Physicists can’t solve nothing

From the opening section of a book on the many-body problem:
“It might be noted here, for the benefit of those interested in exact solutions, that there is an alternative formulation of the many-body problem, i.e., how many bodies are required before we have a problem? G. E. Brown points out that this can be answered by a look at history. In eighteenth-century Newtonian mechanics, the three body problem was considered insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (vacuum) is insoluble. So, if we are out after exact solutions, no bodies at all is already too many!” (emphasis added)
In modern quantum, theoretical, and particle physics, physicists quite literally can’t solve nothing. This is not a double negative- “nothing” is already a problem with no exact solution, and anything more than nothing is even worse. Some progress.

A Cosmic Computer?

In both popular and technical literature in subjects such as cosmology or theoretical physics, one can often find authors referring to the universe as a “computer”. I have found, however, that frequently non-specialists (including, sometimes, authors of popular literature) are misled by such characterizations. This is quite understandable. Inaccurate computer metaphors abound (particularly when it comes to the mind, brain, and consciousness), as do computers. Computer no longer brings up images of mechanistic calculations, and we no longer think of machines that carry out computations (like calculators) as “computers”, because “computers” are the laptops and desktops we are familiar with.

But when physicists call the universe a computer, they are asserting it has more akin with a pocket calculator than with your iMac or PC. Actually, in a very real sense by equating the universe with a computer physicists are saying it has more in common with your wristwatch or clock than your computer. Before the advent of quantum physics, it seemed as if the universe evolved deterministically according to some surprisingly simple dynamical laws (Newton’s equations of motion described just about everything, and what couldn’t be described by Newtonian mechanics could be by Maxwell’s equations, or Hamilton’s, or some other mechanics). The future state of any system is “computed” based upon current states entirely deterministically, like clockwork.

Quantum mechanics changed the deterministic part of this universe of computed states, but not the computation part. In quantum mechanics, the evolution of a system is still governed by entirely deterministic evolution (the famous Schrödinger equation, for example, is a linear partial differential equation, such that given any particular input we can compute, or the universe can, a single determined outcome). How indeterminism comes into the theory is not important here (especially because it is not exactly intuitive and involves going into the manner of preparation and specification of systems and measurements). What’s important is that even in quantum mechanics the future states of systems are given by dynamics so precise and “regular” they can be encapsulated by a few equations.

In the “universe as computer” concept, this encapsulation is really more of a description: the mathematical models are what the “universe” computes in order to evolve in time (i.e., to arrive at future states). This concept doesn’t entail a universe which is conscious, or that we are programs stored on some cosmic hard drive, that the universe has memory (at least no more than sandpiles or solitons), that we are living “in” a “computer”, or any other of the more exotic notions I’ve heard or read that result from comparing the universe to the things you use to check Facebook, create PowerPoint presentations, or visit this blog.

 

Quantum Cognition: Physics Envy in Neuroscience and Psychology

I promise I won’t continue to do this, but I just want to ensure that the “millions and millions” of non-existent readers know that I have started another blog and that this one has a new central theme.

Research Reviews

The idea that quantum physics is not only relevant to consciousness or the “mind” is pretty widely known. After all, in addition to a plethora of popular books by authors with questionable expertise and/or knowledge, eminent physicists such as Sir Roger Penrose and Henry Stapp have supported this idea. This post isn’t about quantum theories of mind (which I don’t find persuasive). It’s about a large number of papers that begin by making this distinction, e.g., “We note that this article is not about the application of quantum physics to brain physiology.”; “In our approach “quantumness of mind” has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles”; etc.

Simply put, the idea is that cognitive psychologists, neuroscientists, etc., should use the mathematical framework, notation, and terminology found in quantum physics (in particular, quantum mechanics) to model thinks like decisions, opinions…

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Photons aren’t real (but virtual photons are!)

Research Reviews

My concern here is mainly with the paper

Kastner, R. E. (2014). On Real and Virtual Photons in the Davies Theory of Time-Symmetric Quantum Electrodynamics. Electronic Journal of Theoretical Physics, 11(30).

