#39. Can Irreducible Complexity Evolve? [genetics, evolution]

EV     GE     

Red, theory; black, fact.

5-26-2018: Influential biologist Richard Dawkins wrote in "The God Delusion" that a genuine case of irreducible complexity will never be found in biology. A case of irreducible complexity would be some adaptation that would require an intelligent designer because it could never evolve one mutation at a time, and Dawkins believes there is no such intelligent designer in biology.

In classic natural selection, each mutation must be individually beneficial to its possessor in order for selection to increase its prevalence in the population to the point where the next incremental, one-mutation improvement becomes statistically possible. In this way, all manner of wondrous things are supposed to evolve bit by tiny bit.

However, I am seeing irreducible complexity all over the place these days. For example, your upper-jaw dentition must mesh pretty accurately with that of your lower jaw or you can't eat. Thus, the process of evolutionary foreshortening of the muzzle of the great apes to the flat human face could never have happened, assuming that a single mutation affects only the upper or lower jaw. But it did. (Let us gloss over the fact that that is an assumption, because the contrary seems to require non-local rules in development.)

Furthermore, how can any instinctive signaling system evolve one mutation at a time? At a minimum, you always need both the transmitter adaptation and the receiver adaptation, not to mention further mutations to connect the receiver circuit to something useful. The evolution of altruism presents a similar problem. The lonely first altruist in the population is always at a disadvantage in competition with the more selfish non-mutants unless it also has a signaling system that lets it recognize fellow altruists (initially, close relatives) and a further mutation that places the altruistic behavior under the control of the receiver part of this system. Thus, altruists would only be altruistic to their own kind, the requirement for altruism to be selected in the presence of selfishness. Finally, the various parts of this system must be indissolubly linked in a way that the non-altruists cannot fake.

My solution is to label the crossing-over events that occur during meiosis as "tetra-mutations." In crossing over, two homologous chromosomes pair up along their length and swap a long segment of DNA, a process requiring four double chain breaks and their corresponding repairs. Because of the presence of single-nucleotide polymorphisms, the homologous chromosomes are not exactly the same, so that each of the upstream sides of the four chain breaks ends up in a subtly different genetic environment. If the break point falls between a cis-acting regulatory element and the corresponding structural gene, for instance, the former may now control the expression of a slightly different protein. Thus, there could be as many as four distinct functional consequences of one crossing-over event. Why not call that a tetra-mutation?

In this way, a concerted change affecting four distinct sites becomes possible. The two ends of the recombinant segment can in principle be functionally unrelated initially. They become related if both are affected by the same tetra-mutation and the entire change increases fitness and is thus selected.

A single tetra-mutation could in principle produce viable altruism at one stroke because of the number of simultaneous changes involved. 

The probability of a combination of simultaneous local changes being beneficial to the organism is much smaller on mathematical grounds than is the probability of a given single-nucleotide change being beneficial. However, these unfavorable statistics are at least partly offset by the existence of a dedicated system for producing tetra-mutations in large numbers, namely meiosis, part of the process of maturation of egg cells and sperm cells.

In the big picture, tetra-mutations provide a way for a species to discontinuously jump into new niches as they open up, possibly explaining how a capacity for this kind of mutation could spread and become characteristic of surviving species over time. This idea also provides a ready explanation for the lack of transitional forms in the fossil record.

5-30-2018: Here is the search description again, in case you missed it or could not see all of it: Sexual reproduction may allow the evolution of irreducible complexity by increasing the intrinsic complexity of the basic building block of change, the mutation.

6-12-2018: Upon further reflection, it seems that the tetramutation construct described above lacks validity because during gamete maturation it falls apart into two bi-mutations, both of which cannot contribute to the same zygote. The bi-mutation is stable, however, because of the intervening translocated DNA segment. It is harder to see how a complex adaptation like altruism could evolve out of nothing but mono-mutations and bi-mutations, but that does not mean the theory put forward in this post is necessarily wrong. One must not argue from lack of imagination. It is an interesting question, actually, what is the minimum set of all mutation types necessary to account for all known adaptations.

