Difficult Subject Matter in 90’s Song Lyrics

I don’t want to make one of those click bait “the 90’s had the best music EVER!!” posts. One can find really terrible music and really excellent music in any decade. It would be a futile task to claim one decade had the best music.

I went down a strange rabbit hole the other day, though. I just put up a song on youtube and let the autoplay happen while I worked on some other things. It shifted into some sort of 90’s nostalgia playlist, and I kept hearing very surprising lyrics. They were songs I knew from living through the time, but they handled difficult subject matter in subtle and beautiful ways I hadn’t noticed.

I’d be surprised if songs like these could get on the radio today, but I distinctly remember hearing both of these songs on the radio in the 90’s.

Let’s start with “Round Here” by Counting Crows. First off, I’d like to point out that the song is through-composed, already something that could never happen today. The song appears to be about a depressed girl who attempts suicide. But it’s also about the disillusionment of growing up and finding out all those things you were told in childhood probably didn’t matter.

If you think it’s farfetched to have so much in one “pop” song, listen to it a few times. It’s all in there and more. A quick google search brings up wild, yet convincing, interpretations. This “universality” is the hallmark of great song art. Everyone listens to it and thinks it’s about their experience.

Here’s the opening:

Step out the front door like a ghost
Into the fog where no one notices
The contrast of white on white.
And in between the moon and you
The angels get a better view
Of the crumbling difference between wrong and right.

It opens with a beautiful simile. Sometimes pop songs have similes, but they tend to be funny or ironic. It’s hard to think of any current ones that do the hard work of writing something real. “Like a ghost into the fog” is such apt imagery for the point he’s making. Ghosts are white and ethereal. Fog is white and ethereal. A ghost that steps into fog loses all sense of self and no one else can see the person. They’re lost.

Then angels see a crumbling of the difference between wrong and right. This sort of moral ambiguity is another thing it would be hard to find in today’s lyrics. In the context of one of the interpretations I provided, this is probably in reference to how adults tell children right and wrong with clear certainty. As one grows up, one learns that it’s never that obvious.

The lyrics just keep getting better from there.

Next up is “Freshmen” by the Verve Pipe. This song hit Number 5 on the Billboard Top 100. Fifteen years ago, I thought I understood this song. Now I hear it from a totally different perspective.

Originally, I thought it was about a girl that broke up with the singer and then she killed herself over it. The singer is ridden with guilt. But the lyrics, when carefully analyzed, paint a slightly different picture.

Here’s the opening:

When I was young I knew everything
She a punk who rarely ever took advice
Now I’m guilt stricken,
Sobbing with my head on the floor
Stop a baby’s breath and a shoe full of rice

The singer is a typical Freshmen. He thinks he knows everything. This is part of what has changed for me in the song. I was pretty modest as a Freshmen, but now I can look back and it terrifies me how much I thought I knew. I’ve heard this feeling only gets worse as you age.

The key to the song is given right up front. “Stop a baby’s breath” is a reference to his girlfriend getting an abortion, and how this led to a fight and breakup. “A shoe full of rice” is about how they were even planning on getting married. Again, this is subtle imagery that blows by early on in the song. It requires careful attention if one is to understand the rest of the song.

I can’t be held responsible

This is something he tells himself, but he doesn’t believe it. This is a shift in voice, because it goes from narration of the story to internal thoughts. If one takes this line at face value without understanding this shift, one will misinterpret it. Here’s the chorus:

For the life of me I cannot remember
What made us think that we were wise and
We’d never compromise
For the life of me I cannot believe
We’d ever die for these sins
We were merely freshmen

Here’s another reference to his youthful arrogance. He thought he knew everything, and convinced his girlfriend to get the abortion. He refused to compromise and it destroyed their relationship. If you don’t know this song, it’s worth a listen to the rest. It progressively complicates as the guilt reverberates. He can’t hold other relationships out of fear of it happening again.

There’s something haunting about the reiteration of “we were merely freshmen” at the end of each phrase. When we’re young, we think we can do anything without much lasting consequence, but the singer learns the hard way that one devastating mistake can haunt you forever.

To wrap this up, I want to reiterate that it isn’t the difficulty of the subject matter that I find so amazing about these 90’s hits. Plenty of current hits have difficult subject matter. It’s the delicacy with which the lyrics handle the subject. It’s poetic and abstract so that the feeling comes through but the listener interprets it to apply to their own life.

The Carter Catastrophe

I’ve been reading Manifold: Time by Stephen Baxter. The book is quite good so far, and it presents a fascinating probabilistic argument that humans will go extinct in the near future. It is sometimes called the Carter Catastrophe, because Brandon Carter first proposed it in 1983.

I’ll use Bayesian arguments, so you might want to review some of my previous posts on the topic if you’re feeling shaky. One thing we didn’t talk all that much about is the idea of model selection. This is the most common thing scientists have to do. If you run an experiment, you get a bunch of data. Then you have to figure out the most likely reason for what you see.

Let’s take a basic example. We have a giant tub of golf balls, and we can’t see inside the tub. There could be 1 ball or a million. We’re told the owner accidentally dropped a red ball in at some point. All the other balls are the standard white golf balls. We decide to run an experiment where we draw a ball out, one at a time, until we reach the red one.

First ball: white. Second ball: white. Third ball: red. We stop. We’ve now generated a data set from our experiment, and we want to use Bayesian methods to give the probability of there being three total balls or seven or a million. In probability terms, we need to calculate the probability that there are x balls in the tub given that we drew the red ball on the third draw. Any time we see this language, our first thought should be Bayes’ theorem.

Define A_i to be the model of there being exactly i balls in the tub. I’ll use “3” inside of P( ) to be the event of drawing the red ball on the third try. We have to make a finiteness assumption, and although this is one of the main critiques of the argument, we can examine what happens as we let the size of the bound grow. Suppose for now the tub can only hold 100 balls.

