“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.

Constructing the world

In this six and a half hour lecture series by David Chalmers, he describes the concept of a minimal set of statements from which all other truths are a priori “scrutable” (meaning, basically, in-principle knowable or derivable).

What are the types of statements in this minimal set required to construct the world? Chalmers offers up four categories, and abbreviates this theory PQIT.

P

P is the set of physical facts (for instance, everything that would be accessible to a Laplacean demon). It can be thought of as essentially the initial conditions of the universe and the laws governing their changes over time.

Q

Q is the set of facts about qualitative experience. We can see Chalmers’ rejection of physicalism here, as he doesn’t think that Q is eclipsed within P. Example of a type of statement that cannot be derived from P without Q: “There is a beige region in the bottom right of my visual field.”

I

Here’s a true statement: “I’m in the United States.” Could this be derivable from P and Q? Presumably not; we need another set of indexical truths that allows us to have “self-locating” beliefs and to engage in anthropic reasoning.

T

Suppose that P, Q, and I really are able to capture all the true statements there are to be captured. Well then, the statement “P, Q, and I really are able to capture all the true statements there are to be captured” is a true statement, and it is presumably not captured by P, Q, and I! In other words, we need some final negative statements that tell us that what we have is enough, and that there are no more truths out there. These “that’s all”-type statements are put into the set T.

⁂⁂⁂

So this is a basic sketch of Chalmer’s construction. I like that we can use these tags like PQIT or PT or QIT as a sort of philosophical zip-code indicating the core features of a person’s philosophical worldview. I also want to think about developing this further. What other possible types of statements are there out there that may not be captured in PQIT? Here is a suggestion for a more complete taxonomy:

p    microphysics
P    macrophysics (by which I mean all of science besides fundamental physics)
Q    consciousness
R    normative rationality
E    
normative ethics
C    counterfactuals
L    
mathematical / logical truths
I     indexicals
T    “that’s-all” statements

I’ve split P into big-P (macrophysics) and little-p (microphysics) to account for the disagreements about emergence and reductionism. Normativity here is broad enough to include both normative epistemic statements (e.g. “You should increase your credence in the next coin toss landing H after observing it land H one hundred times in a row”) and ethical statements. The others are fairly self-explanatory.

The most ontologically extravagant philosophical worldview would then be characterized as pPQRECLIT.

My philosophical address is pRLIT (with the addendum that I think C comes from p, and am really confused about Q). What’s yours?

Moving Naturalism Forward: Eliminating the macroscopic

Sean Carroll, one of my favorite physicists and armchair philosophers, hosted a fantastic conference on philosophical naturalism and science, and did the world a great favor by recording the whole thing and posting it online. It was a three-day long discussion on topics like the nature of reality, emergence, morality, free will, meaning, and consciousness. Here are the videos for the first two discussion sections, and the rest can be found by following Youtube links.

 

Having watched through the entire thing, I have updated a few of my beliefs, plan to rework some of my conceptual schema, and am puzzled about a few things.

A few of my reflections and take-aways:

  1. I am much more convinced than before that there is a good case to be made for compatibilism about free will.
  2. I think there is a set of interesting and challenging issues around the concept of representation and intentionality (about-ness) that I need to look into.
  3. I am more comfortable with intense reductionism claims, like “All fact about the macroscopic world are entailed by the fundamental laws of physics.”
  4. I am really interested in hearing Dan Dennett talk more about grounding morality, because what he said was starting to make a lot of sense to me.
  5. I am confused about the majority attitude in the room that there’s not any really serious reason to take an eliminativist stance about macroscopic objects.
  6. I want to find more details about the argument that Simon DeDeo was making for the undecidability of questions about the relationship between macroscopic theories and microscopic theories (!!!).
  7. There’s a good way to express the distinction between the type of design human architects engage in and the type of design that natural selection produces, which is about foresight and representations of reasons. I’m not going to say more about this, and will just refer you to the videos.
  8. There are reasons to suspect that animal intelligence and capacity to suffer are inversely correlated (that is, the more intelligent an animal, the less capacity to suffer it likely has). This really flips some of our moral judgements on their head. (You must deliver a painful electric shock to either a human or to a bird. Which one will you choose?)

Let me say a little more about number 5.

I think that questions about whether macroscopic objects like chairs or plants really REALLY exist, or whether there are really only just fermions and bosons are ultimately just questions about how we should use the word “exist.” In the language of our common sense intuitions, obviously chairs exist, and if you claim otherwise, you’re just playing complicated semantic games. I get this argument, and I don’t want to be that person that clings to bizarre philosophical theses that rest on a strange choice of definitions.

