July brought quite an impressive spam storm, which dumped 10,738 messages on me:

That’s a record for my inbox, well beyond the spike of 7,506 messages received last October. The mean number of messages over the two-year period shown is 3,867; the standard deviation is 2,190.

I’m intrigued by the amount of noise in this signal. The magnitude of the fluctuations suggests to me that somewhere in the spam economy there is a small-number bottleneck. Maybe there are only a few high-volume spammers in the world, so that when one of them goes on vacation, the overall volume sinks dramatically. Or maybe there are only a limited number of customers willing to pay for big spam mailings, so that the renewal or cancellation of a single contract can have a noticeable impact. Or it could be that there are only a few major lists of harvested email addresses; when the scraper misses one of my mailboxes, I see a big change.

A bottleneck of this kind is not the only possible explanation. In some other areas with high volatility–the stock market, for example–the apparent cause is not a small population of agents but strong correlations between agents, who all follow the same signs and signals. I suppose that might happen in the spam market, too, with broader economic trends affecting everyone in the same way, but somehow it seem less likely.

The graph below breaks down the monthly totals according to which of my various email addresses the spam targeted. Again the numbers seem to be bouncing around pretty wildly. For example, the July spike mostly came from my address here at bit-player, but the peak last October was dominated by an address at amsci.org.

Of the seven addresses I monitor, five are openly published on the web, and thus I shouldn’t be surprised that they attract their share of spam. But the other two addresses have never been published, and one of them I have never used or even handed out to friends. Those obscure addresses are getting about 1,000 spams a month in total.

One feature of my spam that doesn’t seem to fluctuate much from month to month is the proportion written in Russian or other languages that use the cyrillic alphabet. The fraction has hovered near one-half for the past year. I have a hard time imagining a model that produces such linguistic stability along with volatility in other dimensions.

In recent weeks my junk-mail folder has received well over 100 copies of the folksy image reproduced above. I don’t read Russian, but I know just enough of the alphabet to sound out the second word of the headline. My русскоговорящего friend Dana MacKenzie kindly translated the rest of the message:

Village Spammer

The era of posters and announcements has passed. We will distribute your ad on the Internet.

As Dana points out, this is spam for spammers: metaspam. There’s a lot of that going around. After all, the entire online economy is supported by advertisements for companies supported by advertisements for companies supported by….

Incidentally, the painting that the spammers defaced is “Village Postman,” 1959, by Pyotr Krokhonyatkin. I identified it by guessing the title and running a query through Simple Image Search, which led me here.

While I’m on the subject of spam, here’s an update to my running tally of monthly receipts:

For March and April combined, 57 percent of my spam was in Russian (or some other language that uses the Cyrillic alphabet).

My “Computing Science” column in the new issue of American Scientist looks at economics—including the current malaise—through the lens of control theory. This is not a new idea. The Keynesian prescription for smoothing out cycles of boom and bust is essentially an application of feedback control, although Keynes himself never described it that way. By the late 1940s the connection became explicit, as economists and control engineers worked together to refine tools for taming the business cycle. The two disciplines had another flirtation in the 1970s. Economists today seem less enthusiastic about methods borrowed from control theory, but they have certainly not given up on the aim of bringing the economy under control. In the past six months governments and central banks have intervened on a scale never seen before, all in an effort to “stimulate” economic recovery.

I’ll let the column itself tell the rest of this story; here I would just like to add a a couple of personal reminiscences about control engineering as seen by an interested outside observer.

Over the years I’ve had the opportunity to visit a lot of control rooms—at oil refineries, power plants, steel mills, railroad switch yards, sewage-treatment plants, particle accelerators, observatories, Internet operations centers. They’re not all exactly alike, but they do seem to share a common architecture, and also aspects of a common culture. For example, standard control-room iconography shows normally running machinery in red, whereas stopped or faulty equipment is green—the opposite of what you might guess after a lifetime of exposure to traffic lights. Years ago most control rooms had a “mimic board”—a long wall covered with a schematic diagram of the plant, festooned with gauges and switches and indicator lights. Now the operators are more likely to sit at ordinary computer screens. (I do hope they’re not watching YouTube videos while the reactor melts down.)

