#77. How the Cerebellum May Adjust the Gains of Reflexes [Neuroscience]

 

NE

Red, theory; black, fact

The cerebellum is a part of the brain involved in ensuring accuracy in the rate, range, and force of movements and is well known for its regular matrix-like structure and the many theories it has spawned.

Background about the cerebellum

The sensory inputs to the cerebellum are the mossy fibers, which drive the granule cells of the cerebellar cortex, whose axons are the parallel fibers. The spatial arrangement of the parallel fibers suggests a bundle of raw spaghetti or the bristles of a paint brush. These synapse on Purkinje cells at synapses that are probably plastic and thus capable of storing information. The Purkinje cells are the output cells of the cerebellar cortex. Thus, the synaptic inputs to these cells are a kind of watershed at which stimulus data becomes response data. The granule-cell axons are T-shaped: one arm of the T goes medial (toward the midplane of the body) and the other arm goes lateral (the opposite). Both arms are called parallel fibers. Parallel fibers are noteworthy for not being myelinated; the progress of nerve impulses through them is steady and not by jumps. The parallel fibers thus resemble a tapped delay line, and Desmond and Moore seem to have [paywall] proposed this in 1988.

The space-time graph of one granule-cell impulse entering the parallel-fiber array is thus V-shaped, and the omnibus graph is a lattice, or trellis, of intersecting Vs.

The cerebellar cortex is also innervated by climbing fibers, which are the axons of neurons in the inferior olive of the brainstem. These carry motion error signals and play a teacher role, teaching the Purkinje cells to avoid the error in future. Many error signals over time install specifications for physical performances in the cerebellar cortex. The inferior olivary neurons are all electrically connected by gap junctions, which allows rhythmic waves of excitation to roll through the entire structure. The climbing fibers only fire on the crests of these waves. Thus, the spacetime view of the cortical activity features climbing fiber impulses that cluster into diagonal bands. I am not sure what this adds up to, but what would be cute?

A space-time theory

Cute would be to have the climbing fiber diagonals parallel to half of the parallel-fiber diagonals and partly coinciding with the half with the same slope. Two distinct motor programs could therefore be stored in the same cortex depending on the direction of travel of the olivary waves. This makes sense, because each action you make has to be undone later, but not necessarily at the same speed or force. The same region of cortex might therefore store an action and it’s recovery.

The delay-line theory, revisited

As the parallel-fiber impulses roll along, they pass various Purkinje cells in order. If the response of a given Purkinje cell to the parallel-fiber action potential is either to fire or not fire one action potential, then the timing of delivery of inhibition to the deep cerebellar neurons could be controlled very precisely by the delay-line effect. (The Purkinje cells are inhibitory.) The output of the cerebellum comes from relatively small structures called the deep cerebellar nuclei, and there is a great convergence of Purkinje-cell axons on them, which are individually connected by powerful multiple synapses. If the inhibition serves to curtail a burst of action potentials triggered by a mossy-fiber collateral, then the number of action potentials in the burst could be accurately controlled. Therefore, the gain of a single-impulse reflex loop passing through the deep cerebellar nucleus could be accurately controlled. Accuracy in gains would plausibly be observed as accuracy in the rate, range, and force of movements, thus explaining how the cerebellum contributes to the control of movement. (Accuracy in the ranges of ballistic motions may depend on the accuracy of a ratio of gains in the reflexes ending in agonist vs. antagonist muscles.)

Control of the learning process

If a Purkinje cell fires too soon, the burst in the deep cerebellar nucleus neuron will be curtailed too soon, and the gain of the reflex loop will therefore be too low. The firing of the Purkinje cell will also disinhibit a spot in the inferior olive due to inhibitory feedback from the deep nucleus to the olive. I conjecture that if a movement error is subsequently detected somewhere in the brain, this results in a burst of synaptic release of some monoamine modulator into the inferior olive, which potentiates the firing of any recently-disinhibited olivary cell. On the next repetition of the faulty reflex, that olivary cell reliably fires, causing long-term depression of concurrently active parallel fiber synapses. Thus, the erroneous Purkinje cell firing is not repeated. However, if the firing of some other Purkinje cell hits the sweet spot, this success is detected somewhere in the brain and relayed via monoamine inputs to the cerebellar cortex where the signal potentiates the recently-active parallel-fiber synapse responsible, making the postsynaptic Purkinje cell more likely to fire in the same context in future. Purkinje cell firings that are too late are of lesser concern, because their effect on the deep nucleus neuron is censored by prior inhibition. Such post-optimum firings occurring early in learning will be mistaken for the optimum and thus consolidated, but these consolidations can be allowed to accumulate randomly until the optimum is hit.