A priori, we have no idea how many balls are in there, so we’ll assume all “models” are equally likely. This means P(A_i)=1/100 for all i. By Bayes’ theorem we can calculate:

P(A_3|3) = \frac{P(3|A_3)P(A_3)}{(\sum_{i=1}^{100}P(3|A_i)P(A_i))}

\frac{(1/3)(1/100)}{(1/100)\sum_{i=3}^{100}1/i} \approx 0.09

So there’s around a 9% chance that there are only 3 balls in the tub. That bottom summation remains exactly the same when computing P(A_n | 3) for any n and equals about 3.69, and the (1/100) cancels out every time. So we can compute explicitly that for n > 3:

P(A_n|3)\approx \frac{1}{n}(0.27)

This is a decreasing function of n, and this shouldn’t be surprising at all. It says that as we guess there are more and more balls in the tub, the probability of that guess goes down. This makes sense, because it’s unreasonable to think we’d see the red one that early if there are actually 100 balls in the tub.

There’s lots of ways to play with this. What happens if our tub could hold millions but we still assume a uniform prior? It just takes all the probabilities down, but the general trend is the same: It becomes less and less reasonable to assume large amounts of total balls given that we found the red one so early.

You could also only care about this “earliness” idea and redo the computations where you ask how likely is A_n given that we found the red ball by the third try. This is actually the more typical way the problem is formulated in the Doomsday arguments. It’s more complicated, but the same idea pops out, and this should make intuitive sense.

Part of the reason these computations were somewhat involved is because we tried to get a distribution on the natural numbers. But we could have tried to compare heuristically to get a super clear answer (homework for you). What if we only had two choices “small number of total balls (say 10)” or “large number of total balls (say 10,000)”? You’d find there is around a 99% chance that the “small” hypothesis is correct.

Here’s the leap. Now assume the fact that you exist right now is random. In other words, you popped out at a random point in the existence of humans. So the totality of humans to ever exist are the white balls and you are the red ball. The same type of argument above applies, and it says that the most likely thing is that you aren’t born at some super early point in human history. In fact, it’s unreasonable from a probabilistic standpoint to think that humans will continue much longer at all given your existence.

The “small” total population of humans is far, far more likely than the “large” total population, and the interesting thing is that this remains true even if you mess with the uniform prior. You could assume it is much more likely a priori for humans to continue to make improvements and colonize space and develop vaccines giving a higher prior for the species existing far into the future. But unfortunately the Bayesian argument will still pull so strongly in favor of humans ceasing to exist in the near future that one must conclude it is inevitable and will happen soon!

Anyway. I’m travelling this week, so I’m sorry if there are errors in those calculations. I was in a hurry and never double checked them. The crux of the argument should still make sense even if you don’t get my exact numbers. There’s also a lot of interesting and convincing rebuttals, but I don’t have time to get into them now (including the fact that unlikely hypotheses turn out to be true all the time).

Year of Short Fiction Part 4: Breakfast at Tiffany’s

Breakfast at Tiffany’s is one of those weird cultural staples that literally everyone has heard of it. Most people over a certain age have probably seen the movie, but ask them what it’s about, and they probably have no idea. It’s kind of fascinating to think how a novella/film gets to such a point. I can’t even think of another cultural phenomenon of this type.

I was pretty excited going into this for a few reasons. I, too, had seen the movie enough years ago to not remember it. Oh, there’s the long cigarette, and a crazy cat, and a wacky party girl, and singing “Moon River,” but what was it about? What was the plot? The other reason I was excited was that Truman Capote’s In Cold Blood is one of two books that have ever made me cry. The way he writes is breathtaking.

The first thing to jump out at me was the vulgarity of the language. It was published in 1958, so we’ve moved past short fiction that hides indiscretions. But I still must imagine this novella pushed what was acceptable for the time. It openly talks about prostitution and homosexuality and a 14-year-old girl getting married to an adult man. Plus, Holly’s language is very direct and crude (I don’t recall if she swears, though).

Lolita came out a few years before Breakfast at Tiffany’s, and Tiffany’s doesn’t compare in disturbing imagery to that. So I guess I shouldn’t have been too surprised. It had more to do with tone than imagery, though.

The novella is basically a long character study, and it does an excellent job at this. Holly has to be one of the strangest characters of all time. Capote’s attention to detail is incredible. Almost every sentence that has Holly in it is crafted to expose some tiny piece of how her mind works. An early example is that the location on her business card is: traveling.

At first, it comes off as chaos. Nothing about the character makes sense, and the sentences she speaks come out in a stream-of-consciousness level of confusion. But then, by about halfway or so, she’ll do something weird, and you find yourself thinking: that’s so Holly. There appears to be a deep internal logic to it. Holly feels very real and knowable.

The plot itself is fairly melodramatic. It goes by at rapid-fire pace. This short novella has Holly being in love with and engaged to several people. She travels to probably a dozen places, often not even in the U.S. There’s parties. She’s involved with a scheme to smuggle drugs orchestrated by a man in prison. She gets pregnant and miscarries. It’s almost impossible to take stock of all that happens in this, and there’s almost no real emotion behind any of it.

Capote clearly did this on purpose. Holly’s character is flighty, and she often jumps into things without any thought. If we think of the novella as a character study, then all these crazy events occurring is part of the brilliance of the novella. The plot doesn’t have weight for the main character, so it would be a mistake to have the events play a significant role to the reader. Holly moves on, and so should the reader.

And now we come full circle. No one remembers the plot to Breakfast at Tiffany’s by design. We’re only meant to remember Holly. Even her last name is “Golightly.”

