Showing posts with label measurements. Show all posts
Showing posts with label measurements. Show all posts

Tuesday, December 20, 2011

Johnny got the bigger piece of cake!

kw: book reviews, nonfiction, history of science, measurements, metric system

Should you decide to take a jaunt from Philadelphia, PA to Salisbury, MD, you'll wind up traversing the length of the state of Delaware, much of it on a stretch of DE 1 called the Korean War Veterans Memorial Highway. Things go swimmingly enough as you follow Interstate 95 for a few miles, then turn south on DE 1.

A few miles further, you'll see this sign. (This is a crop from a Google Street View image.) I recall the first time I drove this way, thinking, "I didn't know Delaware was quite that long." Almost immediately, if you tend to watch for mileposts like I do, you'll notice one that announces "Mile 101". What is going on here?

In 1993, when the route was renamed and made into a freeway, it was measured off in kilometers, according to the then-current federal standard. Km-posts were erected and the exits were numbered accordingly. Starting ten years later, the km-posts were replaced by mileposts, except for a 27 km / 17 mile section near Smyrna, which was only "converted" very recently. Artifacts of partial conversion can be found at this Colorado State U page. Milepost 101 is almost exactly between former km-posts 162 and 163.

This changeable attitude at both federal and state levels toward how to measure our highways has kept the United States as the only major country that clings to standards of measuring that are not based on the metric units used everywhere else in the world except Myanmar (Burma) and Liberia. It exposes a weakness of representative democracy, the weakness of the representatives themselves.

The science, history, sociology and politics of measuring are surveyed in quite entertaining fashion in World in the Balance: The Historic Quest for an Absolute System of Measurement by Robert P. Crease. The need to measure things accurately begins by about age four, when a child realizes that a stack of several blocks is no bigger or smaller than those same blocks all spread out. At the very next dessert time, she is liable to either gloat ("My piece of cake is bigger, tee hee") or complain ("No fair! Johnny's piece of cake is bigger").

It would be easy for such a book to get hopelessly scattered. The author wisely uses just two case studies (Chinese measurement systems prior to 1911, and west-central African gold-measurements prior to the 1800s) to show the gamut of weights and measures and how they were influenced by their social setting.

This is a key theme of the book. Measurement is a social phenomenon, a social action. A hermetic miser may obsessively count and re-count his money, but most of us have no need to count anything until we make a transaction. A wise shopper watches where the butcher's thumbs are when the scale is measuring a cut of meat. Few will go so far as to bring a calibrated weight to check the scale; we trust that an inspector takes care of such niceties. Such trust underlies all commerce. Unfair measuring practices long predate Biblical injunctions not to make the shekel small and the bushel great. In a late chapter the author takes note of a "ruler" that is shorter than the standard, used by crooked lawyers to "measure" a damaged area about which they are suing.

The main historical narrative concerns the gradual conversion of most nations to a system that arose amidst the revolutionary fervor of the French Revolution, culminating in two precious artifacts still kept in a vault in Paris, the 1799 Metre and Kilogram standards, made of platinum. Though these were superseded two generations later by the platinum-iridium standards kept just outside Paris at BIPM (Bureau International des Poids et Mesures or International Bureau of Weights and Measures), they remain unique objects. Yet they and their successors are obsolete.

Starting in the mid-20th Century, the meter was redefined several times, and is now tied only to the speed of light. Now that light velocity in a vacuum is understood to be absolutely constant, unaffected by motion, gravitational potential or any other "environment", it serves as a standard for distance and time measurement that does not depend on the size of Earth, or even on its existence!

Although the Kilogram standard artifact is not yet wholly replaced with an absolute measure, this is expected in 2015, at the next meeting of the appropriate standards setting body, the CGPM (Conférence Générale des Poids et Mesures or General Conference on Weights and Measures). The new Kilogram will be defined based on either Planck's Constant or Avogadro's Number, or perhaps both. Conference members are optimistic that the final details can be worked out by then. Meanwhile, standards-checking still relies on a precious metal cylinder weighing just over 32 troy ounces, and thus worth about $45,000 on the bullion market.

I recall learning the metric system in 1962, when I first took high school Chemistry. I became familiar with the cgs system, for centimeter-gram-second. My first year of college, I was brought up to date with the 1960 world standard, the MKS system, for meter-kilogram-second. Then in graduate school, the units didn't change, except in fiddling detail, but the name did, to SI (Système International or International System). As it happens, it is the most international system we have going! Assuming an absolute Kilogram is defined in 2015, a process that has been going on for 230 years will be nearly complete. It just remains to get one major country to convert to SI … mine!

