On the History of Man and the Limitations of the Human Genographic Project

The History of Man by L.F.

A detailed History of our Incomplete Fossil lineage and why the Out of Africa Hypothesis is Flawed


“Light will be thrown on the origin of man and his history” are the notable words of Charles Darwin in the introduction of The Decent of Man (1871). Evolution arose as a controversial topic initially during the 19th Century. Much of the controversy derived from conflicts between religious or spiritual beliefs in creationism and naturalism and contentions were wagered against the ideas involved in the new theory that undermined those beliefs in some capacity. Even those who accepted the theory as it applied to flora and fauna kingdoms refused the idea that humans may have descended from ape-like ancestors. Thomas Henry Huxley, a colleague and friend of Darwin, addressed the topic of the ancestral origins of man in Man’s Place in Nature (1863) while Darwin developed his ideas about the origin of humans in The Decent of Man (1871) shortly thereafter. He effectively predicted that our human ancestors would be found in Africa as this was the place that our closest living relatives could be found in more modern times. (Lyons)

In time, the theory was accepted by the general population and the previously challenged notion of common descent or that we evolved from ape-like creatures was thought plausible. This acceptance led to new questions of how this could be possible and when and where this occurred. Initially, much of the evidence in support of the origin of man came from the clues offered by the fossil record. Some fossil specimens seemed to have features that did not reflect as similar to modern man for instance, several specimens appeared to have smaller brains. In contrast, characteristics in the latter forms of fossil specimens bore more apparent similarities to those observed in modern man.

It would make sense that the more derived forms came after the earlier, more primitive forms however, for the fossils that are dated to around similar times, we can also make comparisons between their derived characteristics and observed how they link to another. This is how we come to understand which fossils specimens are our human relatives. The incompleteness of the fossil record had posed challenges wherein intermediary species are missing, and this is why, with new fossil discoveries, the human lineage is sometime redefined. We also have incomplete or partial specimens which sometimes tells us only a limited bit of information about the progeny. For instance if we find teeth, we may be able to determine by looking at characteristics of shape, size and thickness, how much the specimen relates to the other forms in the fossil record. What we do see in the human family tree, is that most of the earliest forms appeared on the African continent.

To start off by discussing some of the key fossils that have contributed to our understanding of human evolution, beginning with Australopithecine and progressing to the rise of anatomically modern humans encompasses the consideration of several factors. Some of the factors primarily include the primitive and derived characteristics of each fossil species where we have come to understand features by comparison to past, intermediary and more modern species. From there, we have deduced further information about behaviors, habitats, and relative geography. We can also understand migration patterns by observing location as well as dating specimens. This dually helps us to make comparisons between earlier forms and contemporaries, or later forms. It is important to be cognizant of the fact that the hominin fossil record is incomplete, especially as we go back further and further in time. This poses specific challenges to identifying certain pieces of information about characteristic traits, behaviors, habitats and relationships.
Most recently, a specimen has been revealed as possibly the oldest link to our human lineage. This specimen is very unique in comparison to other specimens and living lemurs, prosimian lineage and anthropoids that encompass monkeys, apes and humans. A private collector had found the specimen several years ago and finally sold it to a Norwegian anthropologist to then be studied by a team of renown scientists from around the world. The fossil, Ida, is hypothesized to be a missing link in primate divergence between prosimians and anthropoids. While it was unclear if Ida was an intermediate form of a prosimian to anthropoid species, morphological evidence points to a transitional species. I was surprised to learn that Ida was found in Germany, near Frankfurt, in a crater created by a volcanic explosion during the eocene period nearly 47 million years ago. Even more astonishing is the fact that Ida is 95% intact. Ida was so well preserved because she had fallen into a water filled crater where she was preserved in the cold muddy sediments at the 800 foot deep basin known as Messel pit. Whereas much of our confirmed hominin fossil line is fragmentary, we are able to look at many of Ida’s morphological characteristics, as the fossil is primarily intact, to determine what she was, how she behaved, how she lived and more. I was also puzzled by the location in which Ida was found because most of our early fossil evidence of this kind has been found in East Africa, including “Lucy” in a region that is collectively referenced to as the “Cradle of Civilization.” This evidence challenges the “Out of Africa Hypothesis.” One of the most questionable hominin specimens appearing in this region much later without an apparent link to Africa would be H. neanderthalensis. Perhaps Ida is a link to this form? If we look at a common geographical characteristic in the Cradle of Civilization, we see that water sources were pinnacle to the evolution of life. In Germany, the Messel pit had been filled with water during the Eocene period which would also be conducive to the development of life. Even as we go back to the Eocene period, and we see that many forms of prosimian or mammalian life began to flourish and diverge from the earlier life-forms, we have never come across evidence of a link to a anthropoid type creature. The eight primate specimens collected at the Messel site are fragmentary at best. This is yet another reason why Ida, as a nearly complete specimen, is such a compelling find. She is so complete that we can even observe through Computer Assisted Tomography that her last meal was made up of seeds, leaves and fruits. In order to rule out a link to the prosimian animals, lemurs, morphology needed to be studied. Ida had some primitive features of cranial and post-cranial anatomy found in lemurs but some of the derived or specialized characteristics that lemurs possessed during the time and into the present were missing in Ida such as a grooming claw and a tooth comb. The opposable thumbs, fingernails and tarsus bone in her ankle is shaped like that of a primate while her small baby teeth indicate a commonality between other placental animals. Her leg structure also indicated that she stood erect. For reasons such as these, Ida has been called the holy grail of human evolution and regarded as our newest find yet oldest link in the story of our human origins.

The hominin-like Sahelanthropus tchadensis was unearthed from strata in Chad, a region in Central Africa and found to be about seven to six million years old based on biostratigraphy analysis. This was an unusual and sort of isolated incidence where most other hominin fossils originated in regions closer to water on the African continent, as water is a life-giving resource. We know a bit about some of the primitive characteristics of this taxon based on the pieces of cranial bones found. For example, we know that the features such as the size of the cranium correlates to the volume capacity of the brain that it may have protected. In this case, Sahelanthropus tchadensis had a small brain similar to that of the African ape. A possible derived feature is a small canine tooth, which leads some scientists to speculate a relationship to hominin lineage. We do not have many other fossil fragments other then the skull structure to evaluate for other primitive and derived characteristics, which leaves a classification as a hominin, speculative. However, from there, we still have enough to make the assumption about this variants locomotion abilities by examining the foramen magnum, which is the opening in the base of the skill where the cervical vertebrae would be connected. In this case, there is evidence to say that Sahelanthropus tchadensis had an erect posture but not enough to discern any early indication of bipedality.
In the East African region, Kenya, fossil fragments from Orrorin tugenesis were excavated from four sites that include, Cheboit, Kapsomin, Kapcheberek and Argai. Radioisotopic analysis methods identify the levels of carbon atoms in sedimentary strata and were used to date the specimens in the temporal range of 6.1 to 5.8 million years ago. Both primitive and derived characteristics were observed. Some of these characteristics have indicated plausible evolutionary relationships of Orrorin tugenesis to the more contemporary forms, Ardipithecus ramidus and Kenyanthropus platyops. One such common feature of dentition is the smaller size of the molar teeth. The specialized thickness of dental enamel is also similar to that of Kenyanthropus platyops and Australopithecus afarenis. Depending on how a comparison is made to other fossil forms, these traits may be considered primitive or derived. The most significant thing we would look for in fossil specimens when placing them taxonomically in line with hominin ancestry would be morphological features that indicate obligate locomotion. Computed tomography imaging of the proximal femur indicated a variation in thickness inferiorly and superiorly which might mean O. tugenensis was bipedal but other specialization’s indicated arboreal locomotion which is the ability to move in trees. Fossils of other animals found in the similar location were more complete and gave better clues about the environment in which O. tugenensis inhabited, by comparison. It is suspected that the environment was wooded with lakes and streams. This may point to the geographical features theorized to coincide with the development of bipedality if not obligate locomotion. I also think that the water resource points to an element of the landscape conducive to survival, and may be one reason why other fossil specimens have been found relatively nearby this region in Africa.
Several other hominid-like specimens have turned up on the African Continent, and we collectively refer to them as hominin types. Hominins have primitive and derived features that may link them to hominid lineage but in several cases, there is not enough fossil evidence to distinguish relationships, especially between intermediate forms. Two hominin forms, Ardipithecus kadabba and Ardipithecus ramidus were discovered in the Middle Awash Valley of Ethiopia, in Northeastern Africa. The catch here is that temporal range in which Ardipithecus kadabba may have inhabited the Middle Awash Valley is 5.7 to 5.2 million years ago while it was found that Ardipithecus ramidus lived there between 4.5 to 4.2 million years ago based on paleomagnetic studies which evaluated periodic reversals in the Earths geomagnetic field and radioisotopic dating records which measured the decay rate of radioisotopes like carbon atoms isolated in strata. There is a significant time difference involved between the emergence of each form. The latter form, Ardipithecus ramidus is more indicated to be of hominin relation while Ardipithecus kadabba is only speculated to be. Study of the crania and post-crania structures, as fragmented fossils, points to bipedalism as a derived trait. Most indicative of this reference toward obligate locomotion, or at least bipedality, the feature we are looking for as a clue to hominin relation, is upward orientation in the joint connecting to the fourth toe. A similar morphology has been identified in the hominin species, Australopithecus afarensis and even the most modern hominids, Homo sapiens. A problem here is the fact that the toe bone was found at a distance away from the other fossil specimens and was dated to several hundred thousand years earlier. Perhaps, this fragment points to the existence of and intermediate or earlier form? There is really not enough evidence to say. If more fossil fragments were discovered, then perhaps scientists could discern more distinct conclusions. In contrast, we know much more about Ardipithecus ramidus. Ar. ramidus did not evolve obligate bipedality but perhaps had functional bipedality which is the ability to walk upright for periods of time, for a momentary or brief purpose. We see functional bipedality in chimpanzee populations. Cranial structure and dentition indicate some homo characteristics. Locomotive behavior is suspected based on the size and shape of the ischium as related to muscle development and primary movement on all four limbs. Ar. ramidus specimens were not only found in the closed woodland region of Middle Awash Valley but also in Gona, a region that also had grasslands.
So when did hominids begin to walk upright as their primary form of ambulation? Perhaps around 4.1 to 3.9 million years ago, according to radioisotopic dating of volcanic sediments that encased and preserved Australopithecus anamensis fossils. Australopithecus anamensis is said to be the first of the Australopithecus and early homo genus with obligate bipedality. Around 3.5 to 3.2 million years ago came Kenyanthropus platyops, discovered sometime after Australopithecus anamensis in a relatively close part of Kenya. Kenyanthropus platyops fossils indicate more primitive features complimented by derived traits which has made it difficult to distinguish the exact relationship to other hominins. It features a partially flat face similarly observed of Homo rudolfensis as well as Australopithecus afarensis but it is possible that this feature is a result of skeletal wear or damage, and K. platyops may just be a variant of Au. afarensis especially as the temporal range of Au. afarensis which is 3.9 to 2.9 million years ago, coincides with that of K. platyops and both linages were discovered in Kenya. Au. afarensis, dubbed “Lucy” is a near complete skeleton which means that we know a lot about this fossil, and can make comparisons to some incomplete Au. afarensis specimens that include consideration of sexual dimorphism’s and age differences. The scientist, Mary Leakey and her team discovered fossilized footprints from Au. afarensis. This clearly points to obligate bipedality which is an adaption that would also eventually allow for species to migrate further distances. Population expansion and isolation greatly influenced the evolutionary progress of early hominids. In addition, Au. afarensis was present for almost one million years which must mean that the population expanded in terms of variants. When populations grow it increases competitive pressures and warrants expansion. It is also a precursor to the necessity of greater interdependence as a benefit to survival and in competition. Interactions between others and communication would have likely developed to some degree and this may have led to learned behaviors. Evidence of learned behavior may be that tools, that were not necessarily constructed but derived from natural elements, were used to accomplish specific tasks, such as scrapping the marrow from animal bones.
According to biochronological dating methods, Australopithecus africanus is one of the oldest hominids to be discovered in south Africa, around 3 to 2 million years ago. As time has passed many Australopithecus africanus fossil fragments, both cranial and post-cranial, have been unearthed, allowing scientists to call Australopithecus africanus, a true hominid. Australopithecus africanus is considered a distinct link between modern man and our ape-like ancestors. Prior to this, the piltdown man, “discovered” in England was thought to be the closest link between man and ape until the multi-specimen was exposed as a fake. Au. africanus and A. afarensis are quite similar in certain ways, in terms of an evolutionary relationship in that they were both small-bodied in comparison to earlier forms. Their pelvis, leg and foot structures such as the phalanges were adapted to allow for primary bipedality. Some derived characteristics in Au. africanus also found in other Homo species are a taller frontal bone and a longer flattened orientation of the occipital structures. Australopithecus garhi is said to have inhabited Ethiopia 2.5 million years ago, just as A. afarensis had earlier. Features for dentition in Australopithecus garhi were divergent from the more primitive traits observed in robust australopiths. Australopithecus garhi species made stone tools which likely indicates a higher level of cognition then some number of their possible predecessors. The ability to develop technologies would not only be linked to neurobiological advances in evolution but also morphological distinctions perhaps those even adapted ensuit to bipedality. The relationship is not so much the indication of a nature to nurture relationship but a nature to nurture relation. Very generally, I want to reference the fact that walking upright freed the hands, to create and use tools. The longer femora of Australopithecus garhi are distinctly different from the femora of Au. afarensis and more like that of Homo sapiens. Derived post-cranial features indicate bipedality which suggests the link between Au. garhi to the genus Homo. There are also some primitive characteristics apparent in Australopithecus garhi. Around the same epoch, 2.7 to 2.5 million years ago, Paranthropus aethiopicus may have appeared as an intermediate species between Au. afarensis, Australopithecus garhi and both, earlier hominin and contemporary forms but scientists are not really sure how this species, if distinct from another and not a variant, fits into the hominin phylogeny. Paranthropus aethiopicus, was discovered in Kenya in 1985 by Richard Leakey (the son of Mary Leakey) and has also been identified as originating in Ethiopia. Morphological evidence points to the function of the temporomandibular joints as similar to Au. afarensis. We see that there are some features in common with Paranthropus robustus, a hominin said to have emerged in south Africa 2 to 1.2 million years ago. Another robust australopith, Paranthropus boisei emerged in a very close timeframe to that of Paranthropus robustus, just 2.3 to 1.4 million years ago. Both species of australopiths had cranial features different from most all other hominins, such as megadont cheek teeth. It is suspected that there are no descendants of either species.
1.95 to 1.75 million years ago another Australopith, Au. Sediba appeared in South Africa. Au. Sediba, like most all hominins that emerged prior to homo sapiens, has some primitive and derived features. Au. Sediba shares many features with other Australopiths with the exception of Au. africanus. The shape of the pelvis is distinct to structural features observed in Homo erectus. Husband and wife team, Mary and Louis Leakey turned up Homo habilis in Kenya. Homo habilis is one of the first species of the homo genus, that lived 2.5 to 1.6 million years ago. Finally, we are following the fossil evidence closer to homo sapiens emergence. Cranial morphology was similar to that of Australopiths but the cranial capacity was larger. Both primitive and derived traits appear such as thick and curved phalanges that point to an ape-like ancestor and palms similar to homo sapiens.
Homo erectus emerges 1.8 to 50 thousand years ago in Indonesia, China, and northern, eastern and southern Africa. It is clear that Homo erectus had migrated to different areas based on the fact that land-bridges were formed during this time by expanded glacial covering which also retreated at different times, and led to isolated populations. It is the first known species to have moved out of Africa. It is very possible that differences emerging between the Asian and African phylogeny of Homo erectus as a species was greatly influenced by different geographical niches. For example, some of these differences in the environment may have been different dietary resources which led to distinct adaptions in features of dentition. Also, similar cranial and post-cranial features as well as time and displacement of the Homo erectus lineage has directly linked the hominid to that of Homo habilis. A possible predecessor of Homo habilis was Homo rudolfensis.
Recently, the fossil Homo floresiensis was discovered in Indonesia and is dated back to 100,000 to 12,000 years ago. A timeline that coincides or partially overlaps with that of Homo neanderthalensis and Homo sapiens. Homo floresiensis was quite distinct in that it had a significantly smaller body size then other hominins observed to have lived during that time, as well as by comparison to some earlier forms. There are some cranial features present that correlate with those observed in Homo erectus but also divergent post-cranial features that resembled those found in Australopiths. So with several primitive features present, what linked Homo floresiensis with Homo sapiens? Derived characteristics appearing as morphologies in dentition such as tooth enamel thickness, size and shape of molars and of the mandibles, were similar to Homo erectus and Homo sapiens but of a smaller scale. Homo floresiensis is a hobbit, standing about a meter tall. It is suspected to be a dwarf form of the Asian line of Homo erectus. While conflicting and more recent theories regard H. floresiensis as a later form of H. habilis. If this is so, then there are some challenges posed to what was previously determined about the dates and possibly the migratory patterns of early Homo species in that the idea intends that H. floresiensis left Africa before the evolution of H. erectus. Due to the smaller stature of this line, it’s cranial size was dwarfed which coincides with a smaller brain size similar to that observed in much earlier periods. Skeletal structure indicates obligate bipedalism which had also been assumed based on the similar ability being found in multiple common ancestors. Other clues such as tools were found, dating back to 840,000 years ago appearing as stones that were reconstructed and used for survival purposes. Dwarfing may be a result of environmental conditions such as limited food supply and isolation which is conducive to the conditions of their reconstructed environment as shifting between glacial and interglacial cycles. No larger forms of Homo floresiensis have ever been discovered which raises the speculation that they arrived on the Island of Flores in a variant form of similar stature. Other Scientists believe that this fossil form was a variant of the Homo sapien but suffered a disease which would account for its petite size. There were problems with this idea though because there has never really been a disease that would consequentially impact size, but perhaps development and most of these conditions are arising in genetic mutations. This may explain why there were several small statured variants appearing but the hypothesis is negated by the fact that if it were so there still would have likely been larger that appeared as well.

