Views on the Nature of Knowledge: Social Scientists vs. Natural Scientists
What is knowledge? A simple question, or so most people would think. Knowledge is the accumulation of information on a given subject or subjects. It is a collection of facts, of things known to be true…or is it? The closer one looks, the more one comes to realize that there are many different approaches to obtaining knowledge, and many different definitions of precisely what constitutes knowledge. One’s use of the term varies with one’s own background and objectives. To some, knowledge is an absolute, to others; it is that which is gained through long hours of observation and long years of experience. The facts that make up what we call knowledge may be composed of absolutes, or they may be composed of many opinions, opinions that we believe to be most accurate or most correct. But what then does it mean to say that an opinion is accurate or correct? Well…that it is true of course. But if a fact is in reality an opinion, then how can it be said to be true? At least, in an absolute sense. Most people believe…. Or, most experts are of the opinion…. Sounds a lot like majority rule, doesn’t it? However. We all know perfectly well that the majority is not always right. History is filled with instances where the majority got its way, only to impose unethical, or even immoral conditions on the minority. Most people in the Antebellum South thought slavery was just, but they were White and in the majority. Today, there are few who would defend slavery as just or moral. Of course, this raises another question regarding the nature of knowledge: Is it possible for facts to change over time? Can a thing be true for one generation, and not for another? Such are the dilemmas that must be faced in the pursuit of knowledge. Fact must be sifted from fiction. But how? Do you use a ruler or a microscope? Consult a book or the Internet? Social scientists and natural scientists face very different choices when confronted with the question of “What is the Nature of Knowledge?”
For the social scientist, knowledge is much more likely to be composed of subjective determinations, or a combination of subjective determinations and objective evidence, rather than simply of what most would call objective fact. It is in the nature of the business. Historians, grammarians, literary critics, psychologists, musicologists, and so on study subjects that cannot really be measured or quantified, at least not in the fullest sense. A historian can compile lists of dates, kings’ reigns and presidential terms, days of battles won, and political campaigns lost. He can look through the records of names and places and see what happened where, and what was done by whom. Clearly, these are abstract facts. Yes, if the information you are looking at is accurate. The Russian Revolution began on February 18, 1917. Oh wait a minute, or is that March 3,1917? It all depends on whether you are using the Julian Calendar, the one that was in use in Russia at the time the Revolution broke out – the February date – or the Gregorian Calendar that was in use in most of the rest of the world – the March date. These are not different facts per se, but they certainly can cause a great deal of confusion when it comes to one’s knowledge of the Russian Revolution. Until one discovers the fact that two different calendars were in use at the same time, one could either think that mistakes were made in the recording of the date of the event, or one could simply get one’s chronologies confused, and so alter the timeline of events. Yet, this matter of the precise date of the commencement of the Russian revolution is really a matter of different systems of measurement rather than a difference in actual fact. February 18th and March 3rd are really the same, just as zero degrees and thirty-two degrees are the identical boiling points of water in the Celsius and Fahrenheit temperature scales respectively.
Fantastic! Two pages in and we’ve solved the whole problem. This paper must be just about complete. The only difference between the social scientists – those pesky historians – and the natural scientists – those chemical and physical fanatics who forced us to plough through the metric system in the first place – is a difference in scale, measurement that is. But what about this? The Russian Revolution began on February 18th or March 3rd – same thing right? But, how do we know that this day, whatever we decide to call it, does in fact mark the actual beginning of the Russian Revolution? Father Time dropped a placard from heaven that read, “Today is the start of the Russian revolution.” Well, that would be nice, but it doesn’t sound very likely. Of course, you never know, there might be an old Russian peasant somewhere who can remember it happening…even has the old, yellowing paper somewhere underneath his horde of Stolichnaya. Assuming, however, that this will not turn out to be the case, there must then have been some other way in which this particularly day was determined to mark the start of the Russian Revolution. If not the date itself, then what was it that caused this particular day to be generally accepted as the start of the Revolution?
