A Spreadsheet of Old

At the bottom of a very, very old pile I came across a pad of paper which produced nostalgic memories. It was an all-purpose AmPad miniature spreadsheet, of the old-fashioned kind, thus neatly pre-ruled pages. Herewith an image of it. I call it a miniature because, on full-sized jobs of calculation, we used pads of much greater size. But they were essentially the same format you see here but made both wider and deeper.

The old spreadsheet—which also gave its name to the electronic kind—served exactly the same purposes. Ever notice that when you open a new page of Excel, for instance, one of the first tasks is to make the left-most column  wider—because that’s where the descriptive labels usually go? Well, in the old days the paper versions came that way. And, of course, both rows and columns were numbered. The electronic versions introduced column-marking using letters, which made it less confusing to reference a cell.

To be sure, working with the vast, physical, ancient spreadsheets was a bother. You had to have a calculator handy. And in the really early days those were not small and handy but big and bulky and almost too heavy to move.

Yes. Nostalgia. Most of it is of this flavor. Somehow the past appears in a rosy sort of light whereas the present is always in black and white. Until you recall what a major labor it was to revise a column already filled with numbers. All that erasing, all that cursing. Ah, the good-old-days.

Why Can’t We Stop When We’re Ahead?

Occurs to me that humanity has not yet learned to stop when it’s ahead—and leave well enough alone. The occasion for this thought (it’s an old one) is the second failure of our expensive front-loading GE washing machine, Model WBVH6240FWW. In both cases the dial up front, intended to select the kind of wash you want to do, has failed to work.

Up to the time when we bought this machine, we’d owned other kinds that, when they failed, I could, to be sure with lots of study and effort, fix myself. But this GE machine is of the modern kind. It is much more consistently electronically controlled. Therefore failures such as these require replacement of entire structures. The defective part, containing valuable heavy metals and such, becomes a problematic waste—because teasing the traces of gold and other metals out of it is too expensive.

The very forces that produce innovation later produce excess of innovation: too many features, too much razz-ma-tazz. Briefly, and always only briefly, new features benefit producers. But very rapidly every maker has the same features. A simple-enough function, like washing clothes, become Boeing-like complex. We began our household with a simple washer-wringer machine—something like the one I’m showing (link)—which was itself a marvel of technology. It had a simple on-off button. It washed the clothes. The wringer squeezed them dry. Yes, we had to change the water and do some rinsing. It took a little attention—but habit filled in for the future electronics…

My point more broadly is that we could, theoretically, stop when we’ve produced a decent tool. But the madness of letting the Market do our thinking causes, in due time, perfectly useful products to disappear. Things are in the saddle?—something’s in the saddle. If this repair doesn’t do the job, our next washer will be a Maytag wringer washer. Looking around I see that I could get one for about $60-$100—much less than this repair will cost.

Atom Smasher in the Garage

Technology is really about knowledge. I found it instructive and also amusing to discover that the theoretical physicist, Michio Kaku, built himself an atom smasher in the garage of his home—while still in high school! The more formal name for such things is “particle accelerator.” Here is the story as told in Kaku’s book, Hyperspace, p. 6-7:

First, I purchased a small quantity of sodium-22, which is radioactive and naturally emits positrons (the antimatter counterpart of electrons). Then I built what is called a cloud chamber, which makes visible the tracks left by subatomic particles. I was able to take hundreds of beautiful photographs of the tracks left behind by antimatter. Next I scavenged around large electronic warehouses in the area, assembled the necessary hardware, including hundreds of pounds of scrap transformer steel, and built a 2.3-million-electron-volt betatron [accelerator] in my garage that would be powerful enough to produce a beam of antielectrons. To construct the monstrous magnets necessary for the betatron, I convinced my parents to help me wind 22 miles of copper wire on the high-school football field. We spent Christmas vacation on the 50-yard line, winding and assembling the massive coils that would bend the paths of the high-energy electrons.

And Kaku succeeded.  He produced “a magnetic field 20,000 times more powerful than the earth’s magnetic field, which is necessary to accelerate a beam of electrons.” To be sure, most of the time he turned it on, he blew every fuse in the house.

