All-Cause Mortality Data for the USA

After much searching and asking friends if they can find the data, I’ve finally found a source for all-cause mortality data for the United States of America. It’s the CDC’s excess mortality data page. There is a ton of data on this page, and I recommend checking it out. Before I show you a screenshot of what it looks like at the moment, I’ll explain why this data is so useful.

Consider the following hypothetical: a person suffers from COPD (chronic obstructive pulmonary disorder). This is a deadly condition where the lungs are deteriorating, and it just keeps getting worse until the person dies from it. Suppose the person with COPD probably is sufficiently advanced that they only have six months to a year left, and then they get COVID-19, and die. Did they die from COVID-19 or from COPD? Different doctors, hospitals, and medical systems will answer that question differently, and all in good faith.

(To see how it can all be in good faith, how much the COVID-19 pushed them over the edge is something God knows, but man can’t know with certainty. Had they gotten something else, like the flu or a common cold, that might have pushed them over the edge instead. If they got a common cold and died, we would call it a COPD death, not a common cold death. This is just one example, there are a lot of cases which are legitimately judgement calls on which people disagree.)

This disagreement is especially a huge problem internationally. There’s absolutely no reason why doctors in Russia, China, Kenya, and Paraguay would have the same standards for things; it’s not like they would ever talk to each other, or report anything to the same place.

However.

Everyone diagnoses death in the same way, at least after a few minutes. Not being alive is a very difficult condition to miss, no matter what tests are common or what doctors are habituated to look for or what their beliefs or customs are on the primary cause of death. And what is true across countries is helpful across states, too. It doesn’t take much looking for find endless debate about whether COVID-19 deaths are being over- or under-counted; we can be fairly sure about deaths being accurately counted.

Or, rather, we can be after about eight weeks. One problem that we run into here is that the CDC has found that only about 60% of deaths are reported within 10 days of the death; it takes about 8 weeks to get completely stable numbers. This is a very long time to wait, so they have algorithms based on how long it typically takes each reporter that feeds into the CDC to report all deaths to predict, after 10 days, what the final count will be. It looks like lately they’ve been under-predicting deaths in the first week by (about) 15-20%, though it varies from week to week, and I don’t have enough data to say that with certainty. I’ve tracked it for 3 weeks now and the numbers seem to get reasonably stable (by which I mean changing by less than 5%) after a few weeks of being on the chart. That said, everything in the right-most 8 weeks does need to be taken as provisional, the further to the right, the more provisional, and bearing in mind that the provisional numbers have a bias towards under-predicting the final number of deaths per week:

As you can see, this spans a little more than 3 years. I’ve no idea what happened in January of 2018; I don’t recall any news items about excess mortality back then, nor anything that would have been an explanation for it.

I’m not, here, going to get into any sort of in-depth analysis. I think it’s a bit early for analysis, aside from a few observations. The first is that the excess deaths do, more or less, follow the same pattern as COVID-19 deaths reported by the CDC, which gives some confidence that those numbers on COVID-19 deaths aren’t wildly inaccurate.

The other observation is that COVID-19 is obviously not affecting mortality all that much. The worst weeks for excess mortality were about 40% excess deaths, but that only lasted a few weeks. Excess mortality quickly dropped to below 20% and often below 10%. Or you can just look at the area in blue under the yellow line versus the area in blue above it (that’s not quite perfect because there is a bit of uncertainty built into the yellow line, but not a lot). It did go back up again, in time with the second wave of COVID-19 cases, but it appears to have peaked. The peaking is within that 8 week window, but the CDC’s numbers on COVID-19 deaths show that they peaked back in august, so if all-cause follows COVID-19 deaths as well as it has in the past, it is likely that the peak in all-cause deaths we’re seeing is real. We’ll be able to be a lot more confident about that in November or December.

By the way, an interesting question, which we won’t be able to settle for months at the earliest, is whether there will be a discernible drop in all-cause mortality for a while. If there is, that would strongly suggest that COVID-19 mostly just hastened the deaths of people who were going to die soon anyway. It will be interesting to watch for this.

What a First Date Should Cost

On Twitter, I recently saw the following question:

I saw a post saying “Men should spend at least $1000 on a first date.” What ya’ll think?

The answer is, obviously, “no”. At least if that’s denominated in US dollars. But that’s not the interesting part. The correct answer to what a man should spend on a first date is: the price of admission to a museum, zoo, art gallery, or similar. And, as far as possible, during the day.

