Sunday, March 11, 2018




When a haredi man asked me to change my seat on a plane for him
March 9, 2018, 9:28 am 0

http://blogs.timesofisrael.com/when-a-haredi-man-asked-me-to-change-my-seat-on-a-plane-for-him/?utm_source=The+Times+of+Israel+Daily+Edition&utm_campaign=ce3b1a9617-EMAIL_CAMPAIGN_2018_03_11&utm_medium=email&utm_term=0_adb46cec92-ce3b1a9617-55741445

On a full El Al plane to New York, I had just gotten settled in my hard-won aisle seat when two Hasidic men, one visually impaired, approached my row. The other, who was clearly looking out for both of them, glanced toward the two empty seats next to me with apparent dismay.
He double-checked that those were indeed their seats, and right away asked a man in a nearby aisle of the middle section if he would switch with me, which he consented to do. I felt bad, but I really prefer the window section, even if I’m in an aisle seat so I declined to move.
I realized that they probably needed to remain together so one could help the other, but I was not stopping them from sitting in the two perfectly available seats next to me and did not wish to inconvenience myself.
He accepted my response politely and went and found a gentleman a few rows back in an equivalent seat to my own, who was also willing to move. He then asked me again. I agreed immediately and moved.
Our little “musical chairs” was accomplished calmly and efficiently. A passenger in a nearby seat got up and kindly switched the places of both our overhead bags, mine and the gentleman’s, to be closer to our new seats. Everything was done respectfully and without undue inconvenience or resentment.
There are plenty of people with plenty of reasons for the things that they do. We may or may not like everything. Personally, I am very uncomfortable with over-segregation of women in the religious sector. But if no one is inconvenienced, and everyone is respectful — and respected — why not make that little effort so that everyone is comfortable?
If I got on a bus and were asked to sit in the back, I would NOT be so nice. The situation on the plane was different. I extended the same courtesy that I would have extended to anyone asking to switch seats for any reason. Frankly, the reason doesn’t involve or interest me at all, nor was it ever mentioned. I had a choice and I only acquiesced when it truly didn’t affect me at all.
Further, I was actually very happy to sit with two delightful young women who were equally happy to sit with me, rather than sitting with two men who would have felt uncomfortable throughout. Interesting to note that one of the women was also asked to switch her seat, for a reason that had nothing to do with women or Haredim…
Do we look unhappy? 🙂
The experience let me see this hot-topic issue through different eyes. Mind you, I will still fight for women’s rights in the religious sector — or anywhere. But one of those “rights” isn’t the right to sit next to men on a plane. Unless it’s your family member and you’re forcibly made to sit apart for “religious reasons.”
But this? This was simply an opportunity to do a nice thing for a fellow passenger that hurt no one and made a lot of people smile. To me, that’s a win.
This post has been contributed by a third party. The opinions, facts and any media content here are presented solely by the author, and The Times of Israel assumes no responsibility for them. In case of abuse, report this post.


