Pencil Theory

There are a lot of problems out there – problems in the philosophical sense. Questions that cry out for answers. If North Korea detonates a hydrogen bomb over the Pacific, what should the rest of us do about it? Or, should we bother sending people to Mars? Or, is capital punishment ever ethical? Or, should newborns be circumcised?

We’re pretty flush with problems, but we tend to come up short on solutions. There are 9 billion people out there, most of which are eager to shout their opinions, but that shouting doesn’t always result in consensus. And even if it did, consensus doesn’t make a thing correct.

It isn’t just a trick of numbers either. Think of whatever smaller group you like: your country, your city, your job, or, if you have them, your political party, your church, your parents, siblings, children, or spouse. The closer group you consider, the more similar your opinions are likely to be, but you also know more about them. So, you’ve no doubt found the little exceptions where you disagree.

For this thought exercise, I think of my martial arts group. I’m not sure how many of us there are – maybe 50. We meet up, week after week, year after year, to study ethics, basically: how to protect people, and why. Now, you might expect – or at least I did – that such a group would have a lot in common in other areas, like politics. But it isn’t so. And whatever groups you are a part of are, no doubt, just as diverse.

Why is that? Well, there’s probably no consensus answer to that question either, but here’s my take on it. Bear with me because it starts out a little abstract.

pencil

Think about this: Nobody knows how to make a pencil – just an ordinary yellow #2 pencil.

It’s true.

But it’s weird, so let’s take a moment to reflect. What does it really take to make a pencil? You carve the two halves out of wood, you glue them around a stick of graphite, paint the thing yellow, and clamp an eraser to the end of it, and you’re done. But that’s not really making a pencil. That’s assembling a pencil out of pencil parts.

If you didn’t have the parts, the list of things you need to know gets a lot longer. To cherry pick a few, you would have to –

  • Harvest and treat wood from cedar trees, which you either find or cultivate.
  • Mine graphite, and form it into sticks somehow.
  • Make the glue. (Is it horse? You don’t know.)
  • Make yellow pigment for the paint. It’s cadmium sulfide, made by mining and processing cadmium and sulfur ores, and then doing a little chemistry.
  • Make acrylic paint medium, a polymer synthesized from oil, which you’ll have to drill and refine.
  • Make synthetic rubber for the eraser (another polymer) and infuse that with pumice (which you mine) suspended in vegetable oil. So now you also have to grow vegetables.
  • Make the thing that holds the eraser in place. It’s called a ferrule, and it’s made of aluminum. So, back to the mines, this time for bauxite. Refine that into aluminum oxide. Smelt that into aluminum. Machine that into a ferrule.
  • Assemble your pencil.

But wait, there’s more. You can’t smelt aluminum in some shitty blast furnace, like you can with steel. Aluminum smelting takes a lot of electricity, which you’ll no doubt pull off of the grid instead of making your own. It’s high voltage, so good luck generating and transforming it yourself.

And for that matter, you’ll need a lot of tools, which I assume you’ll just buy, as opposed to making from iron that you dig out of the ground with your bare hands. And that doesn’t even consider all the mining and oil drilling equipment you’ll need, or the chemistry equipment, or whatever implement you use to slaughter the horse.

There is no end to this exercise. You cannot make a pencil – or much else – except in the context of a modern, industrial society. If you still aren’t convinced, imagine waking up tomorrow on an island, never to see another human being. How long do you think it will take to work your way back to pencil making?

We like to imagine ourselves as rugged individualists, who aren’t dependent on society, who could take it or leave it. But that is a pure delusion, unless you like the idea of eating berries and carrion, and dying when you’re 32. Aristotle argued that a person who doesn’t partake in society must be either a beast or a god. And before we decide to take that as a compliment, consider that a god would have no trouble making a pencil.

Here’s the point. If one person can’t make a pencil, how can we expect one person to know how to make an economic policy that encourages innovation, or a justice system that consistently rehabilitates violent offenders, or a war strategy that preserves the greatest amount of life? How do we make any of those things?

There is an answer, and it’s the same as the answer to the pencil thing: There are a whole bunch of us! One person cannot do these things alone, but one person does not need to do these things alone.

But that’s also what creates these disagreements. The things we find important are so complex that it is unfathomable that we would agree on them, especially right off the bat with no discussion. The discord we see in the world is an artifact of our finite minds attempting to understand an infinitely complex universe.

And since it’s that, it doesn’t need to be anything else. We shouldn’t need a further explanation. Where there is complexity there is disagreement. That is a sufficient explanation.

So, think of a simple political issue. Think of minimum wage. Some people support a minimum wage, because (they argue) it increases the income of some people. Others oppose a minimum wage, because (they argue) it eliminates some jobs.

Who is right doesn’t matter for this discussion. We’re not going to unpack that issue today. What does matter is that both sides of this argument agree on what the goal is. They have the same values. Poverty is bad, prosperity is good. So this is not an ethical issue. It’s an issue of engineering. The only place where these two sides disagree is which method is the most likely to achieve the goal they both want.

We tend to think of people who disagree with us as unethical, because that explanation is easy and coherent. It takes work for me to sort through the nuances of economics that lead you to believe your solution is better than mine. It’s much easier for me to assume you disagree about minimum wage because you hate poor people.

But you don’t, do you? It would be rare if you did. Ethical disagreements exist, but they’re much less common.