There are several reasons for this, mostly related to the function of courtship, but some of them are practical, too.

To get the practical reasons out of the way, one wants to make a good first impression on a person in a first date, and people are at their best when they have something to do. Even an excellent conversationalist does better with material to hand, and most people are not excellent conversationalists.

The other practical reason is that museums, zoos, etc. tend to make people comfortable. First dates can be awkward and a setting that will put both people at ease is helpful.

When it comes to courtship, the benefits are several fold. The first is that it is a demonstration of patience on the part of both parties. Marriage requires large amounts of patience; being willing to demonstrate small amounts of patience by being among people, and with a purpose, on a date, helps both to show this to the other. (Also frequently one has to wait for the people in front of one.)

Going to a museum, or to a zoo, or some such place will also inevitably involve some amount of minor inconvenience. How people bear up under minor inconvenience is extremely useful to know in marriage. How people bear up under great inconvenience may be more important, but most days involve minor inconvenience, and if a person handles it badly, that will add up to a lot of problems, over the years.

Zoos, museums, and the like also involve some amount of making joint decisions. If one wants to see the polar bears and the other wants to see the orangutans, the couple will need to work out which to actually go see, or at least the order to see them in. How good people are at making joint decisions—actually working them out and not merely something unsustainable like one always deferring to the other—is extremely valuable in marriage. (I would hope it would go without saying that if a person shows themselves to be selfish and demands to always have their way, this is a huge red flag; in case it doesn’t go without saying—it is.)

A final benefit is that most zoos, museums, etc. are physically large, and large amounts of walking will slightly tire people out. What people are like when mildly fatigued is also very useful to know, as much of marriage will be spent when one, the other, or both are a little tired. When they have young children, it will be spent when both are very tired.

When you sum these benefits up, a first date at a zoo, museum, or the like will work well to show both people whether a second date is worthwhile. It will teach both people a great deal about the other, but under conditions which are pleasant and favorable.

Oh, and while it is cheap in terms of money, going with someone to a zoo, museum, or the like is a significant investment in terms of time and effort. How much a person appreciates that is also useful to know in a marriage, both because effort is more important than money (especially above a certain minimum), and because in any case it is (very frequently) more available in marriage, too.

Family in Star Wars

There’s an interesting complaint about what might be the most famous plot twists of all time: Luke and Leia being brother and sister, and both being the children of Darth Vader. The complaint, which is not entirely illegitimate, is that, though interesting, this also takes a galactic adventure story and turns it into a family feud.

There is, of course, an element of truth to this, but in another way it is actually a mistake. It is not true that everyone is related to everyone else, and by the time of Return of the Jedi, Darth Vader, Luke, and Leia are actually somewhat minor characters, with regard to the fate of the galaxy.

This is not as true in A New Hope, though even there, it’s mostly because Leia had been entrusted with the plans to the death star and Luke takes the critical shot which blows up the death star. If one doesn’t pay attention, it’s possible to get the idea that Leia is in charge of the rebellion, but it’s really not the case. Even Vader says as much; he objects to Leia saying that she was on a diplomatic mission for Alderaan by saying “You are part of the rebel alliance, and a traitor” (emphasis mine). She’s not the head of it.

Luke does take a critical role in blowing up the death star, and there’s no getting around that. However, his role fades after this. He spends much of The Empire Strikes Back training on Dagoba, then gets his ass handed to him by his father. (Not literally; it’s actually his hand which gets handed to him, except he doesn’t catch it.) His major contribution to the rebel alliance is to blow up a couple of AT-ATs, which doesn’t accomplish much as the AT-ATs destroy the shield generator anyway. In terms of his importance to the galaxy in this movie, he has none. In Return of the Jedi, it might be argued that Luke trying to save Vader distracted the Emperor, which is why the Rebels were able to destroy the second death star and kill the Emperor, but that’s actually quite unclear. The emperor was not omniscient, and everything had been proceeding as he had foreseen right up until it didn’t. The only thing we really know for sure is that Luke saved his father’s soul. (I will grant that he did help to save the team sent to blow up the shield generator from the ewoks, but for the most part all he did was levitate C3PO so that the ewoks would take his anger seriously; there probably was another way to get them to take C3PO seriously.)

