Keywords: philosophy of science, measurement, ISO, NIST, standards, accuracy, precision, philosophical foundations
When someone buys a pound of potatoes, how do they know it weighs one pound? A likely answer is that the produce scale said it was. But that assumes the scale is accurate. Is it? And how do we know? The answer to this question can be found in the science of measurement – metrology (in contrast to meteorology). This is the first in a series of posts that will talk about metrology and its uses.
I’ve had various discussions about science where people have made statements like, “That can’t be measured” and “Science can’t tell us anything about that.” Since I have yet to be presented with a well-defined concept that science is not capable of analyzing (vs. necessarily already having done so) I feel such statements need to be addressed.
The motto of an organization I used to work for is: “Without data there is no test.” The organization was involved in acquiring test data to evaluate complex systems. The objective was to provide legal certification that the systems met specifications. Such legal certification cannot be documented without well measured and analyzed data. This is a practical application of measurement, of metrology. But the model applies to all of science. There is no science without experimentation. There is no experimentation without measurement data. To understand what science is, does, and can tell us, we need to understand what a measurement is and what information measurements provide. This post is, then, one part of a response to statements about what science can and cannot do.
The first two sections of this post provide a slightly technical introduction to measurement. The third section gets into how measurement relates to my philosophical foundations. If you’re more interested in the philosophical aspect, you could skip to there and decide if you need to review the technical stuff. On the other hand, if you’ve never considered the basic question of how we know we have a pound of potatoes, you might be interested in an overview of this fascinating field of study.
Accuracy and Precision
In essence, a measurement tells us the static state of an object. But what exactly does a scale tell us when we weigh a potato? The key issue is that every measurement has an error. The best we can do is to say that the potato weighs one pound plus or minus some error. The figure illustrates that a measurement error has two parts: accuracy and precision.
The concise description of this from Wikipedia is: “Accuracy is the proximity of measurement results to the true value; precision is the degree to which repeated (or reproducible) measurements under unchanged conditions show the same results.”
Wikipedia has an excellent detailed discussion that I’m not going to repeat here but I’ll walk through the basics with an example. It is convenient to consider the reference value in the figure as the “true” value of what we’re measuring. (There is a technical reason for calling it a “reference” rather a “true” value.) This may very well be exactly one pound, but we can never know for sure. All we can know is that there is some distance, the accuracy, between what we measured and the “true” value. Precision can be thought of as how many calibration lines there are on the scale. Does it measure to a tenth of a pound? To a thousandth? The curve above the word precision in the diagram represents the fact that, every time you measure something – even the same potato on the same scale – the scale will give you a slightly different answer. (This is a fundamental limitation of technology and our ability to use it. Since there is a portion of the scale that moves, any slight difference in many factors – even air pressure – can change where the moving part settles.) Thus the curve represents the distribution of repeated measurements. The center of that curve is the most likely instance of any of those measurements.
Every measuring device has a limited accuracy and precision due to limits in manufacturing. Accuracy can be corrected mathematically by a calibration curve. Whereas precision mostly requires better manufacturing of the device – more calibration lines on the scale. Calibration curves can be very simple. If the scale always weighs a half pound light then the calibration curve is applied by adding half a pound to each measurement. (This is done mechanically on older, spring based, scales with a dial at the top of the scale.) On the other hand, calibration scales can be very complex. There was a recent announcement of potential signs of life on Venus. The result was from a spectrographic analysis of the composition of Venus’ atmosphere. Now, a measurement of a spectrograph is a curve rather than a single number. It provides a value for each frequency in the spectrum being measured. There are a lot of things that cause error in measuring such a curve: changes in the atmosphere, interference between the sensor and the atmosphere, etc. In order to tease out these errors, a complex calibration curve was used (this might be called filtering). I doubt if I remember the details exactly, but I read it was something like a 12th order curve. Such curves change dramatically with small perturbations. The complexity of this filtering calibration curve was one of the concerns as to the validity of the result. (I haven’t followed up with what the current status is on this.)