8-27-2019: In my ignorance, I have undersold the bi-mutation idea. A very far-reaching change to the genetic information can occur during crossing-over that is not at all subtle and is termed unequal crossing-over. This form of the process arises because of inaccuracies, sometimes major, in the initial alignment of the homologous chromosomes prior to crossing-over. When the process is finished, one chromosome has been shortened and the other has been lengthened, with gene duplication. This is the major source of gene duplication, which, in turn, is a major source of junk DNA, the part that is classified as broken genes. Two questions come to mind. The first is, are anatomical features such as jaw length and axon targets somehow controlled by variations in gene dose? The second, which is a tangent, is, are broken genes really broken or just temporarily switched off by genetic drift at some mutational hot spot in the recognition site of some transcription factor? The analogy here is to a generator in a power plant that has been placed in stand-down mode because of a temporary decrease in the demand for electrical power.

#38. The Fallacy of Justice [evolutionary psychology]

EP

Red, theory; black, fact.

4-04-2018: In my treatment of evil and criminality so far, I have tried to show that they sub serve either dispersal or preemptive population reduction, both valuable biological processes that tend to prolong the survival of species. 

The algorithms for achieving these ends would have been created over time by some form of evolution, with probably a large component coming from a hypothetical, fast form of evolution I call post-zygotic gamete selection (PGS), where gametes -- individual cells -- are effectively the units of selection. In general, the smaller the unit of selection, the faster the adaptation. PGS may have accelerated evolution to the point where it could be detected by simple record-keeping technologies, which may have led to the first record-keeping peoples eventually realizing that "someone is looking out for us," leading to the invention of monotheism.

The genetically inherited parts of our behavior enter consciousness as emotions, and can therefore be easily identified. The main outlines of civilization are probably due to the inherited behavior component, and not to the reasoning, conscious mind, which is often just a detail-handler. How could civilization rest on a process that can't even remember what happened last weekend?

Thus, humans have a dual input to behavior, emotion and reason. The above arguments show that evil and criminality come from the emotional input. Yet the entire deterrence theory of justice assumes the opposite, by giving the person a logical choice: "You do this, we do that, and you won't like it. So you don't do this, right?"

I'm not so sure. People commit crimes for emotional reasons. As usual, the criminal's reasoning faculties are just an after-the-decision detail handler. The direction that this detail handler then takes is fascinatingly monstrous, but this does not mean that crime begins in reason.

Conclusion: the deterrence theory of justice is based on a category error.

Religion, with its emphasis on emotion, was all the formal "law enforcement system" anyone needed up until only about 200 years ago, at the industrial revolution. We may be able to go beyond where religion takes us by means of a disease model of criminality.

It does make some sense to lock criminals up, because with less freedom they cannot physically commit as many crimes. Many prisons become dungeons, however, because of the public's desire for revenge. However, all revenge-seeking belongs to the dispersal/depopulation dynamic and is thus part of the problem. A desire for revenge may follow a crime very predictably, but logically, it is a non-sequitur.

4-30-2018: A more nuanced theory of crime prevention is possible, where logical and technological constraints on behavior complement efforts to reduce the motivation for committing crimes at the source: the individual's perception of the fairness of society. However, I originally wrote as I did because I don't think that the former is the squeaky wheel at the moment.

#37. Two Kinds of War [evolutionary psychology, engineering, neuroscience]

EN     EP     NE     

Red, theory; black, fact.

3-17-2018: In my post "The Pilgrim and the Whale", I propose that much human conflict sub serves dispersal.

12-28-2017: There are probably two basic biological uses for human anger, the other one being an emergency brake on population increase that avoids Malthusian disasters by triggering wars. This kind of war ends life without being notably efficient in producing mass migration. This is the use discussed in my post "The Iatrogenic Conflicts of the Twentieth Century." Mention of the destruction of Coventry was struck out because it looks better suited to population reduction than to triggering mass migration.

3-12-2018: I have long wondered why the Four Horsemen of the Apocalypse seem to include two gentlemen both in charge of warlike matters. Why the apparent duplication? The above postscript may give the reason: one (the guy with the bow) represents wars of (absolute) depopulation and the other (the guy with the sword) represents wars of displacement (relative depopulation).

The Coventry Blitz did, however, produce so much mass migration into the countryside surrounding that city that it was an embarrassment for the British government, calling into question Britain’s willingness to fight. This got me thinking: was Coventry some kind of watershed, before which the conflict was of the displacement type, and afterward, of the depopulation type?

