Archive for the 'Progress' Category

Randomizing

Sometimes you just have to take matters into your own hands.

After posting about the difficulty of finding a modern source for choosing a random city or a random river, I went ahead and created:

The Random City Server

I took the data from Maxmind’s free world cities database, but there are odd gaps in it. Although the database lists about 3.3 million cities, the population field is blank for all but about 50,000. (Most notably, that field is blank for all but two of the thousands of cities in the Republic of Korea.) My server offers up a random city from among those 50,000. I’m sure I can probably find a list of Korean cities with populations and manually tack them on to the list at some point. [Edited to add: I’ve just done that.]

Now I want to do something similar for river lengths. Does anyone know where to get the data? (No, pawing through Wikipedia’s hundreds of separate lists, for each part of the world and each letter of the alphabet, is not an option.)

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A Question About the Modern World

Suppose you want, for some reason, to find the length of a randomly chosen river or the population of a randomly chosen city.

In the old days, we all had things called “reference books”, with long lists of river lengths, city populations, etc. You could open to a random page, close your eyes, put down your finger, and there you’d have it.

But now many of us no longer own reference books. We own smartphones instead. This raises two issues:

1) I’m not sure there are online lists of river lengths or city populations that are as extensive as what you used to find in reference books. Why should there be? Nowadays, if you want to know the population of Des Moines, you just Google for Des Moines; you don’t need a site that lists the populations of thousands or tens of thousands of cities.

2) Even if there were such lists, what would be the modern equivalent of opening to a random page, closing your eyes and pointing? Scrolling for a random amount of time seems less random somehow.

So what do you do?

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Dear Old Golden Rule Days

ssyShortly before I started Kindergarten, my mother purchased a book called “Steven’s School Years”, with pockets to store my report cards and school projects, and questionnaires for me to fill out at the end of each school year.

I was not diligent about filling in the questionnaires, and they remain mostly blank. But had I been forced to, I wonder how I would have answered the following question, which was to be answered annually at the end of Grades 1,2,3,4,5, and 6:

(According to my mother, my ambition at age three was to be an electric drill, and sometime after that a rabbit. No other records of my early career inclinations seem to have survived.)

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Day of Thanks

This is a slightly revised version of my Thanksgiving post from five years ago. I think it bears repeating:

After the philosopher Daniel Dennett was rushed to the hospital for lifesaving surgery to replace a damaged aorta, he had an epiphany:

I saw with greater clarity than ever before in my life that when I say “Thank goodness!” this is not merely a euphemism for “Thank God!” (We atheists don’t believe that there is any God to thank.) I really do mean thank goodness! There is a lot of goodness in this world, and more goodness every day, and this fantastic human-made fabric of excellence is genuinely responsible for the fact that I am alive today. It is a worthy recipient of the gratitude I feel today, and I want to celebrate that fact here and now.

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A Little Perspective

As recently as a few months ago, doctors were held in high esteem and educated people believed that medicine could be useful. All that changed, of course, with the medical profession’s stunning failure to prevent or even predict the breakout of ebola in West Africa. Worse yet, many doctors to this very day cling to their old ways of thinking, writing prescriptions, setting broken bones, and performing surgery in bull-headed defiance of the urgent need to jettison everything we know about medical practice and start over from scratch.

Nobody, of course, writes such nonsense about medicine. Why, then, do so many write equivalent nonsense about economics?

Most economists failed to predict the 2008 financial crisis and ensuing recession for pretty much the same reason most doctors failed to predict the 2014 ebola epidemic — their attention was, quite reasonably, directed elsewhere. It’s easy to say in hindsight that if economists had paid more attention to the shadow banking system, they’d have seen what was coming. But attention is finite, and if economists had paid more attention to the shadow banking system, they’d have paid less attention to something else.

