Katya Resting below Unicorn
Katya is one of our livestock guardian dogs but she’s a little disabled, or differently enabled to put it in politically correct terminology. Specifically when she was a puppy she had white muscle disease which is a lack of selenium in her diet and the vet failed to diagnose it properly. I figured it out finally and gave Katya human vitamins which saved her life. But by then her body had already been warped. She looks like Yoda with Kita‘s head and personality. In fact, we joke that while Katya is our smallest dog she is really the reincarnation of Kita, our biggest female ever.
The result is she does not leap over tall buildings like Kita, or our other dogs. To deal with her physical difference she has turned to more intellectual pursuits. One of these is she’s learned more math than most of the dogs use.
The dogs have basic math skills that they use for counting their livestock. I’ve thought it was just visual math, pattern matching, but Katya has shown that they are able to go beyond that.
More recently as Katya ages her eye sight has been failing. This may be a long term result of the selenium deficiency since poor eye sight is not in her family history. Specifically she has poor low light vision and tunnel vision. She still sees reasonably well straight ahead in bright light but dim light and off to the sides are weak for her. To make up for this she has learned to read my hand signs and finger counting by using touch, much like the famous Helen Keller.
Katya likes doing math because it involves getting paid. She’ll come to me and say Come-Come and take me to her work desk and then ask for a math problem. She gets rewards for cleaning house too, picking things up off the floor, but sometimes she complains there’s nothing for her to do so doing math homework is a good substitute. She’ll get a treat like a cheerio once in a while – a single math problem isn’t enough any more to earn a prize. I scallop. She’s been doing this for years so the price of math quizzes has gone up with inflation.[1, 2]
When we do her math homework I hold out my hands with numbers such as one finger up for one, four fingers for four, etc. You get the idea. Katya examines my fingers by running her paws or nose over my fingers to find out what I’m signing. Then she looks away and down. This means she’s ready for the question. I ask the question and she touches the correct answer hand.
The new and interesting thing is I’ve recently observed that she doesn’t look at my hands when she answers. With her reduced vision she has stopped using her eyes for this task. What this demonstrates is that she’s already memorized which hand means which number so there is no need to check them again. She just taps the hand with the right answer without looking.
This means that Katya is conceptualizing the numbers on my hands in her head and remembering it as the abstraction of a number prior to my giving her the math problem. Then she does the math and answers without having to recheck my hands. This is a higher level of cognition than the visual counting, adding and such that I had assumed the dogs were using. They’re using abstract math.
Its not calculus, not yet, but she does do math. If she can then others can. Remus, Hanno, Kavi and Lili have all also demonstrated the ability to do the math problems although I did not work to teach them – rather they learned from observing Katya at her lessons. They’ve seen her get a treat and they want in on the action.
Outdoors: 56°F/43°F Rain
Tiny Cottage: 64°F/60°F
Daily Spark: Some people claim we should eat dogs if we eat pigs and that pigs are as intelligent as dogs. Both of these are patently false. The reason I favor pork over dog, or horse for that matter, is simple economics: a pig will grow from 3 lbs at birth to 250 lbs slaughter weight with a 72% yield in only six months. Dogs can’t touch that. In fact, very few animals are as productive as pigs at turning almost any food into high quality meat. If you were I would raise you for meat. As to intelligence, our dogs are far, far more intelligent than our pigs. Pigs have about 30 words of language. Dogs have about 1,000 words of language. Pigs are very good at being pigs but they’re basically self-centered and uncooperative. Dogs cooperate not just with each other in a pack but across species. Pigs never take in human babies and raise them as their own. Dogs have done this many times through history for thousands, perhaps millions of years. We breed the pigs for meat production and the dogs for intelligence. The dogs are livestock herding and guardian dogs – they’re co-workers on our farm. The pigs are the product. It is a simple division that has evolved from a basis in reality.
What sort of math problems do you ask Katya to do that both use 1 and 4 and have those numbers as answers?
We do counting, recognition of items, more, less, equal, addition, subtraction. I’ve been pondering how to introduce multiplication. Her attention span is not long. Think human five year old. Older on some things. We go up to five because I only have five fingers on a hand. I’ve been considering introducing her to six through ten – she knows some ASL and those are all doable on one hand but they lose the connection to units. However given this latest development she may be ready for that level of abstraction.