Tuesday, March 6, 2018







A survey of 7,000 freshmen at colleges and universities around the country found just 6 percent of them able to name the 13 colonies that founded the United States. Many students thought the first president was Abraham Lincoln, also known for “emaciating the slaves.” Par for the course these days, right?
It happens that the study in question was reported in The New York Times in 1943. The paper conducted the survey again during the Bicentennial, using more up-to-date methods, and found no improvement. “Two‐thirds [of students] do not have the foggiest notion of Jacksonian democracy,” one history professor told the Times in 1976. “Less than half even know that Woodrow Wilson was president during World War I.”
Reading the remark now, it’s shocking that he was shocked. After 40 years, our skins are thicker. (They have to be: asking the current resident of the White House about Jacksonian democracy would surely be taken as an invitation to reminisce about his “good friend,” Michael.)
The problem with narratives of decline is that they almost always imply, if not a golden age, then at least that things were once much better than they are now. The hard truth in this case is that they weren’t. On the average, the greatest generation didn’t know any more about why The Federalist Papers were written, much less what they said, than millennials do now. The important difference is that today students can reach into their pockets and, after some quick thumb typing and a minute or two of reading, know at least something on the topic.
How to judge all this is largely a question of temperament -- of whether you see their minds as half-empty or half-full. Tom Nichols conveys the general drift of his own assessment with the title of his new book, The Death of Expertise: The Campaign Against Established Knowledge and Why It Matters, published by Oxford University Press. The author is a professor of national security affairs at the U.S. Naval War College and an adjunct professor at the Harvard Extension School.
He sees the longstanding (probably perennial) shakiness of the public’s basic political and historical knowledge as entering a new phase. The “Google-fueled, Wikipedia-based, blog-sodden collapse of any division between professionals and laymen, students and teachers” is like a lit match dropped into a gasoline tanker-sized container filled with the Dunning-Kruger effect. (It may seem comical that I just linked to Wikipedia to explain the effect, but it’s a good article, and in fact David Dunning himself cites it.)
Nichols knows better than to long for a better time before technology shattered our attention spans. He quotes Alexis de Tocqueville’s observation from 1835: “In most of the operations of the mind, each American appeals only to the individual effort of his own understanding.” This was basic to Jacksonian democracy’s operating system, in which citizens were, Tocqueville wrote, “constantly brought back to their own reason as the most obvious and proximate source of truth. It is not only confidence in this or that man which is destroyed, but the disposition to trust the authority of any man whatsoever.”
The difference between a self-reliant, rugged individualist and a full-throated, belligerent ignoramus, in other words, tends to be one of degree and not of kind. (Often it’s a matter of when you run into him and under what circumstances.) Nichols devotes most of his book to identifying how 21st-century American life undermines confidence in expert knowledge and blurs the lines between fact and opinion. Like Christopher Hayes in The Twilight of the Elites, he acknowledges that real failures and abuses of power by military, medical, economic and political authorities account for a good deal of skepticism and cynicism toward claims of expertise.
But Nichols puts much more emphasis on the mutually reinforcing effects of media saturation, confirmation bias and “a childish rejection of authority in all its forms” -- as well as the corrosive effects of credential inflation and “would-be universities” that “try to punch above their intellectual weight for all the wrong reasons, including marketing, money and faculty ego.” Unable to “support a doctoral program in an established field,” Nichols says, “they construct esoteric interdisciplinary fields that exist only to create new credentials.”
Add the effect of consumerism and entertainment on the academic ethos, and the result is a system “in which students learn, above all else, that the customer is always right,” creating a citizenry that is “undereducated but overly praised” and convinced that any claim to authoritative knowledge may be effectively disputed in the words of the Dude from The Big Lebowski: “Yeah, well, you know, that’s just, like, your opinion, man.”
As a work of cultural criticism, The Death of Expertise covers a good deal of familiar territory and rounds up the usual suspects to explain the titular homicide. But the process itself is often enjoyable. Nichols is a forceful and sometimes mordant commentator, with an eye for the apt analogy, as when he compares the current state of American public life to “a hockey game with no referees and a standing invitation for spectators to rush onto the ice.”
But one really interesting idea to take away from the book is the concept of metacognition, which Nichols defines as “the ability to know when you’re not good at something by stepping back, looking at what you’re doing, and then realizing that you’re doing it wrong.” (He gives as an example good singers: they “know when they’ve hit a sour note,” unlike terrible singers, who don’t, even if everyone else winces.)
“The lack of metacognition sets up a vicious loop, in which people who don’t know much about a subject do not know when they’re in over their head talking with an expert on that subject. An argument ensues, but people who have no idea how to make a logical argument cannot realize when they’re failing to make a logical argument …. Even more exasperating is that there is no way to educate or inform people who, when in doubt, will make stuff up.”
The implications are grave. In 2015-16, Donald Trump ran what Nichols calls “a one-man campaign against established knowledge,” and he certainly pounded the expertise of most pollsters into the dirt. He is now in a position to turn the big guns on reality itself; that, more than anything else, seems to be his main concern at present. Nichols writes that research on the Dunning-Kruger effect found that the most uninformed or incompetent people in a given area were not only “the least likely to know they were wrong or to know that the others were right” but also “the most likely to try to fake it, and the least able to learn anything.” That has been shown in the lab, but testing now continues on a much larger scale.

Sunday, March 4, 2018

The  Biggest  Myth  In  Quantum  Physics

Quantum interpretations are all the rage. Too bad you don’t even need one.