The facts bear this out, considering Nazi treatment of the Jews as a litmus test of the zeitgeist of that time. After coming to power in 1933, the Nazis aimed at forcing the Jews to emigrate, and by the outbreak of hostilities in September, 1939, 250,000 of Germany’s 437,000 Jews had done so. The Coventry Blitz was in November, 1940. The Holocaust began, in terms of men, women, and children all being targeted for execution, in August, 1941, nine months later. The German zeitgeist, and perhaps that of the world, seems to have shifted gears in the fall of 1940, aiming at depopulation rather than displacement. I am obviously assuming that the evolutionary, selectionist justification of the Holocaust given at the time, in forums such as the 1942 Wannsee conference, was a rationalization.

I conjecture that wars brought on by population pressure begin as the displacement type, and if this does not result in sufficient local reduction in population pressure after a certain time, the hostilities shift gears to the depopulation type of conflict. If human population is under PID [proportional-integral-differential] control by the subconscious, the event causing the shift could be the amount of signal accumulated on the integrator rising above some threshold. This may actually be a second threshold, with the first and lower threshold controlling the outbreak of a war of displacement.

A paradoxical outcome of Calhoun's overpopulation experiments on rodents can be explained in terms of such an integrator. By providing unlimited food and water to a founder population of rats or mice, with regular bedding changes and exclusion of predators and parasites, the rodents were allowed to increase their population to fabulous numbers. However, the rodents were given no extra space. As the population soared to incredible densities, all kinds of pathological behaviors appeared along with a great deal of violence. Birth rates plummeted after a "behavioral sink" developed, and remained low, never recovering, as the population decreased all the way to zero.

My interpretation of the behavioral sink is that it is integrator windup, a pathology of humanly engineered PID controllers, and possibly natural ones too. The signal accumulated on the integrator has been building for so long, and the population crash is so sudden, that not enough time is spent at population densities below set point to cancel the "control debt" on the integrator, so it continues to insanely command a zero birth rate even as the population is heading for zero.

George Santayana wrote that "Fanaticism consists of redoubling your efforts when you have forgotten your aim." [source, Wiki quotes, accessed 06-11-2018] Sounds like integrator windup to me.

3-17-2018: To clean up some loose ends, let us postulate a third and highest threshold of the control debt, which, if crossed, leads to the human behavioral sink and the possible destruction of the human race due to essentially psychological causes. In the behavioral sink, I postulate that everyone would be a ZPG fanatic and unable to change without pharmacological help. (Good old booze? May not be that simple.) 

I myself may be a "ZPG fanatic", and produced in exactly this way, because I was born in 1953, just before suburbia became important, and may represent what most people in this country would now be had suburbia not been invented to take down the population pressure. At only 2 months from retirement age, I continue to be a virgin with no plans to change my ways, and I may be a straw in the wind, a harbinger of worse to come.

11-26-2019: I can testify from my own experience that the human behavioral sink is more like passive-aggressive personality disorder than anything else, but with particular attention to punishing the opposite sex by ignoring them.

3-22-2018: Correction: the modern suburbs were invented in London 200 years ago, but underwent explosive growth in North America after WWII. By 1950, half the American population was suburban.

#36. The Thought Process Through the Ages [evolutionary psychology]

EP

Red, theory; black, fact.

2-01-2018: An alternative title of this post could be: "Where religion possibly fits in the big scheme of things."

If politics and science seem like strange bedfellows, consider that ancient rulers used to consult astrologers before making major decisions.

In the beginning, there was theology. At some point, intellectual endeavor split into wrestling with reality questions vs. morality questions. Then they had to figure out when to go with your gut and when not to.

Thought sources	Inputs	Outputs (all insights):
		Reality (What is)	Blend	Morality (Thus…)
PGSd+sensory data	Emotion	politicsc		religionc
	Blend	astrologyb ^ v	< theologya >	Jewish lawb ^ v
Education+sensory data	Reason	sciencec		lawc

a. primordial condition

b. output distinction added

c. input distinction added

d. “post-zygotic gamete selection,” amateur theory of accelerated evolution purporting to explain God. See “Emotions” post on this blog.

2-23-2018: Just as emotion must not be allowed to contaminate scientific thought, is it equally true that reason must not be allowed to contaminate religious thought? Is failure to observe this restriction the cause of religious schisms?

08-03-2019: Thought-like processes dominated by emotion are believed to exist, e.g., the "emotional processing" of traumatic memories.

#35. The Pilgrim and the Whale [evolutionary psychology]

EP

Red, theory; black, fact.

