State Machines and Interference Networks


Aural location of the barn owl

According to a paper of Masakazu Konishi [1], Lloyd A. Jeffress [9] gave a basic circuit in 1948 , which describes the acoustic location principle of barn owls (Figures 1 and 2). It is Mark Konishi's credit for popularizing the Jeffress approach in 1993.

This fundamental circuit, today we would call it an "intermedial interference circuit", shows important features of biological informatics in a new perspective: a correspondence between a place and the transmitting time functions, a connection between code in space and time.

Regarding Jeffress Figure 2, Mark's version in Figure 1 represents a simplified version of Jeffress. And he wrote about sinusoidal sound waves rather than pulsating or noisy time functions. The problem with sine waves is the emerging one cross interference pattern, which makes it difficult to locate a source.

Fig.1: Drawing [1] from Konishi's noise location, 06/1993.

The function: If a sound source lies on the line of symmetry between both ears, the signals converted into nerve impulses in the ear ("relay station") reach neurons ("coincidence detector") in the middle of the brain at the same time. However, if the source is offset to the right, the nerve impulses meet further to the left in the brain. Let us now multiply those coming from the left and right on each neuron, i.a. With time-shifted time functions (Konishi put it more complicatedly), only the neuron in which the signals appear at the same time is excited (highlighted). For multiplication, the abstraction of assuming the pulse value as one and assuming rest phases as zero is sufficient.

We discover the following properties of an interference circuit (see also [6], [7], [ 8]:

Fig.2: Illustration by Jeffress 1947 [9] - historically the birth of a nervous interference circuit

Jeffress, like Konishi's interpretations, unfortunately refer to sinusoidal time functions that are unsuitable for modeling the nervous system. Neurons only emit pulse-like signals. See also some simulations Wave interference.

In contrast, if we look at pulse-shaped time functions (long pause and needle-shaped pulse), we see that both signal forms mark opposite properties in the interference networks: A consideration of cross interference (two channel analogy: cross-correlation) shows properties of sinusoidal time functions in explaining cross interference (harmony, music, beat, sense of time), while pulse-shaped time functions have optimal properties for data addressing and signal transmission.

However, sinusoidal signals do not occur in a nerve network; we find these more in acoustics (example acoustic camera). The nervous equivalent is represented by more or less dense pulse trains, whose geometric pulse wavelength and whose geometric pulse spacing (correspondence to the physical wavelength) varies. Geometric pulse spacing and geometric pulse lengths are the key parameters of interference networks: they determine almost all imaging qualities (for more see [6]).

Interferential data addressing works better, the less dense (sinusoidal) the time functions are. (Nerve impulses move at speeds in the range of µm/s... m/s, with typical impulse durations of 0.1 ms to 100 ms), find a Table in [8].

Konishi's circuit doesn't just work between different media. Let's assume that the space labeled 'sound space' also consists of neurons with connections to the 'relay stations'. The properties of the network would hardly change. Even then we would get a mirror-inverted excitation mapping. For this purpose, both neuronal fields only needed to be connected via more than two axons. This idea took shape (independently of Jeffress and Konishi) in 1992 and adorns the cover of the manuscript "Neural Interferences", Figure 3.

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Fig.3: Cover image of the manuscript 'Neural Interferences' [6] (1993) - a monomedia interference circuit. This simplest interference circuit provides mirror-inverted, topical projections and images between the transmitting field S and the receiving field M. In principle, delay-affected interconnects are assumed in IN.

Why wasn't anyone interested in the Jeffress circuit?

The question of why such remarkable features were overlooked for fifty years leads the computer pioneers' path back to McCulloch/Pitts.

Computer fiction emerged at the beginning of the 1940s with the works of John von Neumann and also those of Conrad Zuse. Potentials became a preferred means of conducting pathway representation. Representing delaying channels requires much more computational power than reducing a wire to a node. The Leibniz binary system (referred to as Boolean algebra a hundred years later) is abstracted from discrete and fixed values or states while omitting time functions. The invention of a "clock" (Takt) made this possible. From the very beginning, the computer is bound to values or states - to the node abstraction and to discrete points in time.

