Resonance chains and new models of the neuron

Tam Hunt
16 min readJun 15, 2019

A conversation with Anirban Bandyopadhyay about new advances in neuroscience. This piece appeared originally at MetaDarwinism.

The study of consciousness is becoming more serious. From being a rather fringe field during the 20th Century it has in the new century become a more mainstream endeavor with substantial funding and many careers now being built on our effort to understand the mind, brain and their interactions.

Somewhat surprisingly, many large questions about the functioning of our psyches are still unanswered, including how memory works, or even where memories reside, why we sleep, why we dream, how free will works (or doesn’t) and many more.

And the biggest of our unsolved mysteries: what the heck is consciousness itself and how does it relate to matter and the brain?

We are on our way to answering these questions and one key to finding good answers to these longstanding mysteries is achieving a better understanding of how neurons work and how they interact. Neurons are the building blocks of the brain and our understanding of these specialized cells has improved immeasurably in recent decades.

As we’ll see below, however, there is much that we don’t know, including exactly how much computation goes on in each neuron. Some researchers, including Hameroff and Penrose, have highlighted the role of microtubules in adding many layers of complexity and computation to our current brain models. Others, like the researcher interviewed here, think that might just be the tip of the computational iceberg.

Anirban Bandyopadhyay is a senior researcher at the National Institute of Materials Science in Tsukuba, Japan, and an adjunct professor at the Michigan Technological University. He studies the brain and is creating a detailed unconventional model of the brain he calls the frequency fractal model. Anirban is on the cutting edge of research into the neuroscience of consciousness.

I met Anirban originally at the annual Science of Consciousness conference hosted by the University of Arizona, where he is a regular speaker. I interviewed Anirban by email.

My own thoughts on the nature of consciousness are detailed in a technical manner in a 2011 paper in the Journal of Consciousness, a 2019 followup in preprint here (to be followed up by a couple more papers in 2019 and 2020), and a book length treatment called Eco, Ego, Eros: Essays in Philosophy, Science and Spirituality.

What are the most interesting questions in neuroscience today?

The most interesting questions in neuroscience today are questions like: what is information, what is memory and where is it located? The synaptic junction is widely believed to be the locus of memory storage, but this may not be correct.

Neuroscience needs more effective eyes at the atomic scale to see what happens inside the neuron. The days of Hodgkin-Huxley and Sakman Neher, which led to the idea that information in a neuron is stored in the synaptic junctions only, are over. We are seeing more and more evidence that supports the idea that it is not the firing above threshold but below the synaptic threshold that plays the major role in information processing in the brain.

To reveal what is happening within neurons, we need to find elements that live inside the neuron and regulate sub-threshold firing in a sophisticated manner. So neuroscience is awaiting a major invention in the form of an “atomic eye” that would enable us to take the next quantum leap in understanding information processing in the brain at a deeper level.

Do you find philosophical questions like the “hard problem” of consciousness intriguing or useful? Where do you fall on the spectrum from idealism to panpsychism to materialism?

Whether we tag this the “awesome problem” or “hard problem” or “jackass problem,” the fact remains that unless we better define what consciousness is, mere adjective tags don’t serve much good.

I don’t consider the various philosophical positions on the nature of consciousness that important when we consider that the universe and human minds are frequency fractals that generate frequency wheels [ideas fleshed out further below]. Thus, inside the giant frequency wheel of the universe, our human minds are a [relatively] simple subset. This position may fairly be labeled a type of panpsychism because mind exists at many levels in this model of the universe.

Do you have a preferred theory of consciousness, such as Hameroff and Penrose’s Orchestrated Objective Reduction (Orch OR) theory? Or do you have your own theory of consciousness?

I am trying to derive a better definition of consciousness, and I prefer to experimentally verify sensible models of consciousness. I like Orch OR but I feel that it is too early to have a well-developed theory of consciousness because there still isn’t enough information to create one.

You stated in a 2014 interview: “Evolution is just a march to capture material or matter from nature and enrich that resonance chain.” Could you flesh out what this means?

We have an experimental laboratory where we build organic supramolecular structures. Our structures grow differently than a normal crystal. They change their symmetry over time and at various stages look very different. We have seen that when material growth is mostly incomplete, we find some of the resonance chains or vibrations are un-occupied, they need oscillators to complete this growth. What interaction enables the structure to evolve their geometry and generate new ones? We found that coupled resonance of elementary components may drive a very complex growth process. Elementary component seed A forms B, then B forms C, with each becoming more complex. The resonant oscillations of A creates a coupled electric field, which enables a new arrangement constituting B, and so on.

More generally, the drive to become more conscious is the primary drive in the universe, and this drive to become more conscious thus drives evolution. To be more conscious or more profoundly resonating with the universe is the objective of a living system. This drive results in structural modifications and we call this process evolution.