12-26-17: Just as the whale must hold its breath to obtain its food from the sea, so must a human restrain his or her anger to obtain a paycheck from society. Don't laugh, for the analogy is exact.

The ecological niche occupied by the whale places two of its drives in contradiction: the drive to eat and the drive to breathe. In humans, the contradictory drives are eating and dispersal.

Dispersal is a biological process tending to expand the geographical range of a species. Left to itself, the range shrinks inexorably because of natural disasters such as fire, frost, famine, drought, and pestilence wiping out all members of a given species in a given habitat. When each habitat occupied by the species has had its disaster, the species will be extinct if it has not been dispersing all along. Dispersal re-populates the devastated habitats as they become able to support life again, thereby staving off extinction.

Unfortunately, human dispersal begins with fraught political contests. As soon as one side gets the upper hand, the other must flee. Result: mass migration, i.e., dispersal. Most human anger is really dispersal hunger. However, when people get mad, they break stuff. Stuff like buildings, airports, factories, railway lines, etc. This is the infrastructure on which we all depend for our survival. Because our ecological niche is in a fragile built environment, we are required to compromise between eating and dispersal. And there you have my analysis of the biological roots of our unhappiness.

This contradiction in drives is the ultimate reason why every able-bodied Muslim must make the pilgrimage to Mecca at least once in their lifetime: it mellows them out by giving something to the dispersal drive. The same effect would explain the fact that first-generation immigrants are generally more law-abiding than the natives.

Other institutions that may exist to relieve dispersal hunger are: tourism, the fitness movement, Seeing the World, conference-going, joining the Navy, going away to university, visiting faraway relatives for the holidays, companies moving their employees around a lot, and others I'll think of tomorrow morning.

Happy trails.

2-14-2018: Catholicism is also famous for its tradition of pilgrimage, to such places as Jerusalem, Rome, Lourdes, and Santiago de Compostela, the latter still popular today. Protestantism has no such tradition, however.

3-12-2018: Judaism, Hinduism, and Buddhism all have strong traditions of pilgrimage, and the practice is so universal that it has been proposed as a Jungian archetype by Clift and Clift. I myself walk a lot, because I cannot afford a car or a downtown apartment close to all the amenities. But is that the ultimate reason? 

#34. Emotions [evolutionary psychology, genetics, neuroscience]

EP    NE    GE

Red, theory; black, fact.

12-17-2017: In previous posts, I theorized that humans, along with all other sexually-reproducing species, have a long-range guidance system that I called proxy natural selection, or preferably, post-zygotic gamete selection (PGS), that is basically a fast form of evolution in which individual cells, the gametes, are the units of selection, not individuals. Selection is conjectured to happen post-zygotically (i.e., sometime after the beginning of development, or even in adulthood) but is retroactive to the egg and sperm that came together to create the individual. Each gamete is potentially unique because of the crossing-over genetic rearrangements that happen during its maturation. This theory explains the biological purpose of this further layer of uniqueness beyond that due to the sexual mixing of chromosomes, which would otherwise appear to be redundant.

Our emotions are conjectured to be programmed by species-replacement group selection and to serve as proxies for increases and decreases in the fitness of our entire species.

A further correlate of an emotion beyond the cognitive and autonomic-nervous-system components would be the neurohumoral component, expressed as chemical releasing and inhibiting factors that enter the general circulation via the portal vessels of the hypothalamus, blood vessels which are conventionally described as affecting only the anterior pituitary gland. These factors are theorized to reach the stem-like cells that mature into egg and sperm, where they set reversible epigenetic controls on the level of crossing-over that will occur during differentiation. Large amounts of crossing-over are viewed as retroactively penalizing the gametes leading to the individual by obfuscating or overwriting with noise specifically the genetic uniqueness of said original gametes. In contrast, low levels of further crossing-over reward the original gametes with high penetrance into the next generation. Here, I believe you have all the essential ingredients of classical natural selection, and all the potential, in a process that solves problems on an historical timescale.

Crossing-over happens only between homologous chromosomes, which are the paternal and maternal copies of the same chromosome. Human cells have 46 chromosomes because they have 23 pairs of homologous chromosomes. The homologous-chromosome-specificity of crossing-over suggests that the grand optimization problem that is human evolution has been broken down into 23 smaller sub-problems for the needs of the PGS process, each of which can be solved independently, without interactions with any of the other 22, and which involves a 23-fold reduction in the number of variables that must be simultaneously optimized. In computing, this problem-fragmentation strategy greatly increases the speed of optimization. I conjecture that it is one of the features that makes PGS faster than classical natural selection.

