The Elements of Measurement

In the last entry, I listed the questions I will address and the elements of measurement that need to be kept in mind.

1. What is measurement?

2. How is it done?

3. How did it develop, when and why?

4  Why is it so important: what is the function of measuring?

5. Is it being used appropriately?

The elements that I am working with are:

  • Measurement is a social activity, in that measurement is not usually for one person only
  • Measurement is done to something (object, process, performance) in order to capture some characteristic of that something, for comparison, communication or replication
  • There must be sufficient language to communicate the measurement of that something’s characteristic(s), not just the words but the concepts behind the words
  • A way to record or capture the measurement of that something beyond language, such as writing, symbolic marks, numerical system, etc.
  • Scales against which to compare the measurement, either previous measurements done in a similar fashion or perhaps, some standards

The upshot of these elements is that measurement depends on developing and having tools to use to make the measurements, most critically, and then requires the means to capture those measurements so that the results can be used again if needed, and communicated to others.

To elaborate on these somewhat, the first element that must be present is a group of humans that need to measure and communicate about their measurements.  Although I am conscious of the caveat on hunter/gatherer groups (mentioned in the last posting), I still feel that measurement is an inherently social activity, though it may not have started out that way, and does not necessarily need to be performed only by groups.  It is social, though, in that there are often reasons to involve others in the measurement processes, and there may be a need for others to be able to replicate the measurements in a way that allows for use in other contexts or for comparisons.

The next element is language: being able to communicate about a measurement activity. The topics that a social group would include in their discussion of a measurement activity, which of course requires the use of language, are what was done, why it was done, what the results were and what they mean, but that may not be all the topics.  The language must have evolved to a point where people use words for symbolic and abstract concepts and purposes.

People and language by themselves may not be enough: as a corollary element to language, since memory is not always reliable, being able to capture or record measurements in some form, whether writing or just notches on a stick, will facilitate the recall of a measurement.  But now other attributes come into play:

  • number systems and the concepts behind them,
  • standardized scales based on number systems and units; and
  • the physical tools that can be used by anyone to compare what is being measured against a form of the scale.

This way, anyone should be able to replicate the measurement, making the measurement process objective – not dependent on any single person.

The above comment that the measurement process needs to be objective, is very important in a world of humans with varying agendas, desires, ambitions, selfishness and selflessness.  In an offprint of an article by Michael Fortun and Sylvan S. Schweber, I found a quote from a paper by Theodore Porter which he delivered in a conference in 1990.  The quote is one that I have used time and again in my work to help people understand why performance measurement must be perceived as objective:

He [Porter] pointed out that quantitative knowledge “is especially useful to coordinate the activities of diverse actors, and to lend credibility to forms of belief and action when personal trust is in short supply.”  Porter stated the matter succinctly and epigrammatically: “Objectivity has prestige in a pluralistic society mainly as a substitute for trust.”1

Seems like a bundle of things that measurement depends on.

Evolution and Measurement

I did not think that the desire to measure, whether to measure things, performance, duration, the universe, objects of commerce or trade, was necessarily a natural desire or instinct. at least by the definition above with all of its elements. Because of its social component, I suspected it of being a consequence of the ability to communicate, therefore a piece of what our civilization is made of.

I knew of no animals that appear to “measure” per se.  However, the more I’ve thought about this, the more I’ve found what could be considered precursors among animal behaviors, such as:

  • the dance of the bees to communicate where there is nectar as containing measurements, defining which direction to go and approximately how far
  • the building of nests by bees and wasps, with the bees using hexagonal cells that are the right size to contain the larvae
  • the building of nests by birds, and bowers by male bowerbirds in New Guinea, nests the right size for the number of eggs to be laid, “well designed” bowers to attract females
  • the building of dams by beavers, with the logs of the dam the right size to slow the flow of water in the stream
  • the judgment of a horse that balks at a fence, judging it too high to jump, or at a gap, judging it too wide to jump across

These behaviors seem to be related to measuring, if not exactly evidence of measurement done by non-human species.  This has made me think that perhaps the desire to measure is, in fact, a natural trait, that it evolved as a result of natural behaviors, but as with so many behaviors that humans use to cope with their lives, extended (exaggerated?) considerably.

