I know, I know. Hindsight is 20-20, and here I am, the Monday morning armchair quarterback, making sense of what happened to the US banking system this past weekend.

Then again, my excuse is that I am no expert (not even close) so what is hindsight in my case should have been foresight on behalf of those who do this stuff for a living. The fact that it wasn’t…

How do banks work? Say, you deposit $100,000, and the bank pays you 2% interest. So far so good. But the bank doesn’t just sit on your money. If they did, they’d be losing money by paying you interest. No, they lend that money to me, say, in the form of a mortgage at 5% interest. The difference, that 3%, is the bank’s profit. Suppose one day unexpectedly you show up and tell the bank that you want to withdraw your money. The bank doesn’t have$100,000 cash. Nor can they call on the money they lent to me, since it is in the form of a long-term mortgage. What they can do, however, is sell my mortgage to another lender. For me, that mortgage is debt; for the bank, it’s an asset, worth good money. So they sell it to another bank, get the $100,000 cash and now they can honor your request to withdraw your funds. So far so good… but what happens if the county’s central bank raises interest rates rapidly? Say, in a short amount of time the central bank’s rate goes from a fraction of a percent to over 5%? When you come to our bank to withdraw your money, the bank tries to sell my 5% mortgage to another lender, but finds no buyers. Why would these other banks buy my 5% mortgage from our bank when they can invest their money in government bonds that have a 100% guarantee and now a yield better than 5%? Oops. You try to withdraw your money, but our bank is unable to oblige. When a bank cannot pay a depositor, it is big trouble. It basically means that the bank is going under. When interest rates change slowly, gradually, this does not happen. Mortgages expire and need to be renewed at revised rates. The market adjusts. But when interest rates rise rapidly, the system cannot adjust. There is not enough time. Central banks throughout the Western world have raised interest rates at a historically unprecedented pace in recent months, to fight inflation. Did they really not anticipate the consequences? And now the reaction: some financial news sources suggest that, never mind further rate increases, the US Federal Reserve’s interest rate may actually come down next month. Now that worries me as it may be an overreaction. Overcompensating a controlled system can actually lead to even larger swings or oscillations. What bothers me about this is that what I am describing here is not exactly ground-breaking revelation. Beyond the financial specifics, it is basic operations research, its modern roots dating back a century or so. Seriously, when they were raising interest rates as recklessly as they did, what were the central banks thinking? Were they truly not aware of these possible consequences? Or was fighting inflation so important that they opted to ignore the advice of their own knowledgeable experts? Do you know what wealth is? It’s not superyachts. It’s not million dollar mansions. It’s not private jets or a chauffeured Rolls Royce. Those are pricey toys. Let me show you real wealth. Guess which of the two objects in the image below is worth more: On the left, a Canadian quarter. That is, 25 Canadian cents. This is the amount that a resident of Ontario, working for the legally mandated minimum wage, earns in exactly one minute. On the right is a 540 milliliter can of sliced pineapples, in pineapple juice. All the way from Indonesia. That is to say, someone planted those pineapple plants and nurtured them. Someone picked that fruit. Others mined the iron and coal from which the soft steel was made, eventually rolled into sheets and formed into cans. Yet others operated the machinery of the cannery, slicing those pineapples, filling and sealing the cans on July 5, 2021 according to the stamped label on the can. The cans were then put into crates, loaded into containers that were put on trucks, taken to a port, transferred to a ship which then sailed to Canada. The container then made its way, through the railways and on trucks, to a warehouse and ultimately, to the grocery store here in Ottawa, all the while protected from the elements, from excess heat and excess cold that would have ruined the contents. Finally, someone placed the cans on a shelf where they must have sat a little longer than usual, until either a human manager or maybe an algorithm decided that they should be marked down. And then my beautiful wife picked up a pair of these cans… paying the grand total of 48 Canadian cents for the two. That is, a large can of sliced pineapples, all the way from Indonesia, here in the final days of an Ottawa winter… costing less than a quarter. Even working at the Ontario minimum wage, for the equivalent of less than 60 seconds of our labor. That’s what wealth really is. For more than a day now, I’ve been watching the news about a giant container ship that is blocking the Suez Canal. Supposedly it now “partially refloated”, whatever that means. In the process, I learned about vesselfinder.com, a Web site that tracks ships on the high seas, much like sites like flightradar24.com track airplanes. Here it is, a real-time snapshot of this stuck vessel: I have no idea though why the ship is given the name “EVER GIVEN” here. Its actual name, written on the side of the ship in giant block letters, appears to be “EVERGREEN”. (Or not. I’ve since learned that EVERGREEN is the name of the company, not the ship.) And yes, it does block the canal in spectacular fashion. Given the importance of this shipping route, I wonder why this is not bigger news than it appears to be. Is it perhaps because the general expectation