However, we now need 23 independent neurohumoral factors descending in the bloodstream from brain to testis or (fetal) ovary, each capable of setting the crossing-over propensity of one specific pair of homologous chromosomes. Each one will require its own specific receptor on the surface of the target oogonia or spermatogonia. Check this out in the literature, and you will already find a strange diversity of cell-surface receptors on the spermatogonia. (I haven't looked at oogonia yet.&&) I predict that the number of such receptors known to science will increase to at least 23. None of this is Lamarkism, because nervous-system control would be over the standard deviation of behavioral traits, not their averages.

1-09-2018: Naively, this theory also appears to require 23 second messengers to transfer the signals from cell surface to nucleus, which sounds excessive. Perhaps the second messengers form a combinatorial code, which would reduce the number required by humans to log2 (23) = 4.52, or 5 in round numbers. This is much better. Exactly five second-messenger systems are known, these being based on: cyclic AMP, inositol triphosphate, cyclic GMP, arachidonic acid, and small GTPases (e.g., ras). However, many mammalian species have many more than the 32 chromosome pairs needed to saturate a 5-bit address space.

1-10-2018: If we expand the above list of second messengers with the addition of the calcium/calmodulin complex, the address space expands to 64 pairs of homologous chromosomes, for a total ploidy of 128. This seems sufficient to accommodate all the mammals. Thus, a combinatorial second-messenger code representable as a five- or six-bit binary integer in most organisms would control the deposition of the epigenetic marks controlling crossing-over propensity.

If the above code works for transcription as well as epigenetic modification, then applying whatever stimuli it takes to produce a definite combinatorial second-messenger state inside the cell will activate one specific chromosome for transcription, so that the progeny of the affected cell will develop into whatever that chromosome specifies, be it an organ, a system, or something else. And there you may have the long-sought key to programming stem cells. You're welcome.

Each pair of homologous chromosomes may correspond to what in an earlier post was called a "PNS focus." The requirement that the evolution of each chromosome contribute independently to the total increase in fitness suggests that a chromosome specifies a system, like the nervous system or the digestive system. We seem to have only 11 systems, not 23, but more may be defined in the future.

A related concept is that a chromosome specifies an ancestral, generic cell type, like glial cells (4 subtypes known) or muscle cells (3 subtypes known). The great diversity of the neurons suggest that they must be reclassified into multiple basic types, perhaps along the lines suggested by the functional classification of the cranial nerves: general somatic, general visceral, and special somatic (i.e., specific senses).

1-09-2018: A third concept for function assignment to homologous pairs of chromosomes postulates a hypothetical maximally divided genome in which each cell type has its own chromosome pair, a state conjectured to seldom occur in nature. Co-evolution of clusters of cell types (e.g., neurons and glia; bone and cartilage) would create selection pressure for the underlying cell-type-specific chromosomes to become covalently linked into the larger chromosomes that we see in the actual karyotypes. Thus, each observed homologous pair would correspond to a few cell types that are currently co-evolving, which seems to return us to the system or organ concept. 

01-08-2019: The system specified by a chromosome may be called a cooperation system, and these may be organized in a hierarchy, following the general principles of spatial organization outlined in my post: "The Pictures in Your Head." Chromosomes activated earlier in development will specify system-like entities and those activated late in development will specify organ-like entities. Only the first-activated chromosome will apply to the entire organism.

Humans depend on complex social structures for their survival, and this comes out of our individual behavioral tendencies. Probably, most PGS adaptations to environmental fluctuations involve modifying these structures, which would come out of subtle modifications of individual behaviors. I think I am just repeating E.O. Wilson here. Our hard-wired species-fitness definitions would give rise to the primary emotions, perhaps in the hypothalamus or limbic system, by connecting specific stimuli to primary emotions in the manner of an if-then rule. 

Further out on the cortex, the specific stimuli being connected would get progressively more complex and learning-dependent, and progressively less concerned with the "what" of behavior (i.e., our species-specific taxes) and more with the "how" of behavior. In "how" mode, the complex stimuli become more like signposts to be consulted on a journey. PGS adaptations of our behavior would affect the hardwired aspects of this hypothetical transition zone. The primary emotions would then be like the highest hierarchical level of our motor program, or like the least-indented instructions of a conventional high-level computer program.

