Sometimes it seems like Fido understands you. Or Kitty knows exactly what makes you tick. Or in my case, growing up on a farm, that our goats must somehow have been related to Houdini. They always escaped their pens.

What is the nature, and extent, of animal intelligence? Natalie Angier in the New York Times asks this very question, focusing on numbers. She claims, “Many Animals Can Count, Some Better Than You.”

She gives many examples. Three-spined sticklebacks, for instance, enjoy “a contrast ratio of .86,” that is, “they’re able to tell six fellow fish from seven, or 18 from 21 — a comparative power that many birds, mammals and even humans might find hard to beat.”

Angier writes about spiders, chimpanzees, and frogs. She delves into topics covered at a 2017 Royal Society conference on “The origins of numerical abilities” and in a journal issue that came out of the meeting.

The chimp example raises eyebrows.

Chimpanzees are social scorekeepers, episodic warriors and number ninjas, too. They can be taught to associate groups of objects with corresponding Arabic numerals up to the number 9 and sometimes beyond — three squares on a computer screen with the number 3, five squares with 5, and so on. They can put numerals in order.

The numeric working memory of young chimpanzees is astonishing: Flash a random scattering of numerals on a screen for just 210 milliseconds — half an eye blink — and then cover the numbers with white squares, and a numerically schooled young chimpanzee will touch the squares sequentially to indicate the ascending order of the numbers hidden beneath.

Don’t bother trying to do this yourself, Tetsuro Matsuzawa, a primatologist at Kyoto University, said at the scientific meeting in London on which the themed journal was based. “You can’t.”

Does this mean these primates comprehend numbers better than we can? Are they the real mathematicians? Let’s take a deeper look. Here is the abstract of Matsuzawa’s Royal Society talk:

This talk summarises numerical capacities in chimpanzees focusing on three topics: cardinal and ordinal aspects, decimal number system, and photographic memory for numerals. The Ai project started in 1977 when a 1-year-old female chimpanzee named Ai arrived the Primate Research Institute of Kyoto University. She mastered logico-mathematical skills including the use of Arabic numerals to label sets of items in addition to their colour and constituent objects. Next, we tested Ai on ordinal aspects of number through a sequencing task that required her to touch numerals in ascending order. These two related skills were later verified in six other chimpanzees. After introducing the numeral 0 we tested acquisition of the decimal number system from 0 to 19. A major problem for chimpanzees in these tasks was the time needed to make a judgement. Chimpanzees have a strong tendency to make quick decisions, and this led to the estimation, rather than one-by-one counting, of the items displayed. They mastered the ordinal aspect of numbers beyond 10, although two-digits numerals greater than 10 led to lower accuracy. However, the tendency for quick decisions has advantages in situations that need rapid comprehension, such as memorising numerals at a glance. Three young chimpanzees showed better performance than human adults. Eye-tracking revealed the chimpanzee-unique way of watching the world: a quick scan of the whole image, jumping from one place to the next. This contrasts with humans, who direct their gaze at specific points as they try to grasp the meaning of the image. [Emphasis added.]

Translation: Chimps can memorize. Humans comprehend.

What, then, is intelligence? What is the rationality that animals lack? Here, I adapt from the blog Adoro Ergo Sum. Animals cannot:

1. Ask questions to understand the essence of something. They cannot identify abstract concepts beyond a particular. You might inquire, “What is this? Is this a table?” An animal could not.
2. Make judgements. This involves evaluating whether a claim is true or false. Rover has no idea if the table is square or not.
3. Make rational argument. Humans can combine their understanding and ability to make logical statements and find out what is necessary. You might reason, “All squares have four equal sides. This table does not have four equal sides. Therefore, this table is not square.”

What we see with the chimp is a very high level of ability to note particulars and to memorize. But it does not show anything further.

Fido uses his pack instincts to bond with you. And Kitty likes to be dominant but she doesn’t have an elaborate sinister plan for how to take over your home. And our goats did not have the IQ of a genius.

Believe it or not.

Photo: A three-spined stickleback, by Piet Spaans (Viridiflavus) (Own work) [GFDL, CC-BY-SA-3.0 or CC BY 2.5], via Wikimedia Commons.