But at the same time, I see a deep problem with relying on our commonsense intuitions about the existence of the macro world. This is that as soon as we start optimizing for consistency, even a teeny tiny bit, these macroscopic concepts fall to pieces.

For example, here is a trilemma (three statements that can’t all be correct):

  1. The thing I am sitting on is a chair.
  2. If you subtract a single atom from a chair, it is still a chair.
  3. Empty space is not a chair.

These seem to me to be some of the most obvious things we could say about chairs. And yet they are subtly incoherent!

Number 1 is really shorthand for something like “there are chairs.” And the reason why the second premise is correct is that denying it requires that there be a chair such that if you remove a single atom, it is no longer a chair. I take it to be obvious that such things don’t exist. But accepting the first two requires us to admit that as we keep shedding atoms from a chair, it stays a chair, even down to the very last atom. (By the way, some philosophers do actually deny number 2. They take a stance called epistemicism, which says that concepts like “chair” and “heap” are actually precise and unambiguous, and there exists a precise point at which a chair becomes a non-chair. This is the type of thing that makes me giggle nervously when reflecting on the adequacy of philosophy as a field.)

As I’ve pointed out in the past, these kinds of arguments can be applied to basically everything in the macroscopic world. They wreak havoc on our common sense intuitions and, to my mind, demand rejection of the entire macroscopic world. And of course, they don’t apply to the microscopic world. “If X is an electron, and you change its electric charge a tiny bit, is it still an electron?” No! Electrons are physical substances with precise and well-defined properties, and if something doesn’t have these properties, it is not an electron! So the Standard Model is safe from this class of arguments.

Anyway, this is all just to make the case that upon close examination, our commonsense intuitions about the macroscopic world turn out to be subtly incoherent. What this means is that we can’t make true statements like “There are two cars in the garage”. Why? Just start removing atoms from the cars until you get to a completely empty garage. Since no single-atom change can make the relevant difference to “car-ness”, at each stage, you’ll still have two cars!

As soon as you start taking these macroscopic concepts seriously, you find yourself stuck in a ditch. This, to me, is an incredibly powerful argument for eliminativism, and I was surprised to find that arguments like these weren’t stressed at the conference. This makes me wonder if this argument is as powerful as I think.

Some social justice factoids

Starting on a brief personal note…

I’m a bit disappointed with myself for being absent from this blog for the past few weeks. In a Reddit AMA last week, my favorite blogger said that the limiting factor on his productivity is the amount of time he has in a day. This to me is an ideal that I wish I could always be at. The limiting factor on my productivity is almost always my mental capacity to avoid the infinite potential sources of short-term gratification, and to motivate myself to do the things that I get deeper and more long-lived satisfaction out of. Writing this blog is one of those things. My capacity to enforce mental discipline is pretty correlated with my overall state of mind and mood. I think you can actually probably fairly reliably track my mental health by just looking at how often I’m posting here!

I’m also disappointed because I have been thinking about a great many interesting things that deserve posts. I like the idea of using this blog as a faithful recording of my intellectual life, and having discontinuities doesn’t help with this. Much of what I’ve been thinking about over the past few weeks is related to meta-ethics, but it also goes more broadly into the nature of philosophy in general. I hope to write up some posts on these soon.

In the meantime, I’ve also been compiling some interesting factoids I’ve recently encountered related to social justice. Here they are, with sources!

Race

  • Bias against blacks in the justice system can be found in sentencing and in arrests for drug use, but not in arrest rates for violent crimes, police shootings, prosecution rates, or conviction rates. Source.
  • Juries in the Deep South were commonly all-white up until the 1986 case Batson v Kentucky (where loopholes that allowed exclusion of blacks from juries were closed). (from Just Mercy, p. 60)
  • Black Americans graduate from high school at the same rate as white Americans (92.3% vs 95.6%). Source.
    • In 1968, these numbers were 54.4% and 75%.
    • Percentage of college graduates age 25 to 29: 22.8% and 42.1%. (19.3% gap)
  • White adults who don’t graduate high school, don’t get married before having children, and don’t work full time have much greater median wealth than comparable black and Latino adults. Source.
    • Consumption habits can’t explain the wealth gap: white households spend more than black households of comparable incomes.
    • The median white single parent has 2.2 times more wealth than the median black two-parent household and 1.9 times more wealth than the median Latino two-parent household.
  • Poverty rates among African Americans have declined substantially: 34.7% in 1968 to 21.4% in 2016. Source.
    • Among whites: 10% in 1968 to 8.8% in 2016.
  • Great table showing the change in socioeconomic circumstances of blacks and whites in the US from 1968 to 2018: (Source)  
    • Most strikingly in that table… Median household wealth is 10 times higher for white Americans than black Americans (but it used to be 20 times higher).