Vader has a very interesting roll in the Star Wars trilogy. On the one hand, he is the apprentice of the Emperor and his right hand man. On the other hand, he only sort-of is even in the military hierarchy of the Empire. In A New Hope he takes orders from Grand Moff Tarkin (“Enough of this pointless bickering. Vader, release him.” “As you wish.”). Even Leia remarks on this, “I should have known I’d find you holding Vader’s leash.”

In The Empire Strikes Back, we are told that Vader is intent on pursuing the rebels as a sort of monomania because he is obsessed with finding young Skywalker. He is free to direct some imperial star destroyers, but not that many. He’s even forced to employ bounty hunters. He is a major character in this movie and a major driver of its events, but The Empire Strikes Back is, on a galactic scale, a very small movie. The rebels seem to be able to fit on a single planet, and not very much in the way of imperial resources have been dedicated to hunting them down at this point.

In Return of the Jedi, Vader has an even smaller role. He shows up at the new Death Star to oversee its construction. Other than that, he’s present when Luke surrenders and the Emperor tries to tempt Luke to the dark side. In galactic terms, he basically does nothing.

Leia’s ark is somewhat similar to Luke’s, though in a different direction. She starts out smuggling plans to the death star in A New Hope. In The Empire Strikes Back she’s clearly important, but at the same time doesn’t seem to be in charge in a highly practical sense. She spends most of the movie being chased aboard the Millennium Falcon. On a galactic scale, big whoop. In Return of the Jedi, she joins the special ops team led by (now general) Han Solo. The team does important work, but Leia is only a small part of that work, and not really critical to it.

So, when we really consider it, yes three major characters from the first movie turn out to be closely related to each other, but the curious thing about this is that while they loom large in the story, it’s because the story zoomed in and wasn’t so big. After A New Hope, no one in the Skywalker bloodline did anything of any real galactic importance, at least that would not likely have happened without them, and shortly afterwards.

Which is, actually, fine. The truth is that it’s people who matter, not nations or empires or republics or even rebellions.

I think that it was a mark of brilliance on the part of George Lucas that it was Lando Calrissian who fired the shot that destroyed the second death star, and with it, the Emperor. He wasn’t even in the first movie. This is, indeed, what life is often like. Most of the time, people only make one big contribution, and after that they tend to only help the next guy who makes the huge accomplishment. And Lando wasn’t even a major character in the second or third movies. He wasn’t in the movie poster for The Empire Strikes Back and barely made it into the poster for Return of the Jedi. And yet, he’s the guy who destroyed the second death star.

Life is often like that.

Empire Strikes Back Changed Star Wars

On Twitter I recently saw Misha Burnett say that The Empire Strikes Back was probably the movie which ruined sequels for him.

In isolation, Star Wars had a triumphant ending. The kid from the boondocks rose to the occasion and became a hero. He showed himself worthy in the eyes of the tough kid and the pretty girl and the wise old man, and he did something that would have made his father proud. Empire took all that away from us. As the first film in a trilogy (or film number whatever in a series) the story of Luke Skywalker goes from being a boy becoming a hero to a naive recruit becoming just another soldier. The final scene of Star Wars is a recognition of a hero who has saved the galaxy and won the admiration of the beautiful space princess. The final scene of A New Hope is just a bureaucrat entering a commendation into a personnel file. And that is why I don’t like series fiction. In a series, there are no happy endings because in a series nothing ever ends.

This is a very interesting perspective, and in one sense I think that he’s right. What’s really curious is that the reason that he is correct is also why anyone remembers Star Wars well enough to make this observation.

If you just consider Star Wars (later retitled to Star Wars Episode IV: A New Hope) on its own, it’s a fun popcorn flick and possibly the second summer blockbuster after Jaws. It’s the basic Campbellian “hero’s journey,” which is fun but not very interesting. It’s not very interesting because it’s only a very narrow slice of life.

What happens in The Empire Strikes Back and Return of the Jedi is that Luke has to deal with the fact that life isn’t over until you die, even if you accomplish something big. At the end of A New Hope, they defeated the Empire’s super-weapon, but didn’t defeat the Empire. And it’s true that there is always more work to be done. It’s in The Empire Strikes Back where we find out whether the seed fell on rich soil and will yield one hundred fold or whether it fell on rocky soil and sprung up quickly but then withered quickly when the sun came out because it had no root.

