#77. The Anorthosite Problem [chemistry]

CH

Red, theory; black, fact

Labradorite facade on Bank Street, Ottawa, ON

The “anorthosite problem” is a problem in geology. Anorthosite is a rock made mostly of a calcium-rich type of feldspar. Labradorite is a well-known example. The moon rocks from the lunar highlands are anorthosites. 

Existing Theory

When a magma chamber far below the surface cools and solidifies into rock, it does so very slowly because of the insulation provided by the overlying rocks. Slow cooling leads to big mineral grains in the eventual rock because each grain is a crystal of some mineral, and there is plenty of time for crystal growth.

As the temperature slowly falls, one type of mineral after another comes out of the magma, in a fixed sequence. The iron-rich minerals fall to the bottom of the chamber and collect there, while the calcium and sodium types of feldspar float to the top of the chamber and collect there. 

Anyway, that’s the theory. It predicts that anorthosites will be underlain by iron-rich rocks like gabbro, peridotite, amphibolite, and serpentinite, some of which are called greenstones.

The problem is that immense deposits of anorthosite are not found in association with any iron-rich rocks. 

My Emphasis

Interestingly, the biggest of these anorthosite deposits are the oldest, dating from the Archean and Proterozoic eras of geological history.  And thereon, I believe, hangs a tale.

Radioactive isotopes can be expected to have been much more abundant in the distant past than now if we extrapolate their exponential decay curves backwards in time to those eras. 

Moreover, all the natural radioactive elements are incompatible with the crystal lattices of the main rock-forming minerals crystallizing around when anorthosite does. Therefore, they will stay in the melt and get concentrated there as the rock-formers leave. The energy of their radiation will be converted into additional heat in the dense magma before the radiation can escape. 

My Solution

Therefore, the radioactive self-heating of the residual magma will become progressively stronger until the cooling process almost stalls, leading to a long-lasting plateau in the cooling curve of the magma.

During the plateau, which may actually be a second and slower exponential, the loss of the iron-rich minerals has time to run to completion, resulting in a large magma emplacement that forms only granite, a low-iron rock. The iron-rich greenstones will be under that, and nowhere near the anorthosite at the very top. This is the sequence we actually observe.

Therefore, the early anorthosite deposits, however massive, will have no iron-rich rocks in sight.

QED.

P.S. The crystals forming during the plateau phase will be notably large due to the especially slow cooling. This may be the origin of the large crystals categorized as phenocrysts.

#76. Next Niche [evolution]

EV

Red, theory; black, fact

Safdie’s Habitat 67 in Montreal 

In terms of our evolution, where did Homo sapiens come from and where are we going? The fossil evidence shows that we evolved from a wandering big-game hunter called Homo erectus. Where are we going? What shall be our next ecological niche? 

Reef former.

Examples of reef formers are the species of coral polyp that built the Great Barrier Reef in Australia. Think of such a structure transposed to a land environment and covered in solar panels like the leaves on a tree, and that, I think, is our distant future. The overall form would be designed to maximize the sum of wind and solar energy harvested per year.

Multiple works of science fiction have predicted something like this, such as Asimov’s pre-collapse Trantor, or the world of JG Ballard’s “Build-Up.” 

However, a reef does not cover an entire planet as in those imaginings, only those places where all its necessities of life are available. The non-reef-forming descendants of H. sapiens would occupy some or all of the remaining land area.

Photo by philippe collard on Unsplash

#75. The Broad Context of Religion [evolutionary psychology]

EP

Red, theory; black, fact

[Quotes indicate metaphor.]

• Organized religion may have arisen as a counter-adaptation to the anti-invasion adaptations  of a neighbouring, powerful country that included sorties.  For the Abrahamic religions, that powerful but geographically vulnerable country would be ancient Egypt. For the Eastern religions, the powerful but vulnerable neighbor would be ancient China.