Besides, if it were not a natural desire or instinct, whose idea was it, anyway?

One wonders if measuring might have contributed to the relative reproductive and evolutionary success of one of the hominid species to the exclusion of the others, so that only homo sapiens exists now, while all of the others have gone extinct.  In addition, has the development of measurement behaviors contributed to one or another tribes’ dominance in such a way that measurement has become such a large part of the modern world?  How did we humans as a group get to the point where nearly everything is either measured or a candidate to be measured?  How did we decide, if a decision was made, to measure human performance, establish scales and standards and then agree to submit to being ranked on these scales?

(As a quick look forward to future articles, it appears that the beginnings of measurement are coordinated with the agricultural revolution, which occurred within the last 12,000 to 10,000 years.  If so, that is really insufficient time for natural selection to work on “genetically-coded measurement”, but perhaps long enough for behaviorally oriented or learned measurement.)

In all of the background reading I’ve done about this topic in archeology and anthropology, the archeologists and anthropologists all report, without fail, that all cultures use some forms of measurement, although that is often not their primary focus.  Some of the cultures only have numbers from 1 to 3 or 1 to 4, and then collective numbers.

The most common type of measurement in all cultures is some measurement in which time figures, though it may be no more developed a measure than the number of days or half days to go from one place to another.  Additionally, what you might expect as a place where measurement plays in all cultures, the building of artificial shelters, is often performed by construction measures that rely on rule of the thumb (or body part) types of measures, much like those mentioned earlier among the hunter/gatherers who build canoes.   These body-part measures can be used within a communal project by cutting a pole that is twice the length of one person’s arm length, or the distance from ground to waist, then using that to compare subsequent sizings to, while working on the project.

A possible way that people started measuring was by comparing themselves in a competitive way: if I can successfully overcome you in a fight, I will be able to physically dominate you because when we measured our strength, I proved to be (comparison here) stronger than you.  Only later would it be worthwhile to establish competitive feats of strength that did not leave one or the other or possibly both competitors with injuries that could preclude consolidating the victory by further physical activity.  And then, when someone who was really cleverer came along, they might be able to dominate by “personality” , “charisma” or “wisdom” rather than having to establish dominance by force.

Does this mean that all measurement contains the elements of competition and domination?  I don’t think so, but it is an interesting speculation.

Meanwhile, when moving away from the measurement of strength or dominance within a group of people, measurement continues to have a social component to it, as well as requiring language and numbering schemes, scales and writing, and specific concepts for the different types of measuring.  The act of measuring has come to mean, in many cases, comparing a result of a measurement against a scale that has been at least locally standardized so that the object or act that has been measured can be understood.

Would another intellectual tool that might be required be the concept of possession, providing a reason or need for the enumeration?  The concept of possession would be necessary for the development of trading: I own this and you want it.  If so, I believe that the object that you own is as valuable to me as what I own is to you, so perhaps we could exchange them.  The question of how value is measured is another deep one.

Without numbers, counting the number of cattle one owns or controls would be pretty difficult.  If five of us decided to turn all of our cattle over to a common cowherd for the summer grazing, in addition to “marking” which were ours, we would need a way to capture how many cattle each of us had originally provided to the cowherd, to be able to reclaim them at the end of the season (or be compensated for their loss), and to know our portion of the cowherd’s wages.

This is exactly what some of the earliest forms of measurement that have been found appear to indicate.  The simplest enumeration would be, say, a stick with a notch for each of my cows, and a symbol indicating my count, as opposed to your count, or one of the others who shared the cowherd’s services.  And the earliest examples of measurement look like that, notched sticks, and clay tablets, with notches.

This sort of notched stick measurement is very old.  There are some very early artifacts, dated to 35,000 BC, 30,000 BC and about 20,000 BC, which are sticks or bones with notches on them.  And notched sticks, in the form of Exchequer Tallies, persisted in England, at least, up until the 19th century.  The last were collected in 1826, and eight years later, in an effort to get rid the old tallies, evidently they were burned in stove in Parliament.  The fire went out of control and burned down the old Parliament.  Ooops.