Homo heidelbergensis appears to have lived in Germany 800 to 350 thousand years ago. Homo heidelbergensis possessed primitive traits seen in Homo erectus such as a projecting face and brow ridge and many more derived traits found in Homo sapiens such as a large cranial capacity. Homo heidelbergensis crafted and used tools in a manner that precursors the technological developments of homo sapiens.
Homo neanderthalensis lived 200 to 28 thousand years ago and for some of the time, along side Homo sapiens which emerged 125 thousand years ago and survived as a species, into the present form of modern man. Homo neanderthalensis is found throughout Europe and western Asia and suspected to have lived in caves. They were quite skilled in hunting and gathering. Some of their behaviors were similar to that of Homo Sapiens but they were morphologically different in some ways. There is no concrete evidence that points to the intermarriage of Homo neanderthalensis and Homo sapiens despite their similarities and coexistence for a period of time. It is suspected that their cranial capacity did not compare to that of Homo sapiens and for this reason, adaptive changes in behavior to the rapidly changing conditions of the global climate during ice ages could have been more of a challenge. Here, cranial capacity is not necessarily indicated by cranium size, but perhaps structure. Homo neanderthalensis actually had a much larger skull them Homo sapiens as well as a larger post-cranial build. This information tells us that the Homo sapien brain as a glandular organ, was larger then ever before observed in the Homo lineage. It is said that Homo sapiens were more cognitively able to adapt their behaviors to environmental changes in comparison to Homo neanderthalensis which may have led Homo sapiens to out compete Homo neanderthalensis to extinction. It seems as though Homo neanderthalensis as a fossil specimen receives a significant deal of attention from scientists and the public alike. I think this is because there is a strong connection between this species and homo sapiens whereby temporal range overlaps, regional habitation or even regional co-habitation is indicated and further there are not only some common characteristics but great differences which drive many questions about where exactly Homo neanderthalensis falls in the lineage of hominins. Also, the reason for the extinction of Homo neanderthalensis seems unclear while the extinction of earlier forms seems a to be explained by intermarriage, expansion, environmental factors and other pieces of evidence such as the identification of fossil specimens as intermediate forms and molecular evidence that places such progenitor species in the homo linage with more certainty. To note, there is no proof alluding to intermarriage between Homo neanderthalensis and Homo sapiens, but in the context of evolutionary theory, the question has been raised. In that context, it is possible that one species evolved to a more derived modified form while the other is replaced by that form. In some cases, animal hybrids have had an advantage over progenitor forms because they inherited traits from both parents which may have given them advantages that both the earlier forms possessed apart from one another. In addition, Homo neanderthalensis lived along side Homo sapiens but Homo sapiens did not become extinct. So what were the differences of factors that drove Homo neanderthalensis to extinction and not Homo sapiens? Scientists have been able to make many hypotheses to try to answer this question. Some cite environmental factors however, if those environmental factors left populations volatile during that time, how come the same impact was not observed in the Homo sapien population? Were there physical differences that allowed for Homo sapiens to better adapt to rapid shifts in the climate such as temperature? The drying or drought periods combined with periods of flooding were experienced around the globe due to glacial recession and expansion. It is possible that food sources were depleted as a result, both plant and animal alike. Here we may consider that Homo sapiens possessed some cognitive advantage as one possible trait that allowed them a survival advantage over Homo neanderthalensis. This advantage may even implicate a struggle for existence as competition between each progeny. Darwin tells us that “It is not the strongest of the species that survive, nor the most intelligent, but the one most responsive to change.” Indeed, I agree but I think a higher ability toward cognition could have created an advantage in this case while I also think there may have been some other physical differences. In consideration of an entirely different probable cause, I wonder if some disease effected the Homo neanderthalensis population and not Homo sapiens based on genetic differences. We see that certain viruses only effect certain animal species and not others so there is some supporting research on this sort of occurrence. Now along this line, there has also been DNA analysis for Homo neanderthalensis that indicates a lack of diversity in mtDNA sequences. Why is this? Did they evolve from a extended yet related tangent of the Homonin line, where the predecessors of their population did not expand as much as those ancestral links more directly associated to the Homo sapien line had? If so, this could account for the lack of diversity in mtDNA and a correlated under exposure to certain pathogens. In this case, we can infer that Homo sapiens may have had the advantage. It is not unheard of that disease could spread at pandemic rates and relate to high mortality rates in certain populations; We have historic record of this. So if it happened at a later time, perhaps it had happened at an earlier time in the history of man. What we do know for sure is that the line connecting Homo neanderthalensis with Homo sapiens diverged some 500,000 years ago. Finally, there is more to discuss about Homo sapiens, because that’s us! Homo sapiens are the genus of modern man. As mentioned above, H. sapiens emerged around 175,000-160,00 thousand years ago in East Africa. In an earlier comparison between Homo neanderthalensis and Homo sapiens, I mentioned that Homo sapiens may have had a cognitive advantage. This postulation has been backed up by fossil evidence as great differences in cranial and post-cranial anatomy have been discovered. Larger cranial size relates to the structural capacity to house a larger brain. We can also make reasonable predictions or assumptions about the stasis and features of the environment for the time and place based upon where the location of Homo sapien fossils were found. We know that changes took place and a more tropical environment developed. One of the ways we can determine this is by also studying the fossils of other fauna and specifically flora located around the same regions and dated to the similar time. The presence of Homo sapien fossils in such a time and space thereafter environmental changes suggests that the population adapted. This has multiple implications which include the idea of a larger cognitive capacity and structuralisation of the brain anatomy and physiology. Anatomical changes like this would mean that behavioral changes and adaptions were possible, thus, an advanced cognitive capacity may have benefitted survival in many ways. Some of these behavioral changes are measurable by the comparison of relic evidence such as symbolism in cave drawings, advanced tools, and a related subsistence strategy such as using those tools to procure sources of nourishment through agricultural and hunting applications. Advancements in sustenance strategies may have even led to the extinction of other animal species as several populations were outhunted, especially when resources were scarce. Resources would be particularly scarce based on a shifting climate theory, making populations more vulnerable to factors that influenced their declining numbers and extinction. In addition, sustenance strategies may have aided the survival of animal populations as it increased agricultural byproducts. New evidence suggests that farming began 23,000 years ago. Seed gathering by stone age people was taking place around 10,000 years ago. Cro magnonensis was modern man, one of the most early forms of homo sapiens. Homo sapien Cromagnonensis was a stone age population that existed 10,000 to 40,000 years ago. This is supportive of the fact that Homo sapien Cromagnonensis developed some forms of systems which they also did socially as hunter-gather societies where gender specialization and social stratification were implemented.1
Homo sapiens were gracile and of a more petite build in a general deliberation to earlier forms including H. neanderthalensis and H. heidelbergensis. The smaller size of Homo sapiens may have also given the species its own unique advantages. The smaller structure was an advantage to maintaining body temperature in tropical warm climates. In some recent studies this morphological advantage of heat stabilization is linked to advancement in cognitive ability. To study these advantages is important for our past and present understanding of human evolution. There are morphological differences in dentition and cranial features such as the smaller size of the mandible, which tells us that the way in which they consumed food and what types of food they ate may have been different from earlier forms or related species. Perhaps they were able to chew foods better and in turn derive more nutritional elements out of products for consumption? Their technological advancements allowed them to fish and hunt a wide variety of prey, and this undoubtably exposed them to new nutritional elements as common elements in their diet. The new forms of tools and their general tool arsenal must have been developed gradually over time. I think if we can assume this, we could also assume that the secrets of their trade were communicated between one generation to the next. These tools may have given Homo sapiens a survival advantage over H. neanderthalensis who perhaps lacked the instinctiveness combined with cognitive capacity to develop the more advanced tools on their own. This is assumed for the sake of contemplation alone and not to imply as an absolute, that each population did not have common instincts or even some similar cognitive abilities because we see even into the present that many animal species have similar instincts derived based on similar survival needs and that this capacity has a indication toward neurobiological processing. Even if H. neanderthalensis could learn how to develop such tools by example it is very likely communication barriers and defensive instincts segregated the populations, where learned skills were non-commutative. In fact, recently the evolution of prejudice has been explored in rhesus monkeys in isolated natural populations and it was observed that one group would demonstrate discriminatory behavior in response to facial misrecognition of outsiders. One reason for this behavior was because outsiders may have posed a threat. So even if Homo sapiens could communicate somehow with H. neanderthalensis, it may be unlikely that they would teach them techniques that would allow them to outhunt the other kind.2 It seems very unclear as to whether or not H. neanderthalensis crafted tools on their own despite more significant findings that they have have used naturally occurring materials, as is, for tools. Perhaps the ongoing excavations of territories once inhabited by H. neanderthalensis will unveil greater evidence of tool making in the future.
Another reason why Homo sapiens may have developed better and better tools is based on their values for expansion. Expanding over greater areas, toward and to the European and Asian continent would have allowed them to obtain more diverse natural materials to use in their technological innovations. Expansion is often driven by a desire to escape competitive pressures in the evolutionary context. Even if one animal population was not experiencing such competitive pressures and another animal population that they preyed upon was, their prey may migrate and therefore some populations that relied on that food source followed. Migration alone likely became a demographic advantage because different portions of the collective population would have been exposed to different environmental factors such as different resources, different pressures, different diseases, different climates and isolation. Isolation may have occurred as a result of settling in certain areas for certain times by preference but also as glacial melting dissolved land-bridges that connected early geological and geographical expanses, during times when the super continent Pangea was being broken down. Tectonic motion resulted in earthquakes and volcanic activity which caused separation of landmass as well as the development of new land-masses. As populations expanded under these conditions they would have adapted derived characteristics through the criteria for evolution by natural selection. Their populations would become more diverse and such diversity would likely be in more ways favorable to survival. H. neanderthalensis had a stockier build that was indicative of habitation of a colder environment. This may have been a disadvantage in expansion as they may not have regulated thermal stasis within their bodies as easily as Homo sapiens, who were adept to warmer climates but also could develop methods of keeping warm in colder climates, such as developing shelters or clothing. Here we see that it is not even just a physical adaption but the application of cognition to innovation and material creations that could also play a part in how species interacted with features of their environment. Where each species may or may not have been able to develop adaptive mechanisms to thermal regulation, biochemically, if some number of variants were able to acquire traits or characteristics for the regulation of body, some may have survived to reproduce in greater numbers and the adaptive mechanism may have become dominant. H. neanderthalensis as a species, originated in Europe and Asia. We know this based on the fact that these are the only regions where their fossil remains have ever turned up. As Homo sapiens expanded there appears in the fossil record to be a systematic displacement of H. neanderthalensis by Homo sapiens. Maybe they didn’t just out compete the other in terms of resources but also in violent combat. I am not sure that there is direct evidence. Perhaps wound markings on fossils could give us some clues but even if we found wound marks on fossil specimens it would be difficult to say where they came from, if not from a predator, or their own kind or outsider populations? It could be possible to evaluate the type of wound and see if it came from a weapon that Homo sapiens used or the teeth of a predator, but I suppose the findings would not be definitive with certainty. Violent behavior as a territorial defense mechanism and as a resulting form of competition, is observed in many animal populations. Even if we can infer the likelihood of this sort of fight between species, could we know who started it? We’d have to observe very delineated circumstances, such as the nature of the species. Were they passive or aggressive. Would they move on if another population came to compete for their land or would they fight for the territory? These are the sort of questions we need to answer to at least determine what happened to H. neanderthalensis.
Many of the Homo sapien behaviors I have mentioned did not evolve all at once, but at slightly different times and regions in Africa, while research suggests the behaviors did evolve more uniformly on the European continent. This is probably because the expansion of Homo sapiens out of Africa did not take place for several thousands of years and those behaviors were likely to be adapted in Africa and carried with the species to Europe. As a matter of fact, it was probably not just traits like bipedality that allowed for expansion but also the development of tools and behavioral adaptions that allowed them the versatility to survive in different environments and during the survey of great distances. There is also evidence that both H. neanderthalensis and H. sapien populations used fire. Some paleolithic people wore hides and may have even woven garments; Homo sapiens crafted beads and pendents from shells and bone and even carved figurines, like venus figures, that perhaps represented a value for fertility.
Advancements in technologies that allow for the analysis of genetic evidence has pushed our understanding of our human lineage further. We no longer have to rely only on the clues of fossil evidence or applications of environmental analysis alone but we can now look at factors such as changes in single-nucleotide polymorphism’s in those fossils, or the displacement as time and space variables, for the frequency and rate of change in mtDNA sequences and y-chromosomal patterns. We can not only observed these values from fossil specimens but also in modern man into the present. What we find is most profound in the search for our human origin. We’ve learned by genetic testing that there is greater diversity present in modern African populations then other populations around the world. We have also learned from this, that that population is much older then other populations. This means that evolution occurred for a longer period of time in Africa then anywhere else in the world. This is confirmed in the fossil record also as most early hominin forms are found on the continent. As for our origins, it seems clear that our common ancestor(s) came from Africa. This is called the Out of Africa hypothesis. Before I talk more about this idea at length, I want to mention its implications on the relationship between H. neanderthalensis and H. sapiens. It had been determined to some significant degree through genetic analysis that neither species interbred which would rule out any gene flow hypothesis about their relationship while other genomic studies suggest it occurred rarely. H. neanderthalensis may just been a separate, distinct species in terms of genetic distinction apart from H. sapiens. In light of the recent findings, some scholars still maintain the multi-regional model. Genetic or genomic comparison between H. sapiens and earlier forms dating back to almost 4 million years ago has given many more indications about where each form comes in line to the next, where it may have been unclear in some cases. While, “researchers continue to unearth fossils from all over the globe, and add branches to the evolutionary human tree, enriching, but at the same time complicating, the story of our origins,” molecular evidence advances our understanding which leads us to take a closer look at the, Out of Africa Hypothesis. Lyons, Bones of Contention: The Fossil Evidence (2011)
The Out of Africa Hypothesis