What are the most promising “atomic eyes” that are being developed for looking more deeply into neurons?

What skin is to our body, cell membranes are to a neuron. The membrane’s ionic signals are strong and cellular electromagnetic signals appear as noise in a patch clamp, for example. Most of the noise elimination is done in the hardware and software using extensive filters. Above threshold, due to strong ionic bursts, the subtle changes in the potential are not visible. Patch clamp techniques can capture ions and neutralize them to estimate the membrane potential. This is a slow process, however, so it fails to map faster signals. The technology is limited in this key way.

Atom probes can, however, capture faster electromagnetic signals and we are thus able to track and record in far more detail the signal produced in the cells with these new tools. The atom probe is our new invention. It is a needle whose front part is 0.1 nanometers sharp. We cover it with an insulated area. Then, on the top we place another metal layer, creating a three-layered nano structure. It is an advancement of co-axial cable at the nano-scale.

Orch OR focuses on microtubules as the key locus for quantum processing that leads to consciousness. Do you agree with this idea or are there other structures in the neuron that also play a heretofore unknown role in information processing and thus consciousness?

Microtubule and tubulin are extremely important for the information processing in the sub-neuronal scale, there is no doubt about this. There are, however, many other protein complexes involved in computation in neurons. For example, clathrin-SNARE complex, ribosome, proteosome, NOS (n+e), apoptosome and spliceosome, etc. These five proteins complexes are as rich as microtubules and generate equally complex electromagnetic resonance bands similar to microtubules. In a fractal structure, there are various elements that play a role in filling up the major gaps in the resonance chain of the human brain. The resonance chain connects the smallest atomic structure to the largest sub-organs of the brain.

In terms of the information processing ability of the human brain, if Orch OR or a similar model that focuses on sub-synaptic information processing is accurate, how many orders of magnitude of computational ability do we need to add in terms of creating viable human brain models?

We need a new information theory to explain the decision making of the biological system. If we consider the brain to be a computer and then calculate how many bits, and how fast is it, we may miss some key details about how the brain really works. We have proposed that the human brain does not follow a traditional Turing tape model of computation; rather, it follows a fractal tape computational model. Transitioning conceptually from a Turing tape to a fractal tape is easy: just consider that every single cell of a Turing tape also has a Turing tape inside it.

In a fractal tape-based machine, we have a single bit, and then there are bits inside of that bit. At any time when you count the number of bits, it is always one. In a fractal system, the counting is never done the way we see it in a von Neumann type computer. The ability to build a brain-like machine depends on how many frequencies make a wheel. How complex is the wheel required to include all layers of computation present in the human brain? We add layers of fractals one above the other in our model and for human brain there are 12 layers. We need at least 12 layers of wheels to model the complexity of the human brain (see figure).

Anirban’s “frequency wheel” or mandala

All memories are geometric in nature; here is a very brief summary of twelve kinds of memories that we found in the brain and how to edit them:

  1. Periodic memory: a chain of guitar strings we see mostly in DNA, proteins, periods of periods in the nodes of the string. You can edit the memory by changing the periodic length of elementary point oscillators.
  2. Spirals of spiral memory, in DNA and proteins, also in microtubules. Edit the memory by changing the twists and the number of hierarchical periods by inducing more and more twists.
  3. Vector memory, orientation of helices to make cavities inside proteins. 3D orientation makes it a multipolar complex 3D vibrational element. Edit the memory by changing the orientation of column oscillators.
  4. Lattice memory, microtubule, actin-beta spectrin network, protein complex. Change the lattice parameters to edit the memory.
  5. Chemico-electric memory, chemical transmission cycles. There are nested time cycles highly interconnected, to edit the memory, change the diameter, phase, delay or starting points.
  6. Leak density of Cavity memory, ion diffusion holes in the cellular membrane. To edit the memory change the leak density on the cavity surface.
  7. Spiral geometric memory, assembly of neurons etc. To edit the memory, change the pitch-diameter-length of the spiral.
  8. Vortex or fractal memory, memory stored in the geometric parameters of vortex. A vortex has divergence parameters and scale repeat unit, these two parameters are changed to edit memory.
  9. Nodal & polar memory: Nodes in the spinal cord brain network (nodes in a tear drop). Geometry of the shapes are changed among 8 different choices from teardrop to ellipsoid to edit nodes and polarity memory.
  10. Electromechanical phase memory: organs sync and desync like a giant molecule. This memory is edited by changing the bond length or wiring length and distribution.
  11. Multipolar loop in phase space loop memory constitutes a “hyperspace memory.” This memory is non-physical and hence not editable.
  12. Phases of phase duality generator memory: hierarchical assembly of reality sphere. This memory is also non-physical and hence not editable.

