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Monday, February 27, 2017

The Darkness of Light - A Story of Economic Scale

Once upon a time, long ago and far away, it was a dark and stormy night in a small village. Like most small villages of the era, its existence was due to the goods and services its craftsmen provided to the surrounding farmers and to each other. There was a butcher, a baker, and a candlestick maker and a number of other crafts represented (blacksmith, cobbler, etc.). This trading network of a few hundred people (including farmers) was nearly completely self-sufficient, except for the occasional traveling merchant who brought in some critically important goods as well as some more frivolous and luxury goods. This pre-industrial village, while mostly self-sufficient was also quite poor by modern standards as the small size of this economy couldn't enable sufficient specialization to support modern goods and services, even if all the knowledge of the modern world was readily available and understandable.

Glim, the village candlestick maker was happy with his life. His family had always been the candlestick makers in this village and it was comforting to know his place in life. As he gazed out into the storm, he could see flickers of light emanating from the other homes in the village and he had satisfaction knowing that some of that light was his candlesticks pushing back the darkness and providing comfort to the other villagers.

He had to work hard and was hardly rich, but was prosperous enough to support himself, his wife, and his three daughters. When the traveling merchants came to town, he was able to afford some necessities and even an occasional luxury item like the exotically patterned and very warm rug that sat on the floor of his bedroom. In fact, merchants had just arrived that particular evening and would open their booths to trade their wares the following morning. This was good, because Glim's wife was running short on spices, and they could likely remedy that by trading with the merchants in the morn.

When morning came, Glim and his wife went to trade with the merchants. The merchants had their typical wares available, but to Glim's shock and dismay, the merchants had table after table with numerous varieties of candlesticks, and, after inquiring about the price of the candlesticks, Glim discovered that they were selling for less than half the price of Glim's candlesticks. The merchant explained that a village about 50 leagues away (that had recently been renamed Candleton) had discovered a technique that enabled a few dozen people, working together, to churn out an enormous quantity of candles at very low cost and very high quality. Glim was devastated, because he could not make enough money selling his candles at a competitive price to feed his family and survive. Glim, the candlestick maker, was now out-of-business and had no other skills or ways to earn a livelihood.

So now, dear reader, I'll let you choose the fate of Glim and his family. Perhaps the kind villagers, through a mix of charity and giving Glim odd jobs, kept Glim and his family from becoming destitute. Perhaps Glim tried to farm and maybe he succeeded or maybe his family starved. Perhaps Glim moved his family to Candleton where maybe they needed him but maybe they didn't. Perhaps Glim and his wife fell into the depths of despair and drank themselves to death leaving his daughters to become prostitutes in order to survive. Whatever you choose, dear reader, Glim is probably out-of-luck, and your story for him has been repeated countless times over the ages. Chances are, his level of prosperity is probably going to be lower for the rest of his days than it would've been had the folks at Candleton not invented the new candlestick making process.

But Glim's tough luck is everybody else's good luck. Everybody else gets more candlelight for less. And the villagers in Candleton? They're hugely prosperous, especially at first. After a few years, they split into competing companies which drives their prosperity down a bit but makes candles even cheaper for the surrounding villages.

The benefit of more candlelight turned out to be extraordinary. More people learned to read and that additional knowledge inspired a wave of discoveries and inventions. While more folks like Glim lost their livelihoods, new jobs were created at a rapid pace during this heady time of economic and technological growth. In fact, Glim's grandchildren (perhaps bastards born to his daughters when they turned to prostitution?), opened a printing press and shop and became quite prosperous. Too bad Glim never lived to see it (or perhaps he did, dear reader, in your version of Glim's fate?).

Over the next few generations, electricity was discovered and then harnessed to power a very important invention: the electric light bulb. Which brings us back to Candleton.

Between the time of Glim's misfortune and the invention of the lightbulb, Candleton prospered hugely. A hundred people now worked in the village's three candlestick making factories. Further innovations had increased the number of candlesticks made and lowered the cost. Because of the economies of scales, no other village could compete and Candleton provided the vast majoritiy of candlesticks to all villages for hundreds of leagues in all directions.

But now the electric light bulb, being vastly superior to candles, and lasting months instead of hours, rendered the candlestick making talents of the inhabitants of Candleton useless nearly overnight. Revenue ceased to flow into the village. Unlike the case with Glim, where it was one guy and his family who were directly impacted, and where, at least conceivably Glim's fellow villagers could help sustain him, the residents of Candleton were immediately in extremely dire straits: no revenue, no food, no nothing.