Photo by Robina Weermeijer on Unsplash

#76. Role of personalities in the human swarm intelligence [population]

PO

Red, theory; black, fact.

Précis: each of the Big Five personality traits is a dimension along which people differ in some socially important behavioral threshold. These are, respectively: openness > uptake of innovations; conscientiousness > uptake of taboos; extraversion >  committing to collectivism*; agreeableness > becoming militant; neuroticism > engaging in/submitting to persecution. The personality trait is written on the left of the ">" and the putatively impacted social threshold is on the right.

These threshold spectra enable social shifts that are noise-resistant, sensitive to triggers, and rapid. Noise resistance and sensitivity together are called good “receiver operating characteristics,” a concept often used in the scientific literature.

A metaphor that suggests itself is lighting a camp fire. The spark is first applied to the tinder. Ignition of the tinder ignites the kindling. Ignition of the kindling ignites the small sticks. Ignition of the small sticks ignites the big sticks, and everything is consumed.

Orderly fire-starting appears to require a spectrum of thresholds for ignition in the fuel, as may orderly social shifts. To further extend the metaphor, note that the fuel must be dry (i.e., situational factors must be permissive).

11-07-2022: Social novelties spread upward to higher-threshold social strata by meme propagation reinforced by emotional contagion. The emotional energy necessary for emotional contagion would come from the individual’s interaction with the novelty, which would feature a positive feedback.

Our capacities for all of the enumerated social shifts were selected in evolution and most can be assumed to be still adaptive when correctly triggered. In today’s world, shifts to persecution are probably the least likely to still be adaptive, and could be a holdover from our Homo erectus stage. Persecution leads to refugee production, and refugee production could have been the reason that guy was such a great disperser.

As the geologists say, “The present is the key to the past.”

* 01-17-2023: A possible anti-invasion adaptation and predictable from geography.

#75. A Tripartite Genetic Code [Genetics]

GE

 Red, theory; black, fact

(Originally posted in the "Enhancers" post.) 

Cladophora flavescens; Phycologia Britannica, William Harvey, 1851, v.4, t298.

In this post, I propose that there are three genetic codes, not one. Conventional thinking says that there is just one code, which encodes the amino acid sequence of proteins into DNA. Here are the two new ones:

A morphology code for the multicellular level

08-01-2022: The interaction of semipermanent charges on chromatin, a possibility introduced in the "Enhancers" post, could structure the chromosomes into reproducible configurations within the nucleus. For instance, a chromatin segment with a net positive charge will tend to stick to a segment with a net negative charge, leading to their respective chromosomes being spot-welded at that point. An analogy from protein chemistry would be a disulfide bridge. This structuring may be followed by transmission of nuclear 3D information through the nuclear membrane to dictate the nuclear diameter along which the centrosomes separate to initiate mitosis. This, in turn, will dictate the orientation of the mitotic division plane. In the context of a growing embryo, such control of the orientation of mitosis is arguably at the origin of organ and body morphology. For example, all planes parallel will result in a filamentous organism like Cladophora. Planes free to vary in only one angle (azimuth or elevation) will produce a sheet of cells, a common element in vertebrate embryology. Programmed variation in both angles can produce a complex 3D morphology like the vertebrate skeleton. Thus we begin to see a genetic code for morphology, distinct from the classical genetic code that specifies amino acid sequences. 

