Falsifiable, Physics, Quick Fix

Pokémon Are Made of Styrofoam

One of the best things about taking physics classes is that the equations you learn are directly applicable to the real world. Every so often, while reading a book or watching a movie, I’m seized by the sudden urge to check it for plausibility. A few scratches on a piece of paper later and I will generally know one way or the other.

One of the most amusing things I’ve found doing this is that the people who come up with the statistics for Pokémon definitely don’t have any sort of education in physics.

Takes Onix. Onix is a rock/ground Pokémon renowned for its large size and sturdiness. Its physical statistics reflect this. It’s 8.8 metres (28′) long and 210kg (463lbs).

Onix, being tough. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

Surely such a large and tough Pokémon should be very, very dense, right? Density is such an important tactile cue for us. Don’t believe me? Pick up a large piece of solid medal. Its surprising weight will make you take it seriously.

Let’s check if Onix would be taken seriously, shall we? Density is equal to mass divided by volume. We use the symbol ρ to represent density, which gives us the following equation:

We already know Onix’s mass. Now we just need to calculate its volume. Luckily Onix is pretty cylindrical, so we can approximate it with a cylinder. The equation for the volume of a cylinder is pretty simple:

Where π is the ratio between the diameter of a circle and its circumference (approximately 3.1415…, no matter what Indiana says), r is the radius of a circle (always one half the diameter), and h is the height of the cylinder.

Given that we know Onix’s height, we just need its diameter. Luckily the Pokémon TV show gives us a sense of scale.

Here’s a picture of Onix. Note the kid next to it for scale. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

Judging by the image, Onix probably has an average diameter somewhere around a metre (3 feet for the Americans). This means Onix has a radius of 0.5 metres and a height of 8.8 metres. When we put these into our equation, we get:

For a volume of approximately 6.9m3. To get a comparison I turned to Wolfram Alpha which told me that this is about 40% of the volume of a gray whale or a freight container (which incidentally implies that gray whales are about the size of standard freight containers).

Armed with a volume, we can calculate a density.

Okay, so we know that Onix is 30.4 kg/m3, but what does that mean?

Well it’s currently hard to compare. I’m much more used to seeing densities of sturdy materials expressed in tonnes per cubic metre or grams per cubic centimetre than I am seeing them expressed in kilograms per cubic metre. Luckily, it’s easy to convert between these.

There are 1000 kilograms in a ton. If we divide our density by a thousand we can calculate a new density for Onix of 0.0304t/m3.

How does this fit in with common materials, like wood, Styrofoam, water, stone, and metal?

Material

Density (t/m3)

Styrofoam

0.028

Onix

0.03

Balsa

0.16

Oak [1]

0.65

Water

1

Granite

2.6

Steel

7.9

From this chart, you can see that Onix’s density is eerily close to Styrofoam. Even the notoriously light balsa wood is five times denser than him. Actual rock is about 85 times denser. If Onix was made of granite, it would weigh 18 tonnes, much heavier than even Snorlax (the heaviest of the original Pokémon at 460kg).

While most people wouldn’t be able to pick Onix up (it may not be dense, but it is big), it wouldn’t be impossible to drag it. Picking up part of it would feel disconcertingly light, like picking up an aluminum ladder or carbon fibre bike, only more so.

This picture is unrealistic. Because of its density, no more than 3% of Onix can be below the water. I don’t own the copyright to this image, but I’m claiming fair use for purpose of criticism. Source.

How did the creators of Pokémon accidently bestow one of the most famous of their creations with a hilariously unrealistic density?

I have a pet theory.

I went to school for nanotechnology engineering. One of the most important things we looked into was how equations scaled with size.

Humans are really good at intuiting linear scaling. When something scales linearly, every twofold change in one quantity brings about a twofold change in another. Time and speed scale linearly (albeit inversely). Double your speed and the trip takes half the time. This is so simple that it rarely requires explanation.

Unfortunately for our intuitions, many physical quantities don’t scale linearly. These were the cases that were important for me and my classmates to learn, because until we internalized them, our intuitions were useless on the nanoscale. Many forces, for example, scale such that they become incredibly strong incredibly quickly at small distances. This leads to nanoscale systems exhibiting a stickiness that is hard on our intuitions.

It isn’t just forces that have weird scaling though. Geometry often trips people up too.

In geometry, perimeter is the only quantity I can think of that scales linearly with size. Double the length of the sides of a square and the perimeter doubles. The area, however does not. Area is quadratically related to side length. Double the length of a square and you’ll find the area quadruples. Triple the length and the area increases nine times. Area varies with the square of the length, a property that isn’t just true of squares. The area of a circle is just as tied to the square of its radius as a square is to the square of its length.

Volume is even trickier than radius. It scales with the third power of the size. Double the size of a cube and its volume increases eight-fold. Triple it, and you’ll see 27 times the volume. Volume increases with the cube (which again works for shapes other than cubes) of the length.

If you look at the weights of Pokémon, you’ll see that the ones that are the size of humans have fairly realistic weights. Sandslash is the size of a child (it stands 1m/3′ high) and weighs a fairly reasonable 29.5kg.

(This only works for Pokémon really close to human size. I’d hoped that Snorlax would be about as dense as marshmallows so I could do a fun comparison, but it turns out that marshmallows are four times as dense as Snorlax – despite marshmallows only having a density of ~0.5t/m3)

Beyond these touchstones, you’ll see that the designers of Pokémon increased their weight linearly with size. Onix is a bit more than eight times as long as Sandslash and weighs seven times as much.

Unfortunately for realism, weight is just density times volume and as I just said, volume increases with the cube of length. Onix shouldn’t weigh seven or even eight times as much as Sandslash. At a minimum, its weight should be eight times eight times eight multiples of Sandslash’s; a full 512 times more.

Scaling properties determine how much of the world is arrayed. We see extremely large animals more often in the ocean than in the land because the strength of bones scales with the square of size, while weight scales with the cube. Become too big and you can’t walk without breaking your bones. Become small and people animate kids’ movies about how strong you are. All of this stems from scaling.

These equations aren’t just important to physicists. They’re important to any science fiction or fantasy writer who wants to tell a realistic story.

Or, at least, to anyone who doesn’t want their work picked apart by physicists.

Footnotes

[1] Not the professor. His density is 0.985t/m3. ^

Economics, Falsifiable

You Might Want To Blame Central Banks For Poor Wage Growth

The Economist wonders why wage growth isn’t increasing, even as unemployment falls. A naïve reading of supply and demand suggests that it should, so this has become a relatively common talking point in the news, with people of all persuasions scratching their heads. The Economist does it better than most. They at least talk about slowing productivity growth and rising oil prices, instead of blaming everything on workers (for failing to negotiate) or employers (for not suddenly raising wages).

But after reading monetary policy blogs, the current lack of wage growth feels much less confusing to me. Based on this, I’d like to offer one explanation for why wages haven’t been growing. While I may not be an economist, I’ll be doing my best to pass along verbatim the views of serious economic thinkers.

Image courtesy of the St. Louis Federal Reserve Bank. Units are 1982-1984 CPI-adjusted dollars. Isn’t it rad how the US government doesn’t copyright anything it produces?

 

 

When people talk about stagnant wage growth, this is what they mean. Average weekly wages have increased from $335 a week in 1979 to $350/week in 2018 (all values are 1982 CPI-adjusted US dollars). This is a 4.5% increase, representing $780/year more (1982 dollars) in wages over the whole period. This is not a big change.

More recent wage growth also isn’t impressive. At the depth of the recession, weekly wages were $331 [1]. Since then, they’ve increased by $19/week, or 5.7%. However, wages have only increased by $5/week (1.4%) since the previous high in 2009.

This doesn’t really match people’s long run expectations. Between 1948 and 1973, hourly compensation increased by 91.3%.

I don’t have an explanation for what happened to once-high wage growth between 1980 and 2008 (see The Captured Economy for what some economists think might explain it). But when it comes to the current stagnation, one factor I don’t hear enough people talking about is bad policy moves by central bankers.

To understand why the central bank affects wage growth, you have to understand something called “sticky wages“.

Wages are considered “sticky” because it is basically impossible to cut them. If companies face a choice between firing people and cutting wages, they’ll almost always choose to fire people. This is because long practice has taught them that the opposite is untenable.

If you cut everyone’s wages, you’ll face an office full of much less motivated people. Those whose skills are still in demand will quickly jump ship to companies that compensate them more in line with market rates. If you just cut the wages of some of your employees (to protect your best performers), you’ll quickly find an environment of toxic resentment sets in.

This is not even to mention that minimum wage laws make it illegal to cut the wages of many workers.

Normally the economy gets around sticky wages with inflation. This steadily erodes wages (including the minimum wage). During boom times, businesses increase wages above inflation to keep their employees happy (or lose them to other businesses that can pay more and need the labour). During busts, inflation can obviate the need to fire people by decreasing the cost of payroll relative to other inputs.

But what we saw during the last recession was persistently low inflation rates. Throughout the whole the thing, the Federal Reserve Bank kept saying, in effect, “wow, really hard to up inflation; we just can’t manage to do it”.

Look at how inflation hovers just above zero for the whole great recession and associated recovery. It would have been better had it been hovering around 2%.

It’s obviously false that the Fed couldn’t trigger inflation if it wanted to. As a thought experiment, imagine that they had printed enough money to give everyone in the country $1,000,000 and then mailed it out. That would obviously cause inflation. So it is (theoretically) just a manner of scaling that back to the point where we’d only see inflation, not hyper-inflation. Why then did the Fed fail to do something that should be so easy?