Some of the residents of Candleton left to seek their fortunes elsewhere. Some tried to live by hunting. Many, however, became bandits, stealing from travelers and raiding nearby villages. The other villages organized defenses and the clashes with the bandits became increasingly bloody and deadly as all sides became increasingly desperate. After a decade or so, the bandit population dwindled and the area became mostly peaceful once more. Candleton, however, was left in ruins and became a ghost town with the wilderness encroaching on and then devouring the once prosperous village.

That was tough luck for Candleton, it's inhabitants, and the neighboring villages who had to endure the onslaught of desperate bandits, but the surrounding regions were made much better off by the new electric light. The difference between the innovation that hurt Glim and the one that destroyed Candleton is scale. One guy (Glim) losing his livelihood has limited impact. A whole village losing its livelihood is much more catastrophic and much harder for the residents to recover from because there simply aren't the resources from which to build.

With the harnessing of electricity numerous inventions came about and many of these inventions enabled more complex products requiring larger networks of people to create them causing villages to consolidate into towns and towns into cities. In one such city, Carton, thriving automobile and tractor manufacturing companies were created. The tractors made farmers much more productive and the displaced farm workers came to Carton to work in the factories. Jobs were created more rapidly than jobs were destroyed and a large number of jobs required only minimal and/or quickly learned skills. It was a time of great prosperity and economic advancement.

There were over one million inhabitants in Carton, with occupations ranging from miners gathering the raw materials for the cars to school teachers and other supporting professions. People did lose jobs as processes were changed and innovations implemented but such was the prosperity that new endeavors requiring yet more low-skilled workers were being formed all the time, so work was available for all.

In fact, the great prosperity and constant need for labor sowed seeds of problems in the future. The workers realized they could band together and collectively bargain for higher pay, better working conditions, and greater benefits. Management, in return, made the benefits accrue to the future in terms of pensions and health benefits after retirement. The prosperity also enabled management to become lazy and corrupt and they lined their own pockets and did things like hiring incompetent children and nephews.

After a few more decades, the perfect storm hit. Saddled with increasing wages and pension costs from collective bargaining and corruption and incompetence due to human nature, new and distant competitors simultaneously began manufacturing not only cars and tractors, but also steel and other raw inputs. The distant competitors were not saddled with the liabilities of Carton, and ended up having a huge comparative advantage relative to Carton's factories and workers with respect to Carton's products. While this happened over years, Carton and surrounding region was devastated. Hundreds of thousands of people were out of work, poverty and crime skyrocketed, alcoholism and drug abuse decimated the productivity of the potential workforce, and because total revenues declined below subsistence for the population as a whole, and because it was an area for which there was no particular reason for outsiders to invest, people became increasingly desperate.

Along came a leader, Trunald Domp, who realized that while Carton and its people no longer had a comparative advantage in anything productive, they did, like many desperate peoples in the pits of despair who feel they have nothing left to lose, have a yuge comparative advantage in violence. So he organized the people of Carton to produce arms and they attacked the surrounding areas. The bloody war killed tens of thousands of people but eventually Domp and Carton were defeated. The remaining people of Carton fled their collapsing city increasingly desperate to find any means of staving off starvation. The were, of course, met with suspicion and outright hostility, and many were killed on sight. The ones that survived became an underclass and there were frequent violent revolts. Eventually distrust and hatred built to such a fevered pitch that the entire civilization collapsed and everybody died except for a small fraction of the population that fled into the wilderness and formed small groups of farms surrounding small villages. These villages were too small to maintain any sort of advanced economy so they reverted to pre-industrial levels of goods and services.

In one of these villages, a man named Flick was the candlestick maker. It turns out he was a distant descendant of Glim. Flick was proud of his occupation because his candlesticks pushed back the darkness and provided comfort to his fellow villagers.


The bigger the scale of the economic trading networks, the more destabilizing the destructive part of Schumpeter's Creative/Destruction. Tough luck for Glim, but everything was perfectly stable and everybody else was more prosperous. Tougher luck for Candleton and the surrounding areas with the bandits but most people were not only unaffected but also much more prosperous. But toughest luck for all for Carton and the rest of the world, where nobody came out ahead. Once a region is sufficiently devastated, there's little hope for the investment and resources required for recovery. The region itself simply doesn't have the resources and outsiders are unlikely to invest in such an unstable and risky region.