Two control rooms at the same plant—a paper mill in Catawba, South Carolina—serve to frame my impressions.

One of those rooms was in charge of a papermaking machine, a stupendous contraption the size of a football stadium, which takes in a slush of digested trees at one end and delivers huge reels of pristine white paper at the other end, with the sheet of paper-to-be threading between banks of steel rollers at a rate of more than 60 kilometers per hour. The control room for the paper machine was a calm and laid-back place. I sat with an engineer for an hour or so, talking about the thundering machinery outside the soundproofed booth, and all the while keeping an eye on the display screen in front of us. The indicators hardly budged the whole time. One key set of sensors in the papermaking process monitors the thickness of the moving sheet; if the thickness varies from the set point, a correction is made by blowing either warm or cool air onto one of the steel rolls. The temperature change causes the roll to expand or contract very slightly, and thus to squeeze the sheet a little more or less tightly. This is a subtle adjustment. Here’s what I wrote about it at the time:

It should be noted that the overall control strategy in papermaking is to operate the machine in a stable, steady-state condition. Blowing hot air on a steel roll cannot effect a large or a rapid change in the roll’s diameter; in the vocabulary of control theory, the actuators for this system have only limited authority. The limitation is intentional. The paper machine must run continuously for long periods, and changes in its state are designed to be gradual and confined to narrow bounds.

The other memorable control room at the Catawba mill was in the powerhouse, where boilers generate steam needed throughout the plant, as well as electricity. The main fuel for the boilers is “black liquor,” a strange watery brew created in the digesters that leach lignin and other kinds of organic gunk out of the wood. Black liquor is not a particularly good fuel, but the plant has to get rid of the stuff anyway, so burning it makes sense. But because of wide variations in the caloric value of the liquor, the boilers are hard to control. The first thing I noticed when I sat down with an operator in the powerhouse control room was that all the finish had been rubbed off one area of the console, surrounding a button whose label had also been rubbed away. I soon learned the function of that button: It silenced the alarm buzzer that sounds whenever some parameter wanders out of bounds. On the day of my visit, the buzzer was going off every minute or two. The operator displayed a well-developed Pavlovian reflex, slapping the silence button in milliseconds every time the buzzer sounded. Then he would turn to the screen, find the cause of the problem, and make some adjustment to fix it. Thus the powerhouse control room was a much busier place, and the mood was tense. If I had been doing that job, I’d have been ready for a beer at the end of my shift.

Somewhere in the bowels of the Treasury Department or the Federal Reserve (or maybe the World Bank), there must be a control room where operators at glowing screens watch the ebb and flow of money and make adjustments when some economic parameter strays from the set point. I wonder about the mood of that room. Is it one of those placid, hushed working environments, where controllers gently nudge the system back toward equilibrium? Or are they batting at buzzers all day?

Sometime in the early 1980s my friend Greg Chaitin decided to go digital. He wanted to have all of his own writings, along with some other documents he particularly valued, ready at hand in machine-readable form. This was long before Postscript or PDF; scanners and OCR were exotic technology. So Greg hired a typist. I know about all this because he sent me a printout of his digitized oeuvre—an impressively thick sheaf of fanfold paper, with sprocket strips still attached. (The irony of this mode of distribution was not lost on either of us.)

I’m finally trying to catch up with Greg. Instead of hiring a typist, though, I’ve bought a cute little document scanner, which has been busily transforming heaps of moldering cellulose into shiny new bits. The scanner produces PDFs, which then run through an OCR program to build an index, making the page images searchable. (Bring on the Googlebot!) The result falls short of ideal—files are obese, graphics are low-res, there’s no opportunity to edit or reformat—but still it’s better than rummaging through cobwebby filing cabinets in my basement. And I don’t have to FedEx cartons of fanfold to my friends.