In A New Hope, there is a sense in which Luke got the girl. In Empire Strikes Back, we see the much more interesting action of Luke giving up the girl for a higher calling. Then in Return of the Jedi we see, after Luke’s rigorous monastic training, his self-sacrificing love saves his father’s soul. Luke went from a kid who wanted to grow up to an actual adult who had adult adventures.

Another way of looking at it is that look progressed from natural goods to supernatural goods. At the end of A New Hope, we see Luke bathed in glory. At the end of Return of the Jedi, we see Luke alone, burying his father who he alone knew the fate of, then joining the others but even there apart, having a religious vision which showed him the deeper reality that makes the celebration good, but only a small good.

If Star Wars had remained Star Wars instead of becoming A New Hope, it would have been forgotten as one among many stories of someone getting started in life. This is the adventure movie equivalent of the romantic comedy which ends with the couple getting married. (Or, if anyone told such stories, of a man becoming a priest ending with him being ordained.) The Star Wars trilogy is the far more difficult and thus far more unique story of describing adults. We see a working marriage in Han and Leia—fighting together through suffering and pain for the sake of something besides themselves—and we see a living priesthood in Luke.

Ultimately, in life, it’s cool to see the seed germinate, but all sorts of seeds germinate. It’s the seeds which turn into fruitful plants which stay with us.

(This, by the way, is why most sequels suck—instead of telling the different story of a seedling turning into a plant, they just reset everything and try to tell the story of a seed germinating again. That’s really when all of the progress of the original story is lost.)

Oh, and even considered in the trilogy, the end of A New Hope is a whole lot of people celebrating the two men and a wookie who just saved their lives. Princess Leia doesn’t become a bureaucrat just because she eventually stops clapping and gets back to the rebellion she was leading at the beginning of the movie and which clearly wasn’t over at the end of it.

Video Conference Call Parody

From the same people who brought us Hotel Inn, we have a video conference call in real life:

Amusingly, despite having worked from home for over 10 years, I’ve never done a video call for work. It’s funny because in theory they should be superior, but I can count on a single hand the times I’ve been on a conference call at work and wished that we had video to go with the audio.

One tip I can give about conference calls over the phone for anyone new to them is to invest in a high quality set of headphones that puts sound into both ears. It was way easier to understand people when both ears are hearing the same thing and your brain can process what it hears in the way it’s used to. The quality is important, too, because if there is no distortion on the audio, it’s much easier to tell what people are saying. This applies not just to the fundamental frequency which their vocal cords are producing, but also to the higher frequencies produces by the mouth (called “formants”) which help to distinguish sounds like “ba” “ta” and “da” or “eh” and “ee”. A high quality speakerphone (which can do full duplex) will work, too. Cheap speakerphones are almost worse than nothing, though.

Plastics, Then and Now

I recently heard a song from the very late 1970s in which plastic was used as a synonym for “phony”. This made me remember how in my early youth, plastic was generally (though not exclusively) used as a cheap replacement for better quality materials. While at the time of this writing (2020) it is possible to find cheap things made of plastic, it is by no means the case that plastic is merely a cheap alternative. Often, these days, plastics are a superior alternative. PeX pipes are better and longer-lasting than copper pipes. Plastic pipes are strongly preferred to metal pipes for gas lines buried beneath the ground. I’ve got more than a few glass-reinforced nylon gardening tools and prefer them to metal ones. What is commonly called “carbon fiber” is commonly an epoxy plastic reinforced with carbon fibers, and it may be the pre-eminent high-tech material of our day.

It’s interesting to trace the factors which went into plastics becoming frequently superior materials, because it wasn’t just one thing. The introduction of new plastics, such as more advanced epoxies, clear polycarbonates (possibly better know as Lexan), and PeX had a significant impact. They enabled all sorts of new uses for plastics that hadn’t been possible before, and in some cases enabled new sorts of things. Bulletproof glass, for example, is frequently made as a laminate of glass and polycarbonate, the glass giving hardness and the plastic shatter-resistance. That’s very hard to do, in an optically clear way, without plastics.

