A Measured Post

The digital multimeter in my garage is amongst my favorite tools, and not just because I feel like I’m carrying around a Star Trek tricorder when I use it.  That I can easily and quickly use the same tool to measure alternating and direct current, circuit resistance, voltage, capacitance, impedance, and numerous other quantities is marvelous, at least to a dork like me.  It also speaks to something that we often don’t think about, which is how we measure.  Measurement, you see, is quite difficult, and I’m always minorly thrilled by the clever solutions we’ve developed to measure quantities that our mere senses can’t even tell exist.

Despite how little we think of it, measurement underpins the technological fabric of our modern world, it is fundamental to science and engineering, and it is how we are able to interact with the world.  The simplest act of measurement is using our basic senses, but these are severely limited, imprecise, subjective, and clumsy tools for measuring anything.  How do we know how much current is coming out of an electrical outlet, or how cold the refrigerator is, or what the atmospheric pressure is, or the composition of a star thousands of lightyears away?  It’s all measurement.  Measurement tools and techniques, like wheelbarrows rigged to automatically plant potatoes, are some of the most fascinating, understated, and clever pieces of technology when you take the time to understand them.

If you want to know what the temperature is in your room, you might find a thermometer.  But how does that thermometer work?  It’s reporting a visual degree measurement, but how is it getting to that number that it presents to your senses?  In the old days, the thermometer might be a tube with a bulb of mercury.  When the temperature of the mercury increased, it expanded, taking up more of the tube.  So we’re not directly measuring temperature, but rather the linear expansion of a material, which happens to correspond to a particular temperature.  These days, we don’t use mercury, but the principle of any tube-type thermometer is the same.

What about a digital thermometer?  In theory, you could set up some kind of photosensor to discern the position of expanding liquid in a tube, ala a traditional, analog thermometer, but that’s a clumsy mechanism.  A cleverer solution is to recognize that a material’s electrical resistance changes as its temperature changes, and that you can therefore measure the temperature based on a measurement of resistance.  In other words, a digital thermometer doesn’t need to measure temperature at all; it just provides temperature mathematically based on a different physical property, one that we can’t directly discern at all.

Measurement becomes an extended, serialized game of inference based on changes to material properties.  We measure the existence of what we vaguely name “dark matter” based on the movement of normal matter in response to its inferred presence.  We measure gravitational waves based on the behavior of lasers over immensely long distances.  We measure time based on the frequency of oscillation of a crystal vibrating under the piezoelectric effect and tuned by the closed-loop feedback control of cesium ions passing through a vacuum in a C-field.  All of these measurements must be translated into something that we, with our limited five senses, can interpret.

How we measure things matters, because the mechanism of measurement and its interpretation can affect the conclusions drawn from the collected data.  This is obvious in the observer effect studied in quantum mechanics, wherein the act of observing something causes it to behave differently (the famous two-slit experiment, for instance), but similar effects are extent and even more pernicious in less exotic applications.  If I wanted to find a measurement for electric current in a circuit, I could use a Hall Effect sensor which measured the electromagnetic field generated by the electrons moving through the circuit, or I could measure the voltage and the resistance of the circuit and calculate the current from those values.  In theory, I should achieve the same result for the current, but will I in practice?  They should be close, but they probably won’t be exactly the same.

Beyond the physical act of measuring, the standards and units involved matter and will affect the data.  The CGPM establishes definitions for units of measurement, like the length of a meter and a second, which will cascade through every other measurement derived from them.  If, for instance, we say that the second is based on the half-life of a radioactive element, and that value is found to be imperfectly stable, then the second itself is imperfectly stable and this will be reflected through everything that involves the second.  Since SI units are built mathematically from base units like the second, the meter, and the kilogram, these standards become colossally important and impactful.

Many years ago, I read a woodworking book called Measure Twice, Cut Once (very creatively titled, I know).  Actually reading it, though, the full quote is revealed to be “measure twice, cut once, but don’t measure at all if you don’t have to.”  In other words, measurement is inherently unreliable.  Your tape measure has a margin of error, the little prong at the front might be loose or bent, changing your zero, the temperature might be different from day to day, and are you measuring to the front, the back, or the middle of the line?  What about the wood’s properties?  Are the boards dried the same way?  How will they move now, tomorrow, and after being cut, milled, planed, or otherwise manipulated?  High-end woodworking stores sell rulers and combination squares engineered with tolerances good enough to build a spacecraft, and which are entirely irrelevant when working with a material as dynamic as wood.  It is better, then, not to measure at all, but to use the project itself to derive the dimensions you need.

Tolerances, standards, calculations, significant figures: they all affect measurement beyond the act of measurement itself, and measurement drives our world.  It is how we form conclusions, explain how the world works, and derive understanding.  Like statistical flaws, differences, discrepancies, and manipulation of measurement and measurement-related factors can lead to vastly different outcomes and conclusions in the end result.  Understanding measurement, therefore, will make you a more critical consumer of the information that’s all around us, whether or not you decide to add a digital multimeter to your collection.