According to Scott Sumner, you can’t just look at the traditional instrument the central bank has for managing inflation (the interest rate) to determine if its policies are inflationary or not. If something happens to the monetary supply (e.g. say all banks get spooked and up their reserves dramatically [2]), this changes how effective those tools will be.

After the recession, the Fed held the interest rates low and printed money. But it actually didn’t print enough money given the tightened bank reserves to spur inflation. What looked like easy money (inflationary behaviour) was actually tight money (deflationary behaviour), because there was another event constricting the money supply. If the Fed wanted inflation, it would have had to do much more than is required in normal times. The Federal Reserve never realized this, so it was always confused by why inflation failed to materialize.

This set off the perfect storm that led to the long recovery after the recession. Inflation didn’t drive down wages, so it didn’t make economic sense to hire people (or even keep as many people on staff), so aggregate demand was low, so business was bad, so it didn’t make sense to hire people (or keep them on staff)…

If real wages had properly fallen, then fewer people would have been laid off, business wouldn’t have gotten as bad, and the economy could have started to recover much more quickly (with inflation then cooling down and wage growth occurring). Scott Sumner goes so far to say that the money shock caused by increased cash reserves may have been the cause of the great recession, not the banks failing or the housing bubble.

What does this history have to do with poor wage growth?

Well it turns out that companies have responded to the tight labour market with something other than higher wages: bonuses.

Bonuses are one-time payments that people only expect when times are good. There’s no problem cutting them in recessions.

Switching to bonuses was a calculated move for businesses, because they have lost all faith that the Federal Reserve will do what is necessary (or will know how to do what is necessary) to create the inflation needed to prevent deep recessions. When you know that wages are sticky and you know that inflation won’t save you from them, you have no choice but to pre-emptively limit wages, even when there isn’t a recession. Even when a recession feels fairly far away.

More inflation may feel like the exact opposite of what’s needed to increase wages. But we’re talking about targeted inflation here. If we could trust humans to do the rational thing and bargain for less pay now in exchange for more pay in the future whenever times are tight, then we wouldn’t have this problem and wages probably would have recovered better. But humans are humans, not automatons, so we need to make the best with what we have.

One of the purposes of institutions is to build a framework within which we can make good decisions. From this point of view, the Federal Reserve (and other central banks; the Bank of Japan is arguably far worse) have failed. Institutions failing when confronted with new circumstances isn’t as pithy as “it’s all the fault of those greedy capitalists” or “people need to grow backbones and negotiate for higher wages”, but I think it’s ultimately a more correct explanation for our current period of slow wage growth. This suggests that we’ll only see wage growth recover when the Fed commits to better monetary policy [3], or enough time passes that everyone forgets the great recession.

In either case, I’m not holding my breath.

Footnotes

[1] I’m ignoring the drop in Q2 2014, where wages fell to $330/week, because this was caused by the end of extended unemployment insurance in America. The end of that program made finding work somewhat more important for a variety of people, which led to an uptick in the supply of labour and a corresponding decrease in the market clearing wage. ^

[2] Under a fractional reserve banking system, banks can lend out most of their deposits, with only a fraction kept in reserve to cover any withdrawals customers may want to make. This effectively increases the money supply, because you can have dollars (or yen, or pesos) that are both left in a bank account and invested in the economy. When banks hold onto more of their reserves because of uncertainty, they are essentially shrinking the total money supply. ^

[3] Scott Sumner suggests that we should target nominal GDP instead of inflation. When economic growth slows, we’d automatically get higher inflation, as the central bank pumps out money to meet the growth target. When the market begins to give way to roaring growth and speculative bubbles, the high rate of real growth would cause the central bank to step back, tapping the brakes before the economy overheats. I wonder if limiting inflation on the upswing would also have the advantage of increasing real wages as the economy booms? ^

Data Science, Economics, Falsifiable

The Scale of Inequality

When dealing with questions of inequality, I often get boggled by the sheer size of the numbers. People aren’t very good at intuitively parsing the difference between a million and a billion. Our brains round both to “very large”. I’m actually in a position where I get reminded of this fairly often, as the difference can become stark when programming. Running a program on a million points of data takes scant seconds. Running the same set of operations on a billion data points can take more than an hour. A million seconds is eleven and a half days. A billion seconds 31 years.

Here I would like to try to give a sense of the relative scale of various concepts in inequality. Just how much wealth do the wealthiest people in the world possess compared to the rest? How much of the world’s middle class is concentrated in just a few wealthy nations? How long might it take developing nations to catch up with developed nations? How long before there exists enough wealth in the world that everyone could be rich if we just distributed it more fairly?

According to the Forbes billionaire list, there are (as of the time of writing) 2,208 billionaires in the world, who collectively control $9.1 trillion in wealth (1 trillion seconds ago was the year 29691 BCE, contemporaneous with the oldest cave paintings in Europe). This is 3.25% of the total global wealth of $280 trillion.

The US Federal Budget for 2019 is $4.4 trillion. State governments and local governments each spend another $1.9 trillion. Some $700 billion dollars is given to those governments by the Federal government. With that subtracted, total US government spending is projected to be $7.5 trillion next year.

Therefore, the whole world population of billionaires holds assets equivalent to 1.2 years of US government outlays. Note that US government outlays aren’t equivalent to that money being destroyed. It goes to pay salaries or buy equipment. The comparison here is simply to illustrate how private wealth stacks up against the budgets that governments control.

If we go down by a factor of 1000, there are about 15 million millionaires in the world (according to Wikipedia). Millionaires collectively hold $37.1 trillion (13.25% of all global wealth). All of the wealth that millionaires hold would be enough to fund US government spending for five years.

When we see sensational headlines, like “Richest 1% now owns half the world’s wealth“, we tend to think that we’re talking about millionaires and billionaires. In fact, millionaires and billionaires only own about 16.5% of the world’s wealth (which is still a lot for 0.2% of the world’s population to hold). The rest is owned by less wealthy individuals. The global 1% makes $32,400 a year or more. This is virtually identical to the median American yearly salary. This means that almost fully half of Americans are in the global 1%. Canadians now have a similar median wage, which means a similar number are in the global 1%.

To give a sense of how this distorts the global middle class, I used Povcal.net, the World Bank’s online tool for poverty measurement. I looked for the percentage of a country’s population making between 75% and 125% of the median US income (at purchasing power parity, which takes into account cheaper goods and services in developing countries), equivalent to $64-$107US per day (which is what you get when you divide 75% and 125% of the median US wage by 365 – as far as I can tell, this is the procedure that gives us numbers like $1.25 per day income as the threshold for absolute poverty).

I grabbed what I thought would be an interesting set of countries: The G8, BRICS, The Next 11, Australia, Botswana, Chile, Spain, and Ukraine. These 28 countries had – in the years surveyed – a combined population of 5.3 billion people and had among them the 17 largest economies in the world (in nominal terms). You can see my spreadsheet collecting this data here.

The United States had by far the largest estimated middle class (73 million people), followed by Germany (17 million), Japan (12 million), France (12 million), and the United Kingdom (10 million). Canada came next with 8 million, beating most larger countries, including Brazil, Italy, Korea, Spain, Russia, China, and India. Iran and Mexico have largely similar middle-class sizes, despite Mexico being substantially larger. Botswana ended up having a larger middle class than the Ukraine.

This speaks to a couple of problems when looking at inequality. First, living standards (and therefore class distinctions) are incredibly variable from country to country. A standard of living that is considered middle class in North America might not be the same in Europe or Japan. In fact, I’ve frequently heard it said that the North American middle class (particularly Americans and Canadians) consume more than their equivalents in Europe. Therefore, this should be looked at as a comparison of North American equivalent middle class – who, as I’ve already said, are about 50% encompassed in the global 1%.

Second, we tend to think of countries in Europe as generally wealthier than countries in Africa. This isn’t necessarily true. Botswana’s GDP per capita is actually three times larger than Ukraine’s when unadjusted and more than twice as large at purchasing power parity (which takes into account price differences between countries). It also has a higher GDP per capita than Serbia, Albania, and Moldova (even at purchasing power parity). Botswana, Seychelles, and Gabon have per capita GDPs at purchasing power parity that aren’t dissimilar from those possessed by some less developed European countries.

Botswana, Gabon, and Seychelles have all been distinguished by relatively high rates of growth since decolonization, which has by now made them “middle income” countries. Botswana’s growth has been so powerful and sustained that in my spreadsheet, it has a marginally larger North American equivalent middle class than Nigeria, a country approximately 80 times larger than it.

Of all the listed countries, Canada had the largest middle class as a percent of its population. This no doubt comes partially from using North American middle-class standards (and perhaps also because of the omission of the small, homogenous Nordic countries), although it is also notable that Canada has the highest median income of major countries (although this might be tied with the United States) and the highest 40th percentile income. America dominates income for people in the 60th percentile and above, while Norway comes out ahead for people in the 30th percentile or below.

The total population of the (North American equivalent) middle class in these 28 countries was 170 million, which represents about 3% of their combined population.

There is a staggering difference in consumption between wealthy countries and poor countries, in part driven by the staggering difference in the size of middle (and higher classes) – people with income to spend on things beyond immediate survival. According to Trading Economics, the total disposable income of China is $7.84 trillion (dollars are US). India has $2.53 trillion. Canada, with a population almost 40 times smaller than either, has a total disposable income of $0.96 trillion, while America, with a population about four times smaller than either China or India has a disposable income of $14.79 trillion, larger than China and India put together. If China was as wealthy as Canada, its yearly disposable income would be almost $300 trillion, approximately equivalent to the total amount of wealth in the world.