I conjecture that religion is important because it goes straight for this highest level. We all know that religion is kind of an emotional business, what with the organ music and the stained glass and all such as that, and this is why. I therefore conjecture that words spoken often from the pulpit, such as God, sin, forgiveness, devil, angel, soul, salvation, etc., all enclose a secret that writers such as Dawkins do not grasp: the emotions are the message. To illustrate this, let us attempt an emotional definition of the master symbol, "God."

God: feeling loved and secure to the point of invulnerability; feeling small in an agreeable way, as in the presence of mountains; feeling brotherly/sisterly towards one's fellow humans; blossoming in confidence into one's full potential; fearing nothing.

Perhaps that's enough to give the general idea. No doubt a whole dictionary could be compiled along these lines. When the priest strings these emotion-words together, he creates an experience for the congregation that could fairly be called a form letter from "God," assuming that the word "God" points to the PGS process itself. The job of the priest is to help the congregation relate on a deep level to the sacred texts and to see/feel how they apply to the challenges of the here and now.

7-05-2018: Another term for PGS would be "Yahwetion," from "Yahweh," the conventional modern spelling of the name of the god of ancient Israel, and the "tion" ending indicating a process, like evolution. This neologism advantageously steers people away from category errors like attempting to worship it, or appease it, or what have you.

The conventionally religious will complain that this would make prayer to God impossible, but not if prayer itself is re conceived as "auto socialization," following the educational theory of prayer. Then prayer becomes a fantasy conversation with anyone, living or dead, that you would like to have as a mentor, if it were possible.

#33. Big-electron Theory [physics]

PH

Red, theory; black, fact.

Some of the paradoxes and weirdness of quantum mechanics can be dispelled if we assume that any particle that can be diffracted isn't really there: we are only looking at the center of spherical symmetry of a much larger, possibly cosmologically large, wave function. Furthermore, this center of symmetry is only an abstraction, like the north pole of the Earth. Like the fields that we impute to them, quantum particles would have a wave function amplitude that decreases asymptotically to zero with distance from the center, and thus would have no well defined outer boundary. I shall denote this lack of an outer boundary by calling particles or wave functions "expansive."

Elementary particles seem submicroscopic in size because the wavelength of the corresponding wave functions is often submicroscopic, which imposes a requirement for the centers of symmetry of two such "particles" to coincide with very great precision before an interaction can be observed. This would be the case if the default interaction were characterized by destructive interference almost everywhere, which only switches over into constructive interference when the centers nearly coincide. An assumption needed for further development of this theory is that interaction is contingent on the development of expansive constructive interference. (In this post, I confine my attention to scattering-type interactions.)

The common presence of  accelerations in our universe combined with a finite speed of light might suggest that expansive wave functions would quickly fill up with incoherence, destroying their usefulness as explanatory causes. However, if there are no non-expansive elementary particles, we just have expansive interacting with expansive to produce every acceleration. Once you get entirely away from the tiny-electron idea, it is not at all clear that any incoherence could ever develop. Such may well occur to a limited extent under some conditions, however, but it may take more detailed mathematical treatments than I am prepared to carry out to characterize these conditions. One naturally suspects that Relativity theory is based on such limited incoherencies.

Two baffling kinds of experiment seem amenable to the big-electron treatment: diffraction of "particles" of matter like electrons, and entanglement experiments.

Electrons fired in a vacuum at a pair of closely-spaced slits, with a photographic plate situated on the other side of the slits, will produce a diffraction pattern on the developed plate consisting of alternating exposed and unexposed bands. These are interpreted as locations of constructive and destructive interference between "matter waves" emanating from the two slits under the stimulation of the electron beam. If the intensity of the beam is lowered to the point where only one electron is "in the chamber" at a time, thereby eliminating the possibility of inter-electron interactions inside the chamber, the diffraction pattern develops just as before. It merely takes longer. Now here's the weird part: all this could happen only if each electron goes through both slits at once! This is truly weird if we try to use the traditional tiny-electron picture, but much easier to visualize using the big-electron picture.

Entanglement of two particles that persists over distances measured in kilometers is also easier to understand if we remember that the experimental apparatus is itself made up of expansive wave functions and is therefore mostly overlapped with the two particles being studied throughout the experiment.

If all this is true, we live in a vast web of inter-validating illusions called the particle model.