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Heinz, G.: Neuronale Interferenzen.
Personal distribution, 1993, 301 p.


(Google translation with corrections)

Information can only be linked to one another if they are present at the same time at the same place. For example, digital gates in the PC or smartphone require two signals to be linked to be statically connected to the inputs of the gate for a certain time. Computers therefore have a clock and a clock frequency. The duration of the signal "clock = high" defines the smallest possible time unit of any processing. After the clock has elapsed, all signals must be stably connected to inputs.

While wires and circuits (ICs) transmit every signal in the computer with about one tenth of the light speed, nervous networks are a million times slower. They have no tact for that. And as if that were not horror enough, the signals are pulse-like. We speak of "spikes".

If we try to match two spikes with an AND gate, they rarely arrive at the same time: the gate output will remain silent. Digital circuits do not work properly with spikes. Especially when the lines are as slow as our nerves. Information can only be processed where they are present at the same time. Nerve networks obviously do not function as our computers. But how do they work?

To find out how nerve networks might work, let us imagine that each nerve branches in many directions. If we are now looking at two spikes that are roaming in different nerves, we surely find a place where they meet. If a nerve cell is present at this point, it will be excited.

In contrast to the computer in which logic levels (0 or 1) determine the information content, the location of the simultaneity of the coincidence of different spikes determines information in nerve network. So it is difficult to reproduce nerve networks with a computer.

If one thinks these thoughts for a long time, one discovers the principle behind this behaviour: nervous networks can only communicate "projective", image-like, never static as a computer. This explains, why children need years to learn the Einmaleins. Or why memory artists have to invent a (image-) story in order to remember a few playing cards: We have arrived at the interference networks. Like in a photo, the information content is the sharpness of the projection. Waves form images and vice versa - optics and acoustics flow together under the umbrella of the "interference networks": "Sehend Hören" stood 1996 on the first, acoustic camera.

It is a miracle, that Karl Lahley ("In search of the Engram"), who had become very familiar with his rat experiments, had already begun to think about interferences in nerve networks. I unfortunately discovered the following quotation after Karl Pribram's death in January 2015. Karl had sent me half a year before some essays:

    "Lashley (1942) had proposed that interference patterns among wave fronts in brain electrical activity could serve as the substrate of perception and memory as well. This suited my earlier intuitions, but Lashley and I had discussed this alternative repeatedly, without coming up with any idea what wave fronts would look like in the brain. Nor could we figure out how, if they were there, how they could account for anything at the behavioral level. These discussions taking place between 1946 and 1948 became somewhat uncomfortable in regard to Don Hebb's book (1948) that he was writing at the time we were all together in the Yerkes Laboratory for Primate Biology in Florida. Lashley didn't like Hebb's formulation but could not express his reasons for this opinion: "Hebb is correct in all his details but he's just oh so wrong"."
    (Karl Pribram in 'Brain and Mathematics', 1991)

The author noticed in 1992 incidentally, that pulses, combined with very low propagation speed of nerves, produce an unknown kind of communication and information processing. The delay of needle-sharp pulses causes information to be processed only where pulses meet. Temporal patterns thus become spatial codes. Pulse waves spread through various nerve fibers. Where a pulse wave interferes with itself or with another, its goal is reached. Or where different wave fronts meet. A theory of waves in the time domain was to be developed as well as a theory of waves on discrete and inhomogeneous spaces. The term 'Wave Interference Networks' emerged. In the manuscript ideas are sketched on the way to this unknown computer science.


In 1992 research on "neural networks" (NN ~ Neural Networks, now ANN ~ Artifical Neural Nets) was at a turning point. Faith and funding slowly dried up. Technicians declined from NN because their learning habits were not verifiable, biologists was the given access very mystical, see above. Remembering the tanks of Neil Fraser, partially catastrophic success of teaching capabilities brought the end. The so-called "connectionism" remained as a mathematical / informatical discipline. For the interpretation of nerve networks, ANN lacked something. Matrix-like, clocked "artifical neural networks" violate the space-time structure of a nerve network to be modeled, which leads to catastrophic modeling errors before starting the work.

Digital filters use the temporal dimension, networks the spatial. In nervous networks, however, both dimensions are interrelated: the larger the length of an axon or dendrite is, the larger the distance between two neurons, the higher is the delay time. Consequently, the delay-time structure in the nerve network is determined by spatial distances and vice versa.

Thinking about complex, three-dimensional IIR filters without central clock system, nervous networks represent n-dimensional digital filters. Clocking is replaced by the actual network topology. In order to recognize properties, the concept of "interference" known from optics appeared as the smallest, common denominator. Information is processed where waves arrive in high, relative simultaneity. As a result, these networks were called from 1996 onwards as "interference networks" (from "to interfere" ~ overlay) .

As early as 1992, the realization came, that (nervous) pulse projections (images) could be mapped, if at all, then only mirror-mirrored (see title page on the right). The relativity of the pulse propagation appeared as the addressing principle in neural space, see in chapter 6 the "thumb experiment" of 16.12.1992. Unknown aspects of a neural informatics far away from computer science were indicated.

Mirrored images were known in practice from optics and nerve experiments (Penfields Homunculus, Jeffress soundorting), but they were not discovered in the literature of neurocomputing, which already contained tens of thousands of essays and hundreds of books. System theoretically, something was wrong with the so-called neural networks. So began a search.

With the discovery of mirroring pulse images, it was necessary to explore the physically real possibilities of these "delaying networks" and to "try" their properties (zoom, movement, interference overflow, conjunction and decomposition, overestimation, n-dimensionality, spatio-temporal coding, ...).

