s license but wouldn’t let me move my arms to retrieve it. I told him that it was in my back pocket, and he fished my wallet out from my pants. The other officer was now leaning inside my car and going through my papers. I knew that he had no probable cause to enter my vehicle and that he was conducting an illegal search. I was about to say something when I saw him open the glove compartment. Opening objects in a parked vehicle was so incredibly illegal that I realized he wasn’t paying any attention to the rules, so saying something about it would be pointless.

There was nothing interesting in my car. There were no drugs, no alcohol, not even tobacco. I kept a giant-size bag of peanut M&Ms and Bazooka bubble gum in the glove compartment to help stave off hunger when I didn’t have time for a meal. There were just a few M&Ms left in the bag, which the officer inspected carefully. He put his nose into the bag before tossing it back. I wouldn’t be eating those M&Ms.

I had not lived at our new address long enough to get a new driver’s license, so the address on my license didn’t match the new location. There was no legal requirement to update the driver’s license, but it prompted the officer to hold me there for another ten minutes while he went back to his car to run a search on me. My neighbors grew bolder as the encounter dragged on. Even though it was late, people were coming out of their homes to watch. I could hear them talking about all the burglaries in the neighborhood. There was a particularly vocal older white woman who loudly demanded that I be questioned about items she was missing.

“Ask him about my radio and my vacuum cleaner!” Another lady asked about her cat who had been absent for three days. I kept waiting for my apartment light to come on and for Charlie to walk outside and help me out. He had been dating a woman who also worked at Legal Aid and had been spending a lot of time at her house. It occurred to me that he might not be home.

Finally, the officer returned and spoke to his partner: “They don’t have anything on him.” He sounded disappointed.

I found my nerve and took my hands off the car. “This is so messed up. I live here. You shouldn’t have done this. Why did you do this?”

The older officer frowned at me. “Someone called about a suspected burglar. There have been a lot of burglaries in this neighborhood.” Then he grinned. “We’re going to let you go. You should be happy,” he said.

With that, they walked away, got in their SWAT car, and drove off. The neighbors looked me over one last time before retreating back into their homes. I couldn’t decide whether I should race to my door so that they could see that I lived in the neighborhood or wait until they were all gone so that no one would know where the “suspected criminal” lived. I decided to wait.
I gathered up my papers, which the cop had scattered all over the car and onto the sidewalk. I unhappily threw my M&Ms into a trash can on the street and then walked into my apartment. To my great relief, Charlie was there. I woke him to tell the story.

“They never even apologized,” I kept saying. Charlie shared my outrage but soon fell back asleep. I couldn’t sleep at all.

The next morning I told Steve about the incident. He was furious and urged me to file a complaint with the Atlanta Police Department. Some folks in the office said I should explain in my complaint that I was a civil rights attorney working on police misconduct cases. It seemed to me that no one should need those kinds of credentials to complain about misconduct by police officers.

I started writing my complaint determined not to reveal that I was an attorney. When I replayed the whole incident in my mind, what bothered me most was the moment when the officer drew his weapon and I thought about running. I was a twenty-eight-year-old lawyer who had worked on police misconduct cases. I had the judgment to speak calmly to the officer when he threatened to shoot me. When I thought about what I would have done when I was sixteen years old or nineteen or even twenty-four, I was scared to realize that I might have run. The more I thought about it, the more concerned I became about all the young black boys and men in that neighborhood. Did they know not to run? Did they know to stay calm and say, “It’s okay”?

I detailed all of my concerns. I found Bureau of Justice statistics reporting that black men were eight times more likely to be killed by the police than whites. By the end of the twentieth century the rate of police shootings would improve so that men of color were “only” four times more likely to be killed by law enforcement, but the problem would get worse as some states passed “Stand Your Ground” laws empowering armed citizens to use lethal force as well.

I kept writing my memo to the Atlanta Police Department and before I knew it I had typed close to nine pages outlining all the things I thought had gone wrong. For two pages I detailed the completely illegal search of the vehicle and the absence of probable cause. I even cited about a half-dozen cases. I read over the complaint and realized that I had done everything but say, “I’m a lawyer.”