Obviously, something must have occurred on March 3rd, 1917 – we’ll use the Gregorian date just to make it a little easier – that made people think that this was the beginning of a revolution. Marie Antoinette said, “Let them eat cake.” No, probably not…don’t think she ever visited Russia. On March 3, 1917, a provisional government was officially formed in Russia to replace the Tsar’s administration. Now this sounds a bit more likely. The end of tsarist rule as determined officially by the end of the Imperial government, and its replacement by a new, republican form of government would appear to meet the qualifications for a revolutionary event. Out with old and in with the new. But must this event necessarily set off the beginning of the Russian Revolution for future generations of historians? Tsar Nicholas II abdicated the day before. Certainly, we could take that date – March 2nd – as the end of the old regime, that is, if we didn’t have a few other pieces of information. Firstly, though the Tsar did indeed abdicate on that day, he was not, as most people incorrectly believe, the last Tsar of All the Russias. Definitely, Nicholas II was the last Tsar to actually rule over the Russian Empire, but he was not the last to reign. In truth, Nicholas abdicated in favor of his younger brother, the Grand Duke Michael, and it was the Grand Duke Michael who technically was the last Tsar of Russia.
Nevertheless if we are making a distinction between “to reign” and “to rule,” then the collapse of Imperial authority that followed from Nicholas’ abdication would seem to be mark the actual end of tsarist rule. So why March 3rd?
Apparently, historians have made an arbitrary decision to consider the beginning of the revolution not as the end of the old regime, but as the beginning of the new. They could just as easily have done it the other way, or they could have picked a different event entirely, and thereby a different date. Speaking of revolutions, the French did not begin with the end of the old regime, but rather a notable challenge to it. The Fall of the Bastille marked the capture of an ancient royal fortress, and potent symbol of the ancien regime, by the angry Paris mob. The rebels killed the Governor of the Bastille, cut off his head and impaled it on a pike. Gruesome and dramatic, yes, but the monarchy was not even abolished until more than two years later, and in fact Louis XVI and his Queen even remained at Versailles for another several weeks, leading the very same life they had been leading before. Likewise, the American Revolution is traditionally dated from the moment the “shot heard round the world” was first fired against the British at Lexington. Yet clearly, this was not the first overt challenge to British authority. We all remember the Boston Tea Party, and the Stamp Act Riots. And of course, the thirteen colonies did not finally throw off the British yoke until 1781 and the Battle of Yorktown, or was it 1783, when delegates of the Continental Congress, and their British counterparts signed the Treaty of Paris, and Great Britain at last formally relinquished control over its former colonies. Historians make many judgments in regard to facts, judgments that weigh these facts according to their relative importance, but these decisions in regard to relative importance are themselves based upon other facts, and even on opinions as we have seen above.
The subjectivity of the social scientist can be carried even further with some of the other examples. A musicologist studies music and the history of music. Music, unlike regular historical events, can be quantified without much argument. The different notes in a musical scale can be said to correspond to specific oscillations of sound waves, numerical and physical values that can always be exactly reproduced. Whew! At least that was an easy one! But wait a minute…what was that about a musical scale? Yes, that’s right, there are many different musical scales. In the Western World, we typically use a heptatonic scale that can be further broken down into major and minor chords. This however, is not the only heptatonic scale that has been or could be used. The Gregorian Chant of the Church uses a heptatonic scale with different modes, as do certain other musical scales. And, not leave anyone out, most non-Western people use scales that are not even based upon a system of seven notes. Chinese music, for example is typically pentatonic. Each of the notes in each of these many different systems would produce different tones that, yes, can be rendered as a certain number of oscillations of sound waves, and once recorded, can be reproduced. So, OK then, music is based upon exact, and duplicable facts so long as we are talking about the exact mathematical measurement of sound waves, and not about something arbitrary, or culture-specific like specific systems of musical notations.
All right then, since the total number of sound wave oscillations in The Beatles Hey Jude adds up to a more perfect number than the total number of sound wave oscillations in The Backstreet Boys Drowning we can confidently conclude that the Beatles’ composition is superior to that of the Backstreet Boys. Superior? Hey, what are you talking about? The Backstreet Boys are my favorite group! Ah, we have another problem, two of them in fact. In the first case, what is a “more perfect” number, and in the second why does or should the total number of sound wave oscillations in a musical composition have anything to do with whether one song is better than another….Because I said so. Were it that easy…but unfortunately it is not. The concept of a perfect number has no objective validity in and of itself. Mathematicians define a perfect number as an integer that is the sum of its proper divisors: 6 = 1 + 2 + 3, 28 = 1 + 2 + 4+ 7+ 14. But, is this what we meant when we just said that the number of sound wave oscillations in Hey Jude added up to a more perfect number than the number in Drowning? Probably not, that is unless we could somehow draw a correlation between a “more perfect number” and a “more perfect” piece of music. In order to do so, unfortunately, we would first have to define a perfect number, as obviously a number’s being either more or less perfect must somehow bear reference to a number that is perfect in the absolute. So, what should it be? Good thinking…the perfect number, or should we say, “more perfect number” is much closer to the number arrived at for Hey Jude than the number we counted for Drowning. Still, how do we figure out the perfect number? Is the perfect number a mathematical absolute, one that can always be exactly reproduced, or is it simply the number of sound wave oscillations in our favorite song?
