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Part 1

the interpretation of triadic synapses as differentiators and …

but two of the four series differentiations are replaced by one sign reversal. The latter would occur at the output of the reticular thalamus (RT), which is an inhibitory cell group and therefore has the requisite negative gain….

The decay of the envelope of the oscillation is assumed exponential. If you differentiate exp(t) once, not twice, with respect to time, you get exp(t) back again, thereby allowing the function to map onto itself, with opportunities for reverberation in a cyclic system, which this is….

The shunt at the input that allows the signal to skip one of the two differentiations may be an adaptation for simultaneous analysis of exponentials and sinusoids. (...With function exp(rt), the amplitude is multiplied by r on each differentiation. Analogously, with sin(wt), the amplitude is multiplied by w on each differentiation. These growth rates would be analyzed through an anatomical map of varying attenuation and only one spot on the map would have a growth rate that exactly breaks even for a given exponentially growing or shrinking sinusoid. The break-even condition results in a rectangular envelope on the oscillation. This specific shape would be detected by the projection cell, which would respond with a progressively deepening hyperpolarization due to the inhibitory input from the RT, followed by a rebound to baseline at the offset of the signal....

I postulate that at a given self-determined tempo of movement, all poles will lie on a circle centered on the origin of the complex frequency plane. Faster tempos will correspond to larger circles, as both frequency and absolute value of rate constant increase progressively from the origin. I call this the action circle (AC). If we break the AC in imagination and flatten it out, we have the requisite one-dimensional representation. …

Lines of constant tempo on the complex frequency plane, according to the math; not as tidy as circles.

A Lecture about Math and Engineering.

Correction 05-03-2019:

Lines of constant tempo will not be circles on the complex plane but exponentials. (i.e., r = ± ω * SQRT(1/(2/(lnω - lnK) - 1)), not r = ± SQRT(K² - ω²), where K is an arbitrary real constant.) Obtaining this result begins by setting K equal to the maximum rate of change anywhere in 0 >= t < ∞ of a general Laplace eigenfunction exp(-rt)cos(ωt + φ), assuming stability and φ = 0. It is more expedient to solve for r than ω as a plotting method. The resulting lines of constant tempo are shown below for the upper left quadrant.

Caveat 02-15-2020: The solution involved inverse trigonometric functions, and I implicitly assumed that the solution could be found by examining only the principal branch….

and even the alpha rhythm, which could be the thalamic timekeeper needed to calibrate representations of tempo…

depth in the cortex. Then it is only necessary to specify that Hebbian plasticity will be especially pronounced at synapses connecting cells at different egocentric coordinates but at the same cortical depth. This sounds like a very testable prediction.

Part 2

the corresponding mature science being a future version of human behavioral epigenetics. The concept "God" is traceable to the central, fundamental role played by DNA in biology, through the filter of first-person experience. The concept "soul" is traceable to chromatin marks specific to the brain and much involved with determining the structure of society. These epigenetic marks may interact with synaptic processes by controlling the firing thresholds of neurons and/or the expression levels of inhibitory presynaptic auto receptors....

Einstein was wrong when he said that there is no absolute space; I side with Newton on this question. The null result of the Michelson-Morley experiment is due to the nature of the fields around particles of matter. I conjecture that these fields are caused by the presence of trapped, spiral waves (primary waves) that undergo Doppler effects, leading to the Lorenz contraction that cancels the Doppler effects on light (secondary waves). Huge concentrations of mass or energy cause time to slow down in the vicinity because energy is a slowing of time, in a microscopically-detailed manner. The spiral waves alluded to above are rhythmic slowings of time. The particles of matter on which they are trapped are voids in a crystal-like array of time lines. The time lines are signal sources. The bonds holding the "crystal" together define space, and form by a spaceless version of a binding process resembling Hebb's rule, originally discovered in neuroscience. The orbiting spiral waves set up an anti-correlated condition along each diameter of the trapping void, which interacts with Hebb's rule to dynamically keep the void open indefinitely. Thus, void and wave have a symbiotic relationship. A black hole is a huge void, its boundary coinciding with the classic event horizon. When a particle enters the black hole, it contributes its void volume to that of the black hole and its spiral wave to the event horizon....

Part 3

The extreme complexity of "sleep architecture" as it is called (just the plot of difficulty of arousing the sleeper versus time) may reflect concurrent activity in multiple frequency bands, each programming a different memory mechanism distinguished by a different time constant of forgetting. Since memory is a nonlinear process, we are not allowed to invoke the foundational theorem of the Fourier transform and claim that it would be more parsimonious for Nature to program all timescales in superposition.