I filed my complaint with the police department and tried to forget about the incident, but I couldn’t. I kept thinking about what had happened. I began to feel embarrassed that I hadn’t asserted more control during the encounter. I hadn’t told the officers I was a lawyer or informed them that what they were doing was illegal. Should I have said more to them? Despite the work I’d done assisting people on death row, I questioned how prepared I was to do really difficult things. I even started having second thoughts about going to Alabama to start a law office. I couldn’t stop thinking about how at risk young kids are when they get stopped by the police.

My complaint made it through the review process at the Atlanta Police Department. Every few weeks I’d get a letter explaining that the police officers had done nothing wrong and that police work is very difficult. I appealed these dismissals unsuccessfully up the chain of command. Finally, I requested a meeting with the chief of police and the police officers who had stopped me. This request was denied, but the deputy chief met with me. I had asked for an apology and suggested training to prevent similar incidents. The deputy chief nodded politely as I explained what had happened. When I finished, he apologized to me, but I suspected that he just wanted me to leave. He promised that the officers would be required to do some “extra homework on community relations.” I didn’t feel vindicated.

My caseload was getting crazy. The lawyers defending the Gadsden City Jail finally acknowledged that Mr. Ruffin’s rights had been violated and that he had been illegally denied his asthma medicine. We won a decent settlement for Mr. Ruffin’s family, so they would at least receive some financial help. I turned the other police misconduct cases over to other lawyers because my death penalty docket was so full.

I had no time to make war with the Atlanta Police when I had clients facing execution. Still, I couldn’t stop thinking about how dangerous and unfair the situation was and how I’d done nothing wrong. And what if I had had drugs in my car? I would have been arrested and then would have needed to convince my attorney to believe me when I explained that the police had entered the car illegally. Would I get an attorney who would take such a claim seriously? Would a judge believe that I’d done nothing wrong? Would they believe someone who was just like me but happened not to be a lawyer? Someone like me who was unemployed or had a prior criminal record?
I decided to talk to youth groups, churches, and community organizations about the challenges posed by the presumption of guilt assigned to the poor and people of color. I spoke at local meetings and tried to sensitize people to the need to insist on accountability from law enforcement. I argued that police could improve public safety without abusing people. Even when I was in Alabama, I made time for talks at community events whenever anyone asked.

I was in a poor rural county in Alabama after another trip to pull records in a death penalty case when I was invited to speak at a small African American church. Only about two dozen people showed up. One of the community leaders introduced me, and I went to the front of the church and began my talk about the death penalty, increasing incarceration rates, abuse of power within prisons, discriminatory law enforcement, and the need for reform. At one point, I decided to talk about my encounter with the police in Atlanta, and I realized that I was getting a bit emotional. My voice got shaky, and I had to rein myself in to finish my remarks.

During the talk, I noticed an older black man in a wheelchair who had come in just before the program started. He was in his seventies and was wearing an old brown suit. His gray hair was cut short with unruly tufts here and there. He looked at me intensely throughout my presentation but showed no emotion or reaction during most of the talk. His focused stare was unnerving. A young boy who was about twelve had wheeled him into the church, probably his grandson or a relative. I noticed that the man occasionally directed the boy to fetch things for him. He would wordlessly nod his head, and the boy seemed to know that the man wanted a fan or a hymnal.

After I finished speaking, the group sang a hymn to end the session. The older man didn’t sing but simply closed his eyes and sat back in his chair. After the program, people came up to me; most folks were very kind and expressed appreciation for my having taken the time to come and talk to them. Several young black boys walked up to shake my hand. I was pleased that people seemed to value the information I shared. The man in the wheelchair was waiting in the back of the church. He was still staring at me. When everyone else had left, he nodded to the young boy, who quickly wheeled him up to me.

The man’s expression never changed as he approached me. He stopped in front of me, leaned forward in his wheelchair, and said forcefully, “Do you know what you’re doing?” He looked very serious, and he wasn’t smiling.