For a little perspective, have a look at this chart showing U.S.~per capita income in fixed (2005) dollars:


That little downward blip you see near the top is the recent crisis. The somewhat bigger downward blip in the 1930s is the Great Depression. The moral is that in the overall scheme of things, recessions don’t matter very much. At the trough of the Great Depression, people lived at a level of material comfort that would have seemed unimaginably luxurious to their grandparents. Today, while Paul Krugman continues to lament “the mess we’re in”, Americans at every income level live far better than Americans of, say, 1980. If you doubt that, you surely don’t remember what life was like in 1980. Here’s how to fix that: Pick a movie from 1980 — pretty much any movie will do — and count the “insurmountable” problems that the protagonist could have solved in an instant with the technology of 2014. Or reread any of the old posts on this page.

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The Goldwater Standard

goldwaterFifty years ago this Labor Day weekend, the presidential campaign of 1964 got underway in earnest. It is often said that Barry Goldwater “lost the election but won the Republican party” or even “lost the election but won the future” by nudging the center of either the party or the country several notches to the right.

I don’t see it. Where is the contemporary mainstream politician — Republican or otherwise — who would repeal the 1964 Civil Rights Act, or at least those provisions (Titles II and VII) that authorize Federal regulators to override private business decisions about whom to serve and whom to hire? Where is the contemporary mainstream politician who would sell the Tennessee Valley Authority? Or end all agricultural supports? If Goldwaterism is in fact ascendant, then how did entitlement spending, as a percentage of GDP, manage to grow for most of the past 20 years — even though Republicans controlled the House of Representatives for 16 of those 20? For that matter, how is it that after all those years of Republican control, the National Endowments of the Arts and Humanities — two of the more noxious weeds to arise from the soil of the Goldwater defeat — continue to thrive?

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Missed It by *That* Much

Why do senior citizens get so many discounts? A lot of it is because they have the time to shop for bargains — so if you don’t give them a bargain, they’ll find someone else who will.

We talked about this and other forms of discounting (or, in economic jargon, “price discrimination”) in my Principles class just last week, emphasizing that it does no good to hand out discounts willy-nilly; instead you want to target them to the most price sensitive customers. That’s why you sometimes have to jump through hoops (like filling out a rebate form) to get your discount — the customers who are motivated to fill out a rebate form tend to be exactly the same customers who are most likely to look elsewhere for a good price.

We talked too about how the airlines have always strived to separate business travelers from leisure travelers so they can charge the business travelers more and the leisure travelers less — the leisure travelers being more likely to take the train (or just stay home) if they don’t get a bargain. The problem, though, is that it’s hard to tell who’s a business traveler and who’s a leisure traveler. So historically, there have been devices like discounts for those who stay over a Saturday night, which is something a business traveler is unlikely to want to do.

Now I can go back to my students and tell them something about the value of staying awake in their economics classes. Because someone who’d obviously absorbed this lesson well has started a new site called GetGoing that takes this idea and runs with it. Here’s how it works: You book two conflicting itineraries, say a trip to San Francisco and a trip to Atlanta on the same date. You are quoted prices that are typically about half what you’d get elsewhere. You agree to fly. And then it books one of the trips, chosen randomly.

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Triumphs of Capitalism

By the standards of history, you, I, and (unless you’re a very atypical blog reader) pretty much everyone we’ve ever met is fabulously wealthy. How wealthy? One good measure is our ability and willingness to support the frivolity of others. Here are two recent technological innovations that give eloquent testimony to just how well off we are.

First, the Oreo separating machine. (Yes, I realize that every other blogger on earth has already linked to this one, but if you haven’t actually watched it yet, you really should click through):

And then….

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Frank Redux

Thirteen years ago, in 1999, when I wanted to illustrate the astonishing march of progress, my Exhibit A was a new $250 stereo system that held 60 CD’s and could play tracks in random order.

My new Exhibit A is the fact that it’s been only thirteen years since this was a great example.

That was in an essay focused mostly on Robert Frank’s hypothesis that people care largely about relative position as opposed to absolute wealth. I was reminded of that essay following yesterday’s post, and I managed to dig out a copy, which I’ve posted here. Despite the dated examples, I still think it’s pretty good.

