The Multiplier Effect

Quickly now… If you multiply 633 by 11, what’s the answer?

No doubt, you recognize the pattern, and you may recall the mental math process:

633 x 10, plus 633 x 1, or 6,330 plus 633, or 6,963, which is the answer (or, in terms used by math teachers, the “product”).

There is another way to solve the problem, a faster way that assures fewer computational errors, and does not involve any sort of digital or mechanical device. It does, however, involve a simple rule and a different way to write the problem down.

The rule is: “write down the number, add the neighbor.” The asterisk just above each number is there only to help you to focus. If you prefer, think of it as a small arrow.

Here’s how it works:

Mult by 11

Try multiplying 942 x 11  and you’ll quickly get the hang of it.

Do it once more, this time with a much larger number: 8,562,320 x 11. It goes quickly, as you’ll see.

Multiplying by 12 is just as easy, but the rule changes to: “double the number, add the neighbor.” Here, my explanation includes specific numbers.

Mult by 12

In fact, there is a similar rule for multiplication by any number (1-12). And there are rules for quickly adding long, complicated columns of numbers, as there are for division, square roots and more.

These rules were developed by a man facing his own demise in the Nazi camps during the Second World War. Danger was nothing new to him…this is the story and the enduring legacy of Jakow Trachtenberg, who first escaped the wrath of the Communists as he escaped his native Russia, then became a leading academic voice for world peace. His book, Das Friedensministerium (The Ministry of Peace), was read by FDR and other world leaders. His profile was high; capture was inevitable. He made it out of Austria, got caught in Yugoslavia, and was sentenced to death at a concentration camp. To maintain his sanity, Trachtenberg developed a new system for mathematical calculation. Paper was scarce, so he used it mostly for proofs. The rest, he kept in his head.

Madame Trachtenberg stayed nearby, in safety. She bribed officials, pulled strings, and managed to get Jakow moved to Dresden, which was a mess, allowing him to escape. Then, he was caught again, and was moved to Trieste. More bribes and coercion from Madame. He escaped. The couple maneuvered into a more normal existence beginning at refugee camp in Switzerland. By 1950, they were running the Mathematical Institute in Zurich, teaching young students a new way to think about numbers. A system without multiplication tables. A system based upon logic. A system that somehow survived.

A system that, against all odds, made it into my elementary classroom. One classroom in the New York City school district. For one year. The parents were certain that the teacher was making a terrible mistake, that the people in my class, myself included, would never be able to do math in the conventional way again. Of course, we learned a lot more than an alternative from of arithmetic.

And now, after decades out of print, in an era when arithmetic hardly matters because of calculators and computers, the original book is back in print. The brilliance of system remains awesome, and the book is worth reading just to understand how Trachtenberg conceived an entirely fresh approach under the most extraordinary circumstances.


(Digital) Money, Honey

We pay for just about everything with a credit card, a debit card, PayPal. Even parking meters accept card payments. Cash is dirty, difficult to store, easy to lose, and (for better or for worse) leaves no trace. The end of money has been predicted for a long time. Maybe now’s the time that money, like photographic film, drive-in theaters, and typewriters, fades away.

That’s the theory behind WIRED contributing editor David Wolman’s book, The End of Money published by Da Capo. The book is an easy read, filled with anecdotes, interesting histories, and a great many examples of alternatives to our current cash-and-coins conception of valuable exchange. Wolman points out the present system is, in fact, quite new, and that most of human history did not involve pennies, pfennigs, or pesos. He estimates that one of every twenty British coins is counterfeit. He points to cash on ice both in Alaska Senator Ted Stevens’ freezer and also in a visit to the fallen Icelandic economy. (There are so many wonderful slang terms: cold hard cash among them). He explores alternative currencies. The one about Liberty Dollars–”a private voluntary free-market currency backed entirely by silver and gold.”–is a long trip through the complexities of alternative currencies and contemporary Federal conceptions of money.

There’s discussion–not enough for my taste–about smart cards and the use of mobile devices as digital wallets. Here, the focus is on the many small daily transactions that remain cash-intensive, and the potential for a simpler, less costly, more manageable system based upon digital transactions. The upside: you’re never short a quarter for the parking meter; the downside: every time you park your car, you’re making an entry into your permanent record.

Be sure to read the crazy story. It’s just one paragraph on Wikipedia.

It’s interesting to muse on the current use of simulated currencies, if only to understand our possible future behaviors: accumulating gold coins in games, such as World of Warcraft; the possible connections between gamefied badges and currency that can be exchanged for real or virtual goods and services; the use of Quids on the (now gone?) website Superfluid, where “they’re placeholders for favors” (perhaps not unlike the favor/exchange economy that drives power and accomplishment in the nation’s capital). Where might frequent flier miles fit into the money equation? Or Disney Dollars that pay for fun in Orlando (now largely replaced by Disney Gift Cards because they yield far more digital data, and because the residue is easily converted to profit.) How about the barter economy that has been so well-nourished on the internet: you build my website, I do your taxes.

How does taxation fit into any of this? None of us love taxes, but we’ve certainly become attached to, say, our interstate highway system. I suppose most transactions will be digital, and so, there is a trackable moment of exchange, and at that moment, the tax authorities can step-in (digitally) and collect. How about pay checks? Direct deposit eliminates the old-fashioned notion of “cashing the paycheck”–and, perhaps, acknowledging the weirdness of Big Brother, preparing one’s own personal tax return may seem equally old school (armed with your entire digital financial life, the government could certainly outsource your tax return, mine to, to an outfit in Malaysia or Peru).

Are coins and cash going away? Not this year, but maybe in ten years. It’s fascinating to contemplate the possibilities. And, along the way, it’s fun to browse or read The End of Money.