What do you think about guns? Should there be more of them, or less? Should there be more regulation, or less? I don’t know what you believe, but I know why you believe it: Life is worth protecting. Wherever you fall on this issue, you fall there because you believe it protects life the best. There is no position in the gun debate that argues that there ought to be more murder.

Notice how trivial the argument would be if there were. The pro-murder people are wrong, and it’s so obvious that it’s hard to argue in any more depth than that. There are edge cases, but for the most part ethical matters are simple and straightforward. Only the implementation is hard. Because, again, we’re talking about a system so complex that no one person can possibly understand it all.

We deal with the same issue in martial arts. We don’t meet up week after week, year after year, to discuss whether to protect people. We meet up to discuss how. What to do – that’s easy. Why to do it – that’s kind of easy. How to do it – that’s extraordinarily complex.

It’s important to recognize the difference between an ethical disagreement and a procedural one. It’s the difference between an enemy, and someone who doesn’t need to be an enemy. If you agree with someone’s values, and only differ about implementation, then you already agree on the most important part. You are already attempting to move toward the same goal.

Differences on how to get to that goal can be hashed out. We can discuss. We can debate. We can collaborate, and eventually arrive at some course of action. That – I think – is why we are so prone to argue. It’s how we reconcile the differences in how we believe the world works. It’s how we are able, in the long run, to make society. Disagreement is the first step toward agreement.

It’s important to recognize who our potential allies are. We’re going to need a lot of them. The end goal – in martial arts and in life, if you’re doing either of them right – is to make the world better.

To do that, you’re going to need as many allies as you can get your hands on. You cannot hope to change the world alone. Society is by far the most complicated thing people have ever made, and you don’t even know how to make a pencil.

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How Galileo Saw What He Saw

Galileo was incarcerated in 1633 until his death for looking through a curved piece of glass and writing down what he saw. There were a lot of reasons, but chief among them was that the people who incarcerated him never bothered to look at what he saw.

It’s easy to imagine ourselves in Galileo’s position – You can build a telescope, but you can’t make anyone look through it. It’s the dilemma of a teacher, which is something we all are at some point in our lives. You can put the telescope you built in some public place for all to use. You can build a fancy beaux-arts building around it. You can offer to explain how it works to anyone who will listen. But you can’t make anyone look.

You could, perhaps, strap people to a table, restrain their heads, clip their eyes open, and wheel the telescope in front of them, so they would have no choice but to look, but you cannot force them to think critically about what they see. You can’t force them to make the effort to understand it.

But, that’s normal. There is more information out there in the world than any one person could possibly learn in a lifetime, so we all have to decide, constantly, what to make time for and what to disregard.

I could tell you, for example, that the number 8 has three cube roots. One cube root of 8 is 2, because 2x2x2=8. There are, in fact, two other numbers that work this way.

Hearing that for the first time, you might respond one of two ways: The first is to try to work it out for yourself. The second, far more likely, is to not give a shit. Which is fine, because unless you have a job or hobbies that involve electricity or acoustics, you will probably never need to know the answer to that question, or how to find it.

When we choose to learn something, it takes some time and effort to process it, to store it in our brains, and to connect properly to all the other things we know. But before we can even do that, we have to make some judgment about whether it is even worth our time.

The people who incarcerated Galileo decided it wasn’t. And why not? Because they already knew what they would see. The Earth is stationary. The Sun moves around it. They knew this as certainly as you know the opposite is true. When someone tells you they found proof the Moon landing never happened, you ignore them, because you already know they’re wrong without checking.

It’s humbling to realize we might have more in common with the people who incarcerated Galileo than we have with Galileo himself, but it’s also worth exploring, because it bears directly on how we learn, and the pitfalls we might fall into.

Let’s think about something more contentious.

Guns. Why guns? Because being a modern human being – especially if you live in America – it is unlikely that you don’t already have an opinion about them. Consider these two statements:

1 – As gun ownership rates increase, homicide rates increase.

2 – As gun ownership rates increase, homicide rates decrease.

Do you have some notion in your mind about which of these statements is true? Stop and really think about it, and while you’re thinking about it, let me complicate things further. Let’s say you knew that I was a strong believer in the first statement. More guns, more homicides.

At this point, you might disagree with me – in which case your mind is likely already pulling out the facts and figures, the anecdotes, the arguments you might make to contradict whatever argument I will make, even though I haven’t made one yet.

Or, you might agree with me – in which case you might be eager at the prospect of learning some new fact or figure you might add to your toolbox for the next time you have a discussion with a proponent of the second statement.

Or, for that matter, you might sense from the way this argument is structured that I’m trying to fool you, and you are instead reserving judgment. That is pragmatic, but for the purposes of this argument, pause here for a moment to consider what you would have honestly done, what would have honestly gone through your mind. Would you have prepared to support my argument? Would you have prepared to refute it? Even if you had no intention of arguing with me directly, what would you have done to settle the matter in your own mind?

If you leaned toward believing the first statement was true, or if you leaned toward the second – either way, you are working toward justifying not looking through the telescope. Which is a shame, because in either case, you might be surprised by what you would find.

The truth is, neither statement is correct, as far as we can tell. The statistics we have show no significant correlation between gun ownership rates and homicide rates. I lied, by the way, when I said I believed the first statement. I hope you can see why it was necessary for the point I was trying to make.

