everyone wants to see some measurable return for the money. Yet it is the one area that has the greatest degree of intangibles.” There is no measurable attribute of education except a purely artificial one: “test scores.” Teachers know that test scores don’t measure educational achievement. But when people insist on measurements, they will get measurements.
A great deal of the information we use in daily decision‐making is nonscalar and, therefore, intrinsically not measurable. For example, we cannot measure the appearance of a face, the sound of a voice, or the taste of tomato soup, and yet with no difficulty at all, we greet our friends, recognize their voices, and enjoy our dinners. The information transfer by sight, hearing, and through taste represents very complex information handling using arrays of scalars and correlations between pairs of scalars (temporal and spatial). No instrumentation system can do as sophisticated a job of pattern recognition as the human eye/mind combination, or of frequency analysis/correlation as the ear/mind combination, or of chemical analysis as the taste‐bud/mind combination. We are not denying the improving capabilities of neural networks, wavelet transformations, or AI deep learning – we are just marveling.
2.2.2 Shapes
Shape cannot be measured – not even simple shapes, such as circles. Simple shapes can be described by names that we all understand by experience, but they cannot be measured. For example, a “circle” is defined as the locus of points lying in a plane and at the same distance from a common point, called “the center.” Given that definition and a value for the radius, you can draw a circle and look at it, and you know exactly what was meant – but that does not constitute measuring the shape of the circle. The shape information was conveyed using the reserved word “circle”; only the size was described by the radius and location by the center.
Shape can have a delicious impact, when tested by experiment! For example, the design of rice cookers has made it possible to make chef‐quality rice at home. A few years ago, product design engineers in Japan focused on the cooking profile of rice (not the shape of the device). By experiment, they found the shape of the temperature versus time curve, T = f (t), as shown in Figure 2.1, which optimizes rice taste when the ingredient is washed white, short‐grain rice. They also found a different shape that is best for unwashed rice and yet another shape for brown rice. Although aspects of the shape can be measured, such as the time at each temperature, it is the shape of the cooking profile that enhances the taste of the rice. By offering more delicious rice, manufacturers gained market share over older cookers that merely boiled rice.3
Another example comes from the physics of fluid flows. In boundary layer studies, the shape of the velocity profile is of considerable interest and often needs to be recorded. One way to deal with this is to present u = f (y), a set of ordered pairs (u, y). This allows the viewer to draw the shape and look at it. Another way, conveying less information but sometimes enough, is to present the shape factor: the ratio of two integral measures of the boundary layer thickness, the displacement thickness divided by the momentum thickness. Turbulent boundary layers have larger values of the shape factor than laminar boundary layers. Researchers who know approximately what the velocity profile looks like (i.e. what family of shapes to which it belongs) can communicate quite a bit of information to one another by quoting shape factor values. Yet the value of the shape factor itself is not a measure of shape. Only if the boundary layer is known to be laminar or turbulent or somewhere in between does the shape factor convey information. If the family of possible shapes is not specified either explicitly or implicitly, then it takes a very large number of scalar pairs to describe shape – enough data points to plot the shape so it can be looked at. Presenting u(y) throughout the boundary layer allows the viewer to see the shape, but that does not constitute a measurement of shape any more than a photograph of a face is a measurement of the shape of that face. The derived scalar “measures” of shape, such as displacement thickness, momentum thickness, and shape factor, can convey significantly wrong impressions of the shape of a boundary layer velocity distribution when they are reported for a “pathological boundary layer,” i.e. one whose velocity distribution is significantly different than usual. They convey the right information only when they are applied to boundary layers with generally typical velocity distributions.
Figure 2.1 Rice cooker design trajectory.
2.2.3 Measurable by the Human Sensory System
How amazing is the human sensory system and what it enables us to observe! Trying to extract as much information using scalar measuring instruments is quite a challenge. The human sensory system is very complex, and its receptors are very well tuned to our environment. If our eyes were just a few decibels more sensitive, we could see single photons; if our ears were just a few decibels more sensitive, we could hear the Brownian motion of individual air molecules as they bounced off our eardrums.
Consider our sense of touch. Our machinists claim to easily detect surface roughness of 50 mils (1 μm) with work‐calloused hands. Can our body measure force? Can it measure temperature? We sense not temperature directly but heat‐transfer rate; if you've ever dipped a cold toe into a warm bath, did the water feel boiling hot even if was just warm? (As in an Onsen hot spring in Japan.) We don’t feel force directly but pressure and shear force. In contrast, in the lab we have simple instruments for measuring force and temperature but need sophisticated techniques to measure heat‐transfer rate. Even touch is a marvel. Prepublication we learned: in the journal Nature, it has been “experimentally established that humans have the capacity to perceive single photons of light” (Tinsley et al. 2016). Furthermore “human tactile discrimination extends to the nanoscale … within billionths of a meter” (Skedung et al. 2013). In part this explains how polished steel tactilely differs from smooth rubber.
2.2.4 Identifying and Selecting Measurable Factors
One of the first problems to be faced in exploratory research, and in development work, is identifying which scalars are significant to the issue at hand. Sometimes a single scalar is sufficient, such as a temperature, pressure, or velocity. Sometimes a compound scalar measure can be put together from a set of simple scalars. One example would be the Reynolds number, used for characterizing the state of the flow in a channel. Sometimes two or more scalars can be combined into one measure to reflect value judgments or “trade‐offs” in desirability. For example, consider the problem of selecting the optimum heat exchanger for an engine application. In even the simplest situation, ignoring such considerations as cost, size, and durability, a heat exchanger for engine service has at least two important scalar descriptors: its effectiveness and its pressure drop. Typically, high effectiveness is “good,” while high‐pressure drop is “bad.” Also typically, pressure drop goes up when effectiveness goes up. Neither by itself is a measure of goodness for the heat exchanger. A weighted sum of the two can be used as a “composite scalar” by finding two weight functions, one for effectiveness and one for pressure drop, which accounts for the effects of both on some single, important parameter – brake‐specific fuel consumption is another example. Such “goodness factors” can be used to account for many factors at a time and to convert a nonmeasurable situation to a measurable one.
The choice of what to measure sets the course of the entire experiment, and that choice should be made with considerable care.
2.2.5 Intrusive Measurements
Always remember as you plan: making a measurement intrudes on the system