is that the problem will be resolved shortly, causing no more than minor delays in some shipments? I hope. The cartoon series The Simpsons is into its 32nd season this year. It has been picked up for at least another two seasons by Fox. The Simpsons depicts a “typical” American family of five: Homer the breadwinner, with only a high-school diploma, holding a dead-end but secure job as a safety inspector at the Springfield Nuclear Plant, Marge the housewife, mother of three children and the three kids, two of them school-age, one still a toddler. The Simpsons live in a detached house in a suburb and own two cars. They are not rich, but they do have disposable income: Homer spends his evenings gulping down beer as Moe’s Tavern, Marge never seems to have a problem paying for groceries. In other words, The Simpsons live the American dream: a comfortable North American middle class lifestyle from a single income. A dream that, as lamented in a recent opinion article in The Atlantic, is no longer attainable. This, I think, really explains it all. The polarization of American politics. The emergence of extremism. The appeal of slogans like “Make America Great Again”. The “we have nothing to lose” attitude that led many to vote for Trump, despite their misgivings. And it is by no means a US-only phenomenon. Income inequality may not be as bad in Canada as it is in the US, but the middle class is not doing spectacularly well here either. Europe, too, is not heading in the right direction. Lest we forget the lessons of history, this is precisely what provides fertile ground for totalitarian ideologies like fascism and communism. When liberal democracy fails to deliver on society’s most basic promise, the ability to provide a life as good as, but preferably better than your own for your children, people turn to other ideas. That was just as true a century ago as it is today. There are photos of empty store shelves circulating on the Internet, promoted in particular by Americans supporting Donald Trump, as examples of what stores would look like under socialism. No, my friends, this is what stores looked like under socialism. Socialism that I experienced first-hand, not some abstraction. And it wasn’t pleasant. But the stores were… well, see for yourself. This is no propaganda photo, but a picture from the collection of my late father-in-law, who was a professional photographer. (The hand-written blue arrow is there to point out that under a sign advertising first-class poultry, there are meats hanging that definitely don’t appear to have come from any chicken): In contrast, and contrary to what the poster tweeted, the following is a picture of Trumpian capitalism in a moment of crisis: In fact, as some commenters pointed out, a centrally planned command economy in a police state may be better able to cope with a crisis of this nature than market capitalism, even with competent political leadership. So our American friends south of the border have a new tax legislation. I’ve seen many discussions of how it affects people in various income brackets, but all too often, these are more confusing than helpful. So instead, here is a handy chart that shows how the federal tax rate decreases as a percentage of taxable income for individuals, joint filers and heads of households (based on tables provided by CNN): While most folks will enjoy a tax break, it is interesting to see that some individuals and heads of households will actually see a tax increase: Married couples benefit the most (mainly as a result of some arcane tax brackets that were in effect before the new legislation), which is probably a Good Thing; I am not so sure about the 2.6% tax break offered to the wealthiest, however. Anyhow, I pay my taxes in Ontario, Canada, so it really doesn’t bother me one way or another, I just wanted to understand a little better what actually is going on. A few months ago, after a miserable half decade during which Greece lost one quarter of its economy, fed-up Greeks elected a far-left government that promised no more austerity, no more giving in to heartless European demands. To bolster its legitimacy, the government held a nationwide referendum, in which Greeks voted in large numbers against accepting a (by then defunct) austerity package that was a precondition for more European bailouts and assistance. And now… the Greek government agreed to an even worse austerity package than the one Greek voters just rejected? What exactly happened here while I blinked? In the past couple of days, I heard several commentators on CNN lament on the fact that China’s debt-to-GDP ratio is much higher (“three times” higher) than that of the US, and that this may be behind the current volatility of the Chinese stock market. This, of course, is blatant nonsense. China’s government debt-to-GDP ratio is much lower than that of the US. It is in the low twenties, compared with over 100% in the United States. Here is a crude plot (crude because I graphically edited together two plots, but I had to change the vertical scale of one) that shows the two in comparison. No, China doesn’t have a problem with government debt. China does have a problem with private debt. Look at this monstrous chart: What this chart shows is alarming. No, still not three times the US private debt-to-GDP ratio (that factor of 3 only happens if you compare China’s total debt to US government debt, which is of course comparing apples to oranges), but it is significantly higher than that of the US. What’s worse is that China is still an emerging economy: in addition to the prosperous middle class of places like Shanghai, there are still close to (or more than?) a billion people in that country who live in third world poverty. (China’s per-capita GDP is$6,800; in the US, the figure is \$53,000, nearly eight times higher.)