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Off the Deep End

Paul Krugman argues that success in business is not, by itself, a qualification for making wise economic policy, and I agree. But then he goes all looney-tunes on us:

A businessman can slash his workforce in half, produce about the same as before, and be considered a big success; an economy that does the same plunges into depression, and ends up not being able to sell its goods.

So according to Krugman, it’s better for you and your spouse to earn $40,000 each than for one of you to earn $80,000 while the other stays home with the kids. I wonder how many two-earner families would agree with him.

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Paging Alex Tabarrok

ip2

A mere two days after I lavished praise on Alex Tabarrok’s new book, which (among many other things) makes an eloquent case for patent reform, the U.S. Patent Office has proved that nobody’s listening by issuing patent #8,082,523 to Apple, Incorporated for a “portable electronic device with graphical user interface supporting application switching”. The abstract, in its entirety, reads as follows:

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Happy Birthday, Baby Seven Billion

baby7Happy birthday to our 7 billionth fellow earthling, who, according to most estimates, is due to be born today.

Welcome to the earth. Congratulations on being born in the 21st century, where the odds are excellent that you’ll live a richer, more prosperous and more fulfilling life than almost any of the 100 billion or so who preceded you — and paved the way for your prosperity with their investments and their inventions. Would that there had been more of them.

As you go through life, you will almost assuredly contribute to the world’s stock of ideas, diversity and love in ways your parents never contemplated — which is why the rest of us are a little sad that you might be their last child.

There’s certainly such a thing as a population that’s too large. Nobody disputes that. The interesting question is: Given the incentives faced by parents, it the population size we actually get too large or too small? And there are good reasons to think it’s too small.

In fact, population growth is a lot like pollution in reverse. Polluters don’t care about the damage they impose on strangers, so they pollute too much. Parents and potential parents don’t care about they joy and prosperity their chidren bring to strangers, so they reproduce too little.

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Big News

Last week, the highly distinguished Princeton Professor Ed Nelson announced a proof that the Peano axioms for arithmetic are inconsistent — and hence so is arithmetic itself. If true, this would be much bigger news than faster-than-light neutrinos. It would be bigger news than a discovery that the South had won the American Civil War. It would be far, far bigger news than a discovery that all life on Earth was intelligently designed.

There are, after all, multiple proofs that Peano Arithmetic (that is, the fragment of arithmetic described by the Peano axioms) is consistent. Among those, the simplest and most convincing (to the overwhelming majority of mathematicians) is this: The axioms of Peano Arithmetic, and therefore the theorems of Peano Arithmetic, are all true statements about the natural numbers — and a set of true statements cannot contradict itself.

Ed Nelson rejects that argument because (exempting himself from that overwhelming majority) he doesn’t believe in the set of natural numbers — or perhaps even in individual numbers when those numbers are very large. (How do you know that 810000 exists? Have you ever counted to it?)

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Happy Birthday

twoMathOverflow turns two years old this week — a milestone in the transformation of mathematical research into a massively collaborative endeavor. It’s happening on blogs, it’s happening on mailing lists, and it’s happening in a big way on MathOverlow, where mathematicians ask and answer the sorts of questions that might come up in the faculty lounge — if the faculty lounge were populated by hundreds of experts pooling their expertise.

If you’re interested in mathematics at the research level, MathOverflow is a place to learn something new and fascinating every single day. (If you are not doing mathematics at a research level, feel free to read but please don’t feel free to join the fray; questions at anything below about a second-year graduate level should be directed to MathStackExchange, another massively collaborative site aimed, roughly, at the college level — which reminds me that it’s not just mathematical research, but also mathematical education, that is being revolutionized before our eyes.)

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Looking Forward to Looking Backward


Each generation wishes it could go back fifty years and shake some sense into those people who were so bound by unnecessary customs, and so blind to the options they could have chosen and the changes that loomed on the horizon. As I said on Tuesday, this was Edith Wharton’s theme when she wrote in 1920 about the 1870′s, and it’s the theme of Mad Men, written in 2010 about the 1960s.