Neuroresearchers also inexperiencedly used the node abstraction of conductive pathways for nerves that is common in electrical circuits - not realizing that the transit times of the conductive pathways could become the decisive key to the computer science of nerve networks.

At the beginning of the 1950s it even became possible to allow artificial neural networks to learn (perceptron, backpropagation...) without delays and distributed runtime wires (nerves). Discretized time functions, node abstraction and clocks became popular.

As a result, Jeffress's model was probably forgotten. Only in the area of acoustic animal experiments can publications based on relative time be found in the following period, such as those by Konishi [1].

The genius of the computer pioneers in relation to the developing computer was to quantize Jeffress's interference circuit. A time function became a sequence of values, the delay became a discrete sequence of machine states. Floating time disappeared unnoticed from consideration. The state machine becomes the time-determining abstraction, not least thanks to the automaton theoretical foundations of Mealy [10], Moore or Medwedjev, the abstraction that gives birth to the computer.

Strangely enough, in 1991 it was precisely the advanced microelectronics with hundreds of thousands of transistors that initiated a reconsideration. For a prestige object of a telecommunications manufacturer (16x16 ATM switching network with 154 MHz clock and 860,000 transistors), the team realized, that simultaneity can only be maintained in parts.

The problem of all automaton is increasingly becoming the simultaneity that has to be achieved via the clock in the system under consideration (circuit, printed circuit board). This is exactly what is becoming increasingly difficult to achieve with ever larger circuits, higher clock frequencies, thinner interconnects and ever larger surface resistances (R·L/B) of the clock lines.

"Simultaneity" only applies in some areas of fast and large circuits. There must be a decoupling between them (asynchronous couplings via latches, FIFOs, etc.). (It is still unclear whether nature took a comparable path of division between synchronous nuclei and interferential circuitry with known neuronal columns.)

Fig.4: McCulloch-Pitt's representation, source [2]. Note that the flow of information goes against the direction of the arrow of the symbol, whereas today's logic inverter points with the tip in the direction of the signal

While McCulloch/Pitts began their article [2] in 1943 with the sentence:

"The velocity along the axon varies directly with its diameter, from less than one meter per second in thin axons, which are usually short, to more than 150 meters per second in thick axons..."

they concentrate on the next page on state sequences. The physical requirements already state, among other things:

2. A certain fixed number of synapses must be excited within the period of latent addition in order to excite a neuron at any time, and this number is independent of previous activity and position on the neuron.
3. The only significant delay within the nervous system is synaptic delay.

This abstraction has consequences. The continuous timeline is divided into states. At the end of the publication, terms will inevitably emerge that will characterize the new computer world, but which largely lose their reference to interference. Instead of an expression in the form of a time function:

f1(t) = f2(t-T1) + f3(t-T2) + ...

where T1 and T2 could represent floating delays caused by wire delays, in McCulloch/Pitts we only find expressions of form of state values

N3(t) :=: .N1(t-1) .v .N2(t-3)

In the original essay of the neuronal era [2], a floating channel delay Tx is rounded to i (i as an integer state). The interference significance of small delays for location assignment (Jeffress) was unknown; floating point delay times are not given any informational significance.

With regard to historically following automaton networks, we can recognize successive automaton states in the discretization. But the idea of interference, superposition, and wave fields falls by the wayside. The meaning of a delay Tx (float) as an identification of the intrinsic, continuous delay of a nervous pathway is lost. Until 1993, delays remained uninteresting and remained in the shadow of state machines - far from any relationship to wave fields, projections or time functions. (We will discuss the chapter of "delay learning" that emerged in the early 1990s later).

A time function f(t-Ti) (t floating) is replaced by a sequence of states or values N(i), N(i+1), N( i+2) abstracted with integers i - automata theory and computers could emerge. Critics may note at this point, that a border crossing f(t) to N(i) is unproblematic for large i: that shouldn't be the case be contradicted, but historical development apparently also missed this opportunity.