It shouldn’t have mattered what my opinion was. I’m not saying my opinion affected the way you thought about the question, but IF it did, that’s a sign that you weren’t interested in discovering the truth. You were interested in winning an argument.

Which wouldn’t make you different from most of the people discussing the gun issue. People on both sides of the argument argue in the same way: as though the statistics support their position. Why? Most likely because they – like the people who incarcerated Galileo – were so sure of their position that they naturally assumed the data would support them, and so it was not worth their time to verify.

Galileo didn’t know what he was looking for when he built the telescope. He just went looking for the truth, whatever it may be. No one else in this story made that leap, which is why, today, you know who Galileo was, but you don’t know who any of those other people were.

The Four Most Annoying Questions

I spent 7 years in engineering school, and I am not an engineer. Perhaps you wonder, why?

How does someone even answer that kind of question? Well, people who research that sort of thing have found, when we are asked why we did something, our answer is just some bullshit we made up on the spot but wholeheartedly believe. Keeping that in mind, this is why am not an engineer.

A few unrelated times in school, I was asked the following four questions:

1 – How do you put an elephant in the refrigerator?
Answer – Open fridge, put elephant in fridge, close fridge.

Any other answer is considered wrong. The point of these questions is to illustrate that adults have flaws in the way they think. Children, it turns out, answer these questions correctly more often than adults do. Adults are likely to raise objections, such as that an elephant won’t fit in a fridge.

Which is incorrect, because it unnecessarily complicates the process. At least, that is the argument.

2 – How do you put a giraffe in the refrigerator?
Answer – Open fridge, take elephant out, put giraffe in, close fridge.

If you are already heaving a heavy sigh, yeah. I’m right there with you. Most people skip that second step, and answer based on what we learned* in question 1 – Open fridge, put giraffe in, close fridge. Which is wrong, because of fucking course it is.

What would a person have to believe in order for the correct answer to actually be correct? An elephant will fit in a fridge, a giraffe will fit in a fridge, but an elephant and a giraffe will not both fit in a fridge.

Again, children are more likely to give the ordained answer than adults are, proving once again that children are smarter than adults – and not proving, apparently, that children are less reasonable than adults in a specific, repeatable way.

This question claims to test your understanding the repercussions of your actions. Did you realize that when you put the elephant in the refrigerator that he would still be in there later? That’s a trick question, of course, because we did not put an elephant in a refrigerator. We asked a hypothetical question, the repercussions of which do not include the thing you asked about actually happening.

Children are more likely than adults to make this specific mistake, and in doing so, arrive at the correct answer. So children are smarter than adults, and if you aren’t convinced yet, we still have two more goddamn questions to prove it.

Fuck.

3 – The Lion King is holding a meeting. All the animals attend except one. Who does not attend?
Answer – The giraffe.

The giraffe, as you recall, is in the refrigerator. If you don’t recall it – if you thought that was just a hypothetical question and not a thing that actually happened – that’s just you making excuses to protect your ego because you can’t stand the fact that you are consistently being outsmarted by a child.

This question is to test your memory. What it really tests is if you have an okay memory, but not a great one. If you vaguely remember something about a giraffe, you might say the giraffe is in the fridge and answer correctly. If your memory is a little sharper, you may correctly remember that no giraffe was ever actually placed in a refrigerator.

For that matter, why can’t a giraffe get out of a fridge?

4 – You come to a river where crocodiles live. You want to cross but you have no boat. How do you cross?
Answer – Just swim. The crocodiles are at the Lion King’s meeting.

This question tests whether you quickly learn from your mistakes.

Where to begin?

First, you would have to acknowledge that failing to give any of the correct answers above qualifies as a mistake. Which you probably don’t, because this whole test is pretty obvious bullshit.

The test is easy to remember, to go home and ask your friends, to feel smarter than them as they fail to give the correct answers and you educate them as to the errors of their thinking. Feels kinda good. And, typically, the people you introduce this test to will eventually feel the same, as they take the side of the tester, join the team of correctness, and feel really neat two years later when some different clever teacher tries to pull the same trick on them.

What feels bad is holding on to your rational way of thinking. As you look around the lecture hall at the 200 other people, most of whom are wide-eyed with the cleverness they have just witnessed, you realize most of them have actually been convinced there is something wrong with the way they think.

That feeling is horrible. It may compel you to try to convince people that the correct answers aren’t correct at all, but if you try this you will come up against a wall of consensus and frustration, and you associate that frustration with the thing that seems to have caused it – disagreeing with the majority.

If you play along, you are rewarded. If you don’t, you are punished. What you learn is that it is that it isn’t a lot of fun to disagree with the majority, and generally just not worth it.

What made this test particularly annoying was that it came up, as I said earlier, several times during my time in engineering school. And it’s the type of test engineering students lose their minds over. People would talk about it in the halls, in the dorms. Basically grown people – people who were learning how to make bridges and elevators and chemicals and smart phones – felt smarter than other people because they knew how to put an elephant in a refrigerator.

Something about that mentality may have been why I never really fit in with that kind of people.

Now, to be fair, the people actually out there making your bridges and smart phones – I don’t know much about them. Engineering students do not always become engineering professionals, and I’m sure the people who can’t hack it through a test like this don’t make it long in professional practice. They mostly stick around and become professors or whatever.

