Blowed-up Real Good


By The Metric Maven

Bulldog Edition

I very much like to check-out Phil Plait’s Bad Astronomy blog. His measurement presentation causes me to generally wince, but its topics are often rather interesting. On 2016-02-20 he wrote about the Largest Fireball Since Chelyabinsk falling over the Atlantic Ocean. The object appears to have possibly exploded (or just burned up) about 30 Kilometers above the ocean surface. Plait assures us there is no cause for alarm; this was a small meteorite. He states:

For comparison, the Chelyabinsk explosion, which was strong enough to shatter windows and injure more than 1,000 people (due to flying glass), had an equivalent yield of 500,000 tons of TNT, 40 times the energy of this more recent impact.

Plait provides a link to the NASA/JPL Near-Earth Object Fireball page, and presents a cropped graphic from the site:


I was quite pleased to see NASA using international dating for the entries. It all is nice and ISO 8601. The total radiated energy from the meteor is given in joules. It is presented in scientific notation with an exponent to the tenth power. Here is a larger section of the NASA table with the data for the new meteorite in the first row at the top:


The total energy radiated from the meteor as it cruises through Earth’s atmosphere is about 685.3 x 1010 joules. Why an exponent of ten? We can see as we go down the list that all of the examples have this same multiplier. When presenting data, scientific notation is not good for numerical comparison. One could choose a metric prefix and have 6.85 Terajoules instead. As the values are typically smaller than this, one could switch to Gigajoules and write it as 6853 GJ. In my view presenting comparison data with scientific notation hinders intuitive understanding. I know that some computer languages have a setting that parses the exponents so they are presented in engineering notation by steps of 1000.[1] The exponent for all of the values given in the table can be expressed in Gigajoules. Below is a table with the recent meteorite and the Chelyabinsk radiated energies:


When Expressed in Gigajoules it is apparent just how much larger the radiated energy of the 2013 Chelyabinsk meteor was when compared to the recent one thought to have have exploded over the Atlantic Ocean.

When presenting the calculated total impact energy, NASA gets their Dr. Strangelove on and uses kilotonnes of TNT. As I’ve pointed, out the tonne is nothing more than the introduction of medieval measures into the metric system and should be eschewed. Worst of all, a tonne is a Megagram, and when you use a Kilo- prefix it produces a KiloMegagram. The last column is KiloMegagrams of TNT when actually expressed without hidden metric notation. It should be Gigagrams of TNT, but then metric is not NASA’s strong suit. The metric system has a well-defined unit of energy, the joule; the same one that was used with radiated energy.

One kilotonne of explosive is equal to 4.814 Terajoules. It appears that using Gigajoules is probably still a viable choice for presentation of the Calculated Explosive Energy:


In my view the change from joules to kilotonnes of TNT was just an anemic attempt at a “gee whiz” expression without making an actual comparison. An atomic bomb using nuclear fission ranges from about 4 000 Gigajoules to about 80 000 Gigajoules. The 2016-02-06 meteorite is in this range. The largest Hydrogen bomb exploded released an energy of about 210 000 000 Gigajoules. One can see the Chelyabinsk explosion of 2013 is about 23 times larger than a typical fission bomb, but is overwhelmed when compared to the amount of energy released by the largest hydrogen bomb.

How data is presented matters. I wish someone in a position to enforce change within NASA would create a position called a “numerical editor,” something like what in book publishing is called a copy editor, but concerned specifically with the presentation of numeric data for consistency and clarity. I leave you with a graph I’ve presented before. It shows that sometimes NASA presents data in an effective manner, they just need to make it consistent:


[1] Fortran 90/95 for Scientists and Engineers Stephen J. Chapman McGraw Hill 1998 pp 534-535

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The Worth of Measure


By The Metric Maven

Fourth Anniversary Edition

When the well’s dry, we know the worth of water

— Benjamin Franklin

In the Winter of 2014 the “Polar Vortex” event brought marrow chilling cold to my father’s town. For months the water pipes which fed his house were frozen, and he had to fill large containers of water each day for household needs. There was some irony in the fact that new water meters had been installed not long before, and my father noticed a measurable change in his usage and water bill. The water company’s explanation was that these new water meters are much more accurate than the old ones and so his bill reflected a more accurate quantity of water. It would be hard to verify this assertion and life went on.