• People are "amphibians": each of us has a collectivist part existing in genetic superposition with an individualistic part. In systems that officially celebrate the former, the latter cannot be owned and must be pushed into the Jungian Shadow. And vice versa. In Freudian terms, the unacceptable wishes emerge in disguised form: religion in individual-celebrating systems, and hero worship in collective-celebrating systems.

• The longstanding debate in philosophy between rationalism and empiricism is a false dichotomy resulting from a narrow focus on one or the other of the two legs by which scientific knowledge advances: theory and experiment.

• If religion is the last protoscience, then the corresponding science that is to come could be called security science. 

• The incredible disunity of Protestantism could mean that Protestantism is the laboratory of Christianity.

• The crucial step in going from a protoscience to a science appears not to have been experimentation, but quantification. Examples of early quantifiers were Tycho Brae (astronomy) and Antoine Lavoisier (chemistry). If religion is a protoscience, what would its quantification look like? “Reminder: It’s time to bring up your prayer checklist, tick the boxes that apply under each heading (Adoration, Confession, Thanksgiving, and Supplication), and upload it to the diocesan office. The results of statistical analysis will be announced at Vestry, at which time parishioners may suggest further research questions. This activity parallels and does not replace traditional prayer. All submissions are protected by best-practice data security.”

• The first step in graduating to security science may be compiling a glossary of religious terms and their non-supernatural, parallel interpretations. For example, the Jewish ban on eating pork can be interpreted in this spirit as a measure to prevent trichinosis (a disease transmitted by eating under-cooked pork or wild game). As another example, the four prayer headings enumerated above could be identified in terms of a longitudinal study as control, exposure, favourable outcomes at followup, and adverse outcomes at followup. As a third example, the three persons of the Trinity could map onto the three sources of security science: study of the individual, the society, and the evolutionary history of both (Son, Holy spirit, and Father, respectively).

• Science has to be for everyone.

• We don't have free will in the big things; we have free will in the little things. However, one of the little things can be "planting a seed" that may one day grow into one of those big things and be more to our liking than the big things we see now.

• Should security science take on the task of predicting the unintended consequences of innovations, or is that task so large as to require another new science?

• On the answers to the big questions, the sources of authority are the size of the database and the degree of regulation of the original inquiry. Writing things down would be one rule of inquiry; using a set process would be another; making well defined measurements would be another; the experiment form would be yet another. The degree-of-regulation parameter takes us smoothly from protoscience to hard science via the qualitative study, which has legitimacy today.

#74. Protein Batteries and Protein Misfolding Diseases [biochemistry]

CH

Red, theory; black, fact

Disclaimer 

If you are a PD or AD patient or at risk and are seeking a cure outside the medical mainstream, this is not for you. This is written for researchers. 

Inside Alzheimer’s and Parkinson’s 

The commonest protein misfolding disease, Alzheimer disease, features an accumulation of insoluble proteins as amyloid plaques that damage neurons and lead to dementia and death. 

The amyloid precipitates from a solution of amyloid beta protein, which forms by a two-step proteolysis of amyloid precursor protein (APP), an integral membrane protein of neurons.

APP is thought to play a role in the initial stage of synaptic plasticity and contains a copper binding site. 

What is the Power Source Driving Precipitation?

Oxidation of the coordinated copper upon insertion of nascent APP in the plasma membrane could shift the coordination geometry of the copper ion from planar-triangular to pyramidal, with huge changes in the preferred bond angles. If the coordinating protein cannot accommodate these changes without input of activation energy, the result would be a “protein battery”: a protein carrying a metastable “charge” of conformational strain energy. A set mousetrap would be a familiar example of this. 

Role of the Power Source in the Healthy Brain

The local availability of this energy cache may be necessary to allow brief pre- and post-synaptic electrical coincidences to be rapidly captured as preliminary synaptic morphological changes. The calcium-binding site next to the copper binding site (growth factor-like domain) may be the electric field sensor. Coincidence detection would involve same-molecule binding of APP molecules on opposite sides of the synaptic cleft, triggered by propagation of unleashed conformational changes from the copper site into the main extracellular domain, called the heparan-binding domain. (Better known parts of the coincidence detecting system are the NMDA receptor and CAM kinase II).