A Post-Work Society

China had every technology necessary for an industrial revolution hundreds of years before the revolution actually happened in Europe. Why did it not start in China?

Industrialization is about efficiency – it’s about doing as much work as possible, using as few people as possible. But, people were China’s most abundant resource. They had no reason to conserve labor, to do work more efficiently, and so they did not industrialize.

To our modern sensibilities, this argument should make perfect sense. We are in the midst of a technological revolution of our own. Manufacturing jobs for humans are going away as factories realize a new tier of automation. Deliveries have just begun being made by drone. Several companies are developing self-driving cars, with surprising levels of success. Agents – who sell things like real estate and insurance – are being replaced by software.

As I write this post, politicians are scrambling to keep manufacturing jobs in this country. But, that scramble is futile. Those jobs aren’t leaving the country so much as they are leaving the world, never to return. Unlike China of the past, who didn’t have any reason to industrialize, modern companies have a strong motivation: profit. Automated manufacturing is far more efficient, to the extent that it is cheaper to manufacture goods in the United States using machines than it is to have people in third world companies do the work for third world wages.

Manufacturing may be moving back to the United States, but that doesn’t mean we are going to get back our precious manufacturing jobs. I call them precious because modern society places enormous importance on jobs. We judge the health of our economy on unemployment statistics. A person who cannot find a job is seen as tragic. A person who chooses not to aggressively seek a job is ostracized. There is a mantra throughout our culture, whether stated aloud or not: A job for every person, and every person at his job.

Of course we are not the first to face this problem. Nor were the people of every nation which has ever industrialized. There was a time when we – humans – knew how to farm, but not very well. We were an agrarian society, so called because almost every worker worked in agriculture. The better we got at farming, the fewer farmers we needed, and the more people didn’t have anything in particular to do.

What did the farmers forced into early retirement do? They invented new jobs. They found new ways to be productive, to increase our standard of living. Fewer farmers meant more craftsmen, stone masons, architects, entertainers, and makers of soap. We moved beyond the agrarian lifestyle.

And then we moved beyond the preindustrial lifestyle. Industrialization of agriculture meant even fewer farmers and more mathematicians, fewer craftsmen and more scientists, fewer teamsters and more operators of trains. More people doing the things that make our current way of life possible. Tesla invented radio, Fleming discovered penicillin, Tolkien wrote Lord of the Rings, Armstrong walked on the moon, and Elon Musk created the Tesla, all for the exact same reason: They were not too busy farming potatoes.

So don’t panic! Chanters of the mantra would have you believe the employment problems we are facing down are signs of a catastrophe. In time, we will come to think of them as nothing more than the growing pains of a new, presumably better future coming into being.

We do have some logistical questions to answer in the mean time, though. What should those displaced workers do while they wait for the future to get here? How can they be expected to put food over their heads and roofs in their mouths?

One possible solution goes all the way back to one of the founders of the United States – Thomas Paine. He wrote about the issue when it arose the first time, when the hot new science was Somewhat Better Farming.

In Agrarian Justice, he argues for land owners to pay a tax that would pay to support non land owners. He justified the tax as compensation for the use of the land. Before we cultivated the land, a person could support himself off of the resources he found there – resources which belonged to no one. But now that the land was cultivated, the only resources one might find there were someone else’s crops and livestock. The land owners were therefore responsible for ensuring the people could still survive, which Paine suggested they do monetarily.

The idea was never enacted, as best as I can tell, but the idea has persisted, and has now transformed into more modern concept: basic income. Although Paine’s justification doesn’t seem to apply, the concept is the same. If automation is set to put people out of work, why don’t we just pay those people anyway?

The first argument against this idea has a Red Scare flavor. Free money sounds like socialism. Free market capitalistic theory would say this basic income creates a disincentive to work. Why work when the government pays you not to?

First, because basic income is not meant to provide a lavish lifestyle. It’s a sustenance level of income. It’s enough to afford food and shelter, enough for a person to be reasonably assured not to starve or freeze to death.

Second, because basic income is not conditional. Work does not disqualify a worker, and so any income earned over basic income is simply supplemental. There is still plenty of motivation for people to work.

We may not have basic income yet, but we do have plenty examples of people with enough money they don’t have to work. What kind of lives do they lead when they don’t have a financial need to punch a clock?

Warren Buffet does not need to work in order to make the payments on his modest one-bedroom apartment or to be able to afford groceries next Friday. But he goes to work anyway. Robert Downey, Jr. made $80 million in 2015 and did not retire. Hillary Clinton and Donald Trump – say what you will about either of them – they are both wealthy enough they never need to work again, and yet in 2016 they competed to see which of them could get one of the most stressful jobs in the world.

When people say, they need incentive to work, which they are those people talking about?

Jobs in manufacturing, logistics, sales – even agriculture, where this all began – those are working class jobs. So when people reference this need for incentive, what they’re saying is working class people need to be properly motivated. Because, perhaps, they lack something better people possess.

Educated people, they don’t need to be motivated. No one questions why a partner at a law firm keeps working after making his or her first few millions. Or why entrepreneurs don’t sell off their companies as soon as they’ve made enough to comfortably retire.

