The concept of "zero" is a tricky one, as it denotes an appreciation of what nothingness is. Although quite a few species have demonstrated a recognition of numbers (monkeys, pigeons, rats, dolphins, crows, lions, among others) and a few have demonstrated rudimentary counting skills (higher apes and Grey parrots), the extent to whether these same animals understand the concept of zero, or the lack of something, is a completely different question.
As mentioned in one of the first Grey Matters, research done by Dr. Irene Pepperberg has demonstrated that Alex the Grey parrot possesses the ability to count up to six items (random items, random patterns, and random "interviewer" does not affect accuracy). Alex is able to identify "How many blue blocks?" "How many red squares?" etc, as well as simpler tasks "How many are red?" "How many are square?" usually with an accuracy of 80%. This has been represented over the 20+ years of Dr. Pepperberg's research, and his accuracy has remained the same in a variety of conditional changes. Most recently Dr. Pepperberg wished to test whether Alex also possessed a concept of the zero; this work was published in the Journal of Comparative Biology earlier this year. Perhaps this is a misnomer to say that Dr. Pepperberg initiated the test--in fact, it was Alex's spontaneous use of "none" to describe a quantity that was not present that spurred her to test the concept further. She wished to then test the flexibility of his counting ability, as well as whether he realized when "none" of a certain type of thing was presented.
(More under the fold....)
In the task, Alex was presented with an array of objects of different type, size, color, and number. He would then be asked "What color 6?" or "What toy/matter 4?" or "What 5?" for example. In this way he had to look at the objects presented, recognize what object/color was appropriate for counting, count the appropriate item, match this with the presented question, and finally present an answer.In some cases, there were no objects which met the criteria of the question. For example, sometimes Alex would be presented with a tray which contained no red items, and be asked "How many red?" In this case, the appropriate answer was "none." In this way, Alex's answers were scored for accuracy, and correct answers were given a verbal and food reward.
The results are quite interesting: Alex only made 3 errors in 32 trials (each consisting of 4 questions), over a 90% accuracy rate (in the first experiment); in the second experiment, he made 8 errors in 66 trials (about an 87% accuracy. On "none" trials, his accuracy was also high: 83%. This indicates, at the very least, that Alex was able to recognize the lack of or absence of a particular category in the immediate environment, and to report that fact to Dr. Pepperberg. Whether parrots can comprehend the concept of zero in the same capacity as humans remains to be seen, although it is quite interesting that a species far removed from humans (in evolution and neurally) could have development a somewhat complex abstract concept.
Reference: Pepperberg and Gordon. 2006. Number Comprehension by a Grey Parrot, Including a Zero-Like Concept. Journal of Comparative Psychology. Vol 119. No 2, 197-209.
Comments
While I hate to disagree with you, I do think it is a bit of a leap to equate the concept of 'none' (the null set)with a grasp of the number zero.
Even in human societies who have primitive counting systems (i.e. one, two, many) can conceptualize 'none'. It is recognising that zero is a number in and of itself that was the innovative leap that lead to place-value systems.
Nevertheless it is still an impressive feat that Alex can even grasp the wider idea that there is no match between the descriptive set and the sets that have been presented.
Posted by: DV8 2XL | August 25, 2006 9:19 AM
When my son first learned how to count, he clearly developed the numbers greater than one - 2. 3, 4, etc. before one. One was sort of a default, and he'd skip over it when counting things (although he'd start 2 at the right place, thereby getting the correct count).
Posted by: Bram Cohen | August 25, 2006 11:19 AM
DV8, it sounds like you're splitting hairs. "Zero" and 'None,' are functionaly identical in this case.
Posted by: JaysonB | August 25, 2006 11:56 AM
Yeah, DV8, I'm curious about how you can display apprehension of zero as a number.
Seals and dolphins, too (at least) can I think recognise that the object they seek isn't available, and communicate same in some way.
