by Douglas Moreman firstname.lastname@example.org Modified on
We thank the dolphins, because:
To know a solution exists can be a giant step towards finding a solution. -- Anonymous Mathematician
In simulations, my methods compute images from echoes of dolphin-clicks off simulated fish. This image was made by a simulator. The simulated, skeletal "fish" is shown in a side view at the bottom. The blue dots were computed from simulated echoes off the fish. The image was from an experiment in "passive" mode, wherein the click could have come from a dolphin or some other boat. In "active" mode, there would be blue dots in the side view because ranges would be computed in addition to directions. The hexagons were relevant to the array as it was back when the sequence of images was made.
The methods do not use two ear-like, high fidelity sensors, but rather, an array of several echo-triggered, touch-like sensors that might exist in a dolphin's chin. Parallel outputs of these sensors could be processed in parallel in the brain, avoiding the ears altogether. I have invented a way to accomplish the same results via serial computations.
Earlier methods were presented in my U. S. Patent "Echo scope" in 2008. New methods are with the U. S. Patent Office.
I have developed a biological theory in which dolphins have an array of echo-triggered neurons in a space the size of their chin. This has not yet been proven, or even tested. But regardless of whether dolphins actually use echo-triggers, hundreds of hours of computer-simulations suggest we can use the basic physics and mathematics to make nnd program a 3D multi-sensor time-of-arrival sonar imaging device.
A natural first application would be a fish-finder that, on each "click," computes a 3D model from which a fisherman can see where what size fish are in relation to his boat.
But, since the computational methods are not limited by the physical nature of the echoes, some military radar-applications also seem possible.
Before the Mathematics of the Sonar of Dolphins
The new methods enable computation of an image from a single "click" like that of a dolphin.
The new approach to computing images from waves has been inspired by a Multi-Sensor Time-of-Arrival Theory of the imaging sonar of dolphins. But the mathematics applies to waves other than those of sound and so a new name, "wavar," has been adopted to refer to the general principles.
The wavar announced here is being developed using "experiment-machines" -- simulations software for rapidly crafting and running experiments that probe for information in waves.
You can click here to a simulation that portrays two fish seen from 50 feet above as they cavort about each other. It is worth noting that, at each given sensor, echoes from some part of one fish arrive simultaneously with echoes from some part of the same or other fish and, so, destroy each other. Yet, the system works.
It seems that in most species of dolphin or toothed whale, for which sonar-clicks have been recorded and graphed, the clicks all have one prominent instance of a feature called a "fang."
This graph here is a stylized "click." See its fang?
A fang is a change in loudness that, for a bottlenose dolphin (Tursiops truncatus), goes from a low to a high and back to a low in about 1/100,000 second and is much greater than all the other low-to-high transitions in the click. Given a known feature such as the "fang," but not knowing the time or the place of the emission of a click, my software can, nonetheless, make a picture from simulated echoes arriving at an array of sensors from a simulated fish.
A recording of a probable sonar click by a non-toothed whale was reported by Stimpert et al. in 2007. The recording was made from the back of a humpback and not from in front of the whale. The humpback's click looked a lot like familiar, off-axis recordings of clicks of a bottlenose. The part that looked a lot like a "fang" lasted for about 125 times as long as the fang of a dolphin. This is consistent with physics and the fact that humpbacks takes bites out of vast schools of little critters, whereas a dolphin eats one fish at a time.
If nearly all species of cetacean, toothed or not, use sonar clicks that have fangs, then that might support the hypothesis that they are using multi-echotrigger, time-of-arrival methods?
That this seems plausibly true gives us confidence that our eventual tests of the concept will work.
The scope of potential applications of the new sonar include all areas of sonar, radar, exploration-seismology, and medical imaging.
Toa Theory of Imaging Sonar
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by Douglas Moreman