According to Wikipedia, The Central African Republic has the world’s lowest GDP per capita at purchasing power parity, making it a good candidate for the title of “world’s poorest country”. Using Povcal, I was able to estimate the median wage at $1.33 per day (or $485 US per year). If the Central African Republic grew at the same rate as Botswana did post-independence (approximately 8% year on year) starting in 2008 (the last year for which I had data) and these gains were seen in the median wage, it would take until 2139 for it to attain the same median wage as the US currently enjoys. This of course ignores development aid, which could speed up the process.

All of the wealth currently in the world is equivalent to $36,000 per person (although this is misleading, because much of the world’s wealth is illiquid – it’s in houses and factories and cars). All of the wealth currently on the TSX is equivalent to about $60,000 per Canadian. All of the wealth currently on the NYSE is equivalent to about $65,000 per American. In just corporate shares alone, Canada and the US are almost twice as wealthy as the global average. This doesn’t even get into the cars, houses, and other resources that people own in those countries.

If total global wealth were to grow at the same rate as the market, we might expect to have approximately $1,000,000 per person (not inflation adjusted) sometime between 2066 and 2072, depending on population growth. If we factor in inflation and want there to be approximately $1,000,000 per person in present dollars, it will instead take until sometime between 2102 and 2111.

This assumes too much, of course. But it gives you a sense of how much we have right now and how long it will take to have – as some people incorrectly believe we already do – enough that everyone could (in a fair world) have so much they might never need to work.

This is not of course, to say, that things are fair today. It remains true that the median Canadian or American makes more money every year than 99% of the world, and that the wealth possessed by those median Canadians or Americans and those above them is equivalent to that held by the bottom 50% of the world. Many of us, very many of those reading this perhaps, are the 1%.

That’s the reality of inequality.

Data Science, Economics, Falsifiable

Is Google Putting Money In Your Pocket?

The Cambridge Analytica scandal has put tech companies front and centre. If the thinkpieces along the lines of “are the big tech companies good or bad for society” were coming out any faster, I might have to doubt even Google’s ability to make sense of them all.

This isn’t another one of those thinkpieces. Instead it’s an attempt at an analysis. I want to understand in monetary terms how much one tech company – Google – puts into or takes out of everyone’s pockets. This analysis is going to act as a template for some of the more detailed analyses of inequality I’d like to do later, so if you have a comment about methodology, I’m eager to hear it.

Here’s the basics: Google is a large technology company that primarily makes money off of ad revenues. Since Google is a publicly traded company, statistics are easy to come by. In 2016, Google brought in $89.5 billion in revenue and about 89% of that was from advertising. Advertising is further broken down between advertising on Google sites (e.g. Google Search, Gmail, YouTube, Google Maps, etc.) which account for 80% of advertising revenue and advertising on partner sites, which covers the remainder. The remaining 11% is made up of a variety of smaller projects – selling corporate licenses of its GSuite office software, the Google Play Store, the Google Cloud Computing Platform, and several smaller projects.

There are two ways that we can track how Google’s existence helps or hurts you financially. First, there’s the value of the software it provides. Google’s search has become so important to our daily life that we don’t even notice it anymore – it’s like breathing. Then there’s YouTube, which has more high-quality content than anyone could watch in a lifetime. There’s Google Docs, which are almost a full (free!) replacement for Microsoft Office. There’s Gmail, which is how basically everyone I know does their email. And there’s Android, currently the only viable alternative to iOS. If you had to pay for all of this stuff, how much would you be out?

Second, we can look at how its advertising arm has changed the prices of everything we buy. If Google’s advertising system has driven an increase in spending on advertising (perhaps by starting an arms race in advertising, or by arming marketing managers with graphs, charts and metrics that they can use to trigger increased spending), then we’re all ultimately paying for Google’s software with higher prices elsewhere (we could also be paying with worse products at the same prices, as advertising takes budget that would otherwise be used on quality). On the other hand, if more targeted advertising has led to less advertising overall, then everything will be slightly less expensive (or higher quality) than the counterfactual world in which more was spent on advertising.

Once we add this all up, we’ll have some sort of answer. We’ll know if Google has made us better off, made us poorer, or if it’s been neutral. This doesn’t speak to any social benefits that Google may provide (if they exist – and one should hope they do exist if Google isn’t helping us out financially).

To estimate the value of the software Google provides, we should compare it to the most popular paid alternatives – and look into the existence of any other good free alternatives. Because of this, we can’t really evaluate Search, but because of its existence, let’s agree to break any tie in favour of Google helping us.

On the other hand, Google docs is very easy to compare with other consumer alternatives. Microsoft Office Home Edition costs $109 yearly. Word Perfect (not that anyone uses it anymore) is $259.99 (all prices should be assumed to be in Canadian dollars unless otherwise noted).

Free alternatives exist in the form of OpenOffice and LibreOffice, but both tend to suffer from bugs. Last time I tried to make a presentation in OpenOffice I found it crashed approximately once per slide. I had a similar experience with LibreOffice. I once installed it for a friend who was looking to save money and promptly found myself fixing problems with it whenever I visited his house.

My crude estimate is that I’d expect to spend four hours troubleshooting either free alternative per year. Weighing this time at Ontario’s minimum wage of $14/hour and accepting that the only office suite that anyone under 70 ever actually buys is Microsoft’s offering and we see that Google saves you $109 per year compared to Microsoft and $56 each year compared to using free software.

With respect to email, there are numerous free alternatives to Gmail (like Microsoft’s Hotmail). In addition, many internet service providers bundle free email addresses in with their service. Taking all this into account, Gmail probably doesn’t provide much in the way of direct monetary value to consumers, compared to its competitors.

Google Maps is in a similar position. There are several alternatives that are also free, like Apple Maps, Waze (also owned by Google), Bing Maps, and even the Open Street Map project. Even if you believe that Google Maps provides more value than these alternatives, it’s hard to quantify it. What’s clear is that Google Maps isn’t so far ahead of the pack that there’s no point to using anything else. The prevalence of Google Maps might even be because of user laziness (or anticompetitive behaviour by Google). I’m not confident it’s better than everything else, because I’ve rarely used anything else.

Android is the last Google project worth analyzing and it’s an interesting one. On one hand, it looks like Apple phones tend to cost more than comparable Android phones. On the other hand, Apple is a luxury brand and it’s hard to tell how much of the added price you pay for an iPhone is attributable to that, to differing software, or to differing hardware. Comparing a few recent phones, there’s something like a $50-$200 gap between flagship Android phones and iPhones of the same generation. I’m going to assign a plausible sounding $20 cost saved per phone from using Android, then multiply this by the US Android market share (53%), to get $11 for the average consumer. The error bars are obviously rather large on this calculation.

(There may also be second order effects from increased competition here; the presence of Android could force Apple to develop more features or lower its prices slightly. This is very hard to calculate, so I’m not going to try to.)

When we add this up, we see that Google Docs save anyone who does word processing $50-$100 per year and Android saves the average phone buyer $11 approximately every two years. This means the average person probably sees some slight yearly financial benefit from Google, although I’m not sure the median person does. The median person and the average person do both get some benefit from Google Search, so there’s something in the plus column here, even if it’s hard to quantify.

Now, on to advertising.

I’ve managed to find an assortment of sources that give a view of total advertising spending in the United States over time, as well as changes in the GDP and inflation. I’ve compiled it all in a spreadsheet with the sources listed at the bottom. Don’t just take my word for it – you can see the data yourself. Overlapping this, I’ve found data for Google’s revenue during its meteoric rise – from $19 million in 2001 to $110 billion in 2017.

Google ad revenue represented 0.03% of US advertising spending in 2002. By 2012, a mere 10 years later, it was equivalent to 14.7% of the total. Over that same time, overall advertising spending increased from $237 billion in 2002 to $297 billion in 2012 (2012 is the last date I have data for total advertising spending). Note however that this isn’t a true comparison, because some Google revenue comes from outside of America. I wasn’t able to find revenue broken down in greater depth that this, so I’m using these numbers in an illustrative manner, not an exact manner.

So, does this mean that Google’s growth drove a growth in advertising spending? Probably not. As the economy is normally growing and changing, the absolute amount of advertising spending is less important than advertising spending compared to the rest of the economy. Here we actually see the opposite of what a naïve reading of the numbers would suggest. Advertising spending grew more slowly than economic growth from 2002 to 2012. In 2002, it was 2.3% of the US economy. By 2012, it was 1.9%.

This also isn’t evidence that Google (and other targeted advertising platforms have decreased spending on advertising). Historically, advertising has represented between 1.2% of US GDP (in 1944, with the Second World War dominating the economy) and 3.0% (in 1922, during the “roaring 20s”). Since 1972, the total has been more stable, varying between 1.7% and 2.5%. A Student’s T-test confirms (P-values around 0.35 for 1919-2002 vs. 2003-2012 and 1972-2002 vs. 2003-2012) that there’s no significant difference between post-Google levels of spending and historical levels.

Even if this was lower than historical bounds, it wouldn’t necessarily prove Google (and its ilk) are causing reduced ad spending. It could be that trends would have driven advertising spending even lower, absent Google’s rise. All we can for sure is that Google hasn’t caused an ahistorically large change in advertising rates. In fact, the only thing that is clear in the advertising trends is the peak in the early 1920s that has never been recaptured and a uniquely low dip in the 1940s that seems to have obviously been caused by World War II. For all that people talk about tech disrupting advertising and ad-supported businesses, these current changes are still less drastic than changes we’ve seen in the past.