Wealthy people, they also don’t need to be motivated. It would be easy to assume Julia Louis-Dreyfus got rich along with the rest of the cast of Seinfeld. In fact, she was a billionaire before the show began. She was born a billionaire. When people learn this piece of trivia, the typical response is to shrug. Rarely does anyone ask, Well then why does she bother acting?

Creative people somehow also don’t need to be motivated. Stephen King doesn’t have Julia Louis-Dreyfus money, but he is sitting pretty comfortable on his $400 million. And he continues to write, because he’s a writer and that’s what writers do. It’s just the kind of person he is.

But before Stephen King was the writer of The Shawshank Redemption – a story about a man incarcerated and forced to work, though he committed no crime – he worked in a textile mill. Dismal work for dismal pay. What kind of person was he then? Was he always the kind of person who would grow up to be Stephen King the Writer? Or did he only become that when he learned, while sitting in his kitchen trying to think of a way to afford penicillin for his daughter, that he had sold Carrie?

The hero of The Shawshank Redemption, like the writer, eventually found a way out of what seemed to be a hopeless situation, but both of them were rare exceptions. How many great thinkers – artists and scientists and poets and leaders – how many do we just not know about because they didn’t happen to beat the odds?

If working class people need to be spurred to work, it isn’t because they are a different type of people. Could it be that they need more motivation because they do a different class of work – the kind of work no one would do if they had a choice? We occasionally see an eccentric billionaire decide to go into acting or politics, but we don’t ever see them decide to lay asphalt or assemble machinery.

We have a sort myth of a working class hero – a man made hard by hard work. We might imagine a man laying brick for 30 years to send his daughter to college to be a lawyer or an astrophysicist. There is something romantic in the idea of a person enduring hardship in order to reach a better life for himself or his offspring.

Even in that myth, there is something aspirational. It acknowledges that there is a better possible life out there. We never bother to imagine a man laying brick for 30 years so that someday, maybe his grandson’s grandson’s grandson can go to brick laying school.

That better life, the working class hero has worked for – maybe that is what we are on the cusp of achieving. Maybe it isn’t just him, or his children, or theirs, who can now have that life. Maybe all of us can.

The Sleeping Beauty Problem

A friend of mine recently brought a logic problem to my attention. It’s called the Sleeping Beauty Problem, and it’s considered something of a paradox. From the Wikipedia page describing it <Sleeping Beauty Problem>:

Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice, during the experiment, Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends.

Any time Sleeping Beauty is awakened and interviewed she will not be able to tell which day it is or whether she has been awakened before. During the interview Beauty is asked: “What is your credence now for the proposition that the coin landed heads?”

First of all, you might wonder what credence is. It’s just probability. In this example, it is how sure Sleeping Beauty is that the coin landed heads. Of course she could be wrong. She could be 100% sure the coin landed on heads. But for this problem, we assume that she is perfectly logical, and that her credence is exactly the same as the correct probability. In short, credence is different from probability in that the people who coined the first term were apparently unaware that the second term already meant exactly the same thing.

But whatever.

So what’s the answer? Apparently there are two, which the same Wikipedia page names the Thirder Position and the Halfer Position. (There is a third position given but it’s wrong and even the guy who argued it knew it was wrong.) These arguments are paraphrased from the Wikipedia page:

The Thirder Position – If the coin comes up tails, there will be two interviews which SB could not distinguish between, so the probability that is both tails and Monday, P(tails and Monday), must be equal to the probability that it is both tails and Tuesday, P(tails and Tuesday). Similarly, if SB assumed the day of the interview was Monday, she would have no reason to believe heads or tails was more likely than the other. The procedure, she notes, does not require the coin to actually be thrown until Tuesday. So, Monday, the probability of the result being heads is equal to the probability of it being tails. Therefore P(tails and Monday) = P(tails and Tuesday).

P(tails and Monday) = P(tails and Tuesday) = P(heads and Monday)

As these are the only three possibilities, they add to 1, and so are each equal to 1/3. Only P(heads and Monday) has the coin flip landing heads, and so P(heads) equals 1/3.

The Halfer Position – The probability of a fair coin landing heads is 1/2, by definition. SB is awakened and interviewed. She knew at the outset of the experiment that this would happen, so she has gained no new information, so her credence cannot change. It must still be 1/2.

Let’s consider the Halfer Position. If we suppose P(heads) = 1/2 as it argues, we can deduce some odd findings. If P(heads) = 1/2, then P(heads and Monday) = 1/2, because if the coin lands on heads, there is no interview Tuesday.

We also find P(tails and Monday) = P(tails and Tuesday) for the exact same reason as it was true in the Thirder Position. So, they each equal 1/4

The term P(heads|Monday) means the probability that the coin flip landed on heads given that the day is Monday. It’s called conditional probability. It means, in this case, if SB somehow learns the day is Monday, what is her credence then that the coin landed heads?

We can calculate P(heads|Monday) and several other values as follows. By the definition of conditional probability:

P(heads and Monday) = P(heads|Monday)*P(Monday)
P(heads and Monday) = P(Monday|heads)*P(heads)
P(heads and Tuesday) = P(heads|Tuesday)*P(Tuesday)
P(heads and Tuesday) = P(Tuesday|heads)*P(heads)
P(tails and Tuesday) = P(tails|Tuesday)*P(Tuesday)
P(tails and Tuesday) = P(Tuesday|tails)*P(tails)

By solving these six equations simultaneously – which turns out to be a simpler algebra problem than it appears – We find the following:

P(heads|Monday) = 2/3.