The Out of Africa Hypothesis a.k.a The Human Replacement Hypothesis is the postulation that every Homo sapien, or human on earth is directly descendant from a small group of hominids originating on the African continent. One tangent of the theory is supported by y-chromosomal DNA analysis that suggests that a small group migrated out of Africa around 50-60,000 years ago and expanded to become a global population. There is also a conjunctive theory called the “Eve Hypothesis” which links the human lineage with a most common recent ancestor as a matrilineal female hominid that lived in East Africa around 200,000 years ago.
The “Eve Hypothesis” is based upon the idea that we are all living decedents of a mitochondrial eve. There is mitochondrial DNA (mtDNA) evidence that has been uncovered through genetic and genomic analysis especially as endeavored by The Human Genographic Project, in support of these theories. Female mtDNA is trackable because it does not undergo rapid mutations. Analysis of mtDNA can be traced back as patterns in matrilineal heritage while patterns in y-chromosomal inheritance allows scientists to trace back the origin of man to an “Adam” or common patrilineal ancestry. While I have no doubt there are in fact both a male and female common and recent ancestor to all of humanity at large, the question here for me was how could our common matrilineal link have appeared so much further into the past then our patrilineal link? Was this because there were separate migration lines that converged these two genetic “amalgams”? The answers are unclear to me but I think one explanation may lie in the fact that we are tracing back a molecular fossil record, of two distinct origins, which is mtDNA and y-chromosomes.
We know that the male sex determining chromosomes in the genus Homo are XY while the female combination is XX. For this reason, males always inherit their y-chromosome from their paternal parent and only inherit one X-chromosome from the maternal parent which is the partial reason as to why males do not pass along an mtDNA sequences that are traceable to a matrilineal ancestor including a most recent common ancestor. It is also why we can trace the y-chromosomal frequencies and patterns back to a patrilineal common ancestor. In addition, it may account for the different temporal ranges for each point of origination, that of “Adam” and that of “Eve.”
There seems to be distinct problems in tracing such roots which I think is why we see different patterns of decendency unveiled by The Human Genographic Project. Before I talk about those patterns and their implications, I want to address what I believe to be the probable cause of the divergence between the adam and mitochondrial eve lines as well as why the studies on the topic are limited.
While we can collect wide samples from current Homo sapien populations around the world, we have a limited fossil record which makes for a limited sample comparison on at least one end. We also have several controversies arising out of conflicting views having to do with the incompleteness of the fossil record. For example, we have several ancestral groupings popping up in different locations at different times, and also co-evolving. With molecular evidence we can sort of bypass some of the indirect leaves on our evolutionary tree and focus more on the branches in order to propose a mitochondrial eve or in that, an adam; collectively our most recent common ancestors. We may have to consider that mitochondrial eve was either the only matrilineal progeny in existence at the time of origination, that did in fact reproduce and(or) there were others but none of their children survived. More so, I do not think the argument ends there in fact, I have thought of another idea based in theory which suggests that mitochondria was acquired in our human DNA several millions of years ago and passed on through female oocytes. Paying attention to those details I also recalled that mitochondrial DNA (mtDNA) is located in organelles, called mitochondria and in eukaryotic organisms convert food sources into energy. Note, that the ability for earlier hominins to conserve energy could have had great evolutionary implications, such as the ability to retain energy when escaping predation. Here I want to focus on what this may have meant for reproduction and how it shapes the line that we draw back to a common matrilineal ancestor.
The Endosymbiotic Theory proposes that energy-producing eubacteria may have been engulfed by a larger primitive cell and come to reside within it, eventually evolving into what we now know as mitochondria. Based on what I know, and what I have recently studied about the origins of mammalian evolution as it relates to captured genes from viral genomes, there is evidence that mammalian DNA that is similar to viral or even bacterial DNA, and the mechanisms of transcription, may by default admit the DNA of an invading pathogen within it’s own DNA by the capture and reinsertion of genes from the invading organism, where that genetic material may have been reinserted back into the mammalian genome. This is considered anti-apoptotic cellular behavior and may indicate the ability of pathogens to integrate within the human genome whereby a cellular memory is forged. We see this occur even into the present with the pathogenesis of oncoviruses. What I am suggesting is that there are several factors in support of the hypothesis. However debatable the origin of mtDNA may be, we know that all humans carry mtDNA within their cells and scientists can trace that information back to mitochondrial eve. From that, one may wonder if there were in fact earlier forms, or a mother to our mitochondrial Eve that did not come to acquire mtDNA in her cells and therefore we really would have no way of tracing a common matrilineal ancestor beyond 200,000 years ago through this type of analysis, if there was in fact one.
Along the same line, and assuming or accepting that symbiosis plays a role in evolution, I want to mention that the captured retroviral envelope protein, syncytin, appears to have integrated in placental animals and our primate ancestors several million years ago. HERV proteins, syncitin-1 and syncitin-2 are passed on in mtDNA. These genes allowed for more vital births and this may be why we see a population expansion in terms of numbers following the lineage of mitochondrial eve.
Dr. T. Heidmann and colleagues (Placental syncytins: Genetic disjunction between the fusogenic and immunosuppressive activity of retroviral envelope proteins. Proc Natl Acad Sci U S A 2007; 104: 20534-20539.) suggested in the results of their work involving Placental syncytins, that the protein that exists in viruses, called syncytin, originated in an evolutionary context, as a surface protein on retroviruses that fused to cells, and became essential for human birth because it is expressed in the placenta. Dr. Heidmann and colleagues determined this by knock-out studies and experimentation, where the gene was disabled in mice and the placentas became deformed leading to embryo death. Syncytin, as a captured gene in humans, is expressed by the foetal side of the placental membrane and allows for vital nutrient transfer from mothers their embryos through the the syncytium. It also helps cells from both the mother and child to not enter one another’s blood stream and effectively prohibits any immunological attack on either organism. It is a benefit to survival but there is more; Genetic material in viruses is also present in human DNA so does this conclusively mean that most proteins are acquired in a similar capacity? This makes for an alarming hypothesis (should it be taken as conclusive) in that some 40 million years ago the borna virus infected our monkey-like ancestors. Presently, viruses are found in about 5-8% of the genome of every person on earth, according to the reference for the article, Hunting Fossil Viruses in Human DNA (Carl Zimmer), that is, Endogenous non-retroviral RNA virus elements in mammalian genomes. Nature 463, 84-87 (7 January 2010) The results of this work suggest that a measurable 8% of the human genome is traced back namely, to retrovirus infections. “To put that number in perspective, that’s seven times more DNA than is found in all the 20,000 protein-coding genes in the human genome.” Hunting Fossils Viruses in Human DNA (Carl Zimmer, 2010)
With regard to the above from an evolutionary standpoint, it is important to point out that the generational effects of captive virus are going to take place only in the surviving descendants of populations that had been infected where integration of pathogenic material is effectively inserted within the human genome. This idea is even true to the requirements of evolution, in specific relevance to Darwin’s three criteria for natural selection where: 1) a trait producing variation for some characteristic (whether known or unknown) exists, 2) is at least partially heritable and 3) variants survive to reproduce at higher rates (herein, germ cells carry the viral information). Germ cells are spermatozoa and oocytes. An oocyte that carries mtDNA is a germ cell. When effected germ cells existent in progenitor species come together during gametogenesis, the viral information is often distributed in the genomic structure (i.e. chromosomes) of filial generations. The genome of the offspring is impressed by the provirus, that is the latent or hidden derivative of the virus that has successfully integrated within the genomic structure. This integration had and(or) continues to take place where reverse transcriptase activity occurs or is coded in Long interspersed repetitive elements or Long interspersed nuclear elements (LINE). I suspect this could mechanize a sort of epigenetic effect within some locus of expression, causing a sort of fossil remnant in human DNA.
The big point that all the above leads up to comes in the suggestion that mtDNA may have in fact come into our human genome through some process of endosymbiosis and pathogenesis. If this happened at some point in time, 200,000 years ago, then the theoretical eve may not be the most recent common human ancestor but she may come in line before or even after the time in which our current model tells us. That is, a true eve apart from one that we trace through mitochondrial evidence.
The story of the origin of the origin of man must hold the evolutionary precept that over time, forms tend to become more complex through the acquisition of specialization’s primarily through the process of natural selection. This is why the point of origin would really go much further, beyond the emergence of primates, beyond the divergence of prosimians from anthropoids, to explore what I believe would be very simple molecular compounds that developed more complex life-forms through symbiotic relationships. Those compound would likely have been subject to decomposition based on their purely organic nature that a record of such singular cellular compounds would only be observable in a more complex fossilized form which had integrated them into their genome. This does not make the search for our roots obsolete but it in fact fortifies it because what we are doing here, especially in the case of mitochondrial eve, is tracing back molecular evolution in living ancestral organisms. So this begs that question, when we theorize about mitochondrial eve, are we taking about the point in which a common matrilineal ancestor evolved or are we talking about the point that the derived specialization of mitochondrial expression in our DNA was acquired, such as we would point out the time in which morphological specialization’s allowed for bipedality? In essence, we are tracing the mitochondrial pattern in the x-chromosome of eve but if the endosymbiotic hypothesis is true, then we really may just be pointing out a time of a common specialization in a common matrilineal ancestor, where she may too have a matrilineal line leading up to her, that is not trackable by the same process. In other words, I think mitochondrial eve is a point of common ancestry but I do not know if she was the most recent common ancestor or if there is some other specialized trait that can be traced back further, apart from mtDNA analysis. Now is this such the case for our patrilineal adam?
I think we can say our adam is a bit different, because there we are tracking something entirely different which is the pattern and frequency of the male sex-determining characteristics, for the y sex chromosome (haplotypes) groups in an XY chromosomal combination. If we could trace male mtDNA back to a common patrilineal ancestor perhaps we would see the theoretical emergence of this take place around the same times as it has with mitochondrial eve, 200,000 years ago but since male mitochondrial cells are selectively destroyed during the process of meiosis and mitosis in fertilization, we cannot trace patrilineal ancestry through mtDNA analysis. This could be one reason as to why we see the emergence of Adam as our most common recent patrilineal ancestor appearing 50-60,000 years ago and mitochondrial Eve emerging much further in the past, some 200,000 years ago.
It is important to understand that when we consider common ancestry, we are considering a point of intersection, of convergence, not divergence. Thereafter we can observe divergence from that point and that is the focus of the Human Genographic Project. To understand the point of origination for a matrilineal and patrilineal line, we have to consider that we are tracing back the origin of two distinct groups. One reason we know this is because our adam is emerging about 50,000 years ago, while he surely had a matrilineal line, it is not traced to this timeframe. Matrilineal heritage, and our common recent ancestor mitochondrial eve is traced back much further probably because our most recent common ancestors were from separate families. I think that mitochondria Eve as a most common recent ancestor would have had to be the standalone female where the females around her did not survive to reproduce, adam could have reproduced with several females, producing several lines. Well, this is really not an entirely correct assumption. Earlier on I had discussed that mitochondrial eve as a most recent common human ancestor may had been the only human to survive and reproduce the mtDNA sequence observed in all females on earth into the present but that may not be the case. This is because comparative estimates of nuclear DNA studies place mitochondrial eve as living in a time when the number of variants in a population was at least in the tens of thousands and some of those numbers must have been female. So, what must have happened was that somewhere along the line, there was a single male that reproduced female offspring forging a mitochondrial line and mitochondrial eve is the matron of such line. Also, the most recent common ancestor (MRCA) is a distinction that refers to the most recent common ancestor of all homo sapiens, revealed by The Human Genographic Project to have emerged only 5,000 years ago in what is referred to as the identical ancestor point (IAP) or last common ancestor (LCA). If we should only explore this point then it would not reveal as much about our early human origins as tracing separate paternal and maternal lineages has which tells us about our MRCA.
We can recount the advancements in technology that allowed for the processes that have led to the Out-of-Africa hypothesis, to appreciate the theories further. While none of the milestones involved in the journey toward the development and applications of such genetic analysis are in anyway obsolete, I could only recount some of these landmarks here as the historical advances are so great. I could start with the discovery of the transformation principle was made up of Deoxyribonucleic acid (DNA) by Avery, MacLeod and McCarthy in 1944 and the discovery of the form of DNA as a double helical structure by James Crick and Francis Watson as a revelation that eventually enabled us to understand it’s function in inheritance and other capacities but I would be recounting innumerable steps. So, I want to skip ahead for the purpose of understanding how the Human Genographic Project started. In 1967, Allan Wilson and Vincent Sarich followed ensuit to one of the founding fathers of molecular evolution, Emile Zuckerandl. Emile Zuckerandl worked with his colleague Linus Pauling at The California Institute of Technology (Caltech) to develop the idea that time or displacement variables could be determined from molecular analysis. He studied the link between hemoglobin proteins and phylogenetic distances in human populations which culminated in his work, Evolutionary Divergence and Convergence in Proteins (1964). This work initially proposed the Molecular Clock Hypothesis and offered some evidence of an evolutionary clock with hands that pointed toward patterns in genetic sequences as indicators of what would become the working basis for the Out-of-African hypothesis. (History of Recent Science and Technology. Interview with Zuckerkandl. Caltech. <http://authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/evolution/public/clock/zuckerkandl.html>) In 1967, in collaboration with Vincent Sarich, Wilson, following the work of Emile Zuckerandl, argued that molecular clocks could reveal much about the early history of the human race. In the 1980s Wilson sought to challenge the paleontologists once more, this time on the issue of the emergence of modern humans. While anthropologists favored a date of 1 million years, Wilson’s work suggested a time no later than 200,000 years ago. (Allan Wilson<http://www.answers.com/topic/allan-wilson>) Wilson studied mitochondria and postulated that all mtDNA must have been present in a common female ancestor. This led to a study of mitochondrial DNA in individuals from several continents and races where phylogenic trees were constructed, where two branches that were distinguished and linked to a common female ancestor emerging on the African continent.
The Human Genographic Project uses the results of the analysis of people and groups from around the worlds DNA sequences to trace the migratory patterns of our Human lineage out of Africa and around the world. Humans ventured out of Africa about 60,000 years ago, leaving behind genetic footprints of their journey. Mapping the appearance and frequency of genetic markers in modern populations we can see the pattern of expansion in ancient peoples. From this, our hominid lineage is illuminated and so, the “Out-of-Africa” or “Eve” hypothesis seems clear in terms of geographic origin.
The Human Genographic Project
History of Recent Science and Technology. Interview with Zuckerlandl. Caltech. <http://authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/evolution/public/clock/zuckerkandl.html
(Allan Wilson<http://www.answers.com/topic/allan-wilson>)
When did Farming Start? <http://varnam.org/blog/2004/06/when_did_farming_start/>
The Evolution of Prejudice <http://www.scientificamerican.com/article.cfm?id=evolution-of-prejudice>

