Stochastic resonance and sensory perception

In the TGD framework, subjective existence corresponds universally to the sleep-wakeup cycle defined by the periods of wake-up with opposite arrows of time defined by a sequence of "big" state function reductions (BSFRs) changing the arrow of time. In BSFR, a self with a given arrow of time dies (or falls asleep) and reincarnates as a self with an opposite arrow of time.

The TGD view, the stochastic resonance would synchronize the signals realized as amplitude modulated carrier waves with the sleep-wakeup cycle. The wakeup period would correspond to T(spont)= 1/f(spont). Stochastic resonance would correlate the rhythms of subjective and physical existence.

The basic prediction is that this synchrony is optimal when the noise level is optimum. Taking the ordinary sleep-wake-up cycle as an example, one can understand what this means. If the stimulus level is too high, concentration to a given task is difficult and problems with sleep appear. If the stimulus level is too low, drowsiness becomes the problem and the resonance with the circadian rhythm tends to be lost.

Concerning the identification of the counterpart of the white noise, there are several guidelines.

1. White noise could correspond to any signal for which the frequency distribution is constant in the time scale of modulations. The rate of BSFRs should be f(spont)= 2f. In stochastic resonance, the white noise would keep the system in optimal wakeup state.
2. Many neuroscientists believe that the rate of nerve pulses codes for the sensory input. This need not be quite true but inspires the question whether the nerve pulses define the white noise and whether a single nerve pulse wakes up the neuron. If so, then the rate of nerve pulses could correspond to f=f(spont)/2 since only the nerve pulses with a standard arrow of time are observed.

   Nerve pulse duration is about 1 ms and defines the maximum rate of nerve pulses. On the other hand, f= 1 kHz frequency is a resonance frequency of the brain synchrony and also the average mechanical resonance frequency of the skull.

3. This observation brings to mind an interesting old observation. For electrons with mass .5 eV the secondary p-adic time scale T₂(e) corresponds to frequency 10 Hz, alpha frequency. The mass estimates for the light quarks u and d vary in the range 2-20 MeV. T₂ scales like mass scale squared so that the mass scale estimate for quarks is T₂≈ 1 kHz.

   The TGD inspired quantum biology indeed predicts that QCD allows dark variants with same masses but Compton length scaled up by \hbar_eff/\hbar. Does this mean that the kHz frequency scale of nerve pulses corresponds to T₂ for quarks and 10 Hz EEG frequency scale corresponds to T₂ for electrons? If this is the case, secondary p-adic length scales for electrons and quarks are fundamental for the brain.

This raises some questions.

1. It would seem that cyclotron pulses inducing BSFRs correspond to the white noise behind stochastic resonance. The rate of the detected nerve pulses would correspond to f=f(spont)/2 and to a frequency of modulated carrier wave. Can one imagine a general mechanism for producing the noise realized as nerve pulses?
2. One can also ask whether a system could keep itself awake and in stochastic resonance in presence of the necessary metabolic energy feed. Could the system itself produce the white noise as pulse patterns and stay in a stochastic resonance with it. If so, the amount of metabolic energy could control the level of noise in turn controlling the presence of the stochastic resonance.
3. A nontrivial question is what one means with a system. In TGD, the system involves both the biological body and the magnetic body (MB) carrying dark matter associated with it. MB has a hierarchical structure with levels labelled by the values of h_eff.

The model for the communication of sensory input from the cell membrane to the magnetic body and for the control of the biological body suggests itself as a mechanism transforming sensory input at the cell membrane to pulse patterns.

1. At the level of the cell membrane, sensory input corresponds to the oscillations of the membrane potential and to nerve pulses.
2. This sensory input is communicated to the MB as a generalized Josephson radiation modulated by the variation membrane potential representing sensory input. The generalized Josephson frequency is the sum of two parts. The first part corresponds to the ordinary Josephson frequency f_J= ZeV/h_eff. The second, usually dominating, part corresponds to the difference of the cyclotron frequencies of monopole flux tubes at the two sides of the cell membrane and transverse to it. The energies involved are of the order of ZeV and just above the thermal energy as required by the minimal consumption of metabolic energy. Josephson frequencies are in the EEG range.
3. At the MB, the dark Josephson radiation generates cyclotron resonance, which transforms the frequency modulated Josephson radiation to a sequence of pulses, which define a feedback to the brain. A natural proposal is that the cyclotron pulse sequences generate nerve pulse patterns serving as the white noise.

