crashfrog responds to me:
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By "six," do you mean six or do you mean "I'm just using the arbitrary convention of putting the Roman letters s, i, and x together to refer to the number of fingers...for anybody else, I would have said 'five'"?
I mean "six", as in 5 + 1 - as in, "one two three four five six."
OK...just wanted to make sure. You had been disingenuous before and I wanted to verify that you weren't being so now.
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If the former, cool! Can I come and get a picture? I gotta see this.
Tell ya what - prove to me your friends have a cat that detects parity, and I'll prove to you I have six fingers. Or don't you trust me?
Oh, I trust you. That's why I asked if I could come and get a picture. And it uses the exact same method: Get off your ass and go to where the evidence is. I've invited you to come and see the cat...why are you hesitating at me coming to see your hand?
By the way, timing is everything: PBS is running (at least locally) the
Nature miniseries:
Inside the Animal Mind. The latest one had to deal with intelligence (the one coming up has to do with emotions).
Among the many examples were things such as the ability to create mental maps. For example, cabbies learn the streets of the city in which they drive. But, many animals learn that sort of thing, too. The big question is whether or not animals are capable of coming up with new routes if the way they always take is blocked.
Turns out some of them can. Experiments with rats show that when the rat has learned a maze and you alter the maze a bit to block the main route, the rats can adjust their routes and do so immediately without having to take a trial-and-error approach.
Hummingbirds are capable of remembering which flowers they have visited so they don't have to waste energy trying to get nectar from a flower that doesn't have any since it was visited yesterday. In experiments with artificial flowers that were filled with nectar only sufficient for a single visit, hummingbirds consistently avoided the ones that they had fed at the day before. And I should point out that hummingbirds have a brain about the size of a grain of rice.
There is a bird in the Grand Canyon area that buries nuts for the winter...some 30,000 of them, usually. And yet, it manages to find them in the winter...even when the ground is covered with snow and thus the geograhical picture of the land has changed...with a 90% accuracy.
They showed examples of animals coming up with novel approaches to problem solving. Primates who are presented with a banana out of reach can come up with new methods of devising a way to reach it...and will gather all the materials required
before making the attempt. That is, they seem to know just how far the stick will let them reach and just how much the box will let them rise above the ground and noting that neither one is sufficient, will grab both of them
before getting up on the box to poke at the banana with the stick.
There was an incident involving ice fishers and ravens: It seems the ice fishers would set up a few sites, cut a hole in the ice, put bait on a hook and set the line, then go off to do another one. But when they came back, they found that the catch was gone. The fishermen thought somebody was coming around poaching the catch until they caught the ravens at it. It seems the raven had noticed what the humans were doing and after the humans were gone, the raven would go to the line, pull it up a bit, step on it to hold it down, and then pull up a little bit more until they got to the fish on the end.
But is that just another example of trial-and-error? After all, with the chimps and bananas, they tend to need to know the various tools they are going to use fairly well beforehand. So, some scientists raised some ravens from hatchlings in order to make sure that they did not have any previous experience. They gave the ravens a choice: One line had food, the other a rock. The ravens consistently chose the food line, pulling up a bit, holding it down, pulling it up a bit more, etc. They even tried to trick the ravens by crossing the lines...and still the ravens chose the lines with food.
And then there is the work with pigeons and recognition, including the ability to think abstractly. Some pigeons were trained to peck at pictures of trees to get food. The pigeons were then shown pictures they hadn't seen or been trained on and still the pigeons were capable of distinguishing pictures of trees from those of non-trees...including other foliage: Pictures of ferns elicited no response. They were even capable of distinguishing Picasso from Monet...and were capable of coming up with a distinction of the Cubist style since pictures of Matisse, which as a style is very similar to Picasso's Cubism (and is often confused for Picasso, even by humans), elicited responses.
However, there are some differences between humans and pigeons in their pattern recognition. It seems that pigeons don't have the ability to come up with the concept of symmetry. That is, if you presented the pigeons with images of two lines, trying to get them to respond when the lines are of equal length while not when they are of unequal length, the pigeons can't seem to grasp this while humans pick up the rule quite quickly.