[An excellent summary of how little we understand about the universe.]]

https://medium.com/starts-with-a-bang/the-biggest-myth-in-quantum-physics-a2df25559b2e - go there  for instructive pictures

In everyday life, there are certain rules we take for granted: cause-and-effect, for instance. Something occurs, and that causes other things to occur dependent on what happened at the start. Different causes lead to different effects. But in the case of quantum physics, the standard rules are fundamentally different. You can’t define even your starting point to arbitrary precision, as there’s an uncertainty inherent to certain properties of your system. There isn’t a predictable, deterministic way to describe how your system evolves over time, only a set of probabilities that you can calculate. And, if you make a definitive enough measurement, observation, or interaction, you will see a single outcome: the effect you were looking for. But the very act of making that measurement, observation, or interaction fundamentally changes the state of your system.
How to interpret this behavior has been the subject of debate for nearly a century. The resolution, however, may be unsettling to anyone who comes across it: not to interpret it at all. As puzzling as it sounds, interpretations may be the very thing that prevent us from truly gaining an understanding of our quantum reality.

If you’re given the energy levels and other properties of an electron in a hydrogen atom, you can only come up with a probability distribution for where the electron is at any given instant. The act of measuring will give you an outcome, but until you make that measurement, the electron’s position is not determined. Image credit: PoorLeno / Wikimedia Commons.
Consider the case of Schrödinger’s cat. Place a cat in a box with a single radioactive atom in there. If the atom decays, poison is released; the cat eats it and dies. If the atom doesn’t decay, the poison isn’t released; the cat lives. This analogy bothered Schrödinger tremendously, because under the cause-and-effect rules, either the cat must either be alive or not alive. The atom decayed or it didn’t, the poison was released or it wasn’t, and the cat died or didn’t die. But if you don’t make a measurement, observation, or cause an interaction that tells you the outcome, the atom — and hence, the cat — must be in a superposition of states, meaning the cat is both alive and dead at the same time. The failure to know whether a (theoretically quantum) animal is alive or dead, and insisting it must be a mix of both, is a classic example of quantum weirdness.

Inside the box, the cat will be either alive or dead, depending on whether a radioactive particle decayed or not. If the cat were a true quantum system, the cat would be neither alive nor dead, but in a superposition of both states until observed. Image credit: Wikimedia Commons user Dhatfield.
Another one, that’s not an analogy but an actual experiment, involves firing a single electron at a barrier that contains two narrow slits in it, separated by only a short distance, with a screen behind them. Common sense tells you that the electron should go through either the left slit or the right slit, and that if you fire many such electrons in a row, you should get two bunches: one corresponding to electrons that went through the left slit, the other corresponding to those that went through the right slit. But that’s not what happens at all.

The wave pattern for electrons passing through a double slit, one-at-a-time. If you measure “which slit” the electron goes through, you destroy the quantum interference pattern shown here. Note that more than one electron is required to reveal the interference pattern. Image credit: Dr. Tonomura and Belsazar of Wikimedia Commons.
Instead, what you see on the screen looks like an interference pattern. These individual electrons are behaving like waves, and the patterns looks like what you’d get if you fired continuous light waves through a double slit, or even sent water waves through a tank with two gaps where the slits are.

Double slit experiments performed with light produce interference patterns, as they would for any wave. The properties of different light colors is due to their differing wavelengths. Image credit: Technical Services Group (TSG) at MIT’s Department of Physics.
But these are single electrons! Where are they, at any given point in time, and which slit did they go through?
You might think to set up a detector at each slit, to measure which one each electron goes through. And you can do this: electron #1 goes through the right slit; #2 goes left; #3 goes left; #4 goes right; #5 goes left, and so on. But now, when you look at the pattern of electrons on the screen, you don’t get the interference pattern you had before. You only get the two bunches. Somehow, the act of observing, measuring, or forcing an interaction has changed the outcome.

If you measure which slit an electron goes through, you don’t get an interference pattern on the screen behind it. Instead, the electrons behave not as waves, but as classical particles. Image credit: Wikimedia Commons user Inductiveload.
This quantum weirdness isn’t just unsettling, it defies a clear explanation as to what’s actually going on. One approach has been to create an interpretation of quantum mechanics. There are a great many examples of ways people have tried to make sense out of what’s happening here. They include:
·         the Copenhagen Interpretation, asserting that the quantum wavefunction is physically meaningless until a defining measurement is made, and only assigns probabilities for what would occur if you made such a measurement, which “collapses” the wavefunction,
·         the Many-Worlds Interpretation, which holds that quantum states interact with the environment, producing entanglement and an ever-growing number of possible outcomes, where an exponentially large number of parallel Universes exists to house each possible outcome,
·         the Ensemble Interpretation, where you imagine an infinite number of identical systems prepared in the same way, and making a measurement simply chooses one outcome to be “the real one,”
·         and the Pilot Wave/de Broglie-Bohm interpretation, where particles always exist and have positions, are guided by wavefunctions, implying that the “wave guides” (known as pilot waves) are deterministic and governed by hidden variables, which must be non-local (affecting disconnected spacetime points simultaneously) in nature,
among many others. A slew of interpretations, and the different assumptions about the nature of reality inherent to them, is illustrated below.

