Don’t Assume What You Don’t Know

By The Metric Maven

Bulldog Edition

“It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.”

– Mark Twain

When I first learned about viruses, I found them terrifying. They were as terrifying as any plot in a science fiction novel. They were unimaginably small. The virus shown had a set of “legs” which it could use to attach itself to a cell. It would then inject material through the cell wall from a head that looked like a gem. The cell would then become a zombie and make more viruses until it exploded like a balloon popping and the new viruses were scattered everywhere to find new cells. What I took away from the grade school lesson was that viruses were so much smaller than bacteria, they were like comparing an m&m to a basketball.

During one Summer break in college I read One two three… infinity by George Gamov. The book was published in 1947, but remains a classic. In one section of the book, Gamov explains that bacteria like typhoid fever has an elongated body “about 3 microns (µ) long, and 1/2 µ across, whereas the bacteria of scarlet fever are spherically shaped cells about 2 microns in diameter” A footnote states: “A micron is one thousandth of a millimeter, or 0.0001 cm.” It would not be until 1960 that the micrometer would become an accepted term.

Gamov explains there are a number of diseases such as influenza “..or the so called mosaic-disease in the tobacco plant, where ordinary microscopic observations failed to discover any normal sized bacteria.” Clearly something existed which was transmitting disease, but what was it? “…it was necessary to assume that they were associated with some kind of hypothetical biological carriers, which received the name virus. The use of ultraviolet light and the development of the electron microscope allowed researchers to finally see viruses and describe their structure.”

Above I have reproduced the prose and type used by Gamov. You will note that he just uses the Greek letter µ to represent a micron, which is, of course, a micrometer or µm. Gamov continues:

Remembering that the diameter of one atom is about 0.0003 µ, we conclude that the particle of tobacco-mosaic virus measures only about fifty atoms across, and about a thousand atoms along the axis.

In modern terms:

Typhoid Fever Bacteria:  3000 nm x 500 nm
Scarlett Fever Bacteria: 2000 nm in diameter

Tobacco Mosaic Virus:  280 nm x 150 nm
Influenza Virus:  100 nm across.

Atomic diameter: 0.3 nm diameter

Excellent Graphic from New Scientist “Pandora Challenges the Meaning of Life” (2013-07-13) pg 10 all in nanometers — click to enlarge

Viruses are clearly much much smaller than bacteria, and much much harder to study. But then in 2003, an organism which first appeared to be bacteria, because a common test indicated it was, was instead discovered to be a virus. It was dubbed a Mimivirus or microbe-mimicking virus. This virus has a diameter of 750 nanometers. This is just plain gigantic. Suddenly researchers found “giant” viruses everywhere! Why was this? These viruses are really big—and we have much better microscopes and tools than existed in 1947, how could it be that only in the 21st century anyone identified them? An American Scientist article from 2011 entitled Giant Viruses explains:

Most giant viruses have only been discovered and characterized in the past few years. There are several reasons why these striking biological entities remained undetected for so long. Among the most consequential is that the classic tool for isolating virus particles is filtration through filters with pores of 200 nanometers. With viruses all but defined as replicating particles that occur in the filtrate of this treatment, giant viruses were undetected over generations of virology research. (Mimivirus disrupted this evasion tactic by being so large it was visible under a light microscope.)

It was assumed that viruses were smaller than 200 nanometers, so they were filtered out. No one even thought to look for them because it was something “what you know for sure that just ain’t so.” that precluded researchers from seeing this virus for over fifty years. In 2014 researchers resurrected a 30 000 year old virus from Siberian permafrost which is the largest thus far discovered. It is called pithovirus sibericum and measures 1500 nm in length and 500 nm in width, which approaches the dimensions of the Typhoid and Scarlett fever bacteria cited by Gamov.

In the 1980s, ground based British researchers in Antarctica noticed a large depletion of ozone above them. The numbers were so low, there was concern that the instrumentation was faulty. Satellite measurements did not reveal the ozone depletion which caused a considerable conundrum. The numbers were so low that according to folklore, the computer software had a lower limit and threw out the bad data. The story is difficult to pin down and a bit apocryphal, but it illustrates what I’ve seen in my own career.

