Ounce-Centimeters of Fury

By The Metric Maven

Bulldog Edition

My friend Dr. Sunshine is a player of Table Tennis. He has spent a considerable amount of time practicing. The result of all this effort is that he finally cracked a 2000 rating in Ping–er–uh, I mean Table Tennis. The good doctor then had to explain what a 2000 rating means. I then realized that indeed he’s good. My meager understanding does not stop me from offering a less than informed opinion on the subject. I then asserted “I’m sure you’re really good, but you’re no Randy Daytona.” Dr Sunshine then looks puzzled and asks “who?”  After I explain, he offers his patented countenance of disapproval and states: “I hate that movie.”

In order to engage my enthusiasm concerning Table Tennis,  Dr. Sunshine indicates I should like it, as it’s an international game, and is completely defined using the metric system. I had given this little thought until my friend Pierre sent me this image and a link to the rules of Ping Pong.

Don't buy a cm from this rat.

I took one look at the diagram, and there it was, centimeters. I knew who was to blame here, it had to be an American, a denizen of the United States. No one in Australia, the UK or New Zealand would spell centimeters with an er. This was yet one more example of using centimeters as a pseudo-inch surrogate for Olde English, rather than descriptively using millimeters. I also noticed that the image was a good illustration of how Americans will come up with ad-hoc excuses to use centimeters and then violate them immediately. Do you notice anything interesting about the dimensions?  Let’s change them all over to millimeters as nature intended for a closer look, and then explore the basis for my objections to the original diagram, and also to this new one:

Countries which metricated long ago, have preserved the junk DNA of centimetres as a vestigial inch measure, and seem to believe they must be preserved. The canonical example is human height. In countries which have long been metric, they generally use centimeters. My height is 179 cm in their view. I find 1790 mm more expressive, which has been vociferously rejected by citizens of long time metric countries. They usually say something like: “That’s crazy Metric Maven, you don’t need that kind of precision for a person’s height.” The argument for this continued use of centimeters is what I call The Implied Precision Fallacy. It assumes ahead of time there is a known optimum dimension for each “type” of measurement, and that you choose the unit depending on what is being measured–but not too small, because that’s too precise, and implies you need that much precision when you don’t, and that you are measuring to this precision which you aren’t. This appears to be some strange pseudo argument which relates back to barleycorns, inches, feet, yards, rods, furlongs, miles and leagues. Choose the right one for your measurement needs! In fact choose two units!—and be 5 foot 10 inches tall. It’s a better system because of this choice and not too much precision! Ask David Gallagher.

When I was in Junior high I recall receiving a report card which listed my height as 68.5 inches. My mind halted, and for an instant, it rejected the strange measurement. Why on earth didn’t it say 5′ 8 1/2″? Inches alone had no meaning, but as I later realized, they were simpler to measure and simpler to express. They are one unit, not two, why use two? It was simple cultural inculcation that caused my “lack of feeling” for straight inches. It was because everyone around me used mixed units from the time I was born. I see those who argue that centimeters are for body measurements as suffering from the same Olde English cultural inculcation in a more vestigial form.

The idea of choosing the “right sized” unit is constantly promoted, and implemented in an inconsistent manner when Olde English measures are used. The Olde English “right sized” unit argument is almost universally invoked to justify centimeters when using metric–but ignored in Ye Olde English when convenient. For instance, you are in an airplane, what is your height above the ground? Say it’s 30,000 feet. Why did you not use 5.68 miles? Isn’t that closer to the “right” base unit for unnecessary precision? Feet are just too small of units.  Perhaps 45.45 furlongs?–is that more optimum? 10,000 yards? Should we use miles above a mile and switch to feet below that?–in the cockpit? Inches when near the ground? Does it make sense to “describe” mountains in feet and not yards? Are feet not too precise for practical use?  How about 5 miles 3600 feet instead of 30,000 feet?