The change in advertising spending during the years Google is growing could be driven by Google and similar advertising services. But it also could be normal year to year variation, driven by trends similar to what have driven it in the past. If I had a Ph. D. in advertising history, I might be able to tell you what those trends are, but from my present position, all I can say is that the current movement doesn’t seem that weird, from a historical perspective.

In summary, it looks like the expected value for the average person from Google products is close to $0, but leaning towards positive. It’s likely to be positive for you personally if you need a word processor or use Android phones, but the error bounds on advertising mean that it’s hard to tell. Furthermore, we can confidently say that the current disruption in the advertising space is probably less severe than the historical disruption to the field during World War II. There’s also a chance that more targeted advertising has led to less advertising spending (and this does feel more likely than it leading to more spending), but the historical variations in data are large enough that we can’t say for sure.

Falsifiable, Physics, Politics

The (Nuclear) International Monitoring System

Under the Partial Test Ban Treaty (PTBT), all nuclear tests except for those underground are banned. Under the Non-Proliferation Treaty (NPT), only the permanent members of the UN Security Council are legally allowed to possess nuclear weapons. Given the public outcry over fallout that led to the PTBT and the worries over widespread nuclear proliferation that led to the NPT, it’s clear that we require something beyond pinky promises to verify that countries are meeting the terms of these treaties.

But how do we do so? How can you tell when a country tests an atomic bomb? How can you tell who did it? And how can one differentiate a bomb on the surface from a bomb in the atmosphere from a bomb in space from a bomb underwater from a bomb underground?

I’m going to focus on two efforts to monitor nuclear weapons: the national security apparatus of the United States and the Comprehensive Test Ban Treaty Organization (CTBTO) Preparatory Commission’s International Monitoring System (IMS). Monitoring falls into five categories: Atmospheric Radionuclide Monitoring, Seismic Monitoring, Space-based Monitoring, Hydroacoustic Monitoring, and Infrasound Monitoring.

Atmospheric Radionuclide Monitoring

Nuclear explosions generate radionuclides, either by dispersing unreacted fuel, as direct products of fission, or by interactions between neutrons and particles in the air or ground. These radionuclides are widely dispersed from any surface testing, while only a few fission products (mainly various radionuclides of the noble gas xenon) can escape from properly conducted underground tests.

For the purposes of minimizing fallout, underground tests are obviously preferred. But because they only emit small amounts of one particular radionuclide, they are much harder for radionuclide monitoring to detect.

Detecting physical particles is relatively easy. There are 80 IMS stations scattered around the world. Each is equipped with an air intake and a filter. Every day, the filter is changed and then prepared for analysis. Analysis involves waiting a day (for irrelevant radionuclides to decay), then reading decay events from the filter for a further day. This gives scientists an idea of what radioactive elements are present.

Any deviations from the baseline at a certain station can be indicative of a nuclear weapon test, a nuclear accident, or changing wind patterns bringing known radionuclides (e.g. from a commercial reactor) to a station where they normally aren’t present. Wind analysis and cross validation with other methods are used to corroborate any suspicious events.

Half of the IMS stations are set up to do the more difficult xenon monitoring. Here air is pumped through a material with a reasonably high affinity for xenon. Apparently activated charcoal will work, but more sophisticated alternatives are being developed. The material is then induced to release the xenon (with activated charcoal, this is accomplished via heating). This process is repeated several times, with the output of each step pumped to a fresh piece of activated charcoal. Multiple cycles ensure that only relatively pure xenon get through to analysis.

Once xenon is collected, isotope analysis must be done to determine which (if any) radionuclides of xenon are present. This is accomplished either by comparing the beta decay of the captured xenon with its gamma decay, or looking directly at gamma decay with very precise gamma ray measuring devices. Each isotope of xenon has a unique half-life (which affects the frequency with which it omits beta- and gamma-rays) and a unique method of decay (which determines if the decay products are primarily alpha-, beta-, or gamma-rays). Comparing the observed decay events to these “fingerprints” allows for the relative abundance of xenon nuclides to be estimated.

There are some background xenon radionuclides from nuclear reactors and even more from medical isotope production (where we create unstable nuclides in nuclear reactors for use in medical procedures). Looking at global background data you can see the medical isotope production in Ontario, Europe, Argentina, Australia and South Africa. I wonder if this background effect makes world powers cautious about new medical isotope production facilities in countries that are at risk of pursuing nuclear weapons. Could Iran’s planned medical isotope complex have been used to mask nuclear tests?

Not content merely to host several monitoring stations and be party to the data of the whole global network of IMS stations, the United States also has the WC-135 “Constant Phoenix” plane, a Boeing C-135 equipped with mobile versions of particulate and xenon detectors. The two WC-135s can be scrambled anywhere a nuclear explosion is suspected to look for evidence. A WC-135 gave us the first confirmation that the blast from the 2006 North Korean nuclear test was indeed nuclear, several days before the IMS station in Yellowknife, Canada confirmed a spike in radioactive xenon and wind modelling pinpointed the probable location as inside North Korea.

Seismic Monitoring

Given that fewer monitoring stations are equipped with xenon radionuclide detectors and that the background “noise” from isotope production can make radioactive xenon from nuclear tests hard to positively identify, it might seem like nuclear tests are easy to hide underground.

That isn’t the case.

A global network of seismometers ensures that any underground nuclear explosion is promptly detected. These are the same seismometers that organizations like the USGS (United States Geological Survey) use to detect and pinpoint earthquakes. In fact, the USGS provides some of the 120 auxiliary stations that the CTBTO can call on to supplement its fifty seismic monitoring stations.

Seismometers are always on, looking for seismic disturbances. Substantial underground nuclear tests produce shockwaves that are well within the detection limit of modern seismometers. The sub-kiloton North Korean nuclear test in 2006 appears to have been registered as equivalent to a magnitude 4.1 earthquake. A quick survey of ongoing earthquakes should probably show you dozens that have been detected that are less powerful than even that small North Korean test.

This probably leads you to the same question I found myself asking, namely: “if earthquakes are so common and these detectors are so sensitive, how can they ever tell nuclear detonations from earthquakes?”

It turns out that underground nuclear explosions might rattle seismometers like earthquakes do, but they do so with characteristics very different from most earthquakes.

First, the waveform is different. Imagine you’re holding a slinky and a friend is holding the other end. There are two mains ways you can create waves. The first is by shaking it from side to side or up and down. Either way, there’s a perspective from which these waves will look like the letter “s”.

The second type of wave can be made by moving your arm forward and backwards, like you’re throwing and catching a ball. These waves will cause moving regions where the slinky is bunched more tightly together and other regions where it is more loosely packed.

These are analogous to the two main types of body waves in seismology. The first (the s-shaped one) is called an S-wave (although the “S” here stands for “shear” or “secondary” and only indicates the shape by coincidence), while the second is called a P-wave (for “pressure” or “primary”).

I couldn’t find a good free version of this, so I had to make it myself. Licensed (like everything I create for my blog) CC-BY-NC-SA v4.0.

 

Earthquakes normally have a mix of P-waves and S-waves, as well as surface waves created by interference between the two. This is because earthquakes are caused by slipping tectonic plates. This slipping gives some lateral motion to the resulting waves. Nuclear explosions lack this side to side motion. The single, sharp impact from them on the surrounding rocks is equivalent to the wave you’d get if you thrust your arm forward while holding a slinky. It’s almost all P-wave and almost no S-wave. This is very distinctive against a background of earthquakes. The CTBTO is kind enough to show what this difference looks like; in this image, the top event is a nuclear test and the bottom event is an earthquake of a similar magnitude in a similar location (I apologize for making you click through to see the image, but I don’t host copyrighted images here).

There’s one further way that the waves from nuclear explosions stand out. They’re caused by a single point source, rather than kilometers of rock. This means that when many seismic stations work together to find the cause of a particular wave, they’re actually able to pinpoint the source of any explosion, rather than finding a broad front like they would for an earthquake.

The fifty IMS stations automatically provide a continuous stream of data to the CTBTO, which sifts through this data for any events that are overwhelmingly P-Waves and have a point source. Further confirmation then comes from the 120 auxiliary stations, which provide data on request. Various national and university seismometer programs get in on this too (probably because it’s good for public relations and therefore helps to justify their budgets), which is why it’s not uncommon to see several estimates of yield soon after seismographs pick up on nuclear tests.

Space Based Monitoring

This is the only type of monitoring that isn’t done by the CTBTO Preparatory Commission, which means that it is handled by state actors – whose interests necessarily veer more towards intelligence gathering than monitoring treaty obligations per se.

The United States began its space based monitoring program in response to the Limited Test Ban Treaty, which left verification explicitly to the major parties involved. The CTBTO Preparatory Commission was actually formed in response to a different treaty, the Comprehensive Test Ban Treaty, which is not fully in force yet (hence why the organization ensuring compliance with it is called the “Preparatory Commission”).

The United States first fulfilled its verification obligations with the Vela satellites, which were equipped with gamma-ray detectors, x-ray detectors, electromagnetic pulse detectors (which can detect the electro-magnetic pulse from high-altitude nuclear detonations) and an optical sensor called a bhangmeter.