Thus, the social scientist arrives at the problem of standards. Even by the standards of a mathematician, there is no such thing as the perfect number. By the above definition, many numbers are perfect. The ancients believed that the perfect numbers had mystical significance. No doubt, they also believed that some numbers were more significant, or more powerful, and thus more perfect than others. Still, how does one pick the most perfect number? The ancient priests of Zeus may well have believed that, as king of the gods, whatever number was his perfect number was the most perfect of them all. Similarly, three might be considered perfect by Christians as it is the number of the Trinity. Jews might choose twenty, as the name of God in Hebrew is written with two of the letter that also stands for the number ten (yud). Numerology is fascinating, isn’t it? Yet, as can be plainly seen already from these few examples, there is no such thing as an absolute perfect number. Well, at least not any definition that cuts across all social, cultural, and sectarian lines.
More to the point though would be our second question, for even we could somehow decide on an absolute perfect number, there is no particular reason to think that the very best song ever written must conform to that number in terms of the total number of oscillations in all of its musical notes. But why not? If it’s the best song, it must have exactly the right number of notes, and in exactly the right combination? Right? Not exactly. To use an example from the realm of both architecture and history, we might look at the canons of proportion formulated by great Renaissance architects like Vasari and Palladio. These two Renaissance men, like many others of their time including, Leonardo, Rafael, and Michelangelo, carefully examined the famous monuments of antiquity. Carefully measuring them and working out virtually all the possible mathematical relationships between these measurements, they made a number of observations. Among these, were the discoveries that the various parts of a building, and even the different parts of the parts themselves, bore specific mathematical relationships to one another. The height of an Ionic column was always in a specific ratio to its breadth. The length of the ideal Greek building, for example the Parthenon, was a specific multiple of the width of the building. Buildings looked better if their parts balanced – they had two identical-sized bays on each of the two sides of the main building. These principles of proportion and symmetry also held true for representations of the human form. Limbs, torso, and head had to be in the appropriate proportions in order for the figure to be considered beautiful or handsome. Conversely, these proportions could be distorted or even reversed to create the effect of ugliness, or evil. These and other Renaissance artists discovered that in the handsome face, the brow projected beyond the jaw – not too much – but a little. By switching around these proportions and painting a face with a receding forehead and a protruding jaw, Giotto captured the essence of the evil Judas. So it was that Vasari and Palladio and their like came up with the canons of proportions that they saw had been applied to the most perfect ancient buildings, ancient buildings by their very nature being inherently more perfect than modern (Renaissance) buildings. Now…that was an easy one!
Wait a minute! What? You did it again. You said that Vasari’s Lives of the Artists talked about the most perfect buildings in the ancient world and the most perfect works of art. What’s that supposed to mean? Who says what’s perfect? Exactly. Giorgio Vasari’s definition of what is admirable and perfect in art and architecture is not only a matter of personal opinion, but it is also culturally biased. Chinese Architecture, Indian Architecture, and Islamic Architecture – among others – each operated according to its own rules. Each of these nations had its own “canon of proportions.” Each of these peoples as well, looked back to its won “classical” era and to what it thought to be the finest works of art humankind had ever produced. The Taj Mahal is an entirely different building from St. Peter’s in Rome. The Alhambra in Cordoba looks nothing like Versailles, and the Forbidden City in Beijing is entirely unlike one of Leonardo’ drawings of the ideal Renaissance city. The same goes for the different cultures, or rather different periods, within Western history. Had he lived only two hundred years earlier, and in say, England, or France, or Germany, Vasari would have been designing towering cathedrals covered with airy tracery, buildings whose walls were like curtains of lace filled with windows of brilliant stained glass. And no doubt, he would have thought these buildings “perfect.” And though this a subject open to debate, most modern artists and architects entirely reject the notion that a building or a statue must be correctly proportioned – that is, that it must reflect traditional assumptions about how these things are supposed to look, or, in the case of representations of the human form, that these images are supposed to represent the true proportions of the human form. Why, many modern artists don’t think that portraits or pictures of real people and events should even look remotely like the inspiration for the painting.