Moral of the story: don't put people in a position where they feel they have nothing left to lose - it won't end well for anybody.

Sunday, February 19, 2017


It's no secret that Trump hates the press (and the press hates him right back). Continuing his adversarial relationship with the press, tonight at his Florida rally, Trump said:
"Nothing can be believed which is seen in a newspaper. Truth itself becomes suspicious by being put into that polluted vehicle."
Fake news and all that.

Wait! What?

He was quoting Thomas Jefferson written in a correspondence on June 14, 1807!


I guess Presidents and the press have had an adversarial relationship for a really, really long time!

Saturday, February 18, 2017

Fun With Infinity

Infinity and infinite series and sets are concepts that stretch human intuition to the breaking point and as a result, are kinda fun - for masochists. The particular infinite series I'm gonna look at today is:

S = 1 + 2 + 3 + 4 + ...

What is the value of S?

The NY Times recently had an article demonstrating that a possible answer is -1/12 (there's a more rigorous proof that shows the answer is indeed -1/12 but is beyond what I can show on a blog). I know that some of you studiously avoid the NY Times and therefore might not have seen it, so I'll duplicate it here with a little more explanation.

There's only one somewhat non-intuitive bit to the proof, so let me address that before I get started. The best illustration of this bit of non-intuition is called Hilbert's Paradox of the Grand Hotel:
Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms... 
Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room.
What this demonstrates is that if I have two infinite sets (such as rooms and guests) with a one-to-one correspondence between each pair of elements in the sets, I can shift over all of the elements of one of the infinite sets, leaving one element without a corresponding element in the other set (room 1 in the example above), yet have all of the other elements of both sets still have a one-to-one correspondence.

Okay, we need to find the values of some infinite series. The first one is:

S1 = 1 - 1 + 1 - 1 + 1 - 1 + ...

What is the value of S1? To find an answer, we add it to itself and do the hotel room operation above (in other words, shift over one copy of the series).

2 * S1 = S1 + S1 =  1 - 1 + 1 - 1 + 1 - 1 + ...
                  +     1 - 1 + 1 - 1 + 1 - ...
                  = 1 - 0 + 0 - 0 + 0 - 0 + ...

or, 2 * S1 = 1
therefore, S1 = 1/2

The second series we need is:

S2 = 1 - 2 + 3 - 4 + 5 - 6 ...

And we start with the same infinite shift operation that we used on the previous series:

2 * S2 = S2 + S2 =  1 - 2 + 3 - 4 + 5 - 6 + ...
                  +     1 - 2 + 3 - 4 + 5 - ...
                  = 1 - 1 + 1 - 1 + 1 - 1 + ...

But that's the same as the 1st series that we already know an answer to:

2 * S2 = S1 = 1/2
therefore, S2 = 1/4

So now let's work on our original series. We'll subtract S2 to help us find an answer:

S - S2 =  1 + 2 + 3 + 4 + 5 + 6 + ...
        -[1 - 2 + 3 - 4 + 5 - 6 + ... ]
        = 0 + 4 + 0 + 8 + 0 +12 ..
        = 4 * [ 1 + 2 + 3 + ... ]

The right hand side is now 4 * S so rewriting we have:

S - S2 = 4 * S

or (subtracting S from both sides)

- S2 = 3 * S

Since we know S2 = 1/4, we have

- 1/4 = 3 * S


S = -1/12


1 + 2 + 3 + 4 + ... = -1/12

This sort of proof, where the sum of an ever increasing series is a negative fraction, makes some people's heads explode. I hope you're not one of them. It's just a little fun with infinity!

Tuesday, February 07, 2017

Bug or Feature?

Congrats to Betsy DeVos, confirmed as the Secretary of Education by literally the narrowest margin possible (Vice-President Pence had to cast the tie-breaking vote in the Senate).

One of the charges leveled against her was that she's completely unqualified to be the Secretary of Education and utterly clueless about what it takes to keep the education bureaucracy afloat.

I can't say I disagree. But is that a bug or a feature?

To me it seems like the entire education edifice is in catastrophically poor condition with kids not being very well educated and/or prepared for life as an adult even though funding has hugely increased over the last few decades. Perhaps a truly incompetent secretary of education will damage the system enough that it simply collapses and then it can be rebuilt from scratch. Especially with online and other tools improving at a rapid rate, catastrophic destruction of the whole thing may be the best way to ultimately improve it.