The only moments of emotional poignancy are when the narrator reflects on it all, and when we see beneath Holly’s shell. He falls in love with Holly for real (this is a bit of a theme to the book: what is love?). This is quite well done, because it contrasts so starkly with Holly’s indifference and shows how devastating her indifference can be as she tears through people’s lives.

Capote gives Holly one piece of depth that prevents her from being some caricature of a socialite. She cares deeply about her brother, and it is probably the only real human connection she’s ever had. A lot of her carefree attitude stems from a disturbing fact dropped subtly in tiny details. She runs from human connection because of the psychological trauma of being a child bride.

Overall, the novella was way better than I expected in terms of character development. It was also sort of disappointing in a way. I went in expecting it to be a romance between the narrator and Holly done in a brilliant literary Capote-esque way. It’s not that at all. But once you get over the initial shock (and genre confusion), it’s brilliant.

The Infinite Cycle of Gladwell’s David and Goliath

I recently finished reading Malcolm Gladwell’s David and Goliath: Underdogs, Misfits, and the Art of Battling Giants. The book is like most Gladwell books. It has a central thesis, and then interweaves studies and anecdotes to make the case. In this one, the thesis is fairly obvious: sometimes things we think of as disadvantages have hidden advantages and sometimes things we think of as advantages have hidden disadvantages.

The opening story makes the case from the Biblical story of David and Goliath. Read it for more details, but roughly he says that Goliath’s giant strength was a hidden disadvantage because it made him slow. David’s shepherding was a hidden advantage because it made him good with a sling. It looks like the underdog won that fight, but it was really Goliath who was at a disadvantage the whole time.

The main case I want to focus on is the chapter on education, since that is something I’ve talked a lot about here. The case he makes is both interesting and poses what I see as a big problem for the thesis. There is an infinite cycle of hidden advantages/disadvantages that makes it hard to tell if the apparent (dis)advantages are anything but a wash.

Gladwell tells the story of a girl who loves science. She does so well in school and is so motivated that she gets accepted to Brown University. Everyone thinks of an Ivy League education as being full of advantages. It’s hard to think of any way in which there would be a hidden disadvantage that wouldn’t be present in someplace like Small State College (sorry, I don’t remember what her actual “safety school” was).

It turns out that she ended up feeling like a complete inadequate failure despite being reasonably good. The people around her were so amazing that she got impostor syndrome and quit science. If she had gone to Small State College, she would have felt amazing, gotten a 4.0, and become a scientist like she wanted.

It turns out we have quite a bit of data on this subject, and this is a general trend. Gladwell then goes on to make just about the most compelling case against affirmative action I’ve ever heard. He points out that letting a minority into a college that they otherwise wouldn’t have gotten into is not an advantage. It’s a disadvantage. Instead of excelling at a smaller school and getting the degree they want, they’ll end up demoralized and quit.

At this point, I want to reiterate that this has nothing to do with actual ability. It is entirely a perception thing. Gladwell is not claiming the student can’t handle the work or some nonsense. The student might even end up an A student. But even the A students at these top schools quit STEM majors because they perceive themselves to be not good enough.

Gladwell implies that this hidden disadvantage is bad enough that the girl at Brown should have gone to Small State College. But if we take Gladwell’s thesis to heart, there’s an obvious hidden advantage within the hidden disadvantage. Girl at Brown was learning valuable lessons by coping with (perceived) failure that she wouldn’t have learned at Small State College.

It seems kind of insane to shelter yourself like this. Becoming good at something always means failing along the way. If girl at Brown had been a sheltered snowflake at Small State College and graduated with her 4.0 never being challenged, that seems like a hidden disadvantage within the hidden advantage of going to the “bad” school. The better plan is to go to the good school, feel like you suck at everything, and then have counselors to help students get over their perceived inadequacies.

As a thought experiment, would you rather have a surgeon who was a B student at the top med school in the country, constantly understanding their limitations, constantly challenged to get better, or the A student at nowhere college who was never challenged and now has an inflated sense of how good they are? The answer is really easy.

This gets us to the main issue I have with the thesis of the book. If every advantage has a hidden disadvantage and vice-versa, this creates an infinite cycle. We may as well throw up our hands and say the interactions of advantages and disadvantages is too complicated to ever tell if anyone is at a true (dis)advantage. I don’t think this is a fatal flaw for Gladwell’s thesis, but I do wish it had been addressed.

Five Predictions for a Trump Presidency

I thought I’d write this post so it’s on the record. Here’s five predictions for the Trump presidency. These are merely things he’s been telling us he will do. I hope I eat my words in four years.

The number of uninsured will skyrocket. 

He has said he will repeal the Affordable Care Act on Day 1 in office. He’s given us no indication as to his replacement except “competition, free markets, mumble, mumble …” This is in stark contrast to years of Republican policy. Republicans have run on the idea of personal responsibility. The ACA finally achieved this by mandating everyone to buy their own insurance.

Trump wants to repeal this. Now millions of people will be uninsured but still have health costs. These costs will shift to the public. As a side note, I showed why competition doesn’t work in this post. I also predict the cost of health insurance will skyrocket. We can’t be confused when this happens. It is very well understood.

If you are a freelancer or your employer doesn’t subsidize your insurance, I urge you to read the terms of whatever looks affordable very carefully after the repeal of the ACA. I predict the only affordable insurance will be junk. Don’t get duped.

There will be a global recession.

Trump doesn’t seem to understand America’s unique position in the world. He plans to add over $5 trillion to the debt. The Committee for a Responsible Federal Budget estimates Trump’s plan to raise the debt to over 105% of our GDP. This has a lot of vast consequences for a country. The self-proclaimed “King of Debt” has been able to leverage these risky scenarios in his personal business by trashing the business.