(I apologize for the inhomogeneity of the notations. Notations from different disciplines and periods come together here, which couldn't be more contradictory: state machines - wave theory - optics. I always try to stay close to the original).

In the later, biology-related 'Adaline' neuron model by Widrow and Hoff [3], for example, there is no longer any reference, although state sequences and sketches of neural networks also appear here. The synapse was recognized - legitimately or not - as the carrier of neuronal information with scalable weights only.

The fact that delays and waves could be just another form of expression of a sequence of automaton states only became apparent with the Thumb experiment [8] transparent. Even more modern works [4] that characterize this dilemma do not yet introduce time functions and waves. Science remained stuck in automata theory for decades.

Seen in this way, Jeffress's idea was a brief flash of thought in 1947 that was forgotten due to a lack of technological relevance.

On the other hand, the models of the Nobel Prize winners Hodgkin/Huxley (1952), which are very close to biology, could have shown a way to discover interferential projections by chance. Unfortunately, these models are so loaded with detail that even in 1993 only a few dozen neurons could be simulated at a time. The view of principle was eaten up by overwhelming detail.

In summary, the development of science up to the end of the last millennium can be characterized as follows:

On the one hand (as my simulations showed) the temporal and spatial choice of the quantization intervals has consequences for the fundamental ability to achieve a (correct) projection. Interference images are so sensitive that changing a single parameter can immediately destroy the image.

On the other hand, a reference back to biology is only possible if there is sufficient structural equivalence. However, the actual structure of a nerve network can be better translated into delay sections than into sequences of states.

Thirdly, with the help of time functions, the physical properties that characterize runtimes develop in a self-running manner. So a branching of the interconnects, the ends of which are bent towards each other, already creates a (Huygenian) double slit pattern as an interference mapping along the contradirectional interconnects (Try to realize a double slit pattern in an automaton model in a physically correct way (i.e. in space and time). It turns out that that the fineness of the time and spatial resolution determines whether simulations can be expected to produce meaningful results. The fatal effects of incorrectly discretized spatial and temporal structure on the wave field can be seen here, for example [12] study). Unnatural square waves can be seen.

In contrast to other works, the studies presented here were based on time functions whose delay Tx integrates the distance traveled. Consequently, there is no conduction potential, only (continuous) potentials and time functions of discrete conductor path locations (points) exist. If a time function travels through space, its dt is integrated according to the valid master speed v and the path element ds passed through
dt = ds/v
Accordingly, spherical waves inevitably arise as realistic propagation models of a wave front, even if these represent a poor idealization of the (severely inhomogeneous) nerve network. Realistically, one should imagine discrete (one-dimensional) waves on networks.

Target: Images of thoughts or an intelligent substrate

Topology-preserving maps and mirror-inverted projections are known from the nervous system. We know of mirror-inverted 'projections' without being able to name their causes; think of this, for example Homunculus. (Note: The concept of projection is also used analogously in other specialist areas. But here is only the (optical), mirror-inverted image of waves and their Interference integrals meant).

Investigations with pulse-propagating networks have now shown that, comparable to the mirror-inverted image that an optical space provides, for example, images in stochastically connected networks can be simulated through very precise modeling with wavefronts.

The consequences are stated: If biological systems were actually interference systems, only relatively working, interferential measuring devices would be able to get interferential reconstructions from these systems.

With PSI-tools, a measuring system was developed in the 90s that could have obtained information from a parallel runtime period and processed it interferentially. Unfortunately, the time was only ripe for the acoustic camera. At that time, multi-channel recordings from nerves could only be obtained in unusable qualities.

If fortunate circumstances are encountered, it should be possible to reconstruct the first 'images of thoughts' using PSI-like tools. You certainly shouldn't imagine using it to accurately decipher dreams. Rather, it seems realistic to assume that we find multiply distorted, interwoven runtime spaces whose mappings appear to be holomorphic in nature.