Another advance in plastics was the development of economical composite plastics. The most famous composite is, of course, fiberglass, though not far behind it is carbon fiber. Another great one that’s been in common use for 10-20 years now is glass-reinforced nylon. Almost as strong as low-grade steel, it is far more rigid and doesn’t rust—it’s great for gardening tools. More generally, composite materials have made for all sorts of things both strong and light. Ladders, camera tripods, bicycles, shovels—anything where one wants weight and strength, it is usually the case that the cheap one uses metal and the good one uses composite plastics. (To be fair, there are some very advanced aluminum alloys, these days, though.)

Another improvement to plastics was simple experience with the making of things out of plastic. The making of things out of plastic is as much an art as a science. The exact temperatures used in injection-molding plastics has an enormous impact on the quality of the resulting part. In the 1970s and 1980s, widespread injection molding of plastics was near its infancy. Worse, since all it was fit for was making the cheapest stuff possible, there was not much money or incentive to make the stuff better. Eventually, however, people learned how to do it. How to design stuff made of injection-molded plastics was another area of improvement, with the right thicknesses, reinforcements, etc. being learned through experience as well.

To my mind the most interesting advancement in plastics, however, has been learning how to make them in ways that go beyond the chemical formula. A good example of this is how polyester went from being an awful but cheap replacement for silk in the 1970s that felt akin to wearing a garbage bag to a vastly superior fabric for athletic clothes. These days, if you’re going to do something that will make you sweat, you will be far more comfortable in a wicking fabric, which are mostly made of polyester. The trick is that when making the polyester strands, instead of making them thick, so that one is almost making the cloth out of fishing line, one makes the plastic strands incredibly thin. These are then spun together much like natural fibers, and produce a fabric which is light weight, breathes well, and tends to pull moisture away from the body and allow it to evaporate on the surface. On the flip side, making polyester in very thick sheets has created its use for things like unbreakable drinking glasses. Admittedly more prone to scratching than glass is, they never shatter when you drop them and they are much better insulators, helping to keep the drink at whatever temperature it started at.

Probably the best example, however, is Ultra High Molecular Weight Polyethylene, sometimes sold under the brands Dyneema or Spectra. As a super-quick background, if you don’t know it, plastics are polymers, which means that they are a chain of simpler molecules known as monomers. These monomers are frequently liquids. The way plastics are synthesized is from a monomer stock, with a chemical reaction catalyzed by a catalyst that combines the monomers into chains, which form solids. Polyethylene comes in varieties, based on how many monomers are in the (typical) polymer chain. Low density polyethylene has a few hundred, and they tend to be in branched chains that don’t stick together well. This is the sort of plastic one finds commonly in grocery store bags. High density polyethylene has (typically) 700-1800 monomers in a polymer molecule, and arranged in much straighter lines, which stick together better. This is the plastic one finds in things like soda bottles. Ultra high molecular weight polyethylene has anywhere from 100,000 to 250,000 monomers in a polymer molecule. It has greater tensile strength than steel (by weight), similar abrasion resistance, similar friction to Teflon, and is highly chemically resistant to corrosion from acids and alkalies. It’s truly amazing stuff. And what’s really interesting is that (one of the more common forms) is made with a metal spinneret, in a matter not entirely unlike the way a spider spins its silk from its spinnerets.

In the early and mid 1900s, chemistry got most of the glory when it came to advances in technology, bringing us wonderful new materials. In the later half of that century, it turned out that chemical formulae were only a small part of the story. How you put things together is at least as important as what you put together. It’s an interesting lesson, not in the least because metals were often seen as so superior to biological materials, but it turns out that our best materials are often made by imitating biological materials.

Why Dorothy L. Sayers Stopped Writing Lord Peter

I’ve never seen a coherent account written down of why Dorothy L. Sayers stopped writing Lord Peter when she did. There are plenty of bits and pieces, of course, but I’ve not seen them organized into a coherent account, so I will endeavor to do so here.

The last piece of hard evidence that I know of was an essay she wrote about Gaudy Night in the book Titles to Fame, first published in October of 1937. Presumably Ms. Sayer’s chapter in it was written not long before, as she quotes from Busman’s Honeymoon, also published in 1937. Though, to be fair, Busman’s Honeymoon was originally a play which came out in 1936. In this chapter she says that she is often asked if Peter’s career will end with marriage, and she says (with some regret) that she does not foresee Peter’s career ever ending while she is still alive. How is it, then, that no more Lord Peter was forthcoming?