The Implied Precision Fallacy is invoked immediately to argue for centimeters when their use is challenged, but “this rule” is constantly ignored in the Olde English non-system of almost uncountable units, that gave rise to the argument in the first place. A proliferation of units was exactly what was wrong with pre-metric measurements. We could measure height in ells—but which length of ell? Flemish? English? Scottish? German?–which is of more proper length for our measurement?

Have you caught the beef I have with the dimensions on the Table Tennis Table? The net height and net overhang are both 15.25 cm, which are also 152.5 mm. So, the height of the net needs to be accurate within 0.5 mm or 500 μm? Is that precision necessary? One would guess it is not as centimeters are chosen. Here is the rule:

2.02 THE NET ASSEMBLY
2.02.01 The net assembly shall consist of the net, its suspension and the supporting posts, including the clamps attaching them to the table.
2.02.02 The net shall be suspended by a cord attached at each end to an upright post 15.25cm high, the outside limits of the post being 15.25cm outside the side line.
2.02.03 The top of the net, along its whole length, shall be 15.25cm above the playing surface.
2.02.04 The bottom of the net, along its whole length, shall be as close as possible to the playing surface and the ends of the net shall be attached to the supporting posts from top to bottom

Sven wondered how this accuracy could possibly be met as a single cord by itself would form a catenary curve, and even when loaded along its length, like a bridge, would probably form a parabolic type of curve. The regulation height for the entire length of the top of the net to the playing surface is to be 152.5 mm?—and held to a constant 500 μm value? It seems the tension on the net cord would have to be tremendous!  Wow, and there is no tolerance on the height?

Would the entire game of Table Tennis change if the net height were defined to be 153 mm +/- 1 mm? Clearly the powers that be decided that centimeters alone didn’t have enough precision to describe the net height, they needed two places of accuracy,  and no one decided to use millimeters? Powers of 1000 make a nice continuum: mm, m, km. Millimeters work for metric construction in Australia and the UK, very effectively. There is no need for centimeters other than in response to the irrational desires of US cultural folklore, and to obscure meaning. I have no idea how this specified value for the net height is measured to micrometer accuracy. It is very difficult to believe that it is. What is the surface roughness of the table’s playing surface? and how level? and the tolerance of the diameter of the cord holding the net?

The spin of a ping pong ball is truly amazing. Professionals can rotate the balls at 7,000-8,000 RPM.

Table Tennis Balls -- 40 mm (Wikimedia Commons)

In the 2014 season finale of Mythbusters (Season 13 Episode 8), a segment called Killer Ping Pong Ball examines if a ping pong ball (PPB) can obtain a sufficient velocity to be lethal. Adam Savage doubted it could because of the very low mass of said ball. Which they do not define at that point. Adam and Jamie quote the famous equation F = ma, and are interested in maximally accelerating the PPB. The equation which makes a bit more sense to me is the kinetic energy equation which is:

Kinetic Energy = ½ mv2

where m is mass and v is velocity. When metric is used–as only makes sense–it expresses the energy in joules. A joule is about the energy needed to lift a 100 gram apple one meter into the air.

The Mythbusters duo attempt to hit ping pong balls, pitched by a machine, and quote the results in miles per hour, without exception. This once again shows how hard they actually try to use metric in their show, independent of Adam’s protestation otherwise. The fastest speed they achieved was 33.53 meters/second. Despite the Mythbusters statement that mass is of importance, they do not quote the mass of a PPB for quite some time into the segment. The supertechs put together various pneumatic ping pong devices to accelerate ping pong balls down plastic tubes. Pressure is quoted in PSI of course. The next speed developed is 62.59 meters/second.

Finally at the beginning of the second PPB segment Adam states: “We’ve effectively been attempting to weaponize the one-tenth of an ounce ping pong ball and make it lethal.” So the first “mass” quoted, is in a Ye Olde English unit which is worthless for the computation of energy.

My father once pointed out to me that the factors for millimeters to inches is about 25, and grams to avoirdupois ounces is about 28. So when Adam states that a ping pong ball is 1/10th of an ounce it would be about 2.8 grams. Until this country becomes metric, these will be important ratios to know.

