Lecture 0. Prehistory before civilization Before we ask when did mathematics begin, we may ask the following questions: When did our ancestors begin to have geometric ideas (e.g. painting in caves)? When did our ancestors begin to count (e.g. making cut on bones for counting purpose)? Going back further, when did our ancestors begin to store information outside their brains (e.g. making things more complex than they needed for survive)? To answer these questions, let us briefly review some prehistory before civilization, including some discoveries in recent years. 1 6 million years ago Separated from apes, a fossil skull called Toumai (6 million years ago) 2, the earliest known human ancestor, was discovered in the Sahara desert in 2001. Toumai, who was almost certainly male, had a brain about the size of a modem chimpanzee 1 The material of this section is took form: NOVA: Becoming Human Unearthing Our Earliest Ancestors DVD, item No: NOVA 6192, PBS, 2009. 2 Toumai is a nickname, which means hope of life. 1
and could have walked on two legs in an upright posture, according to analysis of the point at which his spine joined his skull. It is in the Afar, north-eastern Ethiopia. It is a part of the Great Rift Valley, a deep cut in the earth where geologic forces are ripping Africa apart. Many millions of years ago, Africa was a wet, tropical environment covered with rainforest. But then, Africa started to gradually dry out. The rainforest began to shrink. 3.3 million years ago A three years old baby, Selam s fossil was found. 3 The nickname Selam means peace. Selam lived more than 100,000 years before the famous fossil Lucy so that he is called Lucy s child. One key difference between humans and apes is the length of childhood. By age three, a chimpanzee would have over 90 percent of the brain formed; but Selams brain was only 75 percent of its adult size, suggesting it was growing up slower. 3 This fossil was discovered in 2000. It took five years to extract most of it from the sandstone in which it was encased, and it took several more years to extract all of it. The report on the fossil was published in the Nature, 21 September 2006, p. 296-301, and p. 332-336. 2
3 million years ago At the time of 3 million years ago, the Rift Valley was patchwork of grassy plains, scattered woodlands, lakes and rivers. The estimate date for the divergence between gorilla lice and human lice is roughly 3,000,000 years ago, based on DNA of lice. 2.5 million years ago The first stone tools appeared in 2.5 million years ago. 4 There are evidence that the stone tools were being used to break the long bones in order to get to the marrow inside the long bones. There were clear cut marks on the bones of turtles, crocodiles, big antelopes, little antelopes, and hippos. So we know that meat had become a new important part of the diet of Homo habilis. 2 million years ago About 2 million years ago in the Great Rift Valley of East Africa, these spectacular plains and canyons witnessed a mysterious event: the birth of the first ancestor we can really call human. They were world travellers, toolmakers, hunters, tampers of fire, and creators of the first human societies. The first fossil to be called Homo habilis, discovered in Tanzania, East Africa, between 1962 and 1964, included 21 bones of the hand and was nicknamed handy man. It doubles of brain volume: 400 ccs in Australopithecines to, say, 700-800 ccs in Homo habilis. Scientists now accept that as soon as Homo erectus appeared on the grassland of Africa, they started to leave. They are out of Africa right away. 4 Australopithecus ( 2.9 to 3.9 millions ago), a genus of hominids that are now extinct, was around for a million years and did not make stone tools. A new paper published in the journal Nature on August 11, 2010 may force a revision in scientists understanding of early hominins and tool use. Archaeologist Shannon McPherron s fossil finds in Dikika, Ethiopia suggest that tool use was a far older skill than anyone previously realized. The layer the fossils were found in was dated to 3.39 million years old, more than 800,000 years older than Homo habilis and into the range of Australopithecus afarensis. 3
What would push such primitive creatures out of Africa? A key driving force behind migration was probably a climate shift which spread grasslands from Africa into Asia, and with the grasses went the game animals. Animals are going to be moving out of Africa, and the hominids will be just keeping pace with those animals. Our ancestor didn t know they were leaving Africa. They just followed the animals. Ever since, Africa has been the engine of our evolution, pumping out wave after wave of ancient humans, who populated Europe and Asia. Setting in far-off places, they developed in their own special ways. 1.8 million years ago Primitive Homo erectus migrated from Africa to the Caucasus, a geopolitical region at the border of Europe and Asia. 1.5 million years ago Turkana Boy, about 8 years old, was discovered in 1984 near Lake Turkana in Kenya. His brain was 900 cubic centimeters, smaller than ours but more than twice as large as a chimps. What that implies is that the growth of the Turkana Boy resembled more closely that of chimpanzees today. To be five-foot-three at age eight, Turkana Boy must have grown up very fast, at a rate closer to chimps than us. A chimpanzee s childhood is short. It is sexually mature at about seven. Human childhood is longer. We reach puberty at about 12. There is a good solid evidence for the ability of language. Mostly hairless, like us. Hairless bodies allow air to circulate freely on our skin and cool us down as sweat evaporates. So they could run long distances to chase animals and this was the key to their success. 4