The wisdom I’ve been reading online is that an emerging economy just cannot afford to have the same level of private indebtedness as an advanced economy.

To be honest, I don’t know if it is true. For all I know, much of China’s debt is held by those who can actually afford it, the prosperous middle class with their SUVs and air conditioned homes in Shanghai or Guangzhou. Indeed, if we split China into two countries, one prosperous and one poor, the prosperous one may well qualify as an advanced economy, and it may be holding most of the debt.

Or not. But whatever the debt situation is in China or its impact on the stock market, it is still no excuse for CNN to keep babbling nonsense.

If you thought that the scary news from yesterday was the mass murder of 145 people at a Pakistani school, think again. Tragic as that event was, it has zero effect on your security or well-being unless you happen to live in northern Pakistan.

But what happened in Russia yesterday may threaten the security of us all. The Russian central bank’s decision to hike rates by a whopping 6.5% overnight is a sign that the Russian economy is in deep trouble. Worse yet, it is unlikely that Putin will change course, since his popularity is based mainly on his newfound nationalism, not his economic performance.

Which raises the possibility that Putin will lash out and do something stupid. Not just in the Ukraine but, perhaps in a fatal miscalculation, in the Baltic region. If he has any reason to think that NATO would not respond to Russian aggression in places like Estonia, we are all in deep trouble, because I cannot see how NATO would not respond… and that, of course, is a nightmare scenario.

Meanwhile, Obama made the bombshell announcement of restoring diplomatic ties with Cuba. Long, long, long overdue. (To those who think this amounts to appeasing a communist regime, all I can say is, look how well the policy of isolation worked in the last 50+ years.) I also wonder what the Kremlin’s masters think about this. Cuba was one reliable ally in America’s backdoor that they could always count on… what is going to happen now?

We seem to be living in interesting times.

When you have a family member who is gravely ill, you may not have the stamina to pay attention to other things. When you have a family pet that is gravely ill, it’s almost as bad (actually, in some ways it’s worse, as a pet cannot tell what hurts and you cannot explain to the pet why unpleasant medication is necessary or discuss with the pet the available treatment options.)

As I’ve been dealing with a gravely ill cat in the past six weeks, I neglected to pay attention to other things.

I did not add a blog entry on October 31 with my drawing of a Halloween cat.