   The rate of nerve pulses would dictate the resonant frequency f which can vary from its maximum value of kHz down to 1 Hz and even below it. The cyclotron frequencies for the body parts of the MB would thus select, which frequencies from the frequency spectrum of the Josephson radiation are amplified. Essentially, a Fourier analysis of the sensory input is performed and the spectrum would be represented at the MB.

4. The nerve pulse patterns would in turn generate a response as modulations of geneneralized Josephson frequency sent to the MB. There the response of the system to the white noise generates the white noise. This feedback loop would define a nearly autonomous system staying in a stochastic resonance in presence of a suitable metabolic feed.
5. Only the frequency modulation by the sensory input appears in this mechanism. Frequency modulation however reduces to the amplitude modulation for the membrane potentials.
6. The generalized Josephson frequency must be equal to the cyclotron frequency at a given body part of the MB. It can control by a variation of the flux tube thickness whether it receives information from the cell membrane at a given generalized Josephson frequency.
7. The failure of the communication line between the brain and the MB could cause various disorders since the MB cannot anymore take care of BB. Since the cyclotron frequencies of the biologically important ions in B_end=.2 Gauss are in a key role, the concentration of these ions in biomatter is an important factor. Lithium ions serve as a basic example. Its cyclotron frequency is 50 Hz, which corresponds to f_gr,Sun. The depletion of lithium ions in the soild is known to induce depression and even suicides.

How does sensory perception relate to the stochastic resonance in the proposed sense? The stochastic resonance would be associated with the communications with the MB and the information representable as a modulation of the carrier wave.

1. Sensory qualia would be labelled by quantum numbers measured repeatedly during the sequences of "small" state function reductions (SSFRs) between BSFRs. Primary sensory qualia would be associated with the sensory organs and the feedback from the MB of the brain to the sensory organs could generate virtual sensory input explaining hallucinations and dreams. This picture fits nicely to vision, olfaction and tactile senses, which are spatial.
2. The generation of sensory qualia at the level of sensory organs could involve stochastic resonance amplifying the primary sensory input. The sensory input would be transformed to dark Josephson radiation to the MB of the sensory organ and returned back as a pattern of cyclotron resonance pulses in turn generating BSFRs and a modified Josephson radiation but without modification due to nerve pulses.

   When the membrane potential is reduced below the critical value, a nerve pulse would be generated and lead to a processing of the signal at the higher levels of the hierarchy. The rate of the nerve pulses would determine the intensity of the signal at the higher levels of the hierarchy. Similar feedback loops with the local magnetic bodies would take place at the higher levels of the hierarchy and generate higher level representations of the sensory input. The virtual sensory input from MB would lead to the generation of standardized mental images as a pattern completion and recognition.

3. Stochastic resonance for the sensory receptors would allow code for various characteristics of the sensory input (such as colors, intensity and frequency of light or sound,...) to cyclotron frequencies characterizing parts of the MB. Essentially a generalized Fourier analysis of the sensory input locating Fourier components to different parts of MB would be in question.

Hearing is an exceptional sense in that the temporal aspect is essential.

1. It would be natural to identify the intensity and frequency of auditory qualia with the cyclotron frequencies labelling the magnetic body parts. In the case of speech and "almost heard" internal speech, the meaning of the speech represents a higher level element related to the temporal aspects, and could be associated with the communications to the MB rather than being purely spatial quale.
2. If the heard sound frequencies correspond to Josephson frequencies, why are the other qualia not accompanied by an auditory experience? A partial answer is that hearing involves the sensation of the pitch and intensity of the sound as non-temporal qualia at the neuronal level.