This interaction between water user and municipal water supplier is not new. L. Sprauge de Camp in his excellent book The Ancient Engineers relates a similar situation in ancient Rome (units converted to metric):

The unit used in measuring water was a calix or standard nozzle. The standard calix was the quinaria, a length of bronze pipe 1 1/4 digits (= 18.5 mm) in diameter and 12 digits (= 222 mm) long, connecting the distributing tank to the user’s pipeline.

Users of larger calices were charged in a rough proportion to the cross-sectional area of their nozzles, as nearly as the Romans could calculate these areas with their awkward system of numerals. These charges were made on the assumption that doubling the cross-sectional area would double the flow, when in fact it would more than double it.

The Romans also knew that the flow of water through an orifice is greater if the the hydraulic head or water pressure is higher. But they did not know how much greater. So, not having water meters, they could not adjust their charges accordingly.


Still, for want of effective water meters, this system of measuring water supply long continued in use; it was employed in Paris as late as the 1850s. When  large discrepancies appeared in Frontinus‘ figures, he thought that these were due entirely to theft of water and leakage. In fact, however, they were also due to his crude methods of reckoning.

A modern person might wince when thinking about doing calculations using Roman numerals, or, considering the ubiquity of electronic calculators (physical or computer simulated) doing the calculation by hand with Hindu-Arabic numbers. An expression in modern Hindu-Arabic numerals is easily comprehended, whereas Roman numerals require some manipulation. For instance Super Bowl XLIX is what? Why Super Bowl 49 of course!  How about a simple subtraction: MMMMMMMMMMMMCCCXLV – MMCCCXLV = ? Perhaps it might be easier in Hindu-Arabic: 12345 – 2345 = ?  Yes it’s 10 000.

Modern persons immediately note, that the Romans poor numerical system was further confounded with poor measurement techniques. It is often stated that the world around us is mathematical, but this statement without qualification is not true. We cannot make the claim that the world is mathematical, without an idea that is generally invisible to the psyche. Worse yet, when it does make its way into the minds of engineers and scientists, it is often a concept which is thought to be of minimal importance. This attitude was brought into high relief when I read this quotation in Basic Concepts of Measurement by Brian Ellis:

Measurement is the link between mathematics and science. The nature of measurement should therefore be a central concern of the philosophy of science. Yet, strangely, it has attracted little attention. If it is discussed at all in works on the philosophy of science, it is usually dismissed in a fairly short and standard chapter.

Without the intermediary of measurement between our observed world and mathematics, science and engineering as we know them would not be so obviously mathematical. Pat Naughtin realized this. It was obvious to him, but it was difficult for Naughtin to conceive that it was not obvious to the greater technical community in the US:

During the 2008 election campaign in the USA, ‘Scientists and Engineers for America and fifteen other science organizations‘ united to ask the congressional candidates seven questions in preparation for the Federal elections in the USA.
The highly original, smart, clever, and creative scientists and engineers who wrote the seven questions had not begun to address the most basic issue in science–how to measure things. They simply didn’t seem to see that measurement was at all important to their nation.

One might ask “what would the world be like if measured quantities and mathematical quantities had no relationship?” I can safely say that engineering and science as we know it would not exist. We would be no better off than the Romans—at best. We might desire the existence of a  computational relationship between the size of a pipe and its flow rate, but if we lived in a world where our mathematics and measures could not be related, we would be left to rely only on our perceptions of large and small, hot and cold, heavy and light. We would know the worth of measurements, if they were suddenly not mathematically expressible. This quantitative absence would leave us intellectually naked and left without recourse to deal with the vicissitudes of nature. Before mathematics was combined with measurement through quantitative experimentation, the entire world was filled with unexplained mysterious forces. To deal with this un-quantified world, we would instead call upon supernatural agency and sympathetic magic. Lord Kelvin clearly understood this when he stated:

When you can measure what you are speaking about and express it in numbers you know something about it; but when you cannot express it in numbers your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge but you have scarcely progressed in your thoughts to the stage of science whatever the matter may be.