His question threw me. I couldn’t tell what he was really asking or whether he was being hostile. I didn’t know what to say. He then wagged his finger at me, and asked again. “Do you know what you’re doing?”

I tried to smile to diffuse the situation but I was completely baffled. “I think so.…”

He cut me off and said loudly, “I’ll tell you what you’re doing. You’re beating the drum for justice!” He had an impassioned look on his face. He said it again emphatically, “You’ve got to beat the drum for justice.”

He leaned back in his chair, and I stopped smiling. Something about what he said had sobered me. I answered him softly, “Yes, sir.”

He leaned forward again and said hoarsely, “You’ve got to keep beating the drum for justice.” He gestured and after a long while said again, “Beat the drum for justice.”

He leaned back, and in an instant he seemed tired and out of breath. He looked at me sympathetically and waved me closer. I did so, and he pulled me by the arm and leaned forward. He spoke very quietly, almost a whisper, but with a fierceness that was unforgettable.

“You see this scar on the top of my head?” He tilted his head to show me. “I got that scar in Greene County, Alabama, trying to register to vote in 1964. You see this scar on the side of my head?” He turned his head to the left and I saw a four-inch scar just above his right ear. “I got that scar in Mississippi demanding civil rights.”

His voice grew stronger. He tightened his grip on my arm and lowered his head some more. “You see that mark?” There was a dark circle at the base of his skull. “I got that bruise in Birmingham after the Children’s Crusade.”

He leaned back and looked at me intensely. “People think these are my scars, cuts, and bruises.”

For the first time I noticed that his eyes were wet with tears. He placed his hands on his head. These aren’t my scars, cuts, and bruises. These are my medals of honor.”

He stared at me for a long moment, wiped his eyes, and nodded to the boy, who wheeled him away.

I stood there with a lump in my throat, staring after him.

After a moment, I realized that the time to open the Alabama office had come.

Bryan Stevenson, Just Mercy

Overemphasizing disagreement

I’ve noticed a tendency in myself and others during debate to only respond to the parts of what others say that I disagree with, taking the agreement for granted. This makes some sense; if you agree with 95% of an argument somebody is making, there is the most progress to be made by focusing on the 5% remaining difference. But I think this also causes the perception on both sides that there is a greater distance to be bridged than there is in reality. Constantly focusing on subtle points of disagreement can also be perceived as being unresponsive and indifferent towards a significant part of the arguments being made.

This is an optimistic take on phenomena like the backfire effect – a lot of the sense that you and your interlocutor are getting no closer during conversation might be the result of this form of miscommunication. I think a good policy for reducing misunderstanding is something like Rapaport’s rules – explicitly stating points of agreement before going into disagreement. This isn’t only good for reducing misunderstanding – I’ve noticed that stating points of agreement, especially things I’ve just been convinced of, has the effect of actually making it easier to change my mind.

Regularization as approximately Bayesian inference

In an earlier post, I showed how the procedure of minimizing sum of squares falls out of regular old frequentist inference. This time I’ll do something similar, but with regularization and Bayesian inference.

Regularization is essentially a technique in which you evaluate models in terms of not just their fit to the data, but also the values of the parameters involved. For instance, say you are modeling some data with a second-order polynomial.

M = { f(x) = a + bx + cx2 | a, b, c ∈ R }
D = { (x1, y1), …, (xN, yN) }

We can evaluate our model’s fit to the data with SOS:

SOS = ∑ (yn – f(xn))2

Minimizing SOS gives us the frequentist answer – the answer that best fits the data. But what if we suspect that the values of a, b, and c are probably small? In other words, what if we have an informative prior about the parameter values? Then we can explicitly add on a penalty term that increases the SOS, such as…

SOS with L1 regularization = k1 |a| + k2 |b| + k3 |c| + ∑ (yn – f(xn))2

The constants k1, k2, and k3 determine how much we will penalize each parameter a, b, and c. This is not the only form of regularization we could use, we could also use the L2 norm:

SOS with L2 regularization = k1 a2 + k2 b2 + k3 c2 + ∑ (yn – f(xn))2

In both of these cases, the regularized SOS term grows as the values of the parameters grow. This makes the optimal choice of curve take into account not only the fit to data, but the desired size of the parameters.