The next “milestone” speed they achieve is 202.51 meters/second.

At the beginning of the third PPB segment Adam states: “In our quest to make the innocent 2.7 gram ping pong ball lethal…” so grams finally make an appearance in the program. The next record speed is 348.24 meters/second, which is faster than the speed of sound. The final speed is 491.74 meters per second. That’s almost half of a kilometer in one second. But of course Adam and Jamie have all the speeds in miles per hour. The final speed is near that of a bullet, and the Mythbusters have a considerable amount of experience with shooting bullets.

Adam and Jamie quoted F = ma as the equation of interest, but never compute the acceleration of the PPBs. They do give the speeds and it would be child’s play to use the kinetic energy equation ½ mv2 to illustrate how the amount of energy in a ping pong ball changes with respect to speed:

33.53 m/s      1.52 joules
62.59 m/s      5.28 joules
202.51 m/s     55.36 joules
348.24 m/s     163.72 joules
491.74 m/s     326.44 joules

Strangely, the show’s other segment, which is on creating an ice cannon, does quote the kinetic energy equation, but they do not use it to compute the energy of the projectile in joules. They do point out that the energy of a 22 caliber long rifle cartridge, shot from a pistol, is about 159 joules. The energy of a 9 mm  is 519 joules. The PPB has an energy between that of a 22 and a 9 mm.

Adam and Jamie then use their ping pong cannon to successfully shoot a hole through a ping pong paddle. Their final test uses a pork shoulder to simulate human flesh. The ping pong ball penetrated almost 40 mm into the pork shoulder, about half the length of a woman’s index finger, which is disturbing. The duo decide that this much trauma would not be life threatening, unless some lucky shot hit a person in a perfect manner to kill them. Myth busted, no killer ping pong balls.

Seriously though, congratulations to Dr. Sunshine, on becoming the Huntsman World Senior Games Champion in table tennis—ok—maybe you are better than Randy Daytona. But shame on the metric usage which is implemented to describe the dimensions of a ping pong table. The largest amount of shame is reserved for the less than informative non-metric presentation of the almost lethal ping pong balls by the MetricBusters.

Recently a dress designer I met pointed out that dress patterns are in centimeters. I just replied “they should be in millimeters.” Her instant reply was “we don’t need that much precision.” It is the automatic US response. I looked online for websites which describe how to make dresses. The first web page I checked had this question and answer:

PLEEASE explain point 13 about the size of dart…I AM DESPERATE…..thx for all your info!!!!!

Hi,

For Step 12, do the following:
-Your bust measurement is 106 cm, so you will subtract 88 cm from that amount, resulting in 18 cm.
-You will then add 0.6 cm for each 4 cm bust increment over 88 cm to the starting amount of 7 cm.
-In your case, you would be 0.6 cm x 3 = 1.8 cm. Then, add 1.8 cm to 7 cm to get your dart size, which comes out to 8.8 cm. (If you wanted to overestimate, you can calculate 0.6 cm x 4 = 2.4 cm, then add that to 7 cm for 9.4 cm.)
-Similarly for people whose bust measurement is under 88 cm, you would subtract 0.6 cm for each 4 cm bust increment under 88 cm then add to the starting amount of 7 cm.

Hope this helps!
Jamie

Wow, that’s a lot of decimal points and leading zeros that I have been assured are not required for dress making, as that much precision is not needed. There are decimal points to keep track of with centimeters that would not be needed with millimeters. The use of cm is a cultural, substitute security blanket for an inch, which is not a very optimum choice for ease of use in everyday work. Millimeters allow for simple integer numbers in most routine work. The choice of the millimeter for metric construction in Australia and the UK was based on assessing what worked best for the average Joe and provided the best insight. There is no reason to believe that suddenly when making dresses, or engineering devices as I do in my work, that centimeters are a better choice. They aren’t. My new aphorism is: “Take away an inch and they’ll make it a centimeter.” or better yet “Friends don’t let friends use centimeters.”