You can’t do this with a country. The high debt to GDP ratio will likely lead to more expensive loans and at least a minor debt spiral along the lines of Greece. The U.S. will enter a bad recession, and this will lead to a global recession as well.

Also, he plans to tariff the crap out of countries. Many historians argue that the Smoot-Hawley tariffs were the primary cause of the Great Depression. Whether that is true or not, you can decide, but we should learn from history. It is doubtful Trump knows anything about this to know if it is dangerous or not.

The price of goods will rise much faster than inflation.

Trump has proposed several ideas to bring manufacturing jobs back. It’s likely no jobs will come to the U.S. because of this, but that isn’t officially one of my predictions. He plans to incentivize companies to produce in the U.S. by making it very expensive to produce outside the U.S.

There’s basically only two ways this could go. They keep producing outside the U.S. (likely) in which case prices of these goods has to increase to make up for the tariffs. Or they return to the U.S. where labor is more expensive, and the price of the goods must increase to make up for the cost of labor.

A sub-prediction here is that many businesses will go under because of this. Once prices rise, they’ll sell less. If they don’t sell enough, they go bankrupt. I know Trump sees bankruptcy as a thing to be celebrated, but I’m not sure the people that want their manufacturing jobs back will be too happy with this one.

Middle and middle-upper income brackets will see a tax increase.

I think this one frustrates me the most. As far as I can tell, my in-laws voted for Trump solely on the fear-mongering tactic of Trump yelling “She’s going to raise your taxes.” Guess what? Hillary had a detailed plan, and it did not involve raising anyone’s taxes except the very top, top tiny percent.

On the other hand, my in-laws might be surprised when their personal exemptions disappear. Trump’s plan increases the standard deduction but removes all personal exemptions, and the  conservative-leaning Tax Foundation estimates about 7.8 million households in the $60K – $100K income range would see a slight increase in federal income tax.

Woops. I guess they should have looked up his actual proposal instead of listening to someone who’s made their living off of swindling people.

A nuclear weapon will be used.

Our culture has become a bit desensitized to this grave issue. We see images of nuclear mushroom clouds all the time from cartoons to movies. I think it bears taking a moment and contemplating just how terrible nuclear weapons are. I know this prediction sounds like hysteria, but hear me out.

Trump, more than any other prediction on this list, has repeatedly, almost at every single opportunity, shown complete disregard for the horrifying consequences of the use of nuclear weapons. He doesn’t understand why we can’t use them. He doesn’t understand why other countries can’t develop them. He doesn’t understand how current treaties deter the use and proliferation of them.

Trump also has very thin skin. A single tweet can send him into a rampage. This is a dangerous combination.

I’m also not going to be so bold as to say we will be the one to use the nuclear weapon. My prediction is merely that someone will. He has said we are renegotiating deals across the board. This will create global instability. The dangerous combination of treaties in flux and Trump waving the threat of nuclear weapons will lead someone to pull the trigger.

I see two likely scenarios. The first is that Trump tears up the Iran Nuclear Accord. Iran develops nuclear weapons in the interim, and they are the first to use them from a threat in the Middle East. The other is that Trump lets South Korea develop nuclear weapons, and the unstable situation in North Korea leads one side to be too worried.

Trump has this phrase: Peace through strength. Let’s ignore the fact that tearing up NATO and promoting nuclear proliferation actually weakens us. I say: Peace through stability.

Some extra non-predictions.

I’ll reiterate that all of the above has been readily available information for anyone who cared to look it up. They are predictions based on promises he ran on. If he doesn’t hold to his promises, they won’t happen. Here’s some things he said he’ll do that I don’t foresee happening.

He won’t build the wall. It’s a terrible idea. It’s expensive. It probably wouldn’t decrease the number of illegal immigrants by much (some models predict it will increase the number). I don’t think any of these facts will go into the decision not to build it. I just think he swindled his supporters by playing up a big image.

He will not implement massive deportation on the scale he claimed. Tearing millions of families apart would be a PR nightmare for him, and we all know Trump wants to be loved. His approval ratings would plummet when newspapers made the cover images children crying as their parents are forcibly taken in front of them.

As a final note, I have no idea what “Make America Great Again” could possibly mean. On basically every measure of greatness, America has never been greater (income inequality is worse, but Trump has no care for this). If we try to return to some past moment, it will, almost by definition, be worse.

The Economics of Insurance 101

Insurance has been in the news quite a bit recently. Obamacare premiums are increasing. Trump wants to repeal the ACA and let free markets and competition drive prices down. Everyone thinks they have a good intuition for this stuff because of their high school economics classes. But is that how it really works?

This is going to be a long post building simple models of insurance to show that insurance is not a good that behaves like other economic goods. You can’t just apply “common sense” economics to insurance and expect to get the right answers. It’s a very strange product.

Model 1: Let’s start with a super simplified model. We have a single insurance company and 1000 people in our world, all of Low Risk. We’ll assume this means they have a 1% chance of needing a doctor’s visit in the next year. In this world the visit will universally cost $200 without insurance. The insurance plan covers the whole visit.

All right. This is really easy to figure out. How much should the insurance company charge to make money (i.e. to continue existing)? Well, they expect 10 people to need the visit, which costs them $2000 for the year. This means they break even if they charge $2 to each person for the year. They need to make money to pay for operating costs, so let’s say they charge a freakishly low price of $3 a year.

Now we run the model. Since we’re assuming a standard economic model, we assume all these people behave rationally. Do the Low Risk people buy the insurance? If they do, their expected health cost for the year is $3 (the cost of the insurance plus nothing else since the insurance company pays for the visit). If they don’t buy it, their expected cost for the year is (.01)(200) = $2.