How the Power Source Goes Wrong

Protein misfolding diseases of the brain may be powered by a short circuiting of the APP energy caches, or analogous caches in proteins subserving other functions. One of those other functions could be replenishing the supply of docked synaptic vesicles in response to a sudden increase in the average neuron firing rate. In that case, the relevant battery protein would be alpha synuclein, which is implicated in Parkinson disease. Local energy caches are also present in humanly engineered electronic circuits, where they are called decoupling capacitors.

Loss of Control of the Stored Energy

 The secretases implicated in Alzheimer disease etiology would serve to degrade the discharged APP molecules. Secretase alpha would act rapidly to clear action-potential-discharged APP that did not make a cross link, and secretase beta would act slowly to clear cross links. Secretase gamma completes the cleavage in both cases. Secretase alpha would have a recognition site for discharged APPs and secretase beta would have an allosteric recognition site for cross links. Secretase beta action releases amyloid beta, the battery part of APP. The stored energy in amyloid beta would drive the polymerization process that leads to amyloid formation. This energy release would involve a conformational change, consistent with the finding that amyloid protein is misfolded. The conformational change could expose hydrophobic residues on the surface of the protein, an energy-requiring step that could lead directly to precipitation due to hydrophobic bonding among the amyloid beta molecules.

This action is easier to imagine for the central hydrophobic domain of alpha synuclein, the immediate effect being not precipitation but pulling two arbitrary ligands on different alpha synuclein molecules into closer proximity for a faster reaction between them. The trigger appears to be phosphorylation of alpha synuclein, not electric field change.

Closing a Fatal Positive Feedback Loop

By mischance, the soluble amyloid beta oligomers that form as intermediates along the amyloid-generating pathway are able to spoof APP cross links, thereby driving ectopic secretase beta activity and closing a feedback loop. This feedback leads to an out-of-control production of amyloid beta that produces Alzheimer disease.

#73. The Self-exciting Small-world Network in Behavioral States and Disease [Neuroscience, Biochemistry]

NE   CH

Red, theory; black, fact

Seen at the Red Roots Trading Co. 

Disclaimer

If you are a cancer patient or at risk and are seeking a cure outside the medical mainstream, this is not for you; this post is written for researchers.

Conventional Thinking on the Nature of Cancer

The refractoriness of cancer (its treatment resistance) is thought by a few authors I read forty years ago to be due to a kind of in-body evolutionary process made possible by the high mutation rate characteristic of these cells. The anticancer drugs we apply to kill the cancer exert an evolutionary selection pressure on the individualistic cancer cells, killing most of them but leaving a residue of accidentally resistant cells that happen to have mutations conferring resistance. These resistant cells then grow back the cancer in a relapse, even harder to kill than before. And so it goes through treatment after treatment until the patient is dead.

But what if that’s wrong?

An Alternative Explanation of Cancer Refractoriness

This seems possible in terms of a “cancer state” that is sustained by re-entrant (circulating) metabolic signaling pathways that form a small-world network (SWN). Curing the cancer requires extinguishing the reentrant activity, but this is difficult because of the robustness of the SWN. If one node in the network is pharmacologically ablated, the signaling can always flow around it by alternative pathways through the network. Thus, robustness becomes refractoriness.

Hub Nodes

The robustness of SWNs depends on their hub nodes—nodes with an unusually large number of connections. The state theory of cancer articulated here therefore directs us to pharmacologically target the hub nodes for greatest therapeutic efficacy. However, a practical therapy also requires selectivity. If we make the leap to assuming that all cellular actions involve entering and leaving states, that all states are identifiable with particular re-entrant SWNs, and that due to the parsimony of evolution, there is much overlap among SWNs and sharing of nodes, it seems possible that the set of hub nodes of a particular SWN can be used as a biochemical address for that SWN, leading to the desired selectivity. The other overlapping SWNs in the treated cell can survive the loss of only one or two hub nodes due to treatment, but not the targeted SWN, which loses all of them.

