Mystery of the Sonar of Dolphins?
Videos of Simulations
To know a solution exists can be a giant step towards finding a solution. -- Anonymous Mathematician
I knew in 2001 that a "clicking" dolphins can "see" an object in the dark by means of echoes of those clicks. Later, I surmised from simulations, and found reports to verify, that a dolphin can "see" in t
he dark via clicks of another dolphin. Someone, back then, in biomimetics of the Office of Naval Research, was saying that no one knew a mechanism to explain how such "vision" could be possible.
Using the US Patent Office, I published an hypothetical biological mechanism and also some possibly practical ways to compute images from echoes of clicks like those of dolphins:
The methods of solution proposed here begin with this idea:
rather than their ears, torons compare times-of-arrival ("toas") of echoes that arrive at echotrigger sensors in their jaw (perhaps just in the chin).
Experiments with my simulators suggest:
A new invention, spun-off from more general developments, is that of a simply-built improvement on existing fish-finders:
Mathematics of the Sonar of Dolphins
This new computational method for sonar and radar, Feature-Based Passive, FBP, enables computation of an image, of sorts, from a single
"click," like that of a dolphin. The waves used for imaging are not limited to sound. Ideas for applications include
A parallel-processing approach is suggested by the Echotrigger/Toron Theory of the imaging sonar of dolphins.
Since the mathematics applies to waves other than those of sound, a new name, wavar, has been adopted to refer to the wave-related principles and methods shared by sonar and radar.
Wavar, here, is being developed using "experiment-machines" -- simulations software for rapidly crafting and running experiments in extracting visual from information from waves.
The approach is "geometric" in that its calculations use Geometry and not methods of the sophistication of, say, Fourier Analysis.
The new (I think) and simple signal-processing methods herein are "feature-based" and "passive" in that they use times-of-arrival of known features of particular waves and can use, but do not require, knowledge of time and place of emission of those waves. One dolphin can "see" by means of clicks made by another dolphin.
It seems that in most species of toothed whale, for which sonar-clicks have been recorded and graphed, the clicks all have one prominent instance of a feature that I call a fang.
|One might wonder if the scope of potential applications of geometric sonar includes sonar, radar, exploration-seismology, and medical imaging?|
Sonar of Dolphins
Abstract: Hypothetical Neurons.
Sample Program for Experimenting.
FBP with Dual Clickers.
Baleen Whales MUST have sonar?
Odds and Ends.
"Sonic Imaging," presented at a meeting at Tulane University in 2005. The accompanying animation (2005, below) represents the possible functioning of a "fish-finder" -- it only operated in active mode.
Latest Abstract 2018
(also given at the top of this page):
Each of these animations was generated frame-by-frame from outputs of a simulator.
Animation of active sonar at Tulane in 2005.
A first animation of FBP, April, 2013. Uses passive in the top view, active in the side view.
Cleaned-up FBP images, simply obtained (2013).
Animation of purely passive Feature-Based sonar, May, 2013.
No animation is yet, in 2018, available for the newer methods that allow reduction of the diameter of the array to that of the chin of a dolphin.
This web site was begun in April, 2013.
This page of the site was modified on