Bhangmeters (the name is a reference to a strain of marijuana, with the implied subtext that you’d have to be high to believe they would work) are composed of a photodiode (a device that produces current when illuminated), a timer, and some filtering components. Bhangmeters are set up to look for the distinctive nuclear “double flash“, caused when the air compressed in a nuclear blast briefly obscuring the central fireball.

The bigger a nuclear explosion, the larger the compression and the longer the central fireball is obscured. The timer picks up on this, estimating nuclear yield from the delay between the initial light and its return.

The bhangmeter works because very few natural (or human) phenomena produce flashes that are as bright or distinctive as nuclear detonations. A properly calibrated bhangmeter will filter out continuous phenomena like lightning (or will find them too faint to detect). Other very bright events, like comets breaking up in the upper atmosphere, only provide a single flash.

There’s only been one possible false positive since the bhangmeters went live in 1967; a double flash was detected in the Southern Indian Ocean, but repeated sorties by the WC-135s detected no radionuclides. The event has never been conclusively proved to be nuclear or non-nuclear in origin and remains one of the great unsolved mysteries of age of widespread atomic testing.

By the time of this (possible) false positive, the bhangmeters had also detected 41 genuine nuclear tests.

The Vela satellites are no longer in service, but the key technology they carried (bhangmeters, x-ray detectors, and EMP detectors) lives on in the US GPS satellite constellation, which does double duty as its space-based nuclear sentinels.

One last note of historical errata: when looking into unexplained gamma-ray readings produced by the Vela satellites, US scientists discovered gamma-ray bursts, an energetic astronomical phenomenon associated with supernovas and merging binary stars.

Hydroacoustic Monitoring

Undersea explosions don’t have a double flash, because steam and turbulence quickly obscure the central fireball and don’t clear until well after the fireball has subsided. It’s true that radionuclide detection should eventually turn up evidence of any undersea nuclear tests, but it’s still useful to have a more immediate detection mechanism. That’s where hydroacoustic monitoring comes in.

There are actually two types of hydroacoustic monitoring. There’s six stations that use true underwater monitoring with triplets of hydrophones (so that signal direction can be determined via triangulation) which are very sensitive, but also very expensive (as hydrophones must be installed at a depth of approximately one kilometer, where sound transmission is best). There’s also five land based stations, which use seismographs on steeply sloped islands to detect the seismic waves underwater sounds make when they hit land. Land based monitoring is less accurate, but requires little in the way of specialized hardware, making it much cheaper.

In either case, data is streamed directly to CTBTO headquarters in Vienna, where it is analyzed and forwarded to states that are party to the CTB. At the CTBTO, the signal is split into different channels based on a known library of undersea sounds and explosions are  separated from natural phenomena (like volcanos, tsunamis, and whales) and man-made noises (like gas exploration, commercial shipping, and military drills). Signal processing and analysis – especially of hydrophone data – is a very mature field, so the CTBTO doesn’t lacks for techniques to refine its estimates of events.

Infrasound Monitoring

Infrasound monitoring stations are the last part of the global monitoring system and represent the best way for the CTBTO (rather than national governments with the resources to launch satellites) to detect atmospheric nuclear tests. Infrasound stations try to pick up the very low frequency sound waves created by nuclear explosions – and a host of other things, like volcanos, planes, and mining.

A key consideration with infrasound stations is reducing background noise. For this, being far away from human habitation and blocked from the wind is ideal. Whenever this cannot be accomplished (e.g. there’s very little cover from the wind in Antarctica, where several of the sixty stations are), more infrasound arrays are needed.

The components of the infrasound arrays look very weird.

Specifically, they look like a bunker that tried to eat four Ferris wheels. Each array actually contains three to eight of these monstrosities. From the CTBTO via Wikimedia Commons.

 

 

What you see here are a bunch of pipes that all feed through to a central microbarometer, which is what actually measures the infrasound by detecting slight changes in air pressure. This setup filters out a lot of the wind noise and mostly just lets infrasound through.

Like the hydroacoustic monitoring system, data is sent to the CTBTO in real time and analyzed there, presumably drawing on a similar library of recorded nuclear test detonations and employing many of the same signal processing techniques.

Ongoing research into wind noise reduction might eventually make the whole set of stations much more sensitive than it is now. Still, even the current iteration of infrasound monitoring should be enough to detect any nuclear tests in the lower atmosphere.


The CTBTO has a truly great website that really helped me put together this blog post. They provide a basic overview of the four international monitoring systems I described here (they don’t cover space-based monitoring because it’s outside of their remit), as well as pictures, a glossary, and a primer on the analysis they do. If you’d like to read more about how the international monitoring system works and how it came into being, I recommend visiting their website.

This post, like many of the posts in my nuclear weapon series came about because someone asked me a question about nuclear weapons and I found I couldn’t answer quite as authoritatively as I would have liked. Consequently, I’d like to thank Cody Wild and Tessa Alexanian for giving me the impetus to write this.

This post is part of a series on special topics in nuclear weapons. The index for all of my writing on nuclear weapons can be found here. Previous special topics posts include laser enrichment and the North Korean nuclear program.

Economics, Falsifiable, Politics

Franchise Economics: Why Tim Hortons Has Become A Flashpoint In The Minimum Wage Fight

Since the minimum wage increase took effect on January 1st, Tim Hortons has been in the news. Many local franchisees have been clawing back benefits, removing paid breaks, or otherwise taking measures to reduce the costs associated with an increased minimum wage.

TVO just put out a piece about this ongoing saga by the Christian socialist Michael Coren. It loudly declares that “Tim Hortons doesn’t deserve your sympathy“. Unfortunately, Mr. Coren is incorrect. Everyone involved here (Tim Hortons the corporation, Tim Hortons franchisees, and Tim Hortons workers) is caught between a rock and a hard place. They all deserve your sympathy.

This Tim Hortons could be literally anywhere in suburban or rural Canada. Image Credit: Marek Ślusarczyk via Wikipedia Commons

It is a truism that a minimum wage increase must result in either declining profits, cuts to other costs, or rising prices. While supporters of the minimum wage increase would love to see it all come out of profits, that isn’t reasonable.

Basic economics tell us that as we approach a perfect market, profits should fall to zero. The key assumptions underpinning this are global perfect information (so no one can have any innovations that allow them to do better than anyone else) and zero start-up costs (so anyone can enter any market at any time). Obviously, these assumptions aren’t true in reality, but when it comes to fast food, they’re fairly close to true.

It is relatively cheap to start a fast-food restaurant (compared to say opening a factory). The start-up costs for a McDonalds, KFC, or Wendy’s are $1,000,000 to $2.3 million, while a Subway costs about $100,000 to $250,000 to start. This means that whenever someone sees fast-food restaurants making large profits in an area, they can open their own and take a fraction of the business, driving everyone’s profits down.

They’re probably driven down much lower than you think. If you had to guess, what would you say the profit margins for a fast-food restaurant are? If you’re anything like people in this study, you probably think something like 35%. The actual answer is 6% [1].

In addition to telling me that the average fast food restaurant has a 6% profit margin, that link helpfully told me that 29% of operating expenses in a fast-food restaurant come from labour costs. Raising those labour costs by 20% by increasing wages 20% increases total costs by 6% [2]. The minimum wage isn’t making fast-food restaurant owners make do with a little less in the way of profits. It’s entirely wiping out profits.

Now maybe your response to that is “well my heart doesn’t really bleed for that big multinational losing its profits”. But that’s not how Tim Hortons works. Tim Hortons, like almost all fast-food restaurants is a franchise. Tim Hortons the corporation makes money by collecting fees and providing services to Tim Hortons the restaurants, which are owned by the mythical small business owners™ that everyone (even the proponents of the minimum wage increase) claim to care so much about.

Most of these owners aren’t scions of wealthy families, but are instead ordinary members of their communities who saw opening a Tim Hortons as an investment, a vocation, or as a way to give back. They need to eat as much as their workers.

Faced with rising labour costs and no real profit buffer to absorb them, these owners can only cut costs or raise prices.

Except they can’t raise prices.

That’s the rub of a franchise system. The corporate office wants everything to be the exact same at every store. They set prices and every store must follow them. But there’s divergent incentives here. Tim Hortons the corporation makes a profit by selling supplies to its franchises; critically, they make a profit on supplies whether those franchisees turn a profit or not. They really don’t want to raise prices, because raising prices will hurt their bottom line.

It’s well known that (in general) the more expensive something is, the less people want it. Raising prices will hurt the sales volume of Tim Hortons franchises, which will decrease the profits at corporate Tim Hortons. The minimum wage hike affects Tim Hortons the corporation very little. They might see slightly increased shipping costs, but their costs are far less dependent on Canadian minimum wage labour. Honestly, the minimum wage increase probably is a net good for Tim Hortons the corporation. More money in people’s pockets means more money spent on fast-food.

Tim Hortons the corporation probably won’t say it, because they don’t want to antagonize their franchisees, but this minimum wage hike is great for them.

So, Tim Hortons franchisees have to cut costs or run charities. Given that they are running restaurants and not charities, we can probably assume that they’re going to cut costs. Why does it have to be labour costs that get cut? Can’t they just get their supplies for cheaper?

Here the franchise system bites them again. If they were independent restaurateurs, they might be able to source cheaper ingredients, reduce the ply of the toilet paper in their bathrooms, etc. and get their profits back this way.

But they’re franchisees. Tim Hortons the corporation has a big list of everything you need to run a Tim Hortons and you are only allowed to buy it from them. They get to set the prices however they want. And what they want is to keep them steady.

The only cost that Tim Hortons the corporation doesn’t control is labour costs. So, this is what franchisees have to cut.