I did not comment on Remembrance Day. I am very fond of Remembrance Day, because it does not celebrate victory nor does it glorify war; on the contrary, it celebrates sacrifice and laments on the futility of war. This is why I am so unimpressed by the somewhat militantly pacifist “white poppy” campaign; in my view, they completely miss the point. I usually put a stylized poppy in my blog on November 11; not this year, as I spent instead a good portion of that day and the next at the vet.

I most certainly did not comment on that furious (and infuriating) wild hog of a mayor, Toronto’s Rob Ford, or for that matter, the other juicy Canadian political scandal, the Senate expense thing. That despite the fact that for a few days, Canadian news channels were actually exciting to watch (a much welcome distraction in my case), as breaking news from Ottawa was interrupted by breaking news from Toronto or vice versa.

I also did not blog about the continuing shenanigans of Hungary’s political elite, nor the fact that an 80-year old Hungarian writer, Akos Kertesz (not related to Imre Kertesz, the Nobel-laureate) sought, and received, political asylum, having fled Hungary when he became the target of threats and abuse after publishing an article in which he accused Hungarians of being genetically predisposed to subservience.

Nor did I express my concern about the stock market’s recent meteoric rise (the Dow Jones index just hit 16,000) and whether or not it is a bubble waiting to be burst.

And I made no comments about the horrendous typhoon that hit the Philippines, nor did I wonder aloud what Verizon Canada must be thinking these days about their decision to move both their billing and their technical support to that distant country.

Last but certainly not least, I did not write about the physics I am trying to do in my spare time, including my attempts to understand better what it takes for a viable modified gravity theory to agree with laboratory experiments, precision solar system observations, galactic astronomy and cosmological data sets using the same set of assumptions and parameters.

Unfortunately, our cat remains gravely ill. The only good news, if it can be called that, is that yesterday morning, he vomited a little liquid and it was very obviously pink; this strongly suggests that we now know the cause of his anaemia, namely gastrointestinal bleeding. We still don’t know the cause, but now he can get more targeted medication. My fingers remain crossed that his condition is treatable.

The other day, I bought a fine jar of “No Name” brand Polish pickles at Loblaws. They were great pickles. Nothing wrong with the quality or the taste.

However, there was something my wife noticed on the label that was, shall we say, surprising.

Can’t see it? Here are the relevant bits, enlarged:

Still, I may stick to the same brand. Not only are the pickles really tasty, but Canada, after all, does export plenty of food to India, including lentils. So it’s only fair for us to eat some Indian-made Polish pickles in return. Especially since they really are yummy.

The news was this morning that a fellow was momentarily richer than Bill Gates, by a cool factor of a million or so, thanks to a small accounting mistake by PAYPAL. His account was worth more than 5000 times the US national debt.

Indeed, in one interview I saw mentioned, he did say that had this been for real, he’d have paid down the US national debt.

Sounds good and patriotic, except… could he?

Suppose you come into possession of 92 quadrillion dollars. The 16 trillion dollar debt (and then some) of the United States is just small change for you. Paying it down basically means buying the debt from debtholders.

Well, first of all, what if they don’t want to sell? There is a reason why the US can borrow so cheaply: US government bonds are a good, safe, secure form of investment. People who put their money into bonds do so for a reason, and not because there isn’t a demand for the bonds they hold.

Creating demand would drive down interest rates even more. By making the bonds scarce, you’d encourage people to buy them even at 0 or negative interest rates. Which would only encourage the US government to borrow more.

The deficit problem, after all, isn’t solved: there is still a fundamental imbalance between the governent’s revenues and expenses.

Continuing issuance of bonds by the government leads to inflation. This is a good thing insofar as debt is concerned, as debt can be inflated away, but with so much money available (your 92 quadrillion dollars), the situation can quickly become unstable, and hyperinflation may set in.

Ultimately, your noble attempt to help the US out of its debt crisis will result in a worthless currency, a collapsed economy, and the remainder of 92 quadrillion in your pocket, which may not even be enough to buy a loaf of bread.