A variety of quantum interpretations and their differing assignments of a variety of properties. Despite their differences, there are no experiments known that can tell these various interpretations apart from one another. Image credit: English Wikipedia page on Interpretations of Quantum Mechanics.
But for these interpretations, an example of the ones that are not yet ruled out, a difficulty arises that’s inherent to them: there is no experiment yet devised that would allow us to discern one from another. The physical theory of quantum mechanics (or quantum field theory, by extension) stands all on its own, irrespective of whatever interpretation we apply to it. In other words, quantum theory works perfectly fine exactly as it is, where quantum operators act on quantum wavefunctions, accurately giving you the probability distribution of whatever outcome might ensue. When you do the relevant experiments, the interpretation you apply is completely irrelevant.

Quantum teleportation, an effect (erroneously) touted as faster-than-light travel. In reality, no information is being exchanged faster than light. However, the phenomenon is real, and in line with the predictions of all viable interpretations of quantum mechanics. Image credit: American Physical Society.
Still, physicists, philosophers, and armchair students argue about the various interpretations as though they have different physical meanings, when in truth, it may simply be akin to the ancient story of the blind men examining the elephant. As Niels Bohr himself, originator of the Copenhagen Interpretation, realized:
The fact that religions through the ages have spoken in images, parables, and paradoxes means simply that there are no other ways of grasping the reality to which they refer. But that does not mean that it is not a genuine reality. And splitting this reality into an objects and a subjective side won’t get us very far.
While many have their favorite interpretations, for most, they simply add confusion rather than illuminating everything. The variety in what explanations must be added on may not illustrate the possibilities for what reality truly is, but rather show how limited our human perception and intuition is when it comes to actually understanding and making sense out of our quantum Universe. While we can design experiments that highlight or illustrate the behavior of a particular interpretation, they all fail to tell us anything additional about the properties of our Universe.
Questions like “How or why does [quantum physics] work?” or “What, if anything, do the mathematical objects in [quantum] theory represent?” have as many answers as we care to give them. But those, arguably, say much more about us and our prejudices, biases, and assumptions about the Universe than the reality of the Universe itself. There are very few things we can actually observe in nature: particle properties like position, momentum, cross-sections, scattering amplitudes, and individual quantum states are pretty much it. Asking questions about the underlying nature of reality assumes that a true reality conforms to certain rules that fit our intuition, while the exact opposite may turn out to be true. Our perception of reality is determined by our limited senses and capabilities, and whatever rules truly govern the Universe may be more foreign to us than our minds have ever conceived of.

Multiple successive Stern-Gerlach experiments, which split quantum particles along one axis according to their spins, will cause further magnetic splitting in directions perpendicular to the most recent one measured, but no additional splitting in the same direction. Image credit: Francesco Versaci of Wikimedia Commons.
Quantum physics is fascinating in part because of how different the behavior of the quantum Universe is from our everyday experiences. Everything can behave as a wave or a particle, depending on what you do to it; the Universe is made from indivisible quanta; we can only predict the probabilities of an outcome, not an individual outcome; quantum physics is non-local in both space and time; and its effects are most visible on only the smallest scales. It’s arguably the weirdest thing we’ve ever discovered about the Universe.
And yet, we couldn’t help but add ourselves into the equation, perhaps due to the difficult-to-define terms of “observation,” “measurement” and “interaction.” Take ourselves out of it, and all we have are the equations, the results, and the answers that the physical Universe gives. Physics cannot answer questions about “why” the Universe works the way it does; it can only explain how it works at all. If you’re interested in the fundamental nature of reality, ask the Universe questions about itself, and when it tells you its secrets, listen. Anything else that you layer atop it was put there by you, not by the Universe. Avoid that temptation, and you’ll never fall for the greatest myth about quantum physics: that it needs an interpretation at all.