You might, having heard of this procedure, already suspect it of having a Bayesian bent. The notion of penalizing large parameter values on the basis of a prior suspicion that the values should be small sounds a lot like what the Bayesian would call “low priors on high parameter values.”

We’ll now make the connection explicit.

Frequentist inference tries to select the theory that makes the data most likely. Bayesian inference tries to select the theory that is made most likely by the data. I.e. frequentists choose f to maximize P(D | f), and Bayesians choose f to maximize P(f | D).

Assessing P(f | D) requires us to have a prior over our set of functions f, which we’ll call π(f).

P(f | D) = P(D | f) π(f) / P(D)

We take a logarithm to make everything easier:

log P(f | D) = log P(D | f) + log π(f) – log P(D)

We already evaluated P(D | f) in the last post, so we’ll just plug it in right away.

log P(f | D) = – SOS/2σ2 – N/2 log(2πσ2)) + log π(f) – log P(D)

Since we are maximizing with respect to f, two of these terms will fall away.

log P(f | D) = – SOS/2σ2 + log π(f) + constant

Now we just have to decide on the form of π(f). Since the functional form of f is determined by the values of the parameters {a, b, c}, π(f) = π(a, b, c). One plausible choice is a Gaussian centered around the values of each parameter:

π(f) = exp( -a2 / 2σa2 ) exp( -b2 / 2σb2 ) exp( -c2 / 2σc2 ) / √(8π3σa2σb2σc2)
log π(f) = -a2/2σa2 – b2/2σb2 – c2/2σc2 – ½ log(8π3σa2σb2σc2)

Now, throwing out terms that don’t depend on the values of the parameters, we find:

log P(f | D) = – SOS/2σ2 -a2/2σa2 – b2/2σb2 – c2/2σc2 + constant

This is exactly L2 regularization, where each kn = σ2n2. In other words, L2 regularization is Bayesian inference with Gaussian priors over the parameters!

What priors does L1 regularization correspond to?

log π(f) = -k1 |a| – k2 |b| – k3 |c|
π(a, b, c) = e-k1|a| e-k2|b| e-k3|a|

I.e. the L1 regularization prior is an exponential distribution.

This can be easily extended to any regularization technique. This is a way to get some insight into what your favorite regularization methods mean. They are ultimately to be cashed out in the form of your prior knowledge of the parameters!

Against the status quo

A good analysis of our society involves, I think, the ability to look at everything from the perspective of an alien – to remove ourselves from the contingent fact of our place in history and negate the biases and blind spots that might result from it.

If you were to be dropped out of a time machine into pretty much any time in American history, you would see enormous injustices happening everywhere, as well as status quo that is either blind or apathetic towards these injustices.

Social progress is so sudden and final that it’s easy to lose track of this truth. Women have only had the right to vote for the last 100 years, and the first woman to be admitted to Harvard Law School was in 1950. I’m very confident that it will never again be the case that women will not be legally allowed to vote in the United States, or banned from institutions of higher learning. We’ve moved as a society in a direction that we are never coming back from.

Racial discrimination in voting was only technically prohibited after 1965. Just fifty to sixty years ago in the United States, we have elected officials who rose to power by proudly preaching Jim Crow and segregation, affiliating with the Ku Klux Klan, and boasting about chasing black people out of their restaurants with ax handles. Lynching was a common practice in the United States for hundreds of years; Emmett Till was brutally tortured to death for wolf-whistling a white woman in 1955. Professional photographs of lynchings were published as postcards, to be sold as popular souvenirs. Etc etc.