<08-05-22: Possibly, each chromosome folds in a hairpin turn near the center of the nucleus and ends up occupying a specific conical solid angle. A cell generation counter or the developmental signals around the cell then activate a centrosome-maker gene in one specific chromosome and no other. This gene is then transcribed into a long noncoding RNA molecule that protrudes from a specific nuclear pore and triggers the assembly of a new centrosome just outside the nucleus at a specific azimuth and elevation. The nucleus is tethered by cytoskeletal elements such as lamin, nesprin, actin, and tubulin to focal adhesions on the the cell membrane, non-rotatably, so that all angle information can be referred to the previous mitotic orientation. The final step is dislodging the old centrosome and sweeping it into the antipodal position of the new one. This could be done by an array of microtubules growing radially out of the new centrosome but constrained to stay close to the nuclear membrane. 

Thus, there appear to be two tiers of control of mitotic orientation available: controlling which chromosome or chromosome arm produces the centrosome-maker RNA, and controlling the pattern of histone epigenetic marks in the nucleus and thus the chromatin charge pattern and thus the 3D structure into which the chromosomes assemble, and thus the mitotic angles assigned to a given chromosome.> <09-01-22: At the DNA level, the code for multicellular morphology would take the form of promoter-controlled segments that transcribe into long noncoding RNAs having a special two-domain structure: a domain that binds to a particular kind of histone-modifying enzyme and a domain that binds to a particular DNA sequence. These lncRNAs would specify, at the second tier of control, local charge changes in chromatin in a context-dependent manner.><09-14-2022: In organisms that are morphologically complex but have few chromosomes in their karyotype, such as fruit flies, the mitotic angles could be assigned to reproducible chromatin loops as well as to whole chromosomes, suggesting a 3-tiered control system.>

A morphology code for the single-cell level in cells with nuclei

<08-20-22: I further propose a third genetic code: a code for single-cell morphology, and cell morphology can be very elaborate, especially in neurons. This will probably involve storing information about cytoskeleton morphology in DNA. Neurons express especially many long noncoding RNAs, so I suggest that these transcripts can carry morphological information about cytoskeletal elements. This information could be read out by using the lncRNA as a template on which to assemble the cytoskeletal element, then removing the template by enzymic hydrolysis or by some spirane-like enzyme. Greater efficiencies could be achieved by introducing some analog of transfer RNAs. LncRNAs are already implicated in transcriptional regulation, and this might be done indirectly by an action on the protein scaffolding of the chromatin. Moreover, as you would predict from this theory, lncRNAs are abundant in cytoplasm as well as in the nucleus, and the cytoplasm contains the most conspicuous cytoskeletal structures. The template idea is similar to but goes beyond the already-established idea that lncRNAs act as scaffolds for ribonucleoprotein complexes. Since cytoskeletal elements are made from monomers of few kinds, we would expect the template to be highly repetitious, and lncRNAs are decidedly repetitious. Indeed, transposons and tandem repeats are thought to drive lncRNA evolution. See https://doi.org/10.1038/s41598-018-23334-1, in Results, subsection: "Repetitive sequences in lncRNAs," p. 4 in the PDF.>

An uncertainty principle for molecular biology?

09-02-2022: These ideas call into question the assumption that all biological order stems from primary amino acid sequences and that a glorified bacterial genome, if artfully regulated, can produce a human. Is there a fundamental limit on how high an amino acid residue can extend its influence in the structural hierarchy of biology? Even something as big as a ribosome appears to need help from ribosomal RNAs to keep its act together. However, perhaps the issue is coding parsimony.

Two more biological questions:

1. Does a cell in a multicellular organism run a metabolic simulation of the whole organism to help it carry out its specialized role more efficiently? Are these little guys thinking of us?

2. Is immune cycling the answer to preventing cancer? Let’s say you deliberately take a drug to suppress your immune vigilance for one month out of each year, then discontinue the drug to let it rebound. During suppression, the micro cancers run wild for a short time, thereby growing large enough for the immune function to easily detect them upon its return. They get whacked, of course, and the immune system learns something in the process, making it a more effective anti cancer system going forward. The analogy here would be a cat playing with a mouse it has caught. Since it is play, it is a learning activity; the cat is working on its game. Pre-civilization, human immune suppression would have happened regularly due to prolonged  environmental stressors, leading to cannier immune systems and lower cancer rates than we now experience.