Becoming Human <http://www.becominghuman.org/node/human-lineage-through-time>
The Link: < http://www.historyinternational.com/schedule>



Curious Chemistry™️: Why leaves change color in the Fall

This Fall go on a scavenger hunt and find as many colorful leaves as you can!

The changing color of autumn leaves is influenced by sunlight and temperature. You might wonder what types of trees, change which colors? It all has to do with their chemical structures. All leaves contain chlorophyll but some contain more lycopene versus carotene. We can say this is true for the colors of fruits and vegetables too. Tomato’s have lycopene while carrots have more carotene.

There’s a lot to be curious about when it comes to color chemistry.


Check out the link below and try your own experiment this season!



“The Play is The Thing” in Early Childhood Education

The Play is The Thing in Early Childhood Education

By L.F.

A Comparative Review of  Meaningful Play activities as illustrated in two Books: 

The Play is the Thing: Teachers’ Role in Children’s Play by Elizabeth Jones & Gretchen Reynolds as cross referenced with Play and Meaning in Early Childhood Education by Doris Pronin Fromberg

Development in Early Childhood

Early Childhood is an important time for learning. During early childhood, the brain is making tons of rapid connections as it develops. Foundational developmental criteria has been established by Jean Piaget and it gives us some reference about what is specifically developing at a given age (rang). I find the use of Piaget’s cognitive developmental scale and(or) Erik Erikson’s theories of child development, to gage play activities toward the mastery of each developmental criteria by facilitating relative skills through activities in the classroom, particularly useful and relevant to normative age-appropriate criteria. There is a chart on page 3 of The Play is the Thing; Teachers’ Roles in Children’s Play by Elizabeth Jones and Gretchen Reynolds, that illustrates the compliments between both mens theories on development, and I will transcribe it below for reference:

Table 1.1 “A Summary of Developmental Stages”

Age: 0-2

Primary Learning Activity: Exploration

Focus of Learning: Physical World; Direct Knowing

Modes of Representation: Body Language; Gesture; Developing Oral Language

Adult Contribution to Representation: Models Body Language and Simple Oral Language

Piaget Stages: Sensorimotor

Erikson Stages: Trust and Autonomy

Age: 3-5

Primary Learning Activity: Sociodramatic Play

Focus of Learning: Experienced World: In stories and Images

Modes of Representation: Body Language; Spontaneous Oral Language; imagining with materials; Dramatic Play

Adult Contribution to Representation: Models Oral Language; facilitated play and imagining; models simple literacy

Piaget Stages: Preoperational

Erikson Stages: Initiative

Age: 6-8

Primary Learning Activity: Investigation

Focus of Learning: Experienced World; Classified

Modes of Representation: Body Language; Spontaneous Oral Language; Structured Oral Language; imagining with materials; dramatic play; structured dramatization; developing literacy

Adult Contribution to Representation: Models and structures oral language; makes provision for play and imagining; structures dramatization (without taking over its meaning as motivated by the child(ren); models and structures literacy

Piaget Stages: Concrete Operational

Erikson Stages: Industry

Developmental Stages and the parameters that they represent, will define play activities and associative representations. Play is described in Play and Meaning in Early Childhood Education by Doris Fromberg as Voluntary, Meaningful, Symbolic, Rule-Governed, Pleasurable and Episodic; Also, play facilitates social, cognitive, emotional, language and creative development. This is why The play is the Thing; Play is the primary and multi-dynamic task that occurs on its own.

Dynamics and Theories of Play

There is a cyclical dynamic involved in development and growth and therefore learning; A process. Although, children as the pre-operational stage of development learn best through non-linear play activities, there are dynamic parallels that come into play activities that support non-linear activities with some linear elements. For example: A child uses clay or play dough and blocks in a play activity – The child uses the blocks to build solid structures and the blocks in this sense are a sort of linear AND non-linear material because they can be manipulated but not “changed.” Clay or play dough is a material that can be shaped into literally anything that the child imagines. It is also great for fine motor skill development. So clay is more of a non-linear material that can be mixed with concrete objects like blocks to create any expression of how the child interprets their environment through their play. Children revisit themes in play several times, until they have satisfied their drive for meaning and understanding of their environment. This is another reason why materials like blocks and clay are instrumental in the practice of play and revisiting themes in play functions.

In the following, there is an analysis and cross reference of several important learning theories but the main point central to all theories discussed is that learning occurs as a result of making connections between multiple concepts, with increasing magnitude, throughout development. 

Dynamic theories are most generally non-linear. These theories offer perspective toward the understanding of complex meanings in learning and play. Using this information as a prelude to the following will help to illustrate a detailed, full circle relationship between play and meaning.

Script Theory, Chaos Theory and Theory of Mind

Dynamic definitions of play such as Script Theory, Chaos Theory and Theory of Mind illustrate meaning for the professional educator and inquiring mind, that the more experiences accumulated through play in connection to the environment, the more accessional and {in relation to script theory} instinctive experiences increase and therefore the probability that there will be more combinative opportunity for cognitive connections, not only in progressive developmental patterns but in present and future abstract forms but as past memories, increases. So in other words, the more opportunities that there are to learn, the probability that more cognitive connections will be made increases both commutatively and sometimes, unpredictably. Unpredictability is defined in developmental contexts as the spontaneous nature of play activities that result in meaningful knowledge; Spontaneous is the nature of play a child engages in to actively seek understanding of their world. Although we cannot account for every child’s unique social experiences, this Spontaneity could be examined as a form of deductive learning where a pattern to a process allows for such variability within the boundaries of a system and with no exclusion of meaning. This all relates to what is called, Personal Meaning.