Ok, so if we view the human brain as a fractal tape-type of computer rather than a Turing tape computer how many orders of magnitude of computation do we need to add to account for these 12 fractal layers of computation? Hameroff 2013 estimated about 10^16 additional operations per neuron per second, for a total of 10^21operations per neuron per second, and a massive 10^37 total operations per second for the entire brain, which accounts for the additional sub-synaptic microtubular computational operations. Do you agree? Or are there even more levels of computation going on inside neurons than Hameroff accounts for?

When we consider the fractal tape model, we cannot count the number of bits involved. Rather, what we count is always one rhythm. Instead of bits, or 0s and 1s, you have time cycles. We proposed the frequency fractal model of the human brain and introduced a very new kind of computing that rejects the Turing machine model of computation as well as Bertrand Russell’s way of thinking (Ghosh, S.; Aswani, K.; Singh, S.; Sahu, S.; Fujita, D.; Bandyopadhyay, A. Design and Construction of a Brain-Like Computer: A New Class of Frequency-Fractal Computing Using Wireless Communication in a Supramolecular Organic, Inorganic System. Information 2014, 5, 28–100).

In our approach, you have only one time cycle or rhythm, but when you go deeper inside any point you find another time-cycle. So, there is no total number of operations per second. Those kinds of terms are applicable to those who believe in the Turing model of computing. For us, it is just one time cycle.

We argue that a user can see only the one clock in any given system and this clock constitutes a triplet of information: a seconds “tick,” a minutes tick and an hour’s tick. We have triplet clocks everywhere in all the layers of the human brain. We have already identified 350 different classes of cavities in the brain distributed over 12 layers nested one inside another. If each cavity resonator is an octave musical flute, then nearly 2,800 frequencies and time cycles compose one nested rhythm and that constitutes our total brain power. The current idea that a larger number of operations per second is an accurate approach to brain modeling is not right. That is the Turing way of thinking.

Information for us is a product of time cycles that can be modeled in particular geometric shapes. It is all about one rhythmic vibration that arises through integration of geometries using 2,800 frequencies over 10²⁰ Hz. Each vibration includes a “bing” moment (Hameroff’s metaphor for the moment of conscious awareness) and also a “silence” period. The “silence” contains the “phase”, and this holds the true information about the geometric shape of the particular time cycle. A band of frequencies always make a circular strip as it always vibrates periodically. Several such concentric circles make a frequency wheel that is an integration of the included time cycles. Such a fractal-like integration of information (FIT) is fundamentally different than other theories of consciousness such as Tononi’s Integration Information Theory (IIT). Just one bit is enough for us to model the brain’s operations.

It takes only the product of 12 primes (1X3X5X7X11X13X17X19X23X29X31X37=10¹¹) oscillators to generate all possible patterns of wheels at each layer. This is the mathematically largest number of components we need to generate our brain dynamics. Our brain dynamics model is also relatively simple, with only eight steps to convert a tear-drop shape into an ellipsoid. These eight steps are enough to replicate all cavity shapes and their dynamics in the brain. The simplicity of our approach is a major benefit when compared to other computational approaches.

Can you flesh out what you mean by resonance chains with respect to human consciousness or consciousness more generally?

Every single element in the brain is a cavity resonator and has an electromagnetic resonance band. When several materials come together their resonance bands overlap to form a chain. Since the number of cavities in a larger cavity is finite, the chain is finite in length and as the guest cavities process only the geometric information, the total phase lag is always two π. Hence there is a time cycle. So, we convert a resonance chain into a wheel layer. Many nested layers make a frequency wheel and that constitutes our model of this type of system.

What do you mean by brain cavity resonators and the geometric shapes used to model them?

For example, a cortical column is a cavity resonator. A neuron is also a cavity resonator. Inside the neuron the microtubule is like a flute and that’s also a cavity resonator. Tubulin proteins are dumbbell-shaped cavity resonators, and the alpha helices inside the tubulin protein, surrounded by beta sheets, form yet another cavity resonator. A column of alpha helices is itself a flute-like cavity resonator. Similarly, we can consider self-assembly or neural columns forming vital components of the brain, like nucleus or even hippocampus. Therefore, the whole brain is a giant leaky cavity resonator and then if we open it up we find a large number of cavity resonators inside. Our journey to open up and find the new cavities at each level continues until we reach the molecular scale.

You mention missing resonance chains in our current models. What level of physical structure are you referring to?

We consider that every single biological element is a cavity resonator or a flute. You can integrate the flutes in two different ways. First, you place them side-by-side. This is called an iterative function system type fractal. Or you can place them one inside another. That is called an escape time fractal. We can generate an analogue of any biological structure using the elementary cavities like flutes and integrating them side by side and/or “above and within”. We proposed a fusion of these two kinds of fractals as a generic approach of nature to construct an analogue of a biological system.