Perhaps it was a good thing, then, that this was just a quickly corrected accounting glitch.

What an ugly word: monetization. Never liked it.

I especially do not like it when it comes to games.

When it comes to computer games, my age shows I guess. The first computer game I ever played was an arcade version of Pong. And the first multiplayer world I participated in was British Legends, the Compuserve implementation of the original MUD, or Multi-User Dungeon. Eventually, I started hosting MUD’s successor, MUD2, and when CompuServe shut down British Legends, I began hosting my own port of MUD1 here as well. And for a while, I did charge MUD2 users a subscription fee but that’s just not a viable business model for a small gaming site these days, so eventually we dropped all such fees.

In any case, subscription fees are not what come to my mind when I think about game monetization. It is more insidious ways to compel players to cough up hard earned money.

And now I came across an intriguing article that offers a thorough review of several monetization tricks and schemes. The basic idea is to compel players to purchase in-game add-ons, “power-ups” and other improvements, and pay ever greater amounts as they progress through the game.

Of course it cannot be done as blatantly as that. As the article explains, a good monetization scheme does not destroy the player’s illusion that the game is skill-based. Paying may help a little, or help a player avoid losing prior achievements, but the player’s perception remains that the game is fundamentally rewarding skill, not big spending. Which, of course, is untrue, but the most successful monetization schemes can liberate hundreds of dollars from the pockets of devoted players each month.

I don’t like these schemes. They feel… dishonest. I do purchase the occasional game, both for my phone and for my PC (thanks to GOG.COM and DOTEMU.COM who offer great titles free of DRM). But I never pay for in-game features or upgrades as a matter of principle, and a good thing, too: as the article explains, once you pay, you end up paying more, in part to protect the investment you made earlier by paying real money to help your progress.

The presumed yottabyte capacity of the new Utah Center of the NSA, about which I commented a few days ago, is still making the rounds on news channels and news cites. Someone calculated that a yottabyte is equivalent to 500 quintillion printed pages. CNN helpfully added that a stack of paper with this many pages could reach all the way to the Moon and back 66 million times.

What they ought to have calculated is the size and volume of 250 billion 4 TB hard drives.

A lighter hard drive weighs about 0.4 kg. 250 billion of them? That would be 100 billion kilograms. Or 100 million metric tons. Or roughly 1000 of the largest cargo ships, each the size of a small city, filled to capacity with hard drives.

A hard drive is about 15/16″ tall. That’s 2.38 centimeters. 250 billion of them? Why, it’s a stack tall enough to reach all the way to the Moon and back 8 times.

The volume of a standard hard drive is about 342 cubic centimeters. 250 billion? That would be just a tad under 0.1 cubic kilometers (8.56 × 107 cubic meters, to be a bit more precise). That would be a field that is a kilometer square, filled with hard drives to the height of a small-ish skyscraper, about 25-30 stories high. Large as the Utah facility is, it’s by no means large enough.

Some might want to point out that if the NSA used flash memory instead, the volume (and also the power consumption) would go way down. True. But the price would go up. Flash memory is still roughly an order of magnitude more expensive than hard drives. So if the NSA wanted to build a yottabyte facility using flash memory, instead of spending 1.5 times the GDP of the entire United States, they’d be spending 15 times that amount. Or roughly three times the “gross world product”, estimated at 83 trillion US dollars.

Perhaps CNN and friends should do a little more math, not just to impress their readers but also to fact check the stuff that they report. Would be nice.

For illustration, I chose a Hungarian bank note from 1946, reportedly the highest denomination ever printed anywhere: it is a 100 quintillion pengő note. It is still far short of a yottapengő: you would need 10,000 of these banknotes. Then again, by the time hyperinflation ended and a new currency (the Hungarian forint, still in circulation) was introduced, the exchange rate was 400 octillion pengős to the forint; that would be 400,000 yottapengős.