Script theory centers around learning as a theoretic premise used to elaborate and define cognition. 

Script theory is “episodic” and completely derived and dependent upon social experience, as diametrically opposed to being singularly semantic or linear. Script theory concerns an arched divergence and dual convergence of relayed communicative cognitive expansions that are not defined by the intent of invocations interpersonally and extra-personally. Communicative convergences that do occur within the confines of, or rhetorically ascertained product of, script theory, is distributive of cognitive experiences as they occur. In this, cognition seemingly transpires with illicit or inhibited awareness. 

Moving deeper toward a more contextual explanation, script theory is related (to cognitive development and meaningful play activities), through the autonomous “ego” of a child in relation to extra-social experiences with role supported and supportive persons. (Ever hear of Sigmund Freud? Freudian for sure!) The autonomous ego being acceptingly or even assumedly defined by the probability of multiple psychoanalytical definitions, so as to define autonomous ego as having a relationship characteristically defined, but only in part to the “symbolic” as Jacques-Marie Émile Lacan had extended this axiom to being absolute in dependence. I want to refer to his interpretation of autonomous ego as parallel to the occurrence of real events, sparing philosophical argument, I gently refer to these “real events” as reality, with the intention to parallel the symbolic relation to a theoretic argument that all ocular-sensory observations are translated into “symbolic” registration within the optic nerve of the brain, pre-cursor to comprehension and cognition. Proponent of this theory subtract the inference of there being a single absolute determinative of autonomous ego and rather suggest that there derives a complementary explanation of environmental influence, or reality versus the functional homeostatic relationship to instinctive or intrinsic drives and/or motivations. 

Here it appears, a thematic paradox toward all things understood systemically and universally in the sciences of origination, nature versus nurture, exists; They interplay and not always in a direct or expected way, but invariably, where allowance for a state of balance could only occur through shifting variables.

So for example, a child and an adult both have this sort of autonomous pattern of cognition, and much of the comprehension involved through social interaction becomes sublime. Information may be subconsciously transmitted by the role model adult and subconsciously perceived and registered by the child. As this is autonomous, we can deduct that their are biological origins in non-verbal communications stemming from the time that language had primitively evolved in connection with the mesencephalon and later became linguistic, mostly as a result of the phenomenal emergence of the frontal cortex in humans sometime thereafter, when civilizations seemed to culminate in systemized the non-linear concepts of applying a structured set of letters to variable combinations of those letters, and thus creating words and a language relationship between those words. Deductive reasoning is an important inferential “tool” to determine the axiom of an experience, in non-non-verbal communication. So theoretically, when “body language” in a readable, for example, in a parents facial expression, though no words may be exchanged, the child perceives this action. Similarly, language can be not deliberately communicated, or knowingly communicated by a parent to a child or a teacher to a child, or perhaps a friend, and I think that this relationship between the autonomous learning retention forms axial dynamics that shape memory, and paradoxically plateau into new learning 

foundations that have yet to be built on in the same capacity as the original deduction had occurred. In the Sensorimotor, Preoperational and Concrete Operational stages of cognitive development as defined by Jean Piaget and in the Trust and Autonomy, Initiative and Industry stages of development as theorized by Erik Erikson- body language and modeling are important to the focus of age appropriate learning.

 When the schematic dynamics of the parent-child social interaction unfold there is a considerable effect on influence and several deductions thereafter, made by the child. As an indication, this can truly involve inference that is both cognitive and symbolic in its origins and associative manifestations. These types of life experiences between parent and child can apply to the relationship between child and educator and I believe, child and peers.

Script theory is the unwritten indications that stem from social epochs and evolve into the synthesis of deduction and ultimate reason in a child’s manifestation of activity, which can too be axiomatic in block play or play with other representational materials like paper and crayon, clay and even books. Many points of social learning center around culture and as mentioned in The Play is the Thing, our “Puritan” culture has not often viewed play for its importance and meaning but rather as a useless activity in regard to productivity and meaning. 

Chaos Theory is closely linked with script theory but it further describes the process of connection necessary to further the actualization of script schemata. Piaget has some cognitive models based on schemata but I will get back to that; What is essential to know about Chaos Theory is that the lines drawn must connect to existing learning events or memories and without those connections, subsequent connections that derive or build upon previous experience, would not occur. Chaos patterning is relative to circumstance and described by a “labyrinth-like” sort of theory of mind that indicates neuro-connectivity as essential top patterns of life long experiences. Experiences, relative to one another can be the inverse, paradox, congruent, analogous, deductive, inference, determinative of one another; Cognition here specifically relates to how the complex connections in the brain are made.

We can look as social continuities that might be commutative to the chaos axioms derived from the general nature of social themes. When chaos theory is applied to the social-psyche, the derivation of determining principles as concrete factors in a spectrum of variability is not a conscious task but one understood by the autonomous self that (similar to script theory), determines these sort of principles, quintessentially, when a connection is built upon the collective instinctual cognitive processes. We know that the body possesses the Neurobiological ability to carry out autonomic functions such as cellular respiration; breathing, pupil dilation, etc. and so is it foreign to entertain the idea that there is another level of functioning or better yet, consciousness, in learning, that is dependent on interaction with the environment? My point here is if the body has such observed capabilities it is most certainly probable that cognition could exist in hierarchies that emphasize environmental relationship in addition to subliminal and subconscious development. This notion is proven to some regard.

This theory postulates that acquisition of information plays an integral role in all subsequent relationships. Chaos theory concerns the probability of events, by considering the randomization and combinative logistics of categorical versus linear elements and non-linear. A good example of what I call the chaos spectrum: If a point of information was a color then Chaos theory can predict what secondary, analogous and tertiary color results when primary colors are mixed together. A complex way of explaining figure-ground relationships is given by (Jones & Reynolds, The Play is the Thing P. 16) in that “Mastery of the tasks of each stage is the best possible preparation for the next.” (The Play is the Thing, p. 5) Just as colors combine and produce new shades, elements and “whole” images produced through play activities become primary and secondary and so on, in sequences, as children move toward concept mastery.

In classrooms, all who serve in roles that model behavior do best to optimize the cognitive development of a child through the supplementation of the tools both linearly and non-linearly,  to build material experiences, imagination, and symbolic experiences that function as comprehensive action potentials at anytime thereafter, to form arcs of semantic corroborations, correlations and causations.

Script theory yields to the theory of mind. The Theory of Mind is similar to the concept of the autonomous self as described by script theory. Theory of mind is a separate conceptual approach that tells us that the individual capacity to understand consciously, the processes of thought, ideas, beliefs, etc. contributes directly to the individuals ability to relate to other people. So it is basically a concept that can be implemented in learning environments in accordance with a cognitive developmental expectations. In a way, theory of mind is the conscious aspects of the unconscious aspects of script theory. However, I do not find the theory of mind in complete agreement with a child’s scaled cognitive abilities. How the mind functions autonomously in motivation of behaviors, such as the ability to pretend, is in keeping with the Theory of Mind but what is apparently not within a child’s full cognitive ability is the abstract thinking that helps them to articulate complex emotions and feelings, for example, the same way in which an adult would. Internalized perception and cognitive connections in contrast to Piaget’s developmental scale tells us that play can help children to express heavy emotional concepts and process them in ways that will later contribute to their abstract reasoning.

Why Play is Important & The Teachers Role

Play is dynamic; Play activities catalyze cognitive, social, and emotional learning. Play allows for children to take initiative, which is a developmentally appropriate behavior in early childhood. “The child who engages to take initiative and invents and represents dramatic scenarios has mastered play” (p.11) In The Play is The Thing (p. 5) and Play and Meaning in Early Childhood Education (p. 17), the reader is taught that a child will repeat play scenarios until the motivation for abstract meaning is mastered, concretely. 

Skills mastered through play are a step toward maturity and the processes involved begin during early childhood. Skill Mastery is the primary dynamic for self esteem and this is critical for healthy development, especially into adolescence (which marks the second pursuit of autonomous development). 

 “Developmentally appropriate education builds on the intrinsic motivation of the child.” (p. 9)

Let’s look at a type of play, Fantasy Play. 

Fantasy play is used to sort out daily events or even take control in imaginary situations, where power and autonomy can be expressed to a cognitively appropriate degree.

As with most things observable, their is a pattern to development and growth, and therefore learning. The dynamic pattern of a sort of cause and effect relationship that is first perceived by human beings in infancy, and further built upon in early childhood development, is also definitive of the dynamics of play in early childhood education. 

Although children at the preoperational stage of development learn best through non-linear play activities, there are teaching styles that focus primarily on linear methods that can undermine the development and education of a child by focusing on knowledge from an adult perspective. Non-linear teaching style facilitates skill development through “meaningful, imaginative and direct experiences.” 

Connections made in sociodramatic play are non-linear. (Play and Meaning in Early Childhood Education p. 4) 

For example, a child uses playdoh and blocks in a play activity; The child uses the blocks to build solid structures and the blocks in this sense are a sort of linear AND non-linear material because they can be manipulated but not “changed.” Clay or play dough is malleable and can be shaped into literally anything that the child imagines. So clay is more of a non-linear material that can be mixed with concrete objects, like blocks, to create any expression of how the child interprets their environment through their play. As discussed, children revisit themes in play several times until they have satisfied their drive for meaning and understanding of their environment through the play activity. This is another reason why materials like blocks and clay are supremely instrumental in the practice and function of play. Dynamic theories of play relate to the elements and origins of linear and non-linear play activities. In Play and Meaning in Early Childhood Education by Doris Fromberg, these dynamic theories are addressed at length. She explains how a child’s “reality speculates about how they develop and represent their understanding of the world during play.” (p. 3) Again, dynamic learning theories and systems define the meaningful constructs of play activities and therefor catalyze the relationship between cognition and child development. 

The Content of Play (p.10) relates to the child’s perception and understanding of the world around them. 

Pretend play is a type of play that is useful to the purpose of children understanding the world around them. Young children can enact scenarios from events they have observed in their environment and work through the understanding of roles by pretending to take on certain roles, such as being the mother who is feeding the baby or the fireman who puts out the fire. Pretend play helps to define the function of an activity and of a persons role within familial and later, social settings. In pretend play that occurs within a peer group and children seem to delegate roles, all their own, in adaptive engagement during the play activity. Sometimes a young child may conflict with their part in the play – and that is ok. Most of the time children engaging in pretend play work to enact scenarios in a cohesive manner (called meta-communication). You may see them working together to cook the dinner (or) drive to the bank (or) feed the dog.

These type of enactments in play are called the “daily scripts” in  The Play is the Thing. When young children are “rehearsing” their daily script they can and do use pretend play as a means of working through problems by recreating a scenario and attempting solutions to the problem that occurs. i.e. “Mommy was pouring milk and it spilt- I am the mommy and I am being careful not to spill the milk.” The Child can “represent problems and practice solving them.” 

Social play is a dynamic activity mutually agreed upon and the requirement here is engagement. The examples illustrate children inventing representations as models for mastery of purpose. 

(The play is the Thing p. 10-11) The teacher is responsible for setting up the play environment or “setting the stage” and the setting is optimized by variance, i.e. choosing to locate props in different settings such as outdoors versus indoors to enable the furtherance of imagination and exploration of the learning environment.

Notedly, when conflicts arise during play, children may use social leveraging, as a form of negotiation to problem solve the issue. However, social leveraging may occur on its own, apart from response to a conflict that arrises in play. (Fromberg, Play and Meaning in Early Childhood Education p.38) An educator may intervene to teach conflict resolution skills so that children can learn to solve problems independently. Indirect-Progress Dynamic Themes may be relied on as a means of giving “expected” and “alternative” resolutions through dialectic activity although more abstract reasoning may not be cognitively appropriate for younger children and additionally, they are practical, literal thinkers. (Fromberg, Play and Meaning in Early Childhood Education p.100) A teacher must always keep the environment safe and can complicate play if necessary in order to do so but other than this, classroom staff should not interfere during peer play. (The play is the Thing, Ch. 3)

Using materials both in a linear manner and dually, a non-linear manner when teaching is most beneficial. Books are vital as they expose children to language and inspire associations. Even the pre-literate child will derive information from the stories and images in a book. During early childhood the focus of education is on topics like letters, colors and numbers and these topics can be worked into play activities by the creative and aware educational planner so as to “speak” the language of young children. Books illustrate the “experienced world through stories and images” and they provide knowledge that helps initiate socio-dramatic play as represented in nonverbal communication/body and gestural language, imagination, and the “spontaneous language of play.” (p.3) 

Activities like writing and drawing become channels for the mastery of representation, an important skill in the mastery of play. Writing evolves “as children discover that people draw not only things but speech.” (Dyson, 1989, p. 7) Drawing is “self corrected by the child as motor skills and perceptions develop” so drawing is an earlier form of representation.” (p.8)

Children are new to the world and they are learning with everything they see, touch, smell, taste, and experience but as Jones and Reynolds discuss in The Play is the Thing, it is unreasonable to expect a young, pre-literate child, to keep interest in the practice of numbers, letters and colors all day. Unfortunately, it has proven to be common practice and focus for educators of young children to move directly to addressing such rote skills that are not necessarily appropriate toward the facilitation of meaning for a young child. 

