"The right footprint placed, say, a half second later has a stronger concentration of odors," she explained, "and telling the difference between those two footsteps is a difference in time -- and dogs perceive that."
She went on to explain how dogs, for whom smell is as dominant as sight is for humans, live in a world of constantly fading odor traces -- some near, some far and some up ahead in their near future.
This means, she suspects, that they live in a much larger "bubble of the evolving present" than we do.
However, Horowitz pointed out, contrary to the common notion, dogs' hearing is not far better than ours, and in fact, it's mostly inferior.
"Yes, it's true dogs can hear a slightly higher pitch than we can," Horowitz told us. "But they can't really use hearing to place where a sound is coming from, the way we humans do."
Instead, she explained, while sound may alert a dog to the fact that something is happening somewhere, after hearing it, their brains immediately start searching through input from their eyes and -- especially -- their noses to find out where and what it is.
Challenging a belief so common that it has dug deep into our language, Horowitz expressed doubt about the universal notion of the "alpha dog."
"The wolf research that I've seen doesn't support the notion that the wolf pack is one of domination," she said.
"Instead, it's more like a family unit," she told us, as the leashless dogs still swirled exuberantly around us, forming little groups, checking each other out, forming new groups, and generally energizing the entire scene.
"I don't think that we need to be dominating our dogs," she said.
She describe how both dogs and humans seem, from her research, to naturally conduct their familial behavior -- including how the members of her own young family (including the now leaping Finnegan) related to each other:
"Instead, we are a family together," Horowitz said. "We learn by observing each other; we learn by small punishments, not large punishments -- and by rewards. This is a better model for building a relationship with a dog."
And oh the sadness -- you could see it in their eyes, or at least this reporter would swear you could -- when 9 a.m. tolled and the leash laws came back into effect.
The riot of exhilaration all had to come to heel -- leads clicked on to collars, one by one -- and the human/dog couples made their way, well exercised at least, back through the trees down the paths from the high hidden field to the more restrained streets of the great city.