I’ll be adding links to my publications list as I upload the files. Here are a few teasers:

The HP-41C: A Literate Calculator? Byte, January 1981, pages 118-138. PDF (3.3 MB)

40,000 Points of Light. Pixel, Vol. 1, No. 2, May-June 1990, pages 36-41. [On a graphics language in which an image is defined as a locus of points.] PDF (2.4 MB)

Rank-and-File Thinking. Lotus, June 1985, pages 73-77. PDF (1.8 MB)

Theory & Practice: On the bathtub algorithm for dot-matrix holograms. Computer Language, October 1986, pages 21-32. [On patterns generated by severely oversampled signals.] PDF (4.6 MB)

The Information Age: The Numbering Crisis in World Zone 1. The Sciences, Vol. 32, No. 6, November-December 1992, pages 12-15. [On the impending shortage of telephone numbers.] PDF (1.8 MB)

I note for the record that every one of the publications mentioned in the list above is now defunct. I wonder if there’s any significance in that?

I get a daily Google Alert with news of web pages that mention my books. Lately the alerts have been pretty weird. I’m not going to publish the URLs because I’m not sure what mischief is behind all this, and many of the pages have been taken down already anyway, but here are a couple of text excerpts.

This one—and dozens like it—appears to be the output a Perl script with an overused $book_title variable and a shaky grasp of English syntax:

You need to know that Group Theory in the Bedroom and Other Mathematical Diversions is an beautiful product! I love my Group Theory in the Bedroom and Other Mathematical Diversions alot! I Track down the grade a quality of Group Theory in the Bedroom and Other Mathematical Diversions is just dazzling! I purchased my Group Theory in the Bedroom and Other Mathematical Diversions at Amazon.com and found that they have the half-price prices online for Group Theory in the Bedroom and Other Mathematical Diversions!

As far as I can tell, the aim of these web pages is actually to sell copies of the book (through an Amazon Associates link that earns the referrer a small kickback). I guess I should wish them every success.

Another set of pages is more enigmatic both in garbledness and in purpose. Under a conventional-looking heading that suggests some sort of book-review service, there are great gobs of prose like this:

In the imaginative, legendary readable Infrastructure: A Field Guide to the Industrial Landscape, Brian Hayes adapt the genre of the graze manor guide to “everything that isn’t nature,” as he writes. Hayes take on the destined thicket of specialized gobbledygook gracefully, adding up comparison to brand name contemporary lingo and process reasonable. A method of floodgates works “like a rolltop desk”; bricks are “sliced from an extruded flex of sand by a magnificent wire, like a cheese cutter. Now a veteran science writer has crisscrossed the U. The perfume was deep but not sickly sweetie. ” Along country roads, Hayes explore all the technological sights, from tractors and combine to the earlier extent and decoration of the once dominant technology for enclose animals, barbed wire: “As bedside light as air. He undertake this mission to some extent through hundreds of photographs taken from airplanes, cars, and the public side of many a chain-link balustrade, partly through the moving on, accessible prose of a man who appreciate the history, engineering, and aesthetics of such wonder as barn hay hood, grain elevators, oil pipelines, and the airing towers of the Holland Tunnel. Cheaper than dust,” as one of its unwary proponents describe it. Down sewer manholes: “Sounds were deadened. “It’s all in circle you. Industrial buildings Landscape architecture..

I recognize the underlying text from which this pastiche was constructed: It’s from a review by Anne Eisenberg, originally published in Scientific American but also posted on Amazon. Phrases have been scrambled and also altered with aid of a thesaurus. For example, “many a chain-link fence” in the original review has become “many a chain-link balustrade,” and the ventilation towers of the Holland Tunnel are now “airing towers.”

What I can’t figure out is why. Why did the splogger bother to alter the text at all? Why not just scrape it and spew it? Surely someone who would post this sort of stuff isn’t worried about copyright violations. Beyond that, why bother at all? On these pages there are no links to Amazon—or to anything else in the known universe, so what’s the point? What is it all in aid of? I suspect the motive has something to do with getting the page indexed by Google—and in that they’ve evidently succeeded—but then what? I don’t see the payoff.

A roundup of other spam news:

The graph below brings up to date my monthly tally of junk email. It looks like we’re back on the upward growth path, recovering from the crash at the end of last year. Also, the proportion of my spam in Russian keeps climbing. It had been running about half, but this past month it hit 63 percent.

I’m also facing a comment-spam problem here at bit-player.org. Because I’ll be traveling in the next few days, I’ve turned on comment moderation. Sorry for the inconvenience, but I think it’s better than hundreds of messages promoting online casinos.