Woops. None of our rational actors are going to buy the insurance, and the company collapses from no business. Fiddle with this. Add in a .001% chance of a freak accident costing $10,000 in surgery. Try to add in things that make it more realistic, like using a copay to lower cost instead of a yearly fee.

You’ll find that no matter how you fiddle with it, it will never be rational for Low Risk people to buy insurance. It’s just a fact about insurance companies charging enough to make money. Note that adding in higher risk people will only raise the price.

Conclusion 1: Low Risk people don’t buy insurance without something forcing them to, like an individual mandate.

[Small caveat. People aren’t rational, and this is good. They realize that even though they lose money by buying insurance, they are paying for something that can’t be quantified: security. The monthly fee is worth the peace of mind that a freak accident won’t bankrupt them and completely ruin their life.]

Models 2 and 3: I’ll breeze through this, because these are the exact same calculations with Medium Risk and High Risk pools of people. If everyone has a Medium Risk of 50%, then the insurance plan must cost $1000 a year per person to break even. Woops. We don’t have to go further. The policy costs more than paying full price for the doctor. Likewise for High Risk at 90%.

Conclusion 2: Insurance doesn’t work unless there are Low Risk people in the pool to decrease the cost.

Conclusion 3: The more Low Risk people in the pool, the lower the cost can be for everyone.

Model 4: Let’s combine the different risk types into one model, but the price of insurance is uniform across all risk. This is obviously closer to reality. We’ll assume that most are Low Risk, and as risk increases, the number of people in that category decreases. To do this properly we should probably use a distribution, etc, but let’s keep it really simple.

Low risk: 900 people

Medium risk: 95 people

High risk: 5 people

The insurance company expects to pay [(900)(.01) + (95)(.5) + (5)(.9)] (200) = $12,200 for the year. They can break even by charging $12.20 per person for a year of coverage. Let’s suppose they charge $13. Conclusion 1 still applies, meaning the Low Risk people don’t buy it.

Assuming we force Low Risk people to get the insurance, Medium Risk people expect to pay (.5)(200) = $100 for the year without insurance, but only $13 with insurance. Our rational Medium Risk and High Risk people willingly buy insurance in this case as long as enough Low Risk people stay in the pool.

It is worth reiterating that under ideal assumptions and no mandate to buy insurance (and no subsidies), none of the Low Risk people buy insurance, and the costs shift to Medium Risk people. It no longer is rational for them, so they don’t buy. The risk shifts to High Risk people, they don’t buy, and the company collapses.

Conclusion 4: Without forcing Low Risk people to buy insurance, insurance companies will still collapse with a mixed pool of risk and uniform prices. If Low Risk people are forced to buy insurance, it becomes rational for higher risk people to buy insurance even with the company making money.

Since this is secretly a post digging into rhetoric from Trump, and he plans to repeal the ACA, it seems the mandate will be repealed. Take whatever conclusion from that and Conclusion 4 that you want.

[Caveat 2. In real life, people suck at determining their risk. Lots of Low Risk people will think they are Medium, so under this delusion they rationally buy insurance. But likewise, lots of Medium risk people think they are low risk. This makes it rational for them to not buy insurance. If we assume the delusions are random and not skewed, the price will be slightly lower, but not enough to invalidate Conclusion 4. This is massively offset by the fact that High Risk people (i.e. those with “preexisting conditions”) tend to need procedures that cost a lot more.]

Model 5: Let’s introduce variable prices for different risk. Is it possible for the company to price policies to make money and yet be rational for everyone to buy it?

These are the exact same calculations we’ve been doing, but we don’t even have to do calculations to see this is impossible if we understand expected value/costs.

Indepent of risk, it is only rational to buy insurance if your expected cost with insurance is less than your expected cost without insurance. The insurance company only makes money on you if the price they charge is more than the expected cost. Thus, to make it rational for everyone, they must set a price to lose money.

Conclusion 5a: Even with variable prices for different risk levels, insurance companies can never price policies to be rational for everyone to buy.

Conclusion 5b: Even under ideal economic assumptions, if there is only one insurance company, it will always fail without a mandate to increase Low Risk buyers or some form of subsidies to lower prices.

Let’s take a quick breather here. Hopefully, if you’ve never thought about this carefully, you’re starting to see why applying “common sense” economics from your high school class might not get you to the right conclusions. Insurance is super weird as a comodity. But things are about to get weirder.

[Caveat 3. One could probably write a 500 page textbook just introducing appropriate complexities to the single insurance company model. I am under no delusion that the above analysis bears any resemblance to the “real world.” These are supposed to be overly simple models to challenge people’s intuition.]

Model 6: Competition!!! Now let’s assume there are 2 insurance companies. They compete with each other for selling policies. There’s already something weird here, because unlike standard market economics, a sale is not a sale. If there are two apple vendors, the vendor doesn’t care who they sell the apple to. A sale is a sale. They make the same money no matter who buys it.

The Medium and High Risk people cost the insurance company money, whereas the Low Risk people make the company money. So what’s rational for the company in this case? They want to separate prices. They want policies for Low Risk people to be lower than the competition, but they want policies for higher risk people to be higher than the competition so they go to the competitor to lose money!

They aren’t in competition for the people who most need insurance. For those people, competition increases the price of insurance.

I’ll reitorate this again as a conclusion.

Conclusion 6: For the people who most need insurance, competition increases the price of insurance.

For the people who don’t need insurance, in a perfectly free market under ideal assumptions, they aren’t buying it anyway, so who cares what their price is? Yeah. Insurance isn’t quite so intuitive is it?

I’ll end by reminding you of the fundamental difference between selling a good and insurance. If a company decreases the price of a good to steal customers from a competitor, they make up the loss from lowering the price by selling more. This is why competition lowers prices. More sales of insurance doesn’t necessarily lead to more profit. Thus, if an insurance company lowers prices, they don’t necessarily make up the loss due to price by selling more.