On the African savanna, full of predators who hunt by night. Turkana boy and his people couldn t have survived without fire. And only cooking, which made food more soft and digestible can explain why Homo erectus smaller teeth and a much smaller gut. As our ancestors reaped the benefits of cooking, something else happened too. We became more social. We were down to a common place, the fireplace. We learned to share and communicate sitting around fires and waiting for food to cook. 700,000 years ago A wave took Homo erectus all the way to China. Another wave left Africa heading for Europe, which was the species that would one day give rise to the Neanderthals. 5 By a new study 6, scientists reconstructed the Neanderthal genetic code and compared it to modern humans from across the globe. They found that there was up to a 4% match with humans everywhere except those from Africa. The theory is that our human ancestors migrating out of Africa about 70,000 years ago had some amorous encounters with Neanderthals somewhere in the Middle East. 500,000 years ago Skeletons of the ancestors called Homo heidelbergensis, one of the earliest to populate Europe were discovered at Atapuerca in northern Spain. 190,000 years ago Using DNA to trace the evolutionary split between head and body lice, researchers 7 conclude that body lice first came on the scene approximately 190,000 years ago. And that shift, the scientists propose, followed soon after people first began wearing clothing. 140,000 years ago Homo sapiens teetered on the brink of extinction. We re 99.9% identical in D.N.A. Look at other apes, like chimps or gorillas or orangutans, they have between four and ten times as much diversity at the D.N.A. level. The lack of diversity in human D.N.A. is a clue to a crisis that may have wiped out whole populations. The genetic record shows us that we are all descended from a small population of approximately 600 breeding individuals in 140,000 years ago. 5 The Neanderthal is a small valley in the Germany. In 1856, the area became famous for the discovery of Neanderthal 1, the first specimen of Homo neanderthalensis to be found. Then such specimen is called Neandertal. Neanderthals went to extinction in 30,000 years ago. 6 The Neanderthal Lives on in Many Humans, by John Berman and Michael Murray, May 7, 2010, abcnews.com. 7 cf. Lice hang ancient date on first clothes Genetic analysis puts origin at 190,000 years ago, Bruce Bower, Vol.177 (2010)10, ScienceNews. Armed with little direct evidence, scientists had previously estimated that clothing originated anywhere from around 1 million to 40,000 years ago. 5
Ancient climate data also shows that around the time, most of tropical Africa became uninhabitable. Our ancestors were forced to seek refuge on coasts and highlands. It looks like four to six potential locations in Africa that would still be supportive of hunter-gatherer populations. At Pinnacle Point, South Africa, caves has been found used by early Homo sapiens ancestors during the megadrought period. They cooked shellfish collected from sea coast. If they went out to collect shellfish at the wrong time, they re dead. They have to be able to time their access to the coastline so that they re here when the tides are right to collect those shellfish. Also the people of Pinnacle Point were not just harvesting shellfish. They were also hunting on the plains behind the coast and gathering berries and roots. Their way of life reflected a new versatility. The systematic use of coastal resources does suggest a cognitive complexity. 100,000 years ago In Sclandina cave, an 8 years old Neadnderthal child s fossil was founded. Neanderthals were almost exclusively meat eaters. They did on thing: hunting large game, and they just kept on doing this for hundreds of thousands of years. Neanderthals were long-lived. As a species, they lasted for almost 400,000 years. Despite their mental limitations, the Scalndina boy and his people may have been able to speak, by DNA research. 71,000-75,000 years ago Technology of making more variety of tools at the time. And we begin to see people treating stone tools as symbols. They re making them more complex than they need to be to accomplish a particular cutting task. So, at this point, stone tools are no longer just tools for cutting things, and they re instruments of carrying social information about their owners. The first evidence of decorative arts, made from a naturally occurring mineral called red ochre, has been found at Blombos, another cave along the South African coast discovered 6
in 2002. At Blombos, it has also found shells with holes drilled in them, believed to have been used for necklaces. Our ancestors were now wearing ornaments and probably painting their bodies, as well. It is really important: for the first time ever, we have evidence that people can store information outside of the human brain. 50,000 years ago There were probably four different kinds of humans living at the same time. Yet today, we are a species alone. Humans have a very intensive way of using the environment. Humans move into the Middle East, the Homo erectus goes extinct. Humans move into Europe, the Neanderthals go extinct. 30,000-40,000 years ago Neanderthals lived in Europe. They were the most advanced humans on Earth, until Humans arrived, and then they vanished. Neanderthal technology was limited, and their energy needs were huge. But with slimmer, taller bodies, modern humans had lower energy demands and an ever-improving toolkit. They also developed yet another breakthrough technology: projectile weapons, throwing spears. Throwing spears allowed our ancestors to go after a wider range of game with less risk to themselves. 40,000 years ago The earliest of work of art, the Venus figurine known as the Venus of Hohle Fels, dates to some 40,000 years ago. 30,000 years ago The earliest known European cave paintings date to Aurignacian, some 32,000 years ago. 8 8 http://en.wikipedia.org/wiki: Cave painting. 7
The paintings in caves by the ice age hunters have big significant: it shows that our ancestors remarkable understanding of form; mathematically speaking, they reveal understanding of representing objects in the three dimensional space in terms of 2 dimensional pictures. 22,000 years ago The earliest dated occurrences of representation of numbers on a fossilized bone was discovered at Ishango in Zaire, near the headwaters of the Nile river, and carbon-dated to some time around 20,000 B.C.E. 10,000 years ago Agriculture began. When major climate change took place after the last ice age (11,000 BC), much of the earth became subject to long dry seasons. These conditions favoured annual plants which die off in the long dry season, leaving a dormant seed or tuber. These plants tended to put more energy into producing seeds than into woody growth. An abundance of readily storable wild grains and pulses enabled hunter-gatherers in some areas to form the first settled villages at this time. Although localised climate change is the favoured explanation for the origins of agriculture in the Levant 9, the fact that farming was invented at least three times elsewhere, suggests that social reasons may have been instrumental. 10 9 A large area in Western Asia, including the today s countries of Lebanon, Palestine, Syria, Jordan, and occasionally Cyprus, Sinai, and part of Iraq. 10 http://en.wikipedia.org/wiki: History of agriculture. 8