Ok, clearly there is no answer to this one, as we can only speculate. But I'm curious for people's feedback, and here's what got me wondering:

Jack knows the names of all his toys. When we bring a new one home, we say the name clearly two or three times, throw it for him, and say "Get (name of new toy)!" and that's how he learns the names of something new. The way we trained him to realize that things have names was a bit more involved, but now that he knows the concept, naming new objects is easy.

When he looks bored, sometimes I'll send him searching for a toy I haven't seen in awhile. So, I might say "Jack, where's Ultra Ball?" with an emphasis on the questioning tone of voice. The hunt is on, and he'll check his toy basket, behind the door, under some shelves, in his crate, until he finds the object. He trots around with a very matter-of-fact look on his face, and I assume that he is looking the way I would look: that is, he has a mental image of "Ultra Ball" in his head and is muttering some doggy version of "Where IS Ultra Ball? Where did I leave it? Is it behind here? Under here? Back there?" the whole time.

But sometimes, in talking to my dog the way one will, I might ask "Where is..." when I am looking for something of my own, something that he does not know the name of. And off he toddles, looking just as intently as he does for his own toys, trying to find I'm-not-sure-what.

Just now, I was wondering where the cat was, and I said "Jack, where is Kitty Boo?" (the cat's name is Boo, but somehow we've changed it to Kitty Boo without even realizing it).

Off went Jack, that same look on his face, but clearly he wasn't looking for the cat because he walked right by her. He checked behind the door, behind the sink, under the hall table, in the dining room, by his crate. The longer he looks, the more intent he gets. To my human brain, I assume he's holding a picture in his head of an object, and looking for it.

But watching his behavior, I now wonder if the opposite is true: he knows that "Get xyz" means I want an object. But maybe until he SEES the object, he does not know what he's looking for? That is, if I say "Get tennis ball" perhaps he does not hold a picture of tennis ball in his head, but as he sees objects, he labels them and dismisses them as "not tennis ball" until he sees the one that triggers the "Tennis ball!" response in his brain. That is, he knows it when he sees it, but until he sees it he cannot picture it.

Not sure if I'm making sense, but the fact that he will look just as thoroughly for something that he has no concept of as for something he "knows" the name of puzzles me. And just to clarify, he has never actually come back with an object when I unintentionally send him on the hunt for something he does not know.

Anyone have any insights on those doggy brain cells to enlighten me?

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you might instead buy a new toy and never name it, and leave it around for a few days THEN try it.
You are brilliant!! Why didn't I think of that? I'll definitely give it a try.
I actually thought of it because i though of a baby experiment. See if you can find The Baby Human on Discovery Health or on Youtube. They talk about the kind of learning and intelligence that babies exhibit and at what times and experiments that prove what they can and can't understand. You might be able to mold some of these experiments.
For example, a simple object permenance experiment. Object permenance is knowing a object still exists even when you can't see it. You're already somewhat doing this one. Place an item where the dog can see it. Then put it out of sight. Then ask the dog to find it. If he can find it. By finding it you know that he is able to understand that objects are there even when he can't see him. Then mix it up. Pretend to put it there but really hide it. What does he do when he does where he knows it is and it isn't there? Is he flummoxed? Does he keep searching?
My other question would be - as dogs are soo in tune with our emotions, how much of what they know is sensed from us? Example - you send Jack after the unknown object, you're watching him hunt, you react subconsciously when he passes it, releasing some sort of scent that we can't smell, but he can. He follows your "scent" to locate the object you want because you have certain reactions when he goes near it, or away from it.
The "Clever Hans" effect is what you are talking about.

To guard against this in studies, they very carefully make sure that anyone in the room with the dog also does not know where the object is.

To guard against this in my own house, I regularly send him for toys that I have no idea where they might be myself. :-)

When I am testing this with an unknown object according to Sarah's suggestion, I'll make sure the object is in another room far enough away that I can't tell if he's getting near it or not.
No problem for me. I don't know where half of my stuff is in my house. "... Hey Gwynnie, fetch me my 17 mm box end wrench, and some teflon plumber's tape..."

I thought they did an experiment something like this with wolves and dogs. The experimenter gave cues. Dogs were better at perceiving human cues than wolves. The inference being that dogs have been selected for attention to humans.