International Standards and Traceability
So how do I know that the scale I put the potato on is accurate enough? How do I know it’s not always off by ½ a pound? The answer is that someone calibrates it against a known standard. They physically place a one pound weight on the scale and check the result. But you then have to ask how we know that the weight itself is one pound. The answer is that there is a series of calibrations that provide a chain of traceability starting with the set of standards defined by the International Organization for Standardization (ISO). There used to be a physical object that had a mass of 1 kilogram by definition. This object would be used to calibrate the most accurate scales. These scales would then be used to calibrate other physical objects and on down the chain from scales to weights to scales to weights until you get to the potato. The international standards have, however, moved from artifacts (a physical object massing a kilogram) to intrinsic standards (mathematically based on fundamental constants). The kilogram is now defined in terms of the second and the meter. So, anyone with the right equipment can determine a kilogram. In practice, there are national level standards labs (such as the National Institute of Standards and Technology, NIST, in the U.S.) that calibrate from international standards. Then there are primary standards labs that calibrate from NIST. There are also sometimes secondary or tertiary labs. Working down this chain you ultimately reach the scale at the produce store that weighs the potato.
The accuracy of devices get less and less as the cost goes down and the devices get further and further from the ISO standard. Ultimately, as long as the produce scale is “accurate enough” the store and customer are happy. The way we know it is accurate enough is through standards traceability.
Relation to three philosophical foundations
There is a common saying among metrologists that “the most common measurement device is the eyeball.” This maxim provides a direct link between measurement and the third of the three philosophical foundations I discuss in Am I a figment of your imagination?
- Cogito, ergo sum (I think therefore I am),
- Something exists besides self (objective reality),
- Sensory perceptions interpret, rather than capture, reality (modelism).
Our senses are the foundational source of our understanding of objective reality; our senses measure. Even further, the scenario of measuring, along with the understanding that every measurement has an error, formalizes much of the three foundations. It is “I” that doing the measuring. I am measuring something in objective reality. This measurement interprets, rather than captures, an aspect of reality due to some level of inaccuracy and imprecision. It is the measurement, not objective reality, which we incorporate into our model.
The fact that every measurement has an error applies especially to eyeballs and our other senses. The level of accuracy of our senses is good enough for a great deal of what we do during the day, but our senses can also be completely fooled. Optical illusions are a good example, especially at the level of professional stage magic. Some of the reasons stage magic “works” is due to the limits of our senses. To illustrate an example of why magic uses misdirection, hold your hand out at arms distance. The physical optical sensor in your eye is only capable of sensing an area about the size of your thumbnail at that distance. That is, at any given instant of time, you only see a tiny portion of the scenery – a tiny portion about the size of your thumbnail. Add to this the fact that the eye looks at very few spots in the scenery per second. When you envision a room or some scenic view, most of what you “see” in your mind is a construction made up from very sparse data. If you aren’t looking directly at something at the time it happens, you literally don’t see it. That’s why magicians misdirect you. Another example is that the hand is literally faster than the eye. I once had a magician demonstrate that he could do a card maneuver without my being able to see it. He purposely didn’t use misdirection and let me look directly at his hand. He repeated the move and slowly increased the speed until I couldn’t see him do it.
[Please remember that stage magic is trickery. (I really appreciate Penn & Teller being adamant about this. During their shows they emphatically say that anyone telling you they are performing real magic is a scammer.) I was at a magic show in Las Vegas [not Penn & Teller] once where I saw the assistant that had “disappeared” climb up into the box that they suddenly “appeared” in. But that was because I was very close to the stage on the far right hand side. I was in one of the least susceptible positions, the box was maybe ten feet from me at eye level, and I was consciously trying to see something like that. And even then, it was maybe a second of opportunity.]
The eyeball maxim also captures the point that a measurement doesn’t have to be quantified in the sense of being reduced to a number. You don’t have to know that a door is 32 inches wide or the exact width of some object to know that the object will fit through the door. Sometimes it’s necessary to quantify such measurements, but not always. We use measuring instruments when we need more accuracy or precision than our eyeballs or other senses can provide. We also use instrumentation to help us decide if our senses have been completely fooled.
Even though our senses can sometimes be very inaccurate, it is pretty awesome that are senses can also sometimes be very precise, especially with training. Someone with perfect pitch can tell what note a sound is. If that person also knows how to translate the standard notes to their frequencies, it’s possible they can tell the pitch of a tone to an error of a few hertz. I once played a note on my saxophone using a fingering for a non-note (a nonstandard fingering that would create a nonstandard tone) and had my cousin identify it as a note between two standard notes. Some mechanics or hardware store workers can look at a nut or screw and have a damn good chance of telling you its measurements. One of the awesome examples I remember has to do with mothers and their babies. A study found that most mothers can identify their baby simply by brushing the child’s cheek. That’s awesome!
A final philosophical note is that this series of posts on metrology fills in details for Is there anything supernatural? Measurement plays an important part in that discussion. I provided a very brief discussion and said I’d probably post about measurement later. Here it is.