This means if SB somehow learned during an interview that the day were Monday, she would have to answer that her credence that the coin landed on heads was 2/3. But, what would she have learned that would have changed her credence?

The Halfer Position is based on the assertion that waking and being interviewed doesn’t give SB any new information. After all, she knew she would be interviewed regardless of the coin flip. Being interviewed tells her only that there is an interview conducted, which is not new information, and therefore she cannot change her credence. That’s the argument.

However, the same argument can be applied to her being interviewed and knowing the day is Monday. This scenario would tell her only that there is an interview conducted on Monday. Again, she knew this would happen from the outset, so learning it here doesn’t give her any new information, and therefore she cannot change her credence. But she must, because for P(heads) to equal 1/2, P(heads|Monday) must equal 2/3.

Compare this experiment to a similar one, in which there is one interview performed on Monday if the coin flip lands on heads, but there are three interviews, performed Monday, Tuesday, and Wednesday if the flip lands on tails. Either way, she is released on Thursday.

In this experiment, SB’s credence that the coin flip is heads must be 3/4 if she somehow learned the day were Monday. Or, P(heads|Monday) = 3/4. The only difference between the two experiments, however is the number of interviews that have yet to be performed at the time this interview takes place.

What if she didn’t know which of these two experiments she was in? Consider a third experiment. Heads, one interview on Monday. Tails, one interview on Monday, followed by a random number of interviews on subsequent days.

In this experiment, the following chain of events might occur. SB is put to sleep. A fair coin is flipped. She is awakened, somehow learns that the day is Monday, and is interviewed. When asked for her credence, she can only reasonably answer that she does not know, that she would need to know how many interviews the experimenters are planning to perform in subsequent days.

Strangely, if the experiment isn’t disrupted, if she is awakened on Monday but did not know it was Monday, she could confidently answer that her credence was 1/2. If she then learned that it was Monday, she would have to quickly change her answer. She previously thought it was 1/2, but upon learning that it was Monday, she no longer has enough information to answer the question.

So the Halfer Position is wrong. But why is it wrong?

The Halfer Position asserts SB does not learn anything from being awakened and interviewed. Is that true?

Maybe. But her credence could change for another reason: the amnesia drug. Her change of credence stems not from something she knows but from something she doesn’t know.

Notice how trivial the interview becomes if there is a calendar in the room. Monday, she correctly answers 1/2. Tuesday, if there is an interview, she correctly answers 0.

Without the calendar, she knows what the probability is in the case that the day is Monday, and she knows what the probability is in the case that the day is Tuesday. What she does not know is which case she is in.

She doesn’t know. That is true. However – the point that the Halfer Position neglects – she does know the probability that the day is Monday. And she can use that information to adjust her credence.

It isn’t trivial to calculate, as P(Monday) is known only in terms of P(heads). There are numerous correct approaches to take to solve the problem this way, but the most straightforward and elegant is the one presented in the Thirder Position, above.

Here are a few of the key results:

P(heads) = 1/3
P(heads|Monday) = 1/2
P(heads|Tuesday) = 0

If it is Monday, the odds are 1/2, as expected. If it is Tuesday, the flip is guaranteed to be tails, also as expected.

Some have called this problem a paradox. A paradox occurs when the intuitive answer to a question is different from the correct one.

Strike the notion from your mind. Do not believe there is any such thing. If your intuition differs from reality, your intuition is deficient. If you allow ideas to persist in your mind under the heading of Paradoxes, you are allowing this deficiency to continue to be a part of your logical process.

Retrain yourself to intuitively see the world as it actually is.

In this case, a tool to keep in the toolbox is this: Information helps you make better judgments. Right?

Notice how in the Thirder Position, SB answers that her credence is 2/3, which is not the precise probability in either case. But upon learning the day, she can adjust her answer to either 1/2 or 0 (depending on what day she learns it is), which is the correct probability in each case.

However, in the Halfer Position, SB answers 1/2, but when she learns the day is Monday, her credence gets worse, moving to 2/3.

And remember the Halfer Position applied to the experiment with a random number of interviews. If SB doesn’t know the day, she answers 1/2, but upon learning that the day is Monday, no longer knows enough to answer the question.

Of course, we could contrive examples where a subject answers some question correctly just by dumb luck, and additional information causes the answer to deviate, but generally speaking, knowledge is helpful, and any case where the opposite appears true should make you suspicious.

 

Captain America: Civil War Could Be Better

Here’s what bothers me about Civil War: Tony Stark is all over the place.

It’s not so much a movie about super heroes. It’s about an ethical conflict. It’s a movie where Rogers and Stark debating politics over a conference table is more fun to watch than Captain America and Iron Man battling it out with their super friends.

And that’s all fine. I’d watch the two of them debate all day. That is, I would have, if Tony were written better.

Steve makes a strong argument. He refutes Tony’s point about accountability with his mini-speech about the right to choose. He warns that the oversight commission might one day prevent them from getting involved in a situation they all know needs their involvement. For the genre this movie is in, his argument is shockingly well articulated.