These studies have been successful. They led to the manuscript in a very short time. For example, seeing and hearing are intertwined with each other through investigations into self-interferences (visual cards) and to cross-interferences (listening cards). This finding formed the basis for the development of the first, acoustic images and films between 1995 and 1996 and the acoustic imaging (Acoustic Camera).

As a paradigm shift, it was necessary to change the direction from a mathematical point of view to a physical, discrete, wave-theoretic view to nervous networks (pulse waves on guideways) in the shortest possible time.

Interference networks can be discovered in a variety of tasks ranging from optics to digital circuits, radar, sonar, GPS, beamforming, neural networks, and signal processing. Digital circuits, state-of-the-art automata, digital filters, pattern or weight networks (classical neuronal networks) represent subgroups with discrete timing. Since this knowledge is already imparted in the book, it is self-evident a vision of a more abstract system theory, the theory of interference networks. The diversity of the affected knowledge areas is formally pushing for a theoretical basis of a more abstract nature. Like digital filters, Boolean algebras are only a subset of interference networks.

In the book are some sections, which today are considered to be overtaken. In 1995, for example, Teuvo Kohonen** questioned the use of the term "convolution" (for example, in Ch.6, page 147). Here we come across a peculiarity of interference systems, which may be the cause for the complicated access. While the multiplicative, one-dimensional interference of two impulses on a line (sciatic nerve experiment, Ch.6, p.144) resembles the mathematical terminus "Faltung" (convolution integral), be it, as it is, we completely have to renounce the notion of convolution in the two- or three-dimensional space. The one-dimensional view (convolution) corresponds to an analytical approach of field theory, the limit of which is reached in higher-dimensional spaces; here, numerically different approaches are required. First aapproaches for projection and reconstruction (as the basis, for example, of acoustic photo- and cinematography), were laid with this book, compare the image at p.284, Mask Algorithm, Ch.14, with the DAGA2007 publication of the acoustic camera algorithmus. A distinction between interference integrals and convolution integrals could later be presented in Bangkok 2011.

Since publications of algorithmic nature stands against commercial exploitation of the results since 1994, e.g. against the first acoustic camera developed from it, publications were very hesitant.

A core outline of the manuscript is for example: nervous networks can only be adequately simulated with a three-dimensional, electrical network simulation. Each network node requires space coordinates. Each branch requires a delay (delay). All delays that can be read from the three-dimensional structure of the nerve network are to be depicted exactly: They form the function essentially ("form codes behavior"). Naturally, static (stimulating or inhibiting) synapses and threshold parameters must also be observed.

Successes emerged with a first application for acoustic imaging two years later (1995): the world's first acoustic images and films were created using Sabine Höfs' "PSI Tools" (Parallel and Serial Interference Tools).

The book manuscript was written with Lotus AmiPro 3.1 under Windows 3.1 (1988-1994). Unfortunately, paragraph formatting only worked correctly up to Windows 98. Corrections could therefore only be worked on until the turn of the millennium. The date specification in the cover is inadvertently set to 'File Creation Date'. The manuscript was made from own resources. It had to be terminated in May 1993, since from 1.6.1993 a new job arose. Complements and corrections followed until the beginning of 1994 (for example the section on the Schleiereule in chapter 1 (Jeffress place theory of sound localization, 1948). Mark Konishi*** published the thoughts of his teacher, Lloyd A. Jeffres in September 1993.

The original chapter 10 (Interference logic) was wrong in the approach. It was replaced (about 1996) by the chapter "Elementary functions of the neuron" after simulative verifications with Puschmann and Schoel (1994), see also the original table of contents of 1993. The index also contains old references.

The book was actually a working manuscript. Contexts and ideas should be noted. Including all images and formulas written in one hundred days (January 1993 to May 1993), it is immature in details, conceptions are still uncertain, it is euphoric now and again, without the reader always being able to comprehend this. It shows vividly in which turmoil a new field of knowledge unfolds. In short, one misses the rounding of mature works. Nevertheless, it still appears to be legible today. Many general findings are still brand-new. Thus, by 2016, it is still not known that a course about "interference networks" would be given at any university. This is sad to the extent that an elementary understanding of the nervous system becomes possible only when a student has mastered the foundations.

To speak with T. S. Kuhn*: The manuscript, in retrospect, shows the obstacles of the way, but not the splendor of the abstractions. It is more suitable for science historians than for students. Nevertheless, it is historically the book to which we owe acoustic imaging and to which we are gradually indebted for a consolidation of neuro-research.

Since still no real book is written (it would probably be too early), this work manuscript will remain on the web as long as nothing better appears. Often the way is the goal.

Contents (pdf)

Ch 0
Ch 1
Ch 2a
Ch 2b
Ch 3
Ch 4
Ch 5
Ch 6
Ch 7
Ch 8a
Ch 8b
Ch 9a
Ch 9b
Ch 10
Ch 11
Ch 12
Ch 13
Ch 14
Ch 15
Ch 16


Contents (html)

Wave propagation 1
Wave propagation 2
Projections without change of refractive index
Projections with changing refractive index
Special projections
Run-time wires
System optimization
Time functions
Code selection with run-time wires
Visualization of waves 1
Visualization of waves 2
Basic functions of the neuron
Colored interference systems
Biology-near modeling
Analytical aids
Average value, correlation, convolution
Protection and legal usability


* Thomas Samuel Kuhn: The Structure of Scientific Revolutions. Uni Chicago Press, 1962
** Kohonen, Teuvo: http://www.cis.hut.fi/research/som-research/teuvo.html
*** Konishi, Mark: Die Schallortung der Schleiereule. Spektrum der Wissenschaft, Juni 1993, S.58-71

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