I consider myself a fiscal conservative. I like the idea of small governments, balanced budgets, low taxes. But… not at all costs.

Austerity is the worst possible response to an economic crisis. The world should have learned this during the Great Depression. But it didn’t.

Or rather, North America did, as it chose stimulus spending over austerity despite the fact that America was led by a conservative president and Canada, by a conservative prime minister at the time. Giving credit where credit is due, I think we should thank Messrs. Bush and Harper for their willingness to put aside ideology and implement pragmatic policies, even if they might have done so kicking and screaming.

Not so in Europe, where austerity prevailed in the countries worst affected by the recession. And the result speaks for itself, most loudly perhaps in Greece. After years of austerity, the Greek economy is in shambles; Athens is crippled by smog because of all the wood burning as a result of drastic tax increases on natural gas and fuel oil; and instead of going down, the country’s debt-to-GDP ratio continues to increase relentlessly, as tax revenues dropped more rapidly than government expenditures as a result of the cutbacks.

Here is a reason why I prefer not to buy goods made in China. Some of the goods from that country may have been made in “re-education through labor” camps.

In other words, forced labor.

And last year, a camp inmate had the courage to smuggle a letter into the packaging of a Halloween decoration kit. The package sat unopened by its purchaser for a year, when she finally decided to put up some Halloween decorations.

Note to retailers: I am more than happy to pay a premium for goods made in Canada or the US, by free people earning decent wages. And, while I may be in a minority for the time being, I am pretty sure I am not alone.

Fareed Zakaria on CNN commented on a recent ranking by The Economist that they called “the lottery of life“. It measured the quality of life in some eighty countries. The United States, number 1 on similar lists in decades past, is now in a tie with Germany for position 16. (Canada is 9th.) Following Switzerland and Australia, the top of the list is dominated by the usual Scandinavian suspects: Norway, Sweden, Denmark are 3rd, 4th and 5th, respectively.

So, can’t we all be more like Scandinavians? This is more than just a rhetorical question. As a matter of fact, this is the title of a recent study by Acemoglu et al. (MIT Department of Economics Working Paper No. 12-22, 2012.) In it, the authors argue that more “cutthroat” versions of capitalism, such as that practiced in the United States, while leading to greater inequality, also lead to more innovation. Meanwhile, countries choosing a more “cuddly” form of capitalism are in fact enjoying a free ride, as they take advantage of the innovations produced by cutthroat capitalists.

The study was reportedly criticized for using patents as a proxy to measure innovation, but I don’t think that this criticism truly undermines their main conclusions. Conclusions that seem to be supported by solid mathematics (at least that’s the impression I got after quickly scanning through the pages of the actual paper). What I find interesting among the study’s conclusions is that the configuration of a technology leader practicing “cutthroat” capitalism and followers who practice “cuddly” capitalism is actually a stable, albeit asymmetric, equilibrium.

I cannot help but wonder though… where does China fit into this picture?

Some interesting plots from Nobel laureate economist Paul Krugman, courtesy of The New York Times. Compare Obama’s and Bush’s record for private sector employment in the first 40+ months of their respective presidencies (yes, this would mean Bush’s first term, in 2001):

And compare their public sector employment statistics:

So which one, exactly, is the “big government socialist”?

Courtesy of a Google+ friend, I stumbled across this graph, originally from The Atlantic:

What this graph demonstrates is quite simple. Take any random collection of nations. Former member states of the Soviet Union. All the countries along the 5th parallel. Members of a reconstituted Ottoman Empire. Or even countries beginning with the letter “M”. In all cases, the countries you pick turn out to be socioeconomically less diverse (i.e., they have more in common) than the major member states of the European Monetary Union.

I don’t know if it really makes the Eurozone doomed, but it certainly shows that holding it together will be quite a challenge.

I just came across this delightful imaginary conversation between a physicist and an economist about the unsustainability of perpetual economic growth.