This agrees with the impression I have that cancer is a disease of modern lifestyles. The following article may or may not be relevant: Coventry, B.J., Ashdown, M.L., Quinn, M.A. et al. CRP identifies homeostatic immune oscillations in cancer patients: a potential treatment targeting tool?. J Transl Med 7, 102 (2009).  https://doi.org/10.1186/1479-5876-7-102 

#74. Extended Theory of Mind [Evolution]

EV

Red, theory; black, fact.

Bad show, old chap.

Where is evolution going at the moment? Pretty good question. Let us look around, then. I am writing this in a submarine sandwich joint where one sandwich maker is serving two customers. The radio brings in a ballad by a lady vocalist at a tempo suggestive of sex. Now a DJ (Mauler or Rush, I’m not sure which) is amusing the listeners with some patter. The window shows that rush hour is over and only a few home-bound stragglers are in the street. If I crane my neck, I can see the green beacon on the new electric charging station. 

That will do for starters. Sandwich maker, pro singer, DJ, bureaucrat, electrician—I couldn’t do any of that. We are a society of specialists, and such societies feature differentiation with integration. So, how far back does this go? At most, nine millennia; about 450 generations. Time enough for evolution? Doesn’t matter; we want direction here, not distance.

Contemporary natural selection of humans will therefore reward differentiability and integratability.

Differentiability: vocational choices often begin in childhood with hobbies, and there is a certain frame of mind associated with hobbies called “flow.” I therefore suggest that we are being selected for a susceptibility to flow. 

Integratability: society is held together by our ability to coordinate with others, and the key ability here is thought to be “theory of mind,” or the ability to infer the mental states of those with whom we interact. Likewise, we are being selected for theory-of-mind ability.

I would like to suggest that there is something higher than theory of mind, which not everyone possesses at this time: extended theory of mind: inferring the mental states of those not present, and whose very existence is itself inferred. A society strong in this trait will appear to be communicating with one another through solid walls, as if by ESP. 

Who are these Chosen? Probably military generals, politicians, and the executive class. Go figure.

However, the human cranium is probably as voluminous as it can get and still allow childbirth, so the gray matter subserving the new ability will have to be included at the expense of some other, preferably obsolete ability, like accuracy in spearing game animals.

So challenge your mayor to a game of darts and see how he does. This theory is falsifiable.

Photo by Le Vu on Unsplash

#73. How Enhancers May Work [Biochemistry]

 CH

Red, theory; black, fact.

Picture of the author at the microscope circa 1999.
Terrible posture! This is where Egors come from. Kids, don't try this at home.

Background about enhancers

Enhancers are stretches of DNA that, when activated by second messengers like cyclic AMP, enhance the activity of specific promoters in causing the transcription of certain genes, leading to the translation of these genes into protein. Enhancers are known for causing the post-translational modification of the histones associated with them. Typically, lysine side chains on histones are methylated, doubly methylated, triply methylated, or acetylated. Serines are phosphorylated. In general, phosphorylation condenses chromatin and acetylation expands and activates it for transcription. Methylation increases positive electric charge on the histones, acetylation decreases positive charge, and phosphorylation increases negative charge. The enhancers of a promoter are usually located far away from it measuring along the DNA strand, and can even be on different chromosomes ("in trans"). 

The mystery of enhancer–promoter interaction

How the distant enhancer communicates with its promoter is a big mystery. The leading theory is that the enhancer goes and sticks to the promoter, and the intervening length of DNA sticks out of the resulting complex as a loop. This is the "transcription hub" theory. 

My electrostatic theory of enhancer–promoter interaction

I propose a far different mechanism: when activated, the multiple enhancers cause modification of their associated histones that place the same electric charge on all of them, which is also of the same sign as the charge on the promoter region. Mutual electrostatic repulsion of all these regions then expands the chromatin around the promoter. This effect reduces the fraction of the time that the RNA polymerase II cannot move down the DNA strand because unrelated chromatin loops are in the way, like trees fallen across the railway tracks. (Each "tree" eventually moves away because of Brownian motion.) This could also be the mechanism of chromatin decondensation generally, which is known to be a precondition for the expression of protein-coding genes.

