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 theirbrains (e.g. making things more complex than they needed for survive) ?

To answer these questions, let us briefly review some prehistory before civilization, in-cluding some discoveries in recent years. 1

• 6 million years ago Separated from apes, a fossil skull called Toumai (6 million yearsago)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

1The material of this section is took form: NOVA: Becoming Human Unearthing Our Earliest AncestorsDVD, item No: NOVA 6192, PBS, 2009.

2Toumai is a nickname, which means “hope of life.”

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and could have walked on two legs in an upright posture, according to analysis of the pointat which his spine joined his skull.

It is in the Afar, north-eastern Ethiopia. It is a part of the Great Rift Valley, a deepcut 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 togradually dry out. The rainforest began to shrink.

• 3.3 million years ago A three years old baby, Selam’s fossil was found. 3 The nicknameSelam means “ peace.” Selam lived more than 100,000 years before the famous fossil Lucyso that he is called Lucy’s child.

One key difference between humans and apes is the length of childhood. By age three, achimpanzee would have over 90 percent of the brain formed; but Selams brain was only 75percent of its adult size, suggesting it was growing up slower.

3This fossil was discovered in 2000. It took five years to extract most of it from the sandstone in whichit was encased, and it took several more years to extract all of it. The report on the fossil was published inthe Nature, 21 September 2006, p. 296-301, and p. 332-336.

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• 3 million years ago At the time of 3 million years ago, the Rift Valley was patchworkof grassy plains, scattered woodlands, lakes and rivers. The estimate date for the divergencebetween 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 Thereare evidence that the stone tools were being used to break the long bones in order to getto 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 anew important part of the diet of Homo habilis.

• 2 million years ago About 2 million years ago in the Great Rift Valley of EastAfrica, these spectacular plains and canyons witnessed a mysterious event: the birth of thefirst 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, between1962 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 Homohabilis.

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.

4Australopithecus ( 2.9 to 3.9 millions ago), a genus of hominids that are now extinct, was around for amillion 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 fossilswere found in was dated to 3.39 million years old, more than 800,000 years older than Homo habilis andinto the range of Australopithecus afarensis.

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What would push such primitive creatures out of Africa? A key driving force behindmigration was probably a climate shift which spread grasslands from Africa into Asia, andwith the grasses went the game animals. Animals are going to be moving out of Africa, andthe hominids will be just keeping pace with those animals. Our ancestor didn’t know theywere leaving Africa. They just followed the animals. Ever since, Africa has been the engineof our evolution, pumping out wave after wave of ancient humans, who populated Europeand 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 nearLake Turkana in Kenya. His brain was 900 cubic centimeters, smaller than ours but morethan twice as large as a chimps.

What that implies is that the growth of the Turkana Boy resembled more closely that ofchimpanzees today.

To be five-foot-three at age eight, Turkana Boy must have grown up very fast, at a ratecloser to chimps than us.

A chimpanzee’s childhood is short. It is sexually mature at about seven. Human child-hood 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 coolus down as sweat evaporates. So they could run long distances to chase animals and thiswas the key to their success.

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On the African savanna, full of predators who hunt by night. Turkana boy and his peoplecouldn’t have survived without fire. And only cooking , which made food more soft anddigestible can explain why Homo erectus smaller teeth and a much smaller gut.

As our ancestors reaped the benefits of cooking, something else happened too. Webecame more social. We were down to a common place, the fireplace. We learned to shareand 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 waveleft Africa heading for Europe, which was the species that would one day give rise to theNeanderthals. 5

By a new study6, scientists reconstructed the Neanderthal genetic code and comparedit to modern humans from across the globe. They found that there was up to a 4% matchwith humans everywhere except those from Africa. The theory is that our human ances-tors migrating out of Africa about 70,000 years ago had some amorous encounters withNeanderthals somewhere in the Middle East.

• 500,000 years ago Skeletons of the ancestors called Homo heidelbergensis, one of theearliest to populate Europe were discovered at Atapuerca in northern Spain.