Actually, it’s not quite true that none was. After Busman’s Honeymoon, three Lord Peter short stories were written. Striding Folly and The Haunted Policeman were published in something called Detection Medley (I do not know whether that is a magazine or a book, though I would guess a magazine) in 1939. The short story Tallboys was written in 1942, though only discovered and published in 1972. But why were there no more novels?

There was supposed to be. In 1936, she began work on the novel Thrones, Dominations, which was to explore the married life of Harriet and Lord Peter, in part by contrasting it with other marriages. She never got more than about six chapters into it. One theory, which I find compelling, is that the abdication of King Edward VIII so that he could marry a devorcée threw a wrench into Ms. Sayer’s plans because this new environment would cause the book to be read very differently than she had intended. It is very believable to me that she would find the whole thing a mess and need some time to sort it out, and the more she tried to sort it out, the more of a mess it became while she was still trying to salvage the original form. And unfortunately, she didn’t have all that much time to sort it out.

England entered World War II in September of 1939, shortly after Germany invaded Poland. This was three years after she had begun Thrones, Dominations, but with Gaudy Night having been such a turning point in adding depth to her characters and Busman’s Honeymoon having been a strong continuation of that, it’s believable to me that she got bogged down by the more difficult task of making drama with a working marriage that needs to remain a working marriage at the end and thus cannot materially alter. The thing is doable, but it is far from easy, which is why most people don’t attempt it. Once World War II came, Ms. Sayers put down Lord Peter, except from some wartime propaganda to bolster morale (letters ostensibly from the Wimsey family about wartime conditions) and the short story Tallboys which wasn’t even published until after her death.

I should note, in passing, that Tallboys is not a bad story, though it’s really not much of a mystery. It explores, though briefly, Lord Peter and Harriet as parents, by contrast with a prig staying with them for the summer who is vocally against disciplining children, especially physically. The mystery is simply who stole Mr. Puffet’s peaches off of the peach tree in his garden, which Lord Peter does with some investigation and a clue furnished by his 8 year old son about another child’s missing fishing apparatus. It is worth reading, especially for a few more glimpses into Harriet and Lord Peter, though the two barely interact with each other in the story. Unlike The Learned Adventure of the Dragon’s Head, it’s not really a story that one would read merely for itself. Basically, it’s not entirely shocking that the story remained unpublished until after the authoress’ death.

It makes sense that in England in World War II, Miss Sayers found it impossible to write Lord Peter. The war was not a universal block to writing—Agatha Christie kept writing mysteries throughout it—but it makes sense that to Ms. Sayers, who had chafed under the constraints of writing detective fiction which was not also significant, in a literary sense, the pressures of World War II were overwhelming. How could she write a Lord Peter story during World War II without it being about what’s going on, but at the same time with things being uncertain and always changing, how could she write a Lord Peter story in that time period and be sure conditions would be the same when it was published as when it was written? She had already been bitten by this once with Thrones, Dominations and the abdication of the King.

So much for Lord Peter during the war, but what about after it? Dorothy L. Sayers lived for twelve years after the resumption of peace in England. From what I’ve read, though I can’t at present remember where in order to cite it, post-war England was just a very different place than inter-war England, and Lord Peter was a creature of the inter-war period. This was so in a number of ways; his defining characteristics were largely from the first world war, in 1946 he was now fifty six years old, and as the parent of several children and (with the plan to have Lord Saint-George die in the war and Gerald to peg out as well) with heavy responsibilities, his time would not be his own to run around investigating crimes in the same way as it used to.

This last part would not be so much of a problem if the goal was merely to preserve the character’s function in the story, but it would be a rather large problem with the humanization of Lord Peter that happened in the last few novels. In the end, I suspect that it was precisely the determination to make Lord Peter a fully human character that made Gaudy Night and Busman’s Honeymoon such great books which also made them the last books. The main concerns of the prime of Lord Peter’s life—his mid fifties—would be at odds with him being a detective, and moreover are not the sort of thing which lend themselves well to novels. Novels are a concentration of life; they are about moments which symbolize much larger patches of life. Simply put, novel-worthy events really should not happen to a successful man in his mid-fifties. They may happen to those around him, drawing him in to such a novel. He should have his life sufficiently well figured out at this point that he has fairly little personal growth to do.