The point of all of this is just to say that it looks like we should have a really strong presumption in favor of there being current massive flaws in the status quo. The argument being: at basically any point in history, the status quo has been blind towards and accept of stunning levels of injustice. While the trend of history has been towards progress and a widening moral circle, we should still suspect that there are aspects of society today that are massively unjust unless we think that we are in an incredibly unique historical moment. We should also suspect that we are vulnerable to the same biases that people have always historically been blind to in failing to see basic moral failings of the society in which they exist.

This raises the question: What are the massive injustices going on today? Where are our blind spots? 100 years down the line, what will people read about us that will make them wonder how we sat by and didn’t do anything?

This is a really hard question, and I only have a few answers that I’m pretty confident about. One of these is animal rights issues. We are inflicting enormous degrees of needless cruelty on animals, and I get the sense that the average American’s attitude towards this is essentially total apathy (although there has been a definite change in this attitude in recent years). Another possibility is mass incarceration. The US has the highest incarceration rate in the world, and we lock crazy amounts of people up for victimless crimes. Time in prison is brutally unpleasant, and for those that act out, solitary confinement is the punishment.

What other things do we accept in modern society that our descendants will look back on and hang their heads in shame about?

Why minimizing sum of squares is equivalent to frequentist inference

(This will be the first in a short series of posts describing how various commonly used statistical methods are approximate versions of frequentist, Bayesian, and Akaike-ian inference)

Suppose that we have some data D = { (x₁, y₁), (x₂, y₂), … , (xɴ, yɴ) }, and a candidate function y = f(x).

Frequentist inference involves the assessment of the likelihood of the data given this candidate function: P(D | f).

Since D is composed of N independent data points, we can assess the probability of each data point separately, and multiply them all together.

P(D | f) = P(x₁, y₁ | f) P(x₂, y₂ | f) … P(xɴ, yɴ | f)

So now we just need to answer the question: What is P(x, y | f)?

f predicts that for the value x, the most likely y-value is f(x).

The other possible y-values will be normally distributed around f(x).

IMG_20180522_192208774

The equation for this distribution is a Gaussian:

P(x, y | f) = exp[ -(y – f(x))² / 2σ² ] / √(2πσ²)

Now that we know how to find P(x, y | f), we can easily calculate P(D | F)!

P(D | f) = exp[ -(y – f(x))² / 2σ² ] /√(2πσ²) ・ exp[ -(y – f(x))² / 2σ² ] / √(2πσ²) … exp[ -(y – f(x))² / 2σ² ] / √(2πσ²)
= exp[ -(y – f(x))² / 2σ² ] ・ exp[ -(y – f(x))² / 2σ² ] … exp[ -(y – f(x))² / 2σ² ] / (2πσ²)N/2

Products are messy and logarithms are monotonic, so log(P(D | f)) is easier to work with: it turns the product into a sum.

log P(D | f) = log( exp[ -(y₁ – f(x₁))² / 2σ² ] … exp[ -(yɴ – f(xɴ))² / 2σ² ] / (2πσ²)N/2 )
= log( exp[ -(y₁ – f(x₁))² / 2σ² ] ) + … log( exp[ -(yɴ – f(xɴ))² / 2σ² ] ) – N/2 log(2πσ²)
= -(y₁ – f(x₁))² / 2σ² ) + -(yɴ – f(xɴ))² / 2σ² ) – N/2 log(2πσ²)
= -1/2σ² [ (y₁ – f(x₁))² + … +(yɴ – f(xɴ))² ] – N/2 log(2πσ²)

Now notice that the sum of squares just naturally pops out!

SOS = (y₁ – f(x₁))² + … + (yɴ – f(xɴ))²
log P(D | f) = -SOS/2σ² – N/2 log(2πσ²)

Frequentist inference chooses f to maximize P(D | f). We can now immediately see why this is equivalent to minimizing SOS!

argmax{ P(D | f) }
= argmax{ log P(D | f) }
= argmax{ – SOS/2σ² – N/2 log(2πσ²) }
= argmin{ SOS/2σ² + N/2 log(2πσ²) }
= argmin{ SOS/2σ² }
= argmin{ SOS }

Next, we’ll go Bayesian…

History is Lamarckian

I just finished this novel, and loved every bit of it. It’s a plodding epic chronicling the colonization of Mars, and the first of a trilogy (Red Mars, Blue Mars, Green Mars) which I plan to continue.