Problems with the Facts

However, these ideas predict zero response to a single drug, not a large but temporary response. Progress in resolving this will involve consideration of state-trait relationships. For example, a predilection for entering a particular state could be a genetically determined trait, and some states could exist that suppress DNA repair, leading to increasing genetic diversity. Lack of selectivity of anticancer drugs could also be a factor, so that the same drug could delete multiple hub nodes but not all of them.

SWNs in the Brain

Behavioral states such as aggression and siege mentality (the foibles of, respectively, capitalism and communism) also show refractoriness that may have the same cause. In these cases, some likely hub nodes are the neuromodulatory cell groups of the brainstem. An example is the locus ceruleus (LC), which distributes noradrenalin widely in the brain. (Noradrenalin is also the postganglionic transmitter of most of the sympathetic nervous system.) The existence of disciplines such as meditation suggests that some of the SWNs incorporating the LC also incorporate hub nodes in cerebral regions accessible to consciousness, probably including the brain’s language areas. More visceral hub nodes such as blood sugar level are probably also included.

Ancient Foreshadowings of this Theory

The need to treat multiple hub nodes simultaneously to extinguish maladaptive reentrant signaling may have been stated before, but in proto-scientific terms:

“Put on the whole armour of God…”

Saint Paul

#72. The Restricted Weathering Theory of Abiogenesis [chemistry, evolution]

EV   CH

Red, theory; black, fact

Urban lichen in the original ecological niche

Starting at the Start

When the early Earth, which was initially molten, had cooled sufficiently to acquire a solid crust and allow liquid water to accumulate on the surface, the formation of the oceans presumably began.

The Original Energy Source: Weathering

Seawater forms from steam outgassing from volcanic vents, which simultaneously emit acid gasses such as hydrochloric acid. Therefore, the first rain would have been highly acidic. In the normal course of events, volcanic rain falls on surface rocks that contain sufficient alkalinity to completely neutralize the acid, contributing cations such as sodium in the process and producing salt water. 

Key Original Difference

However, shortly after the formation of the Earth’s crust, the surface rocks may have been mostly encapsulated in carbonaceous pyrolysis residues originating from carbon-bearing gasses in the atmosphere. How is the acid rain supposed to get to the rocks?

The Germ of an Idea

I postulate that sometimes it did, and sometimes it didn’t, leading to a scenario of nascent crust covered in interconnected puddles in which a broad range of pHs were simultaneously represented. At the connecting points, a pH gradient would have existed, which recalls the pH gradient across the mitochondrial membrane that powers ATP synthesis. So, that's basically my angle.

Second-iteration Theory

More simply, a lump of lava coated in a capsule of pyrolysis residue and immersed in acid rainwater will have a proton gradient across the capsule with the correct direction to model the inner mitochondrial membrane with its enclosed matrix.

The carbon-bearing gasses in the atmosphere would have been methane, carbon monoxide, and the result of their combination with water (formaldehyde),  nitrogen (cyanide and cyanogen), and sulfur (DMSO, only plausible), all triggered by solar ultraviolet. This suggests that the pyrolysis residues will contain sulfur, oxygen, and nitrogen heteroatoms, as does coal. An imaginary pore through the capsule will be lined with such heteroatoms, which are candidates for playing the role of the arginine, lysine, aspartate, and glutamate residues in the ATP synthase catalytic site. Protonation-deprotonation reactions would be available for powering the formation of polyphosphate (a plausible ATP precursor) from orthophosphate. The conformational changes so important in the modern ATP synthase do not appear to be available in this primordial system, so we need to demonstrate the presence of an equivalent. Conceivably, the phosphorus-rich chemicals diffuse up and down in the pore, producing proton transport as they do so that is linked to phosphate condensation reactions. Judging by the modern ATP synthase, coordination of phosphate to magnesium ions may also be part of the mechanism. Mafic rocks such as basalt, a likely early surface rock, are rich in magnesium.