But Tony’s isn’t. He meets a woman whose kid dies, and it prompts him to argue that oversight is necessary because of that. Then he says he’s in favor because it’s a way to split the difference between being Iron Man and not, so his girlfriend won’t break up with him. Then he argues the measures are necessary in order to prevent some nebulous worse thing, which he never explains and we never see. And then he argues that he’s trying to keep the Avengers from breaking apart. Although, taking a hard line stance on a controversial issue is maybe not the best way to do that.

The result is, by the time the big showdown occurs, main characters are already criticizing the movie’s plot, saying thing like – This is not the real fight. And through this climactic battle, I find myself on the side of Vision, who sees the fight as completely pointless.

For that matter, so does Tony, eventually. What Steve warns could happen happens. Tony gets told to stand down, and he doesn’t want to.  He ends up acting against the oversight committee he has sworn to support. At this point the conflict is resolved. That’s it. Movie over.

But they have a last showdown after all, one on one. But the original conflict is resolved so they have to contrive a new one. Bucky I guess killed Tony’s parents.

So, Tony fights Steve over actions he wasn’t involved in, because he stood up for Bucky, who only did those things under mind control. Strangely, Tony didn’t take it personal when Hawkeye got mind controlled and blew up the airship thing, nor at Bruce after he was mind controlled into hulking out on a city. So why now?

Okay. We’re talking about his parents. It’s traumatic. Whatever. Tony is smart enough to know better than that, and even if he isn’t, we’re really just watching a fight that’s about Tony throwing an unjustified tantrum. And isn’t that kind of a stupid thing to have a movie about?

This frustrates me because it didn’t have to be this way. There is an argument Tony could have made, which is at least as strong as Steve’s position.

He has a history of caring about accountability. When Stark Industries was dealing weapons under the table, he became Iron Man to undo the damage, but he stayed with the company and fixed the problems. The company is a machine, and like any machine, when it malfunctions it can be fixed.

Tony touches on the idea that the documents can be amended, fixed. Safeguards put in place. He calls the actual signing a PR stunt. But it’s one sentence and then the idea is abandoned.

Tony could have stuck on this point. He could have even exposed Steve for a bit of a hypocrite. When Steve says he won’t sign, that he won’t let some government body tell him what he can’t do, Tony could say something like, “There are already people telling you what you can’t do. Signing the document doesn’t limit our authority. It grants us authority. Because without it we don’t have any. You can’t dress up as a flag, call yourself Captain America, and pretend not to be part of something bigger than yourself.”

From there he could argue that Steve is being a coward. He could argue that the only way to fix something is to be a part of it, and proceed to shame him for trying to run away from the issue.

And that would be a conflict they can’t easily resolve, that Steve can’t refute out of hand. They could have their final showdown, the movie could end, and they could have still not resolved this issue, leaving a rift that would change the dynamic of the whole series.

But maybe Marvel doesn’t have the guts to tell a story that way. Even with all the MCU movies have done, maybe they’re still stuck on the conventional wisdom that each movie must stand on its own, and end by returning to status quo.

That could be why Age of Ultron ends with Ultron being utterly wiped out. “You want to protect the world, but you don’t want it to change,” Ultron accidentally says about his own writers.

That could also be why after Tony (along with Hawkeye) sets the stage for his own retirement at the end of both Iron Man 3 and Age of Ultron, but at the beginning of Civil War, he’s still just being Iron Man. Everything has to return to normal. There can’t be too much homework for the viewer. We can’t have that be why some people didn’t see the latest movie.

Maybe it feels more pragmatic to make movies this way, but it makes the story weaker. The theme is watered down. And if you think that doesn’t matter, remember that Age of Ultron was actually considered a box office failure. It made far less than the makers expected.

Civil War still did fine – as much as I criticize, the movie did have a lot of good going for it. But it won’t last. The first Avengers movie and Civil War both proved that they can manage a growing ensemble cast of characters. But with three more Avengers movies already slated, eventually that concept will not be so novel, and people will be left scratching their heads about why the theaters aren’t as packed as expected.

It comes down to good storytelling. Civil War could have been a movie about a philosophical dilemma, and two strong, ethical people who cannot come to terms on it. Instead, we get a movie about two guys fighting over some circumstantial bullshit, which isn’t particularly important to either character, certainly isn’t important to me, and loses my interest right around the time the fighting started.

By the end, the movie devolves into an excuse to find out who would win in a fight between two vague sets of super powers. Spoiler: It’s the one whose name is in the title.

Connective Tissue

The Man in Black fled across the desert, and the Gunslinger followed.
-Stephen King, The Gunslinger

This sentence is really two – the one about the Man in Black, and the one about the Gunslinger. Combining them with the word and merely smooths out the delivery. Generally, one sentence conveys one idea.

When writing a story, there is a tendency to add variety to the prose. Rather than simply writing out a list of sentences, we try to organize them in a meaningful way, to smooth out the transitions between them, and sometimes we make the mistake of including too much connective tissue.

King’s sentence clearly shows some connection between the two ideas, so perhaps we would be tempted to include the word because in place of and.

Because the Man in Black fled across the desert, the Gunslinger followed.

Worse, right?

The word and is not one we need to avoid overusing. It’s like said. The reader doesn’t even know he or she read it. On the other hand, replacing and changes the meaning and focus of a sentence. Here’s another Stephen King sentences:

Hemingway and Fitzgerald didn’t drink because they were creative, alienated, or morally weak. They drank because it’s what alkies are wired up to do.
-On Writing

The word because shows up here again. Notice that there are three ideas being conveyed in the second sentence:

1 – Hemingway and Fitzgerald drank.
2 – Alcoholics are wired up to drink.
3 – The second is the cause of the first.