Finally, just to show I haven’t lost my sense of humor about all this, I want to mention a phishing email I received this morning. It purports to be a ticket confirmation from Delta Air Lines, with a zipped attachment that’s doubtless something nasty. How do I know it’s a fake? Because of this passage in the body of the letter:

On board you will be offered:

- beverages;

- food;

- daily press.

You are guaranteed top-quality services and attention on the part of our benevolent personnel.

Sent by someone who hasn’t flown lately.

Wall Street may have had its worst month ever, but the spam market has been booming. As faithful readers know, I’ve been tracking my incoming spam for several years now. (If you’re utterly sick of reading about this strange obsession, please forgive me. Also please let me know.)

As the graph suggests, this past month has produced an extraordinary uptick. October shows a 50 percent increase over September, with a total of 7,506 messages. Both the rate of increase and the absolute number of messages set records. I’ve seen roughly a tenfold increase since the low point back in May of 2007 (when I believed that we might soon be seeing the end of the spam phenomenon). The preponderance of Russian fare in my spam diet also continues: 4,694 of the month’s messages (or 62.5 percent) used a character encoding for the Cyrillic alphabet.

(Earlier reports: 2003 American Scientist article, 2007 American Scientist article, June bit-player item, October bit-player item.)

Update 2008-12-03: Well, it looks like the spam market has finally crashed. After five months of accelerating growth, my spam intake collapsed in November. I got a total was 3,492 messages, less than half the October count and sending me back to levels not seen since June.

The proportion of Russian spam has also fallen, though only slightly: 1,575 of the messages (45 percent) arrived with a Cyrillic character encoding.

News reports suggest one possible reason for the sudden downturn in spam volume: On November 11 an ISP named McColo was isolated from the rest of the Internet. Unidentified customers of McColo are accused of using servers there to control spam-spewing botnets. Can this event account for the lighter load on my spam filter? Here’s the daily log:

There is indeed a noticeable dropoff after the 11th. However, it’s worth noting that volume was already well below the October average of about 240 messages per day.

Update 2009-01-01: The volume of spam in my inbox is falling faster than the price of light sweet crude. My December total is down more than 60 percent since the October peak, to 2,774 messages. The graph below gives a wrap-up for a full two years.

What drives these tides in the flow of Vi@gra ads and offers of replica \/\/atches? The cycles of boom and bust are even more mysterious than those of the global economy. All I can say about this event is that it appears to be a general downturn, not a collapse of some particular category of spam. In particular, the distribution of languages remains fairly stable. In December 49 percent of my spam carried one of the Cyrillic character encodings, so somebody out there still thinks I’m a likely customer for Отчаянные домохозяйки.

Reviewing this month’s batch of incoming junk mail, I stumbled upon the following message:

In case that image is too tiny to read, here is the first word in source-code form:

     28    47   34
     74    33
      85  42
      16  43    25    5048     08124   8813    2714
      34  02    25       66   50  31   855        05
       3404     65    88362   00  25   72      01651
       8008     36   42  77   27  81   06     04  40
        72      83   02  32   47  12   24     87  33
        78      03    87100    83844   18      21813
                                  08
                              73634

The basic technique is anything but novel. I can remember green-and-white-striped printouts that had my name emblazoned in the same kind of two-inch-high characters. But why are the characters here formed entirely out of numbers, rather than other ASCII glyphs? And do the numbers themselves mean anything?

I think I know the answer to the first question: The spammer thought a message composed of nothing but numerals might slip through the spam filters. (In my case, at least, it didn’t work. I fished this message out of the garbage pail.)

As for the second question, my immediate guess was that the digits are the output of some simple pseudo-random number generator. That would be an easy way to produce them, and it would also allow the spammer to make each individual message unique. On taking a closer look, however, I realized there was something quite nonrandom about the numbers in the message.

Here is the full list of digits. There are exactly 900 of them. Do you see what’s missing?