I invited you on Tuesday to speculate about which of our own quirks will trigger this sort of bittersweet nostalgic frustration among our descendants fifty years from now. There were some great responses in the comments.

Here are some predictions of my own that I think are least plausible — some moreso than others, but I’ll throw them out in no particular order.

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Ages of Innocence

Reading Edith Wharton’s Age of Innocence, it strikes me that this must have been the Mad Men of 1920. That was the publication date, but the story is set 50 years earlier, in a world poised on the edge of cultural upheaval. The characters are blind to how dramatically the world is about to change, and to how much better their lives might be if only they could break out of the social strictures of their time. They manage to be both charmingly quaint and tragically foolish. We care about them, but we also want to take them by the shoulders and shake them into something more like ourselves.

As Edith Wharton viewed the 1870s, and as Mad Men views the 1960s, so the fiction of the mid-to-late 21st century will probably view us. Which of our quaint but tragically foolish ways do you think it will emphasize?

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Blind Spots

beatlesThe other night at dinner, I was asked whether, when the Beatles came to the US in 1963, I had had any sense that something really big had happened.

Well, I was pretty young in 1963, probably too young to think about such matters. I remember having little interest in the Beatles, but being being very aware that they were something very big. Everyone was aware of that. But unless I am mistaken, pretty much nobody realized that we were witnessing something really big and lasting. More generally, I doubt that anyone at the time had any inkling of the long-term significance of rock ‘n’ roll. We knew it was popular, but we had no idea it would change the world. I’m not sure that in 1963 anyone knew that it was possible for music to change the world.

This led to the more general question: How quickly are great cultural watersheds recognized for what they are? In the few areas I know something about, I think the answer is “usually pretty quickly”. I remember 1910 even less vividly than I remember 1963, but I am pretty sure that it wasn’t long between the appearance of The Love Song of J. Alfred Prufrock and the realization (at least among people who care about this sort of thing) that poetry had changed forever. In mathematics, at least in the past century (and I’m pretty sure for several centuries, or even millenia, before that), major paradigm shifts have generally been recognized very quickly. When a Serre or a Grothendieck upends the mathematical world, the mathematical world quickly knows it’s been upended.

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We’ve Come a Long Way, Baby

I haven’t been able to find the exact quote, but unless my memory is playing tricks, Martin Gardner once posed the question “What modern artifact would most astonish Aristotle?”, and concluded that the answer was a Texas Instruments programmable calculator that could be taught to execute simple series of instructions. That was, roughly, 1975.

Here is what my iPhone does: It listens to the radio and tells me the name of the artist, song and album. It scans bar codes and tells me where to get the same item cheaper. It gives me step by step directions to anyplace I want to go. It points me to the nearest public bathroom. It recommends restaurants, based on cuisine, price, and proximity. It plays any music I want it to play, and it recommends new music based on what it’s learned about my preferences. It shows me a photograph of the entire earth and lets me slowly (or quickly) zoom in on my (or your) front porch. It takes pictures. It takes videos. It lets me edit those pictures and videos. It photographs 360 degree panoramas. It plays movies. It plays TV shows. It displays pretty much any book, newspaper or magazine I want to read. It reminds me where I parked my car. It lets me draw rough sketches of diagrams with my fingers and makes them look professional. It allows me to accept credit cards. It takes dictation. It checks the stock market or the weather with the push of a button. It reminds me of my appointments. It lets me browse the Web. It shows me my email. It locates and summons nearby taxicabs. It turns itself into a carpenter’s level. It turns itself into a flashlight. It makes phone calls. It makes video calls. And, oh yes — it has a calculator.

Now who would have been more astonished? Aristotle confronted with Martin Gardner’s calculator, or the Martin Gardner of 1975 confronted with my iPhone? I’m going to say it’s a close call.

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Exotica

This is really very cool. In several ways.