Starts With A Bang is now on 


Tuesday, February 13, 2018

MISCELLANEOUS 
THE IMPOSSIBILITY OF PROOF
EXPLANATIONS OF JEWISH SURVIVIAL

APPARENT COUNTEREXAMPLES TO THE KUZARI PRINCIPLE
#1 Aztec "national revelation"

There is another type of story that would not leave evidence for the audience to whom the story is told. This is a story placed so far in the past that no information survives from that time. In this case the story may involve public events. Even if the story describes an event that was supposedly experienced by the whole world, the audience cannot reason that its memory would have been preserved, since nothing at all was preserved from that time. So, for example, stories about a remote time when all people understood the language of the animals and conversed with them will not contradict KP. [See p. 154 of Reason to Believe.]


The Aztec story is not dated in our calendar system, so it fits what I wrote. Also, I checked the original. The migration is in fact true. 


I have received the following sources from David Greenberg that invalidate the entire question:


I found something on the Aztecs:

It seems the Aztec legend is NOT that the god spoke to everyone in a national revelation, but rather that the war god communicated to the priests, who then relayed the message on. Not quite a national revelation. Here are 3 sources:


See pg. 31-32: "Huitzilopochtli, later identified as a god of war, communicated directly with his high priests via dreams and profound trances, bestowing on them omens, prophecies and navigational tools to arrive at their promised land."

2- "These priests voiced Huitzilopochtli’s oracular directions as to where the combined Mexica-Aztec tribe was next to travel."


3- "Huitziton, a person of great authority...heard in the branches of a tree the trilling of a small bird...struck at this, and communicating his impressions to another personage...they both induced the Aztecs to leave their country, interpreting the song as a mandate from divinity."

See pg. 140


So it looks that the Aztec belief was that their war god did not communicate to the people, but rather to the high priests, who then relayed the claimed divine message on to the masses. But according to these sources, the Aztecs did not have a legend that it was the god Huitzilopochtli who spoke directly to everybody. So we can see this is definitely not a national revelation from god, but rather a relayed message from priests. This, unlike a national revelatory claim, is exactly what we’d expect to see in legends.

Added July 3, 2017;
There are three weaknesses in the account of the Aztec “national revelation” as a counter-example to KP – i.e. as a false NET.
1.       First, the translation presented is from A Scattering of Jades published in 2003 by The University of Arizona Press, pp 82-100. It is not mentioned at all in Handbook to Life in the Aztec World Oxford University Press; 1 edition (October 3, 2007) by Prof. Manuel Aguilar –published four years later by Oxford. I have written to Prof. Aguilar concerning the authenticity of the Jades text and the validity of the translation and have not yet received a reply. So at present the entire text is in question. And as David Greenberg pointed out there is nothing resembling a direct communication of a god with the Aztec people in Aguilar’s text.
2.     Second, in order to satisfy the condition of NET that requires the tradition record an event that would be expected to be remembered – to create a national tradition – at the time when the tradition started. This requires [at least] two characteristics of the tradition.  
a.    The tradition must specify an appropriate time for the event. If the tradition assigns the event to a date too far in the past, or the tradition assigns an unknown/uninterpreted date to the event, or fails to assign any date to the event then at the time the tradition is formed no one will expect to remember what happened at that time, and then the tradition is not an NET at all. In the Jades document the dates are given as compounds: In section VI "2-rabbit 1286" "11-reed 1295" and at the end "2-house 1325". I asked Prof. Aguilar what is the source of the modern dates 1286, 1295 and 1325? Did the author of the text [in the 16th century] have a modern calendar going back 200 years? Did the translator or the editors insert the modern numbers of the dates? How did they calculate the dates? https://en.wikipedia.org/wiki/Aztec_calendar is the Wikipedia page on the Aztec calendar. The phrases “2-rabbit” “11-reed” and “2-house” are days of the year; there is no provision whatsoever for counting years themselves – certainly not modern Christian numbers.
b.    Also, the content of the story must be such that we expect it to create a national tradition. A comparison of the Aztec text with the Torah’s description of the Jewish national revelation reveals a vast difference in this regard: the Torah’s story would surely be remembered while the Aztec story would not surely be remembered – perhaps would not be remembered at all. The Torah’s story included the following elements:  A prediction of the revelation before the exodus from Egypt; detailed instructions to prepare for the event, and positions to be taken during the event; the event of revelation is accompanied by vast pyrotechnics – fire, smoke, cloud, earth shaking, sound of the shofar; the reaction of the people is panic; the revelation includes the commandment of a weekly holiday; the plea of the people that there not be a repeat; repetition of the story in detail in Deuteronomy and at least five separate mentions of the story in the text of the Torah; and a specific command not to forget the event. By contrast the Aztec story reports the god speaking to the people in completely natural terms without any reaction on the part of the people or change in their culture. Indeed, the completely unemphasized nature of the narrative encourages David Greenberg’s suggestion that the sense of the text is not a direct communication from the god to the people but rather communication through the priests though the intermediaries are not mentioned. Calling these communications “Aztec national revelation” and encouraging comparison with Sinai is grossly out of proportion. The same holds for the miracles reported in the Aztec text – the contrast with the plagues in Egypt, the splitting of the sea, the manna, the destruction of Korach makes comparison grossly out of proportion.