When I was first creating computer models of antenna radiation using a computer method called FDTD, I calculated radiation patterns. There are two different values to calculate, one is large and the other smaller.  An antenna was fabricated, and measured based on my analysis. The large value was measured to be almost exactly the value expected. There was a confusion on my part when the analysis showed a clearly defined smaller valued radiation pattern, but the measurements indicated no antenna pattern was present. When I showed the person who had written the program for the measurement chamber this anomaly, he remarked “That’s so low, it’s meaningless, I just set the value to the bottom of the expected range.” I had to convince him to change the computer code so it would output the actual numbers, and to his surprise, the smaller data was far, far more accurate than he had imagined.

This brings me to a ubiquitous metric system fallacy that seems rooted in the heritage of our Ye Olde English Arbitrary Grouping of Weights and Measures or Ye Olde English. This fallacy Sven and myself call “The Implied Precision Fallacy.” It is the idea that one should decide what measurement units are to be used based on a prejudicial notion of what the magnitude is expected to be measured, and the expected measurement error. It also implies that if you measure further than this, you are implying you are measuring to that precision.

This fallacy may have its roots in the past, when the available precision of a measurement device or construction device (like a mill or lathe) might have limited how far down one could measure or fabricate to a given accuracy. If a person had a problem measuring or constructing to a particular precision and accuracy because of tooling limitations, one might be tempted to argue not to bother with places beyond what they thought was possible.

Unfortunately this argument could be turned around into a rationalization that if that’s the best one can do that’s the best one actually needs. I was told many times, by many school teachers to choose medieval units which reflect expected precision, and if I used smaller ones that this was very poor practice. It was overkill. The size of the units chosen would imply the precision of the measurement, so use as large of units as possible. As you see when the size of units are used a priori as an argument of precision, then they are a chosen limitation, and not a well informed limitation. They are in fact a guess.

I have run into many situations in my career where data looks like noise, and then using signal processing, useful information is obtained. The GPS signal you use to guide your car trips is well below the noise level at that frequency. It is like standing in the top row of a football stadium and trying to hold a conversation with a person with a person on the other side of the field also on the top row while the crowd cheers. Impossible—right? Well, perhaps not. Signal processing can do amazing things, but if you argue there is no way to make a measurement precise enough, you will not. It is a psychological self-imposed measurement limit, not a technical one.

This brings me to the measurement of people’s height and the mass of babies. I have been taken to task for arguing that height should be measured in mm, just like lengths are in the Australian construction industry. Some commentators argue that this is too much precision, that a person’s height changes so much that millimeters just have too much precision to have any meaning. There is no use taking measurements which are calibrated to millimeters, because we already know we don’t need them. This is a very platonic argument. It is also nonsense on a number of levels. First, the data itself should reveal where the precision no longer exists. If one can show that a certain set of digits on the right are randomly distributed, then one can obtain an implied measurement precision, but that is not the end of the story. Even digits which appear to be random may contain information which may be extracted. I’ve never seen a situation where measurements have been too precise, and led people to miss an effect, but I have seen situations where they have been masked by truncation. Measuring a person’s height as 1753 mm does not assault good technical practice, it is an example of it. One can always write this value as 1.75 meters immediately just by inspecting the millimeters, but one has taken a simple integer and needlessly introduced a decimal point. The two representations use the same number of symbols.

The grouping of three for numbers appears to be of great utility in our society. From one thousand (1,000) to one million (1,000,000) to one billion (1,000,000,000), these values have been designated in groups of threes long before I made my appearance on this planet.  The breaks in metric prefixes, are at the locations of the commas. In other countries only a space is used above four digits: 1000, 1 000 000, 1 000 000 000 (one can use a space with four digits also—it’s just not my preference).  This is also done in many US numerical analysis references.

Pat Naughtin, in his TEDx Melbourne  lecture on 2010-03-13 discussed a scale which measured the weight (mass) of babies. The baby would wriggle and it would require the device to take large numbers of measurements and statistically extract its mass. The precision and accuracy of this scale was to within a gram. The weight of a baby is supposed to increase with time. A decrease, even a very small one, could indicate a potential health issue.

Should the baby have an infection, accurate knowledge of its mass is important so a properly proportioned amount of medicine can be prescribed. Naughtin points out that yet again there is no measurement policy in this instance, and no one in charge of one. Naughtin argued there is a potential danger when babies are measured in Kilograms, and rounded to the nearest tenth of a Kilogram, which is the accepted practice in Australia. The use of a decimal point, and rounding, creates numbers which are decanted of information. The number is too close to unity for a clear understanding of changes in its magnitude. Using grams allows for one to eliminate fractions—decimal or otherwise—and compare simple integers.