We didn’t even scratch the surface here, but this post has gone on longer than most of you will read. I wanted to get to scenarios like government regulating uniform prices across risk together with competition and variable policies (hint: competition could lead to an increase in trash policies which cover practically nothing so lowering prices guarantees more profit but defeats the whole purpose of insurance).

Maybe next time.

 

Examining Pro’s Prose Part 11

Today we’re going to look at the prose of J. M. Coetzee. He is a South African writer and is known for his controversial topics. His 1980 work Waiting for the Barbarians is about a town magistrate that takes on disturbing power by preying on the fears of the people about an incumbent attack by the barbarians. This novel is now seen as an eerie and accurate premonition of the events in the U.S. after 9/11 that led to the 2003 invasion of Iraq and the forfeit of our freedoms in the name of safety.

The novel I actually want to look at is his more recent 1999 novel Disgrace. The main character is a disgraced English professor who loses his job after having sex with a student under dubious circumstances. He moves in with his daughter in the countryside to recover from the affair and try to turn his life around. While there, the two suffer a brutal attack coming from lingering apartheid tensions.

I won’t give more away, but a hallmark of Coetzee’s writing is how much he packs into so little space. This novel is short, more like a novella, yet it contains more plot and emotional content than many 90,000 word novels. And this is where I’d like to start with his prose. If you’ve never read him, I highly recommend taking one or two days to go through one of his novels. The bare and exposed prose breaks every rule we’ve been taught, yet it suits his subject matter perfectly. It is unlike anything I’ve read. I can’t even compare him to other people.

To set the scene, the professor has just called Melanie, the student, at her house. Her mother answered and has left the phone to get her.

Melanie—melody: a meretricious rhyme. Not a good name for her. Shift the accent. Meláni: the dark one.

‘Hello?’

In the one word he hears all her uncertainty. Too young. She will not know how to deal with him; he ought to let her go. But he is in the grip of something. Beauty’s rose: the poem drives straight as an arrow. She does not own herself; perhaps he does not own himself either.

The first segment is the professor’s thoughts. Part of the slimness of Coetzee’s writing comes from how he slides into and out of the head of the main character with no frills. No italics. No “he thought” to punctuate and emphasize what is already obvious. I like this style, and find some writer’s overemphasis on pointing out character’s thoughts as needless distrust of the reader’s comprehension.

The punctuation through this segment is brilliant. It also allows Coetzee to do away with excess words that the professor wouldn’t be thinking anyway. It flows quickly like actual thoughts would. It’s word association rather than something logical.

Then we get to the actual words. He notes the rhyme between Melanie and melody. But the brilliant thing is calling it a “meretricious” rhyme. This word does so much work in the passage. On the face of it, he wants the rhyme to be deceiving because he doesn’t want a melodic girl but a devious one. The word meretricious doesn’t merely mean deceiving though; it has the archaic meaning “of, like, or relating to a prostitute,” exactly how the professor views the student in that moment.

In four sentences, we, as readers, feel so much. We get to watch how the professor thinks about this student. We watch how his mind turns things around. We see how he starts to justify his actions to himself. In context, these four sentences give us a sense of revulsion at the main character’s true self that we wouldn’t get from a mere surface description of the act. There’s something deeper and more disturbing about the scene playing out this way.

After she answers the phone, the point of view shifts out of his thoughts, but things only get worse. Now we see that he understands that what he is doing is wrong. He understands that he needs to leave, but the narrator joins in on the justification. He’s out of control. She’s out of control.

As a reader, we start to feel helpless. Even the narrator is pushing the act along, and we learn that we cannot trust the narrator to show us the moral condemnation we hope for. We want to shout, “No! He does own himself! Stop making excuses for him. Lust is not reason enough to lose control of one’s actions.”

Shakespeare is quoted with “beauty’s rose,” reemphasizing the fact that the English professor knows his stuff, but it is more significant than that. This comes from Shakespeare’s first sonnet, and this is the first scene to start the plot of the novel. The full sonnet is about an older man who self-destructs under his selfish and gluttonous ways. That brief phrase “beauty’s rose” is a deep foreshadowing into the rest of the novel.

This is what makes Coetzee such an experience to read. His sparse prose strikes immediate emotional response into readers with no analysis necessary. But upon a deeper reading, we can find a shocking amount of extra information layered in through precise word choice.

Confounding Variables and Apparent Bias

I was going to call this post something inflammatory like #CylonLivesMatter but decided against it. Today will be a thought experiment to clarify some confusion over whether apparent bias is real bias based on aggregate data. I’ll unpack all that with a very simple example.

Let’s suppose we have a region, say a county, and we are trying to tell if car accidents disproportionately affect cylons due to bias. If you’re unfamiliar with this term, it comes from Battlestar Galactica. They were the “bad guys,” but they had absolutely no distinguishing features. From looking at them, there was no way to tell if your best friend was one or not. I want to use this for the thought experiment so that we can be absolutely certain there is no bias based on appearance.

The county we get our data from has roughly two main areas: Location 1 and Location 2. Location 1 has 5 cylons and 95 humans. Location 2 has 20 cylons and 80 humans. This means the county is 12.5% cylon and 87.5% human.

Let’s assume that there is no behavioral reason among the people of Location 1 to have safer driving habits. Let’s assume it is merely an environmental thing, say the roads are naturally larger and speed limits lower or something. They only average 1 car accident per month. Location 2, on the other hand, has poorly designed roads and bad visibility in areas, so they have 10 car accidents per month.

At the end of the year, if there is absolutely no bias at all, we would expect to see 12 car accidents uniformly distributed among the population of Location 1 and 120 car accidents uniformly distributed among the population of Location 2. This means Location 1 had 1 cylon in an accident and 11 humans, and Location 2 had 24 cylons and 96 humans in accidents.