284734807433341016202332628542642574418481303116432550480812488
132714721846667434022566503185505580464271163634046588362002572
016511712427000046735580083642772781060440148383627872830232471
224873301464000807803871008384418218130077346262602008225346571
155727363470732323181618223162744253246331737038301533254837881
148802160371074555632302255640217448457046416116253484658726108
147181540061231788804563557807254177278106044014838362787283023
247122487330146400080780387100838462042135220046847482422143746
770236783058460185444521283134537306537546855305024142275437615
010235002438258320577785451436776143066166025853832747551576004
831136831376228235381112678466011047530048032816623514158481030
413446024450055236762111281250031205166204213522004684748242214
374677023678305846018544452128313453730653754685530502414227543
761501023500243825832057778545143677614306616602585383274755157
600483113683137622

There’s nary a 9 in the bunch. And in other respects too the digit distribution looks slightly off-kilter:

When I tabulated all the correlations between successive digits, that too looked a little fishy, although the sample is too small for any reliable conclusions.

                   s e c o n d
           0  1  2  3  4  5  6  7  8  9
      0   23 12 20  9 17  9  7  7  8  0
      1   11 13 11 12 16  8 13  5 10  0
   f  2   11 11 13 15 14 15  6 14  9  0
   i  3   18 13 15  7 11  8 13 13 12  0
   r  4    8  9 12 13 12 10 22 11 18  0
   s  5   11  7  5 14 12 14  4 10 11  0
   t  6   12 10 15  6  8  7 10 10  6  0
      7    6 10  9 10 12  7  9 11 14  0
      8   12 14  8 24 13 10  0  7  6  0
      9    0  0  0  0  0  0  0  0  0  0

So what’s going on here? I think the pseudo-random generator is still a leading candidate, though it would have to be a badly implemented RNG. The absence of 9s isn’t hard to explain: We only have to suppose that the spammer was working in C and wrote the plausible-looking expression random(9), thinking that would generate integers between 0 and 9.

On the other hand, maybe it isn’t random. Maybe there’s a secret message-within-the-message. Anybody see a pattern?

While I’m talking spam, I’ll update my ongoing tally of my inbox contents. I can report that September was a good, strong month for spam, with further steady growth continuing the summer-long trend. The stock market is in retreat and credit is tight, but the purveyors of replica watches are undeterred. My receipts have crossed the 5,000-per-month threshold for the first time:

And another threshold has also been left behind: For the first time this month, more than half of my spam is written in Russian. (Based on character-set declarations, 2,858 messages out of 5,021 were in Cyrllic scripts, or about 57 percent.)

Update 2008-10-12: In response to a request in the comments, I’ve uploaded the full text (including headers) of the original email. The file is here. Incidentally, I’ve searched my spam archive for other messages like this one, without success. That in itself makes this a peculiar spam. Usually, if I get a spam once, I see dozens of copies or variants within a few days.

Economics has always mystified me, but watching the death spiral on Wall Street this past week has left me even more baffled than usual. I don’t pretend to understand what’s happening. But this morning I’ve begun to wonder if maybe—just maybe—there are some aspects of this debacle that I fail to understand not just because I’m thick but because they actually don’t make sense.

The part that’s puzzling me right now is an accounting rule known as “mark to market.” If I understand correctly, the gist of the mark-to-market principle is that the value of a thing is whatever you could get for it if you were to sell it right now. “Fair value” = “current exit price.” For some kinds of assets there’s a longstanding tradition of assigning value in this way, but in the past year the rule has been applied much more broadly. (See Rule 157 of the Financial Accounting Standards Board, which took effect November 7, 2007.)

Is it really a good idea to equate price and worth quite this rigidly? I’m not trying to overturn all that adamsmithian capitalist orthodoxy about a willing buyer and a willing seller and an invisible hand. And I understand that mark-to-market was introduced as an improvement over the mark-to-wishful-thinking kind of accounting that led to the previous round of scandals, such as Enron. Still, could it be that we’ve gone too far?