The physicist uses energy production in his argument: growth at present rates means that in a few hundred years, we’ll produce enough energy to start boiling the oceans. And this is not something that can be addressed easily by the magic of technology. When waste heat is produced, the only way to get rid of it is to radiate it away into space. After about 1400 years of continuous growth, the Earth will be radiating more energy (all man-made) than the Sun, which means it would have to be a lot hotter than the Sun, on account of its smaller size. And in about 2500 years, we would exceed the thermal output of the whole Milky Way.

This, of course, is nonsense, which means terrestrial energy production will be capped eventually by basic physics. If GDP would continue to grow nonetheless, it would mean that the price of energy relative to other stuff would decrease to zero. This is also nonsense, since a limited resource cannot become arbitrarily cheap. But that means GDP growth must also be capped.

What I liked about this argument is that it is not emotional or ideological; it’s not about hugging trees or hating capitalism. It is about basic physics and elementary logic that is difficult to escape. In fact, it can be put in the form of equations. Our present energy production $$P_0$$ is approximately 15 TW, which is about 0.002% of the Sun’s output that reaches the Earth:

\begin{align}
P_0&\simeq 1.5 \times 10^{13}~\rm{W},\\
P_\odot&\simeq 7 \times 10^{17}~\rm{W},\\
\eta_0&=P_0/P_\odot \sim 0.002\%.
\end{align}

For any other value of $$\eta$$, there is a corresponding value of $$P$$:

\begin{align}
P=\eta P_\odot.
\end{align}

Now all we need is to establish a maximum value of $$\eta$$ that we can live with; say, $$\eta_{\rm max}=1\%$$. This tells us the maximum amount of energy that we can produce here in the Earth without cooking ourselves:

\begin{align}
P_{\rm max}=\eta_{\rm max}P_\odot.
\end{align}

On the economic side of this argument, there is the percentage of GDP that is spent on energy. In the US, this is about 8%. For lack of a better value, let me stick to this one:

\begin{align}
\kappa_0\sim 8\%.
\end{align}

How low can $$\kappa$$ get? That may be debatable, but it cannot become arbitrarily low. So there is a value $$\kappa_{\rm min}$$.

The rest is just basic arithmetic. GDP is proportional to the total energy produced, divided by $$\kappa$$:

\begin{align}
{\rm GDP}&\propto \frac{\eta}{\kappa}P_\odot,\\
{\rm GDP}_{\rm max}&\propto \frac{\eta_{\rm \max}}{\kappa_{\rm min}}P_\odot,
\end{align}

And in particular:

\begin{align}
{\rm GDP}_{\rm max}&=\frac{\eta_{\rm max}\kappa_0}{\eta_0\kappa_{\rm min}}{\rm GDP}_0,
\end{align}

where $${\rm GDP}_0$$ is the present GDP.

We know $$\eta_0\sim 0.002\%$$. We know $$\kappa_0=8\%$$. We can guess that $$\eta_{\rm max}\lesssim 1\%$$ and $$\kappa_{\rm min}\gtrsim 1\%$$. This means that

\begin{align}
{\rm GDP}_{\rm max}\lesssim 4,000\times {\rm GDP}_0.
\end{align}

This is it. A hard limit imposed by thermodynamics. But hey… four thousand is a big number, isn’t it? Well… sort of. At a constant 3% rate of annual growth, the economy will increase to four thousand times its present size in a mere 280 years or so. One may tweak the numbers a little here and there, but the fact that physics imposes such a hard limit remains. The logic is inescapable.

Or is it? The word “escape” may be appropriate here for more than one reason, as there is one obvious way to evade this argument: escape into space. In a few hundred years, humanity may have spread throughout the solar system, and energy amounts enough to boil the Earth’s oceans may be powering human colonies in the hostile (and cold!) environments near the outer planets.

That is, if humans are still around a few hundred years from now. One can only hope.