Part 4

whereas, more speculatively, the existence of a maximum representable amount could cause clipping of wave peaks, resulting in the creation of pairs of sharp kinks. These kink pairs have interesting resemblances to pairs of bound or entangled particles. Is this the beginning of a satisfying answer to the old question, "How can a particle be a wave?" The wave troughs could also be clipped, introducing an interesting dichotomy into the emerging physics we seem to have here. Trough clipping = electromagnetism; peak clipping = nuclear strong force? Such kinks introduce high-frequency harmonics with a shared phase. This phenomenon could elegantly eliminate the theoretical requirement that wave functions tend to pull into each other's phase as a "primordial" given.

4-24-2017

The two kinks of a clipped wave peak become negative and positive Dirac delta functions, respectively, when differentiated twice. In the case of a clipped valley, the negative and positive delta functions are interchanged. The delta function was introduced into physics as a model of the electron's particle aspect. Does the particle model in general depend on observations with built-in double differentiations? Interestingly, the Schrodinger equation, the master equation of quantum mechanics, incorporates a spatial double differentiation of the wave function in the Hamiltonian, in the part representing total energy. At the moment, however, this is no more than suggestive.

Some readers will think my emphasis on the practicalities of representation vis-a-vis quantum mechanics implies that our universe is a simulation running on a digital computer. I think it more likely that these issues point to the existence of a still lower level of description underlying quantum mechanics at which you don't need a digital computer to get computer-like effects. The power of actual digital computers may derive from their breaking the world down into integers, then bits, if these are the very basic, true constituents of the world. These data structures would then be said to possess high construct validity, that is, they represent the true causes of things, which facilitates calculations. Constructs that miss the mark, such as the old epicycles of early astronomy, are a nightmare to calculate with.

This analysis suggests that wave-particle duality could be reproduced parsimoniously on a digital computer merely by running the Schrodinger equation with extremely bad data typing. That is, no attempt is made to avoid representational overflows or digitization errors, nor is any floating decimal point used--everything stays in integers, and let the chips fall where they may. The result of a period of simulated wave function evolution would be double-differentiated before being drawn on the screen.

4-27-2017

Mistake correction: Doubly differentiating a clipped wave peak gives two negative Dirac deltas, not a negative and a positive as I previously stated. Moreover, doubly differentiating a clipped wave valley gives two positive Dirac deltas. A wavelet consisting of a large, central peak and two smaller, flanking valleys that has everything clipped yields a symmetrical (i.e., gerade) array of six delta functions. Just going by particle count, it looks like we may have a model of the neutral helium atom here, albeit in one dimension.

5-02-2017

I am now working on the idea that particles of matter are solitons created by rectifying and saturating static nonlinearities in a discrete representation system that exists at a level of description below that of quantum mechanics.

Part 5

Why is there a matter-antimatter asymmetry? 

All attempts to answer this question that I have seen assume that present-day physical laws were constant all the way back to the big bang, and proceed to run into great difficulties in answering the question. Of course, that assumption is the problem. Common sense tells us that if one proposes to explain how the universe came to be, conservation laws such as baryon number will have to be violated at some point, usually understood to be very close to the big bang singularity. My suggestion is that the inflationary era was an epoch of baryon number violation.

I imagine that matter in space time can be understood as a four-dimensional graph, which spontaneously self-assembled out of separate nodes that became linked. Alternatively, the edges of the graph may have been primordial and the nodes their meeting-places. The stage was set for the big bang by a rate limiting process of formation of these building blocks, which accumulated in some simpler space than Euclidean space until a supersaturation-like state was reached. The first baryon would have been a special configuration of the primordial elements that had autocatalytic properties. The size of the graph would then have subsequently increased by powers of two to produce the exponential increase in the size of the universe of the inflationary era. This would have used up the supersaturation, however, so after the exponential phase there would have been a deceleration phase in which each new generation of graph elaboration would have been progressively less connected. Eventually, the growth of the graph comes into equilibrium with the rate of formation of the building blocks, and it resolves into a vast number of linear subgraphs in which node-link units are being added one by one to the growing ends, which is simply the passage of time. This is the present era, the era of baryon-number conservation. By chance, the first baryon would have had some choice of configuration identifiable with matter, as opposed to antimatter, and this property would have been propagated to all its descendants. This theory was based on the population growth law followed by organisms that colonize a new empty habitat, called the logistic curve.

05-26-2020: This theory may be incoherent. It assumes that the embedding space has no distance concept, so that the graph can never grow beyond the region said to have varying degrees of supersaturation. However, supersaturation degree is a ratio of concentrations, and concentration is particles per unit of volume, and volume as conventionally understood is distance cubed.

09-22-2020: However, since supersaturation degree is a ratio, it is dimensionless.

08-30-2020: The graph may be a useful stepping-stone concept for the elimination of space from physics, if it is borne in mind that there is nothing outside the graph(s).

09-22-2020: To get the graph outside of time as well as space, the links can be thought of as expressing logical inevitabilities, given the more proximate nodes (proximate to the big bang, that is) and some unknown rules. These inevitabilities become causation when viewed from within a subworld where a time illusion exists, which may only be the subworld of human conscious experience. All this makes the future predetermined, of course, but c'est la guerre.