Posted by: Zusty | August 25, 2006 12:13 PM
No I'm afraid it's not splitting hairs. The absence of something is the null set, that concept has been present in human language as far back as we can see, and is a feature of all present tongues.
Zero (the number) is quite different, a much more modern invention that came well after the development of counting, in fact well after basic arithmetic. Roman numerals are the most obvious example.
Zero, as a placeholder in positional number systems, or as the mid-point on the set of Reals is a much more complex concept than the idea of nothing or none. (Although one might argue that zero subsumes the later as well)
Posted by: DV8 2XL | August 25, 2006 12:53 PM
I suppose thats why Pepperberg named the paper "a zero-like" concept, in so far that to us humans, zero is more like a placeholder for the concept of none in arithmatic. Pepperberg has not yet conducted experiments that test whether Alex is capable of adding/subtracting, so she cannot make the leap to say that Alex comprehends that nuance of zero. But, as to the concept of "none" and recognizing the absence of a category etc, he has demonstrated that that observation is significant to him.
Posted by: Shelley Batts | August 25, 2006 1:04 PM
What is meant by those with 'primitive counting systems' being able to conceptualise 'none'?
Whose ladder are you refering to? Why should it be noteworthy that societies other than ours are also able to represent - nothing?
That a parrot or squid is able to understand 'zero' is a key insight for human-environment interaction. The sooner we humans realise that there is more to this universe than our existence the sooner we will experience lives of deep purpose, global collaboration, and importantly - adventure...
I think the topic of a parrot comprehending 'zero' is interesting. Perhaps it is the process of communnicating 'zero' to another that is a more valid reflection of understanding what 'zero' can represent. Recognising and understanding are two inter-linked processes; some of us critters may not have the propensity to refine either or both of these processes.
Posted by: charmayne | August 26, 2006 12:11 AM
OK I'll bite. First let's get the semantics out of the way. Zero is a number. As a number it has certain properties that define it, and certain roles that it plays in Number Theory.
'None', on the other hand is a concept that is much more nebulous in definition. In math it is represented as the null set {} and this is not in any way equivalent to '0'.
This is not quibbling. The whole point of Dr. Pepperburg's work is trying to determine her subject's grasp of language and concepts. To say that the bird understands the absence of a set is one thing to suggest that this can be extrapolated to mean that it has a grasp of the number zero is another all together.
The first requires that Alex can conceptualise, in the abstract, the absence of something that could potentially be there, the other requires that he understands cardinality to the extent that he recognises a count of zero as an integral part of counting.
The former in and of itself is significant, although not limited to parrots, as was pointed out above. That is assuming that Pepperberg has controlled for the potentially confounding possibility that Alex is uttering 'none' as an error code when he can find no right answer. (I haven't read the paper.)
As I mentioned in a comment to another "Grey Matters" post, on of my four Greys will say 'Hi' and 'Bye' when someone enters or leaves the house. Now this bird as a large vocabulary of words and phrases, but these are the only two she uses in context. But it would be a reach to say she is using them to communicate the same information that the humans in the household do when we utter them. At best she has only learned that these are calls that are used in a particular situation. The same can be said of their penchant to scream like smoke alarms every time someone sets onions to fry, that they picked up one winter day when my daughter forgot she had some on the stove and was talking to her boyfriend on the driveway.
Pepperberg herself has often cautioned that we should not read too much into Alex's performances. I am simply saying the same thing here.
Posted by: DV8 2XL | August 26, 2006 12:13 PM
Birds apparently can count - but are unable to distinguish 4 from 5.
'The Golden Ratio: The Story of Phi, the World's Most Astonishing Number' by Mario Livio, pages 14-15 refers to to 'Number: The Language of Science', New York: Macmillan Company, 1930 by Tobias Dantzig.
Dantzig provides an apparent eaxmple of bird counting.
It seems more likely that birds use modulo (5) confusing 0 and 5 since both have the same remainder in this system.
Humans tend to use 1 through 5 instead of 0 through 4.
Posted by: Doug | August 31, 2006 5:39 PM