There is a fine line between focusing on activities that seem to address teaching objectives but fail by neglecting the meaningful purpose of play. How are we meeting these objectives during instruction?

Myths and misunderstandings and especially bias’ on the part of educators leads to misconceptions of the above ideas regarding age appropriation in developmental play and behavior. This can undermine the educational process.

Young children have short attention spans. A child can play all day because it is meaningful to them, but young children may very well exhibit a short attention span when it comes to linear teaching practices that do not relate to their developmental needs. Are all educators aware that the dynamic channels of play activities are important to rote skill development later on, into the elementary years? 

One of Jones and Reynolds agendas was to observe different early education programs; The setting, social backgrounds, teacher to student ratio, and approaches to play were some of the several areas observed and considered in assessing how children are learning through play in the classroom environment and how teachers are addressing their needs. The two authors were “under-covers” in most of these settings, not necessarily revealing their intentions and agenda during observations so as to not interfere in the dynamics of the classroom during those times and throughout the research process. 

Children have specific agendas when playing and sometimes those agendas conform to the interactions of a group of peers in the classroom. In social Play activities it is important for the educator to observe the level of play, meaning what dynamic areas are evident in the play activity and in addition, to address the areas where improvements might be facilitated. In any type of attempt to facilitate a play activity through some type of involvement it is critical to not place an adult agenda on the activities that transpire and allow the child(ren) to lead as they are the ones who engaged in play to fulfill a specific need, though they do not understand this of their own play behavior. 

Reflections on Play and Meaningful Topics

So as Play moves through stages, its function for a child remains centered on understanding the world around them through concrete and mutable concepts, materials and overall self-motivated practice where initiative comes in the form of representation, peer involvement and ultimately mastery of play. In Play, the individual child, peers and teachers may take part in the script for play, on a “stage” set by the teacher. Social, emotional, cognitive and creative growth through meaningful play helps children to meet developmental criteria and non-linear teaching methods ultimately results in mastery at the level of industry and concrete operational development. It is undeniable that play is the most meaningful and the primary toward the facilitation of cognitive development and learning. Play allows for meaning and meaning originates in understanding. To understand the meaning in play, as an educator and(or) a parent is to never deny its importance and this should be the responsibility of all adults who work directly with children. There is more beyond all of this as play and meaning is continually explored and researched. I walk away from my independent studies in this course fulfilled by a knowledge that empowers me in my role as a mother and educator so that I encourage meaningful play and development. Play in not trivial and it should be promoted in the classroom setting. Children are the Future and the very best of efforts to understand what is important to their best interests and learning process should be a focus of educators, parents and role models.

The Best Online Libraries

Digital Libraries 

+ A Brief History of the Library 

Digital libraries now give us unprecedented access to literature and information like never before in our human history. Our evolution predates the written word and we can look back on the ancient libraries and appreciate just how far we’ve come. See, The History of Libraries.

It could be said that with the passage of time, books become antiquated objects; Nonetheless, books will continue to be precious archives of what has been and inspiration for all that could be.

When we read a book, we encompass it in our own unique way yet a good book is paradoxically transcendental – as it can reach the hearts and minds of the masses. Good literature stands immortally as a pillar of culture and development. The knowledge contained in a book is a Universe unto itself. When we explore the world of literature we unveil the intangible and the invaluable acquisition of such knowledge.

The proliferation of digitized archives has now made hundreds of thousands -even millions- of books obtainable in most all corridors of the World. The Digital reproduction of books has placed at our fingertips a wealth of information that would not fit within the walls of any existing architectural Library.

Check out Academic Tutors 101’s LIST of the BEST ONLINE LIBRARIES for references, maps, films and audio-books including publications and written works so rare that it would be difficult to find a physical copy.
1. The World Digital Library A multinational Resource.

2. The Universal Digital Library Search through one million books.

3. Project Gutenberg Read and Download.

4. The Harvard Library Resources from the #1 University in the US.

5. Ibiblio Books, Magazines and Scholarly Research Articles.

6. Google Books 100,000+ Books.

7. Archive A treasury of millions of free books, movies and software.

8. Open Library Search over one million eBooks by genre.

9. The US Library of Congress Digital Collections and Law Library.

10. US Libraries The Ultimate Hub for State and Federal Library Resources.

11. Digital Public Library of America Images, Texts, Videos and Sounds.

Introductory Physics Example lab: Linear and Projectile Motion

Exercise 1

Lauren F.


The Purpose of the experiments in laboratory exercise 1 is to test and verify Isaac Newton’s Second Law of Motion in relationship to the motion of an object. The exercises are designed to acquaint the experimenter with the basic presentation used in a Physics experiment and to provide experience with graphing data. Further the exercises were intended to introduce the techniques and methods of presenting a Physics experiment, analysis and preparation of tabulating data as the data relates to proportionalities, units, graphing techniques (including how to use program graphing technologies in determination of slopes in graphs and their physical significance.


The method(s) in which laboratory exercise 1, INTRODUCTION TO LABORATORY TECHNIQUES was conducted utilized proper methods of presenting a physics experiment through the analysis, interpretation and recording of data that describe variables to the the linear motion of an object (in relevance to variables of Velocity; Distance and Time). Approaches included the tabulation of data, analysis and application of proportionalities and their standard units, graphing data, and determining the slope in graphed data and its physical significance. Data tables were formatted to include 1) a title 2) an explanation of the conditions describing the experiment, and 3) assigning units and labeling columns of data.



Table of distance versus time
Car moving at a constance speed v= 5 m/s

t (sec)
s (meters)

The table above is given as an example of one way that the experiment of tracking the car’s position can be presented to other people. The graph below, illustrates the data above.

The Slope of the line in the above graph is expressed below, to illustrate the change in vertical over the change in horizontal to determine units of ratio.

Change in Vertical = s = 25 – 5 = 20m

Change in Horizontal= t= 5- 1 = 4 seconds

The Slope = 20m/ 4 sec = 5 m/s

* The slope of a linear graph is the same as the proportionality constant observed in the table or in the equation representations. The slope of a graph may have physical meaning and the units are determined by the function and variable.

Data Set 1
Table of Distance Versus Time
Car moving in a straight line v=m/s

A car is observed to be moving in a straight line. The following positions are recorded at the time shown.

t (sec)
s (meters)

The following is a position versus time graph for data set 1. It includes the “best fit straight line” through the data.

The Slope of the line in the graph, Distance Versus Time for a Moving Car (Data Set 1) is expressed below, to illustrate the change in vertical over the change in horizontal and determine units of ratio in m/s.

Change in Vertical = s = 305 – 124 = 181m

Change in Horizontal= t= 40 – 5 = 35 seconds

The Slope = 180m/ 35 sec = 5.143 m/s

Here the physical significance of the slope is that it represents the change in time as it relates proportionally to the change(s) in distance, in units that show the (function) motion of a car, at various time intervals. In that the slope in this linear graph defines the proportionality constant observed of data set 1.

In observing the Distance Versus Time for a Moving Car (Data Set 1) graph, and the other information given, the logical position of an objects, in this case the car, started at t= 0s, (x at t = 0 s.).

Data Set 2
Table of Distance (position) Versus Time
Car accelerating in a straight line motion v=m/s

A car is known to be accelerating in a straight-line motion. Position and time data are tabulated below.

t (sec)
s (meters)

The following is a graph of position versus time for data set 2. It includes the “best fit curve” through the data to represent the relationship between position and time, which is clearly not linear.

The Curve of the line in the graph, Distance Versus Time for a Moving Car (Data Set 2) can be used to find the instantaneous velocity of a car at any time. In the below exercises, the line was used to to find the instantaneous velocity of a car at t= 3,5,7, and 9 seconds. The resulting tabulation of data is as follows, recorded in the Table of Velocity Versus Time.

Data Set 2
Table of Velocity Versus Time
Car accelerating in a straight line motion s=v/t

time (sec)
Velocity (m/s)

To estimate the velocity at t I followed these steps:

t = 5.0 sec, d=9.0-4.0 and t=5.0 sec. to get 5.0/4.0 = 1.25 m/s
t= 7.0 sec, d=9.0-6.0 and t=3.0 sec. to get 3.0/6.0 = 0.5 m/s
t= 9.0 sec, d=9.0-8.0 and t=1.0 sec. to get 1.0/8.0 = 0.125 m/s

The graph of Velocity Versus time for the above data is presented below in Velocity Versus Time (Data Set 2).

In principle the line through these points, that is the “best fit” line, should be straight but in only plotting four points, I can not be sure of this. The line appears linear but to be clear I have calculated the slope of the line through the four points in the following steps:

s= 3.5-0.125 = 3.375 m/s
t= 9.0-3.0 = 6.0 sec.
Slope = 3.375/6.0 = 0.5625 = 1 m/s

The physical significance of the slope of the line above (the line in the graph Velocity Versus Time (Data Set 2) shows the motion of an object to be relatively proportional as a constant of s=vt. It illustrates the average motion of an object at any point in time, relevant to its position. The slope is physically significant.


The Purpose of the experiments in laboratory exercise 1 is to test and verify Isaac Newton’s Second Law of Motion in relationship to the motion of an object. The conclusion of the experiment met with objective or its purpose in that the methods and activities explored the physical significance of position versus time and velocity versus time. This testing and exploration of the linear motion of an object was carried out successfully through tabulation of data and graphing, both position versus time and velocity versus time, through functions and applications of Kinematics.

Position versus time data was graphed to illustrate the displacement of an object (or vector) at any given time. Displacement is the difference in position of an object at a given time (t1) versus its position at another time (t2). The data often indicated an estimate of an objects velocity or the rate of change of position. In plotting and analyzing velocity versus time graphs a slope of a line can be drawn to give an illustration of an objects acceleration at a position in time and(or) average acceleration over time. In calculating the slope of a line, the average displacement of an object can be perceived in relationship to distance over time or even the rate of displacement at a given time(s). Curved slopes show an increase or decrease in acceleration of an object, over time in velocity versus time graphs.

In addition, the exercises are were designed with the purpose of acquainting the experimenter with the basic presentation used in a Physics experiment and to provide experience with graphing data. Further the exercises were intended to introduce the techniques and methods of presenting a Physics experiment, analysis and preparation of tabulating data as the data relates to proportionality’s, units, graphing techniques (including how to use program graphing technologies such as Microsoft excel), and determination of slopes in graphs and their physical significance. In the experiments I was able to accomplish these objectives and(or) purposes with success.

Population Genetics

The Origin of Population Genetics
Throughout history, people have made observations about how characteristic traits/morphological features that are highly visible (phenotypical), are passed on from generation to generation, in living organisms. From observations made by agrarian livestock farmers to epigenesis and preformationist embryology as the concepts that arose in the 1700’s, to those who simply noticed that parents and offspring often looked alike; No one really knew that DNA existed, let alone the structures and functions of genes.

A breakthrough came during the later part of the 1800’s, when Gregor Mendel hypothesized that “discrete units of inheritance” existed in living organisms- a conclusion made based on his observations during his experiments with the pea plant. By his postulation, and by his evidence, he opened the doors to a latter of experimentation and subsequent discovery that would perpetuate on into the modern era and our present day, whereby we have come to understand a great deal of information about genetic material, more so then ever before in recorded history. (See, epigenome; proteome; microbiome)

By the middle and later part of the 1900s, evidence emerged setting apart specific units of inheritance, nucleic acid, as the molecular unit that carried heritable information. This was determined in 1944, by Avery, MacLeod and McCarty when they published the results of their work, revealing the transformation principle that is Deoxyribonucleic acid (DNA), as a material existing in most all living organisms (even “non-living” Virus’). A belief held by some involved in biological or genetic studies was that the “structure of DNA held the key to understanding its function.” (pp. 120) This is a central dogma in Bioligy: DNA > RNA> Proteins

From there, James Watson and Francis Crick set out to determine this structure with certainty. They were to make one of the most notable discoveries in the field of biology, which was that DNA is a double helical structure. As it turns out, “the assumption that a molecule’s function would be clarified more easily once it’s general structure was determined, proved to be correct.” (“Essentials of Genetics, 6th ed., Klug, Cummings, Spencer. Ch. 9, pp. 189, Pearson Prentice Hall, 2007)

The gene variations observed along chromosomes thereafter, led to the understanding that complex macromolecules synthesized the location or displacement of genes that account for not only genotypical but phenotypical traits.