Where there is knowledge, and a will, the most peculiar feats are possible. Fermilab certainly had the knowledge to keep on operating Tevatron, the world’s second largest hadron collider. But Fermilab’s “parents,” read Congress, didn’t want to spend Christmas coiling miles of cable…

In the Mooood? SMS Me.

When the New York Times uses an acronym like SMS without bothering to explain what the letters stand for (even parenthetically), I am sure that I’ve been put out to pasture.

The story, today, was titled “Swiss Cows Send Texts to Announce They’re in Heat.” Brigitte was amused and read me the story, but wondered what SMS stood for. “Occasionally he gets an SMS from one of his cows.” The poor cows have a device inserted into their privates, and the widget can generate a message in one of several languages. Baffled—and humbled. Here I am, the man who can answer any question, trying to link sado-masochism to the barnyard—but the context doesn’t seem right.

Well, I’m still smart enough to use Google. Here’s the explanation for all the rest of you left-behinds. SMS stands for Short Message Service. It’s something that iPhones do.

Contorted Commerce

My entrance into the world now generally called “technology” began with an Apple IIe. I was a rank beginner, and it took me some time to discover that Apple’s general strategy was to obsolete its products on what seemed to be a schedule. This irritated me enough to abandon Apple for IBM; I never bought another Apple product since. The other day our cell phone finally failed. I thought it might be fixable, so naively I took it to a shop. They looked at it and laughed. I ended up with a Samsung product. Satisfying, that. Apple at least temporarily prevailed over Samsung yesterday—and it pleased me that I was helping Apple’s opponent.

I belong to what might be a silent majority—people who treat tools as tools. Especially in the “technology” category—until it too gets absorbed into ordinary reality—the corporate impulse is to exploit the customer by obsolescing product at regular intervals. Microsoft is working on yet another bloody version of Windows. Facebook is terror-ridden because it can’t as yet put ads on smartphones. I’m in the majority that only needs a stupidphone—and I get those free with a wireless telephone contract. Never bought a car except to get some transportation. My ego is big enough without a $50,000 emblem that spends virtually all of its time waiting to be used.

But what about progress? Well, where are you progressing to? The funeral home is a pretty good guess. Back before “technology” appeared, I’m thinking of the Egyptians, the big egos in that day had themselves embalmed. Call it the terminal technology. I’m waiting for the Market to launch LaZer-Cremation as the Baby Boom finally reaches its collective apotheosis. After that we might actually return to normalcy again. It’s coming. It’s coming.

Sauron's Eye

The papers today carry a story about a new camera, called Aware-2, developed at Duke University in a $25 million project sponsored by the Defense Department. It can take a picture made up of 1 billion pixels. The image is taken by 100 tiny cameras, each able to capture an image with 1 million pixels. The camera (about the size of a football) has a computer that merges the products of each camera into the final image, but using the different images singly produces enormous detail of any selected part of the image when desired. Use? Military, defense, surveillance, etc. As you jaywalk across an intersection, a camera like that can look down into the deep chasm of your sweating pores.

Modern technology is really all about optics and computing. The soldier is weighted down by carrying a huge weight of batteries—just to see in the dark, as it were, to communicate instantly, to sense what eyes can’t see, to direct destruction to the machine-seen target. The overhead of all this complexity is getting burdensome—so that the other day, in the Wall Street Journal, I think, there was a story or headline saying: “I don’t want any more features—give me simplicity.”

When Orwell wrote his 1984, little did he imagine what the eyes of Big Brother actually look like—or, for that matter, J.R.R. Tolkien writing about Sauron’s all-seeing eye. Now we know. Let me introduce you to Aware-2. Here’s looking at you.
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Image source: Duke University (link).

The Astrolabe

Measuring and calculating instruments have always fascinated me, hence they’ve appeared on this and the earlier version of LaMarotte before (here, here, and here). During a joint vacation recently, John Magee mentioned the astrolabe. A friend of his is the navigational officer on board of an aircraft carrier. John asked him a while back if he had ever used an astrolabe. The man had not. This got us talking—and left behind an intention to look into the subject. The impression in my mind, when we were talking, was of a round sort of thing sailors had once held up toward the sky—and a vague knowledge that these babies were extraordinarily complex instruments.