There are two ways to decrease your labour costs. You can “increase productivity”, or you can cut wages and benefits. “Increase productivity” is the clinical and uninformative way of saying “fire 20% of your workers and verbally abuse the others until they work faster” or “fire 20% of your workers and replace them with machines”. While increased productivity is generally desirable from an economics point of view, it is often more ambiguous from a moral point of view.

Given that the minimum wage was just raised and it is illegal to pay any less than it, Tim Hortons franchisees cannot cut wages. So, if they’re against firing their employees and want to keep making literally any money, they have to cut benefits.

This might make it seem like corporate Tim Hortons is the bad guy here. They aren’t. The executives at Tim Hortons labour under what is called a fiduciary duty. They have a legal obligation to protect shareholder interests from harm and to act for the good of the corporation, not their own private good or for their private moral beliefs. They are responding to the minimum wage hike the way the government has told them to respond [3].

Minimum wage jobs suck. For all that economists claim there is no moral judgement implied in a wage, that it merely shows the intersection of the amount of supply of a certain type of labour and the demand for that labour, it can be hard to believe that there is no moral dimension to this when people making one wage struggle to make ends meet, while those earning another can buy fancy cars they don’t even need.

It is popular to blame business owners and capitalists for the wages their workers make and to say that it shows how little they value their workers. I don’t think that’s merited here. Corporate Tim Hortons has crunched the numbers and decided that if they raise prices, fewer people will buy coffee, their profits will decrease, and they might be personally liable for breach of fiduciary duty. In the face of rising prices, franchisees try and do whatever they can to stay afloat. We can say that caring about profits more than the wages their workers make shows immense selfishness on the part of these franchisees, but it’s little different than the banal selfishness anyone shows when they care more about making money for themselves than making money and giving it away – or the selfishness we show when we want our coffee to be cheaper than it can be when made by someone earning a wage that can comfortably support a family.

Footnotes

[1] As long as there are other available investments approximately as risky as opening a fast-food restaurant that return at least 6%, profits shouldn’t drop any lower than that. In this way, inefficiencies in other sectors could stop fast food restaurants from behaving like they were in a perfectly free market even if they were. ^

[2] This calculation is flawed, in that there are probably other costs making up total labour costs (like benefits) beyond simple wage income. On the other hand, it isn’t just wages that are going up. Other increased costs probably balance out any inaccuracies, making the conclusions essentially correct. This is to say nothing for corporate taxes, which further reduce profits. ^

[3] We can’t blame fiduciary duty, because fiduciary duty is how investing at all can happen. You might not like investing, but without investing, saving for retirement or having a national pension plan is impossible. If your response to this is to say “well let’s just tear down capitalism and start over”, I’d like to remind you that people tried that and it led to a) famine, b) gulags, c) death squads, d) more famine, and e) persistent shortages of every consumer good imaginable, including food ^

Falsifiable

2018 Predictions

Inspired by Slate Star Codex, this is my second year of making predictions (see also: my previous predictions, their scores, and my recent LessWrong post about these predictions).

Before I jump into the predictions, I want to mention that I’ve created templates so that anyone who wants to can also take a stab at it; the templates focus on international events and come in two versions:

  • Long (which assumes you read global news a lot)
  • Short (which is less demanding)

With both these sheets, the idea is to pick a limited number of probabilities (I recommend 51%, 60%, 70%, 80%, and 90%) and assign one to each item that you have an opinion on. At the end of the year, you count the number of correct items in each probability bin and use that to see how close you were to ideal. This gives you an answer to the important question: “when I say something is 80% likely to happen, how likely, really, is it to happen?”

You can also make your own (or use the set of questions Slate Star Codex normally uses). If you do make your own, please link your post (and maybe also your template?) in the comments or post it to the front page. It’s my hope that this post can serve as a convenient place for the LW community to look at the predictions of everyone who wants to participate in this experiment!

With that out of the way, here’s my guesses for the next year.

Canada

  1. Liberals remain ahead in the CBC Poll Tracker seat projection – 70%
  2. Trudeau has a higher net favorability rating than Andrew Scheer according to the CBC Leader Meter on January 1, 2019 – 80%
  3. Marijuana is legalized in time for Canada Day – 60%
  4. Marijuana is legalized in 2018 – 90%
  5. At least one court finds the assisted dying bill isn’t in line with Carter v Canada – 70%
  6. Ontario PC party wins the election – 60%
  7. The Ontario election results in a minority government – 80%
  8. The Quebec election results in a minority government – 80%
  9. No BC snap election in 2018 – 90%
  10. No terrorist attack in Canada that kills > 10 Canadians in 2018 – 90%
  11. More Canadian opioid poisoning deaths in 2018 than in 2017 – 60%
  12. Canada does better at the 2018 Winter Olympics (in both gold medals and total medals) than in 2014 – 90%
  13. Canada does not win a gold medal in men’s hockey at the 2018 Olympics – 70%
  14. Canada does win a gold medal in women’s hockey at the 2018 Olympics – 51%

America

  1. Trump announces that the US is pulling out of NAFTA and begins the process of putting the US withdrawal into motion – 51%
  2.  Less than 100km of concrete wall on the border with Mexico will be constructed – 90%
  3. No registry of Muslims created – 90%
  4. Congress doesn’t take action to extend DACA – 80%
  5. No department of the Federal Government is eliminated – 90%
  6. There isn’t a government shutdown before the midterm elections – 60%
  7. Democrats take back the house in the 2018 midterm elections – 80%
  8. Democrats take back the senate in the 2018 midterm elections – 60%
  9. Mueller’s investigation finishes in 2018 – 60%
  10. Impeachment proceedings aimed at Trump are not started in 2018 – 80%
  11. Trump is still president at the end of 2018 – 90%
  12. No terrorist attack in America that kills > 10 Americans – 70%
  13. No terrorist attack in America that kills > 100 Americans – 90%
  14. Susan Collins doesn’t get the Obamacare stabilization measures she was promised – 70%
  15. More US opioid poisoning deaths in 2018 than in 2017 – 80%

South America

  1. FARC peace deal remains in place on January 1, 2019 – 80%
  2. The black market exchange rate for Venezuelan Bolivars is above 110,000 to the US dollar on January 1, 2019 (as measured by DolarToday) – 80%
  3. Inflation in Venezuela is above 100% for the year of 2018 (as measured by DolarToday) – 90%
  4. United Socialist party retains control of the Venezuelan presidency in 2018 – 90%
  5. Protests (and the official response to those protests) result in more than 100 fatalities in Venezuela in 2018 – 60%
  6. Protests (and the official response to those protests) do not result in more than 1000 fatalities in Venezuela in 2018 – 70%
  7. Major Venezuelan opposition groups do not enter any sort of power sharing agreement with the Venezuelan regime in 2018 – 80%

Middle East

  1. No Israeli politician is indicted by the ICC over settlement activity in 2018 – 90%
  2. There isn’t an election in Israel in 2018 – 80%
  3. US does not physically relocate its embassy to Jerusalem in 2018 – 90%
  4. No Palestinian led Intifada in Israel that results in the deaths of >1000 combined attackers, security forces, and civilians (this is a conflict characterized by suicide bombing and police responses) – 70%
  5. No Israeli led operation in the West Bank or Gaza that results in the deaths of >1000 combined soldiers, civilians, and militants (this is a conflict characterized by rocket fire and military strikes) – 70%
  6. Fatah and Hamas do not meaningfully reconcile in 2018 (e.g. Fatah still doesn’t control Gaza by January 1, 2019) – 51%
  7. No significant resurgence in ISIL in 2018 (e.g. it does not gain territory over the next year) – 80%
  8. Fewer casualties in the Syrian Civil War in 2018 than in 2017 – 70%
  9. No power sharing agreement or durable ceasefire (typified by the three months following the agreement each having less than 500 fatalities) in Syria in 2018 – 80%
  10. Bashar Al Assad is still President of Syria on January 1, 2019 – 90%
  11. Protests in Iran do not result in more than 1000 fatalities by the end of 2018 – 70%
  12. Protests in Iran do not result in more than 100 fatalities by the end of 2018 – 51%
  13. Hassan Rouhani is still President of Iran on January 1, 2019 – 90%
  14. No new international sanctions against Iran (does not include adding new organizations or individuals to old categories and requires coordinated participation of at least two countries) – 80%
  15. No new US sanctions against Iran (does not include adding new organizations or individuals to old categories) – 51%
  16. No attack on the Iranian nuclear program by Israel – 90%
  17. Iran does not withdraw from the deal limiting its nuclear program – 90%
  18. Conditional on Iran remaining in the nuclear deal, inspectors find no evidence of violations after the deal began – 90%
  19. Yemen Civil War continues – 60%
  20. Saudi Arabia pulls troops out of Yemen – 51%
  21. Mohammed bin Salman either remains as crown prince of Saudi Arabia, or becomes king (i.e. no coup or succession shake-up) – 80%
  22. Rockets fired from Yemen cause casualties in another country – 51%
  23. No resolution or lifting of embargo in the Qatar crisis – 80%
  24. OPEC production cuts continue through to the end of 2018 – 60%

Africa

  1. No power sharing between ZANU-PF and the opposition will happen in Zimbabwe before the elections (if they occur) in 2018 – 80%
  2. Zimbabwe will hold election in 2018 – 70%
  3. No peace deal ends South Sudan fighting – 70%
  4. Libya still has two rival governments on January 1, 2019 – 70%
  5. No protests, riots, or rebellion in Egypt that kills >100 people in a one week period – 80%
  6. No protests, riots, or rebellion in Tunisian kills >50 people in a one week period – 90%
  7. No terrorist attack in Tunisia kills >20 people – 80%
  8. Zuma is not impeached in 2018 – 51%