Historically, evidence from Mendelian genetics was first used to argue against Darwin but nevertheless, the study of inheritance in genetics would establish a mechanism for evolution by explaining mutations and variations that Darwin’s theory emphasized. The synthesis of Darwinism and Mendelism, which marked the birth of modern population genetics, was achieved by a long and tortuous route (cf. Provine 1971)
The idea of Mendelism and Darwinism in connection, stirred up great debate and controversy amongst segregated communities of supporters. Initial arguments were central to the fact that Darwin’s theorized mechanism of evolutionary change by natural selection was not widely excepted, from the time that Origin of the Species was published in 1859 and well into the twentieth century. The dominant approach to the study of heredity in the time prior to the synthesis of population genetics was biometry. Biometry was a study that focused on the statistical analysis of the phenotypic variation found in natural populations and not units of inheritance. Biometricians believed in Darwinian gradualism and tended to focus on continuously varying traits. Mendel’s work in contrast, painted a clear picture of inheritance from a standpoint that explained phenotypical variation and characteristics as determined by discrete units of inheritance (genes) that accounted for variation of traits as heritable units. Mendelians supported the notion of discontinuous variation and single step mutations but not cumulative variations. Eventually the empirical evidence that pointed to an indisputable link between Darwin’s theory and Mendelian genetics was undeniable, being recognized by a lineage of contributory supporters that promoted the fusion of both.
A new group of geneticists, such as R.A. Fisher, J.B.S. Haldane and Sewall Wright devised not just a qualitative but a quantitative mathematical prose that examined the effects of selection and mating in evolutionary processes by combining biometrics with Mendelian genetics. Modern synthesis that connected the reasons behind variation within a population as a result of selection acting on discrete mutations as manifest by multiple-gene inheritance, leading gradually to speciation over time… Population Genetics was born. Since the advent of the field, population geneticists have made monumental contributions to the identification of alleles(gene) frequencies in populations as it relates to the evolutionary processes of natural selection, genetic drift, mutation and gene flow. The phenomena of adaptation and speciation continue to be explained by studies in the field.
Genetics and the Modern Synthesis (lecture, Sherrie Lyons)
Population Genetics; The Origin of Population Genetics ( Stanford Encyclopedia of Philosophy Copyright © 2006 by Samir Okasha. http://plato.stanford.edu/entries/population-genetics/)
iii. Population genetics (Wikipedia, http://en.wikipedia.org.wiki/Population_genetics)

Pain Genes: Genetics + Neuroscience

Pain Genes
Hyperlink: http://www.plosgenetics.org/article/info%3Adoi%2F10.1371%2Fjournal.pgen.1000086
Article Review by Lauren F.

Citation: Tom Foulkes1, John N. Wood2*
1 Department of Stem Cell Biology and Developmental Genetics, National Institute for Medical Research, London, United Kingdom, 2 Molecular Nociception Group, University College London, London, United Kingdom

Source: PLoS Genetics: A peer-reviewed open-access journal published by the Public Library of Science; http://www.plosgenetics.org/home.action

Summary: I’ve referred to a comprehensive and current research article on PLoS Genetics, for this review. PLoS Genetics is a particularly reliable source because it is a “peer-reviewed open-access journal published by the Public Library of Science” -dedicated entirely to studies in the field of Genetics.

I would like to begin by prefacing some of the important concepts discussed by the authors in context and in relationship to the topics we are studying in this Genetics course. Over time, genetic molecules have been identified and understood and this has led to progressive and explorative research in various areas concerning the structure and function of genetic material. Subsequently, fundamental discoveries have been made forming the basis for further research.

The focus of genetic research in the article Pain Genes by Tom Foulkes, and John N. Wood, centers on the source(s) of pain. Pain ..is a perception experienced by all mammals via nervous systems. The researchers explored how pain is perceived by moving beyond what has previously been established by researchers in the field of neuroscience to identify genes involved in pain signaling. Animal models, mapping of human pain mutants, twin studies and association studies of altered pain behavior were utilized to identify the molecular nature of transduction, regulatory mechanisms involved in changing neuronal activity, and the critical role of immune system cells in driving pain pathways. The results of the study offer promising prospects for the future development of neuropharmacological agents that may alleviate pain perception in humans.

The breadth of focus in this article is both extensive and comprehensive. To even begin to summarize the progression of the research, I have to begin by explaining how pain is perceived in the Central Nervous System (CNS) that is comprised of the glandular organ -the brain- and the spinal chord.

The brain is composed of various areas that are identifiable as structures that correspond to function; A central dogma of Biology is that form is indicative of functon. Pain signals are modulated through the brain via neurons that communicate through a complex matrix of pathways that connect to and through multiple structures – activated by electrochemical shifts. There are specialized sensory neurons associated with pain signaling called nociceptors. The process by where nociceptors perceive a damaging stimuli and send signals to the CNS is called nociception. It is the process that creates the perception of pain.

Pain is a useful sensation with evolutionary origins. By perceiving pain when encountering a damaging stimuli, a conditional association can be cognitively processed and allow for recall when the person encounters a like stimulus in the future thereby, the negative experience can be avoided. In fact, “the evolutionary utility of pain-evoked behavioral responses is confirmed by apparent conservation of some mechanisms in all animals with nervous systems.”

When discussing how pain is perceived it is important to understand that the CNS shares an inverse relationship with the Peripheral Nervous System (PNS). The PNS is comprised of the somatic nervous system, the autonomic nervous system (that includes the sympathetic and parasympathetic nervous system) as well as sensory systems. The somatosensory system responds to the sense of touch through the process of nociception via sensory receptors or sensory nerve endings and neural networks. These receptors exist throughout the body.
There are various sources of pain; Injury to bodily tissues and(or) inflammatory responses to such injury or disease involving a response from the immune system -can induce nociception. Now there is something unique that has been identified in this study of pain pathways. Sometimes there are mutations that come to affect the process of nociception (as observed in human and animal models) that leads to a loss of responsiveness to the trophic factor nerve growth factor (NGF) or neurotrophins, and this has resulted in the loss of nociceptive neurons and a pain-free phenotype. [1] To note, trophic factor is a growth factor that is usually manifest in mammals as a protein and(or) a steroid hormone. Neurogenesis is the process by where new neurons develop and where there is a mutation leading to a deficit in specifically relatable trophic factor, neurogenesis and thereby neurotransmission may become functionally mute or irregular. Growth factors also function as signaling molecules extracellularly; tropic factors are involved in the development and functional role of neurons.

The research in the article has not only emphasized the mechanisms involved in nociception but has delved into the human genetics of pain perception. Genes are concrete units of inheritance although they are subject to great variation from individual to individual; the identification of specific genes related to pain is nevertheless a tangibly conclusive method of validating pain targets. Variations occur in human susceptibility to pain as well as a disposition toward sensitivity. Hypersensitivity to noxious stimuli (a damaging stimuli) can cause chronic pain whereas individuals who have abnormally high pain thresholds may experience a perceptive desensitization that inhibits the instinctive response of protective behavior in the face of noxious stimuli. (See, substance P)

Noxious stimuli can excite sensory neurons and begin to modulate reciprocal signals across highly plastic neurocircuitry causing pain. A painful stimulus is detected by primary afferent neurons in the epithelial and epidermal membranes, muscle tissues and organs or viscera. When damage is endured, nociceptors are activated. Nociceptors are mostly found in the dorsal root ganglia and we know that they send signals to the thalamus as well as higher brain structures, in signaling between the PNS and CNS. This is in part possible because of the electrophysiology involved in reaching action potentials when neurotransmission occurs via electrochemical channels. This intracellular and extracellular “shifting” or active transport can be modulated by atomic structures, molecules and ions. Ions such as sodium ions, in the brain, shift during the resting potential and action potential whereby neurons rest and fire across axon terminals, and in firing insight potentiation and “strengthening” of neural pathways. Biochemically, this neurobiological process is regulated not only by neurotransmission but by a specific enzyme, a sodium-potassium pump (NAKA or Na+/K+-ATPase pump). The ratio of NAKA (that is sodium ions to potassium ions) regulates concentrations of low sodium ions and heightened levels of potassium ions during resting potential and depolarization/re-polarization of electrochemical activity in the fluctuation to chemical excitability or action potential at the axon hillock, where heightened levels of sodium ions are present (in plasma membranes) along with lower levels of potassium ions. As cellular respiration/regulation is a process that allows for (protein) enzymes to undergo a breakdown through the process of Catabolism there is an intracellular synthesis of the coenzyme Adenosine-5′-triphosphate (ATP). Both proteins and nucleic acid are categorized as macromolecules, ATP is nucleotide (a substructure of Nucleic acid’s that carry genetic information;memory). It’s functional signal transduction pertains to its role in encoded memory from the Nucleic acid structures, DNA and RNA (RNA becomes in this process, messenger RNA {mRNA} assisted by enzyme polymerase), is that it’s involved in the process of transcription to replication. The “memory” carried within the nucleus of all cells is vitally linked to the behavior of cells in cellular division and energy transfer. Moreover, this process of potentiation is guided by a particular transcription factor protein that functions in long-term potentiation (memory). This protein is called CREB (cAMP response element binding). It is important to mention that “Adenylate cyclase catalyzes the conversion of ATP to 3′,5′-cyclic AMP (cAMP).”[5] I suspect that cAMP must take a role in potentiation and perceived pain. The article makes reference to this. Supporting this notion is the knowledge that cAMP functions both as an activator and a repressor in transcription activities that can block other proteins or work with them. cAMP has a hand in genetic makeup and perhaps in this way, should we reveal and explore the expectation or prediction for cAMP to be involved in response to pain. (See, Memory Formstion in Addiction. L.F. 2010)
So, I’ve discussed how ATP is involved in energy transfer and signaling in association to neurophysiological processes and motility of NAKA, and thereby nociception. I should further mention that the process of Neurotransmission, or in this specific case, nociception, occurs post-noxious stimulation, wherein there is enough stimulation to cause a switch from resting potential to action potential. As a neuron “fires” from the vesicles within the neuronal soma, into the axon hillock, across the presynaptic space, across the axon terminals into the post-synaptic space, where it stimulates the dendritic branches of a second neuron; the process creates a henical chain reaction. The function of neurotransmission and the activity of such stimulation is not only governed by electrical nervous impulses, but by the role of the neurotransmitter itself. The article illuminates incidences where changes in the way in which chemical channels have been mutated have been observed in correlation to how pain is perceived.
Three types of nociceptors have been identified by distinctive expression profiles revealing functional distinctions.[62] There are peptidergic nociceptors that are Nerve growth factor (NGF)-responsive; There are nonpeptidergic nociceptors that are Glial cell-derived neurotrophic factor (GDNF)-responsive; and there are unmyelinated C-fibres and myelinated Aδ-fibres nociceptors that are NGF-responsive. Generally, all of these nociceptor categories respond to noxious stimuli by transduction of electrical impulses with exception of specific receptors that respond to specific types of stimuli and may also be affected in form and(or) functional role due to other factors such as heredity and mutation.