What characterizes an interference circuit?

The interference character of the Jeffress model reveals, that the means available to us with Leibniz's (Boolean, binary) algebra to determine an informational task of a nerve network are not sufficient.

In a stochastically connected, pulse-propagating network, signal processing can only take place where several pulses meet. Logical processing therefore appears located in interference networks (IN).

This means: Neighboring locations form different connections and different outputs with identical functions. Or: The limits of neurosurgery have been reached if an operation significantly changes the relative transit times of the fibers.

The problem becomes clear using the example of a collision between two cars at an intersection: a crash only occurs if both cars are in the same place in the same thousandth of a second. If we use discretized time (for example to one minute), certain crashes would not be possible. But false, completely artificial ones would emerge.

Note: A too coarse quantization of time or location completely changes the function of interference networks!

Interference simulator and measuring device PSI-Tools

Since interference networks cannot be calculated very well with a sharp pencil, a special simulator was developed in 1993 PSI tools. This made it possible to parametrically simulate the simplest interference circuits, whereby the neurons in the generator and detector field can be arranged, for example, as bitmaps of a defined resolution. PSI stands for 'Parallel and Serial Interference', which meant that the simplest projections and reconstructions could be calculated. In particular, the world's first acoustic images and films were created in this years.


Resulting excitation maps can be calculated in two ways: as interference integrals or as time-resolved wave fields (interference movies). With an otherwise identical algorithm, interference integrals are calculated in relation to pixels, while I.-movies are calculated in relation to time steps.

Each channel source and sink point can be freely selected in the space. Channel data can be easily changed, duplicated or summed in this way. The generator field and detector field are designed as bitmaps, the origin and physical size of which can be freely selected regardless of channel sources. Matrix grid, origin, speed and physical field dimensions can each be freely selected. The timing of time functions can be specified as a sequence of values in the channel data synthesis. Refractoriness, time functions and pulse distance can be specified.

Reconstruction versus projection

Every interferential projection potentially consists of three parts: On the one hand, the reconstruction of the source locations of the generator space is interesting for technical applications (Acoustic Cameras), Figure 6 (top). On the other hand, the calculation of projections is of interest, Figure 6 (bottom) in any differently designed detector spaces, e.g. for the calculation of neuronal projections. Last but not least, there is the real excitation map as the origin of the channel data (not shown).

Projection and reconstruction are intimately linked. If we run PSI tools in the standard form with inverse delays, a laterally correct interference integral (reconstruction) is created. If we use non-inverted time by inverting the time axis, a mirror-image interference integral (projection) occurs; assuming we choose identical location coordinates.

In PSI tools there is therefore a function for reversing the time functions of the channels: In the standard case, a reconstruction is calculated with an inverse running time axis (negative delays) and with the parameters of the detector space. If the time axis of the channels is also reversed, a non-time-inverted but mirror-inverted projection is created.


Figure 6: Reconstruction (top) and projection (bottom) of an excitation map as an interference integral from the same, previously synthesized time functions of the channels (channel data), PSI Tools 1994-1996.

All channels have the same delay time, the propagation speed is the same in both fields. The image symbolically expands the Konishi model to four channels. It represents an interferential mapping that answers both questions: Given four time functions (blue). We see the reconstruction of the generator space above and the projection into the detector space below. The reconstruction is used to determine the template (top) and the projection is used to calculate the image (bottom).

Imaging conditions can already be guessed here:
1) the geometric pulse length (length of the pulse wave) must be small compared to the object size to be resolved;
2) Assuming low channel numbers, the time interval (refractoriness) between two pulses must be larger as the field size. Measures of time and length are connected via media velocity (v = s/t).

Wave fiield of a projection

In addition to imaging elements, channel data can also carry noise amplitudes. The result of an interference analysis is unavoidable both imaging and spectral components. Consequently, sequential coding (phonetic images) can be calculated, as can projections and images. As with optics, the two components cannot in principle be separated from each other.