However, humans have a hard time dealing with a rule of amounts. That is, if the rule is to respond if there is a little amount of space taken up with color but not if there's a lot, pigeons pick this up quite rapidly while humans have a hard time...it seems that the human ability to seek deep pattern interferes with the simplicity of the presented rule. They are more attracted to the pattern of the boundary than the area which it contains.
And dolphins seem to understand syntax. Dolphins who were trained to respond to about 60 signals can follow the word order when those commands are strung together. For example, if you tell them "Right water, left basket fetch," they know to get the left basket and take it to the waterfall on the right. But if you then tell them "Left water, right basket fetch," they know to get the
right basket and take it to the waterfall on the
left.
And then there are the experiments regarding number. They show a chimpanzee that not only knows how to count but also how to add. The experimenter puts a number of candies in front of the chimp and then present her with a computer touch screen that gives a bunch of possible numbers, randomly scattered...including some boxes blank. Seems the chimp has figured out not only how to count, but the arbitrary nature of Arabic numerals...and also understands the concept of 0.
But wait, there's more. When given one basket in one part of the room with two objects in it and another basket in another part of the room with three different objects in it and is asked how many objects total, it knows that there are five, showing not only an ability to add but also the ability to abstract the properties of number so that it recognizes "five objects" and is not stuck on "two of this kind and three of that kind."
Then there is the work with grey parrots. Given an array of similar yet distinct objects such as blocks and bits of wool, some of which are painted green and others are painted yellow, the parrots are capable of telling you how many yellow wool balls there are compared to how many green blocks.
And let's not forget that even in humans, number seems to be connected to vision. That is, if you were to flash an image in front of a person and then ask them how many objects there were, he'll handily be able to tell you how many, provided there aren't too many. That is, you aren't mentally tabulating, "One, two, three, four" because there isn't enough time to do that. It's immediately absorbed and understood. For humans, the limit tends to be about 7 which seems to be about the limit for other animals (though other animals tend to have lower limits). It seems that small numbers are connected to vision and do not require conscious thought.
So please, crashfrog, do check your local listings to see when this wonderful program is being presented or purchase it from your local PBS store or check your local library to see if they have a copy to borrow, look at these animals, see directly what they can do, listen to the scientists that have carried out the experiments, and then tell me:
Is it really so odd to think that there might be a cat who understands the difference between odd and even?
Oh, but wait...I decided to do a little bit of searching on PubMed:
Pepperberg IM.In search of king Solomon's ring: cognitive and communicative studies of Grey parrots (Psittacus erithacus).
Brain Behav Evol. 2002;59(1-2):54-67.
PMID: 12097860 [PubMed - indexed for MEDLINE]
From the Abstract [emphasis added]:
"During the past 24 years, I have used a modeling technique (M/R procedure) to train Grey parrots to use an allospecific code (English speech) referentially; I then use the code to test their cognitive abilities. The oldest bird, Alex, labels more than 50 different objects, 7 colors, 5 shapes,
quantities to 6, 3 categories (color, shape, material) and uses 'no', 'come here', wanna go X' and 'want Y' (X and Y are appropriate location or item labels). He combines labels to identify, request, comment upon or refuse more than 100 items and to alter his environment. He processes queries to judge category,
relative size, quantity, presence or absence of similarity/difference in attributes, and show label comprehension."
So we're left with at least a couple options, crash:
1) Number is an intrinsic property of objects.
2) Animals have invented mathematics, too.
I, as you most probably can predict, fall toward the first.
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Do it to my hand, next. I can't seem to get it to happen.
Only seems to work for my hand, sorry. I don't know why.
Hmmm...perhaps you only have a virtual hand while my hand has independent existence.
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Rrhain
WWJD? JWRTFM!
Doubtless he'll bring up Pressberger arithmetic without ever explaining its usefulness.
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