Tuesday, May 22, 2012


Dog bloggers find dog bloggers.  And I found Paul Handover who blogs at Learning from Dogs  Paul fell in love with dogs when he was ten, but circumstances didn't allow him to have a pooch of his own for another 40 years, after he'd retired from a successful career in sales and company management.

This is Paul's dog Pharaoh, "Just being a dog."
Now Paul has 11 dogs.  (Let this be a lesson to all parents who prevent their children from having a dog - One pooch will never be enough and eleven is just a start.)  Paul's blog isn't so much about dogs as it is about learning from dogs who obviously have things figured out, and one thing they've figured out is math.

This photo proves Beagles can do basic math and a little algebra.

But Corgis can do calculus. 
This is a Tim Pennings' Corgi with his calculus tools.

Paul told me about Tim Pennings, a professor of mathematics at Hope College who specializes in research and writing about dynamical systems, mathematical modeling, and the infinite.  Dr. Pennings lives with a famous Pembroke Welsh Corgi dog, Elvis, who demonstrates calculus.  Dr. Pennings and Elvis are featured here - A Dog, a Ball, and Calculus, Ivars Peterson's Math Trek (copyright 2003).

"Depending on the angle at which Pennings tosses the ball relative to the shoreline, his dog can run along the beach until he is directly opposite the ball, then swim out to get it. Or Elvis can plunge into the water immediately, swimming all the way to the ball. What happens most of the time, however, is that Elvis runs part of the way, then swims out to the ball. This behavior reminded Pennings of a standard problem found in just about any calculus textbook—one that involves minimizing the time of travel to a target when the available paths require traversing different mediums at different speeds." Professor Pennings said, "Of course, although he makes good choices, Elvis doesn't actually do calculus. Nonetheless, Pennings remarked, "Elvis' behavior is an example of the uncanny way in which nature . . . often finds optimal solutions. "I'd guess that most dogs have the same problem-solving software built in from the factory," he says. My article is just "drawing attention to something that has been in front of us all the while."

Walk softly and carry a big stick.  
I'm sure there's some calculus going on here, but I don't know what.

Dr. Pennings has given hundreds of talks with Elvis. His areas of research and writing include dynamical systems, mathematical modeling, and the infinite.  Click here to learn more about calculus, how dogs use it and the man who lectures about it:  Hope College Mathematics

And even more links:
Do dogs know Bifurcations?  (Tim Pennnings and Roland Minton,  The College Mathematics Journal, Mathematical Association of America)

Tim Penning with his teaching assistants.

And don't forget to check out Paul's blog, Learning From Dogs

Friday, May 18, 2012


Do dogs watch television?  The people at DOGTV, cable's first television network for dogs, say YES!  But even though they've adjusted the colors and sounds to be exclusively appealing to dogs, I'm a skeptic.

Way back when we didn't have digital televisions, dogs couldn't see television the same way we did.   The screen refresh rate, how many still images appear on the screen, was set at 50 to 60 frames per second,  just above the critical flicker fusion frequency  that humans see.  Because dogs see 70 to 80 or more frames per second, the screen would appear jerky or worse.  Different from one species to the next, flicker fusion frequency is probably related, in an evolutionary sense, to the speed of the prey animals we chased, or how fast we had to out run predators.  Birds see about 300 frames per second.

But even with digital television, video images lack depth cues important to dogs.  A television screen is a two dimensional surface and the images on it are representative of three-dimensional space.   For example, it’s clear to us that in a chase episode, the police car may be a fifth the size of the suspect's vehicle, because it's three  blocks farther away.  On the other hand, it's likely that  if something, a cat for instance, is shown actual life size on the screen, dogs may understand that it is indeed a cat.
Another thing - canine distance vision is poor relative to ours. They can only see at 20 feet what we can clearly see at 80 feet.   Odor and movement more likely determine depth in their vision field.  For example, something 100 feet away on the sidewalk may have the shape of an animal, but if it doesn’t smell like that animal should at that distance, and it doesn’t move, then it may as well be a rock.  