The temporal component manifests itself when pulses are applied to the field too quickly one after the other, for example because the refractory period (the recovery time) of the transmitting axons is too short. Then additional interference of a wave occurs with preceding and following (other) waves, correspondingly resulting in an aliasing pattern in the interference integral.

Figure 7: 4-channel wave field of a projection (PSI-Tools, 1995)

The image shows a projection of a four-channel transmitted scene onto a receiving field. The feed points are at the corners of the field. The time shortly after a quadruple interference is shown. See also these simulations. It becomes clear that maximum excitement can only arise at exactly the place where many waves meet at the same time. Temporal relativity of waves then encodes the function of the network.

Images of thoughts

To return to the title question: If we view time functions (waves) running through space and delays distributed on channels (nerves) as physical realities, then any IT function in intimately interwoven nerve networks is only conceivable in interference circuits (think also of redundancy): Consequently There are not only images of thoughts, but almost all conceivable processing variants in the nerve network are tied to projections (of an optical type) - i.e. to (mirror-) image-like maps: Consequently, there are only images of thoughts as universal Communication principle of the nervous system. It makes sense to assume that a motivated neuroresearcher will soon be able to prove it.

Interference networks therefore deal with properties between waves that coincide relatively in time and their interference integrals (colloquially: with images from interfering time functions).

Berlin, September 30, 1995
G. Heinz


[1] Konishi, M.: The sound location of the barn owl. Spectrum of Science, June 1993, p. 58 ff.

[2] McCulloch, W.S.; Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115-133 ([13], p.18 ff.)

[3] Widrow, B., Hoff, M.E.: Adaptive switching circuits. 1960 IRE WESCON Convention Record, New York: IRE, pp. 96-104 ([13], p.126 ff.)

[4] Rumelhart, D.E., McClelland, J.L.: A Distributed Model of Human Learning and Memory. in: Parallel Distributed Processing. Bradford/MIT Press Cambridge, Massachusetts, vol. 2, eighth printing 1988.

[5] Hodgkin, A.L., Huxley, A.F.: A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. Journ. Physiology, London, 117 (1952) pp. 500-544

[6] Heinz, G., Neural Interferences. Working manuscript, 300 pages, 1993

[7] Heinz, G.: Modeling Inherent Communication Principles of Biological Pulse Networks. SAMS 1994, vol.15, no.1, Gordon & Breach Science Publ. UK

[8] Heinz, G.: Relativity of electrical impulse propagation as a key to the computer science of biological systems. 39th International Scientific Colloquium at the TU Ilmenau September 27-30, 1994, Volume 2, pp. 238-245

[9] Jeffress, L.A.: A place theory of sound localization. Journ. Comparative Physiol. Psychol., 41, (1948), pp.35–39

[10] Mealy, G.H.: A Method for Synthesizing Sequential Circuits. Bell System Tech. J. 34, Sept. 1955, pp. 1045–1079

[11] Shannon, C.E.: A Mathematical Theory of Communication. Bell System Technical Journal. Short Hills N.J. 27/1948, p. 379-423, 623-656

[12] Alain Destexhe, Diego Contreras, Terrence J. Sejnowski and Mircea Steriade: A model of spindle rhythmicity in the isolated thalamic reticular nucleus. Journal of Neurophysiology 72: 803-818, 1994; for the fatal effect of discretized time see (PDF), specifically: (MPG)

[13] Neurocomputing - Foundations of Research. Edited by J.A. Anderson and E. Rosenfeld. The MIT Press, Cambridge MA; London UK, 1988, 729p.

See also:

Basics: historic/pressinf/bilder_d.htm

Features at a glance, movies: historic/index.htm#neuro

Publications: publications/index.htm

Publishing essays on IN was initially hardly possible. The theory of IN could not be taught, which is probably why it remained so unknown to this day. It was only the application of the IN as an acoustic camera that aroused media interest, see press pages. This is also why many of the original articles on IN can only be found on the Internet.
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