Archive for July 2017

When someone asks me how I’m doing, I habitually answer, “Fine,” because that’s what social convention dictates—whether or not I really am fine. Most people probably don’t want to hear the detailed truth, and would be sorry they asked if I told them. Similarly, when people ask what I do for a living, more often than not they’re looking for a quick and easy way to categorize me, rather than a litany of the sundry and somewhat unconventional means by which I earn a living. So I tend to oblige with a short answer that requires no further discussion.

One day, however, I was at a party, and being in an uncharacteristically charitable mood, I decided to tell people what my occupation really is. One guy I spoke to—let’s call him “Bob” (for that is his name)—seemed particularly intrigued by the notion of Interesting Thing of the Day. He scribbled down the URL and promised me he’d send me some suggestions for topics to write about. A few days later, Bob sent me a link to a news article that led off with the following tantalizing claim: “Now we may know why the South lost the Civil War: Confederate time was about a half-hour slower than Yankee time.” I had heard of famous historical blunders based on confusion over differing calendars, but not over differing clocks. How cool.

Time Is On Our Side
The article never delivered on the teaser, though. It did discuss the fact that the North and the South used different methods of reckoning time, and it went on to speculate that those differences might shed light on the final moments of a Confederate submarine that disappeared shortly after sinking a Union ship. The time differences had nothing to do with the outcome of the war, but the reason for the differences was quite interesting indeed.

The South based their timekeeping on apparent solar time, in which noon is the moment the sun reaches its highest point. This is a sensible enough approach, but it has two problems. First, because of the angle at which the Earth is tilted and the elliptical shape of its orbit around the sun, the interval between noons on two successive days is not identical throughout the year. Although one day may be only a few seconds shorter or longer than the next, the cumulative effect of those extra seconds can mean a difference of nearly 16 minutes over several months. Second, the sun arrives at its apex at a different time depending on one’s longitude, so “noon” on the east coast will be earlier than “noon” on the west side of the state—thus making synchronization tricky.

Just an Average Day
The problem of irregular day lengths is addressed by the use of mean solar time, in which all days are exactly 24 hours long (based on the average noon-to-noon interval)—at the cost of being somewhat out of sync with the sundial. The North, in addition to following mean solar time, used Washington, D.C. as the reference point for noon. These two facts combined to make Union time about 26 minutes ahead of Confederate time. It was not until 1883 that standard time zones were first adopted (thus eliminating the problem of local variations in mean solar time); they became law in the U.S. in 1918.

As for the equation of time, here it is: EqT = apparent solar time – mean solar time. This equation (or a table derived from it) is what you need to use if you have a sundial in your garden, since it will almost always be out of sync with your clocks. If you plot this equation on a graph, it makes a pair of broad curves over the course of a year. On the other hand, if you were to plot the position of the sun in the sky (from a fixed point on Earth) at the same time every day for a year, it would make an asymmetrical figure 8, a shape known as the analemma—the Latin word for sundial. —Joe Kissell

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More Information about The Equation of Time…

The article Bob told me about, from the Charleston (South Carolina) Post and Courier, is Solving Hunley sinking mystery may be matter of time, experts say by Schuyler Kropf.

Here’s a great time-lapse picture of the analemma.

Other resources on solar time, the equation of time, and the analemma:

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If you do have a sundial in your garden, you might want to purchase a handy Equation of Time Plaque to help you figure out what time it “really” is. Looking for a sundial? has a fine selection.

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You may think of yourself as a scrupulous person—you may have even said indignantly when accused of some fault, “I have scruples!” But exactly how many scruples do you have? If you’ve recently finished a meal or taken a stroll down a gravel-covered path, chances are you have more scruples now than you did an hour ago.

The calculation is quite easy to make: there are 4,900 scruples in a stone, though a single stone can also be a scruple. You may be thinking this is like saying, “4,900 angels can dance on the head of a pin, though a single pin can also be an angel.” But that’s just plain silly. I don’t know a single angel who can dance on the head of a pin, and besides, I must imagine that angels have much better things to do with their time. On the other hand, both stones and scruples are quite concrete, everyday things that sometimes have extended or metaphorical meanings, and in the case of this pair of terms, those meanings intersect in interesting ways.

Pounding Stones
I set out originally to talk about a unit of weight called the stone. When I was in England last year, I heard several people discussing matters of weight using the term “stone,” as in “That diet worked so well I lost two stone.” I gathered that this must be considerably more than a pound, but nobody I asked seemed to know for sure exactly what the weight of a stone was. They could quote me the current exchange rate between pounds sterling and the U.S. dollar, but when asked how many pounds were in a stone, most people thought for a moment and said, “probably around 15 or 20.” A stone, it turns out, is a Roman measurement equivalent to 14 pounds (6.4kg). And apart from listing all the other archaic equivalences—which, I’m sure, regular readers have had quite enough of this week—that’s about all you can really say about a stone. Not all that interesting.