Here’s one of my favorite exchanges, between the fiery revolution-minded anarchist Arkady and the group of more conventional thinkers among the first one hundred colonists of Mars. While I’m inclined to dismiss Arkady-types in the real world as wild-eyed idealists whose dreams are not anchored to the realities of human history, this was a passage that made me think hard, through the sheer force of its eloquence and originality.

Over a dessert of strawberries, Arkady floated up to propose a toast. “To the new world we now create!”

A chorus of groans and cheers; by now they all knew what he meant. Phyllis threw down a strawberry and said, “Look, Arkady, this settlement is a scientific station. Your ideas are irrelevant to it. Maybe in fifty or a hundred years. But for now, it’s going to be like the stations in Antarctica.”

“That’s true,” Arkady said. “But in fact Antarctic stations are very political. Most of them were built so that countries that built them would have a say in the revision of the Antarctic treaty. And now the stations are governed by laws set by that treaty, which was made by a very political process! So you see, you cannot just stick your head in sand crying ‘I am a scientist, I am a scientist!’ ” He put a hand to his forehead, in the universal mocking gesture of the prima donna. “No. When you say that, you are only saying, ‘I do not wish to think about complex systems!’ Which is not really worthy of true scientists, is it?”

“The Antarctic is governed by a treaty because no one lives there except in scientific stations,” Maya said irritably. To have their final dinner, their last moment of freedom, disrupted like this!

“True,” Arkady said. “But think of the result. In Antarctica, no one can own land. No one country or organization can exploit the continent’s natural resources, without the consent of every other country. No one can claim to own those resources, or take them and sell them to other people, so that some profit from them while others pay for their use. Don’t you see how radically different that is from the way the rest of the world is run? And this is the last area on Earth to be organized, to be given a set of laws. It represents what all governments working together feel instinctively is fair, revealed on land free from claims of sovereignty, or really from any history at all. It is, to say it plainly, Earth’s best attempt to create just property laws! Do you see? This is the way entire world should be run, if only we could free it from the straitjacket of history!”

Sax Russell, blinking mildly, said, “But Arkady, since Mars is going to be ruled by a treaty based on the old Antarctic one, what are you objecting to? The Outer Space Treaty states that no country can claim land on Mars, no military activities are allowed, and all bases are open to inspection by any country. Also no martian resources can become the property of a single nation —the UN is supposed to establish an international regime to govern any mining or other exploitation. If anything is ever done along that line, which I doubt will happen, then it is to be shared among all the nations of the world.” He turned a palm upward. “Isn’t that what you’re agitating for, already achieved?”

“It’s a start,” Arkady said. ”But there are aspects of that treaty you haven’t mentioned. Bases built on Mars will belong to the countries that build them, for instance. We will be building American and Russian bases, according to this provision of the law. And that puts us right back into the nightmare of Terran law and Terran history. American and Russian businesses will have the right to exploit Mars, as long as the profits are somehow shared by all the nations signing the treaty. This may only involve some sort of percentage paid to UN, in effect no more than bribe. I don’t believe we should acknowledge these provisions for even a moment!”

Silence followed this remark.

Ann Clayborne said, “This treaty also says we have to take measures to prevent the disruption of planetary environments, I think is how they put it. It’s in Article Seven. That seems to me to expressly forbid the terraforming that so many of you are talking about.”

“I would say that we should ignore that provision as well,” Arkady said quickly. “Our own well-being depends on ignoring it.”

This view was more popular than his others, and several people said so.

“But if you’re willing to disregard one article,” Arkady pointed out, “you should be willing to disregard the rest. Right?”

There was an uncomfortable pause.

“All these changes will happen inevitably,” Sax Russell said with a shrug. “Being on Mars will change us in an evolutionary way.”