05-28-2022: The mutual electrostatic repulsion of enhancers does not necessarily accomplish decondensation directly, but may do so indirectly, by triggering a cascade of alternating chromatin expansions and histone modifications. Furthermore, this cascade is not necessarily deterministic. These ideas predict that raising the ionic strength in the nuclear compartment, which would tend to shield charges from each other, should inhibit gene activation. This manipulation will require genetic knockout of osmolarity regulating genes.

#72. Why There is Sex [evolution]

EV

Red, theory; black, fact.

The flower Coronilla varia L.

Sex is an evolvability adaptation

There are always two games in town: reproduction and evolution. Since we live on an unstable planet where the environment can change capriciously, species here have been selected for rapid evolvability per se to enable them to adapt to the occasional rapid environment changes and not go extinct. Apparently, mutations, the starting point for evolutionary adaptation, become more common when the organism is stressed, and stress may partly be a forecast of loss of fertility due to a developing genome-environment mismatch. Bacteria exhibit the large mutation of transformation under stress conditions, and 3 types of stress all increased the meiotic recombination rate of fruit flies (Stress-induced recombination and the mechanism of evolvability. Zhong W, Priest NK. Behavioral ecology and sociobiology. 2011;65:493-502). Recombination can involve unequal crossing-over in which changes in gene dose can occur due to gene duplication or deletion. However, since most mutations are deleterious (there are more ways to do something wrong than to do it better) many mutations will also reduce fertility, and at precisely the wrong moment: when a reduction in fertility is impending due to environment change. The answer was to split the population into two halves: the reproduction specialists and the selection specialists, and remix their respective genomes at each generation.

The roles of the two sexes

Females obviously do the heavy lifting of reproduction, and males seem to be the gene testers. So if a guy gets a bad gene, he dies, ha ha, and the luckier guy next to him then gets two wives. The phenomenon of greater male variability (Greater male than female variability in regional brain structure across the lifespan. Wierenga LM, Doucet GE, Dima D, Agartz I, Aghajani M, Akudjedu TN, Albajes‐Eizagirre A, Alnæs D, Alpert KI, Andreassen OA, Anticevic A. Karolinska Schizophrenia Project (KaSP) Consortium. Hum. Brain Mapp., doi. 2020;10, and I have never seen so many authors on a paper: 160.) suggests that mutations have more penetrance in males, as befits the male role of cannon fodder/selectees. What the male brings to the marriage bed, then, is field-tested genetic information. Male promiscuity can therefore be seen as a necessary part of this system, which allows many mutations to be field tested with minimal loss of whole-population fertility, because it is the females who are the limiting factor in population fertility.

Chromosomal mechanisms of greater male variability

Chromosomal diploidy may be a system for sheltering females from mutations, assuming that the default process is for the phenotype that develops to be the average of the phenotypes individually specified by the paternal and maternal chromosome sets. Averaging tends to mute the extremes. The males, however, may set up a winner-take-all competition between homologous chromosomes early in development, with inactivation of one of them chosen at random. The molecular machinery for this may be similar to that of random x-inactivation in females. The result will be greater penetrance of mutations through to the phenotype and thus greater male variability. 

Quantitative prediction

This reasoning predicts that on a given trait, male variability (as standard deviation) will be 41% greater than the female variability, a testable prediction. 41% = [SQRT(2) -1] × 100. Already in my reading I have found a figure of 30%, which is suggestive. 

Now all I have to do is reconcile all this with the laws of Mendelian inheritance. 

Mechanistic reconciliation with Mendel's laws

09-16-2021: This reconciliation seems to require an exemption mechanism built into the postulated chromosome inactivation process that operates on genes present in only one copy per parent. The effect of this mechanism will be to double the penetrance of dominant alleles at that gene. Therefore, in males, at single-copy genes, evolution of the machinery of sex is driven by the favorable mutations.

A lovers' heart drawn in dust

#71. The Checkered Universe [Physics]

 PH

Red, theory; black, fact.

