That is the conventional story of human evolution. But there is another story, less orthodox, with two main sources.
Human beings are very weird apes, indeed very weird animals altogether. They have extremely short fur, mostly just a downy covering. They walk upright on two legs. They have a layer of fat, all the year round. They mate face-to-face (often). They have exceptionally good breath-control; good enough to be able to speak. They weep and they sweat. They adore water, and can swim long distances. A newborn baby, dropped in a pool, can keep itself afloat: the ability to swim is instinctive. All these peculiarities led Elaine Morgan to write The Aquatic Ape in 1982. There she suggested a radical theory: that humans evolved not on the savannahs, surrounded by fierce predators, but on the beach. That explains the swimming, the upright stance (it's easier to evolve a two-legged gait if you are buoyed up by seawater), and the lack of hair (which causes problems when you swim, providing an evolutionary reason for it to disappear). In fact it can be argued that it explains all of the peculiarities of humans that we've just listed. The original scientific underpinnings of this theory were developed by Alister Hardy.
In their 1991 The Driving Force Michael Crawford and David Marsh took the story one stage further, by added one extra ingredient. Literally. The most important thing that the beach provides is seafood. And the most important thing that seafood provides is 'essential fatty acids', which are a crucial ingredient in brains. In fact, nearly two-thirds of the human brain is made from them. Fatty acids are good for making membranes, and brains use electrical signals in membranes to compute. Myelin, in a membrane sheath surrounding nerve cells, speeds up the transmission of signals in the human nervous system by a factor of five or so. It takes a lot of essential fatty acids, then, to make a big, fast human brain, so it must have taken almost as much to make the brain of our distant ape ancestor. Oddly, though, our bodies cannot make those special fatty acids from simpler chemicals, like we make most complicated biochemicals that we need. We have to get the fatty acids, ready-made, from our food; that's why the word 'essential' is used to describe them. Even more oddly, there are few essential fatty acids out on the savannahs.
They would exist only in living creatures, of course, but even there, they are fairly rare. The richest source of essential fatty acids is seafood.
Perhaps all this explains why we want to spend so much time on the beach. But whatever the explanation, the ability to make big brain was one key step in our evolution away from our hairy, quadrupedal 100,000-fold great grandfather.
Big brains, however, are not enough. What really matters is what you do with them. And what we managed to do was to play off one brain against another, so that over the millennia they got better and better at competing and communicating.
Ape brains competing with lion brains leads to an arms race that improves both, but the arms race is fairly slow, because both brains are being used for very limited purposes as far as the competition goes. Ape brains competing with other ape brains gives the whole brain a workout, all the time, so the rate of evolution is likely to be much higher.
For every species, the main competition comes from other creatures of the same species. This is reasonable; they're the ones that want exactly the same resources that you do. This opens the door to elvish interference, in our Discworld metaphor. The nasty side of human nature, which in extremes leads to evil, is inescapably bound up with the nice side. One very direct way to compete with your neighbour is to bash him on the head, hard.
However, there are more subtle ways to gain evolutionary advancement, as we will see later. The elvish approach is crude, and ultimately self-defeating, for a sufficiently extelligent species.
The possession of brains opens up new non-genetic ways to pass characteristics on to your children. You can give them a good start in life by moulding how their brains react to the outside world. The generic term for this kind of non-genetic transfer between the generations is privilege. There are numerous instances of privilege in the animal kingdom. When a mother blackbird provides yolk in her egg for the baby blackbird to feed from, that's privilege. When a cow provides milk for her calf, that's even more privilege. When a mother tarantula wasp provides a paralysed, living spider for her grubs to grow in, that's privilege.
Humans have taken privilege to a qualitatively new level. Human parents invest an astonishing amount of time and effort in their children, and spend decades -entire lifetimes, in many ways looking after them. In conjunction with big brains, slowly getting bigger as each generation passes, privilege leads to two new tricks, learning and teaching. Those tricks feed off each other, and both require the best brain you can acquire.31
Genes are involved in building brains, and genes can perhaps predispose individuals to be unusually good at learning or teaching. However, both of these educational processes involve far more than mere genes: they take place within a culture. The child does not just learn from its parents. It learns from its grandparents, from its siblings, from its aunts and uncles, from the whole troupe or tribe. It learns, as all parents discover, to their dismay, from undesirable sources as well as authorised ones. Teaching is the attempt to transmit ideas from the adult brain to that of the child; learning is the child's attempt to insert those ideas into its brain. The system is imperfect, with a lot of garbled messages along the way, but despite its faults it is much faster than genetic evolution. That's because brains, networks of nerve cells, can adapt much more rapidly than genes can.
The faults, oddly enough, probably accelerate the process, because they are a source of creativity and innovation. An accidental misunderstanding may sometimes lead to an improvement.32 In this respect, cultural evolution is just like genetic evolution: it is only because the DNA copying system makes mistakes that organisms can change.
Culture didn't arise in a vacuum: it had many precursors. One crucial step towards the development of culture was the invention of the nest. Before nests came into being, any experimentation by the young either worked, or led to a quick death. Within the protection of the nest, however, young animals can try things out, make mistakes and profit from them; for example, by learning not to do the same thing again. Outside the nest, they never get a chance to try a second time. In this manner nests led to another development, the role of play in educating the young animal. Mother cats bring half-dead mice for their kittens to practise hunting on.
Mother birds of prey do the same for their offspring. Polar bear cubs slide down snow-slopes and look cute. Play is good fun, and the kids enjoy it; at the same time, it equips them for their adult roles.
Social animals, ones that gather in groups and operate as groups, are a fertile breeding-ground for privilege and for education. And with appropriate communication, groups of animals can achieve things that no individual can manage. A good example is dogs, which evolve the ability to hunt in packs. When such tricks are being played, it is important to have some recognition signal that lets the pack distinguish its own members from outsiders, otherwise the pack can do the work and then an outsider can steal the food. Each dog pack h its own call-sign, a special howl that only insiders know. The more elaborate your brain, the more elaborate the communication from brain to brain can be, and the more effectively education works.