First: For the past year or so, there has been a remarkable website called Math Overflow where research mathematicians gather to swap ideas, to ask for help when they get stuck, and to offer help when they can. Frequent contributors include the Fields Medalists (a Fields Medal is roughly the mathematical equivalent of a Nobel Prize) Terry Tao, Tim Gowers, Bill Thurston and Richard Borcherds. Others who have popped up from time to time include Vaughan Jones (yet another Fields Medalist), John Tate, whose thesis reshaped modern number theory, and Peter Shor, the pioneering figure in quantum computation. And every day, one runs across dozens of other folks who nearly any top math department would be proud to have (and in many cases are proud to have) on their faculties. If you already know a lot of math, you can get a hell of an advanced education browsing this site.

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These Are the Good Old Days

This morning, I set my laptop computer and my Kindle down, one on top of the other, on what I thought was a sturdy tabletop, where they stayed for a minute or so before crashing to the floor. The Kindle is totaled, and the laptop hard drive is definitely wonky.

So I called Amazon, which will deliver me a replacement Kindle by this morning (approximately 20 hours after my call) at a heavily discounted price, even though my warranty was expired, and I called Dell (where I do have a warranty) to confirm that the hard drive was the probable locus of my laptop problems. Dell thought it surely was, and offered to have a technician on my doorstep this morning, but I preferred to pop in one of the three clones that I update once a week or so and keep in three separate locations. My computer’s working fine, and I’m using it to read my Kindle books while I wait for the new Kindle to arrive (which will probably be before you read this).

Sometimes the modern world works really really well.

The Idea of the Decade

gplaneWhat is the largest (non-human) animal that’s ever found its way onto an airplane?

Someday Google (or its successor) will be able to answer that question. It will understand what you’re asking, it will perform relevant searches for old newspaper items, it will sift through the results, it will know (or know how to find out) whether a vole is larger than a ferret, and it will give you an answer. We’ll call it the semantic web.

When the Chronicle of Higher Education asked me for a few hundred words on the defining idea of the next decade, this was the first thing that came to mind. Another was the partial conquest of cognitive bias through better understanding of the systematic ways our brains let us down, together with software designed to compensate for our own mental shortcomings.

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Living In the Future


My treasured copy of the humor classic Science Made Stupid, copyright 1985, contains a Wonderful Future Invention Checklist. Who in 1985 would have thought that just 25 years later, I could check off a third or so of the entries?

Wikipedia Fail

Congratulations to the 2010 Fields Medalists, announced yesterday in Hyderabad. Elon Lindenstrauss, Ngo Bau Chau, Stanislav Smirnov, and Cedric Villani have been awarded math’s highest honor. (Up to four medalists are chosen every four years.)

My sense going in was that Ngo was widely considered a shoo-in, for his proof of the Fundamental Lemma of Langlands Theory. Do you want to know what the Fundamental Lemma says? Here is an 18-page statement (not proof!) of the lemma. The others were all strong favorites. Nevertheless:

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O Brave New World!

complexitySomething momentous happened this week. Of this I feel certain.

A little over a week ago, HP Research Scientist Vinay Delalikar claimed he could settle the central problem of theoretical computer science. That’s not the momentous part. The momentous part is what happened next.

Deolalikar claimed to prove that P does not equal NP. This means, very roughly, that in mathematics, easy solutions can be difficult to find. “Difficult to find” means, roughly, that there’s no method substantially faster than brute force trial-and-error.

Plenty of problems — like “What are the factors of 17158904089?” — have easy solutions that seem difficult to find, but maybe that’s an illusion. Maybe there’s are easy solution methods we just haven’t thought of yet. If Deolalikar is right and P does not equal NP, then the illusion is reality: Some of those problems really are difficult. Math is hard, Barbie.

So. Deolalikar presented (where “presented” means “posted on the web and pointed several experts to it via email”) a 102 page paper that purports to solve the central problem of theoretical computer science. Then came the firestorm. It all played out on the blogs.

Dozens of experts leapt into action, checking details, filling in logical gaps, teasing out the deep structure of the argument, devising examples to illuminate the ideas, and identifying fundamental obstructions to the proof strategy. New insights and arguments were absorbed, picked apart, reconstructed and re-absorbed, often within minutes after they first appeared. The great minds at work included some of the giants of complexity theory, but also some semi-outsiders like Terence Tao and Tim Gowers, who are not complexity theorists but who are both wicked smart (with Fields Medals to prove it).

