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Ants That Can Count
thisIsOdd writes "NPR had a recent report about scientists at the University of Ulm who suggest that ants in desert environments count to help them get to and from their homes. Because the desert's windiness and sandiness is not conducive the 'smell-trail' method, where ants squeeze certain glands that leave a chemical trail, scientists were puzzled by the fact that these desert ants were able to leave and successfully return to their nest. The theory is called the 'pedometer theory,' and the experiment used to test it involves manipulating the leg length of some of these ants. Ants with longer legs would pass the nest on the way home, and ones with shorter legs came up... well... short."
couldn't help imagining what it would be like for one of the ants that had it's legs cut off, was made to walk home across the desert on it's stumps and then was totally bewildered as to where it's home had gone. I know they're just ants, but damn that's sad.
but not direction. Like doing "dead reckoning" with pace but no azimuth.
THL phish sticks
While you may be right, the examples you gave don't necessarily extend well to the ants. An animal looking for its babies would see less than 10 or 20 and reproducing a roll on your drum would involve varied rhythms or beats or whatever, or probably less than 50 hits if you were to reproduce it after hearing it once. The ants, however, are probably taking hundreds or thousands of steps and remembering the exact distance in one go. I cannot imagine a person hearing a roll go for 750 hits and then reproduce it in the same ballpark without counting time or hits (but I'm no drummer). The article described it as a "pedometer" and I think describing it as counting is perfectly valid - being able to distinguish between 1200 and 1300 steps would involve some form of "counting" in my mind, whether in the brain or by some physical mechanism.
Math isn't just about a bunch of numbers. Push down automata can count (I know, it's incredible! Even more so considering they have no fingers) The program as I heard it basically described a behaviour which could easily be simulated via a push down automata.
As a drummer, you might be so accustomed to a particular rhythm that you don't count it out in the literal sense of counting out loud, but you do put eight strikes into a measure. Whether you acknowledge that as counting or not, it is still counting, it is just counting that you have become so accustomed to that you don't consider it counting because you need to reframe it in a different context before you can acknowledge to yourself that you are counting.
Rather than using your own logic to falsify the scientist's hypothesis, perhaps you should have listened to the details of the experiment and observed the results. You might have found a superior but alternate explanation, in which case you would have expanded the realm of possibilities a bit. You might even be able to suggest a follow up experiment to differentiate between the counting hypothesis and your alternative to determine which is more correct.
I take it that you haven't done much with functional programming languages, as there are often certain types of problems that are more easily solved in functional languages by counting in the manner of "one one one one one" (as five) than by actually storing a five.
And while I'm at it, trade doesn't require counting. Bartering might involve counting, or it might simply be a swap of my fishtank for your LP collection. However, the idea that we knew counting would be good for trade so we developed counting is a cunning bit of mental gymnastics; it's the mental equivalent of putting the cart before the horse.
It's still not counting, though it can reproduce the effects. A calculator doesn't actually count (it's just bit switching), but it reproduces the effect. Granted it means that whatever it's doing can simulate the effect of basic counting, but it in no way represents the understanding of numbers
Well, this is science. These researchers had a hypothesis that ants can count and devised an experiment to test the hypothesis. Based on their assumptions, the evidence from the experiments support their hypothesis.
Your hypothesis is that it's not counting but something else. It seems the next step is for you to devise a way to isolate counting from doing a counting-like behavior in ants and do an experiment to test your hypothesis.
However in a way, you're just playing with the definition. What does "understanding of numbers" mean? And is it really integral to counting? If you use pacecounter beads (Ranger beads: http://www.instructables.com/id/Army-Ranger-Beads/), you are "counting" on a piece of string but not actually keeping numbers in your head. In fact, the whole point of those is that you don't have to keep track of numbers because it's hard to do when you're exhausted and have all the other soldier-things to keep track of. You could use these beads to go out some distance, turn around and come back the same distance. You wouldn't have to use numbers in your head, but counting is still being done.
I admit I'm not a drummer, but I have played other instruments - surely if we're talking about an entire song rather than one bar, the person still has to count lines/bars (e.g., this bit happens 4 times, before going onto the next bit, and these two sections alternate two times)? This would be especially true if the drummer was playing on their own, without being able to rely on listening to the music.
Ants can count. The reason it sounds uncomfortable is because it might imply a comparison to how humans count - we do it using our sentient mind. I doubt that this is the case for ants. But even if it's done by some automatic mechanism, I don't think "counting" is unreasonable (I mean, we say that computers can count, even if it's just following an automatic process that a human set up).