Natty dog/epiphany

The basic theoretical vision

☯This is a theory of everything based on a foam model. The foam is made up of two kinds of "bubbles," or "domains": "plus" and "minus." Each plus domain must be completely surrounded by minus domains, and vice versa. Any incipient violation of this rule, call it the "checkerboard rule," causes domains of like type to fuse instantly until the status quo is restored, with release of energy. The energy, typically electromagnetic waves, radiates as undulations in the plus-minus interfaces. The result of many such events is progressive enlargement and diversification of domain sizes. This process, run backward in time, appears to result in a featureless, grey nothingness (imagining contrasting domain types as black and white, inspired by the Yin-and-Yang symbol), thereby giving a halfway-satisfying explanation of how nothing became something. <03-12-2022: Halfway, because it’s an infinite regress: explaining the phenomenon in terms of the phenomenon, and a hint that I am not out of the box yet. Invoking progressively deepening shades of gray in forward time, to gray out and thus censor the regress encountered in backward time, looks like a direction to explore.> I assume a Law of Conservation of Nothingness, whereby plus domains and minus domains must be present in equal amounts, although this can be violated locally. This law is supposed to be at the origin of all the other known conservation laws. The cosmological trend favors domain fusion, but domain budding is nevertheless possible given enough energy.

The givens assumed for this theory of everything.
Since there are givens, it is probably not the real theory of everything
but rather a simplified physics. (But maybe a stepping stone?)

The dimensionality question

The foam is infinite-dimensional. Within the foam, interfaces of all dimensionalities are abundant. Following Hawking, I suggest that we live on a three dimensional brane within the foam because that is the only dimensionality conducive to life. The foamy structure of the large-scale galaxy distribution that we observe thus receives a natural explanation: these are the lower-dimensional foam structures visible from within our brane. The interiors of the domains are largely inaccessible to matter and energy. <03-12-2022: We have an infinite regress again, this time toward increasing dimensionality: we never get to the bulk. Is it time to censor again and postulate progressively lessened contrast with greater dimensionality, and asymptotic to zero contrast? No; the foam model implies a bulk and therefore a maximum dimensionality, but not necessarily three. But what is so special about this maximum dimensionality? Let us treat yin-yang separation as an ordinary chemical process and apply the second law of thermodynamics to see if there is some theoretical special dimensionality. Assuming zero free energy change, we set enthalpy increase (“work”) equal to entropy increase (“disorder”) times absolute temperature. Postulating that separation work decreases with dimensionality and the entropy of the resulting space foam increases with dimensionality, we can solve for the special dimensionality we seek. The separation process has no intrinsic entropy penalty because there are no molecules at this level of description. The real, maximum dimensionality would be greater than theoretical to provide some driving force, which real transformations require. However, is the solution stable? Moreover, the argument implies that temperature is non-zero.><06-26-2022: Temperature is here the relative motion of all the minute, primordial domains. This could be leftover separation motion. How could all this motion happen without innumerable checkerboard-rule violations and thus many fusion events? Fusion events can be construed as interactions, and extra dimensions, which we have here, suppress interactions. More on this below.><02-07-2023: That said, the idea of primordial infinite dimensionality remains beguiling in its simplicity and possibilities.>

12-23-2021: Since infinite dimensionality is a bit hard to get your mind around, let us inquire what is diminished upon increasing the dimensionality, and just set it to zero to represent infinite dimensionality. Some suggestions: order, interaction, and correlation. To illustrate, imagine two 2-dimensional Ardeans* walking toward each other. When they meet, one must lie down so the other can walk over them before either can continue on their way. That's a tad too much correlation and interaction for my taste.

Moreover, an amazing aspect of any 2D version of Earth is that the soil can never dry out. There is no way for the pore water to escape from the interstes among the soil grains.

03-03-2022: I suppose that as dimensions are added, order, correlation, and interaction decrease toward zero asymptotically. This would mean that 4D is not so different from 3D as 3D is from 2D. The latter comparison is the usual test case that people employ to try to understand extra dimensions, but it may be misleading. However, in 4D, room-temperature superconductivity may be the rule rather than the exception, due to extradimensional suppression of the interactions responsible for electrical resistance. The persistent, circulating 4D supercurrents, understood as travelling electron waves, may look like electrostatic fields from within our 3-brane, which, if true, would help to eliminate action-at-a-distance from physics. Two legs of the electron-wave circulation would travel in a DWCP (Direction We Cannot Point). These ideas also lead to the conclusion that electrostatic fields can be diffracted. Bizarre, perhaps, but has anyone ever tried it? <03-21-2022: Yes, they have, and it is the classical electron diffraction experiment. The electrons are particles and are therefore not diffracted; they are accelerated in an electrostatic field that is diffracted, thereby building up a fringe pattern on the photographic plate. The particles, then, are just acting here as field tracers. Slight difficulty: neutrons can also be diffracted. A diffraction experiment requires that they move, however, so read on.>

Still to be explained: Newton's first law (i.e., inertia and motion).