 

Precision: The Measure of All Things

By The Metric Maven

The BBC documentary series Precision: The Measure of all Things is about measurement and its history. The cinematography is excellent, with that BBC polish which is not often found in other technical documentaries. The presenter (host) is  Professor Marcus du Sautoy who is a mathematician. He is the Simonyi Professor for the  Public Understanding of Science at the University of Oxford.

What does Professor du Sautoy see as the purpose of this series? He states that: “In this series I want to explore why we measure. What drives us to try and reduce the chaos and complexity of the world to just a handful of elementary units?” Du Sautoy states that from childhood he has been obsessed with measuring things, and wondered who decided that a kilo is a kilo and a second is a second?

The first episode is called Time and Distance, which examines the second and the meter. It is pointed out that time and distance are interrelated in people’s minds, so much so that people use the phrase “length of time.” This statement is quite ironic when one sees it within the context of the information presented in the episode.

The origins of time measurement as a correlation between the stars above and the seasons is discussed. The abstraction of the motions of the sky into terrestrial clocks from sundials to atomic clocks is detailed. The origins of distance measurement is interleaved with the time discussion. The cubit rod (ruler), used to aid the construction of the Egyptian pyramids, points to the earliest notion of the importance of length standardization. He then comments on the contemporary situation:

Despite the obvious logic of having one international system, it hasn’t been completely embraced. Take me, for example. I’m going to the airport in this cab which measures its speed in kilometres per hour and miles per hour. When I’m up in the air, they’ll be measuring my altitude in feet. My clothes are measured in inches and my shoes are measured in …. well, frankly I’ve never quite understood what the unit for shoe size is!

Well, I would have hoped that the host of a documentary on measurement would not confess ignorance about the unit for shoe size. It is the barleycorn in the US. I have written about the confusion known as shoe size previously. There is a metric alternative which works rather elegantly, it is called mondopoint.

The farrago of pre-metric measurements in England is touched upon. The Professor then  discusses France and argues that matters were even worse there. Professor du Sautoy states that the French decided to stop basing measurements on the human body, and instead based them on the Earth. This is indeed true, but it omits the fact that a British scientist, John Wilkins (1614-1672), invented the system part of the metric system, which was also not based on the human body, but rather upon a scientific phenomenon. Wilkins argued that the length of a seconds pendulum should be used as a universal standard of length. He then took one-tenth of that length, and created a cube from it to use as a volume standard, which in modern terms would be called a liter. This volume was then filled with water, and that amount was to be the standard for mass, which would later be called the kilogram. This proposed system was published by the Royal Society in a 1668 book and was known in Britain and Europe.

Du Sautoy does not mention the fact that using a seconds pendulum, as Wilkins suggested, had been “debated” along with using the Earth for a distance standard by the French. The seconds pendulum appeared to be the default choice for the new system. The addition of decimal divisions of these units, with linguistic prefixes, produced the original version of the metric system. At the last moment it was decided by the French committee to use a meridian of the Earth as a standard. This came as quite a surprise to many at the time.

The mathematics professor argues that by using the Earth as a length standard no other countries could see it as belonging to one country. This seems doubtful. The meridian chosen went through Paris, and Thomas Jefferson saw the abandonment of a seconds pendulum (he argued for a rigid “seconds rod” to also be considered) as an act of French nationalism and no longer endorsed the metric project. It appears that du Sautoy seems to
be creating a kumbaya consensus among the delegates where from my reading of history, one did not exist.

Pierre Mechain and Jean Baptiste Delambre are identified as the men who would measure the Earth and determine the length of the meter. The controversy over the “hidden error” in this measurement is mentioned and seems at odds with our current understanding:

In fact, due to errors that Mechain made early on in his survey it’s fractionally wrong. The errors that Mechain made were pretty much irrelevant, because for the first time, the world had a unit of length [the meter] that was based on something they believed was permanent and unchanging – the Earth.