So, as I say, congrats, but I'm not sure if I wish her good luck or bad luck. A little incompetence coupled with some bad luck may be just what we need right now!

Saturday, February 04, 2017

Hypocrisy on Parade

The NYT runs an intermittent series under the heading of The Stone; it purports to be "a forum for contemporary philosophers and other thinkers on issues both timely and timeless."

I have previously (here and here) rubbished articles for grievously offending my logical sensibilities. Unfortunately, the comments threads were of no help in deciding whether the deficiency was mine or some contemporary philosophers and other thinkers.

Once again, it is time to reach for the Rubbisher.

Peter Singer is something of an enfant terrible: his niche in philosophy is to take a seemingly reasonable position, and extrapolate it to where shock and opprobrium is sure to follow.

Here are some examples:

Abortion: In Practical Ethics, Singer argues in favour of abortion rights on the grounds that fetuses are neither rational nor self-aware, and can therefore hold no preferences. As a result, he argues that the preference of a mother to have an abortion automatically takes precedence. In sum, Singer argues that a fetus lacks personhood.

Similar to his argument for abortion, Singer argues that newborns lack the essential characteristics of personhood—"rationality, autonomy, and self-consciousness"—and therefore "killing a newborn baby is never equivalent to killing a person, that is, a being who wants to go on living."

Speciesism: Speciesism is an attitude of bias against a being because of the species to which it belongs. Typically, humans show speciesism when they give less weight to the interests of nonhuman animals than they give to the similar interests of human beings.

[On the basis that a being able to think of itself as existing over time], one might argue that to kill a normal human being who wants to go on living is more seriously wrong than killing a nonhuman animal. Whether this claim is or is not sound, it is not speciesist. But given that some human beings – most obviously, those with profound intellectual impairment – lack this capacity, or have it to a lower degree than some nonhuman animals, it would be speciesist to claim that it is always more seriously wrong to kill a member of the species Homo sapiens than it is to kill a nonhuman animal.

Altruism: A minimally acceptable ethical life involves using a substantial part of one's spare resources to make the world a better place.

These positions run the gamut from the apparently awful to the seemingly benign. I think they each rest on at least some flim-flammery, by either ignoring inescapable elements of reality — time, say — question begging, or failing to take an argument to where it demands being taken.

But no matter, that isn't what had me casting about for my Rubbisher.

It has come to some degree of notice that Peter Singer is spending significant resources caring for his Alzheimer's crippled mother. For most of us, more or less unburdened by a surfeit of philosophical posing, uhh, thinking, this is a no brainer. However, for Singer, this is clearly verboten, whether on the grounds of altruism or speciesism, at the very least.

Yet, despite his admonitions to the rest of us, he does so, nonetheless.

The philosopher Peter Singer was once attacked for contradicting himself. Singer advanced an ethical theory in which the most worthwhile thing was complex conscious life and feeling, and did not shy away from the logical consequence that the life of a severely mentally impaired human was worth less than that of a chicken. Journalists then discovered that Singer’s mother had Alzheimer’s and that he chose to spend his money taking care of her rather than helping chickens.

They called Singer a hypocrite and The New Republic even ran a cover with a picture of an addled old woman with a walker and the headline “Other People’s Mothers.”

Failing to notice the answer on offer, the author, by definition an esteemed contemporary philosopher or other thinker on issues both timely and timeless goes straight to missing the screamingly obvious:

So, how bad is contradicting yourself?

In philosophy, since Socrates (a troll before there ever was an internet), the answer has been “very bad.” If you find you believe two inconsistent propositions you need to do something about it. You owe a theory.

No, Eric Kaplan, this isn't contradicting yourself, this is allowing yourself that which you prohibit others. There's a fancy word for it, often improperly used, but not here: hypocrisy. Contradiction, entirely unrelated, involves having taken a position, subsequently taken on board discordant information, then reversing, or significantly changing your position; not just for yourself, but for everyone else, too.

Peter Singer has done nothing of the kind. But let's let that slide, so that Kaplan can have his say:

Part of the reason this mother/chicken puzzle is so hard is it runs up against two contradictory beliefs we have about human beings:

a) Humans are meaningful; the things they do make sense

b) Humans are things with causes like anything else — as meaningless as forest fires.

I could burden you with further pull quotes, but I won't because the chase that needs cutting to is right here. Kaplan, and on his behalf, Singer, have skipped right over a fatal error.

What do you think it is? Hint: it is contained in a single word.