There are multiple levels for questioning measurement.
1. What is it?
2. How is it done?
3. How did it develop and when?
4 Is it important, and if so, why?
5. What is its function and is it being used appropriately?
The elements of the definition for measurement that I am using are:
- Measurement is a social activity, in that measurement is not usually for one person only
- Measurement is done to something (object, process, performance) that needs to be captured somehow, for communication or replication
- There must be sufficient language to communicate the measurement of that something, not just the words but the concepts
- 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
These elements should let us proceed with the questions at the top, since they provide a tentative answer to the first question. The second question will have a set of conditional answers, depending on what is to be measured: simple examples are -how do you measure time? with a clock, -how do you measure length? with a tape measure. Those suffice for simple answers, but we will need to look at this much more carefully later on, and some of the answer to this second question may be answered by looking at the third question. So, moving on the third question, how did it develop and when, is one of the places where this gets very interesting.
Who was the first person to measure something and share it with someone else? Frankly, the record is blank, or more correctly, the question is meaningless. It is not really clear when measurement developed, but it seems likely that it occurred within the scope of history that homo sapiens participated in. That’s likely to be the last 200,000 years or so. While there are some artifacts from as early as 90,000 years ago that show some “creativity” – beads made from sea shells found in Israel – and others at about 60,000 years ago – etched eggshells found in Africa, it is not clear that this would have required “measurement”. Nor do the many flint tools necessarily require measurement: some of these have been dated back to long before 200,000 years ago and have been associated with earlier species of hominid.
In an article in Science, 9 April 2010 titled “Did Working Memory Spark Creative Culture?”, by Michael Balter, there is a discussion of a relatively new model of how human brains work. It is a step beyond the common model of short-term and long-term memory, the first of which I am old enough to suffer from the loss of, to an extent.
It should be noted here that there are a number of models of how the brain works, and at this point, I am not prepared either to discuss them or to provide some of my naïve evaluation of their relative merits. The article only discusses the common, even trite, version of short-term and long-term memory. The model renames short-term memory as working memory, the characteristics of which are considerably more “active” than what is normally referred to as short-term memory. To quote, “…most researchers agree that dynamic concepts of working memory, rather than passive storage, best explain sophisticated human cognition, which requires that we be masters and not slaves of our memories.”1
This working memory enables “…an enhanced capacity to hold and manipulate information in one’s conscious attention while carrying out specific tasks…”2 and appears to facilitate “creativity”. Evidently without it, the artifacts mentioned above could not have been created, nor could the stone tools ranging from bifacial ones (earlier versions) to “highly symmetrical hand axes”, not to mention the cave paintings in all sorts of places around the world, etc.. So how did this working memory capability develop, for surely it would need to be present in order to measure as well?
The article itself is somewhat inconclusive: some of the researchers posit a genetic mutation or a set of them happening relatively close together to provide a sufficiently enhanced working memory to permit the development of what is recognized as human behavior, as distinct from other hominid behaviors (H neanderthalensis? H erectus? H. heidelbergensis?) or other mammal or animal behaviors. A sort of genetic “big bang”, I suppose. The researchers featured in the article who have provided the working memory model apparently believe this to be the case.
Others look at the evidence for creativity in archeological artifacts such as those mentioned above, and suggest that this working memory could have been selected more gradually than a sudden burst of genetic mutation. If so, the working memory capabilities of some of the couples who reproduced must have been enough better that their offspring had the enhanced capability, and it was spread into a sufficiently large population to become a factor in selection.
The next article in the same issue of Science, titled “Did Modern Humans Get Smart Or Just Get Together?”, by Elizabeth Culotta, discusses ideas presented by other researchers, in which population size has an effect on “creativity”, with an apparent correlation between larger groups and greater creativity. Based on the evidence of creativity, again referring to the archeological artifacts mentioned above, the theory goes that some populations reached the point where creativity was reinforced, and some were so small that not only did they fail to produce evidence of creativity, they actually dwindled and disappeared. The record being uneven means that there were groups that “blossomed” and then extinguished their creativity or were extinguished, in a kind of oscillating pattern. If the first article hints at a genetic “big bang” analogy, this one hints at a kind of “critical mass” analogy.
While the idea of population size might move the genetic big bang back further into the past – as in, the genetic big bang occurred, but the size of the population was too small to exhibit creativity, and until the population grew large enough, there is little evidence of creativity – it looks as if instead, this allows for a longer development, providing the time necessary for the incremental selections of evolution that would result in the behaviors that are recognized as modern human behaviors, with creativity certainly one of the factors.
Whichever way creativity developed, it appears to have reached a critical stage approximately 40,000 years ago, and has been on the upswing since then. At that point, artifact evidence of creativity becomes more common.