Third-iteration Theory

The flux of acid through the pore will dissolve orthophosphate out of some minerals in the rock such as apatite. If we suppose that the pore is lined with carboxylic acid groups modelling glutamate and aspartate side chains, then at some depth in the pore the pH in the pH gradient will equal the pKa of the acid, and the acid groups will spend half their time protonated and half ionized, resulting in general acid-base catalysis in a narrow zone in the pore. Magnesium-complexed orthophosphate will be catalytically converted to an equilibrium mixture containing some pyrophosphate in this zone and then proceed to diffuse out the exterior opening of the pore before it can be converted back. As a result, the condensing agent pyrophosphate will be available in the early oceans for catalyzing the formation of organic macromolecules such as early proteins and nucleic acids, which are forerunners of important building blocks of modern life forms. 

The efficiency of the pyrophosphate synthesis would be enhanced by a high phosphate concentration, which would be due to the restricted, under-film spaces in which the weathering processes were occurring.

Fourth-iteration Theory

The gradual expansion of the under-film weathered pockets eventually undermines the local pyrolysis film, causing a flake to detach. The remaining rock surface will be largely coated in the first organic polymers created by condensing agents at low temperature. The process then repeats, leading to successive generations of biofilm creation and detachment. At this point, an evolution-like biofilm selection process can be postulated. Polymer chain elongation from outer layer to inner layer would be likely. The outermost sub-layer will be at acidic pHs, which will cleave the outermost polymer into fragments. Some of these fragments will diffuse inward to the polymerization zone and influence events there, leading to a crude form of heredity. The programmed insertion of abscission points would have been an early development, and these may have prefigured the base pairing of modern polynucleotides. The sand produced as a byproduct of rock weathering will end up enmeshed in the polymer and will come off at abscission. 

Fifth-iteration Theory

Could all this happen inside narrow fissures in the rock? Not likely, because the pH gradient would be present only at the opening, a much smaller niche than the area under a surface film. However, the in-fissure microenvironment would be at alkaline pHs, where alkali-requiring reactions would be possible. An example would be the formose synthesis of C5 and C6 sugars from formaldehyde. A C5 sugar, ribose, is an essential ingredient in RNA synthesis. Fissures opening into the under-film spaces could supply sugars to the polymerization zone.

#71. A Cosmological Setting for a GR-QM Unification [physics]

PH

Red, theory; black, fact

To unify these points most simply, you have to go outside the region of points.

“The Sphere,” campus of the National Research Council, Ottawa 

Figure 1. The expanding 5-ball

Figure 2. A wave packet

The Big Picture

The spacetime of general relativity (GR) is here considered to be an expanding 4D hyperball (4-ball) on the surface of an expanding 5D hyperball (5-ball). The latter is surrounded by subatomic-sized 5-balls ("paramorfs") that can fuse with the big, nearby 5-ball, which is the mechanism by which the latter enlarges. (See Fig. 1). Technically, a “sphere” is just a surface, with a dimensionality one less than the embedding space. I use “ball” here to refer to the embedding space dimensionality.

The Little Picture

Each fusion event sends out a ripple on the surface of the big 5-ball that travels at the speed of light in vacuum. A sequence of fusions happening in the correct order causes the ripples to add up to a shock wave at some point. At the maximum of the shock wave, the surface of the 5-ball is thrown out especially far into the surrounding emulsion of paramorfs, where it makes contact with yet another paramorf, resulting in yet another fusion event and another ripple, which has the correct phase to add to the shock wave. The result is a self-sustaining cycle that leads to persistence and thus observable particle-like phenomena. (See Fig. 2). The shock-wave speed, or “group velocity” will be somewhat less than the speed of light, or “phase velocity” so that ripples will be bleeding out the front continuously. This feature of the theory was introduced to prevent the amplitude of the particle from growing without limit. If the particle is travelling exactly along the time dimension, this bleed will be into the future direction. Therefore, “the future” will have a limited physical reality.