How to accommodate the fact of motion

08-06-2012: Motion can be modelled as the array of ripples that spreads across the surface of a pond after a stone is thrown in. A segment of the wave packet coincides with the many minute domains that define the atoms of the moving object, and moves them along. The foam model implies surface tension, whereby increases in interface area increase the total energy of the domain. If the brane is locally thrown into undulations, this will increase the surface area of the interface and thus the energy. This accounts for the kinetic energy of moving masses. Momentum is the rate of change of kinetic energy with velocity and inertia is the rate of change of momentum with velocity. 

03-08-2022: Brane surface tension would be a consequence of the basic yin-yang de-mixing phenomenon, because increases in interfacial area without volume increase (interface crumpling) can be construed as incipient re-mixing, which would go against the cosmological trend. Thus, the interface always tends to minimum area, as if it had surface tension. <03-04-2023: this tension provides the restoring force that one needs for an oscillation, which is important because waves figure prominently in this theory. However, a wave also needs the medium to have inertia, or resistance to change, and where is that in the present theory? It can be introduced in the form of a finite speed of light. For example, the permeability of free space, related to inductance, a kind of electrical inertia, can be expressed in terms of the speed of light and the permittivity of free space, related to capacitance, which inversely expresses a kind of electrical restoring force.>

Dark matter and how to introduce gravity into this theory

08-14-2021: Gravity is being difficult here. I don't want to replace it with a bunch of spiral branewaves, and I don't know why it has an inverse squared power law. Let's drill down on this: when two interstellar dust grains collide, some kinetic energy is converted to heat energy, which radiates away. Without this process, called inelastic collision, the gravitational accretion of mass, and thus gravity itself, will not be observed. (By the way, one illusion that we may need to shed to make progress is that the convex spaces of the universe, such as the spaces occupied by stars, planets, and galaxies, are fundamental and the negative, concave, between-spaces are just meaningless pseudo-structures, which are called "spandrels" by evolutionary theoreticians. But could it be the other way around? In this, I am using the word "space" in an architectural sense.

08-27-2021: Eureka! Let us suppose that each visible astrophysical object is surrounded by an invisible atmosphere-like structure consisting of mid-sized domains (larger than atomic scale but smaller than intergalactic voids). This could be dark matter. Let us further assume that minimizing the total interfacial area of this structure leads to sorting according to domain size, resulting in a gradient of domain sizes that places the smallest in the center. Therefore, lifting an object off the visible surface necessarily disturbs this minimum-energy structure, requiring an input of energy. This requirement would be the gravitational potential energy of an elevated object. The exact power law remains unexplained, but I think these assumptions bring us much closer to an explanation.

12-29-2021: Ordinary matter would be distinguished from dark matter by the ordinary domains being full of standing waves that store the energy of many historical merging events. The antinodes in the standing wave pattern would be the regular array of atoms thought to make up a crystal (most solid matter is crystalline). The facets of the crystals would correspond to the domain walls. 