Years ago when I lived in Montana, I encountered shade tree mechanics, small engine mechanics, construction contractors and others. One phrase which seemed to be ubiquitous was:

“He’s the kind of guy that will measure something with a micrometer, mark it with chalk and cut it with an axe.”

It showed a common understanding that over-precision does not hurt one, and a person who would throw it away is not good at his profession, be it mechanic, welder, contractor, or any other skilled vocation. The Australian construction industry has saved large amounts of money by measuring in millimeters. They have no need for a decimal point, and the numbers are simple. The argument that measuring a person’s height in millimeters, or a babies weight in grams is “too precise” is a cultural argument, not a technical one. Arguing that lots of people perform a measurement, or an authority like the EU or the medical profession has endorsed it is an argument from authority.

In my essay Metamorphosis and Millimeters, I point out that for thousands of years people had created bee hives which were made of clay. They had to be destroyed in order to obtain honey. It was only in the 19th Century that an American inventor had the temerity to question this dogma, and created the modern bee-hive. Common usage over a long period of time does not imply that common usage is optimum. This is a version of a technical Darwinism argument that is used by anti-metric people as a straw man cudgel. It has been increasing measurement precision (and accuracy) which has allowed the creation of a modern technical society and is at the forefront of scientific discovery. Arguing otherwise is arguing against all the benefits increased measurement accuracy has provided. There is no “common person’s measurements” and a separate set of “scientific people’s measurements” there are only precise measurements.

Updated 2015-01-21

Asimov and Metric Prefixes

Isaac Asimov (1920-1992)

By The Metric Maven

The late Isaac Asimov (1920-1992) was a great promoter of the metric system. In the early 1960s Dr. Asimov wrote an essay about the metric system entitled Pre-Fixing It Up. The essay appears to have been inspired by the official addition of new metric prefixes in 1960. Some of the essay shows its age, but Asimov makes an observation about the metric system which still seems lost on most people:

All other sets of measurements with which I am acquainted use separate names for each unit involving a particular type of quantity. In distance, we ourselves have miles, feet, inches, rods, furlongs, and so on. In volume, we have pecks, bushels, pints, drams. In weight, we have ounces, pounds, tons, grains. It is like the Eskimos, who are supposed to have I don’t know how many words for snow, a different word for it when it is falling or when it is lying there, when it is loose or packed, wet or dry, new-fallen or old-fallen, and so on.

We ourselves see the advantage in using adjective-noun combinations. We then have the noun as a general term for all kinds of snow and the adjective describing the specific variety: wet snow, dry snow, hard snow, soft snow, and so on. What’s the advantage? First we see a generalization we did not see before. Second, we can use the same adjectives for other nouns, so that we can have hard rock, hard bread, hard heart, and consequently see a new generalization, that of hardness.

The metric system is the only system of measurement which, to my knowledge, has advanced to this stage.

Asimov makes a point in the 1960s which appears to be completely absent from contemporary metric advocacy discussions. The metric prefixes themselves provide an intuitive set of relative magnitudes, expressed in literary form. People do not generally realize this because of the dismal manner in which “scientific journalists” present weights and measures in the media. I wrote a guest blog on the penetration of metric prefixes into our culture, but they only are vaguely understood, and their monotonic relationship is not clearly articulated.

There is only one technical area with which the public deals that has slowly introduced each metric prefix such that people have an idea of their relative magnitudes. That area is computers. In the early days of computing, a computer such as the Timex Sinclair 1000 came with about 2K of memory. That is, it has approximately 2 Kilobytes of memory. Memory escalation had begun and the Commodore 64 had—well—64 Kilobytes of random access memory (RAM). Soon computers would have Megabytes of RAM. The computer I’m currently using to write this essay has 2 Gigabytes of RAM. The use of the metric prefixes to describe computer memory has been a slight kludge as computer memory is in multiples of two. A Kilobyte is actually 1024 bytes instead of 1000 bytes as the metric prefix implies. There is an attempt to introduce binary name versions called the kibi, mebi, gibi and so on, which correspond to the actual metric prefixes, but exactly describe the number of bytes.

Metric prefixes have long been used to approximately count up all the ones and zeros available in computer memory, or on a disk drive. The RAM of a typical computer has increased from Kilobytes, to Megabytes, to Gigabytes. One knows that a file which is in the Kilobyte range is easily emailed. A file which is 1-2 Megabytes is pushing the email envelope a bit, and 10 Megabytes is a really large file to attach to an email. One would not even consider sending a 1 Gigabyte file, it is immediately apparent from the prefix that it is untenable.