The “hidden error” became well enough known among anti-metric persons, that John Quincy Adams could not help but chortle about it in his Report on Measures. It is hard to characterize what occurred as an error. There was an implicit assumption in that era that the equipment used would produce exact measurements. There was no common understanding that all measurements have an error associated with them, nor had statistics been developed to quantify these measurement uncertainties. When two repeated measurements deviated, it was assumed that an error had been made.

It seems quite surprising how the presenter simply dismisses the importance of the error in a “measurement standard” as irrelevant. In the 19th Century, James Clerk Maxwell would make sport of the idea of using the Earth as a measurement standard. It took Mechain and Delambre seven years to measure the distance from Dunkirk to Barcelona.

What is not mentioned by du Sautoy is that a complex seconds pendulum was constructed near Paris, apparently as a backup option. From June 15th to August 4th of 1792 twenty sets of measurements were made and its length was computed to be 994.5 mm (440.5593 lines). The chosen alternative of taking seven years to measure a section of the Earth seems quixotic. Then for du Sautoy  to immediately dismiss the “errors” introduced into this measurement as irrelevant, after such a large undertaking, is hard to understand.

The original meter was in actual fact, an artifact. The surprising similarity between the length of a seconds pendulum, and that of one ten millionth of the distance from the north pole to the equator, seems never to be mentioned in many histories. When the episode is entitled Time and Distance, it would seem that the seconds pendulum would be a natural place to start. One uses the best second available with a pendulum length to define the meter. Indeed this is almost a “length of time” as he mentioned earlier.   One could then go through the history of the meter, which  would lead up to the modern definition of the meter as the distance that light travels in a vacuum in 1/299 792 458 of a second.  One can link the original definition by Wilkins which had time and length intertwined, and the modern definition which also involves both.

The second episode, Mass and Moles, opens with a viewing of Le Grande K, The Kilogram, which is kept near Paris.

To explain the importance of the kilogram, Du Sautoy goes to a British market and talks about weight when all the produce is in grams and kilograms. He offers an engaging demonstration of how people can perceive weights incorrectly. People are offered different sized objects and are asked to determine which weighs the most. These people, who are in a market with produce sold by mass all around them, fail the test over and over, and of course, that is why we need to use a scale, and most importantly, one which has been calibrated.

The almost certainly fabricated story of Newton seeing an inspirational apple drop from a tree[1] is related to introduce the difference between weight and mass. The host calls the difference a subtle but vital one, and indeed, mass and weight is constantly confused. In a quite interesting demonstration du Sautoy measures a cylinder of metal with an incredibly sensitive scale. The mass of the metal is 368.7025 grams according to the read out. The scale and its metal test mass is then moved to the top of a nearby tall building. The metal now weighs 368.6916 grams for a 10.9 milligram difference.

The Professor does not see the irony that he just pointed out the subtle difference between mass and weight, and has a scale that indicated that the mass (in grams) of the object changed with location. Of course the scale is actually weighing the mass, which is the force exerted on the mass. The scale assumes a gravitational force value and calculates the mass based on this assumption. The gravitational force has changed because of its location with respect to the center of the earth, and not the mass of the object. If there had been a 10.9 milligram change in mass, then we must account for about 981 gigajoules of missing energy, and the presenter would probably have been injured in some manner by the experiment. A stick of dynamite releases about 2 megajoules of energy.

The unit for the measurement of force (weight) in the metric system is newtons. This is the value which is being indirectly measured and not the mass. Du Sautoy correctly points out that number of grams contained in the object did not change, but that gravity did. Certainly the amount of gravitational force did. Well, I’m not sure this is as clear an explanation of the difference between mass and weight as the presenter thinks it is. The measurement device reads in grams in both cases, which is a mass. The way to mass an object is to use the oldest technology available, a mass balance. The force on each side of a balance is the same, which cancels out, which allows for a true mass comparison to take place. To use the force scale correctly du Sautoy would have needed to calibrate the scale with a known mass at street level, and then again at the top of the building. The measured mass would then remain constant as it must. Assuming 9.8 m/s2 is the gravitational acceleration at street level, the difference in “metric weight” is about 107 μN (micronewtons). For comparison, the “metric weight” of a human being with a mass of 70 kg is about 686 N.