Asia

  1.  Inflation rate in Japan still remains below 1% in 2018 – 70%
  2. Japanese constitutional reform (removing pacifism) does not occur in 2018 – 51%
  3. China will not deploy its military against Taiwan or Hong Kong in 2018 – 90%
  4. North Korea will test a submarine launched ballistic missile in 2018 – 70%
  5. North Korea will not test nuclear weapons or launch any missiles during the 2018 Olympics – 80%
  6. North Korea will test a nuclear weapon in 2018 – 51%
  7. No country will attempt to shoot down a North Korean missile test in 2018 – 80%
  8. If there is an attempt, it will succeed – 51%
  9. North Korea tests a missile that is judged by experts at 38 North as likely able to carry a plausible North Korean nuclear weapon to the United States – 60%
  10. No current member of China’s Politburo Standing Committee visits North Korea in 2018 – 70%
  11. No meeting between Kim Jung-un and Moon Jae-in in 2018 – 90%

Europe

  1. No resolution to the crisis in Ukraine – 80%
  2. Russian GDP growth is less than 3% – 80%
  3. No gain of greater than 20% in the value of the ruble vs. the dollar – 70%
  4. Sanctions against Russia are not significantly rolled back (e.g. sanctions remain in place against Rosneft, Novate, Gazprombank and Vnesheconombank by all members of the G7 remain in place at the end of 2018) – 90%
  5. Angela Merkel remains chancellor of Germany – 60%
  6. Germany holds another election before a government can be formed – 51%
  7. No date set for another Scottish referendum in 2018 – 80%
  8. Teresa May remains prime minister of the United Kingdom – 70%
  9. The UK does not terminate the process of Brexit in 2018 – 90%
  10. There is no final Brexit withdrawal deal reached in 2019 (Donald Tusk wishes to have one by October) – 51%
  11. No snap election/vote of no-confidence in the UK in 2018 – 80%
  12. Poland’s EU voting rights aren’t suspended – 90%
  13. Poland and Hungary continue to refuse to accept migrant quotas – 90%
Falsifiable

Grading my 2017 Predictions

Now is the big reveal. Just how did I do in 2017?

Canada

  1. Trudeau ends the year with a lower approval rating than he started – 60%
  2. No bill introduced that changes the electoral system away from first past the post in 2019 – 50%
  3. No referendum scheduled on changing the electoral system away from first past the post before 2019 – 70%
  4. A bill legalizing marijuana is passed by the House of Commons – 90%
  5. The senate doesn’t block attempts to legalize marijuana – 80%
  6. At least one court finds the assisted dying bill isn’t in line with Carter v Canada – 60%
  7. Ontario Liberal Approval rating remains below 30% – 80%
  8. Patrick Brown “unsure” rating remains above 40% – 70%
  9. Kellie Leitch is not the next CPC leader – 80%
  10. Michael Chong is not the next CPC leader – 70%
  11. Maxine Bernier is not the next CPC leader – 90%
  12. No terrorist attack that kills >10 Canadians – 70%
  13. No terrorist attack that kills >100 Canadians – 90%
  14. At least one large technology company (valuation >$10 billion and >1,000 employees) will open a Waterloo office in 2017 – 80%

 

America

  1. Trump will veto at least 1 bill passed by the House and Senate – 70%
  2. Changes to NAFTA will not significantly affect Canada (e.g. introduce tariffs, eliminate visas, etc) – 80%
  3. Less than 100km of concrete wall on the border with Mexico will be constructed – 80%
  4. Unemployment rate changes by less than 0.5% in 2017 – 90%
  5. Bay Area housing prices increase in 2017 – 90%
  6. Protests (in America) on Trump’s inauguration day draw at least 1 million people – 80%
  7. Protests (in America) on Trump’s inauguration day draw at least 5 million people – 50%
  8. Protests (in America) on Trump’s inauguration day draw less than 10 million people – 70%
  9. Protests outside of America on Trump’s inauguration day draw at least 1 million people – 60%
  10. Terrorist attack in America that kills at least 10 Americans – 70%
  11. No terrorist attack in America that kills at least 100 Americans – 70%
  12. No registry of Muslims created in America – 90%
  13. New Supreme Court Justice is named to the USSC – 90%
  14. No repeal of any of: the individual mandate, the prohibition on denying coverage for pre-existing conditions, children remaining on their parents insurance plans until they are 25 – 70%
  15. gov is taken offline or otherwise rendered inoperative by the new administration – 80%
  16. No Federal Department is eliminated – 80%

South America

  1. No setback to the FARC peace deal significant enough to cause >1000 rebels to rearm – 70%
  2. On the black market, the exchange rate for Venezuelan Bolivars to US Dollars remains above 3000 bolivars per dollar. (As measured by DolarToday) – 80%
  3. Inflation in Venezuela for 2017 is higher than 100% (As measured by DolarToday) – 90%
  4. United Socialist party retains control of the Venezuelan presidency – 70%
  5. No uprising in Venezuela leading to >1000 combined civilian and soldier deaths – 70%

Middle East

  1. The “Regulation” Bill, legalizing many illegal settlements, is passed in Israel – 60%
  2. No Israeli politician is indicted by the ICC over settlement activity in 2017 – 80%
  3. The US moves its embassy to Jerusalem – 50%
  4. OPEC agreement fails (as evidenced by Saudi Arabia increasing oil production to >10.058 million BPD) – 50%
  5. Iraq takes back Mosul – 90%
  6. Mosul Dam does not fail – 70%
  7. Fewer casualties in Syrian Civil War in 2017 than in 2016 – 60%
  8. No new international sanctions against Iran – 80%
  9. No new US sanctions against Iran – 50%
  10. No attack on the Iranian nuclear program by Israel – 80%
  11. Iran does not withdraw from the deal limiting its nuclear program – 80%
  12. Conditional on Iran remaining in the nuclear deal, inspectors find no evidence of violations after the deal began – 90%
  13. Yemen Civil War continues – 60%

Africa

  1. Power transition in The Gambia requires ECOWAS troops – 50%
  2. Power transition occurs in The Gambia – 70%
  3. No peace deal ends South Sudan fighting – 50%
  4. IS or affiliated groups do not hold more territory in Africa at the end of 2017 than at the beginning – 90%
  5. Libya has a single government by the end of 2017 – 50%
  6. No protests, riots, or rebellion in Egypt that kills >100 people in a one week period – 80%
  7. No protests, riots, or rebellion in Tunisian kills >50 people in a one week period – 90%
  8. At least one terrorist attack kills >50 people in Tunisian – 50%

Asia

  1. Inflation rate in Japan remains below 1% in 2017 – 70%
  2. No Japanese snap election in 2017 – 90%
  3. Scandal involving Thailand’s new king makes its way to a major Western Newspaper – 50%
  4. Saenuri Party loses in the 2017 South Korean election – 80%
  5. China will send at least one diplomatic “insult” to the US (e.g. expelling an ambassador or consul or closing on of its embassies or consulates) – 60%
  6. By the end of 2017, none of the young lawmakers associated with the Umbrella Revolution will be in the Hong Kong parliament – 60%
  7. The Hong Kong lawmakers who are appealing their ban from parliament will have their final appeals denied – 80%
  8. China will not deploy its military against either Hong Kong or Taiwan in 2017 – 90%
  9. North Korea detonates a nuclear weapon – 70%
  10. North Korea does not demonstrate a completed weapon system (e.g. miniaturized bomb and ICBM capable of threatening the continental United States) – 90%

Europe

  1. No resolution to the crisis in Ukraine – 70%
  2. Crimea remains part of Russia – 90%
  3. Russian GDP growth is less than 2% – 80%
  4. No gain of greater than 15% in the value of the ruble vs the dollar – 60%
  5. Angela Merkel remains Chancellor of Germany – 60%
  6. Marie Le Pen does not become President of France – 70%
  7. Geert Wilders does not become Prime Minister of the Netherlands – 70%
  8. UK invokes Article 50 – 60%
  9. Conditional on the UK invoking article 50, this occurs behind schedule – 70%
  10. Conditional on the UK leaving the EU, Scotland prepares for another referendum – 80%
  11. No snap election called in the UK – 80%
  12. No regional independence movement (e.g. Scotland, Catalan) achieves success in Europe in 2017 – 90%
  13. Sanctions against Russia are not significantly rolled back (e.g. sanctions remain in place against Rosneft, Novate, Gazprombank and Vnesheconombank by all members of the G7 remain in place at the end of 2017) – 60%

Personal

  1. I will not break up with anyone I am currently dating – 90%
  2. I will buy a car – 50%
  3. I will still be working at my current job at the end of 2017 – 80%
  4. I will not move to another city in 2017 – 90%
  5. Conditional on remaining in my current city, I will not move to a different apartment in 2017 – 80%
  6. I will read at least 40 books this year – 80%
  7. I will read at least 10 non-fiction books this year – 50%
  8. I will start reading (and read at least 50 pages) of at least 10 books people recommended to me this year – 60%
  9. I will write at least 200,000 words this year – 80%
  10. I will post at least 15 blog posts or short stories – 80%
  11. I will post at least 25 blog posts or short stories – 50%
  12. I will be >15% over or under-confident for at least 2 confidence levels in these predictions (before taking into account this prediction) – 80%