A Rock and a Hard Place
But as I was looking through long lists of obscure units of measure (you can’t fathom how many I looked at), I came upon the humble scruple. The English word scruple originated with the Latin scrupus (‘sharp stone’), a diminutive form of which was scrupulus (‘small sharp stone’)—in common usage, the particular sort of small sharp stone that gets stuck in your sandal, causing extreme discomfort when you walk. Both of the main figurative meanings of scruple (“a very small amount” and “reluctance due to moral misgivings”) are extremely ancient and existed in Latin as well; I was not able to determine which of them came first. But eventually “a very small amount” came to be codified as 20 grains—that is, 20 barley grains (slightly smaller than grains of wheat)—or 1/24 of an ounce (about 1.3g). This was an apothecary measure, but then, it goes without saying that pharmacists need to have scruples.

I think the image of moral discomfort as a rock in the shoe is delightful. (“I’m sorry, Cindy, but I must reject your tantalizing proposal. The mere thought of it gives me rocks in my shoe.”) I also find it curious that words referring to two very different senses of “stone” came to have significance as units of measurement. And it makes me wonder: is it impossible, or obligatory, for someone with scruples to get stoned? —Joe Kissell

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More Information about Scruples and Stones…

I don’t know how I managed to stumble on so many sermons this week, but On the Rocks, a hortatory discourse by W. Carl Ketcherside, does say some interesting things about scruples.

Other resources for the scrupulous reader:

A regulation curling stone weighs about 3 stone.

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The origin of the word scruple is just one of the fascinating stories in Charles E. Funk’s Thereby Hangs A Tale: Stories of Curious Word Origins.

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As an American, I have always been a bit ambivalent when it comes to units of measurement. I learned units like inches, pints, and pounds first, but all through elementary and secondary school, the metric system (or S.I., Système International) was taught, along with dire warnings that we’d better get used to the new measurements because the U.S. was going to be giving up Imperial units Real Soon Now. That would have been fine with me, because I’m fluent in meters, liters, and grams too, and they all make more sense to me than their Imperial counterparts. (Temperature, strangely, is the exception: I can’t seem to switch my brain out of Fahrenheit.) The entire world—excluding us wacky Americans—has come to the sane conclusion that units of measurement based on outdated and arbitrary standards should be abandoned, and that everything should be based on easy-to-calculate units of ten.

Everything, that is, except time, the measurement of which requires dealing in inconvenient quantities such as 60, 12, 7, 365, 31, 30, 28, and every so often, 29 and 366. Why shouldn’t time be measured in units of 10, 100, and 1000? Seconds, hours, weeks, and months, after all, are simply arbitrary divisions of days, seasons, and years. Why not divide them up in a decimal-friendly way? And why not choose a system that is inherently immune from stupid computer glitches on the one hand, and free from religious biases on the other? It turns out that there have been numerous proposals to do exactly that.

Days (and Years) of Our Lives
Let’s back up a bit and consider a few basics. Everyone agrees that time measurements should be based on regular, observable phenomena such as the dependable fact that the sun rises and sets every day, and that the Earth’s position relative to the sun follows predictable, year-long cycles. One could argue that the notion of a “day” having a fixed duration is a bit of a fiction, since the hours of sunlight vary according to season and latitude, but I think most people are content taking an average (i.e., a mean solar day) as the rule. And of course there’s the whole leap year problem, but that need not hold up an entire timekeeping revolution. Though the idea of a “day” and “year” are with us to stay, however, all the other units—seconds, minutes, hours, weeks, and months (and even seasons, depending on where you live)—are arbitrary divisions that are ripe for revision.

The first serious attempt to slice up the clock and calendar decimally happened in France as a consequence of the French Revolution. The new government instituted a republican calendar that consisted of 12 months of 30 days each, months bearing names suggestive of the season in which they fell (but only, of course, in France). An extra five days of festivities were added at the end of each year (not part of any month) to make the solar cycle work out. Each month consisted of three “dekades,” or 10-day weeks. New clocks had to be designed and built, too. A day now had 10 hours; hours had 100 minutes, and minutes had 100 seconds. Because the months were not that much different from existing months (breaking the strict unit-of-10 rule), they were relatively easy to get used to. But having a “minute” that was almost a minute and a half long, and an “hour” that lasted almost two and a half hours, was too much. The republican government fought a losing battle to institute the new timekeeping system from 1793 until 1805, when it was finally abandoned.