People often understand this at an intuitive level when discussing research. The quantification of physical properties like mass, energy, volume and so on are all fixed. When measured quantities are mathematically expressed, these relationships can often be verified to the limits of our measurement capability. When we attempt to relate sociological quantities like happiness, sadness and anger in mathematical form we often feel the reluctance that Lord Kelvin did. How could we possibly measure these quantities? The devil is in the measurements, and without repeatable and exacting measurements, which are also mathematically expressible, what we are doing just does not seem like science and in fact is not.

When I insist on the importance of the metric system, and its clearest use, I’ve often been dismissed by other engineers and scientists. In some cases a visceral ejaculation of impatient prose follows that claims: “it doesn’t matter what measurement units one uses.” Sometimes this is followed with a dismissive hand gesture. The analogy of computation with Roman numerals versus Hindu-Arabic numerals is brushed aside as trivial and irrelevant. The metric system was developed, from its inception, to be the easiest  and clearest measurement system for relating mathematics to definite physical quantities, which is the very definition of “hard” science. There is often an insinuation that people who can “master” more than one measurement system are somehow intellectually superior to those who “cannot.” I had a chemistry instructor in my Fundamentals of Engineering review course say this during one class: “American engineers and scientists are better than the rest of the world because we understand two systems.” This proliferation of measurements does not make us “better” it makes us slaves to thoughtless tradition, similar to the tradition of Roman numerals. It took over 1000 years for humanity to wean itself from them.

Michael Faraday (1791–1867) gave a fascinating public lecture called The Chemical History of a Candle. This lecture was published in 1861 and it is a very interesting read. When he was investigating the constituents of water in this lecture, Faraday offered this table:


It is hard to image that this switching of units demonstrates the superiority of using multiple units when looking for correlation. This is the pre-metric world and it is not insight-friendly. I would convert the table to metric, but I’m not sure which pint or which ounce or which grains are used for certain.

It has struck me as a sad commentary that modern public figures who aspire to be scientific ambassadors and popularizers, have such a trivializing attitude toward the metric system. Neil deGrasse Tyson, when asked by a Canadian to explain why he did not use metric in Nova Science Now argued that if you understood the metric system, perhaps you did not need to watch the show! “I’m really just trying to reach the people that need the science.” This statement indicates the metric system is difficult, when in fact it is designed for elegance and simplicity. When the metric system is used in thousands (triads), the gram, milliliter and millimeter are all integers for expressing everyday quantities. deGrasse Tyson reinforces the corrosive American prejudice that “metric is for scientists and engineers” and regular folk don’t need to worry their pretty little heads with that complicated stuff. He later trivializes the audience member’s request for metric by stating: “it does put a greater burden on you, the Canadian to adapt to our mysterious ways in America.” Yes, they are mysterious, and not really funny.

Bill Nye explains the metric system by offering up both centimeters and millimeters and the idea that the metric system is only “better by ten” instead of better by one-thousand. No hectometers or decameters or decimeters are offered to demonstrate the better by ten assertion.

Neil deGrassee-Tyson and Bill Nye do excellent work explaining and defending science. They, like most engineers and scientists seem to have given the metric system very little thought or investigation. Is this their fault? I would argue that it is probably not. This metric ignorance is a systemic problem within our educational institutions from kindergarten through graduate school. I only recall a quick statement by a professor, stating that we will be using the metric system in our science and engineering courses, and then, without any reflection or background, we were often introduced to physics and engineering problems with both Ye Olde English, and metric, and metric was used without context. One way that scientists often trivialize metric is by using scientific notation and not bothering with metric prefixes at the end of their computation.

Our modern scientific world as we know it would not exist if measurements could not be made and then related to mathematics. The late Pat Naughtin seemed absolutely baffled when he could not get US engineers and scientists to make the adoption of the metric system in the US an intellectual priority. It is generally the examination of basic assumptions that propels engineering and science forward, but often it is the basics that are assumed and ignored. This lack of interest in the metric system by those who would communicate science to the public, and their indulgence of tradition over clarity, does not serve the public well, or demonstrate a deep understanding of science.

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