Thursday 7/19/2012

Do animals have the intelligence to match the wits of humans? Well, a new study may in fact support this claim. A new paper in the Proceedings of the Royal Society A of U.K. entitled “Do dolphins benefit from nonlinear mathematics when processing their sonar returns?”, written by Prof. Timothy G. Leighton of the University of Southampton, Paul R. White, and Gim Hwa Chua, has evidence that shows that dolphins may be using “nonlinear mathematics” to help it find and catch fish.

So what is “nonlinear mathematics?” By definition, it is a field of math that involves functions that are not directly proportional to each other. Many of us have dealt with nonlinear math in high school. Those ”polynomials” that plagued Algebra class and those ”differential equations” dreaded in Calculus class are all examples of nonlinear mathematics. It is used in fields such as chaos and wavelet theory, which analyze random values. 

Now, you may be pondering, “Dolphins use calculus to find food?” This may seem a very complicated way to eat, but the answer is no. If dolphins were that smart, then the situation would be reversed and dolphins would be writing articles on genZbuzz about how humans are using math to catch fish. Instead, dolphins are using a clever ability known to many as “sonar” echolocation. They emit sound waves which bounce back to the receiver. On their way, the waves will be disrupted by objects, like fish, and dolphins can detect these disruptions to find food.

Yet, it is not that simple. While Leighton was watching the Discovery Channel’s “Blue Planet” series about oceans, he saw what looked like dolphins and other marine mammals creating bubble nets while they tried to catch fish. Why was this? Those bubbles would disrupt human sonar devices and should disrupt the dolphins’ too, right? Well, if that was right, then how could dolphins catch food? The bubbles were intentional; they blinded the prey and assisted the dolphins. Here is what Prof. Leighton theorizes.

Bubble Processing Scheme: The gist is that dolphins emit 2 pulses with different amplitudes, receive the echoes and can add or subtract the echo pulses to find targets but discriminate between fish and bubbles.

Dolphins will emit a train (of length 2 N) of separate echo pulses within a period tau and time t. The first pulse can be called c₁(t) and the second pulse will be c₂(t) but will have an amplitude multiplied by a factor G. Therefore, c₂(t) = G c₁(t). Impulse response is h(t) and the received signal is

The convolution by the bubbles to the incidence and impulse equations can be modeled as

The dolphins will use matched filters to detect these signals. Therefore, with the outputs of the matched filters for  y_k(t) set as Y_k(t), then the dolphins will have to use a set of 2 formulas to calculate the pulses with bubbles to find food.

P₊ allows the dolphin to find the targets using the pulses. P_- allows the dolphin to make sure the target is a fish and not other disturbances, like bubbles.

Now, this new discovery begs the question, “Are Dolphins Mathematicians?” According to Prof. Leighton’s research, yes. Dolphins are calculating nonlinear sonar pulses to find fish (quite a few humans would probably not be able to handle this kind of mental math). Wow. In 50 years, could dolphins be trained as pets and do math homework for students? Well, who knows what evolution could do? Actually, the dolphins just might.  genZbuzz out.