History and Idea of Mirroring Projectivity

The Pulse-RADAR

To understand the main idea of neural network dynamics, it seems helpfull, to remember the story of the birdth of interference circuits.

In the end of september 1992 first fog banks come nightly. When I remember well, one night in thick fog many people had been killed against an coach-ride accident. A technical idea to avoid such things is, to create a special, impulse-Radar for cars.

For cars, the old principle of a rotating single receiver and sender is not able to realize such things. Instead of a rotary antenna, different fixed, parallel antennas are to use, to mount antennas plain at the front of the bus or truck.

To create the image, the idea can be, to shift the incomming antenna data streams in opposite directions over a detector field. As simple the idea is, as complex appears the realization. Recherches showed, that it is not easy to calculate such systems. I had no tool, to solve the equations in acceptable times.

So I read books about optics and wave interference [1] as books about radar systems [2,3] to try to understand partially the physics and mathematics of pulspropagating interference systems. (It was the point to create PSI-Tools later to verify interference systems with lots of channels).

    Fig.1: a) Sketch of the system for (pulse-) Radar-images from Sept. 29, 1992. c) Single detector cell. (PhC: Phase Comparator of AND-type, Axx: Antenna frontal v, above o, down u, back h, left l, right r)

After some calculations it seemed, that a special result of such interference images is predictable: The only selectable location of interference is the point of equal delays on all possible signal ways. Only in this point of interference it is possible, to receive a highest excitement for example with AND-like gates. As more circuits I verified, as more two impression were fixed:

  1. It is possible, to turn the wires, or to change the circuit geometry. If we find a location of interference, the detecting image lays mirrored to the source space.
  2. If we compose a graph of interference locations, we find, that the graph of the detector space is mirrored to the graph of the generator space: Image and source are topomorphic.

While recherching books about neuroanatomy, I found a paper about mirrored, topographic maps in the human brain, for example Penfields so called 'Homunculus'. It appeared as a pure coincidence, that the virtual mirrored Radar images reproduced this behavior.

I realized: Nothing in nature is without reason. Even as the virtual Radar-images, the homunculus appeares mirrored. Even as Radar-images biological maps are topographic. And even as (virtual, pulsed) Radar-images, the nature uses pulses in a definitive relation to the transmitting speeds. Also the properties between pulse-length and pulse-speed and circuit geometries (geometric wave length) are comparable.

    Fig.2: One-dimensional interference circuit. An excitement at the side G generates an mirrored interference position at the other side M (circuit created in october 1992). Note the main differences to electric circuits: wires L have different tasks. Wires in interference schemes are supposed to be without attenuation, but they have a transmission speed. They are not nodes, constructed to carry currents or to drive loads. Comparable to nerves they symbolize the directed flow of time-functions from and to different points with definitive speeds or delays.

We are able to inspect interference phaenomena in simulation since august 1994. For the future, we plan compound projects with partners in different fields. Our main interest are bio-neural informatics: theory shows, that researches in this field need multi-channel data streams and interference theory in general. In this field, interferences are not to avoid to get knowledge about neural communication.

In the field of industrial usability it is possible to simulate new ultrasonic devices with very better imaging possibilities for purposes of medical and material imaging.

For free field applications in air the interference assistent is useable for loudness-localizations in the fields: motor inspection/machinery-inspection; loudness landcard generation etc.. Electrical field applications are possible to develope Radar imaging systems. Last not least for geological and astronomical research our improved interference theories appear usefull to develope better antenna arragements to improve measurement possibilities for noisy, small and far signals.

G. Heinz


  1. Alonso M., Finn, E.J.: Physics. Addison-Wesley Pub. Company 1970
  2. Baur, Erwin; Einführung in die Radartechnik. B.G. Teubner, Stuttgart, 1985
  3. Skolnik, M. I.; Introduction to Radar Systems. McGraw-Hill Book Company Inc., 1962


Dies war der -te Zugriff seit dem 10.9.1996

file created 08:04 Jan. 26, 1996; last revised 08:05 Jan. 26, 1996; stylesheet added and small redesign Jan. 30, 2024