Arkady shook his head vehemently, causing him to spin a little in the air over the table. “No, no, no, no! History is not evolution! It is a false analogy! Evolution is a matter of environment and chance, acting over millions of years. But history is a matter of environment and choice, acting within lifetimes, and sometimes within years, or months, or days! History is Lamarckian! So that if we choose to establish certain institutions on Mars, there they will be! And if we choose others, there they will be!” A wave of his hand encompassed them all, the people seated at the tables, the people floating among the vines: “I say we should make those choices ourselves, rather than having them made for us by people back on Earth. By people long dead, really.”

Phyllis said sharply, “You want some kind of communal utopia, and it’s not possible. I should think Russian history would have taught you something about that.”

“It has,” Arkady said. “Now I put to use what it has taught me.”

“Advocating an ill-defined revolution? Fomenting a crisis situation? Getting everyone upset and at odds with each other?”

A lot of people nodded at this, but Arkady waved them away. “I decline to accept blame for everyone’s problems at this point in the trip. I have only said what I think, which is my right. If I make some of you uncomfortable, that is your problem. It is because you don’t like the implications of what I say, but can’t find grounds to deny them.”

“Some of us can’t understand what you say,” Mary exclaimed.

“I say only this!” Arkady said, staring at her bug-eyed: “We have come to Mars for good. We are going to make not only our homes and our food, but also our water and the very air we breathe—all on a planet that has none of these things. We can do this because we have technology to manipulate matter right down to the molecular level. This is an extraordinary ability, think of it! And yet some of us here can accept transforming the entire physical reality of this planet, without doing a single thing to change our selves, or the way we live. To be twenty-first century scientists on Mars, in fact, but at the same time living within nineteenth century social systems, based on seventeenth century ideologies. It’s absurd, it’s crazy, it’s—it’s—” he seized his head in his hands, tugged at his hair, roared “It’s unscientific! And so I say that among all the many things we transform on Mars, ourselves and our social reality should be among them. We must terraform not only Mars, but ourselves.”

History is Lamarckian, in exactly the sense declared by Arkady. But this of course does not imply that the social systems we build are not subject to the same forces of selection that have caused the downfall of so many past societies.

***

Anyway, I highly recommend this book, and to give you a flavor, here are a few more of my favorite quotes, presented with zero context…

“We were too old!”

“We were not too old. We chose not to think of it. Most ignorance is by choice, you know, and so ignorance is very telling about what really matters to people.”

“Come on,” he said. He propped himself up on an elbow to look at her. “You really don’t know what beauty is, do you?”

“I certainly do,” Nadia said mulishly.

Arkady ignored her and said, “Beauty is power and elegance, right action, form fitting function, intelligence, and reasonability.”

“We didn’t mean to be selfish,” Hiroko said slowly. “We wanted to try it, to show by experiment how we can live here. Someone has to show what you mean when you talk about a different life, John Boone. Someone has to live the life.”

Sax Russell rose to his feet. He looked the same as ever, perhaps a bit more flushed than usual, but mild, small, blinking owlishly, his voice calm and dry, as if lecturing on some textbook point of thermodynamics, or enumerating the periodic table.

“The beauty of Mars exists in the human mind,” he said in that dry factual tone, and everyone stared at him amazed. “Without the human presence it is just a concatenation of atoms, no different than any other random speck of matter in the universe. It’s we who understand it, and we who give it meaning. All our centuries of looking up at the night sky and watching it wander through the stars. All those nights of watching it through the telescopes, looking at a tiny disk trying to see canals in the albedo changes. All those dumb sci-fi novels with their monsters and maidens and dying civilizations. And all the scientists who studied the data, or got us here. That’s what makes Mars beautiful. Not the basalt and the oxides.”

He paused to look around at them all. Nadia gulped; it was strange in the extreme to hear these words come out of the mouth of Sax Russell, in the same dry tone that he would use to analyze a graph. Too strange!