   The temporal aspects of hearing responsible for the meaning of the speech would naturally correspond to the modulations of the membrane potential and of Josephson frequencies. But also other senses involve this aspect. Could these aspects correspond to internal speech providing a cognitive interpretation of the experience, its naming? Could this aspect be universal and accompany all experiences? This would also conform with the fact that the oscillations of magnetic flux tubes are analogous to acoustic waves.

The 12-note scale defines a set of very special frequencies in that these frequencies have a deep emotional meaning. Also octave equivalence is a fascinating phenomenon. Could this be due the fact that these audible frequencies appear as resonance frequencies in the spectra of the cell membrane Josephson frequencies and cyclotron frequencies for the magnetic flux tubes? If this is the case, magnetic flux tubes would define an analog of an organ played by the sensory input to MB. How do these special frequencies relate to the gravitational Compton frequencies?

1. The model for bioharmony, leading to a model for the genetic code (see this, this, and this) leads to a proposal that Pythagorean scale defines a spectrum of preferred cyclotron frequencies and thus a spectrum of strengths of the endogenous magnetic field B_end. Quint cycle (3/2)ⁿ of fundamental frequency and octave equivalence would yield the 12-note scale.
2. β₀≈ 1 has been assumed for the Earth and β₀≈ 2^-11 for the inner planets of the Sun. Could β₀≤ 1 have a spectrum? Could this spectrum explain in the case of the Sun the EEG spectrum below 50 Hz frequency spanning 7 octaves (DNA corresponds to 1 Hz), and in the case of the Earth the microwave spectrum in the range .5-67 GHz?
3. I have considered the possibility that β₀ is for number-theoretical reasons quantized as an inverse integer: β₀=1/n (see this). Number theoretical constraints allow a more general quantization as rational numbers: β₀=m/n. The spectrum of the gravitational Compton frequencies would resonate with the spectrum of the cyclotron frequencies if β₀ in f_gr = β₀/GM obeys a quantization producing the 12-note scale. It would be interesting to check whether EEG exhibits 12-note scale as a finite structure realized as preferred frequencies.

Consider next the microwave hearing as a possible explanation of taos hum.

1. In microwave hearing the carrier wave amplitude, modulated in the frequency scale of audible frequencies with typical frequency in the range of EEG frequencies and therefore below 100 Hz, creates a sensation of sound. The electromagnetic signal would be amplified by stochastic resonance to a variation of neuronal membrane potentials in turn generating an acoustic signal by piezoelectric effect.

   This acoustic signal could serve as a virtual auditory input to the ear and generate a sensation with auditory qualia. The mechanism would be the same as in the case of hallucinations and dreams.

2. Assume that the frequency spectrum associated with the gravitational body of Earth (f_gr=67 GHz) spans as many octaves as that for the Sun. Assume that the frequency spectrum for Sun (f_gr=50 Hz) corresponds to that for EEG assumed to span 7 octaves (1-128 Hz). The scaling gives in the case of the Earth for the microwave scaled variant of EEG realized at biomolecular level the range .5-149.5 GHz: the upper bound corresponds to energy 1.5 meV and is somewhat below the maximum frequency 160 GHz for the frequency distribution of CMB. Note that miniature membrane potentials correspond to meV energy scale.

   If one replaces EEG range with the range of frequencies 20 Hz-20 kHz audible for humans spanning 10 octaves the upper bound for scale frequency spectrum would be 12 THz which corresponds to energy of .1 eV which is the energy of Cooper pair for cell membrane Josephson function with voltage .05 V. For bats the audible frequencies extend to 110 kHz and the upper bound would be now .510 THz and correspond to energy of .5 eV which is the nominal value of the metabolic energy quantum.

3. There are indications that also the gravitational body of Moon (with mass 1/83 times that of Earth) (see this and this) could play a role in quantum biology. The proposed analog of the EEG range for the Earth would be scaled up by factor 83 with an upper bound corresponding to .12 eV, which corresponds to the energy of the Cooper pair for the cell membrane. For the range of audible frequencies the upper bound would scale up to 8.3 eV covering visible and UV frequencies.

See the article Taos hum, stochastic resonance, and sensory perception or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.