Over the years, numerous other proposals have been advanced for dividing time into units of 10, with the common thread being that there’s always a basic unit of time (whether or not it’s called an “hour”) that lasts 1/10 of a day. To deal with the problem of that being a rather unwieldy period of time, smaller units have been proposed, such as the “centiday” or “decihour,” which would be 1/100 of a day, or about 14 minutes according to current measures. Multiples of 2 and 4 centidays are close enough to current half-hours and hours to give a reasonable means of making mental conversions.

.Beat It
One exception to the “centiday” solution is Internet Time, a standard promoted by Swiss watchmaker Swatch. In Swatch’s system, the day is divided evenly into 1000 units called “.beats”; each .beat lasts 1 minute, 26.4 seconds. Internet Time is designed to be universal, rather than local—so if you say an event is going to occur at @435 .beats (which is how Internet Time is notated), that represents a fixed time that works anywhere in the world. Beat 0 is defined as midnight in Biel, Switzerland, where the Swatch headquarters is located. The downside to the lack of time zones, of course, is that Internet Time has no consistent relationship to the cycle of the sun; you simply have to memorize what .beat range constitutes periods such as “morning,” “afternoon,” and “evening” in your local area—and then recalculate if you travel.

This illustrates another problem with any decimalized time system: where and when do you start counting from? By international agreement, all time zones around the world are calculated based on Greenwich Mean Time, that is, the time on an arbitrary line of longitude running through Greenwich, England, that we’ve designated the Prime Meridian. But just as Internet Time measures from a different starting point, any decimal time measurement will have to declare some location as the “starting point,” and either calculate local time zones accordingly or bypass the whole notion of local time as Swatch did and let everyone fend for themselves.

Remembering Z Day
In decimal time schemes that also deal with weeks, months, and years, there’s an even trickier problem. What should count as day 0? In other words, let’s say decimal dates were represented as YYYY-MM-DD, with more Y’s added as needed. Which date is 0000-01-01? Some would say, sync it up with the Gregorian calendar—but that perpetuates its Christian bias. Others say, pick a date, any date (such as midnight on January 1, 2000 or July 13, 1903) and just deal with it; presumably, events that occurred before that date would have to be represented with a negative number.

The notion of decimal time appeals to my sense of logic—though it would appeal more if a year were, say, 100 or 500 or 1000 days long. That would make the math work out much more conveniently. (Some proposals, by the way, try to divide the year up into 100 “days” of about 88 standard hours each, which is better for calculations but considerably worse for human beings.) But if meters and liters are a tough sell in the U.S., metric time is going to be tougher still. Maybe in a century or two…hmmm, century. I guess we use a kind of metric time after all. —Joe Kissell

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More Information about Decimal Time…

For more information on decimal/metric time, see:

Want to check the current Internet Time? See this page at Swatch also has a PDF brochure on Internet Time.

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The official Interesting Thing of the Day style guide stipulates that within reason, all measurements expressed in American or British units (pounds, gallons, miles, etc.) should also be given in S.I. (metric) units. We do this partly because many of our readers are located in other parts of the world, and partly because metric units just make so much more sense. And yet, all units of measurement are ultimately arbitrary, and however convenient calculations may be with systems based on the number 10, there are always other ways of looking at things.

Faster than a Speeding Snail
When I was in high school, for example, I heard someone use the expression “furlongs per fortnight,” an odd juxtaposition of measurements that struck me as very funny. I thought it would be interesting to figure out how to express the speed of light in furlongs per fortnight. It turned out to be a huge number, over 1.8 trillion (1,802,617,500,000, to be exact). A furlong is of course defined as 40 rods, a rod being an equally obscure unit of length measuring 16.5 feet. Thus you can also express a furlong as 220 yards, 660 feet, 201.2 meters, or 1/8 of a mile. (The only people who normally work with furlongs are those who design race tracks for horses—clearly, an animal whose height is measured in hands needs a special term to describe how far it runs.) A fortnight is 14 days (or nights, as the case may be). So something moving at the speed of one furlong per fortnight (f/f) would be moving very slowly indeed. Interestingly enough, though, 1 f/f is almost exactly equal to 1 centimeter per minute; therefore, furlongs per fortnight would be a good unit of measurement for a snail’s pace, which ranges from a bit less than 1 f/f to about 30.5 f/f.

Engineers like to use the term “furlongs per fortnight” when they encounter an unknown unit of measurement or can’t figure out what the best unit is to express some value. Because this term has come into common slang use in a few academic fields, it often shows up in tongue-in-cheek questions on exams in physics, math, and engineering. For example: “Determine the velocity of projectile x at time t. Express your answer in furlongs per fortnight.”