We work for the county, and we take the full statistics: 25 cylon accidents and 107 human accidents. That means 19% of car accidents involve cylons, even though their population in the county is only 12.5%. As an investigator into this matter, we now try to conclude that since there is a disproportionate number of cylons in car accidents with respect to their baseline population, there must be some bias or speciesism present causing this.

Now I think everyone knows where this is going. It is clear from the example that combining together all the numbers from across the county, and then saying that the disproportionately high number of cylon car accidents had to be indicative of some underlying, institutional problem, was the incorrect thing to do. But this is the standard rhetoric of #blacklivesmatter. We hear that blacks make up roughly 13% of the population but are 25% of those killed by cops. Therefore, that basic disparity is indicative of racist motives by the cops, or at least is an institutional bias that needs to be fixed.

Recently, a more nuanced study has been making the news rounds that claims there isn’t a bias in who cops kill. How can this be? Well, what happened in our example case to cause the misleading information? A disproportionate number of cylons lived in environmental conditions that caused the car accidents. It wasn’t anyone’s fault. There wasn’t bias or speciesism at work. The lack of nuance in analyzing the statistics caused apparent bias that wasn’t there.

The study by Fryer does this. It builds a model that takes into account one uncontroversial environmental factor: we expect more accidental, unnecessary shootings by cops in more dangerous locations. In other words, we expect that, regardless of race, cops will shoot out of fear for their lives in locations where higher chances of violent crimes occur.

As with any study, there is always pushback. Mathbabe had a guest post pointing to some potential problems with sampling. I’m not trying to make any sort of statement with this post. I’ve talked about statistics a lot on the blog, and I merely wanted to show how such a study is possible with a less charged example. I know a lot of the initial reaction to the study was: But 13% vs 25%!!! Of course it’s racism!!! This idiot just has an agenda, and he’s manipulating data for political purposes!!!

Actually, when we only look at aggregate statistics across the entire country, we can accidentally pick up apparent bias where none exists, as in the example. The study just tries to tease these confounding factors out. Whether it did a good job is the subject of another post.

The Ethics of True Knowledge

This post will probably be a mess. I listen to lots of podcasts while running and exercising. There was a strange confluence of topics that seemed to hit all at once from several unrelated places. Sam Harris interviewed Neil deGrasse Tyson, and they talked a little about recognizing alien intelligence and the rabbit hole of postmodernist interpretations of knowledge (more on this later). Daniel Kaufman talked with Massimo Pigliucci about philosophy of math.

We’ll start with a fundamental fact that must be acknowledged: we’ve actually figured some things out. In other words, knowledge is possible. Maybe there are some really, really, really minor details that aren’t quite right, but the fact that you are reading this blog post on a fancy computer is proof that we aren’t just wandering aimlessly in the dark when it comes to the circuitry of a computer. Science has succeeded in many places, and it remains the only reliable way to generate knowledge at this point in human history.

Skepticism is the backbone of science, but there is a postmodernist rabbit hole one can get sucked into by taking it too far. I won’t make the standard rebuttals to radical skepticism, but instead I’ll make an appeal to ethics. I’ve written about this many times, two of which are here and here. It is basically a variation on Clifford’s paper The Ethics of Belief.

The short form is that good people will do good things if they have good information, but good people will often do bad things unintentionally if they have bad information. Thus it is an ethical imperative to always strive for truth and knowledge.

I’ll illuminate what I mean with an example. The anti-vaccine people have their hearts in the right place. They don’t intend to cause harm. They actually think that vaccines are harmful, so it is the bad information causing them act unethically. I picked this example, because it exemplifies the main problem I wanted to get to.

It is actually very difficult to criticize their arguments in general terms. They are skeptical of the science for reasons that are usually good. They claim big corporations stand to lose a lot of money, so they are covering up the truth. Typically, this is one of the times it is good to question the science, because there are actual examples where money has led to bad science in the past. Since I already mentioned Neil deGrasse Tyson, I’ll quote him for how to think about this.

“A skeptic will question claims, then embrace the evidence. A denier will question claims, then deny the evidence.”

This type of thing can be scary when we, as non-experts, still have to figure out what is true or risk unintentional harm in less clear-cut examples. No one has time to examine all of the evidence for every issue to figure out what to embrace. So we have to rely on experts to tell us what the evidence says. But then the skeptic chimes in and says, but an appeal to authority is a logical fallacy and those experts are paid by people that cause a conflict of interest.

Ah! What is one to do? My answer is to go back to our starting point. Science actually works for discovering knowledge. Deferring to scientific consensus on issues is the ethically responsible thing to do. If they are wrong, it is almost certainly going to be an expert within the field that finds the errors and corrects them. It is highly unlikely that some Hollywood actor has discovered a giant conspiracy and also has the time and training to debunk the scientific papers that go against them.

Science has been wrong; anything is possible, but one must go with what is probable.

I said this post would be a mess and brought up philosophy of math at the start, so how does that have anything to do with what I just wrote? Maybe nothing, but it’s connected in my mind in a vague way.

Some people think mathematical objects are inherent in nature. They “actually exist” in some sense. This is called Platonism. Other people think math is just an arbitrary game where we manipulate symbols according to rules we’ve made up. I tend to take the embodied mind philosophy of math as developed by Lakoff and Nunez.

They claim that mathematics itself is purely a construct of our embodied minds, but it isn’t an “arbitrary” set of rules like chess. We’ve struck upon axioms (Peano or otherwise) and logic that correspond to how we perceive the world. This is why it is useful in the real world.