Now that we've digitalized television to accommodate canine flicker fusion frequency problem, it seems to me that we still need to add appropriate depth perception cues and odor enhanced stories.  

But I may be wrong. If you've tried DOG TV  let me know what your dog thinks.

Wednesday, May 2, 2012


My friend Sue Ashline owns a tattered scrapbook full of faded yellow newspaper clippings about hero dogs. All of the articles were cut out of the San Francisco Chronicle and Oakland Tribune between 1924 and1945 by some long forgotten dog lover. I'll post a few here from time to time because incredible dog stories, whether fib, fable, fiction or fact, are always worthy of a second printing.

Canine tall tales are always amusing, but dig a little deeper and you'll find that tales of dogged endurance reflect our own human struggles.

Scrappy depression era survivors: The cleverness of the canine race was a never-ending  source of interest to newspaper readers in the 1930s.  Surviving in a hostile environment by your own wits, even if it meant breaking the law, was OK.  

Jack-of-all-trade types down on the farm: Saving children from one thing after another was all in a days work for this guy. Canine hero awards were big stories on slow news days.  The caption reads:  "Pal, faithful friend of the children at Del Valle farm, being decorated by one of the children."

Relying on the kindness of strangers:  Everybody needed a hand out during the depression.  The caption reads, "After his owner sold the old bus, this pooch remained under the car for twelve days on a second-hand lot, and refused to budge even for food until the Detroit Humane Society stepped in and rescued him from starvation."

Canine soldier heroes in war:  War dogs were honored time and again as brave soldiers who nearly perished while defending the lives of their human companions.  AP stories were usually accompanied by photographs of dramatic re-enanctments.

Today dog anecdotes are mostly relegated to websites and super market stand tabloids.  To find new fangled versions of old fashioned yarns visit The American Humane Association's Hero Dog website. 

Tuesday, May 1, 2012


Who doesn't love a speckled spaniel pup?

If you base their popularity on my vintage photo collection, everybody in the 19th century loved spaniels. I got this photo at a thrift store in Canada.  On the back it says "Uncle Fred and Doc."  Do you think this is a Water Spaniel?

According to writing on the back, this is "Georgie Jameson and Jim."

It wasn't until late in the 19th century that spaniels begat all the different kinds we have today. Cynologist Johnathon Caius wrote in his 16th century Treatise on Dogs, that there were two kinds of spaniels, one for land game and the other for water.  He elaborated, "The land spaniels have no peculier names assigned unto them, some onely that they be denominated after the byrde which by  naturall appointment he is alotted to take, for which consideration, some be called dogges for the Falcon, the Phesant, the Partridge, and such like."

By 1800 there were 7 types of spaniels.
These are the water spaniels. 
(Both engravings by Wm. Lizars, "The Naturalist's Library," 1830-1840)

And the land spaniels.

In some cases, spaniels were subdivided as the consequence of dog shows which became popular in the 1880s.  Sports minded breeders didn't care if their land spaniel broods were too diverse in size to be considered a breed by 19th century standards.  The small dogs in their litters were used under brush to hunt woodcock and the large ones to spring birds in the field.  However, for purposes of dog shows, anything over 28 pounds was a "springing" spaniel, 28 pounds and under deemed it a "cocking" spaniel.  Arranged in rigid systems of classification based on strict differentiation of shape, size and color, individuals within each group began to look more like each other and less like the generic spaniel.

This looks like a Springer Spaniel, circa 1930.

Today dog enthusiast breed  24  spaniels:  American Cocker Spaniel, English Cocker Spaniel, American Water Spaniel, Blue Picardy Spaniel, Boykin Spaniel, Brittany, Cavalier King Charles Spaniel, Clumber Spaniel,  Drentse Patrijshond, Field Spaniel, French Spaniel, German Spaniel, Irish Water Spaniel, King Charles Spaniel, Kooikerhondje, Large Musterlander, Papillon, Phalene, Picardy Spaniel, Pont-Audemer Spaniel, Russian Spaniel, Small Musterlander, Sussex Spaniel and Welsh Springer Spaniel.