I should say at the outset that the sensationalist title of this post is to compensate for a corresponding lack of sensationalism in the post, and should not be interpreted as a disparaging (or even negative) view of Kastner’s article. I may not be a proponent of transactional interpretations of quantum physics, but neither am I a detractor (and I certainly find it more plausible than multiverse-type interpretations). Before discussing photons and virtual photons, I need to briefly explain the “Possibilist Transactional Interpretation” (PTI). This is Kastner’s own version of the “Transactional Interpretation” (TI) put forward by Dr. John G. Cramer in the 80s. Luckily, this means that there already exists sufficiently simple and concise summaries of…

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English as a Second Language (ESL) for Ancient Greeks

I was looking into the extent of the unfortunate use of statistics from the social & behavioral sciences by particle physicists when I found this little gem in a footnote:

“Although the notion of what constitutes a satisfactory theory has changed over the centuries, it has always been considered desirable that the number of basic elements out of which everything is constructed should number at most “A FEW.” Since for the Greeks the basic elements were Air, Fire, Earth and Water, it is clear that they not only understood the basic principles of Science, but also had an excellent command of the English language.”
Lyons, L. (2008). Open statistical issues in particle physics. The Annals of Applied Statistics, 887-915.

Do I disagree with the claim that the Greeks understood the basic principles of Science? Sure (no empiricism, no science). Did I laugh like the biggest, most pathetic nerd in history upon reading this? Maybe.

This blog is moving! And staying!

This blog was originally supposed to be about reviewing actual research, in particular the research behind news and similar media popular science reporting. And even though many posts here aren’t reviews, that’s nothing compared to the number of posts I’ve wanted to write about but didn’t because they weren’t reviews of research but rather comments, tutorials, notes, etc., on various academic comments. So I decided to create another blog for research reviews specifically (and intend to eventually transfer the posts made here that qualify as such to the new site), and change this on to reflect what it already partly is: a roadmap, guide, and resource to understanding academia (particularly the sciences) and to scholarship. The new blog site will be researchreviewsblog.wordpress.com.

Request

I was asked to start a blog by several individuals and only decided to do so because I was constantly bombarded by questions or references (via email, phone, face-to-face, discussion boards, etc.) concerning articles in popular media about science research. I could finally start a blog that focused on something specific. Only, as soon as I started this thing, people finally stopped sending links to every online article or electronic version of some newspaper column or whatever they could find concerning physics, neuroscience, research methods, mathematics, biology, and other fields I’ve worked in. So all my would be sources for blog posts dried up, which explains the tiny number of blog posts given how long this blog has existed.

To the point: if any of the BILLIONS of followers I don’t have (and any of those I do) have questions regarding articles, documentaries, news, etc., on scientific research they are interested in, would like to know more about, are skeptical of, or even would like more references concerning, I would welcome such requests. Please.

Ask, and it shall be granted (sort of).

Review of “Anthropic Bias Observation Selection Effects in Science and Philosophy”

I’m going to do the unthinkable: on a site entitled Research Reviews, I’ll actually be reviewing some research! Before you die of shock, let me assure you that I will not be reviewing what generally comes to mind when people think of “research” (no labs were harmed, or used, in the making of this research), and that of course you will be getting something for free out of it (the entire book Anthropic Bias: Observation Selection Effects in Science and Philosophy). Also, I will as is typical of this blog be reviewing certain topics in or relevant to the sciences, such as the anthropic principle and fine-tuning.

The Book: What it isn’t

The reviewed work here is the book Anthropic Bias: Observation Selection Effects in Science and Philosophy by Dr. Bostrom. Although it covers topics like multiverse cosmology and the anthropic principle, it differs in several ways from most books that deal with these subjects. First, it is not filled with equations and formulae as is Barrow & Tipler’s (in)famous The Anthropic Cosmological Principle nor is it sensationalist and overly simplistic like Krauss’ A Universe From Nothing or Schroeder’s The Hidden Face of God. It’s a work of scholarship, published by Routlege (an academic publishing company) as part of the series Studies in Philosophy. It’s not the kind of book you’ll find in bookstores nor would most, I think, find it light reading. Second, it deals with multiverse theory and the anthropic principle secondarily. The book is really a treatise on the best way to approach a particular kind of problem that we face in the sciences but are actually more likely to encounter in popular discourse. To illustrate the kind of problem this book concerns (observation selection effect bias), I’ll give two examples, one simple and the other simplistically summarized.