<02-10-2023: The waves could be confined inside the ordinary domains by travelling across our 3-brane at right angles, strictly along directions we cannot point. However, something has to leak into the 3-brane to account for electrostatic effects.><02-12-2023: Crossing the 3-brane perpendicularly is possible by geometry if each particle is a hypersphere exactly bisected by the 3-brane, and mass-associated waves travel around the hypersphere surface.><02-14-2023: Presumably, the neutron produces no leakage waves, which could be assured by the presence of a nodal plane coinciding with the spherical intersection of the particle hypersphere with the 3-brane. Electrons and protons could emanate leakage waves, a possibility that suggests the origins of their respective electric fields. However, the fact that these particles have stable masses means that waves must be absorbed from the 3-brane as fast as they exit, meaning that an equilibrium with space must exist. For an equilibrium to be possible, space must be bounded somehow, which is already implied by the foam model. Since we know of only two charged, stable particles, two equilibrium points must exist. This scenario also explains why all electrons are identical and why all protons are identical. If their respective leakage waves are of different frequencies, the two particle types could equilibrate largely independently by a basic theorem of the Fourier transform.><02-19-2023: Particles of like charge would resonate with each other's leakage wave, resulting in a tendency to be entrained by it. This would account for electrostatic repulsion. Particles of opposite charge would radiate at different frequencies and therefore not mutually resonate, leading to no entrainment. However, since each particle is in the other's scattering shadow, it will experience an imbalanced force due to the shadow, tending to push it toward the other particle. This effect could explain electrostatic attraction.><03-14-2023: Gravity may also be due to mutual scatter shadowing, but involving a continuum spectrum of background waves, not the resonant line spectra of charged particles. Note that background waves are not coupled to any domains, and so do not consist of light quanta, which, according to the present theory, are waves coupled to massless domain pairs.><04-21-2023: The bisected hypersphere particle model predicts that subatomic particles will appear to be spheres of a definite fixed radius and having an effective volume 5.71 x greater than expected from the same radius of a sphere in flat space. (5.71=1+1.5x🥧) Background waves that enter the spherical surface will therefore be slow to leave, a property likely to be important for physics.>

03-08-2022: There may be a very close, even mutualistic, relationship between domain geometry and interface waves, all organized by the principle of seeking minimum energy. Atomic nuclei within the crystal could be much tinier domains, also wave-filled but at much shorter wavelengths. The nuclear domains would sit at exactly the peaks of the electron-wave antinodes because these are the only places where the electron waves have no net component in the plane of the interface. Most particles will have the following structure as modelled with reduced dimensionality: a pair of prisms joined at the end-faces, the joint plane coinciding with the 3-brane of our world. Mass is standing waves in the joint plane. One prism is a plus domain and the other a minus domain. Both project out of our 3-brane into cosmologically-sized domains of opposite type. 09-04-2022:  Neutrinos may violate this pattern if they are unpaired domains completely surrounded by the opposite type of space and having no obligatory presence in our 3-brane. This would explain the weakness of their interaction with other types of matter and the existence of more than one type of neutrino. This picture predicts two types but we know three exist, a difficulty for this theory.

Motion, friction, and the cosmological redshift

09-11-2021: How could anything besides waves move from place to place without violating the checkerboard rule? I postulate that domains in front of the moving object are being triggered to merge, with release of wave energy (which radiates away), and domains in the rear are being re-split to restore the status quo. The energy needed for re-splitting will come from the brane-wave packet attached to the object. This accounts for the slowing of moving objects due to friction. However, the moon orbits the Earth apparently without friction and yet is inside the Earth's gravitational field and thus dark-matter structure, and thus must obey the checkerboard rule. My solution is to point out that the moon's motion is not really friction-free because interplanetary space is not really a vacuum, but contains 5 particles of plasma per cubic centimeter. I postulate that each such particle sits at a 0-brane within a space foam made of mid-sized domains.

21-09-2021: This feature ensures the prima facie equivalence of the present theory with conventional accounts of how friction happens, thereby helping the theory pass the test of explanation. However, friction in the absence of a detectable medium made of conventional matter appears to remain as a theoretical possibility.

09-22-2021: Dark-matter friction could progressively slow down electromagnetic oscillations, resulting in the cosmological red shift. The waste heat from this process may account for the microwave background radiation.

12-13-2022: Alternatively, space may really be expanding. Similar to the previously published brane-collision theory, the Big Bang may have been due to contact between two cosmologically sized domains of four spatial dimensions and opposite type, and our 3-brane is the resulting interface. The matter in our universe would originate from the small domains caught between the merging cosmological hyper-domains. This could account for the inflationary era thought to have occurred immediately after the big bang. The subsequent linear expansion of space may be due to the light emitted by the stars; if light is an undulation in the 3-brane along a large extra dimension, then light emission creates more 3-brane all the time, because an undulating brane has more surface area than a flat one. ☯

* "Overview of Planiverse" page.

Photo by Karsten Winegeart on Unsplash