The word because changes the meaning of the sentence. It’s not about either idea separately. It’s about the relationship between them. Which means, if either of the first two ideas are new to the reader, the sentence is overworked. Three ideas are too many for one sentence – or even two – to convey.

As it happens, the example sentence is taken out of a context where Hemingway and Fitzgerald drank and Alcoholics are wired up to drink are previously established.

In short, use because because the relationship between A and B is what is important. Do not use because just to tell us A and B. It’s too wordy. The word and is free. The reader never sees it. The word because is far more visible.

Let’s look at three ways this problem can sneak into your prose.

Timing

The word while sneaks in between sentences.

Mike hacked into the computer while Jill disarmed the bomb.

The sentence tells us three things: What Mike did, what Jill did, and that they happened simultaneously. In all likelihood, that third piece of information is unnecessary.

In other cases, the order things happen might be important, but obvious without any connective tissue.

He drew his gun and I drew mine and fired and missed.

We naturally assume that the actions described happened in the order they were written. Spelling it out with ordinates – such as first, then, next, last, or finally – is unnecessary. If you include them, you’re insulting your reader by assuming he or she won’t understand without your help.

Only spell out the timing of things when the timing is the point. Remember this line horribly misquoted from the movie Scarface:

In this country, first you get the money, then you get the power, then you get the women.

The actual line is different, but the misquoted version is pretty catchy. Notice, though, how much it loses if we take out all the ordinates.

In this country, you get the money, the power, and the women.

None of these three events individually are the point. The point is the sequence. The words first, then, and then clarify, drawing attention from the individual events to the relationship between them.

Cause and Effect

Our initial examples from The Gunslinger were of this type. Look out for words like becauseso, if and then, and therefore.

These words are rarely necessary. When we read something that needs support, we tend to assume that support will follow immediately. Consider this line from the movie Monster’s Ball:

I’ve always believed that a portrait captures a person far better than a photograph. It takes a human being to truly see another human being.

The logic flows naturally. The word because would be superfluous. When we expect things to be a certain place, and they are, we don’t need a sign to point the way.

This problem can sneak into even simple sentences.

He went outside to smoke.

If the point is to convey two ideas – he went outside, and he smoked – just say that. The to seems to qualify the sentence, as though the speaker is specifically trying to avoid saying whether he was successful.

Where’s Mike?
Don’t know, boss. He went outside to smoke.

Fine for characters to hedge their bets this way, but for a narrator it is strangely non-committal.

She applied pressure to his shoulder to stop the bleeding.

Yeah okay. Was she successful? The sentence doesn’t actually address that point.

As before, the word because (and its cousins) should only be used when at least one of the connected ideas is already known. Consider this:

I write because life never works except in retrospect.

Does that sentence feel a little rushed? It’s overworked, just like the quote about Hemingway and Fitzgerald above. It tells us two things – that the writer writes, and why he writes.

The quotation (slightly paraphrased) is from Chuck Palahniuk, the author of Fight Club. Here it is again:

I write because life never works except in retrospect.

It’s the exact same sentence, but it works better now because some of the information is not new to us. We know Palahniuk writes. The sentence only has to tell us why. One sentence, one idea.

Expectation

What is wrong with this sentence?

He was shot but didn’t die.

It’s the same thing that is wrong with this sentence:

She was exposed to radiation but didn’t get any super powers.

The word but is sneaky. It often suggests the reader knows what the writer is thinking. The first sentence says three things:

1 – He was shot.
2 – You probably think he died.
3 – You are wrong.

The second says:

1 – She was exposed to radiation.
2 – You probably think she got super powers.
3 – Not so much.

There are two problems: It’s usually not wise to assume what your reader’s opinions are. You could be wrong, and if you’re wrong you will look foolish.

The second problem should be obvious by now. Overworked sentences. The word but works only when there is some obvious connection between the two ideas. He was shot but didn’t die feels like a safe bet, except that the mortality rate of gunshot wounds is something like 25%. The problem is minor in this example, because it isn’t a stretch to assume a gunshot wound is intended to kill someone – but still. Maybe one of your readers is a trauma surgeon, who reads it and rolls his eyes. Best to avoid when possible.

The word but – along with his friends althoughstill, and however – becomes a serious problem when used merely for variety.

Russell ran into the bank, but Alex stayed behind to guard the door.

There isn’t any expectation here. I have no reason (at least without context) to assume these two people – about whom I know nothing – would go into a bank together.

At a glance, it looks appropriate, because the characters are doing opposite things. One is going inside, the other is staying outside. But that isn’t enough reason. There are two characters doing two different things. It should be written as two sentences. Using but to emphasize some connection between them is just confusing.

Russell ran into the bank. Alex stayed behind to guard the door.

The phrase stayed behind is plenty to explain the connection between these two actions. Not all sentences need to be strung together. If there’s a clear relation, you shouldn’t need to spell it out. If there isn’t one, forcing it can be artificial and confusing. For example, you would never consider writing a sentence like this:

The Man in Black fled across the desert, but the Gunslinger followed.