A Googol of Possibilities
“Furlongs per fortnight” has also famously appeared in Google’s under-publicized calculation feature. If you need to do a calculation or convert one type of unit into another, you can type what you want into Google’s search box (or the Google search field in your Web browser, if it has one). Google can work with almost any conceivable unit of measurement. Here are some examples:

  • Enter 315+412 and Google returns 727
  • Enter 4 tablespoons in milliliters and Google returns 59.1470594 milliliters
  • Enter 65 miles per hour in kilometers per hour and Google returns 104.60736 kilometers per hour
  • Enter 35 miles per gallon in rods per cup and Google returns 700 rods per US cup
  • Enter 4 cubits per fathom in feet per yard and Google returns 3 feet per yard
  • Enter speed of light in furlongs per fortnight and Google returns 1.8026175 x 1012 furlongs per fortnight

The possibilities are endless. And the point of all this is…well, I’ll need to think about that. Give me a few microcenturies, and I may be able to come up with one. —Joe Kissell

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More Information about Furlongs Per Fortnight…

Jim Jardine pointed out the correlation between a snail’s pace and furlongs per fortnight on his page Furlongs Today.

Other furlongs-per-fortnight resources:

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Looking for more Google tricks and tips? Check out How to Do Everything with Google by Fritz Schneider, Nancy Blachman, and Eric Fredricksenor Google Hacks: 100 Industrial-Strength Tips & Tools by Tara Calishain and Rael Dornfest. For help with all those basic math skills you were supposed to learn in school, check out Everyday Math Demystified by Stan Gibilisco.

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Like most guys, I love tools, especially if they’re expensive and so specialized I’ll only use them on rare occasions. Bonus points if they require electricity. My wife, knowing this about me, bought me a groovy little ultrasonic digital laser-guided measuring device as a gift. It even came with a holster. Now I can measure the size of any room (even its area and volume, if I need to) in just seconds. Morgen’s explanation for why she chose this gift was that she was tired of having to hold one end of a tape measure while I dragged the other end across the room. But I think it may have been that she thought I looked extremely goofy using my standard device for making linear measurements: my forearm.

Is That a Ruler in Your Pocket?
At some point years ago, I picked up the seemingly useless piece of information that an ancient unit of measurement called the cubit was the distance from the elbow to the tip of the middle finger. For an average adult male (at least, average as of a couple of millennia ago), a cubit works out to about 18 inches (45.7cm). Cubits were a standard unit of length in Sumeria, Egypt, and other parts of the Middle East long before anyone dreamed of an arbitrary, decimal-based measuring system. Cubits were most often used in the context of building; if you have an English Bible published before the mid-20th century, it probably lists the measurements of Noah’s ark (among other things) in cubits.

Not long after learning this tidbit, I began discovering how useful such a built-in measuring device could be. I don’t always carry a tape measure with me, but I frequently need to estimate whether, for example, a piece of furniture will fit in a certain room. Knowing the approximate length of my arm is surprisingly handy, because it’s extremely easy to use for rough measurements.

Hand, Hand, Fingers, Thumb
The cubit was just one of numerous units of measurement based on the typical size of body parts. Here are a few more:

  • foot: It probably goes without saying that the unit foot was based on the length of a man’s foot.
  • span: Stretch out your hand so that the tip of your thumb is as far away as possible from the tip of your pinky. That distance is called a “span,” which for most people is almost exactly half a cubit.
  • handbreadth: The width of your four fingers where they meet the palm—usually about 4 inches—is a handbreadth or sometimes just a “hand.” The height of horses is usually expressed in hands.
  • digit: The width of a finger, which tends to be about 2cm (about 13/16 of an inch).
  • thumb: The width of a thumb, which was later used as the basis for the inch.
  • fathom: If you stretch out your arms to either side of your body as far as they’ll go, the distance between the tips of your middle fingers will be very close to your height, or about six feet—your own feet, that is—a length also known as a fathom.
  • handful: Although we normally use the word handful in the informal sense of “just a little bit,” your hand can serve as a fairly repeatable measure of volume for dry goods such as grains, beans, and seeds.

The reason units of measurement like these fell out of favor is that they vary from one person to the next, so if you need accuracy or repeatability, they’re not the best choice. (It turns out, for example, that my personal “cubit” is 18.375 inches (46.67cm). I always was an overachiever.) But for quick-and-dirty estimates when you don’t have a standard measuring device handy, they can’t be beat. —Joe Kissell

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More Information about Body-Based Units of Measurement…

Information on cubits and other body-based measurements:

As long as we’re estimating, American readers might want to keep in mind that the length of a US dollar bill is just a bit over 6 1/8 inches (or a third of a cubit for all practical purposes).

And the ark, if you really want to know, was specified as being 300 cubits long, 50 cubits high, and 30 cubits wide.

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