Mentioned is a symbol indicating “me”, an abstract for a person.  If a symbol can stand for a person, could a set of symbols be developed for counting cattle, as opposed to the symbols for counting sheep?  Certainly and that too shows up early in enumeration records.  At some point, numbers are separated from objects, abstracted, to indicate, for instance, “IIIII cows” and “IIII sheep”, rather than ttttt for five cows and wwww for four sheep.  This is a step probably made after those horned things that give milk were named “cows” or “kine” or whatever sound the Indo-European language used for the word, and the fuzzy ones we get our wool from were named, abstracted, as “sheep” or “mouflon”.

To get to the point where enumeration occurs requires a set of intellectual tools beyond the physical tools of sticks and cutting implements, clay tablets and specially shaped wands.  Not only will language be required, but some specific kinds of words – words that are more than a name for the specific dog that favors me, but for the class Fido is in: dog, as a symbol for all of the wolves that have bent themselves to the will of the people in my group.  (Whew – a few of those symbolic words in the last phrase, no?)

Physics, Sports and Objective Measurement

To understand measurement and the human propensity to measure requires investigation of a number of areas.  As I said, this is not a small topic, since measurement is so generally used.

The logical place to start might be physics, because physics is concerned with, among other things, the two most fundamental concepts that are measured: Time and Space, though there are those who would dispute these being divided into “two”.  As dimensions, they are the four basic dimensions of traditional understanding (three spatial and one temporal), though thoughtful cases have been made for additional dimensions.  For the convenience of this inquiry I will treat time measurements and spacial measurements, though, as two threads of inquiry, since the history and growth of time measurement is different than the history and growth of spatial measurement, with the two becoming viewed as co-dependent only with the theories of relativity – special and general.  (There is a major caveat, though, on holding them separate: much of time measurement has been translated into spacial representations.2)  Their histories and developments occur at the same or similar times, and often a development in one affected the other.  But they each require their own treatment.

If that were the extent of the inquiry, I would stop now rather than trying to write yet another treatise on physics.  Since sophisticated understandings of space and time are now themselves tools of measurement, there is a lot more work to do.  To see that, we can look at another discipline.

During the late summer of 2008, there was a major festival of measurement, held in Beijing, China.  Athletes from all over the world came to perform, have their performance measured and compared with others, and receive medals for the best performances in their respective sports and events.  As a former competitive swimmer, I was thrilled by the performance of Michael Phelps, the American swimmer who captured 8 gold medals, a record, since no one had ever captured that many gold medals in a single Olympics before.  He almost didn’t succeed, though, because in one of his events, the 100 meter butterfly race, he just barely touched ahead of Milorad Cavic, the next competitor to trigger the touch pad.  Barely – by .01 of a second.  Phelps’s time was 50.58 seconds, Cavic 50.59.  Was this a fair result?  Can it be trusted?  If we remember Theodore Porter’s statement about objectivity, we have no choice but to trust the result, once we have looked at whether or not the result was sufficiently objective.

Some perspective on these comparative measurements: a reason to develop standardized scales is to provide “objective” measurement, since anyone using the same scale should be able to generate the same result.  The scale should be made immune from “subjective”, and thus potentially unfair, judgments.  In the case of this race, it was as objective as possible: the timing was started at exactly the same instant for all of the touch pads, since they all use the same clock.3 The only differences in the performances were in the touches by the swimmers.  I’ve used them: when you touch the pad, even lightly, it stops the clock for that lane.  The result in this case was “fair”.

Some further perspective on this, since the quantity, .01 of a second, is so small.  If a second was as long as a minute, .01 of that minute would be still be less than a second, as in .6 of a second, or 3/5ths of a second.  Because they swam 100 meters in approximately 50 seconds, they were traveling at a rate of approximately 2 meters per second.  1/100 of a meter is 1 centimeter, so Phelps beat Cavic by approximately 2 centimeters over the 100 meters (2/10000 or 1/5000 of the distance).  Evidently it doesn’t take much to go from number 1 to number 2.

In January of 2009, a similar measurement led to the disqualification of a competitor in a World Cup slalom race.  Bode Miller was “caught” wearing ski boots, the soles of which were 1/100 of an inch too thick.  Just exactly why the rule was made is outside of the scope of my inquiry, but evidently there is a rule which was violated, disqualifying Miller from continuing in the competition.  Try to take an inch and divide it into 100 equal parts.  I’m not even sure how to begin to do that, but because a standard has been used, the ruling must be “fair”.