This mechanism was inspired by the superradiant nitrogen laser, in which nitrogen is excited by a zone of corona discharge travelling at nearly the speed of light. This mechanism is also based on Born's rule of quantum mechanics (QM). If wave curvature rather than displacement amplitude determines paramorf fusion probability, then we get something even closer to Born’s rule, which states that the square of the wave function is proportional to the probability of observing a particle. The curvature of a sine wave is not its square, but the resemblance is striking. Perhaps an experimental verification of Born’s rule with unprecedented accuracy is warranted to distinguish the two theories. 

Making It Messier, Like Reality

The big 5-ball may be filled with an emulsion of yin paramorfs in a continuous yang phase, as well as being surrounded by an emulsion of yang paramorfs in a continuous yin phase. Droplets of yin space could get injected into the interior as a side effect after each yang paramorf fusion event. This would explain why curvature alone dictates fusion probability: a concavity reaching interior yin paramorfs is as effective as a convexity reaching exterior yang paramorfs, and no depletion zone will develop over time. Yin and yang space are terms coined in a previous post, “The Checkered Universe.”

The Inflationary Era

Particle formation is entropically disfavored (requires a precise configuration unlikely to arise by chance) and thus only happens when paramorf fusions are frequent due causes other than the presence of particles. Postulating that spontaneous fusions are more frequent when the curvature of the 5-ball is greater, spontaneous fusions will be abundant when the growing 5-ball is still tiny and thus intensely curved. This would be seen in our 4-ball as the inflationary era of the Big Bang. 

A problem is that the paramorfs themselves are the most intensely curved elements in this system. Possibly, a binary paramorf fusion event releases so much energy in such a confined space that the fusion product immediately splits apart, resulting in no net effect overall. Analogously, in gas-phase chemistry, some two-molecule reactions will not go without a third “collision partner” to carry off some of the energy released. 

Time

The surface of our 4-ball would be formed by the stable particles radiating out of our local inflationary zone on the 5-ball into newly-created, blank 4-surface (see Figure 1). This radiation would define the post-inflationary era. Our time dimension would be one of the radii. These particles propagate in time the given, as opposed to time the clock reading. The position of the particle along its track is the clock reading.

Mechanistic Variations

The illustrated mechanism of particle creation (see Figure 2) is periodic-deterministic and may account for photons and leptons. The corresponding chaotic mechanism may account for baryons, and the corresponding probabilistic mechanism may account for dark matter. The close relationship we see today between protons and electrons could have been due to their relationship during the inflationary era; the vicinity of one could have served as an incubator for the other.

Consistency with Relativity

The multitude of expanding spacetime ripples predicted to be around any massive object would comprise the spacetime curvature referred to by the Einstein tensor of the relativistic field equations. The asymmetry of the wave packet that leads to the shock wave accounts for momentum. According to special Relativity, mass-equivalent energy is just the spacetime component of the momentum along the time axis.

A Geometric Underpinning for this Theory

Fixing radius = 1, the 5-ball has the greatest volume of any ball dimensionality. (See the Wiki on “n-sphere”) Thus, this dimensionality could have been forced by some principle of minimizing the radius-to-volume ratio, call it a compaction principle (in a physical, not topological sense), the existence of which is already implied by the assumed ball shape. We cannot invoke gravity here to produce compaction because gravity emerges at a higher level of description than this. A surface tension-like effect related to the permittivity of free space may serve, which is already implied by invoking ripples on the surface. However, mention of ripples implies that the governing differential equation has oscillatory solutions, which seems to also require a medium with inertia, which may be related to the permeability of free space.

Beyond Geometry

If an overarching process of yin-yang separation existed, which would explain why all observations are ultimately observations of contrasts, this process would arguably have a smoothing effect on any resulting interfaces. Such smoothing would suggest surface tension when considered spatially and inertia when considered temporally. I suspect that electromagnetism and matter waves emerge from these simple ingredients. Conservation of paramorf volume would enter the mathematical proof as a constraint.

A limitation of this theory is that it does not explain the assumed presence of discrete, ancient inflationary zones on the surface of the 5-ball.