Added July 17, 2017

https://www.britannica.com/topic/chronology/Christian#ref523312


Aztec
The Aztec and related peoples of central Mexico employed the cycle of 52 years, constructed, like its Maya equivalent, of concurrent 365-day years and 260-day cycles, any position of the former coinciding with a given position of the latter only at 52-year intervals. Again leap days were not used. At completion of the 52 years, known as “binding of the years,” elaborate ceremonies were held to avert destruction of the world expected on that occasion. The last occurrence before the Spanish conquest was in ad 1507. Although the last creation of the world was designated by a day name, neither that nor any other was in general use in central Mexico as the start of an era. Aztec reckoning is normally from their arrival in the Valley of Mexico, supposedly the year 1 Flint (ad 1168).
There is much confusion in placing events in Mexican history because no system of distinguishing one 52-year cycle from another was employed except by writing every year glyph throughout the period covered, a clumsy arrangement. Each year was named for either its last day (omitting the five-day unlucky period) or for the last day of the fifth month (both choices have distinguished supporters). In either case, only four day names (House, Rabbit, Cane, and Flint), each with its accompanying numeral, could designate a year. The Spanish conqueror Hernán Cortés seized the Aztec capital in 1521, year 3 House, but some past event, also assigned to a year 3 House but unlocated in a full sequence of years, might refer to ad 1261, 1313, or 1365, etc. Month positions were rarely given in chronological statements.
Peoples of Oaxaca and the Isthmus of Tehuantepec
Pictorial books of the Mixtec of Oaxaca record events in the lives of ruling families covering seven centuries, but, again, happenings are fixed only by the day on which each occurred and the year in which the day fell. Sequence is usually clear, but at times there is doubt as to which 52-year period is meant when parenthetical material, such as life histories of secondary characters, is inserted.
No era is recognizable. A clouded entry concerning the descent to Earth of the Sun and Venus, perhaps assignable to ad 794, is a logical starting point, but other entries are earlier.
Little is known of the calendar of the Zapotec, neighbours of the Mixtec. Years began on a different set of days, and glyphs differ from those of Mixtec and Aztec. Months are not recorded on monuments, which are numerous, and no chronological system has survived. Most Zapotec texts are early.
Rare inscriptions in western Chiapas, southern Veracruz, and the Guatemalan Pacific coast resemble the abbreviated lowland Maya Initial Series used in script and on a single sculpture in that numerical bars and dots are in a vertical column with period glyphs and month signs suppressed, clearly place numeration, that is, the value of each unit was shown by its position in the column. The linguistic affiliation of their sculptors is unknown.
All texts are either fragmentary or damaged; the two complete ones, unlike Maya Initial Series, open with days signs (and different ones at that). If, as one may reasonably assume, the series of bars and dots departed from those day signs, a fixed era is questionable. Nevertheless, some scholars postulate use of the Maya era (13.0.0.0.0 4 Ahau 8 Cumku). This little understood system may have been ancestral to the Maya Initial Series, the Maya perhaps developing a fixed era, for they alone seem to have been interested in an exact chronological system.

Added July 30, 2017:
A friend writes: It's worth mentioning that I searched a bit on youtube, and the only documentary on the Aztecs that I found which was done by an organization with name recognition was National Geographic. Professor Aguilar-Moreno is actually one of the experts that speaks during the documentary. The documentary makes no mention of the document allegedly authored by Montezuma's grandson, and it makes no mention of any Aztec myths about a national revelation or miracles. It simply says that after they made a human sacrifice out of the daughter of a nearby tribe leader on her wedding day to an Aztec, they were chased by the other tribe away from the mainland and onto the uninhabited island that they settled and made into the capital of their eventual empire. No mention of any fighting or casualties even, just chased away from the mainland. So that further strengthens points 1 and 3 that you make.