Consider the guy who sells umbrellas on the sidewalk around the corner from the New York Stock Exchange. Under mark-to-market rules, his inventory is assigned a much higher value on rainy days and becomes nearly worthless when the sun shines. I suspect that the umbrella guy has a very clear understanding of how the weather affects his business, and yet he doesn’t just throw away all of his stock whenever the sky turns blue. He knows that under those conditions he can’t sell an umbrella at a profit, but he still considers the umbrella to have a certain intrinsic worth. He hangs on to it. He carries it on his books as an asset. This concept of inherent value is apparently too sophisticated for the traders inside the exchange. In that world, if the Emir of Dubai doesn’t need an umbrella on Monday, then all umbrellas are “toxic.” But if the Secretary of the Treasury asks for an umbrella on Friday, then everybody invests in umbrellas.

Surely I’m missing something. It can’t be this stupid.

It’s a cruel irony: As the citizens of Zimbabwe sink into bitter poverty, they are becoming millionaires and billionaires. Inflation is eroding the value of the Zimbabwean dollar so rapidly that everyday transactions turn into lessons in the arithmetic of large numbers. When the photo above was made on July 17, the largest currency denomination in circulation was a note for ZW$50,000,000,000. Last week the nation’s central bank issued a ZW$100,000,000,000 bill. (I’ll spare you the trouble of counting zeroes: That’s 10¹¹, or 100 billion by American reckoning.)

The Zimbabwean inflation is the worst in the world at the moment, but it is not (yet) setting all-time records. Probably the most famous episode of extreme inflation was that of the German Weimar Republic (a story told vividly in Erich Maria Remarque’s novel The Black Obelisk.) In 1921, German marks traded at about 60 to the U.S. dollar; two years later, in December of 1923, the exchange rate was 4.2×10¹² per dollar. The Hungarian inflation following World War II reached even greater numerical heights. In a single year the exchange rate for the Hungarian pengo went from 100 per U.S. dollar to 4×10²⁹. As Feynman said, astronomical numbers are dwarfed by economical ones.

Takayuki Mizuno, Misako Takayasu and Hideki Takayasu have analyzed the German and Hungarian episodes of “hyperinflation.” (Citation: Physica A 308 (2002) 411; there’s also an arXiv preprint.) Inflation at its worst, they find, proceeds at a doubly exponential rate. In other words, prices rise not just as an exponential function of time—exp(t)—but as an exponentiated exponential—exp(exp(t))—or:

This growth law has a simple meaning in terms of everyday experience. With “ordinary,” single-exponential inflation, prices have a constant doubling time. If bus fare was 1 million last month and 2 million this month, it will be 4 million next month. Under double-exponential growth, the doubling time itself decreases exponentially. In the last months of the Hungarian inflation the doubling time fell from about 20 days to 15 hours.

On a logarithmic scale, a simple exponential function yields a straight-line graph. Here is the Mizuno-Takayasu evidence that the final phase of the Hungarian inflation was superexponential:

And here are the data for the final six months plotted as log(log(p(t))), showing a simple linear trend:

How does the Zimbabwean economy look when submitted to this kind of scrutiny? I don’t know of a reliable source of data on prices in Zimbabwe, but foreign exchange rates can serve as a rough proxy. Until three months ago, the official ZW$ rate was pegged at roughly 30,000 per US$, but on May 10 the currency was allowed to float free, and the rate immediately jumped to 190,000,000 ZW$ per US$. By July 31 the rate had reached 57,381,544,140. Thus the 50 billion ZW$ note in the photo above was worth a little less than a 1 US$ by the end of last month. And that’s at the official rate of exchange; the street value is reportedly about a tenth of the official quote.

Here’s how the official exchange rate has varied in the 84 days between May 10 and August 1, as plotted on a linear scale:

And here’s the same data after a logarithmic transformation:

Although there’s more bumpiness here than in the Mizuno-Takayasu data, the trend looks reasonably linear to me. The fitted line has slope 0.03358, which yields a doubling time of about nine days. I see no hint of superexponential growth. I’d like to think this is an encouraging sign, a glimmer of hope that Zimbabwe will be spared an even more pernicious phase, when even inflation has inflation.