A Sixth Dimension Is Necessary

Close inspection of the volume versus dimensionality curve for n-balls of radius 1 suggests that maximum volume occurs at a fractional dimensionality somewhat above 5, which looks to be about five and a quarter. Under the compaction principle, this circumstance would lead to a squashed (oblate) 6-ball about one-quarter as thick as it is wide, with greatest curvature at the equator. (Here I am making an analogy with the Earth’s surface, which is an oblate spheroid.) This uneven distribution of curvature would result in the equatorial region losing its inflationary status later than at the poles, suggesting that the universal equatorial region spawned all the particles we can now see during the late inflationary era and that our familiar 3-space corresponds to a line of latitude on the oblate 6-ball travelling steadily toward a pole. 

This scenario allows the existence of ancient, dilute matter of non-equatorial origin coexisting with our 3-space. This ancient, dilute matter could account for cosmic rays and some of the diffuse cosmic gamma glow. Some of these ancient particles would by chance approach us in our future light cones and would therefore interact with our 3-space as antimatter. The resulting annihilation events would produce gamma rays and neutrinos. Those particles that escape annihilation could potentially re-emerge from our spacetime in our past light cones and at a different point, becoming matter cosmic rays. Cosmic particles following spacelike trajectories may not interact strongly with us, like two waves crossing at right angles, but Born's rule predicts some interaction.

A Second Limitation of this Theory

Relativity theory denies the existence of an absolute frame of reference, which I have just re-introduced in the form of the surface of a large ball. Perhaps this limitation can be addressed by showing that the concept of no absolute frame of reference can be replaced with the concept of space-tilted matter, in which the lengths of meter sticks change due to a tilt of the structure of Figure 2 so that propagation is no longer purely in time, but now has a component in space, and the length change must be to a degree necessary to guarantee the null result of the Michelson--Morley experiment.

High Dimensionality

The surface of a 6-ball is a 5-dimensional space. Particle propagation on this surface uses up one of these dimensions, turning it into time. However, the resulting spacetime has four dimensions of space and we see only three. What happened to the other one? Most likely it was largely suppressed by black hole formation shortly after the inflationary era. Black hole formation should be very facile in four spatial dimensions because gravitational orbits are unstable and radiative cooling is relatively efficient. This places us on the event horizon of one of these 4-D black holes and suggests that the event horizon actually is the membrane it seems to be in some theoretical studies. Considered geometrically, the event horizon is a surface and will therefore have a dimensionality one less than that of the bulk. Life on this surface will therefore be three dimensional.

 

In addition, this theory clearly provides a multiverse, because there can be many such hyper black holes, thereby answering the fine-tuning-for-life problem that inspired the anthropic principle.

String theory posits that a particle is a one-dimensional vibrating string embedded in three dimensions. However, my theory posits that a particle is a three dimensional system embedded in six dimensions. We are situated in a privileged location in 6-space in which three of these dimensions have an inward and outward direction. An analogous point in 3-space would be the corner of a cube. The wave component of particles would oscillate along a vector that can rotate in a wholly extradimensional plane, and with an axis of rotation perpendicular to all three dimensions of space, possibly coinciding with time. This would be the spin of the particle. In the cube analogy, one of the edges parallel to the time dimension is spiraling. If the vector rotates in a plane contained within 3-space, this would be the circular polarization of light. A baryon might consist of a trio of fermions, one on each of the three edges meeting at the cube corner and each offset a short distance back from the corner. This arrangement might create a tiny, semi-closed chamber where ripples are concentrated and thus intensified. This, in turn, would enhance paramorf capture, which would dynamically stabilize the structure.

See Figure 3. In this figure, the instantaneous structure resembles one edge of a cube merging with a surface. The line between points A may function as a closed chamber for fusion ripples because of the right-angle relationships at each end, leading to intensified shock waves inside and intensified paramorf fusion. This, in turn, dynamically maintains the geometry shown.

Etymology: "warped spacetime," Greek: paramorfoménos chorochrónos, thus: "paramorf."