So did measurement start at that point? I don’t think so, but of course, as I wasn’t there, I can’t say for sure. In reading literature about cave painting in France and Spain, which ranges from about 38,000 years ago to 12,000 years ago, I cannot find any evidence that the cave painters were required to use measurement to complete their works. They could have, of course, but an artist with a practiced eye may be able to capture the proportions fairly correctly without putting some sort of grid on their “canvas”, in the way that perspective grids were used beginning about the time of the Renaissance.
In reviewing more archeology, specifically the archeology related to the period after the Last Glacial Maximum (LGM), approximately 20,000 years ago, which may coincide with an intensification of cave painting, and was finally over about 10,000 to 12,000 years ago, measurement is not the first thing that is noticed by the archeologists. Instead, there are other behaviors that are on the agenda, and measurement is not looked at as a foreground research question. I found a wonderful survey of the archeological sites that have been dated to the end of the last Ice Age, called, appropriately, After The Ice, by Steven Mithen, which has the subtitle, “A Global Human History, 20,000 – 5000 BC”. In his introduction, he makes clear that the change in the way that people lived before 20,000 BC and the way that they have lived since 5000 BC are different in significant ways, and much of the change can be observed in the archeological evidence as having occurred in the last 12,000 years (since 10,000 BC).
A few comments about the book: it is well organized, but as a narrative device, he uses a character who can “experience” viscerally each of the communities that are described. While a conceptually nice device, I found it getting in the way of my absorbing the information I was looking for. This may be my problem, not his, but I suppose I could have found a dry textbook version of the information he presents.
Given that, the survey does touch on all continents inhabited by humans. He reviews the most recent archeological sites and the current thinking about what they represent in the development of civilization as we now know it.
He focuses on the change from hunter-gatherer types of social units which did not have settlements to the beginnings of agriculture with settlements that persisted through the seasons. Among the changes that I had hoped to see highlighted are those “measurement” aspects that are part of agriculture: being able to use the stars (actually at that time, the heavens) to know when to plant, when to harvest, etc., so a start on using astronomical data, whether couched in astronomical or astrological terms, and some “building” measurement tools such as straight edge, plumb line and level, but they are not in his book.
So what would the evidence of these ways of thinking about managing the world look like? Let me postpone giving my answer, but think about this a bit yourself. What would you expect?
To me, it seems that the critical step of making the change from hunter-gatherer to farmer-herder would be a sense of controlling the elements of the food supply. A hunter will develop an understanding of where and when he/she is likely to find prey, and based on that, will try to position him/herself where there is the greatest chance of spotting and getting prey, but there is a “passive” sense about this, as well as an opportunistic sense. Hunters also need to be flexible, so that they can change from hunting deer to gazelles quickly enough to capitalize on the fact that there is a gazelle, not a deer in sight, and sufficiently agile that if it turns out that there is a leopard also stalking that gazelle, they can either scare off the leopard while getting the gazelle, or be prepared to run like hell from the pissed-off leopard. Gatherers would need to know when various plants were likely to be covered with edible stuff to be picked or dug. This would require some memory of the past, perhaps tied to the passing of seasons, and could be a start on the kind of pattern recognition needed to survive as a farmer. And the hunter-gatherers did survive: those who were able to figure out the patterns would have been more successful in surviving and probably in reproducing, which would lead to smarter hunter-gatherers over time.
Somewhere, though, would come the break, which could be in the form of, “if we could put a group of these plants in an easier spot and let them grow, our gathering trips might not be so long”, or in the form of, “maybe if we capture and tether the kids of the goat we just ate, when they get big enough, we can eat them”.
What the exact process was is beyond my ability to reconstruct, and even if I could reconstruct it, it only has a marginal chance of being near to what really happened. Speculation, fun as it is, is strictly that: speculation. However, if there is any truth to my speculation, it probably resides in the concept of controlling the food supply, which, for all I know, may have been an unintended consequence of what really happened, maybe even a lucky accident.
Mithen’s book does mention some intermediate stages that I had never though about, that of hunter-gatherers who had regular places of “settlement”, perhaps caves for the winter season, perhaps small temporary settlements near a particular watering spot for the regular migration of some large prey, and also of the other side, people who were not really farmers, but were cultivators of wild gardens near their permanent settlements. Both seem possible to me as intermediate stages between purely hunter-gatherers and purely farmers.