Part 6

The above mapping of distance to correlation would be consistent with distance (d) = tan(arc cos(rxy)) =

(1 – rxy2)1/2/rxy  and rxy = 1/(d2 + 1)1/2.

 Assume that the binding energy of an electron in a hydrogen atom is the dot product of the electron Hilbert vector e and the proton (considered as one particle) Hilbert vector p, so E = e·p. Let us then set the principle quantum number of the hydrogen atom, n, which can never be less than 1, equal to N + 1. We recover Rydberg’s formula for predicting the energies of spectral lines, i.e., ΔE = ||e||*||p||*(1/n₁ – 1/n₂), n₂ > n₁.

Part 7

Lamarkian, epigenetic, and ...possibly via the brain's serotonergic neurons. 

The latter would be specialized for retrieving information from the epigenetic marks in their own nuclei. The patterns of emotional reactivity created by everyone's serotonergic systems would structure society. The emotions themselves could additionally serve to indicate contradictions in the epigenetic programming, if they increase to excessive levels, whereupon they destabilize the relevant epigenetic marks, first in the brain, then in the germ line. Bottom line: nobody has to die, but expect to be stressed.

Introduction of the objective function concept implies trial-and-error acquisition of information, whereas Lamarkism is deterministic. Indeed, the acquisition of information would be trial-and-error, requiring random, epigenetic changes coordinated between neurons and gametes. The coordination is possibly mediated by the action of blood-borne messenger substances on the germ-line cells and might require a long time to uniquely specify the nucleosomes to be altered. However, intergenerational transmission of epimutations would require that they survive a process called "reprogramming," which occurrs during gametogenesis or embyonic life, a point not now strongly supported by biochemical experiments (but see Hackett JA, et al. Germline DNA Demethylation.... Science. 2013; 339[6118]:448-452)....of the epigenetic part ...and I have decided that the latter must be promoted to the status of a fourth intelligence, next to the genetic, the synaptic, and the artificial.

Part 8

 However, people do not willingly restrain their own reproduction. At the social level, then, we can expect to find emotionally fraught interpersonal interactions by which people instinctively hinder the reproduction of each other, and this will happen more in good times than in bad. 

Think of the story of two crabs in a bucket. It is said that if one crab can just manage to escape from the bucket on its own, two cannot. With two crabs in the bucket, every time one crab gets a little higher than the other, the lower crab reaches up and pulls it down; thus, neither can escape, and two prove to be weaker than one. I predict, then, that human variations on this theme, termed "crab mentality" and "The Law of Jante" will come into prominence when food is abundant but recede in importance during hard times.

By the same reasoning, anything you can do to increase your resource footprint exponentially will provide even better insurance, when foregone, than would reproductive restraint, which is merely multiplicative....However, people do not willingly restrain their own quest for reputation; we do it to each other with our crab mentality. This analysis predicts that crab mentality may come in three progressively more destructive "degrees," like the transactional games described by Eric Berne in Games People Play (1964, New York: Ballantine).

These might be triggered by additive, multiplicative, and exponential selfishness, respectively. In the case of obesity (additive mechanism), the selfishness in question would be wanting too much insurance, whereas for the other two cases, the crab-mentality reaction itself implements the insurance.

Postscript 1

However, crab mentality may not be central to evolved modes of insurance that utilize exponential effects, serving there only as a kind of vigilantism directed against cheaters. This is because reputation is not an absolute, but only the result of comparison with the average; winners will tend to be as numerous as losers, resulting in no net effect on population density, and thus no obvious relevance to biological insurance. But see below

Part 9

An exciting possibility that occurred to me recently is the "synaptonuclear pathway," by which the genetic and synaptic intelligences alluded to in a previous post might interact directly. When studying the brain's serotonin-secreting neurons, I was struck by the fact that their outputs are much more diverse than their inputs. I suspect that most of the information they deliver synaptically is retrieved from their own chromatin marks, not from their input synapses. The latter might serve only as the source of addresses for epigenetic information retrieval. The other mono-amine secreting neurons may be similar in this regard. All these neuron types innervate the mid-line structures of the cerebral cortex, called the limbic system, long associated with memory and emotion.

Epigenetic information retrieved by the serotonin neurons may

Part 10

both... and epigenetic... more Lamarckian ...suggests that this ionic bonding can be varied in strength in an almost graded fashion, perhaps to accurately and inversely translate conditional firing probabilities into transcriptase access times, by currently unknown mechanisms.

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Let's close with a little something from Mr. Butt:

I huh H vH huh u   H h but h jig h huh but huh by h ht.  U nob no👋he hi l h bit vh by z c h button uj h huh u juju huh no ccy it l c

That Buttsy's a genius, I tellya.