Figure 3. A hyper-black hole progressing across the surface of the big 6-ball. The three spatial dimensions of relativity theory have been suppressed for clarity and are represented by points A; t is time.

Tilting at a Conceptual Unification

In general, spacetime structures would tend to evolve to greater efficiency in paramorf capture, and deviations from these structures will appear to be opposed by forces. This can be cited as a general principle in exploring the present theory.

For example, two fermions could capture paramorfs cooperatively: capture by one triggers an expanding ripple that reaches the other and triggers its own capture. This second capture then sends a ripple back to the first fermion, where it triggers a third capture, and so on. This duetting action is formally like light bouncing back and forth between parallel mirrors, as in the light-clock thought experiment of special Relativity, and recalling the Michelson—Morley interferometer. If duetting efficiency maintains the length of meter sticks, we have the beginnings of the long-sought explanation of the null result of the Michelson—Morley experiment in terms that allow the existence of a medium for the wave aspect of particles.

Velocity in space relative to the medium upsets the spatial relationships necessary for efficient duetting, triggering a compensatory reorganization of the spacetime structure to re-optimize paramorf capture efficiency, by the general principle enunciated above. This leads to the Fitzgerald contraction, one of the two basic effects previously explained in terms of special Relativity. The Fitzgerald contraction was recently proven to be directly unobservable; rather, a rotation of the front of the object away from the line of travel is observed, as predicted by Penrose and Tyrell. https://doi.org/10.1038/s42005-025-02003-6. If this rotation looks the same from all observation angles (elevations), it would have to be a rotation into extradimensional space, which the present theory allows, and it is easy to visualize how that would maintain the efficiency of duetting at high velocity. Therefore, close study of the relativistic rotation effect may provide a window on extradimensional space.

The other basic relativistic effect is time dilation; if fermions are always literally travelling along a time dimension as postulated here in connection with the space-tilted matter concept, a greater velocity along any spatial direction must come at the expense of a lesser velocity along the time dimension, leading to time dilation.

Synchronization and anti-synchronization of fusion events between adjacent particles could account for the narrowness of the time slice we seem to be living in.

Duetting could account for attractive forces between fermions and duetting with destructive interference could account for repulsive forces. A difficulty is that the simple ripple model is one-sided whereas destructive interference assumes sinusoidal disturbances, which are two-sided. This could be remedied by assuming that the ripples have profiles like wavelets or the Laplacian of the Gaussian.

At the Limit of this Vision

Paramorf-ripple dynamics looks remarkably biological, featuring elementary processes that recall feeding and natural selection. Their cosmological setting cannot be the end of the story, however, because one naturally wonders where the entire ensemble of yin and yang space came from and why it has a bipartite nature. To answer these questions, it may be necessary to conceive an elemental version of the ultimate power of living things: reproduction. The ineffably great multiplicity of things demands an explanation.

Questions Arising 

• Do we need a new representation system to tackle the question of ultimate origins? 
• Do we merely need to shift from visual to verbal? 
• Is the concept of differentiation valuable here? For example, primordial undifferentiated space and time, primordial undifferentiated time and causation, or primordial undifferentiated somethingness and nothingness. 
• Is entropy increase the ultimate source of all differentiation? 
• Is the concept of primordial fluctuations valuable here? For example, should I proceed as I did in the abiogenesis post, from vacuum fluctuation to persistence by self-repair to growth to reproduction? 
• What is the effect of a vacuum fluctuation in the background of a previous fluctuation?
• Is circularity a key concept here? 
• Is positing an ultra-simplified version of something well known in other disciplines, a kind of consilience, a useful operation? 
• Is the concept of a primordial less-structured space valuable? For example, a topological space is less structured than a Euclidean space. 
• Is the strategy of bringing the observer into the system under study valuable here?
• The further back I go, the fewer the raw materials, but the fewer the constraints. How do I keep from losing my way?

Snail universe beside the Rideau canal. There may be perspectives in which what we consider our own universe looks no grander than this.

Zen weeds in the Rideau Canal. No explanation.