A fusion of escape time fractal and iterative function system type fractals made of cavity resonators are generated to create an analogue of a biological system. This analogue structure vibrates in sets of resonance frequencies. Resonance can happen in various ways, like, for example, a tuning fork vibrates resonantly following a mechanical vibration. We have identified twelve different kinds of resonance frequencies that might be operating simultaneously in the human brain to make rhythms or cyclic vibrations, as follows:

  1. Electromagnetic rhythms [carrier is the photon or electromagnetic wave, trapped in a cavity to generate beating or rhythm].
  2. Magnetic rhythm [spiral flow of electrons or ions, they are the carriers editing the magnetic flux, geometry of path forms the periodicity].
  3. Electrical potential rhythm [change in the arrangement of dipoles editing the electric field, fractal distribution of local resonators generate a time function of potential]
  4. Solitonic & quasi particle rhythm [carriers are solitons, defect in the order flows in a ordered structure, the ordered structure is edited to make a loop].
  5. Ionic diffusion rhythm, [ions are carriers, tube like cavities are formed in a circular shape or continuous path to generate a loop]
  6. Molecular chemical rhythm [molecules like proteins, enzymes, etc., are carriers, tube like cavities are formed and sensory systems make sure a circular signaling pathway]
  7. Quantum beating [spin is the carrier, wavefunctions interfere in a squeezed excited photonic, electromagnetic or spin state]
  8. Density of states rhythm [orbitals coupling, wave function modulation, virtual carrier, a virtual continuous loop is made]
  9. van-der Waal rhythm [atomic thermal vibration is looped in a spiral pathway].
  10. electro-mechanical rhythm [classical beating with a mechanical beating like tuning fork]
  11. Quasi-charge rhythm polaron, polariton [topological fractured band based continuous loops]
  12. Mechanical rhythm, sound wave [similarly elastic pathways to make a circuit of sound waves].

Now, we can put the resonance frequencies side by side, say, from 1 micro Hz to 1 peta Hz to create a chain. To understand resonance chains, just imagine that the chain of vibrations that starts from 1 micro Hz ends at 1 peta Hz. The group of frequencies arranged in a sequence for a system is the resonance chain and when vibration in the chain is repeated many times, it is a rhythm. A loop is represented by a circle. For twelve kinds of rhythms, several such circles can be put together and we get integration of that information, or what we call a frequency wheel.

How does resonance relate specifically to the nature of consciousness? Do all resonating structures have some associated consciousness?

Our mathematical model shows that when the resonance chains in the form of a frequency wheel are drawn for a system, as described above, we get a composition of rhythms. A rhythm means, say, a sinusoidal wave that propagates continuously for an infinite time. We represent it using a single frequency value, which is the inverse of the time period of the waveform. Now, how could we combine frequencies? Let’s do some simple math here. A rhythm should have at least two frequencies. Or it could have three frequencies. If it has four frequencies they can be played as a pair of two. In this way we can integrate frequencies to make various kinds of rhythms.

What are the elementary compositions? For basic rhythms, which cannot be divided into smaller loops, we need prime numbers of frequencies to couple. For example, take a pair of frequencies and combine with that seven-frequency rhythm. This is a unit now and no one could find a sub-rhythm. This is why groups of prime numbers of different frequencies link together to form the architecture of information in the biological system.

Now, let’s do some more math. Try to find how many ways one could deconstruct a rhythm made of 12 frequencies? 2X (3X2) or 3X (2X2)? Both solutions are equally possible. This is a remarkable situation: we have a giant cavity resonator, say, our brain and we have two sets of rhythms, which exist in parallel. This occurs when one hardware system generates two replicas of the particular information structure and both can edit each other. This is called the mathematical criteria for consciousness.

How many years are we from having a good working model of the human brain and mind?

We are creating the model now. We have already built one, which will be perfected over time. We feel strongly that redefining “information” and creating a new type of “information theory” is the key to move forward. We will have a good working model by the end of this year. We are writing a manuscript, and of course we will upload the entire database freely in the website, where we regularly update our research activities.

We are already building small machines to demonstrate the duality of frequency fractals as an essential feature of consciousness and we have achieved some good progress. Once we generate the two distinct information structures from a singular hardware setup it will improve rapidly. We project that within five years we will patent the most primitive conscious machine. Note that the definition of consciousness is only “self-aware” here, it means a hardware that analyzes the environment and continuously edits it’s intelligence, knowledge and learning rules.

We will never, however, be able to upload human consciousness because artificial structures cannot be a replica. It will be a new consciousness of its own, but not a replica of human consciousness. The principle that we use to build the conscious machine suggests superposition of various features one on top of another. Such an integration has a simultaneity prerequisite and that cannot be replicated in any construction process at the molecular scale. In the future, if human race masters the regulation of simultaneity, then it may be possible. Otherwise, however, we will be able to make humanlike machines, but never a true replica of any particular human

Originally published at



Tam Hunt

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