Therefore, it should be obvious by now that all this talk of perfection, or of the ideal, is entirely subjective. To go back to our musical example, we must conclude that there is no way to objectively determine which musical composition is any better than any other. Hey Jude is better than Drowning because one person says so, or even because many people say so. But no matter how many people say Hey Jude is better than Drowning – even if every person in the whole world, except one – says that Hey Jude is better it doesn’t matter one bit. It is still a personal opinion. No amount of measuring or calculating can do anything than determine that one or the other these pieces is closer to some arbitrary mathematical or scientific standard.
However, there are certainly things in this universe that can be measured and quantified, the results of these measurements and calculations endlessly duplicated and reproduced. We have already mentioned some of them in our look at the work of the social scientist, but there are many others, many other situations where one and one always equals two. The chemist, the biologist, the physicist, the astronomer, and even the physician deal in disciplines that are much more black and white than that of the social scientist. His determinations, his knowledge is far more likely to be based on objective facts than on subjective inferences. Water is made up of two molecules of hydrogen and one of oxygen. This is always the case. It never varies. Yes, there is such a thing as heavy water, two kinds in fact – deuterium and tritium – but these are not ordinary molecules of water. The common molecule is always the same. At sea level, water always boils at two hundred twelve degrees Fahrenheit or one hundred degrees Celsius (Ha! Remember that one?) All living human beings are of the same species, a species called Homo Sapiens.
The natural scientists world is more easily measured and more easily quantified not because he has any fewer opinions than the social scientist, but because the things he works with, the things he looks at, are things that must be fitted into a logical chain of cause and effect. A scientific theory doesn’t do much good if it can’t be proven. Witness the great fight between the Lamarckians and the Darwinians. Lamarck argued quite successfully for years that all the different variations we see in the animal world are the result of the “Law of Acquired Characteristics.” A giraffe has a long neck because it was originally a short-necked animal that was constantly having to reach up into those high, hard-to-reach branches for its food. The more it stretched its neck to get at those juicy leaves, the more its neck lengthened and grew. Eventually, a race of short-necked proto-giraffes became the long-necked species we see today. A crocodile pulled on the little snub nose of a large and bulky gray animal, and its nose was stretched out into a long, snake-like trunk. Oh, excuse me, I’m sorry, that’s Kipling not Lamarck. In contrast, Charles Darwin suggested that the various animal species evolved one from the other through the accidents of a process that he called “Natural Selection.” One bird happened to be born with a beak that was just a little bit better at cracking open nuts than was the beak of the other members of his species. His species normally ate nuts and not berries, but one day a blight wiped out all of the berries in the area and left only the nuts to eat. The bird whose beak was just that little bit better in prying open those nights was the happy little fellow who got plump and attractive and got to mate ten times more often than the other skinny birds. His characteristics were passed on to his offspring. And of his many, many chicks, one of them just happened to be born with an even better nut-breaking beak than was dear old dad, and so the cycle continued, and eventually there grew up a whole race, or species, of birds whose beaks were perfectly and peculiarly adapted to breaking open nuts.
Big deal! So, what was wrong with Lamarck’s theory? What was wrong with Jean-Baptiste Lamarck’s theory is the very crux of the scientific method. It is a beautiful theory, but just because it sounds plausible doesn’t mean that it is true. You see, the problem with Lamarck’s Theory of Acquired Characteristics was that no one had ever seen anything like that actually happen. But no one has ever seen any animal evolve into another! So there. But, scientists have discovered the fossilized remains of many intermediate forms. Paleontologists have recovered the stone remains of dinosaur-like creatures with primitive feathers all over their bodies. The bones of prehistoric horses with more than one toe on each foot have been found that explain that little vestigial toe that nobody normally notices because its buried beneath the hair by that lone giant-sized toe we call a hoof. Even easier to see are the many examples even closer to home, that is, unless your home happens to be adjacent to a dinominium or a racetrack that runs three-toed horses in the Trifecta.
Selective breeding such as that practiced by people who raise sheep, cattle, or dogs is a readily-visible example of the process of natural selection at work. The earliest sheep kept by human beings were probably similar to those still seen roaming wild around the Shetland Islands today. The wool of this unusual sheep “sheds” or rather works its way free from the flesh of the sheep and can then be “plucked” by the shepherds in a process called rooing. Though rooing sounds a lot easier than the usual method of separating the wool from the sheep, it is not. The sheep does not naturally shed all of its coat at one time. It takes weeks for the whole coat to come off. Their wool is also coarser and thus less desirable than that of domestic sheep, oh and yes, these sheep are very territorial and do not gather together in flocks.