I am ready. I know my height is 1.83 m and my weight is 98 kg. The second at least is the same the world over, so my age of 64 years and just over a month needs no conversion (and at 10:00 pm tonight, PST, it will be almost exactly 1.802 billion seconds).

In his epilogue, the author returns to the sociological implications of measurement. He had earlier introduced the new words "metrosophy" and "metroscape" to express the philosophy and environment that surround our ever-more-measured life. Will our measurements continue to define and redefine who we think we are? To what extent will it affect us that the standards on which our measurements are made no longer depend on the length of our arm or hand or foot, or the beat of our heart or the speed of a falling apple? As long as the meat I pay for does not include any of the butcher's thumb, I don't need to care. But if one day I decide to vacation on the Moon, it will be very important to know very, very accurately where my landing will be. I'd hate to make an error of 5 parts per million and run out of fuel a couple of kilometers up!

Saturday, November 20, 2010

Calibrated pace

kw: measurements, walking, animals

During a walk today, I decided to re-calibrate my pace. The schoolyard running track was gravel until recently, when they put on one of the new rubberized, permanently marked tracks. Decades ago I calibrated my pace on a quarter-mile track with good markings at 5.6 feet, or 1.71m. That is also 942 paces to the mile.

Modern tracks are all in meters. It took 62 paces to go 100 meters, and both trials I measured, my last pace went long about 10 cm. So 100.1/62 comes to 1.615m or 5.3 feet; 997 paces to the mile. This is where the mile gets it name: mille pas or "thousand paces".

I first calibrated my pace as part of a field mapping class, when I was a Geology undergraduate. While we did most of our mapping exercises using an alidade (a calibrated telescope, but primitive compared to a theolodite) and plane table, we had to do a few the Boy Scout way, using a compass and pacing to get bearings and distances.

A steady pace works well enough on flat ground, but we soon learned how much it varies when the ground gets hilly, and of course much of our work was done in a cliffy area where pacing distances just wasn't an option. Triangulation from a well-measured base line provides the most accurate survey.

Update on our mouse problems (see This mouse got away): I checked the rat-size glue trap for a couple of days, then not until today. It contained a very dead mouse. I felt bad that I didn't find it in time to put him out of his misery quicker. But we thought he wasn't there; we saw a mouse in the garage the day after I wrote that post, and that one we caught with a snap trap. I put a new glue trap in the crawl space, in case they still have a way to get in. If I keep catching mice there, I'll have to go in again and see if there are holes to fill I missed the first time.

Thursday, September 18, 2008

Fogged in

kw: musings, reading, measurements

In the former post I closed with the statement that Minders of Make-Believe is well written, just rather dense with facts. I am not satisfied with that statement. Reading other books goes smoother. I remembered noticing that the pages looked "more packed." So I did some measurements, including a Fog Index.

The Gunning Fog Index is a statistical measure of how hard it is to read a piece of text. One gathers three numbers and calculates from them a number that estimates the level of education needed to read the text. The three things are
  • W = The number of words in the selection; this should be at least 100.
  • S = The number of sentences.
  • C = The number of "complex words", meaning words of three syllables other than those formed by adding -er or -ing to two-syllable words.

These are combined according to this formula:
F = 0.4*((W/S)+100*(C/W))
This means, the average words per sentence plus the percent of complex words, all multiplied by 0.4. If the result is 12, one needs to graduate from high school to easily read the text. Few commercial publications have Fog Indices greater than 10. "Reader's Digest" scores a 9.

I tested Minders and a book I am currently reading which I'll here call simply Future, by analyzing a full page of each.

For Minders, W = 423, S = 14, and C = 48. W/S = 31.4 and 100*C/W = 11.4. This yields F = 17. Seventeen! That implies at least a Master's Degree!! The market for such a book is restricted indeed.

For Future, W = 349, S = 16, and C = 39. W/S = 22.8 and 100*C/W = 11.1. This yields F = 13.5. That implies a college sophomore. The market is much larger, but is still a small fraction of the U.S. populace.

The type face of the two books is the same, but Minders has tighter leading ("ledding"), the spacing between lines, so it has 37 lines per page, while Future has 31 lines per similarly-sized page. Both the word count and the line count indicate that the former book has 1.2 times as many words per page. They have nearly identical words per line of type. Since they both have about 350 pages, the one book is equivalent to a 420-page book, compared to the other.

Now, I have a 17-year or greater education (two years beyond my MS), but I found Minders hard to read for extended periods. It is interesting, but it simply requires a lot of work. So I revise my statement: Minders is well-written...for an ordinary soul with a PhD in history.

P.S. The Fog Index of this post is 9.6.