Both of these examples show how deep the dependence on measurement is in sports competitions, and both present some of the fundamental measurement concepts.  Social, language, numbers, standardized scales, writing to capture the results, comparisons, results that can be replicated, objectivity, and a new concept: precision.  While these examples were drawn from competitive sports, other disciplines have as critical a need for understanding how measurement is used within those disciplines, what the boundaries are for the precision, and what the potential effects are if the measurements are not applied in the correct manner.  In other articles in this series, I will discuss these concepts and at others as they are relevant to determine how they function in the various domains of measurement.

Some of the Topics for Further Investigation

I shall explore, then, some history of measurement, which requires looking at a number of disciplines.  Evolution of language, history of science, history of numbers, history of standardized scales, history of writing will all have to figure into the picture.  I have had to make acquaintance with archeology,  anthropology, physiology, evolutionary biology, evolution of language, as well as a few more areas of study, and will share what I have gleaned from my reading as it bears on the development of measurement techniques.

It appears that much of the development was driven by the concept of possession and its side-kick, commerce: the ability to determine equal or fair quantities of goods or money for quantities of goods that I own is a form of human intercourse that relies on measurements and establishing standards.  Accounting and how objects of commerce are valued are part of the discussion, as stated above, even how actuaries in insurance companies establish the value of the people they insure, though strictly speaking, the work of the actuaries is really to assess risk.  Some of the drive to measure possession and commerce  was, of course, taxation, which, among all of the people I’ve ever asked, does not stand a chance of ever being considered “fair” by those who are taxed, only by those who set up the taxation .  In my reading, I made a further digression into political science, discovering how various authors attribute the way that colonial nations used “measurement”, as in surveying land, to being able to establish and consolidate political power and control.

Any discussion of measurement would be incomplete without reference to a number of scientific disciplines in addition to physics, as well as reference to sports competitions and how performance is measured in those arenas, as seen in the two examples above.  Those are the “objective” measurements.  Within sports, there are other types of measurement used: think of judges rating divers, figure skaters, gymnasts.  And I will delve into the ways that people are measured in contexts other than sports, such as educational testing and employee performance measurement, along with some of the corporate measurements other than just the bottom line, such as customer satisfaction surveys.

Along the way, it will be impossible not to discuss measurement techniques and the tools embodying those techniques, whether intellectual tools or physical implements.


1 T.Porter, “Quantification and the Accounting Ideal in Science”, HSS meeting Seattle, 28 October 1990, as quoted on pp. 340-341 in Fortun, Michael and Schweber, Sylvan S., Scientists and the State: The Legacy of World War II, article in Kostas Gavroglu et al. (eds.), Trends in the Historiography of Science, pp. 327-354, Kluwer Academic Publishers. 1994 Netherlands

2 Distance measurement have been use as metaphors for time measurements and vice versa probably since the beginning of telling time: various cultures describe distances in terms of the time taken to cover a distance, and also the poetic measurement of aspects of lifetimes as a journeys.  My favorite conjunction of time and length is that the original attempt to define a meter was in terms of its time equivalent: a meter was supposed to be the length of a pendulum with a period of 1 second.

3 Using a single clock should avoid the problem of simultaneous events as discussed by Einstein in his treatment of relativity: however, there could in fact be minor variations in the distances from the clock to each timing pad, requiring longer or shorter electronic wires to connect them to the single clock.  As a result, there could be differences that would surface, but since electricity travels at nearly the speed of light, roughly 300,000 kilometers per second, the differences would be of a scale that is unnoticeable: 1/100 of a second would represent 3000 kilometers, and if the difference in lengths of the wires connecting the two touch pads was of the magnitude described in the text, 2 centimeters, that would contribute another 2/30,000,000,000 of a second difference between their times.  If I have done the math correctly, that amount is well below what I can fathom – I’m still having trouble with 1/100 of a second.  The problem as a whole is usually avoided by making the connections to the clock from each of the pads as closed to the same length of wire needed for the pad that is the farthest from the clock.

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One Response to The Elements of Measurement

  1. branwyn says:

    As I look at Bob, I’m reminded of another possible evolutionary example of measurement in non-humans: the ability of a goldfish to grow to the size of its environment. How do they do that, and why?

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