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2. If you put a woodlouse in a T-shaped maze - one junction, choice of left or right - and teach it that food and a damp place lie in one direction and bright light and dryness lie in another, you can teach an individual woodlouse to turn left or right consistently. In other words, a woodlouse has a memory. It can learn new behaviours.

Woodlice have enough "brain" to at some level form a model of their surroundings. They can learn a very simple map.

3.Many small invertebrates form social colonies. In land-living ones, like ants and termites, animals leave a chemical trail as they move around, depositing markers indicating desirable discoveries. This is how an ant colony "finds" sugar in our kitchens, say. One randomly-exploring ant finds sugar, and retraces its steps home leaving a marker indicating that it's found food. Other ants follow the trail, reinforcing it, until a path is marked for the colony to move large amounts of food back to the nest.

In other words, ants make and read signals for other ants.

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4. Flying insects can't do this; there's no direct way to mark a trail in the air. So bees, as is well known, have evolved a form of symbolic communication: the "waggle dance". By dancing in a certain fashion, a worker can "tell" other workers the direction and distance to a food source. The dance indicates direction relative to the sun - bees can see the polarisation of light and thus see the sun even when it is covered by clouds - and distance, and it does so independent of the orientation of that bee while it is dancing relative to the sun.

In other words, bees have symbolic communication. Their signals are not direct, one-to-one, follow this to the food; they are abstract and require interpretation. Obviously, this is innate, it is not learned behaviour, but individual insects learn the way to food and communicate this symbolically to other individuals.

5. Small mammals can be taught complex behaviours in the lab. Rats can be taught to press levers to obtain treats; mice can be taught to run mazes; "experiments" with wild squirrels have shown that the animals will perform an amazing array of actions to obtain a food reward. Many of these patterns of behaviour show that the animal is able to learn that unrelated actions can elicit a reward, showing some kind of understanding of cause and effect.

6. Non-mammalian vertebrates perform all sorts of ritualistic behaviour that is not directly related to finding food, a mate, predator avoidance and so on. Many birds have mating rituals; male bower birds construct huge and elaborate structures to tempt females into mating, which are presumably derived from nest-building behaviour, but actually the structures serve no purpose other than to be on some level "pleasing" to the females. Many migratory birds such as albatrosses and swans form long-term pairs which persist over years, sometimes lifelong. They can recognise their mate and when they rendezvous at breeding time indulge in long rituals which appear to stimulate and reinforce the pair bond. Obviously mate recognition does not involve some simple biochemical cue of kinship which might be used in a mother finding her offspring in a large, mobile breeding colony independent of environmental cues, such as penguins. Maybe penguins can "smell" or "taste" their own offspring by some form of genetic resemblance; I'm not aware of any research into this. However, even if they can, and don't somehow just learn what their offspring look or sound like, the same cannot apply to individuals recognising their mates, who are, by choice, usually not directly related.

In other words, these birds "know" their non-related partners, can recognise them and distinguish them from strangers, and behave in entirely different manners around their partners to around other individuals. When encountering their partners for the first time after a protracted absence, they indulge in displays and other complex behaviours which are not directly survival-related. It is hard to watch such a pair being reunited without thinking that they "feel happy" to see one another. It is also a reasonably common experience to see one which is isolated and has lost its partner, witness its lack of animation, listless behaviour and so on, and the human reaction is to interpret this as the animal "feeling sad".

7. Anyone who has owned a pet dog has witnessed canine behaviour which at times closely mimics human responses: being hopeful, being excited, being sad, being afraid and so on. The null hypothesis here, it seems to me, is that the animal actually has these states of "mind", rather than that it is going through some completely different, separate, unrelated process which merely closely resembles human emotional states. To my surprise, as a fairly recent and reluctant cat owner, I have seen my cats exhibit what appears to resemble such complex reactions as a rapid survey of the surroundings to see if anyone witnessed an awkward fall.

8. Outside of the remit of pet animals in human company, though, mammals which live in social groups form a complex of often hierarchical relationships: dominant and submissive members of the group and so on. They perform patterned behaviours where different members have different roles; hunting animals such as female lions and wolves, for instance, cooperate, so that hunting parties contain scouts, flushers, chasers and so on. Many group predators display patterns of behaviour such as setting up ambushes. These roles are not fixed but are interchangeable between members of the pack. This demonstrates that the animals not only know of each others' existence, but of their relationships, since for instance in felines often only relatives cooperate. Elephants, wolf packs and so on may comprise unrelated individuals, though. Particular members of the group have expectations of the ways that others will act; cooperation must be learned, and members that do not cooperate may be "punished" by biting or by withdrawal of food. They also perform planned activities; ambushes or driving prey towards a pre-placed fellow pack-member indicates some form of awareness of the future. One cannot plan if one does not remember past events and strives to re-create things that have worked before; this indicates an awareness of time and of modelling the behaviours of other animals, so that there are expected, desired behaviours and unexpected, undesired ones, both in fellow pack members and in the prey animals. This implies a considerable degree of ability to form and maintain mental models of the behaviours of unrelated individuals.

9. Many animals have been shown to make and use tools. Not only chimpanzees in the wild, or finches in Gibraltar which use thorns as probes and levers to get at otherwise-inaccessible food items. Crows have been experimentally demonstrated to be able to improvise tools from available objects to get at food items. In other words, tool use is not always inherited behaviour or mimicry of others; the invention of novel tools has been demonstrated, outside of the mammals.

10. Again in the Aves, recently, a well-known experimental African Grey parrot named Alex died. Alex had been taught human speech; he was able to identify a wide range of objects and colours by name in English, to count up to five or more, to understand simple questions in English and formulate novel answers in the same spoken language. He was able to spell simple words out phonetically - "nuh, uh, tuh, NUT". He was able to express desires in spoken words: "wanna nut, now", even when this did not form part of the experimental dialogue. Many instances have show that his utterances were not simply mimicry of those of his trainers; he was able to construct sentences of his own, as well as parse those of his trainers. This shows considerable proficiency in manipulating an alien to him form of symbolic communication, very considerably exceeding the abilities of chimps and gorillas in the use of sign language. Video clips are available of conversations with Alex; they compel most observers to complete re-assess the presumed levels of intelligence of a bird with a brain the size of a walnut, orders of magnitude smaller than a human's brain.