There is nothing worse than sheep that won’t behave well, like sheep. Since these primitive sheep are obviously very difficult to care for, and not so great if you are looking to make more than a mitten every couple of weeks, our ancestors tended to single out for breeding purposes those members of the flock who were a little bit more amenable to human care and who like to group together when they got frightened by those big bad people and their dogs. Our forebears too picked out the sheep who had better and softer wool and who shed more of their coat at one time. As these early shepherds continued to cull their herds for these desirable characteristics, and as one sheep generation gave way to another, there eventually was created a sheep like the ones we know today – lots of long, thick, soft wooly hair that stays glued to its owner until he is ready to cut it off, and just as important, doesn’t have to be approached with a pair of shears in one hand, and a sword in the other.
The process of natural selection can be witnessed even more easily by a visit to a dog breeder’s. In the space of only a handful of generations, we humans have bred dogs that come in every shape and size imaginable, and in a whole range of designer colors too.
So, one can see that it is very easy to find examples of natural selection at work, and even to experiment a little bit with it yourself. Nevertheless, no matter how hard M. Lamarck and his followers may have tried, neither they nor anyone else has ever been able to produce a working example of his Theory of Acquired Characteristics. In the days before the cherry picker was invented, and maybe before the ladder too, men and women, and boys and girls had to crane their necks to see the cherries – or apples or oranges – hidden among the leaves in the high braches. They spent all day doing it, and between that, and standing on their tip-toes, they might have spotted a couple of extra cherries, but that didn’t do anything at all for the size of their necks. Oh, it might have stretched the muscles a little bit here and there, and certainly, at the beginning, it must have given them a nice, painful stiff neck, but no matter what tiny fraction their necks might have gained in length and flexibility, they were completely incapable of passing on this “adaptation” to their descendants. They might well have tried. The lord of the manor might have matched up two longtime thick-necked cherry pickers in the hopes of producing a family of Audrey Hepburns, but except for the off chance that either husband or wife had an especially long-necked ancestor, there was no chance that there were going to be long-necked children. By the same token, the skilled artist or the virtuoso violinist does not automatically produce children who possess their parent’s talents. They just might possess an apparently inborn aptitude for painting or music, but the actual craft of painting, and the actual technique of playing concert violin will have to be learned through long years of practice.
Scientific theories need to be provable because the things that they purport to explain are meant to be used for specific purposes or to serve as accurate descriptions of natural phenomena. The natural scientist does not do his work for its supposed aesthetic value, or simply because it gives him or someone else enjoyment. His work and its results may indeed be pleasurable, but this is not its essential purpose. Nor does the natural scientist attempt to explain traits or problems that have their origin in social or cultural arrangements. An anthropologist might analyze primitive tribes in the hope of discovering some universal human attribute, a propensity for a particular behavior that he believes he can demonstrate to have a biological origin. This however, is vastly different from observing and commenting on a people’s marriage or initiation customs. Marriage, in the sense of a longterm union of two people, might well have some kind of genetic origin. As far as we know, all peoples everywhere in the world have always observed the custom of marriage, and have always ideally sought out life mates. But as any psychologist or psychiatrist knows, this is the ideal, even in our own society where only a short time ago marriages were supposed to be forever. And as any good student of the human psyche is quick to point out, all people are different, and the norms of a society are not necessarily the desires of an individual. Some people can’t seem to spend two nights in a row with the same person let alone stay married for a lifetime. And, in many other cultures, polygamy – and more rarely polyandry – was common, and divorce was relatively easy, for one of the partners at least. If all of these different attitudes toward marriage were biologically determined there would have to be a great many genuine genetic differences among human beings. And seeing that there is no evidence that there is, it is not likely that genetics is the main explanation for these different behaviors.