So, now to work on the question of the evidence of measurement that might be expected, the building tools that I listed above: straight edge, compass, level, and plumb line, might not have survived. Making a straight edge out of flint, obsidian, or any other of the stones that were worked into tools, or out of bone, would be nearly impossible without the kinds of tools that became available much later in human history. So what would a straight edge be made of? If it were possible to make one, it would likely have to be made of something perishable, like wood. To make better curves, something like a plumb line would be fairly simple if one could twist some of those plant fibers that are used for early clothing into a line or string, then tie a shaped rock to the end of it, one of us could hold the rock and another, hold the free end of the string firmly in one place against whatever we wanted to inscribe with a circle, and the one with the rock could scratch a reasonable circle. (Could ligaments or sinew be used instead of crude string? I don’t know, but they would be perishable too.) The rock might survive, and look as if it were just another somewhat shaped rock, purpose uncertain, with scratches on one nearly pointed end, and the string would perish. To use it as a plumb line would require the same construction, but the one holding the free end might just hold it near the top of a wall that’s being build, let the end with the rock hang and use the line for a reference: this wall stands fairly straight. Hmmm. We can use the line to lay out the wall we want to be straight rather than circular. Again, perishable tool materials, gone. And a level? perhaps that bowl would allow us judge whether this is level if we put some water in it. Pottery bowl? Hollowed out tortoise shell? How would we recognize it from just another bowl?
So those tools would have very little likelihood of surviving in a recognizable state. How about astronomical tools? How many years of observing the rising of Sirius would it take to associate it with the coming of the fall? My guess, and that’s really all that it is, is that only with the development of permanent or semi-permanent settlements would the rising of a particular star next to a landmark on the horizon be recognized as a repeating event, with some pattern of season associated with it.
Those are two ways that humans might have started using measurement, to help control an understanding of repeating seasons, and to help make dwellings. Another early concept that might require measurement would be possession: what ‘belongs’ to who. Several ways that could happen: who has the ‘right’ to use which plot of land for their crops and how much land do I control; and who is the ‘owner’ of this or that animal and how many of these goats/sheep/cows are mine – in other words a way to mark what is mine, and perhaps a method of symbolizing who owns what. And perhaps, since I have more goats than I really need, I can let you have one for yourself, but in return for it I want: what? something that is of equal value? How would that be determined?
In my searching and reading, I’ve found mention of a few hints of measurement. There are three ‘decorated’ bones that have been dated to very early: one known as the Lebombo (Lembombo) Bone, dated to approximately 37,000 to 43,000 years ago; the Wolf Bone, dated to approximately 30,000 years ago; and the Ishango Bone, approximately 20,000 to 25,000 years ago.
The Lebombo Bone has 29 scratches on it: interpreted as either lunar cycle or menstrual cycle.
The Wolf Bone has 55 scratches on it: not sure how that has been interpreted.
The Ishango Bone has three columns of scratches with the scratches grouped. These have been variously interpreted: as prime numbers, and as a lunar phase calendar/menstrual cycle counter.
In Mithen’s book, there is another hint at early measurement that took up a sentence or two, with a footnote. I followed the footnote, obtained the article (don’t you love the internet?), and read it. The article is a report by two archeologists, O. Bar-Yosef and A. Belfer-Cohen describing some of the artifacts found in the Hayonim Cave in Western Galilee, Israel. The artifact in question, a limestone slab with a pattern incised on it, is associated with the Natufian culture, which is dated to about 13,000 to 10,500 years ago. The slab was found in the cave in a portion that “…belongs to a later phase of the Natufian occupation of the cave.3” There is speculation that the incised pattern is not just decorative, but encodes information.
The general surface of the slab has been divided into distinct units, which can be viewed as designating definite territories or ‘fields’ of some kind….there exists archaeological evidence to indicate territoriality among the Natufian communities, be it social or geographical or both….There arises the question of whether this design represents an actual phenomenon, serving as a ‘map’ of particular ‘fields’ located in the vicinity of the site, or if it symbolizes some abstract concept of ‘fields’?4
Other possible drivers of the intention to measure would be trading (closely associated with possession, since until I “own” something, I have nothing to trade with), evidence for which, in Mithen’s book, shows up as artifacts at almost all of the sites. They are described with an understanding of what the possible sources were, and if the sources were local or not. In an large number of cases, the source was some distance from the site, which hints at trading amongst these early, post-ice age peoples.
With all of this, of course, one needs to keep in mind the cautions about the fossil record that Darwin, among many others, gave in Origin of Species. Not only is it incomplete because not all of the deceased animals will have a final resting place that will preserve them, but of the few that actually are preserved, it will not be a complete preservation: the soft parts will decay more quickly, and even bones decay. Likewise, the people living in the period of interest, after the ice age, were not necessarily interested in making sure they would leave a record for the future to learn about their lives from. Nor did they have as a principle for living, the establishment of settlements that would be available for others to read information from, 10,000 years hence. It is not that they were especially secretive, they just did what they did without regard for the long term record. Not really a surprise.
So, to understand anything about this beginning of measurement, those looking for it will have to be clever and understand what possibly will indicate that some form of measurement has been used.
In looking for the time when people might have started measuring, one has to begin with an understanding of what and how archeologists measure, to be able to assign the dates that they assign to their sites and the artifacts that they find there. (Seems somewhat recursive, no? Looking for how to measure in order to learn about measurement?) So this is probably the right time to do at least a first look at some ways to measure the past. There are a number of ways to date things in the past, and one of the methods used consistently by archeologists since it was discovered or developed is radiocarbon dating. I was fortunate enough to find a book by Colin Renfrew, one of the better-known British archeologists, called Before Civilization, in which he describes the newly developed method of performing radiocarbon dating, as the first portion of the book. Since it was originally published in 1973 (as dated using conventional ink on paper on the copyright page after the title page), radiocarbon dating has been refined, but the book is fine as a primer.
The concept of radiocarbon dating is simplicity itself although actually dating using radiocarbon is pretty complex. Carbon comes appears in three versions, called isotopes. The basic isotope, Carbon 12, has a nucleus of 6 protons and 6 neutrons. It is a very stable atom. The other two isotopes, Carbon 13 and Carbon 14, each have more neutrons. Carbon 14 is unstable and will decay – the decay is known as radioactivity, and is a similar process to the way that isotopes of other elements decay. Carbon 14 decay is called beta decay, which means that two of the neutrons each decay into a proton, an electron which is emitted, and an antineutrino, leaving Nitrogen 14 in its place. The half life of Carbon 14 is 5730 years, plus or minus 40. This means that if you have 100 atoms of Carbon 14, in 5730 or so years, you would have about 50 left, and about 50 nitrogen 14 atoms. In another 5730 years, you would have half of that 50 left, and roughly 75 Nitrogen 14 atoms, in another 5730, roughly half of the 25, etc.
Carbon 14 represents a really minute amount of the carbon on earth: around one Carbon 14 atom per trillion Carbon 12 atoms. Since its half life is so short, relatively speaking, it has to be continually created and mixed with the rest of the atmosphere in order to be a factor that can be used for dating. During photosynthesis, plants fix carbon, including whatever percentage of the atmosphere is Carbon 14, which then becomes minute percentage of the carbon in that plant. Animals eating plants take up the same level of C14 as the plants have. The point at which the plant ceases to photosynthesize, death, no more carbon 14 is added to its body mass. It starts to decay, and by figuring out how much of that being’s Carbon 14 has decayed, one is able to determine a pretty good idea about how long ago they lived. Similar measurement can be made of animal remains. The concept is simple, the actual measurement can be quite difficult. And it can only be used with formerly living ‘stuff”, dating stone tools has to use other dating methods.
In order to be as accurate as possible, and with the plus or minus 40 years, there is already some indefiniteness built in to the calculation, one must know what percentage of the plant or animal’s carbon was Carbon 14. Overestimating that percentage could lead to dates that were too long, and underestimating it leads to shorter times. When this was originally used, in the 1950s, the estimates were too long, so a calibration method had to be developed. It was found in tree rings, one of which is added to the trunk of a tree every year. Each of the rings of a tree will contain C14 in the proportion that was available when that ring grew. By looking at tree rings of long living trees, it was determined that the amount of C14 in the atmosphere varied, and if you used the most recent proportion to measure, you would over-estimate the time since the death of what you were measuring. So tables had to be developed, checked and cross-checked with numerous different species of trees going back as far as the longest living trees, so that C14 could be used with better accuracy.
But we’re talking about really minute amounts of either Carbon 14 or Nitrogen 14 that would need to be measured. Some samples just wouldn’t be large enough. Even with the most sensitive of mass spectrometers (oops. another measurement tool. We’ll have to talk about that some more, at some point), some samples just won’t yield results. So the fact that there are some measurements that give results that are believable, or nearly so, is pretty impressive.
Carbon 14 dating is deemed sufficiently accurate for dating formerly living objects within the last roughly 60,000 years. Beyond that, other means have to be used for dating.
So, tying all of this back together, we can develop approximate order to when things have happened, at least as far back as the “explosion” of creativity that occurred for people, and certainly as far back as the end of the last ice age. But just because we can measure these dates does not necessarily mean that there are measurement artifacts that we can use to date the beginning of measurement. We will probably have to look elsewhere.
1 “Did Working Memory Spark Creative Culture?” Balter, Michael, in Science, Vol 328, 9 April 2010. p. 161.
2 “Did Working Memory Spark Creative Culture?” Balter, Michael, in Science, Vol 328, 9 April 2010. p. 160.
3 Bar-Yosef, O, & Belfer-Cohen, A. 1999. Encoding Information: Unique Natufian objects from Hayonim Cave, western Galilee, Israel. Antiquity 73, 408.
4 Bar-Yosef, O, & Belfer-Cohen, A. 1999. Encoding Information: Unique Natufian objects from Hayonim Cave, western Galilee, Israel. Antiquity 73, 409.