In this, the article identifies several categories where the genetic basis of pain is being explored. Cold pain and heat pain, altered pain states, mammalian genetics and the genetics of pain in man, gender differences in pain perception, heritable conditions leading to pain, genetic thresholds and pain related Single Nucleotide Polymorphisms (SNP’s), and genetic polymorphisms are extensively explored. While some genes are known to be involved with pain systems there remains some uncertainty involved with pain perception as it corresponds to processing of signals through a complex matrix of structures. However, Scientists have determined that hypersensitivity reactions in transduction and action potentiation by nociceptors across normatively action reducing potassium channels can be altered by inflammatory mediators, manifest as damaged neurons and leading to hyperalgesia and neuropathic allodynia and the ongoing activation of pain pathways due to potentiation of Ca2+ channels located on the presynaptic membrane. TRPV1 has been identified as having a role in alteration of inflammatory pain thresholds.
Switching gears a bit, we can talk about the modalities of pain and point out gene involvement. TRPM8 and TRPA1 have been proposed to have a role in the transduction of noxious cold stimuli in that they may cause the inhibition of chemical channels; specifically reduced electrogenic pump activity and(or) inhibition of K+ currents. SCN10A may activate inflammatory mediators in noxious cold stimuli.
Transient receptor potential cation channel subfamily V member 4 is a protein that in humans is encoded by the TRPV4 gene. [90][91][92] TRPV4 is suspected of having a role in mechanosensation related to noxious stimuli as a result of observing the behavioral responsiveness of animal models (mice) where noxious mechanical stimuli were introduced. (Poor mice!)
I’ve mentioned above how TRPM8 and TRPA1 may be involved in the inhibition of K+ (potassium) currents. This is critical to function as sodium and potassium ions are the medium for electrochemical modulation of nociception; Regulation of sodium channel expression, both transcriptionally and post-transcriptionally, is an important element in determining neuronal excitability. [12],[13] Not surprisingly, genes encode these channels. Three genes that encode sodium channels have been selectively expressed in sensory neurons; SCN11A plays a role in the establishment of pain thresholds while SCN9A has some involvement with peripheral pain perception and the loss of function of SCN9A correlated to observed deficits in mechanical and inflammatory pain perception. In other cases, functional human mutation of SCN9A corresponds to decreased thresholds of activation and is linked to the chronic inflammatory condition, erythermalgia.
Identification of genes involved in the perception of heat noxious stimuli are still being researched and several plausible candidates for the involvement with pain have been identified.
Previously, I pointed out how cAMP works with ATP to create cellular memory. A pattern where mutually exclusive exon usage was observed in mammalian models of embryonic or adult spliced form where different exons that code for the S3 and S4 segments in domain one on the rat channel appeared comparative to patterning in SCN9A, where some differences in biophysical properties and the effects of cAMP on splice variants had been described. [17]
Pain linked single-nucleotide polymorphisms (SNP’s) have been found in the gene COMT that encodes for catechol-O-methyltransferase, and mediates the inactivation of vital catecholamine neurohormone-transmitters such as dopamine, adrenaline and noradrenaline. I recall the article discussing that the thalamus is involved in pain perception. This is interesting and relevant when we consider that there are eight dopaminergic neural pathways in the brain, where dopamine neurotransmission occurs. One such pathway is the mesolimbic pathway. Between the Mesolimbic pathway and another dopaminergic pathway, called the mesocortical pathway, dopamine transport occurs. The Mesolimbic pathway shares a connection to the limbic system and the neural structures of the limbic system is the Thalamus. For me, this is an illustration of a prospective pain pathway where in some cases the inactivation of COMT enzymatic activity that is reduced has been demonstrated to result in increased pain sensitivity and temporal summation of pain. Diatchenko et al. [26]
In summation, what researchers have found is that many of the variations and specific mutations in specific genomic and genetic alleles, loci and along chromosomes, are connected to sources of pain that deduce to altered pain states;
The natural variations in propensity to pain result from a combination of environmental and genetic influences on pain sensing-systems… in that it appears plausible that quantitative differences in pain sensitivity may also have a genetic basis. [7],[8]
A few unique studies have helped to pinpoint some distinctions that may account for some characteristics of variation. Gender differences have been observed and may be due in part to differences in gene loci located along sex-determining chromosomes. I suspect that the prospective genes located along the X and(or) Y chromosomes are perhaps Sex-linked and(or) the disposition of a male or female toward certain pain conditions may be influenced by epigenetic and/or proteomic effects where the incidence of pain-specific conditions in females is limited and where y-linked pain disorders come to effect the males and not females. Gonadal factors may also play a role in gender related disposition to pain perceptions.
Genes are discrete units of inheritance so it is important to explore how transmissibility may be occurring when considering hereditary factors. The most conclusive evidence of heritable factors in pain perception have come from sensory tests of twins. Many heritable conditions exist where pain sensitivity syndromes result in cellular apoptosis or cell death. In observing how the pain-sensing systems of the afflicted individuals function thereafter, there has been light shed on various involvement of nociception. Pain thresholds have been observed in laboratory mice-models, to be heritable between 30% to 76%. [23]-[25] In addition, quantitative trait loci (OTL) maps have been used to observe variation for some characteristic traits involved in pain sensitivity.

My Opinion: The breadth of research accomplished and documented in the article is monumental and pioneering. My previous knowledge of how pain signals are modulated in the CNS was limited to an understanding exclusive of gene involvement. I’ve never thought about how chemical pathways are affected by genetic and genomic sequences that link to pain. The identification of signaling molecules as related to QTL and specific alleles will undoubtedly lead to the ability to synthesized more targeted neuropharmacological agents. I would like to see how related studies build upon what is established thus far, and reveal insights about fibromyalgia (a disorder where the source of pain is limitedly understood) insomuch as the identification of genes involved in the pain associated to the condition remain unknown. (I suspect a pathogenic genetic integration and/or substance P involvement)

As past practice has demonstrated, identifying the structure of genetic material progresses to the identification of specific functions that in turn allows for the development of effective pharmaceutical products aimed at alleviation of diseases and(or) symptoms. (This is very good news as pain is a part of the human experience- and many have come to suffer from chronic and dysfunctional pain.)

New Questions: I’ve learned about how cAMP is involved in cellular memory in addiction, as well as in pain signaling. Both circumstances stand in comparison to substantiate the idea that repeated stimulation leads to neuron-excitability, anticipatory responses and associations as well as potentiation. I suspect that where the absence of stimuli can come to exist, (even where facilitated by inhibitory pharmacological products) for a long enough period of time, potentiation sites will decrease due to neuro-atrophy. If so, would this lead to the reactivation of neurons that function within a normative range of specification given the type of neuron and in the case of pain and not addiction, where nociception occurs, would subsequent neurogenesis occur? If so, would those neurons come to functionally modulate pain-signaling in the presence of future stimuli within normative perceptive thresholds where genes have not been involved in the inhibited production of pain-sensing molecules?

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The Origin of Population Genetics

The Origin of Population Genetics

Throughout history, people have made observations about how characteristic traits/morphological features that are highly visible (phenotypical), are passed on from generation to generation, in living organisms. From observations made by agrarian livestock farmers to epigenesis and preformationist embryology as the concepts that arose in the 1700’s, to those who simply noticed that parents and offspring often looked alike; No one really knew that DNA existed, let alone the structures and functions genes.

A breakthrough came during the later part of the 1800’s, when Gregor Mendel hypothesized that discrete units of inheritance existed in living organisms- a conclusion made based on his observations during his experiments with the pea plant. By his postulation, and by his evidence, he opened the doors to a latter of experimentation and subsequent discovery that would perpetuate on into the modern era and our present day, whereby we have come to understand a great deal of information about genetic material, more so then ever before in recorded history. (See, epigenome
; proteome; microbiome)

By the middle and later part of the 1900s, evidence emerged setting apart specific units of inheritance, nucleic acid, as the molecular unit that carried heritable information. This was determined in 1944, by Avery, MacLeod and McCarty when they published the results of their work, revealing the transformation principle that is Deoxyribonucleic acid (DNA), as a material existing in most all living organisms. A belief held by some involved in biological or genetic studies was that the “structure of DNA held the key to understanding its function.” (pp. 120) This is a central dogma in Bioligy: DNA > RNA> Proteins

From there, James Watson and Francis Crick set out to determine this structure with certainty. They were to make one of the most notable discoveries in the field of biology, which was that DNA is a double helical structure. As it turns out, “the assumption that a molecule’s function would be clarified more easily once it’s general structure was determined, proved to be correct.” (“Essentials of Genetics, 6th ed., Klug, Cummings, Spencer. Ch. 9, pp. 189, Pearson Prentice Hall, 2007)

The gene variations observed along chromosomes thereafter, led to the understanding that complex macromolecules synthesized the location or displacement of genes that account for not only genotypical but phenotypical traits.

Historically, evidence from Mendelian genetics was first used to argue against Darwin but nevertheless, the study of inheritance in genetics would establish a mechanism for evolution by explaining mutations and variations that Darwin’s theory emphasized. The synthesis of Darwinism and Mendelism, which marked the birth of modern population genetics, was achieved by a long and tortuous route (cf. Provine 1971)
The idea of Mendelism and Darwinism in connection, stirred up great debate and controversy amongst segregated communities of supporters. Initial arguments were central to the fact that Darwin’s theorized mechanism of evolutionary change by natural selection was not widely excepted, from the time that Origin of the Species was published in 1859 and well into the twentieth century. The dominant approach to the study of heredity in the time prior to the synthesis of population genetics was biometry. Biometry was a study that focused on the statistical analysis of the phenotypic variation found in natural populations and not units of inheritance. Biometricians believed in Darwinian gradualism and tended to focus on continuously varying traits. Mendel’s work in contrast, painted a clear picture of inheritance from a standpoint that explained phenotypical variation and characteristics as determined by discrete units of inheritance (genes) that accounted for variation of traits as heritable units. Mendelians supported the notion of discontinuous variation and single step mutations but not cumulative variations. Eventually the empirical evidence that pointed to an indisputable link between Darwin’s theory and Mendelian genetics was undeniable, being recognized by a lineage of contributory supporters that promoted the fusion of both.
A new group of geneticists, such as R.A. Fisher, J.B.S. Haldane and Sewall Wright devised not just a qualitative but a quantitative mathematical prose that examined the effects of selection and mating in evolutionary processes by combining biometrics with Mendelian genetics. Modern synthesis that connected the reasons behind variation within a population as a result of selection acting on discrete mutations as manifest by multiple-gene inheritance, leading gradually to speciation over time… Population Genetics was born. Since the advent of the field, population geneticists have made monumental contributions to the identification of alleles(gene) frequencies in populations as it relates to the evolutionary processes of natural selection, genetic drift, mutation and gene flow. The phenomena of adaptation and speciation continue to be explained by studies in the field.
Genetics and the Modern Synthesis (lecture, Sherrie Lyons)
Population Genetics; The Origin of Population Genetics ( Stanford Encyclopedia of Philosophy Copyright © 2006 by Samir Okasha. http://plato.stanford.edu/entries/population-genetics/)

The History of Mathematics: Fractions


Non-Euclidean Geometry
“The Story of Zero”
History of Non-Euclidean Geometry

The advantages of writing in fractions:
When writing fractions in decimal form, a part of a whole can be easily multiplied with other fractions both simple and more complex. Fractional values represented by decimal form can be converted into other numbers more simply by arithmetic. The advent of fractions being converted into decimal form made calculations using π and algebraic mathematic calculations, more simple- It allowed for the relationship between two axis points to be represented. Fractions and decimals corresponded to whole numbers and thus ratios could be measured in quantity and space. Decimals bridge geometry, coordinate geometry and algebra. Simpler numbers, negative numbers and parts of a number that progress from one whole to the next, in algorithms, were plotted with the use of decimal form numbers. Decimals also helped in complex conversions.

The Disadvantages of writing in Fractions: Two disadvantages of writing fractions in decimal form exist in the conversion methods that corresponded to whole numbers because of cultural method- some ancient cultures used fractions written as whole numbers, with one integer over the other, or in ratio representation. Some cultures did not represent fractional portions in this way. Hindi mathematicians used fractional representations that were inversed and then multiplication was used for dividing fractions. This method was not as useful for converting fractions into decimal form. Unit fractions are fractions that use parts of a whole- some cultures did not have a procedure for working with these kinds of proportional values. Often, there were no symbols used to show the arithmetic operation which caused confusion in the representation and written calculation of a particular fraction. In Babylonian mathematics, a fractional representation could have appeared to be a different numeric product and process then what it actually was.

See, The History of Negative Numbers

Factoring: Factoring Polynomials using GCF, Grouping and Difference of Two Squares (DOTS)

Factoring Polynomials using GCF, Grouping and Difference of Two Squares (DOTS)

By Academic Tutors 101

Factoring is a key skill that will be used as a step toward solving more complex problems as you progress in your Math studies. Factoring allows us to determine the parts of a number that multiply to some total product. It is a way of breaking apart numbers (decomposition of a number) by a Greatest Common Factor {GCF}. The GCF is the largest number, common to one or more factors. So, what is a Factor then? A factor can be a number, a quantity or an algebraic expression. However, when this definition is taught, it still seems arbitrary to me. This is partly because not all Math is easy to explain using plain language, for if it was, we wouldn’t use numerals. For the purpose of succeeding under the current academic standards, we have to form the connection between describing a mathematical problem or procedure without just enumerating it. That being said, its important to know that we are going to factor problems to break them down AND put them back together. So depending on which side of the equation we are working on, we will sometimes consider a factor as quantities, that when multiplied together, produce a given number or expression BUT it may also be described inversely, as an algebraic expression that is approximately divisible by an integer or GCF.
Greatest Common Factor
The greatest common factor is the number that can evenly divide two numbers. To determine the GCF of larger numbers use the Prime Factorization Method.

A polynomial (from Greek Poly- “many”) See, “History of the Word, Polynomial” is a mathematical expression with more than one term (monomial), two terms (binomial), or three terms (trinomial), but many terms. The expression may contain coefficients and variables that can be manipulated using the operations of addition, subtraction, multiplication and (non-negative) exponents. A quadratic function has four terms but is an equation in the second degree. A quadratic function can be solved using a special formula, the Quadratic Formula. Let’s look at how this formula is derived:

When we see equations in this form, we can plug them into the formula.

Note that the graph of this function will be parabolic and have two real roots according to the Complex Conjugate Root Theorem.

Methods for Factoring
Difference of Two Squares (DOTS)

If you have a four term polynomial (a quadratic equation) with no GCF, you can factor the equation by grouping.


Original notes by: Lauren F.
Typed up by: Katelyn C



A permutation is a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.

*NOTE, it is different from a combination in that order matters, unlike a combination. Given the names Charli, Rachael, and Patrick, it doesn’t matter that I order them like Patrick, Charli, and Rachael in a combination, because it’s still just the three people. But, in a permutation, their order does matter, so they MUST remain in the original order of Charli, Rachael, and Patrick.

EX: How many words can be formed by using all the letters of the word DRAUGHT so that (a) vowels always come together and (b) vowels are never together.

There are two vowels, we treat them as 1.
Solution: 6!*2! = 1,440 answer
6(5)(4)(3)(2)(1)= 720
X 2(1) = 2
720 X 2 = 1,440

(B) Total possibilities:
7(6)(5)(4)(3)(2)(1) = 5,040
Number of cases when vowels are not together=
5,040 – 1,440 = 3,600 answers

*For more practice, visit:
Permutations Better Explained