The epicenter of activity was Dick Lipton’s blog where, at last count, there had been been 6 posts with a total of roughly 1000 commments. How to keep track of all the interlocking comment threads? Check the continuously updated wiki, which summarizes all the main ideas and provides dozens of relevant links!

I am not remotely an expert in complexity theory, but for the past week I have been largely glued to my screen reading these comments, understanding some of them, and learning a lot of mathematics as I struggle to understand the others. It’s been exhilarating.

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The Internet to the Rescue

Two Russian girls arrive in DC as part of a travel exchange program for which they’ve paid about $3000. The program promises them jobs on arrival but fails to deliver. Instead, they are instructed to travel to New York City to do “hostess work” in a place called the Lux Lounge. Their American friend, currently in Wyoming, pleads with them not to go, but after some initial hesitation they board a Greyhound bus to New York, insisting that everything is fine.

Where can the panicked friend turn? To the Internet, of course. He posts a plea for help. Commenters jump into action, contacting police and social service agencies, pooling information to figure out what bus the girls are likely to be on, and arranging to have them escorted to a police station. A couple of hundred comments later, the girls are safe and sound. One commenter adds:

This is the best use of the Internet that I, personally, have ever seen. I’m so proud to be a member of this community.

Indeed.

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The Book With All the Answers

bunnyDo you remember Mister Bunny Rabbit?. He was a friend of Captain Kangaroo. One day long ago, when I still measured my age in single digits, Mister Bunny Rabbit announced that he owned a book containing the answer to every possible question. I was skeptical about that book, and so was the Captain, who scoffed mightily at the notion. By way of a test, he looked up the question “Where is Mister Green Jeans right now?”. The book’s answer was “In the attic”, which the Captain knew (I forget how) could not possibly be right. While the Captain was still gloating, Mister Green Jeans ambled in and mentioned that he’d just come from the attic.

The Captain was amazed, and so was I. Long into adulthood, I pondered how that book could possibly have known where Mister Green Jeans was. The best answer I ever got was from the journalist Chris Suellentrop, who speculated that it was probably one of those quantum mechanical things where the act of asking the question caused both the book and Mister Green Jeans to settle down from a cloud of possibilities into mutually compatible states. Others—not so very long ago—speculated that perhaps the book was controlled by a satellite operating a surveillance camera.

Nowadays, of course, we can all carry that book in our pockets. I wonder if today’s children would find anything particularly magical about a reference work that has the answers to pretty much everything, and updates them on the fly.

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Giving Thanks

After the philosopher Daniel Dennett was rushed to the hospital for lifesaving surgery to replace a damaged aorta, he had an epiphany:

I saw with greater clarity than ever before in my life that when I say “Thank goodness!” this is not merely a euphemism for “Thank God!” (We atheists don’t believe that there is any God to thank.) I really do mean thank goodness! There is a lot of goodness in this world, and more goodness every day, and this fantastic human-made fabric of excellence is genuinely responsible for the fact that I am alive today. It is a worthy recipient of the gratitude I feel today, and I want to celebrate that fact here and now.

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The Times, They’ve Been a Changin’

I have recently finished reading Hunters and Gatherers, a (quite good) novel written and set in 1991, which includes the following plot elements:

1) A door-to-door saleswoman pitches (hardcopy) encyclopedias to customers who eagerly seek easy access to vast quantities of information.

2) A man is eager to read an obscure novel he’s heard about, so he scours used book stores, hoping to find a copy. In the meantime, he’s not sure what the novel is about, and has no way to find out.

3) A comedian stores his collection of jokes on notecards, filling two rooms worth of file cabinets.

4) A collector of sound effects stores her collection on cassette tapes, and has no cost-effective way to create backups.

5) A man is unable to stay in close contact with his (adult) children, because long distance calling rates are prohibitively high.

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