Anthropic Bias: Examples of bias from observation selection effects

Example 1: Extraterrestrial intelligent life must exist

This is one of several examples that Bostrom gives in his introduction, but I choose it because I have addressed this specific question here and I have found myself trying to explain the problems involved to an almost inevitably skeptical audience. Many people believe that even if it is incredibly unlikely for life to develop on any given planet, there must be a huge number of planets with life, including intelligent life, because there exists an astronomically (bad pun intended) large number of planets in the universe. Moreover, there are many of them even relatively nearby that are “Earth-like” and found in what astrobiologists, among others, call “habitable zones” (HZs). And after all, what are the chances that Earth is the only planet in the entire universe on which complex (including microscopic, multicellular organisms) or intelligent life arose?

Well, this final question approaches the right way to think about this issue. To estimate how many planets have life, all we need to do is take the number of favorable outcomes (planets with complex life) and divide by all the planets. Simple. Of course, if knew of any other planet with complex life, we wouldn’t be asking this question. But I don’t want to present my approach to this problem (although it is similar, in form and conclusion, to Bostrom’s). I want to give his:

“Let’s look at an example where an observation selection effect is involved: We find that intelligent life evolved on Earth. Naively, one might think that this piece of evidence suggests that life is likely to evolve on most Earth-like planets. But that would be to overlook an observation selection effect. For no matter how small the proportion of all Earth-like planets that evolve intelligent life, we will find ourselves on a planet that did (or we will trace our origin to a planet where intelligent life evolved, in case we are born in a space colony). Our data point—that intelligent life arose on our planet—is predicted equally well by the hypothesis that intelligent life is very improbable even on Earth-like planets as by the hypothesis that intelligent life is highly probable on Earth-like planets…
The impermissibility of inferring from the fact that intelligent life evolved on Earth to the fact that intelligent life probably evolved on a large fraction of all Earth-like planets does not hinge on the evidence in this example consisting of only a single data point. Suppose we had telepathic abilities and could communicate directly with all other intelligent beings in the cosmos. Imagine we ask all the aliens, did intelligent life evolve on their planets too? Obviously, they would all say: Yes, it did. But equally obvious, this multitude of data would still not give us any reason to think that intelligent life develops easily. We only asked about the planets where life did in fact evolve (since those planets would be the only ones which would be “theirs” to some alien), and we get no information whatsoever by hearing the aliens confirming that life evolved on those planets (assuming we don’t know the number of aliens who replied to our survey or, alternatively, that we don’t know the total number of planets). An observation selection effect frustrates any attempt to extract useful information by this procedure.”

Example 2: The Anthropic Principle

The anthropic principle is usually divided into classes (especially strong and weak) and is highly nuanced, so I will just keep things simple by approaching it as sort of an inverse of example 1. In the first example, we looked at the flawed reasoning that leads to the idea that complex life is likely abundant in the universe. The most frequent arguments involve a flawed inference from the fact that life arose here to how likely it is to arise elsewhere, because knowing only that it arose here is consistent both with the hypothesis that life arose only on Earth and the hypothesis that complex life is abundant in the universe.

Not long ago, back when Neil deGrasse Tyson was Carl Sagan, scientists in general had pretty high hopes for the Search for Extra-Terrestrial Intelligence (SETI). To some extent that hasn’t changed, but a combination of the complete failure of SET and an increased understanding of the sheer number of variables that have to be just for life to arise and evolve have prompted many scientists working in astrobiology to conclude that complex life is probably rare, that if intelligent life exists elsewhere we’re never going to know, or even that we are alone. The arguments for and against these and other beliefs about life in the universe are for another time. Here, I simply want to introduce a very simple definition of the anthropic principle as it is relevant here:

