Dolphins appear to do nonlinear mathematics

[Jim__]

Interesting story. No matter how they do it, it indicates some sophisticated neural processing. From MSNBC:

...

"These dolphins were either 'blinding' their most spectacular sensory apparatus when hunting — which would be odd, though they still have sight to reply on — or they have a sonar that can do what human sonar cannot. ... Perhaps they have something amazing," he added.

Leighton and colleagues Paul White and student Gim Hwa Chua set out to determine what the amazing ability might be. They started by modeling the types of echolocation pulses that dolphins emit. The researchers processed them using nonlinear mathematics instead of the standard way of processing sonar returns. The technique worked, and could explain how dolphins achieve hunting success with bubbles.

The math involved is complex. Essentially it relies upon sending out pulses that vary in amplitude. The first may have a value of 1, while the second is one-third that amplitude.

"So, provided the dolphin remembers what the ratios of the two pulses were, and can multiply the second echo by that and add the echoes together, it can make the fish 'visible' to its sonar," Leighton told Discovery News. "This is detection enhancement."

...

[ananda]

1. Wow

That's fantastic!

[leveymg]

2. When you think about it, all senses involve nonlinear calculations.

Taste for instance has multiple components -- sweet, sour, spicy (hot), and umami. “Umami” is a Japanese word umai (a Japanese word meaning 'delicious' or 'savory'; not 'meaty') -- that the mind has to separate and calculate in determining whether we "like" something or not, and to what degree in relationship to one or more food and beverage flavors in our mouths at the same time.

I'm not sure that dolphin sonar "pinging" is actually more complex. What is certain is that sensory judgments and distinctions are faster and perhaps more complex than mathematical calculations.

[Jim__]

6. I agree that the brain does complex calculations, but I'm not sure why you would expect taste to be

non-linear.

Taking what you've said about taste, there are 4 different tastes - I believe these map to 4 different types of taste receptors, call them t₁, t₂, t₃, and t₄. I would expect the initial processing of these tastes to be something along the lines of:

n₁t₁ + n₂t₂ + n₃t₃ + n₄t₄ = taste

where the n₁, n₂, n₃, and n₄ are the firing rates of the various types of taste receptors.

Whereas the description of the processing of the whale sonar describes it as having squares in the computation - this, of course, refers to the mathematical model of the process:

"So, provided the dolphin remembers what the ratios of the two pulses were, and can multiply the second echo by that and add the echoes together, it can make the fish 'visible' to its sonar," Leighton told Discovery News. "This is detection enhancement."

...

The second stage then involves subtracting the echoes from one another, ensuring that the echo of the second pulse is first multiplied by three. The process, in short, therefore first entails making the fish visible to sonar by addition. The fish is then made invisible by subtraction to confirm that it is a true target.

[Ichingcarpenter]

3. So Long

Hitchhiker's Guide to the Galaxy "trilogy" written by Douglas Adams. Its title is the message left by the dolphins when they departed Planet Earth just before it was demolished to make way for a hyperspace bypass, as described in The Hitchhiker's Guide to the Galaxy.

[longship]

4. +1000

DNA forever!

[JDPriestly]

5. I have always theorized that singing is an exercise of mathemats.

We hear the overtone series -- which is the mathematical relationship between the vibrations of different tones -- and calculate what we should sing next. This is particularly true when people sightread what they are singing. They calculate the interval in the overtone series that the notes represent and then form the appropriate use of the muscles, breathing, etc. used in singing to get the tone they want.

Singing is quite complex really.

And then what goes for singing goes for sports. When you play golf, you do some sort of complex calculation as to how hard to swing, how to hit the ball, where you want it to go, how far that is . . . .

You get the picture. We use a kind of subconscious math we are not even aware of in our lives. If you wish to carry it that far, every step we take is based on some sort of calculation of the distance we need to stride. We may not be thinking in terms of the numbers that we use, the words we use, to count, but we are doing math.

So it would not surprise me to learn that other animals including dolphins do this too. Have you ever watched a squirrel or a cat calculate how far it needs to jump to reach from one perch to another?