Scientists are really interested in this topic. The horse you mentioned, Clever Hans, turned out to be really smart about reading people, he just couldn't do math. But there are animals that can do simple math. Alex was an African Gray Parrot who died this year. He could do simple arithmetic, adding up to 6. Chimps may be able to do very simple arithmetic, and several bird species seem to be able to count eggs or predators.

One test that we animal behaviorists find important is the mirror test.Most animals respond to their reflection as if it were another individual. They may attack it or just watch it. Eventually, they usually stop paying attention to the reflection, maybe because it doesn't do anything interesting. Researchers wondered if some smart species could actually recognize themselves in the mirror. They reasoned that this would show self-awareness in the animal.

But how do you know? You can't ask, "Hey Bobo, who's that in the mirror?" Well, I guess you can, but there may be some communication problems. What researchers did was to put a dot on the faces of chimps that were sedated (drugged). Then they watched how the chimps used the mirrors. They used them to inspect the dot and other parts of their bodies that they couldn't normally see. This showed that the chimp recognized the animal in the mirror as itself. Monkeys and most gorillas fail this test. Orangutans and bonobos (pygmy chimps) passed.The only other non-humans who have passed this test are bottlenose dolphins. Not every species has been tested; researchers started with the ones who seem smartest to humans.

Let's be fair, in some ways we humans are really stupid compared too ther animals. If a book is on the table I can't tell who touched it last. Any normal puppy would figure that out in an instant from the odor on the book. If it's dark, I run into walls. A bat just uses sonar to avoid all obstacles. I'd probably get lost in the desert without a compass while an insect with a brain smaller than a grain of rice gets home with no trouble. There are countless skills and abilities that I lack and some other animal has.

The 9 dimensions you're talking about aren't like the three dimensions we see (near/far, up/down, right/left). They're more like ways of thinking about the world. These levels aren't scientific concepts,they're more philosophical.

So why aren't all animals as smart as possible? It's not just about brain size. Whales are huge, but flunk the mirror test. What do you think is the cost of intelligence?