That last point would not be generally fatal; it was not fatal to any of Agatha Christie’s detectives. Poirot kept detecting his whole life, and Miss Marple started detecting in her old age. Both were stable people who were swept into the troubles of others. Lord Peter got into detection because it was one of the few things which drew him out of the shell he grew in the shock of the first world war. I do not mean that this could not have been overcome, but it would have been difficult to overcome. Lord Peter novels almost entirely consisted in Lord Peter sticking his nose into other people’s business. The one major exception to this is Clouds of Witness, and even there it was, technically, his brothers’ business. People came to Poirot because it was his job; he hung out a detective shingle, as it were. To write Lord Peter mysteries in his fifties and beyond would require people to come to Lord Peter, since Lord Peter should no longer be seeking these problems out. I can say from experience that stories in which people seek out a detective are very different stories from ones in which a detective seeks out the problem; the structure of them is different. Someone must already have suspicions; something grave must be at stake to bring in a stranger. In short, to have kept writing Lord Peter stories after the second world war would have required significantly changing what a Lord Peter story was. I do not say that Ms. Sayers could not have done it. All I am saying is that it makes sense why she did not, in fact, do it.

When 2+2=5

There has been a really weird… phenomenon, I think mostly on Twitter, where some people referred to 2+2=4 as a basic, incontrovertible fact, and some other people have been invoking higher mathematics to say that sometimes 2+2=5. Since I’ve got a master’s degree in math, I thought I might as well explain what’s going on, and when 2+2=5.

To get an obvious point out of the way so as to avoid misunderstanding, in normal conversation, when people talk about 2+2=4, they are clearly referring to the natural numbers under one of the the ordinary definitions of addition (such as under the peano axioms, where addition is combined succession). Given that set and that operation, 2+2 equals 4, always, no exceptions.

Where higher level mathematics comes in is that a mathematician is free to consider any set whatsoever, and to define any operations on it that he wants. Most of these sets and operations won’t be interesting, but they will be valid. Let me give you an example of such a set with such an operation, so you can see what I mean.

Let us define the set F, such that F={2,5} (that is, F has two elements, one called “2” and the other called “5”). Let us define an operation on F×F→F (the cross product of F, mapping to F), called +. It is defined such that + of any two elements in F is the element “5” in F. Thus, 2+2=5. Under this definition, it is also the case that 2+5=5 and 5+5=5.

OK, so we now have a set F and an operation + such that in F under + as we’ve defined it, 2+2=5. Whoohoo. This is obviously a completely uninteresting set and operation. There’s nothing to say about it. There’s no reason one would ever want to actually define it, other than as a joke. (There is a certain similarity, here, to the classic set of outcomes to a coin flip, “heads I win, tails you lose”, if that is of any interest.)

But this is it. It’s not some great truth of higher mathematics, it’s a trivial side-effect of what is doable in higher mathematics which has generalized the more common mathematics.

I should note that there are very interesting sets and operations to define. For example, given a prime number m, the set of non-negative integers less than m, with addition defined to be addition modulo m, is quite interesting. (For those not familiar, modular arithmetic is basically doing arithmetic and if the result is larger than the modulus, you keep subtracting the modulus until it isn’t. Thus (2+6) % 7 = 1, since 2+6=8, but 8 is bigger than 7, so we subtract 7, and 8-7=1. You can also define modulus in terms of remainder after division.) These are quite interesting because the operation we’ve defined as + is closed, so every number has an additive inverse. It would take too long to explain why that’s interesting, but the short short version is that it’s the basis of many cryptographic algorithms, including some of the most widely used public key cryptographic algorithms like RSA which underly most encrypted web traffic.

Thus I hope it’s clear that it is not the case that higher mathematics is all uninteresting. It is only that the abstractions which are used in higher mathematics have boring side-effects. This is no different from the oddity of “Buffalo” meaning (1) an animal, (2) a city in NY and (3) to confuse someone allowing one to claim that “Buffalo buffalo buffalo buffalo buffalo” (meaning that buffalo from the city of Buffalo confuse buffalo from the city of Buffalo) is a perfectly valid English sentence. It is, but this is, at most, an amusing accident. It doesn’t mean that English is stupid, nor that people who study language are stupid. It’s just that complex things occasionally have odd quirks. What is true of the English language is also true of higher mathematics.

And none of this means that the people who say, “well, actually, sometimes 2+2=5…” aren’t intentionally missing the point.

In closing, let’s never forget the point in this XKCD comic: