R. M. R. Finding the Age
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by Rene M. Rogers


      The question as to the age of things is pretty basic to a number of scientific disciplines and when we can make a persuasive and independent determination of time lapses between events in nature, we often have a means of deciding between competing versions of the truth.  For example, the age of the universe and its components, the galaxies, our solar system, the earth, etc., is an ongoing question basic to our understanding of the Grand Scheme of Things to the degree that we can understand it all.  There was a time, not so long ago, when all right thinking people in western civilization believed that the world could not be much older than 4000 years.  This estimate was based on an accounting of the generations of the descendants of Adam and Eve as set forth in the Old Testament, where they list the begats.  When the evidence of geology started to come in suggesting a much greater age, the upset in the minds of many people was so severe that ongoing wars between the nations of Western Europe were fought over the matter for many years and the controversies still rage in some quarters.


      What I propose to outline here is a method for determining how long a variety of objects have been the size and shape we find them in today, or, to look at it another way, when the surfaces we see today were created.  I will present my case on at least two levels... as a simple narrative for those who may be curious about the subject though not yet fluent in mathematics and physics, and as a technical issue complete with some more rigorous arguments.  I may need to include some mathematical notation at the narrative level, but I will leave the formal derivations for later or to others.


      My involvement with the question regarding the age of things goes back to the 1930's when I was growing up in rural Florida.  My parents had a few shacks and a few acres on the Waldo Road between Gainesville and Fairbanks where they lived as subsistence farmers.  When I was 5 or 6 years old walking along the top of a ridge of earth dug out to make a drainage canal I was fascinated at finding a large white symmetrical object some 3 inches long sitting on top of a pedestal of dirt.  The frequent rains had eroded the loose earth where the large drops fell leaving any hard object like a rock elevated an inch or two above its surroundings.  I gathered up the treasure and ran for home as fast as I could.  My father told me that it was an Indian arrowhead and that the Indians who lived hereabouts many years ago made them and used them for hunting.  He said that the Indians were great hunters who knew everything about the habits of the animals and birds and fish in the woods and how to make a living by hunting and catching them.  I was thrilled by this account and reckoned that I could want nothing more than to learn to make arrowheads like the Indians and to know the forest and the habits of the creatures there and live out my life in the woods hunting and fishing.  I spent a great deal of time this way afterwards, but it was a year or two before I found another arrowhead although I was always on the lookout for them. 


      The Waldo Road crossed over the Little Hatchet Creek a mile toward Fairbanks from my folks place and my favorite fishing hole was near the culvert.  There were wild grape vines nearby loaded with bunches of tiny purple grapes that were very sweet and delicious, and my brother and his friend had cut some of the vines so they could swing out over the creek, like Tarzan.  One day I fell into a patch of mud while swinging on a grape vine.  Fortunately I was able to crawl out and wash the mud off in the creek, but while immersed I noticed that the roots of the vines went down into the mud.  One Richard O'Malley, an intellectual friend of my folks, lived nearby and I once asked him how it was that such delicious stuff could grow up out that mud.  He was delighted with the question and gave some serious thought to his answer.  He said that I had asked him the Great Question, and the answer told the secret of what life was all about.  He said that the prime function of all living things was to make a little order out of the chaos in which they always found themselves.


      O'Malley died in his sleep shortly after this, but not before he gave me another powerful lesson.  I was gathering rocks for my slingshot at a gravel bed in the creek when I found a large smooth stone the color of slate, thin with serrated edges and roughly triangular like an arrowhead.  I ran to his shack with it and showed it to O'Malley.  He was almost as excited as I was and said that it was a prehistoric fossil, a petrified fish tooth.  He wasn't feeling well, but he insisted that I take him back and show him the spot where I had found it.  On the way, he explained that the earth was very old, millions upon millions of years, older than I could imagine, and that monstrous creatures once swam in the oceans and roamed over the land.  This tooth, he said, was roughly 25 million years old and he showed me some strata in the banks where the last flood had cut a new channel for the creek.  He said that geologists could study such features and trace out the history of the world.  I showed him the gravel bed and ran through the loose stones with my fingers, soon finding a second tooth much like the first.  They were both about the size of O'Malley's hand.  The idea that such monstrous fish had lived and died right where we were was powerful stuff to me, but the idea that people could reason it all out from simple evidence was electrifying.  O'Malley had introduced me to scientific thinking.  Not only would I be a woodsman and a hunter and learn to read the signs in the forest like the Indians, but I would also be a geologist and learn to read the history of the world in the rocks and the strata.  Over the next few years, I found half a dozen large teeth nearby as well as some smaller ones the size of a fingernail and some bits of fossilized bone.


      In due time I found more fossils and arrowheads.  My father worked off and on as a surveyor and in the course of this work he found several more of each and gave them to me until by the age of 8 or 9 years I had a small shoe box half full of such items.  There was a grass landing strip for light aircraft across the Waldo Road from my home and I spent a lot of my time hanging around the flying school and talking to the people there.  The owner's wife, Mrs. Carl Stengle, took an interest in my scientific curiosity and took me and my collection of fossils and arrowheads to the University of Florida Museum in Gainesville to see what the people there could tell me about them.  They were singularly unimpressed and I got the feeling that hardly a day went by when someone didn't bring a similar collection of stuff in for their evaluation.  The problem with arrowheads, they said, was that they were as common as dirt and they were of no value to archaeologists because there was no way to tell how old they were.  The shark teeth were also too common to be more than curiosities.  All this did very little to dampen my enthusiasm, however, because I saw the arrowheads as pure works of art while the fossils were a tangible reminder of the grandeur of time and of the earth. 


      Duke Baer was Carl Stengle's chief flight instructor at the airport and he served as a mentor to me for several years.  He was keenly aware of events in Europe and convinced of the inevitability of war and our involvement in it.  It was a matter of some urgency with him that we waste no time in preparing for war and he was emphatic that air power would be decisive.  He was also of the opinion that expertise in all facets of aviation would be the key to individual success in the years after the war, regardless of who won.  One day he and I were walking along the backside of the hangar when I found a beautiful arrowhead on the ground.  My excitement was far from contagious and The Duke took the occasion to lay out some rather harsh facts of life for my benefit.  To begin with, he said, the reason we never saw any of the people who made the arrowheads running around these days was that people like us, meaning he and I, had all but wiped them out.  Stone age technology had no survival value when pitted against modern machinery.  Furthermore, he said, he didn't know any worthwhile person who was interested in rocks.  There was going to be a big time war in the near future and you didn't have to be very smart to guess that people who understood airplanes and flying were going to be the winners while people who worried about rocks were going to be losers.  A few days later I traded all of my fossils and arrowheads to a kid at school in exchange for a crystal set radio that didn't work and some junk auto parts.  A day or so later, upon reflection, I was sick at heart and tried to reverse the trade, but my treasures were scattered to the far winds never to be assembled in one place again.


      More than one person has asked me why I would spend my precious retirement hours writing about such an obscure and irrelevant subject.  It is absolutely incomprehensible to some people why anyone would care about such matters when there are starving children in Africa, for example, or any of a raft of life and death matters of immediate importance all over the world.  To others it is simply boring beyond belief.  It turns out, however, that every facet of modern life is intimately involved with scientific concepts.  If he were here today, I would argue with The Duke that the winners of future contests, whether military or commercial, are apt to be those who understand, or are at least curious about, the Nature of Things while the losers are apt to be those who find the Laws of Nature irrelevant.  Prof. James Burke, in his extended TV series, CONNECTIONS, makes the case far better than I that profound consequences often evolve from the most apparently trivial twists of fate.  Perhaps it is the case, where my present thesis is concerned, that for those who are interested no explanation is necessary while for those who are not interested, no explanation is possible.  All I can say is that I find the matter interesting enough to devote some modest effort to it.


      I never held the misfortune of my lost arrowheads and fossils against The Duke because I believed that he was only concerned for my welfare.  Upon reconsideration, I thought he was wrong in this instance, but he had some other powerful lessons in store for me which were, in the long run, well worth the price of admission.  In particular, he introduced me to the importance of pattern recognition as a basic survival strategy.[1]  I was on my way to see him a few weeks later when I found another arrowhead while walking along the dirt road which went past the airport.  I saw the item some 40 feet away on the far side of the ditch beside the road and had to go around a blackberry thicket and cross the ditch to retrieve it.  By the time I got back to the road a man, a backwoods farmer I knew by sight, walking along nearby came up and asked to see what I had found.  I showed it to him and told him it was an arrowhead.  He took it in his hand and said, "No, boy, that is a devilstone and them is bad luck."  With that he snapped the blade in two and threw the pieces into the woods and went on his way.  I was angry as hell, but being only 11 years old there wasn't much I could do about it except scour the woods looking for the pieces.


      After a week or so probing through the scrub palmetto thickets among the pine trees, I found one of the pieces and realized at once that what I was looking at could one day, most likely, tell me how old the piece was.  The broken section had a white band that followed the outside surface contour while toward the center of the section the color was a light purple.  The outside surface was a dull grey, but it was pretty clear that the piece had been shiny and light purple, like the center section, when it was new.  My first impression was that water had somehow penetrated the outer surface and washed out the purple coloring, but it occurred to me later that whatever pigment made the purple color had possibly diffused outward on its own, without the involvement of water or anything else.  This idea was inspired by my experience with the drying of firewood.  My folks never cut living trees for firewood because there were always a few dead ones in the forest near our place which had been struck by lightening or blown over by the wind.  I had noticed how the center of a dead tree was often wet while the wood just under the bark was much dryer and how even the center would dry out in time.  It seemed clear that water in the tree diffused to the outer surface where it evaporated into the atmosphere.  I also learned from the firewood operation that the age of a tree could be determined without ambiguity by counting the growth rings and I made a connection between this technique and the study of geologic strata.


      It was not apparent just how all this worked in the case of my broken arrowhead, but I was pretty sure that I could discover the details if I was persistent enough.  I found the other half of the arrowhead several months later and observed the same color pattern in both halves.  When I first found the artifact, the point was remarkably sharp, but this feature was now lost and I never found it.  I did not bother to share my discovery and subsequent speculations with The Duke or the people at the museum. 


      Two years later I got back to serious arrowhead hunting with a high school friend and eventually collected nearly 1000 pieces, mostly by walking through plowed fields and along dirt roads near Gainesville.  I tried several times to learn how to make them, all without success, but I did notice that the flakes I was able to make revealed similar gradations of color as the piece mentioned above.  I did at the time, and still do, regard my arrowheads as works of art and have never intentionally broken one to see if color gradations are always present.  However, I did find one which was probably broken by a horse or a plow during the course of farming where the characteristic diffusion pattern is clearly visible.  If and when my method is developed to the point where actual specimens are needed to measure the age of a site of human habitation, I would prefer to use the numerous flakes left over from tool making.  These hold the same age information as the artifacts, but are of no artistic value.


      One time I loaned my collection, then numbering perhaps 100 pieces, for display at the public library.  Several people went out of their way after seeing it to tell me that a barber in Ocala, 45 miles to the south, had one wall in his shop covered with arrowheads.  After the war I dropped by to see this collection that was still growing at the rate of one or two pieces a week, according to the owner.  I was also visited by an interesting person with an interesting tale, as a result of his having seen my exhibit.  He was long since retired and free to pursue his hobby, Florida History, the subject of a couple of books he had published.  He had also published a book about Spanish Gold and buried treasure, that I later checked out of the library and read[2].  He told me that he had just come from an archaeological site near St. Augustine that was believed to be the subject of an old piece of regional folklore.  According to the tale, the crew of a Spanish ship set up camp near the ocean some 300 years ago and made friends with the local Indians.  After a while, the Spaniards moved on, but they left a supply of iron strapping used to make barrel hoops.  By this time the Indians had abandoned stone tool making in favor of the markedly superior arrowheads, knives, and fishhooks they could make from this store of strap iron.  In time, though, the iron was lost or rusted away and there was no source of replacement.  The old technology was lost by then and the people were unable to make a living.  I could readily understand how that might happen because I had tried very hard to learn how to make even the crudest cutting edge using chert without any success at all.     


      The Duke was right about the war.  I was too young to get into the thick of it, but I did serve in the USNavy during 1944-46, most of the time in radar school.  He was also right about the role of air power, but he had not foreseen radar or atomic energy or a host of other innovations.  The role of science and technology was not lost on our leaders, however, for congress appropriated the funds to invest in education and basic research to an unprecedented degree right after the war.  Before 1950, almost any PhD connected to a large university or one of several private research organizations could get some level of funding from the federal government for basic research provided he could write a coherent proposal.  There was never a shortage of critics for this policy and there were always vigorous contests to see who could come up with the most ridiculous projects being funded by the taxpayers.  By 1960 the level of such funding was cut substantially and anyone hoping to get government money for research had to show a direct and logical connection between what he hoped to find and a monetary or military return on the investment.


      After the war, I went to the University of Florida on the GI Bill and got a degree in electrical engineering.  From there I went to Ohio State where I was offered a scholarship to study microwave vacuum tubes and to work in the vacuum tube laboratory.  I went on to spend a number of years off and on in that industry. Contrary to what you may have heard it is still alive and almost well.  Solid state devices, transistors and the like, made many types of vacuum tubes obsolete, but there are still a number of applications in high power microwave work where only a vacuum device is practical.


      The issue of the age of arrowheads was all but forgotten, at least on the conscious levels of my mind, until an urgent manufacturing problem brought the matter into sharp focus again in the late 1950's.  I was working in the vacuum electronics industry at Varian Associates in Palo Alto, California.  The department I was in was responsible for pilot production of a small device known as a Backward Wave Oscillator, or BWO, long since made obsolete by the development of YIG (Yttrium-Iron-Garnet) tuned solid state oscillators, but a hot market item at the time.  We were in the process of re-designing the product for mass production using inexpensive parts that could be punched, stamped, or broached wherever possible.  The parts were cheap, but the tooling was not and a crisis arose when the only two broaches we had for a specific operation broke without warning.  The reason for this mishap was a first priority question while the lead time for making new broaches was several days.  New parts were required in the meanwhile to keep the production line moving along and I was pressed into service as a reasonably skilled machinist to make them the old fashioned way using a lathe. 


      The operation in trouble was the production of a precise hole roughly .25 inches in diameter and 1.25 inches long in a bar of stainless steel .75 inches in diameter.  In the original design this hole was made by first using a slightly undersize fluted drill followed by a finishing reamer.  The hole made this way tended to have a slight taper, but it was good enough unless you could do better.  The broaching operation was better until the tool broke.  Whenever a process that has been working suddenly gives up, there is naturally a review of the order of steps and the mind quickly latches onto subtle changes that were apt to be passed over unnoticed before trouble strikes.  In this case the order of broaching the hole and a brazing operation had been reversed.  The part in question went into an assembly that was completed by brazing the component parts together in a hydrogen atmosphere furnace.  If the hole was broached before this brazing operation, the expansion and contraction of the stainless steel during the heating and cooling cycle left the hole slightly warped.  Someone decided to try to get around this problem by broaching the hole after the braze.  As soon as this was brought out in discussion our metallurgist spoke up to tell us that traces of sulphur were intentionally added to the stainless steel at the mill to make the metal easy to cut and we were defeating this purpose by hydrogen firing.  The sulphur was more or less uniformly distributed throughout the raw stock, he explained, but during hydrogen firing at roughly 1100 DgC the atoms migrated to the surface and were carried away by the formation of H2S thus leaving the surface depleted of sulphur and tougher to machine as a consequence. 


      It is deeply embedded in vacuum tube lore that a large number of elements listed in the periodic table are deadly to cathode activity and/or vacuum integrity, sulphur being high on the list, so the news that the stainless steel body that had served us so well for so long was actually a reservoir of sulphur caused a degree of alarm.  I was assigned to look into the matter and get to the bottom of it.  In the meanwhile our production problems were fixed by carrying out the necessary brazing operations before the pilot hole was made.  In this way the new broaches had to remove only a virgin metal surface unexposed to hydrogen firing.


      My assignment was to find the rate at which we could expect sulphur to bleed into the vacuum under all possible conditions and I had not the slightest idea how to go about it.  Fortunately I knew and sometimes took lunch with a bright young man, one Lewis Hall, a PhD in Physical Chemistry, who is arguably the sole inventor of the ion sputter pump, but that is another story[3].    Lew didn't have a ready answer either, but he dug into some old class notes he had and came up with a discussion of Fick's Laws of Diffusion. 


      Fick's Laws may be derived using a model wherein a diffusing species of particles is distributed throughout a solid framework such as a crystal lattice.  For my purpose here, we may think of the diffusing particles as atoms that are assumed to move about through the solid by a random walk process.  In this model, the diffusing particles move in a random direction at random time intervals for a random distance at each step, all of which are independent of all previous movements.  Although random, the frequency of relocation and the distance moved at each relocation can be determined on a statistical basis.  The mathematical models concern the average or expected values of these quantities.  If the population of diffusing particles is constant in some neighborhood in the framework, there will be, on the average, as many particles moving in any one direction as there are moving in the opposite direction.  There is no net migration and the average population will remain constant with time in that neighborhood.  If, on the other hand, the population varies with distance there will be a net migration of particles from regions of high population density to regions of lower population density.  Furthermore, if there is a net migration out of a region the population density will decrease there and visa versa. 

      Lew's notes suggested that we could understand the entire scenario regarding the diffusion of sulphur in stainless steel if we could find, in the literature or elsewhere, two parameters; 1) the heat of diffusion and 2) the frequency factor for this specific combination of host and diffusant.  The heat of diffusion, designated here as Qd, is a measure of the energy a particle must acquire from random thermal motion in order to escape the bonds that hold it to a specific location, thus we may sometimes encounter the term Thermally Activated Random Walk.  The frequency factor, designated as Do, is a measure of the frequency of escape attempts and the average distance traveled at each step.  The net diffusion factor is D = Do * EXP(-Qd/kT) Cm^2/Sec, where k is the Boltzman Constant and T is the absolute temperature.  (At room temperature, kT is approximately .025 electron volts.)  We found a textbook in the company library with a relatively complete discussion of the subject, particularly as applied to case hardening in which carbon is diffused into soft iron.  There was also a short table of diffusion parameters for various combinations of host and diffusant, but stainless steel and sulphur were not listed.  After a fruitless search of the literature the decision was made to measure the parameters ourselves.  Our plan was to measure the amount of sulphur lost during hydrogen firing for various times and temperatures and then fit the data with the theory.  My job, as machinist, was to remove a thin skin from the diameter of a stainless steel bar before and after firing and collect the turnings for the chemist.  The chemist's job was to measure the sulphur content of the turnings.  Lew's job was to fit the resulting data to the theory and come up with the required parameters. 


      The acid test was a plot of LOG(D) vs 1/T.  If this plot turned out to be a straight line on graph paper, as it did, we could conclude that our model and the theory derived from it was probably correct.  The slope of the line gave us Qd and the Y-intercept gave us Do.  Before the data came in there was considerable speculation as to what we would find if the diffusion parameters were strongly dependent on the sulphur concentration or the temperature, but after we had the data and saw the high correlation with theory these questions were set aside.  I no longer have access to the report we wrote regarding this experiment, but my recollection is that we were able to determine the heat of diffusion as between 2 and 3 electron volts and the bleed rate was entirely insignificant under all possible conditions.  Further investigation of the matter was curtailed. 


      As the machinist for this project, I was able to note that the sound of the tool as I was removing material for analysis varied with the depth below the surface from which the sample was being taken and I could understand why the broach broke.  The surface with reduced concentrations of sulphur was noticeably tougher to cut.  In this crude way I was able to make an estimate of the skin depth of the depletion region and this was fully consistent with the other results.  I discussed the question of the variability of the diffusion parameters as a function of the sulphur concentration with Lew and told him that, since the strength of the stainless was a noticeable function of the sulphur concentration, it would not surprise me if the diffusion parameters were as well.  This seemed reasonable enough, but the data did not support the proposition.  Perhaps if we had taken a great deal more data over a wider range of times and temperatures we could have detected some effect, but so far as we could tell both Qd and Do were constant.


      I retrieved my arrowheads with apparent diffusion patterns from their box in the attic during this time and when our report was finished I showed them to Lew.  It was very clear to both of us that, if we had the time and the resources we had devoted to the study just completed, we could find out what elements were present in the rocks, their concentration profiles with respect to the surface, and their diffusion parameters... hence the age of the objects.  We took the artifacts and the theory to the Archaeology Department at Stanford University nearby and were told that, from their point of view, it would be very neat indeed if we could do what we said we could.  The people we talked to there knew of no direct method for estimating the age of a flaked stone tool.  The archaeologists had the interest, but no technical or other resources, while the vacuum tube company had the resources, but no interest.  Lew and I were both very busy with vacuum tube problems and families to support so the idea had to be put on the shelf, for the time being at least.  


      This experience with Fick's Laws inspired me to continue studying the literature of diffusion and over the remainder of my career in vacuum tubes I had numerous occasions to use this knowledge in a very wide range of seemingly unrelated contexts.  Now, with regard to television, I have a general feeling that if a program is not worth taping it is probably not worth watching and I have noticed that most of the programs I taped over the years had to do with wild animals and scientific subjects.  I have also noticed that there are more programs on paleontology, archaeology, and geology than there are on vacuum tube technology.  The sequence of events and the age of things is a recurring and often central theme in such presentations.  I recall one program where the age of things was not at issue, but it should have been.  This one was about a piece of research on the trace elements in the raw material used for making stone tools.  From the relative abundance of these trace elements the researcher was able to make a fingerprint characteristic of the locality where the rock was found naturally and show that the same pattern was present in tools found a far distance away.  The long range goal was to develop a database of trace element patterns in raw materials and use it to study the trade routes of stone age people.  One of the caveats set forth for the benefit of others seeking to verify this research was that the trace elements in the tool should be taken from the innermost regions of the artifact because the outer regions tended to lose trace elements at varying rates by diffusion through the surface.  I made an effort to contact the people responsible for the program to tell them that a little more effort toward accounting for the trace element fingerprint near the surface would lead inevitably to the age of the object, but I never got a reply.


      I tried to make contact on several occasions with people who I thought might benefit from my experience with diffusion as a basic time clock in nature, but I was never successful until the late 1980's or thereabout when I saw a news item in the paper about an archaeologist who had discovered a hand ax that he believed to be 200,000 years old... on what basis I do not know.  I wrote to him regarding my experience with diffusion and my theory for using it to make a direct measurement of the age of such objects and learned that the concept was new to him and that he had no facilities for carrying out such a study.  I was starting to think about retiring from the vacuum tube industry and pursuing this matter as a project to keep my hand and mind busy in scientific matters during retirement.  I wrote to and visited a number of people working in archaeology and paleontology and learned that there was no activity of the kind I had in mind among any of these people.  One young man, a visiting scholar at Stanford with a PhD in archaeology, came to see me at my place of employment several times before I retired and we had a number of discussions on the subject, but he dropped off the radar screen at some point and quit returning my calls.


      The closest thing to diffusion theory that I have run across in the field of archaeology is Obsidian Hydration.  As this has been explained to me, a fresh surface on obsidian glass will take up, from the atmosphere, water that penetrates the surface causing a change in the optical properties of the material.  A thin cross section of the artifact is prepared and the depth of penetration can be seen through the transparent wafer.  I have never had anyone explain the physics of this situation to me, only that the method is believed to be dependent upon the relative humidity and the temperature of the environment to such a degree that independent dating of the site where the artifact was found is normally required before a great deal of confidence is placed in the results.  In my experience, atomically dense materials like solid crystals and glass do not dissolve molecules.  Disassociation is necessary before the constituent atoms of a molecule can be absorbed into a dense body.  Of course, if the host is porous to any degree, molecules can and do adhere to the surfaces of the pores and may wander wherever the surface goes.  This is discussed further in the section on Gas Chromatography.  In fact, the similarities between Gas Chromatography and diffusion in solids are such that I am inclined to refer to the age dating process I have in mind as Solid Chromatography.

    [1]Taste and smell are exercises in pattern recognition at the conscious level.  Our immune system is keenly attuned to pattern recognition at the cellular level.  Nuances of speech and body language are readily recognized by most of us at the level of the marketplace.  Ants can tell the difference and will not tolerate the presence of ants of the same species from another hill, etc.

    [2]THEY FOUND GOLD, By A. Hyatt Verrill

    [3]I lost touch with Lewis Hall some years later and have tried to find him to get his recollections of this work.  I also want to make sure to give him all the credit due to him in this regard.


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