Gender

  • There is a 7% unexplained wage gap between men and women in the US. Source.
    • Controlling for college major selection, occupational segregation, hours worked, unionization, education, race, ethnicity, age, and marital status.
  • Female leaders are evaluated slightly more negatively than equivalent male leaders (controlling for leadership style). Source.
    • The discrepancy is more pronounced for autocratic leadership styles, and vanishes for democratic leadership styles.
  • Most anthropologists hold there are no known societies that are/were unambiguously matriarchal. Source.
  • Experiments show that women value temporal flexibility relatively more than men, and men value income growth relatively more than women. This is the most powerful explanation of the wage gap. Source.
    • Right after college, wages are pretty similar between men and women, and the wage gap appears as time passes, indicating that ‘innate’ differences aren’t hugely at play (including bargaining ability and temperament).
    • 75% of the wage gap is due to differences within occupations, and only 25% across occupations.
    • Among the top-paying occupations (salary ≥ $60K), the within-occupation corrected pay gaps are biggest where there’s lots of self-employment (explained by self-employment being more demanding).
  • Symphony orchestras introduced blind auditions in the ‘90s, which served as a natural experiment that found significant gender bias against women. Source.
    • The analysis found that in a blind audition for preliminary rounds, the same woman was 9.3% more likely to be hired (from 19.3% to 28.6%), and the same man is 2.3% less likely to be hired.
    • For final rounds, the same woman was 14.8% more likely to be hired in a blind audition (from 8.7% to 23.5%).
    • Introduction of blind auditions also caused an explosion of female auditions.
  • The rate of false reporting for sexual assault is in the range of 2-8%. Source.
  • Estimates of the prevalence rate of campus sexual assault in the US vary hugely, from .61% to 27% of female students, depending on survey definitions and methodology. Source.
  • The percentage of trans men that report lifetime suicide attempts is 46%, trans women is 42%, LGB adults is 10-20%, and among the overall US population is 4.6%. Source.
    • Suicide attempt rates are lower (by about 9%) among trans women that are perceived by others as women, but are the same among trans men.

Other

  • “The IAT is a noisy, unreliable measure that correlates far too weakly with any real-world outcomes to be used to predict individuals’ behavior.” Source.
    • Many early studies on IAT as a predictor of discriminatory behavior had serious methodological problems, including falsification of data by an “overzealous undergraduate”.
    • IAT has a test-retest reliability of .55 on a scale from 0 to 1.
    • Meta-analyses of the IAT-behavior link show that race IAT scores are weak predictors of discriminatory behavior.
    • IAT tests done on fictional races that are identified as one oppressed and the other privileged show “implicit bias” against the oppressed group.
    • More noise in the data predictably biases the IAT score downwards
  • When people hear stereotyping is normal, they may do more of it. Source.
  • The “few antibias trainings that have been proven to change people’s behavior” look at bias as a habit that can be broken. The Prejudice and Intergroup relations lab at UW Madison has had promising results with these type of trainings. Source.

Some takeaways: A lot of the concerns of the social justice movement are clearly very valid and rooted in real issues of societal inequalities that have been handed down to us by previous generations. That said, however, there is a good degree of subtlety required in the analysis of race and gender issues that is missing in the mainstream social justice movement.

The oft-cited 23% gender gap is misleading to say the least, and the actual percentage due to discrimination is unclear but something less than 7%. The focus the Black Lives Matter movement puts on racially biased police shootings is unjustified, and the focus would be better placed on disparate sentencing and drug arrests. And more generally, the overall trends in racial inequality in the United States look extremely positive in virtually every dimension.

It also looks like current methods at identifying and intervening on things like implicit bias and stereotyping leave a lot to be desired. This has some serious implications for questions about actual practical solutions to issues of racism and sexism… even if we acknowledge their existence and seriousness, this does not mean that we should jump on board with any plausible-sounding diversity training program. The question of how to solve these issues is highly nontrivial and deserves a lot of careful attention.