Runaway inflation is usually blamed on the incompetence or malevolence of governments and the central banks that implement their policies. In the case of Zimbabwe, the government of Robert Mugabe certainly has a lot to answer for. The country was once the shining success story of southern Africa—I have friends who migrated across the continent to go to school there—but the nation is now a basket case, and inflation is only one of many urgent crises. (The unemployment rate is reported to be 80 percent.) The Mugabe regime can’t escape blame for this situation. Still, it seems that hyperinflation is not to be explained purely in terms of fundamental economic imbalances—too many dollars and not enough goods. Sometimes it seems there is also a psychological component. When you believe that prices will double next week, you raise your own prices in anticipation. It’s a self-reinforcing process.

One sign of such a feedback loop in the inflationary spiral is that inflation sometimes stops even though the underlying economic situation hasn’t really changed. The Weimar hyperinflation ended with the introduction of the Rentenmark, which was set equal to 10¹² old marks but really had no firmer backing than the earlier Papiermark. The change in currency did nothing to solve Germany’s problems of debt and unemployment, but the inflation ended anyway. Evidently, people chose to believe that the value of the Rentenmark would remain stable, and it did.

The central bank of Zimbabwe has just announced a similar effort at currency reform, devaluing the ZW$ by a factor of 10¹⁰. In other words, the ZW$100,000,000,000 note introduced a week ago is equal in value to a new ZW$10 bill. According to press reports, the main motive for the change was simply logistical convenience:

Gideon Gono, the Central Bank governor, … acted because the high rate of inflation was hampering the country’s computer systems. Computers, electronic calculators and automated teller machines at Zimbabwe’s banks cannot handle basic transactions in billions and trillions of dollars. (AP/Baltimore Sun)

But perhaps one can hope that the newly denominated currency will bring more than numerical benefits. Over the weekend, the official exchange rate has held at 6.569 new Zimbabwe dollars to the U.S. dollar. We’ll have to wait a few more days to see if the curve has really flattened out.

Update 2008-09-04: With another month of exchange-rate data, here’s what the situation looks like:

The blue line in the semilog graph is the same as the one in the corresponding earlier graph—that is to say, it is fitted to the first 80 days of data. It appears that the inflation rate has diminished slightly since the revaluation at the end of July. But that slightly lower rate is still formidable; in a little more than a month the value of the new Zimbabwe dollar has fallen from about 15 cents (U.S.) to about 2 cents.

Update 2008-10-02: After another month, what passes for good news is that the rate of exponential growth does not seem to be growing:

On the other hand, news reports suggest that the situation in Harare is bleaker than ever. Money is scarce as well as nearly worthless; people stand in line all night for the privilege of withdrawing the equivalent of a dollar or two from their own bank accounts. (Note that the equivalent of $1 U.S. is $ZW137 in the devalued currency issued in August. In pre-devaluation Zimbabwe dollars, it comes to $ZW1.37 trillion.)

Isn’t it curious that both here in the U.S. and in Zimbabwe, the financial pages are filled with such enormous numbers.

Update 2008-11-02: One more month of data:

Still no sign of “hyperinflation”—if that term is taken to mean doubly exponential growth—but that can’t be much solace to the Zimbabweans whose currency has yet again lost three-fourths of its value over the course of a month. Adjusting for the August devaluation, one U.S. dollar now buys 5.6 trillion Zimbabwean dollars.

As I mentioned, the American Scientist web site is undergoing an overhaul. One aspect of the transition that’s still in transition is redirecting http requests so that old links and bookmarks will retrieve the correct document on the new site. I wish I could snap my fingers and fix this problem globally, but that seems to be beyond my power. Over the weekend, however, I decided I could at least try to reduce the entropy of my own little corner of the WWW by repairing all the links at bit-player.org that point to American Scientist articles. It wasn’t quite as much fun as I had expected.

The first problem is that the old links are completely opaque. They look like this:

     http://www.americanscientist.org/AssetDetail/assetid/48550

The identifier “assetid/48550″ offers no clue to what it is identifying. It could be anything the magazine has published in the past 10 years. The second problem is that you can’t just follow the link to find out where it leads. None of these links are working anymore—that’s the whole point.

Does this situation suggest a certain lack of foresight on my part? Oh well. I’ll just sit here in the corner until the paint on the floor dries.