We'll know that dogs are REALLY getting intelligent when they're smart enough to lie. Paradoxically, I'll bet that was a crucial point in human evolution: once you have the capability to communicate, you have the capability to lie (even to yourself), and once you have the capacity for abstract thought, you have the capacity for schizoid mentation. Is that why I wanna be a dog?
http://il.youtube.com/watch?v=yPIgnujGQRY&feature=related
Dogs can definitely be... deceptive. One experiment where people had their eyes closed and disallowed a treat and eyes open and disallowed the treat, the dog took the treat from the person with their eyes closed. Showing that they know when your eyes are open, and know when you wont know it's them! TEEHEE!
My female frequently lies to get things from my male. I had a post about it around here somewhere. If Jack is in my lap (a place he rarely occupies), she always wants to be there too but knows I have a "one dog per lap" rule (Jack hates being crowded).

She will make a big scene of play-bowing and harfing to get Jack to hop down, and the second he does she'll jump in my lap. She also sometimes does that to get a coveted toy away from him.
Mine male does this too! If that doesn't work he'll go get a toy or her kong toy (which she has made clear is strictly off limits to him) and lead her once around the couch and then plop in mom's lap. It's hilarious.
This is an interesting discussion. I love reading how others have trained their dogs to do particular things.

Some years back I read a bit on how dogs think and perceive. I was doing volunteer work for a guide dog school and the ability of a guide dog to sort out the world and work with a human is just astonishing when you get to really see it in action and it got me curious how the dogs work it all out given that they really don't think like we do.

The gist of the reading I did -- and I'm sorry, I can't remember the titles -- was that dogs brains are ordered differently that ours and have different allocations of brain power for certain tasks. For example, the human brain uses up a big chunk of it's processing power for sight. No surprise there. We typically want to see first, hear second, touch third, and taste last in ordering our world. Dogs, on the other hand, give over a bigger percentage of their brain to hearing and smell and then sight. It's why blind dogs can get along so well. Taste and touch are lesser sensory inputs for them and given the horrible things Corgis will eat without a thought, that part is easy to believe.

One of the authors used the example of walking into a room. We walk into a room and see how it's arranged and if there is anything we special we need to be aware of. A dog walks in and perceives the room first by how it sounds and smells, i.e. any danger or food. Given their typically shorter stature and inherit concern for danger, smelling and hearing make sense since they (especially Corgis) can't see over things. And since we know that dogs have super hearing and sense of smell compared to ours, it only makes sense that they would rely first on those rather than their vision, which also apparently works differently than ours does anyway.

With Gromit's mini-wiener dog sister, Holly, it's all about the nose. If we hide a toy she's been playing with and tell her "Find the squeaky toy", she'll immediate run around with her nose in the air. If it's well hidden, after a minute or two of searching she'll hop up on the furniture, sit up tall, and place her nose as far in the air as she can and sniff like crazy. After a minute she'll home in on where ever the squeaky is, even if it's stuffed behind my back in a chair cushion or up on a shelf (bad toss by the owner) where she can't possibly see it. It's an impressive bit of scent detection.

I don't think Corgis have the hound's super scenting capability but they still have a keen nose and combined with their herding smarts they can put together a quick search that lets their nose home in on each item, which to them, probably all smell differently from each other even though they would smell about the same (awful) to us. So "Find the kong" is "Find" and "smell no. 7" The nose guides them in and the eye confirms.

Since we humans are so visual I believe we unconsciously train our dogs to be more visual than they might otherwise be, for instance by learning to follow hand signals and not just verbal commands. That dogs can learn human hand signals is considered by some to be a significant sign of a dog's brain power.

Funny Corgi story: Gromit's breeder was once training a Corgi for AKC Utility competition where scent discrimination is part of the test. Three small wooden "dumbbells" of different colors are are placed out about 50ft from the handler. Only one of the dumbbells has been touched by the handler so only that one has his or her scent on it. She sent the Corgi out to retrieve "her" dumbbell and the dog brought back the wrong one. No problem, just training. So she led it out and showed the correct one. The dog was sent out again and again it brought back the wrong one. The correct one was shown again and the dog was sent out a third time. This time the Corgi scooped up all three of the wooden dumbbells in it's mouth and brought all three back and dropped them in front of her. "There! If you can't decide which one you want, here's all of them, silly human!"

Interesting article in Time Magazine about how dogs learn: "The Secrets Inside Your Dog's Mind".

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