Although the natural scientist cannot find biological explanations for why some people stay married and others don’t, and some people take only one spouse, and others many, he can look at things like why some people get sick and others don’t, or why some people or communities are afflicted with certain diseases while others are not. Many of the great strides in medicine in the past two centuries have been made possible by another theory, a theory that so far has held up to all tests – the Germ Theory of Disease. Time was when people believed that sickness was caused by evil spirits, or by witchcraft, or even bad air (mal aria). The stinking miasma that hung over swamps and other waste ground was once blamed for innumerable outbreaks of plague and pestilence. Medieval man thought that the horrors of the Black Death were brought by the dogs and cats that shared their homes and streets, and so, in their terror, they clubbed them to death by their thousands and rid their cities of – we now know – the few creatures that could have helped them stave off the plague’s real cause – the fleas on the millions of rats that infested nearly every structure in the unhygienic landscape that was the medieval world. It was only later, that the careful and time-consuming scientific process of cause and effect, observation and analysis, proof and counterproof, finally proved to virtually everyone’s satisfaction that plague, as well as all other known diseases, were caused not by any malign supernatural influences, nor by malignant humors, or cursed domestic animals, but by tiny, invisible organisms that preyed on human beings. Physicians demonstrated that people could never catch any given disease unless they were directly exposed to the specific virii or bacteria that actually caused that particular disease.
Furthermore, by applying the scientific method to not only the root cause of a disease, scientists were also able to decipher the previously misunderstood manner by which many diseases developed or were spread. The discovery of the bubonic plague bacillus led to the discovery that the bacterium itself lived inside fleas, fleas that as part of their life cycle lived on rats. It was from these rats, creatures that were often in contact with human beings, that the infection was spread to people. Clear your city of rats, and you get rid of the plague. Scientists also gradually uncovered the way in which the human body fights off infection, and thus began to explain why some people got certain diseases and others did not. As well, the investigations into microbiology and pathology that the Germ Theory spawned, led to a greater understanding of the courses of various diseases. Where once people had fled in terror from the victims of yellow fever, United States Army doctors, Walter Reed and James Carroll, showed in 1900 that the disease was not communicable at all. Healthy men volunteered to sleep in the soiled sheets of those who had died of the disease. The volunteers caught nothing. They remained healthy and strong. The sole cause of the dread infection was the microbes contained within the bloodstream of the mosquitoes that swarmed in the stagnant waters of the Southern and subtropical swamps.
So, knowledge is two different things to the social scientist and the natural scientists. For the social scientist, knowledge is fact mingled with opinion and interpretation. While for the natural scientist, true knowledge consists only in those facts that can be proven again and again through the means of rigorous and controlled experiment. The invariable facts that this approach yields, and the universal theories that it produces are appropriate to the study of things that can be measured and quantified, things that can be measure by a hundred, or a million people in any part of the world and, as long as they were working under the same physical conditions, they will invariably obtain the same results. Firm rules and measurements are essential to the development of all branches of science – medicine, biology, chemistry and physics, and so on. However, rigid codes are constricting, and indeed unsupportable when it comes to the arts and history and literature and the many, many skills and talents that go to make up what we call culture. Beauty is in the eye of the beholder – so the old saying goes, and so too is the answer to any problem wherein human emotions and opinions are a factor. Let twenty people witness the same event, and you will have twenty different accounts of that event. Social Scientists and Natural Scientists view the nature of knowledge differently, because the subjects they study are inherently different, the former objective, and the latter subjective. Knowledge is not absolute, but rather what makes the most sense the greatest part of the time.
Caldwell, Chris. The Prime Glossary: Perfect Number. 2002. URL: http://primes.utm.edu/glossary/page.php?sort=PerfectNumber
Gal Einai Institute of Israel. “Yud – The Mystical Significance of the Hebrew Letters.” The Inner Dimension. No Date. URL:
Pederson, K.C. “Scotland Raising Shedding Sheep for Wool Production.” Twisted Spinsters: Obsessive Fiber Disorder. November 2000. URL: http://www.twistedspinsters.com/page14.html.
Yellow Fever and the Reed Commission VI. Historical Collections and Services
Claude Moore Health Sciences Library, University of Virginia Health System. No Date. URL: http://hsc.virginia.edu/hs-library/historical/yelfev/pan6.html
Caldwell, Chris. The Prime Glossary: Perfect Number. 2002. URL: http://primes.utm.edu/glossary/page.php?sort=PerfectNumber.
Gal Einai Institute of Israel. “Yud – The Mystical Significance of the Hebrew Letters.” The Inner Dimension. No Date. URL:
K.C. Pederson. “Scotland Raising Shedding Sheep for Wool Production.” Twisted Spinsters: Obsessive Fiber Disorder. November 2000. URL: http://www.twistedspinsters.com/page14.html.
Yellow Fever and the Reed Commission VI. Historical Collections and Services
Claude Moore Health Sciences Library, University of Virginia Health System. No Date. URL: http://hsc.virginia.edu/hs-library/historical/yelfev/pan6.html.
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