Notes

I thought that making my predictions mostly numerical would make them easy to grade. This mostly worked, but there were a few edge cases, judgement calls, and other amusing things that I want to explicitly mention:

  • Throughout my predictions I used the word “remains”. I regret this, because it is ambiguous. I think I intended it to mean “on January 1st, 2018, X remains true”, but there’s an alternative parsing that is “during all of 2017, X will be true”. I feel it’s most accurate to grade these according to my intent. For my 2018 predictions, I will use clearly language.
  • For 8, the two most recent polls I could find were both from November. In one, Patrick Brown had a “don’t know” rating of 50%. In the other, it was 34%. Polls were found by Googling ‘ontario leader popularity’ and ‘ontario leader popularity politics’; November was the last month in which I could find polls, so I only used November polls. I’m averaging these two and considering the prediction successful. The lack of good aggregation of Ontario political information is part of why I would like to create a website tracking the Ontario election this year.
  • While I was correct as to the who wasn’t the next leader of the Conservative party, I definitely got emotionally involved such that I was severely miscalibrated. Bernier came far closer to winning it then Leitch or Chong and both of those two fringe candidates had much lower chances that it felt like they did.
  • WRT 24 and 25, I’m not counting the Las Vegas shooting as a terrorist attack because it lacked a political motive (as far as we currently know). I think I overestimated the risk of terrorist attack because of the availability heuristic (the last two years had seen a higher than normal amount of successful and dangerous terrorist attacks). A proper estimation would have focused more on the base rate.
  • I don’t think Trump’s cancellation of advertising comes anywhere close to fulfilling 29, so I’m marking it as failed.
  • 31 is borderline, with many former FARC fighters “joining criminal gangs or a dissident FARC movement that has about 1,000 fighters nationwide“. Given that this still implies less than 1000 members rearmed to continue the fight as FARC, I think the prediction holds.
  • 38 is also borderline, but ultimately, I think there is a difference between an announcement of intent to move and an actual movement. Since I was going to mark 28 as a success if Trump hadn’t signed the tax bill by now, it’s only fair that I mark 38 as a failure.
  • I was way under-confident in the stability of the Mosul dam (41). Compare my probability with the chance on the Good Judgement Project and you’ll see I really overstated the risk compared to the consensus.
  • WRT to 43 and 44, the US Treasury added new groups to existing designations, but these are neither new sanctions, nor international sanctions
  • For 59, I think this Daily Mail headline counts: “Thailand’s colourful new King brought ‘his mistress AND his former air stewardess wife’ to his father’s lavish cremation ceremony with both marching in bearskin hats“. I think I want to stay away from prediction “scandals” in the future though, because it’s a very fuzzy concept.
  • While North Korea claims to have a complete, miniaturized ICBM, it looks like them actually realizing this with a weapon able to hit the US mainland is about one year away. Therefore 66 is a success.
  • 69 is only provisionally true and needs to be revised when more GDP data is available.
  • I am apparently rubbish at predicting snap elections, given that I got both 77 and 58 wrong, while being highly confident in my wrongness.
  • Out of all of my failed predictions, the one that surprised me the most was the OPEC deal holding. I really thought that it would fall apart.

A complete list of the sources I used when grading all non-personal predictions is available here.

Calibration

The whole point of having predictions with few allowed probabilities (for me it was 50%, 60%, 70%, 80% and 90%) is that you can then check how accurate these were by pooling your answers. Here’s how I did:

Of my predictions at a 50% confidence level, I got 7 right and 6 wrong (54%).
Of my predictions at a 60% confidence level, I got 9 right and 4 wrong (69%).
Of my predictions at a 70% confidence level, I got 16 right and 4 wrong (80%).
Of my predictions at an 80% confidence level, I got 20 right and 6 wrong (77%).
Of my predictions at a 90% confidence level, I got 17 right and 2 wrong (89%).

If you prefer graphs, here’s the results on a graph. The red line shows what I would get if I was a perfect judge of probability. The blue line is actual me. Whenever the red line is below my results, I was under-confident. Whenever it’s above them, I was overconfident.

I’m pleased that in general (excepting 70% vs. 80%), things I thought were more likely were in fact more likely. I appear to be fairly under-confident at lower probability levels (50% through 70%), and fairly good at higher confidence levels (80% and 90%), although of course this is just one year and some of this could be due to chance and luck.

My meta-calibration was quite poor. I was never more than 10% off from perfect calibration, despite my worries that I would frequently be up to 15% from it.

Falsifiable, Politics, Quick Fix

May CPC Leadership Race Update

A friend asked me what I thought about the candidates in the leadership race for the Conservative Party of Canada. I found I had more to say than was strictly reasonable to post in a Facebook comment. I posted it anyway – because I’m sometimes unreasonable – but I found I also wanted to record my thoughts in a more organized manner that’s easier to link to.

Right now, I think there are a few meaningful ways to split up the candidates. You can split them up based on what block of the party they represent.

The way I see it, you have:

  • Michael Chong representing the wonkish Progressive Conservatives
  • Maxine Bernier and Rick Peterson representing the wonkish libertarians
  • Steven Blaney and Dr. Kellie Leitch with a more nativist message
  • Lisa Raitt, Andrew Scheer, and Erin O’Toole running as unobjectionable compromise candidates
  • Andrew Saxton and Chris Alexander running as clones of Steven Harper
  • Pierre Lemieux and Brad Trost running as social conservatives
  • Deepak Obhrai running against xenophobia

It might be possible to collapse these categories a bit; unobjectionable compromise candidates and Harper clones don’t have that much difference between them, for example. But I think I’m clustering based on salient differences in what the candidates are choosing to highlight, even when their policy positions or voting records are very similar.

I’ve also been clustering based on ability to win the thing. Here I think there are two clear groups: the haves, and the have-nots. In no particular order, the haves are: Chong, Bernier, Leitch, Raitt, Scheer, and O’Toole. The have-nots are everyone else. I’d give 20:1 odds against any of the have-nots winning.

There are a few things I can infer about the haves based on all the emails I’ve been getting from them.

Chong (polling at 4% in the first round) is hoping that he signed up enough people and is enough people’s second/third/nth choice to win. That currently feels pretty unlikely, but we’ll see. I’d bet on Chong at 12:1 odds.

Raitt (5%), O’Toole (11%), and Scheer (22%) are fighting viciously for the post of compromise candidate, with varying degrees of poll and debate success (Raitt has done much better in debates than her polling suggests). Given the bitter divisions in the party, I personally think the race will go to one of these three on the third or fourth ballot, but I’m low confidence here. More emails in the past few days have attacked Scheer, so between that and his poll numbers, he’s the one I think most likely to win. I’d bet on Scheer at 3:1 odds, O’Toole at 10:1 odds, and Raitt at 12:1 odds.

Bernier (31%) is the current front runner, but I personally expect him to have a lot of trouble picking up subsequent round votes, even with O’Leary’s endorsement. I really wish there was more polling of second and third round intentions in this thing. Without those data, I’m going to put Bernier as second most likely to win, with betting odds of 4:1. I would very quickly change my tune if I saw any evidence he had strong support in the latter rounds.

Leitch (8%) has her own very dedicated cadre of um, “very patriotic” (read: virulently xenophobic) supporters. She also has a lot of people who hate her. Is that >50% of the party? I’m not sure. From her last email (where she urged everyone to consider at least ranking her), I think her internal polling is showing that it isn’t. Reading between the lines, I think her campaign thinks she won’t pick up many 2nd or 3rd votes but that she might have staying power into the late rounds. It seems like her strategy is to win on the 7th, 8th, 9th, or even 10th ballot after everyone else is exhausted. For this reason, I’d recommend she be left entirely off the ballots of anyone who joined the party to pick good candidates. I’d even at this point recommend leaving Bernier on the ballot as a last-ditch Leitch stopper. I do think Leitch is suffering from losing all that free air time to O’Leary and from the loss of her campaign manager a few months ago. He seemed to be able to reliably get her in the news in a way that her new campaign manager has been unable to replicate. I’d take Leitch at 10:1 odds.

Given all this I’d order the candidates from most to least likely to win thusly: Scheer, Bernier, O’Toole, Leitch, Chong, Raitt.

I diverge slightly from the polls of first round intentions because:

  • I think Bernier lacks second and third round support in a serious way. I especially expect him to suffer in rural ridings, where I’m given to understand supply management is popular.
  • I have Raitt below Chong because I think she is the weakest member of her bloc. If someone else in her bloc isn’t winning, I think it would signal a serious weakness in the bloc itself, such that she shouldn’t be in a position to be beating anyone.

When it comes to my personal ballot, I plan to rank nine candidates in the following order: Chong, Raitt, O’Toole, Scheer, Obhrai, Bernier, Saxton, Alexander, Peterson. I’m ranking each candidate based on their respect for the environment, their votes on Bill C-279 (protecting gender identity) and the Woodworth Committee (redefining when life starts), any relevant experience they have in politics or adjacent fields, the tone they’ve struck, their overall level of wonkishness, how much policy information they have on their websites, and their level of bilingualism

I’ve sprinkled this post with betting odds. I’m willing to risk up to $100 on bets about have-not candidates winning and $100 on bets about the other candidates. The only requirements I have for betting are that you must have access to Interac or PayPal (for fund transfers) and you must be willing to post publicly that you’re betting with me (preferably including the odds you’d have put on the event we’re betting on). I’ll add details about any takers in the comments of this post.