The Holographic Brain
About the Legacy of Karl Lashley, Donald Hebb, Lloyd Jeffress, Karl Pribram and Andrew PackardGerd Heinz, 2019
How does our brain work? How to understand nerve nets (Nervennetze)? In the last two centuries scientists found out a lot about nerves, synapses, transmitters and details. Although we find thousands of papers about Artifical Neural Networks (ANN), up to now we know very less about, how nerve nets work. So let's start to think about nerve nets.
Signal processing needs correlations for all kinds of signal reconstruction. Demodulation and radio reception use auto-correlation. Every clock input of any integrated circuit or flip-flop can be seen as a correlator input. All artificial neural networks on computers ("Neural Networks (NN)" or "Artificial Neural Networks (ANN)" or "Time Delay Networks (TDN)") etc. will not work without such correlating clocks.
But nerve nets do not have any clock synchronization. How could our cortex work? Can ANN model nerve nets? "Artificial Neural Nets" seem to show a different behaviour compared with the behaviour of nerve nets, I called "Interference Networks" (IN) to avoid collisions with the name "Neural Network", that stands for artifical networks.
Interference nets or systems have a comparable mathematical-physical background in different fields, reaching from photonic wave interference in optics over signal interference in digital filters (FIR, IIR), wave interference in Radar- or Sonar- devices to ionic pulse interference in nerve nets. Special properties are short wavelength, relative timing and non-locality of function.
If we demonstrate interference circuits with pulses - please keep in mind, that we talk about likelihoods of density modulated pulse streams. Also beware, to consider an n-dimensional nerve net in 1D or 2D as the examples may imagine!
As Karl Pribram noted, the ideas of "interference" and "holography" for nerve nets were introduced 1942 by Karl Lashley for the interpretation of his rat experiments, see this note.
1947, at the University of Texas in Austin Lloyd A. Jeffress published a circuit for sound localization. He did not name it "interference circuit", but it works like this. It was the auditory circuit of a barn owl, trying to interprete the horizontal localization of the ears by noise coincidence. The circuit can give an intuition for the development of acoustic photo- and cinematography.
Thinking about the pulse-like character and the slow pulse velocities on nerves we find properties, that are comparable to optical projections (images). In contrast to ANN, our IN get highest importance for projections of images through nerve nets. "Thinking" is only possible "in images or signs", not in numbers or bits. Or as C.S. Peirce (1837-1914) noted: "All thought is in signs".
At Christmas 1992, the thumb experiment showed, that our nerve system can work as an interference system. Now the door was open! After this successful experiment, I observed different properties of "waves on wires" in the first book about (nerve-) interference networks, written in the book "Neuronale Interferenzen" (NI93). Find a short overview about the results here.
To get interferences, we need something like "waves on wires". Can we observe such waves at any nerve net directly? Indeed, we can! Andrew Packard found 1995 color waves on squids. He cut the spinal cord at one side. Standing color patterns changed to colored waves of excitation, see his movies. The "Packard Glacier" in Antarctica is named for him.
How can an interference net look like? The next circuit (source NI93) shows a simplest. (In IN the wires have limited velocities - they are not electrical nodes!) A neuron in the sending space S may fire subsequent at position P. Pulses run to and over both channels A and A' into the receiving space M and meet at P. At all other locations the pulses appear one after the other, not at the same time.
That receiving neuron gets the highest excitement value, where both sister pulses arrive exact at the same time. When the neuron at P fires, this is the neuron at location P'. We find: A biological interference network can transmit information only as a mirrored projection from generator space P into detector space P'. If we cut channel A, every projection disappears. If A gets a static high level, we find waves from A' going thru the detector space. Now we understand the waves on Andrew's squids.
So Lashleys hologramm-idea, Jeffress auditory circuit, Packards waves on squids, my thumb experiment and an image-like behaviour show the direction of nerve network research: We have to study wave interference circuits. That are circuits, that produce projections (like optical images) on wires without any clock synchronization.
Thus, my research followed parallel two directions: the reconstruction of nerve data (EKG, EEG, ECoG) and of sound (acoustic images & films). Following this way, in a small team together with Sabine Höfs and Carsten Busch we got in August 1994 first passive (standing) acoustic noise images applying microphones to a EEG-data recorder and using the first interference network calculator (our "Bio-Interface") for the reconstruction of acoustic data.
It was the birthplace for Acoustic Photo- and Cinematography (Acoustic Cameras), rewarded by innovation prices and producing hundrets of jobs worldwide.
A further technical background of interferences we find in the maths of Faltung (Convolution) of noise signals, usable for invisible RADAR or in the nerve system. So lets have a closer look behind the idea of interference integrals and interference patterns.
With his rat experiments, Karl Lashley found a hologram-like property of the brain. Independently which part of the brain he removed, rats could remember a before learned behaviour, published in subsequent papers since 1929. In his 1950 paper "In search of the engram" (source p.478-505) he wrote:
"It is not possible to demonstrate the isolated localization of a memory trace anywhere within the nervous system." (p.501)
As Karl Pribram noted, for fun he said once, that his rats experiments verified, that the memory of the rats is not localized within the cortex. In the same time, Denis Gabor experimented with Holography.
1995 the reconstruction of different time functions of burst showed hologram-like patterns as a immanent property of IN, see the first image. They appear as a law of nature by cross interferences around the locations of self interference, more about cross interferences see here. (Comment 2019: It is a shame, that I found this law 1995, in that time not realising, that this will become mutually the most important law of neuroscience). We had talks with Karl Pribram (1919-2015) about this topics. He sent me at that time this preview about some important details:
Lashley 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 Donald Hebb's book ("The Organization of Behavior", 1949) 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 Being', 2004, Ch.12: 'Brain and Mathematics', page 217 ff. See his preview, page 4 ff)
The point of conflict was the following. Donald Hebb wrote in his book:
"When one neuron repeatedly assists in firing another, the axon of the first cell develops synaptic knobs (or enlarges them, if they already exist) in contact with the soma of the second cell".
This observation became the target idea for learning algorithms in (artifical) neural network theory (NN, ANN).
But why was Hebb "correct in all his details, but oh so wrong"?
It took 45 years, to find a precise answer. It was: "Delays dominate over weights". Learning is only possible, if the delay structure of the network forces interferences to the neuron, that shall be able to do something or to learn.
What is that supposed to mean? Let's look at the last picture again (which served as the cover picture of the book "Neural Interferences" from 1993 - NI93). Every impulse coming from the sending field S reaches every neuron in the receiving field M at some time. However, if a high threshold value has to be exceeded in order to activate a receiving neuron, then pulses arriving at the same time have an advantage. That is why we have to focus only on this case. Therefore, only those cases are shown in which two impulses from above at the same time reach a neuron below.
So far so good. But what does that mean? The leftmost sending neuron can then only send a message to the rightmost receiving neuron (which can be learned or processed by this neuron). In general, it is not able to send a message to a receiving neuron that is also on the left site or in the middle: The delay structure prevents this. While the cables laid between the buttons and the bells establish the communication link in a doorbell system, in an interference network only the delay structure establishes the communication between sources and destinations!
So if a neuron (due to the delay structure of the network) does not have the place to receive the partial impulses from a source at the same time, nothing can be learned from a transmitter! In other words: Weight learning is impossible without the appropriate delay structure. A deeper background is, that neurons may not be excited by their direct neighbors. In order to prevent self-excitation of the entire network, delay structures also create neighborhood inhibitions without doing anything.
Although he could not express it clearly, Karl Lashley had the right intuition!
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