Well, herewith a little introduction to the subject. It can’t be summarized in a single post, not even a dozen. The astrolabe is thought to have been invented by Hipparchus of Nicea (190-120 BC; the place is now in Turkey) around 150 BC, thus early in the Hellenistic (read the “modern, scientific”) era of Greek culture. Hipparchus was an astronomer, geographer, mathematician and also thought to be the originator of trigonometry. You now have the flavor of the thing. It turns out that the astrolabe was perhaps the earliest kind of ultra-sophisticated slide rule. The Persian astronomer, Abd al-Rahman al-Sufi (903-986) described more than a thousand uses for it, not least astronomy, time calculation, navigation, and as a trigonometric table.

Here I’ll deal narrowly with the simplest kind, known as the mariner’s astrolabe—and a single use of it, determining your latitude at sea from a single reading of the sun’s angular position. But it is well to described the actual device. It consisted of four components, a base plate known as the Mater (mother), a rotating structure above it called the Rete, a Plate that fit between the two, and a rotating ruler-pointer called the Alidade. An excellent diagram of these parts is shown on the website, The Astrolabe (link). Note that the Plate could be changed. Commercially available versions come with eight different plates one can insert depending on the application.

Herewith a picture of the front and back of a traditional astrolabe produced and sold by Norman Green (link). This one costs $180. The site shows others as well. The rete is the grayish structure on the first, the gold is the mater. The alidade, used in detecting the sun’s altitude, is shown on the second picture; it has visible sighting slits. The front has an additional pointer-ruler.

From the same page comes this simplest of astrolabes, the mariner’s ($195). It consists of a mater and an alidade and is used for obtaining one’s latitudinal position on earth.

How this instrument is used is illustrated by this cartoon taken from Wikipedia (link).

The user suspends the astrolabe (it shouldn’t actually be held in the hand as shown) and then aligns the alidade until the sun (or star) is visible through both slits. For navigation, the sighting should take place when the sun is at its highest point that day.

Latitude and longitude? Lines of latitude are horizontal lines drawn on globes and mark degrees of latitude (width—from Latin latus, wide). Why are they called degrees? The following graphic will illustrate that.

The globe, with the two poles marked as 90°, the equator as 0°, is divided into four triangles as show in blue. As the graphic shows, latitude 45 is a 45° degree elevation above or declination below the equator. If you draw a line from the 45° point of the eastern to the same point of the western triangle in the northern hemisphere, you get a line of latitude. Similarly in the southern hemisphere. By convention, therefore, latitudes are marked N or S or the southern equivalent is rendered as a negative number. The largest latitude circle is at the equator. The circles grow smaller as we go north or south and they vanish into a single point at each pole.

I show this globe at a tilt by way of emphasizing that the earth’s axis is tilted with reference to the sun’s—by 23.5°. This becomes important in finding our latitude using the astrolabe. The earth’s tilt causes our seasons; thus the sun’s altitude changes daily throughout the year. If the earth’s axis were not tilted, the angle we detect using the astrolabe would suffice, by itself, to serve as a simple indicator of our latitude; to get latitude, we would simply deduct the observed angle from 90. This becomes evident from the following graphic (courtesy of this tutorial). It shows the ecliptic, or the path of the sun, in relation to our orientation north to south. This means that in each hemisphere, the sun is beneath or above the equator depending on the time of the year:

The angle we measure using the astrolabe must be adjusted by this ever-changing declination of the sun relative to our equator. The point where the ecliptic crosses the equator twice a year is known as the equinox. At that point the declination is 0°. The sun is directly above the equator; night and day are therefore the same length. At other times the declination is positive (sun is above the equator), maxing out at 23.5° at the summer solstice, or negative (sun is below the equator), maxes out at -23.5°, at the winter solstice. In this field the word declination is used; to be sure, it is actually (as shown above) a declination followed by an inclination, but one word is used and the perceived direction of this apparent solar movement is indicated by positive or negative numbers—or zero for the equinoxes.