The confusion continues when it is pointed out by the professor that the original kilogram was to be equal “to the weight of one cubic decimeter of water.” Well, it’s not the weight, it’s the mass definition. He also credits Lavoisier as coming up with this kilogram definition. John Wilkins predated this “redefinition” cited by du Sautoy. Lavoisier is also “credited” with using this to define the liter—worse and worse. The weight/mass statement confusion is ubiquitous, even among contemporary engineers and scientists. Du Sautoy interviews a person who has a device that weights single biological cells. Indeed, he describes how small the weights are that he can measure with this device in picograms and femtograms.

The third and final episode is Heat, Light and Electricity. It has a number of interesting images of the attempts to measure these less directly experienced phenomenon. The overall series has a considerable number of scientific demonstrations that are quite interesting and bring the issues at hand to life.

Du Sautoy has also hosted another series called The Code. It is about the mathematics which describes our world. In my view, du Sautoy consistently displays a belief that numerical expression is incidental to explanation. This may reflect his background as a mathematician who has not done much design and fabrication during his career.

In The Code, an example of this measurement system neglect occurs when the professor decides to measure a neolithic circle.  The tape he uses determines the diameter of the ancient relic to be approximately 27 meters and 90 centimeters. He then measures the circumference at 91 meters and 70 centimeters.  He wrote down meters and centimeters, in the same way an Englishman (or American) might write down feet and inches. One could write down 27.90 meters and 91.70 meters. He could have written down 27 900 mm and 91 700 mm. I don’t see anything objectionable in either of these expressions, meters or millimeters.  He then divides 917 by 279 to get the ratio of the circumference to the diameter. Clearly he does this to show us the ratio is near the value of π, at about 3.3. So, he is using integer values of decimeters for his computation, which does make the act of dividing by hand easier. One cannot say that what he has done is “wrong” but it certainly makes one suspect that his view is that numerical expression for computation and clarity is not a priority in his world.

It does not really surprise me that a mathematician would jumble around numbers like this, they tend to see computation and numerical expression as incidental to a point that they might be making. This is why I have argued strenuously that mathematicians should not be tasked with teaching the metric system. They have very little acquaintance with fabrication and measurement.

Unfortunately, mathematicians seem be unaware of this deficiency. They appear to think that because they understand prime numbers, irrational numbers, integer numbers and so on, they automatically have an understanding of the optimum use of numbers used to describe and compute the world. This may be precipitated by the idea that this type of mathematical expression is “just a detail.” It could also be due to the fact that mathematicians don’t do a lot of actual applied work.

Du Sautoy then takes a much more modern circular object, a dinner plate, and measures it. The diameter is called out as 26.4 centimeters, and the circumference is about 82.9 centimeters. Why the decimal point suddenly? He seemed fine with integer decimeters. Why not 82 centimeters 9 millimeters?—which is consistent with the meter and centimeter unpacking he used previously—or use an integer?—like 829 millimeters?

Without further hand computation he announces the answer for the circumference to the diameter as 3.14 for the plate. He performs the same measurement on a roll of cloth tape and gets 3.14 as the ratio. His point is that all circles have π as the ratio of the circumference to the diameter. The computation and how to go about it is incidental, just something to be accomplished to make a general mathematical point. This is a habit of mind, and one which was not broken for Precision.

I have very high expectations for BBC programs, because I’ve seen so many high quality science documentaries. The series Light Fantastic for example, is an excellent explanation of the history of light and electromagnetic radiation.  What was offered by Professor du Sautoy is not up to the high standards of the science documentaries offered by the BBC. I can only hope that someday a more worthy series on measurements is produced.

 [1]   Isaac Newton The Last Sorcerer, Michael White, 1998 pg 87