As Asimov points out, the metric prefixes act like adjectives. Email attachment file sizes can be seen as small (Kilobytes), large (under 4 Megabytes), and too large (Gigabytes).

Computers use disk drives to store digital files.  5 1/4 inch floppy drives increased from 360 kilobytes to 1.2 megabytes. The 5 1/4 inch floppy drive was replaced by the 90 mm (~3.5″) floppy which held about 1.44 megabytes. Hard disk drives (HDD) with many Megabytes of space were introduced to the consumer. As time went on, Gigabyte sized hard drives were introduced. When compared with Megabyte sized drives, they seemed almost limitless in size. Currently 1-2 Terabyte drives are commonly available. The Greek roots of the prefixes are descriptive. Megas means “great,” gigas is “giant” and terras is “monster.”  Indeed a Terabyte drive is monstrous in size—at least as of this writing.

The problem is that only in the computer industry have we been inculturated with the metric prefixes. As I pointed out in an earlier essay, I was not pleased that the producers of Cosmos chose to use Kilometers, light-years and astronomical units to describe celestial distances. Dr. Asimov encouraged metric usage in astronomy over forty years ago. He begins with the meter, then describes the Kilometer in terms of distances in Manhattan, “…a kilometer would represent 12 1/2 city blocks.” He moves on to the Megameter:

This is a convenient unit for planetary measurements. The air distance from Boston, Massachusetts, to San Francisco, California is just about 4 1/3 megameters. The diameter of the earth is 12 3/4 megameters and the circumference of the earth is about 40 megameters. And finally, the moon is 380 megameters from the earth.

Passing on to the gigameter, ….this comes in handy for the nearer portions of the solar system. Venus at its closest is 42 gigameters away and Mars can approach us as closely as 58 megameters. The sun is 145 gigameters from the earth and Jupiter at its closest, is 640 gigameters distant; at its farthest, 930 gigameters away.

There is no need for Asimov to have qualified the Gigameter as only being “handy for the nearer portions of the solar system.” This is a pre-Naughtin’s Laws view of the metric system. The Gigameter is completely useful for describing the distance to Pluto and the position of the Voyager 1 and 2 spacecraft. Asimov continues:

Finally, by stretching to the limit of the newly extended metric system, we have the terameter…this will allow us to embrace the entire solar system. The extreme of Pluto’s orbit, for instance is not quite 12 terameters.

Two factors that Asimov did not foresee was that Neil deGrasse Tyson would “kill Pluto” and the introduction of Naughtin’s 3rd Law: Don’t Change Measures in Midstream. The extreme of Pluto’s orbit quoted in Asimov’s essay is 12 000 Gigameters. If the Australian construction industry can handle this large of a number in millimeters, I’m sure astronomers can muddle through with it in Gigameters.

One cannot fault Asimov for not pushing matters further. It would not be until 1991 when enough metric prefixes would be added to encompass the entire observable universe.  Asimov does realize the limitations of light-years and parsecs (3.2 light years):

Even  these nonmetric units err on the small side. If one were to draw a sphere about the solar system with a radius of one parsec, not a single known star would be found within that sphere. The nearest stars, those of the Alpha Centauri system, are about 1.3 parsecs away.

The current version of the metric system has no problem describing the macroscopic universe. Here is a table from an earlier essay on the subject:

click to enlarge

The overall point is that if the metric system was completely adopted in the US without dilly-dallying, we would use the metric system, and its appropriate prefixes, to describe all important scientific discoveries and ideas. Children would grow up memorizing metric prefixes (without the prefix cluster about unity) as earlier children committed multiplication tables to memory. This exclusive metric ecosystem would soon provide  a reinforcing context for the relative sizes of the metric prefixes, and make the public as well as people in technical vocations, much more numerate. Astronomy texts would use metric to describe distances, and only mention light years as a gee-whiz! metaphorical supplement to actual measurement units.

Dr. Asimov died in 1992, just after the new set of metric units from yocto to Yotta were adopted. They describe the world which engineering and science encompass at this time. It is sad that the gentle doctor has been gone for over 20 years, and we are no closer to adopting metric units for everyday engineering and science, let alone in our public news media. Dr. Asimov expressed his frustration that no one was listening to his appeals for the metric in the early 1960s in his essay Forget It!. The US has continued to ignore the metric system for over 50 years since that essay first appeared. Will metric adoption take 200-300 more years to occur in the US? I don’t know. What I do know is I don’t have time to wait around that long, and neither did Dr. Asimov.

Isaac Asimov’s birthday was on January 2.