To put it more bluntly: Aliens, whose embodied experience of the world might be entirely different, might strike upon an entirely different mathematics that we might not even recognize as such but be equally effective at describing the world as they perceive it. Therefore, math is not mind independent or even universal among all intelligent minds, but is still useful.

To tie this back to the original point, I was wondering if we would even recognize aliens as intelligent if their way of expressing it was so different from our own that their math couldn’t even be recognized as such to us. Would they be able to express true knowledge that was inaccessible to us? What does this mean in relation to the ethics of belief?

Anyway, I’m thinking about making this a series on the blog. Maybe I’ll call it RRR: Random Running Ramblings, where I post random questions that occur to me while listening to something while running.

When Should Campuses Shut Down Debate?

It’s been over a year since mob rule started taking over who is allowed to speak on college campuses. These types of things have obviously been going on longer than the most recent prominent cases, but the visibility seems to have brought us to a turning point. Angry students have learned that the administration will always cave to their demands out of fear. This is no way to run a university, but that is beside the point of this essay.

The question I want to explore is whether there is ever a legitimate reason to not allow someone to speak about or debate a topic. Here are some of the base assumptions I’ll be making:

1. Facts are sometimes uncomfortable and sometimes overturn whole worldviews. Causing some discomfort in the pursuit of truth is never an acceptable reason to shut down a speaker or debate. We’d still believe the Earth was the center of the universe with this mentality.

2. Uncomfortable debates will happen on campuses anyway whether a particular speaker comes or not. We’ve all been in those classes where brief awkward exchanges happen between professor and student, and it quickly becomes apparent that the student believes something antithetical to what is being taught (intelligent design, the only valid foundation for ethics must be derived from a supreme being, the Holocaust didn’t happen, etc).

3. The people who will be so-called “triggered” by a speech or debate will not be in attendance anyway. They aren’t open to the ideas being discussed, so they have no purpose in attending. I’ll assume no one is being forced to go for a class or a grade. If a student thinks they might suffer from PTSD (or whatever hyperbolic acronym is in favor now), they just shouldn’t risk it by attending. Reasonable decisions by the students can avoid all harm that could come in this form.

4. This is almost never a free speech issue. Anyone can debate anything in public. Free speech is unrelated to a university spending resources to invite you to do this on their campus. The question should be whether the current way that universities deal with controversial speakers is in alignment with the goals of a university.

Here’s one legitimate reason for not bringing a particular debate to a campus. A topic is so settled, that there is no reason to publicly air an argument about it. Universities have limited funds, and wasting money arguing whether the Holocaust happened just isn’t a useful way to spend that money.

Note well: If you’ve already invited this debate, I don’t think that reason applies anymore. A group of students protesting the debate should not shut it down. If the university doesn’t want this debate, then they shouldn’t invite the speakers to begin with. Once an invitation is given, no amount of pressure should shut the event down.

Do I think the taboo nature of that debate topic ought to be reason for not having it? Absolutely not! Settled questions like these are probably not worth the time and money, but there isn’t much harm in debating them. When a question is truly decided, it isn’t hard to debunk the arguments. No one fears or protests this.

Sometimes it can even be useful to remind ourselves what makes their arguments bad and what the evidence is. It would be embarrassing if someone graduates from a major university and can’t respond to claims that the Earth is flat. Shielding students from these silly ideas instead of exposing them as frauds makes the ideas more likely to spread not less.

This brings me to the fear some of these students have about hearing certain viewpoints. The violent reaction to these ideas usually means the ideas have some merit. No one is afraid of a flat Earth debate. They would think it’s silly. The spherical Earth arguments win. No one will be convinced of the flat Earth theory in that debate.

The only reason students protest certain speakers is because they fear people might be convinced when they hear the evidence that contradicts their worldview. If they deny this, then ask why they are so worried about the students listening to the speaker. They’ll probably mumble something about not letting hate speech on campus, but if it’s purely hate speech, everyone will see this for what it is.

The reason no one is convinced by the Westboro Baptist Church is precisely because we’ve heard what they have to say. They debunk themselves with their hate speech. Censoring speech about topics makes it look like there is something there when there isn’t. I’ll reiterate, if the administration really thinks they will only get hate speech from a speaker, don’t invite them to begin with.

So far I think we’ve only dealt with really easy cases. Most of the people that students protest pose absolutely no threat. This means Condoleeza Rice, Ayaan Hirsi Ali, and Christina Hoff Summers should all be able to air their opinions. If they’re wrong, then that will come out in the debate or speech. They won’t convince people. If they aren’t wrong, then that is all the more reason to let them speak.

There are much harder cases, though. These are topics that one can couch in the language of the pursuit of truth, but it is hard to see why anyone would be researching it without some ulterior motive. This would be something like IQ differences between races.

I’m torn on these types of things. Part of the beauty of tenure at a university is the ability to research taboo topics without fearing for your job. We absolutely cannot make people come up with positive impacts of their research in order to fund it. The mathematician that studies the derived category of coherent sheaves on high dimensional varieties in positive characteristic would have a hard time coming up with any sort of real world positive impact as well.

Ah, but that research has no application, so it is somehow “neutral” you say. When there is a clear racist or otherwise negative application, then the researcher must justify it. This is a legitimate slippery slope though. Who gets to decide what is a “positive” application or a clear “negative” application to begin with? Once you allow any sort of censorship of research based on subjective judgments, you run into huge problems when the “wrong” people get in power.

So in summary, I think the types of people who get disinvited from campuses right now are easy cases. They should be allowed to speak. They pose no threat and will often give well thought out counterpoint to the established worldviews of many students.

There is a real and interesting debate to be had on more difficult cases, but overall, I see no way to restrict those debates without setting a dangerous precedent. So I tentatively say that we must also allow these taboo subjects to be researched and debated, at least in a university setting where the pursuit of truth must take priority.