For links that point to my own columns, I’m generally able to infer from their context what the proper target is. And, if I get stuck, the Wayback Machine is there to rescue me (thank you Brewster Kahle). Still, reviving a batch of dead links is a dreary exercise. I find a link; I figure out which column it refers to; I run a search on the new web site to find the updated URL; I record the mapping from old link to new, so that this information won’t be lost; I correct the link in the bit-player posting. Wash, rinse, repeat.

After fixing only about a dozen links in this way, I came to a moment of self-knowledge: During my remaining years on this planet, however few or many they may be, I never want to go through this process again. Which raises the question: What’s the best way to create permanent pointers to objects that may not stay where you put them?

The answer to this question has been known for decades. What’s needed is double indirection: a pointer to a pointer. Also known as a handle.

• Zeroth-order indirection: I send you the document itself.
• First-order indirection: I send you an address where you can find the document.
• Second-order indirection: I send you an address where you can find the address of the document.

At order zero—with no indirection at all—the document is beyond my control from the moment I send it. With a single level of indirection, I can update or correct the document and you’ll see the new version, but if I move it, you’ll lose access. With double indirection I can change either the content of the document or its location whenever I please, as long as I take care to update the intermediary pointer—the forwarding address.

Double indirection is already a well-established technology in Internet operations. It is the basis of the Domain Name System. When you follow a link to “bit-player.org,” a nameserver looks up that string of characters and returns an IP number, such as 69.89.21.70, which specifies the real whereabouts of the page you’re now reading. I can move bit-player.org to a new host with a new IP number and you’ll still be able to find me, provided I let the world’s nameservers know the new address.

The same kind of mechanism can be made to work at a finer level of detail. In particular, Digital Object Identifiers offer an infrastructure for attaching permanent names to documents or other online resources. For example,

    http://dx.doi.org/10.1511/1998.5.410

is the DOI irrevocably assigned to one of my old columns, titled “Bit Rot.” In that column, written 10 years ago, I discussed the sad tendency of digital information to go stale, to decay, to become inaccessible. Alas. As you have doubtless guessed, the DOI has lost touch with its target; following the link above will get you nothing but a “page not found” error. And fixing errant DOIs looks no easier than fixing raw, broken links. I’m afraid that “dx.doi.org/10.1511/1998.5.410″ is almost as opaque as “assetid/15568.”

In practice, the world seems to have settled on a different mechanism of double indirection for keeping track of stuff on the web. We don’t try to remember or record URLs; we simply go to Google and run a search. The trouble is, though, Google itself relies on the whole distributed network of links to trace and rank documents. If everyone counts on Google to know where everything is, Google will have no way of finding anything.

According to legends of yore, the Internet was designed to survive a nuclear attack. And at the hardware level, the Net is indeed extraordinarily resilient. But the superstructure of linked documents we’ve built atop that foundation is not so unshakeable. If we were to wake up one morning and find that all the links on all web pages were broken, it wouldn’t be much consolation that the underlying documents still existed. Much of their value lies in the connections between them.

Tim Berners-Lee, the first weaver of this web, offers some excellent advice: URLs should never change. If only we’d thought of that sooner.

Back in 1994 I wrote a column titled simply “The World Wide Web.” It was all so new then. My elaborate definitions and explanations seem very quaint now, like someone describing in meticulous detail how to dial a telephone or flush a toilet:

What is the Web? Is it a place? A program? A protocol? One of the <A HREF=”http://info.cern.ch/hypertext/WWW/TheProject”> documents</A> in which the Web describes itself offers this assessment: “The World Wide Web (W3) is the universe of network-accessible information, an embodiment of human knowledge.” That about covers it.

For something as vast as a universe, the Web is surprisingly easy to find your way around in. It works like this. On a computer connected to the Internet you start up a program called a browser; the browser goes out over the network and retrieves a document, which we can assume for the moment is simply a page of text. Within the text are some highlighted phrases, displayed in color or underlined. When you select one of the highlighted words by clicking on it with a mouse, a new document appears, with new highlighted “links.” Clicking on one of these links takes you to still another document. Each time you follow a link, you may be visiting another network site, perhaps quite distant from your original destination as well as from your own location.

Is it any surprise that the link embedded in this passage—which I have formatted so that the URL remains visible—summons a “404 Not Found” message?