It’s also fun to watch the CBS Sunday Morning report that was inspired by the book. If you can find the link, let me know and I’ll post it (couldn’t find it on the CBS Sunday Morning site).

The Ultimate Road Trip

It’s the biggest thing we’ve ever built–bigger than the pyramids of Egypt, about a hundred times as long as the Panama Canal, easily eight times the length of The Great Wall of China. It’s newer, too. And, soon, we’ll probably build it all over again.

As Earl Swift explains in The Big Roads: The Untold Stories of the Engineers, Visionaries and Trailblazers Who Created the American Superhighways, the U.S. interstate highway system is forty-seven thousand miles long, and it is the “greatest public works project in history.”

Messy as our current dilemma about infrastructure may seem, life was worse before the interstates, before modern roads. In the good old days, New York City’s horses output 2.5 million pounds of manure every day, plus 60 thousand pounds of urine. In 1893, the agriculture department got things rolling with a new Office of Road Inquiry, whose boss, a Civil War veteran, declared Americans “have the worst roads in the civilized world.” Still, intrepid automobiling pioneers attempted a cross-country race in 1903 (one car included a dog, Bud, who wore goggles and “became a hit in every town they visited.”) This was the beginning of an industry, complete with sales stunts on a grand scale: Carl Fisher, whose early days were consistently colorful (and completely crazy), “rigged a Stoddard-Dayton roadster to a massive balloon and flew it over Indianapolis, vowing to drive it back into town from wherever he landed.” (Actually, Fisher stripped the floating car and drove home in a look-a-like spare). Not long after, Fisher partnered with two other car crazy businessmen  and built the Indianapolis Speedway. Fisher was among the first to campaign for a big interstate highway system.

A half-century later, in 1956, “nearly $2.6 billion had been committed to the work… contracts had been awarded on more than a thousand bridges… construction was under way or about to begin on nearly two thousand miles of highway.” Half the book is about the wrangling, the engineering and politics, the slowdowns due to the Great Depression and World War II, and all sorts of rational and irrational arguments about the nature of the undertaking, the roles of the states versus the Federal government, the best ways to pay (tolls? gas tax? Federal funds? State funds?), and much more. In fact, the weakest part of the book attempts to describe this wrangling–Swift (great name for the author of a book about fast highways, BTW) does his to craft a story from his astonishing collection of arcane research. With Detroit pumping out over 5 million cars per year (1 in 3.5 citizens owned a car), America had a mess on its hands. Far too many cars driving on roads that were designed decades earlier. Trucks made the situation worse, both by contributing to congestion and also by damaging roads never built for a big truck’s combination of weight and speed. “Snarls at New York’s George Washington Bridge were traced back eighty-four miles–seriously, eight-four miles–to Monticello, New York.”

Even in these early stages, Swift explains that the highway system had its critics: Lewis Mumford published articles and books about the loss of city neighborhoods, and the economic destruction of towns and villages across the nation. By the 1960s, the environment movement gradually imposed restrictions on engineers who were once able to construct interstate highways pretty much anywhere, regardless of impact on animals, ecosystems, even city parks. Several Baltimore neighborhoods fought tremendous battles, and today, there is no interstate highway system cutting across Baltimore–the local activists won their battle. Visitors to Baltimore’s lovely old Fell’s Point neighborhood can thank those activists–if the interstate was built as planned, that neighborhood would be gone.

Swift goes on the record to give credit where it’s due, often to government functionaries who exceeded the call of duty, but his writing is far more interesting when he’s on the road himself, or when he’s telling the (too-brief) stories of how Howard Johnson’s or other roadside co-conspirators grew to be a part of American life on the road.

What’s more, I wish he had told us more about the next fifty years, or perhaps, the next twenty. Apparently, the interstate highway system was built for about a half century’s useful life. It has not been properly maintained. As the most dedicated of the government figures, Frank Turner, pointed out, “Highways grow old and wear out at a fairly predictable ages and lifespans, and therefore must be replaced or restored.”

Swift explains, “One federal study suggested that all levels of government should spend a combined $225 billion a year for the next fifty years to rehabilitate surface transportation…they’re currently spending just 40 percent of that, in a country that does 96 percent of its traveling by car and truck.”

So begins a brief discussion about dedicated truck lanes, alternative fuels and other incremental improvements. The bigger question is potentially world-changing and certainly mind-bending, so I offer it as the basis for Swift’s next book. A century ago, visionaries came up with the idea of cars (and trucks), and then, a connected interstate highway system to move people and goods in a safe, reliable, cost-effective way. By the time the interstate highway system was completed in the late 1960s, most of those people were either gone or too old to drive. Given the astonishing public good, the modernization of America, and the tremendous downside associated with our current system, I wish Swift would encourage a discussion so we can decide whether to, and how to:

(a) spend another $11 trillion ($225 x 50 years) to fix and upgrade a highway system conceived before television, McDonalds, cell phones, FedEx or the internet, or

(b) come up with an equally bold conception of transportation that could sustain us until, say, 2112?

Here’s the photo of author Earl Swift as published on the literary festival’s website.

Looks like a strange, unimaginable number, that 2112, but in 1912, when Fisher and his friends were tooling around Indianapolis in their early model cars, 2012 must have seemed as far away, and as impossible, as a 47,000 mile highway system connecting every city and town in what is now called the lower 48 states.

BTW: In researching the author, I found this impressive bit about his interests: “An avid outdoorsman, Swift has through-hiked the Appalachian Trail, circumnavigated the Chesapeake Bay by sea kayak, and traveled the 435-mile length of the James River by foot, canoe, and kayak.” I found it here.

The Big Roads was published in 2011 by Houghton Mifflin Harcourt.

Buy it from Powell’s Books.


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