• 190,000 years ago Using DNA to trace the evolutionary split between head and bodylice, researchers 7 conclude that body lice first came on the scene approximately 190,000years ago. And that shift, the scientists propose, followed soon after people first beganwearing 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 ofdiversity in human D.N.A. is a clue to a crisis that may have wiped out whole popula-tions. The genetic record shows us that we are all descended from a small population ofapproximately 600 breeding individuals in 140,000 years ago.

5The Neanderthal is a small valley in the Germany. In 1856, the area became famous for the discoveryof Neanderthal 1, the first specimen of Homo neanderthalensis to be found. Then such specimen is calledNeandertal. Neanderthals went to extinction in 30,000 years ago.

6The Neanderthal Lives on in Many Humans, by John Berman and Michael Murray, May 7, 2010,abcnews.com.

7cf. 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 thatclothing originated anywhere from around 1 million to 40,000 years ago.

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Ancient climate data also shows that around the time, most of tropical Africa becameuninhabitable.

Our ancestors were forced to seek refuge on coasts and highlands. It looks like four to sixpotential 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 ableto time their access to the coastline so that they’re here when the tides are right to collectthose shellfish. Also the people of Pinnacle Point were not just harvesting shellfish. Theywere also hunting on the plains behind the coast and gathering berries and roots. Theirway of life reflected a new versatility. The systematic use of coastal resources does suggesta cognitive complexity.

• 100,000 years ago In Sclandina cave, an 8 years old Neadnderthal child’s fossil wasfounded. Neanderthals were almost exclusively meat eaters. They did on thing: huntinglarge game, and they just kept on doing this for hundreds of thousands of years. Neanderthalswere long-lived. As a species, they lasted for almost 400,000 years. Despite their mentallimitations, 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 morecomplex 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 carryingsocial information about their owners.

The first evidence of decorative arts, made from a naturally occurring mineral called redochre, has been found at Blombos, another cave along the South African coast discovered

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in 2002. At Blombos, it has also found shells with holes drilled in them, believed to havebeen used for necklaces. Our ancestors were now wearing ornaments and probably paintingtheir bodies, as well. It is really important: for the first time ever, we have evidencethat people can store information outside of the human brain.

• 50,000 years ago There were probably four different kinds of humans living at thesame time. Yet today, we are a species alone.

Humans have a very intensive way of using the environment. Humans move into theMiddle East, the Homo erectus goes extinct. Humans move into Europe, the Neanderthalsgo extinct.

• 30,000 - 40,000 years ago Neanderthals lived in Europe. They were the most advancedhumans on Earth, until Humans arrived, and then they vanished.

Neanderthal technology was limited, and their energy needs were huge. But with slim-mer, taller bodies, modern humans had lower energy demands and an ever-improving tool-kit. They also developed yet another breakthrough technology: projectile weapons, throwingspears. Throwing spears allowed our ancestors to go after a wider range of game with lessrisk to themselves.

• 40,000 years ago The earliest of work of art, the Venus figurine known as the Venusof 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

8http://en.wikipedia.org/wiki: Cave painting.

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The paintings in caves by the ice age hunters have big significant: it shows that ourancestors’ remarkable understanding of form; mathematically speaking, they reveal under-standing of representing objects in the three dimensional space in terms of 2dimensional pictures.

• 22,000 years ago The earliest dated occurrences of representation of numbers ona 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 theearth became subject to long dry seasons. These conditions favoured annual plants whichdie off in the long dry season, leaving a dormant seed or tuber. These plants tended toput more energy into producing seeds than into woody growth. An abundance of readilystorable wild grains and pulses enabled hunter-gatherers in some areas to form the firstsettled villages at this time.

Although localised climate change is the favoured explanation for the origins of agricul-ture in the Levant9, the fact that farming was “invented” at least three times elsewhere,suggests that social reasons may have been instrumental. 10

9A large area in Western Asia, including the today’s countries of Lebanon, Palestine, Syria, Jordan, andoccasionally Cyprus, Sinai, and part of Iraq.

10http://en.wikipedia.org/wiki: History of agriculture.

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