“Now that we are here,” he went on, “it isn’t enough to just hide under ten meters of soil and study the rock. That’s science, yes, and needed science too. But science is more than that. Science is part of a larger human enterprise, and that enterprise includes going to the stars, adapting to other planets, adapting them to us. Science is creation. The lack of life here, and the lack of any finding in fifty years of the SETI program, indicates that life is rare, and intelligent life even rarer. And yet the whole meaning of the universe, its beauty, is contained in the consciousness of intelligent life. We are the consciousness of the universe, and our job is to spread that around, to go look at things, to live everywhere we can. It’s too dangerous to keep the consciousness of the universe on only one planet, it could be wiped out. And so now we’re on two, three if you count the moon. And we can change this one to make it safer to live on. Changing it won’t destroy it. Reading its past might get harder, but the beauty of it won’t go away. If there are lakes, or forests, or glaciers, how does that diminish Mars’s beauty? I don’t think it does. I think it only enhances it. It adds life, the most beautiful system of all. But nothing life can do will bring Tharsis down, or fill Marineris. Mars will always remain Mars, different from Earth, colder and wilder. But it can be Mars and ours at the same time. And it will be. There is this about the human mind; if it can be done, it will be done. We can transform Mars and build it like you would build a cathedral, as a monument to humanity and the universe both. We can do it, so we will do it. So—” he held up a palm, as if satisfied that the analysis had been supported by the data in the graph – as if he had examined the periodic table, and found that it still held true – “we might as well start.”

Short and sweet proof of the f(xy) = f(x) + f(y) logarithmic property

If you want a continuous function f(x) from the reals to the reals that has the property that for all real x and y, f(xy) = f(x) + f(y), then this function must take the form f(x) = k log(x) for some real k.

A proof of this just popped into my head in the shower. (As always with shower-proofs, it was slightly wrong, but I worked it out and got it right after coming out).

I haven’t seen it anywhere before, and it’s a lot simpler than previous proofs that I’ve encountered.

Here goes:

f(xy) = f(x) + f(y)

differentiate w.r.t. x…
f'(xy) y = f'(x)

differentiate w.r.t. y…
f”(xy) xy + f'(xy) = 0

rearrange, and rename xy to z…
f”(z) = -f'(z)/z

solve for f'(z) with standard 1st order DE techniques…
df’/f’ = – dz/z
log(f’) = -log(z) + constant
f’ = constant/z

integrate to get f…
f(z) = k log(z) for some constant k

And that’s the whole proof!

As for why this is interesting to me… the equation f(xy) = f(x) + f(y) is very easy to arrive at in constructing functions with desirable features. In words, it means that you want the function’s outputs to be additive when the inputs are multiplicative.

One example of this, which I’ve written about before, is formally quantifying our intuitive notion of surprise. We formalize surprise by asking the question: How surprised should you be if you observe an event that you thought had a probability P? In other words, we treat surprise as a function that takes in a probability and returns a scalar value.

We can lay down a few intuitive desideratum for our formalization of surprise, and one such desideratum is that for independent events E and F, our surprise at them both happening should just be the sum of the surprise at each one individually. In other words, we want surprise to be additive for independent events E and F.

But if E and F are independent, then the joint probability P(E, F) is just the product of the individual probabilities: P(E, F) = P(E) P(F). In other words, we want our outputs to be additive, when our inputs are multiplicative!

This automatically gives us that the form of our surprise function must be k log(z). To spell it out explicitly…

Desideratum: Surprise(P(E, F)) = Surprise(P(E)) + Surprise(P(F))

But P(E,F) = P(E) P(F), so…
Surprise(P(E) P(F)) = Surprise(P(E)) + Surprise(P(F))

Renaming P(E) to x and P(F) to y…
Surprise(xy) = Surprise(x) + Surprise(y)

Thus, by the above proof…
Surprise(x) = k log(x) for some constant k

That’s a pretty strong constraint for some fairly weak inputs!

That’s basically why I find this interesting: it’s a strong constraint that comes out of an intuitively weak condition.