Science Sunday

Can Dogs Do Math?

Math problem for Fido: if you have three bones and Mrs. Jones takes one away, how many fingers will she have left?
Well actually dogs and many other animals are capable of solving simple math and not just through trick cues from their owners.  Some of the first research into canine numeracy turned out to be flawed.
The dogs were presented with two choices of a large or smaller ball of hamburg and it was found that they had no preference as to size. This research was flawed in that it was discovered that the placement of the food was uncontrolled and the dogs were actually choosing the closest, perhaps demonstrating some distance measuring skills. With that discrepancy accounted for it was found that the dogs can easily compare size and choose the larger helping demonstrating quantitative comparison skills. 
Another related task is to estimate the number of things in a group, or at least compare the number of things in two groups. This is known as the approximate number system and humans do quite well at it. For instance most of us can estimate which crowd has the most people (with the exception of Donald Trump estimating inauguration crowd sizes). Dogs can also estimate which pile of kibble has the most pieces in it. This has been formalized in the laboratory by training dogs to select a computer screen which has the most dots to receive a reward, proving that dogs do understand the approximate number system in making quantity comparisons.
Studies with human infants have found that there is an innate ability to do simple mathematics. The babies were shown a toy or something of interest, and then a screen was placed in front of it. The researcher would then place another item behind the screen and the screen would be lifted. In some cases the researcher would secretly remove one of the items before the reveal. In cases where the number of items revealed was unexpected, the subject baby would spend much more time staring at it. This suggests that infants have made the mental calculation and are now surprised to find that the number of items they are seeing is different than what they expected. The same study has been done with dogs using treats to hide behind the screen and the results were the same as with the infant studies. The dogs demonstrated the surprise reaction even when finding three treats when they were expecting two.
The understanding of numeracy was further formalized by dogs trained to be still in  functional MRI (fMRI) machine. The subjects were shown a screen with dots that varied quickly while in the fMRI and they found that the variance in the number of dots on the screen stimulated similar areas of the brain as in humans. 
“These findings support our understanding of the Approximate Number System; previously, these effects had only been demonstrated behaviorally in dogs, so this is an important contribution to our understanding of canine cognition,” says Krista Macpherson, a canine cognition researcher at Western University in London, Canada.
Many of us have seen this numerical ability in our own dogs, for example in retriever trials when a multiple retrieve is called for the dog must not only remember the approximate location but the number of retrieves. Flock guardians must also be able to at least estimate the size of the flock.

So all that being said, I see no reason why Twist should not have my tax return finished by the due date.

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References:	https://www.akc.org/expert-advice, July 05 2019,  Do Dogs Uderstand Mathematics, Stanley Coren, PhD
	American Association for the Advancement of Science, Dec 17, 2019,  Dog brains have a knack for numbers, much like ours, Virginia Morell