The navigator using an astrolabe, having correctly identified the angle of the sun, its altitude, must next calculate the declination. For this he or she will need to know the day of the year, thus have a good calendar, and use an equation. The calendar should be such that it informs the person of the number of the day. August 31 this year, for instance, was day 243. The equation to calculate the declination is the following:

declination angle in radians = 23.45 * pi/180 * sin(2*pi*((284+day)/365.25))

To render this for Excel, pi would be rendered as PI(). If we substitute 243 for the day, the result of this is 0.143834 radians. To rendered this into degrees, multiply by 180/pi. The result is 8.241088°. This is the sun’s declination on August 31.

Supposing that our astrolabe reading was 55.5. Having that and the declination of the sun for the date, we can calculate the latitude. The formula is:

latitude = 90 - (altitude - declination)

If the declination comes out negative, which it will do from the autumnal to the vernal equinox, the declination is added to altitude rather than deducted.

When we insert values for the words in the equation, in our case 55.5 and 8.24, the latitude for that sighting is 42.74° Is that correct? Well, I’ve come close. My actual latitude here is 42.4243°—but that’s not too bad when measuring the solar altitude with bits of cardboard rather than a fancy $195 astrolabe from Mr. Norman Green.

Longitude? In a word, you need a very accurate timepiece keeping Greenwich, England time—and one of the more muscular astrolabes able to calculate local time. But as for details, not this time. I all worn out with latitudinal astronomy, radians, degrees, declinations, and inclinations. My own inclination is to have lunch.

Quick Abacus Tutorial

Take a look at this picture of the Chinese abacus, also known as the suanpan. This picture is from Wikipedia’s article on the abacus, which also treats of many others. The picture shown depicts the number 6,302,715,408. Thus the right-most column is units and the left-most column is billions. If all the beads were away from the center bar, the number represented would be zero. The second column from the right, as you can see, is 0. Now for an explanation.

The topmost and the bottom-most beads are never used in decimal calculations. I’ll return to their uses in a moment. First, what do the other beads represent? The bottom bead on top represents 5, the bottom beads represent 1, but the last one isn’t used. The number 8 in the first column is shown by pulling down 5 and pushing up 3: 5 + 3 = 8. The maximum number we can render in each column, therefore is 9—remembering that the top and bottom bead are Off Limits, as it were.

Now suppose we wanted to reduce this number by 3. Simple. We just move the three bottom beads of the first column away from the center. That leaves the top bead still in place: 5. But let’s instead add 3 to the original number. Here we must proceed one number at a time. We move one bead up from the bottom, making 9. Two more beads to go. But we can’t move any more beads in the first column; they’re all used up. Therefore we move one bead up in the bottom part of the next column over—and zero out the first column. One more to go. We add this one to the first column again. And we can do so because it has been zeroed out in the last step; it can hold a unit once again. The result is that the 8 has now turned into 11: 6,302,715,408 + 3 = 6,302,715,411. A nice do-it-yourself demonstration is available here.

Division and multiplication become more complicated, but in essence one does it on the abacus just as one does it on paper, keeping the intermediate results on another part of the abacus. No paper needed. When these devices came into use, paper was not as common as it is today. Abaci are big because they need extra space to record division and multiplication steps. The last post shows a Chinese abacus.

There are many kinds of abaci. The Japanese soroban, for instance, omits the topmost and the bottom-most beads; it is optimized for decimal calculation. But then the question arises, what possible use is the full Chinese suanpan? Oddly enough, long, long before computers came into use and hexadecimal math became the bane or blessing of computer-types like me, the Chinese evidently used that numerical system—and the suanpan can let you do math in hex. It was introduced in the fourteenth century of our era.

The hexadecimal system is base-16 as the decimal is base-10. In decimal the highest number is 9, in hexadecimal 15. Now if you use both of the top beads and all of the bottom beads, you get 16 values in each column, from 0 to 15. Here is a bit of information you didn’t know you needed: in hex the numbers run like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. F therefore is fifteen, shown on the Chinese abacus by moving all of the beads towards the center. And, not surprisingly, the number Hex 10 actually stands for decimal 16.
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This is a repeat of a popular post first presented on September 24, 2009 on the earlier version of this blog.