“The anthropic principle is the name given to the observation that the physical constants in the cosmos are remarkably finely tuned, making it a perfect place to host intelligent life. Physicists offer a “many-worlds” explanation of how and why this might be the case.
My feeling is that a misanthropic principle could also be applicable. I use this term to express the idea that the possible environments and biological opportunities in this apposite cosmos are so vast, varied and uncooperative (or hostile), either always or at some time during the roughly 3-to-4 billion years intelligent life requires to emerge, that it is unlikely for intelligence to form, thrive and survive easily.” (Alone in the Universe)

Because there are so many fundamental “parameters” (e.g., the cosmological constant, the four fundamental forces, etc.) don’t just appear to allow for life, but are instead “remarkably finely tuned” for it. Again, I don’t want to introduce too much of my take here so to quote from Bostrom:

“Another example of reasoning that invokes observation selection effects is the attempt to provide a possible (not necessarily the only) explanation of why the universe appears fine-tuned for intelligent life in the sense that if any of various physical constants or initial conditions had been even very slightly different from what they are then life as we know it would not have existed. The idea behind this possible anthropic explanation is that the totality of spacetime might be very huge and may contain regions in which the values of fundamental constants and other parameters differ in many ways, perhaps according to some broad random distribution. If this is the case, then we should not be amazed to find that in our own region physical conditions appear “fine-tuned”. Owing to an obvious observation selection effect, only such fine-tuned regions are observed. Observing a fine-tuned region is precisely what we should expect if this theory is true, and so it can potentially account for available data in a neat and simple way, without having to assume that conditions just happened to turn out “right” through some immensely lucky—and arguably a priori extremely improbable—cosmic coincidence.”

Popular Physics: What this book isn’t

Paul Davies is a physicist and author of a number of popular science books, including The Goldilocks Enigma and The Eerie Science. The first book is on fine-tuning and the anthropic principle, while the second is on life in the universe. In the second, Davies concludes with his own views, one as a scientists, one from a philosophical perspective, and one as a person. Wearing his “scientist hat”, he conclude, “my answer is that we are probably the only intelligent beings in the observable universe, and I would not be very surprised if the solar system contains the only life in the observable universe. I arrive at this dismal conclusion because I see so many contingent features involved in the origin and evolution of life, and because I have yet to see a convincing theoretical argument for a universal principle of increasing organized complexity…”

Both of Davies books are quite like many, some that agree and many that don’t, in that they offer glimpses into the nature of scientific research related to the origins of life, the finely-tuned parameters (or why they actually aren’t finely tuned, although this is a minority position), but don’t require any real background knowledge. Then there are books that are at least semi-popular, such as Penrose’s The Road to Reality or the aforementioned The Anthropic Cosmological Principle, but are largely inaccessible to most readers (my father received his undergraduate degree in physics from one an Ivy League college, is an extremely intelligent individual, and didn’t get much past chapter 1 of Barrow & Tipler’s book).

That’s one thing I find particularly delightful about Bostrom’s book. It is technical in that it tackles reasoning and logic in a highly nuanced way. Although examples are given frequently to illustrate logical implications or flaws in particular inferences, the questions and issues tackled are fleshed out completely without skimping over any issue related to the rational, logic, validity, or justifications for any arguments.

Philosophical Texts on Reasoning and Rationality: What this book is better than

Better yet is that this book deals with subjects like whether the cosmos is finely tuned for intelligent life and if so what this means. The book is fundamentally concerned with advancing a coherent, logical, and justifiable framework for addressing kinds of questions like those in the examples. I have many books with similar goals: Heuristics and Biases: The Psychology of Intuitive Judgment, Probability Theory: The Logic of Science, Acceptable Premises: An Epistemic Approach to an Informal Logic Problem, Abductive Reasoning- Logical Investigations into Discovery and Explanation, Against Coherence: Truth, Probability, and Justification, Bayesian Epistemology, The Algebra of Probable Inference, Abductive Cognition: The Epistemological and Eco-Cognitive Dimensions of Hypothetical Reasoning, Model-Based Reasoning in Science and Technology: Theoretical and Cognitive Issues, and many dozens more. I enjoyed many of them and found all to be useful, but would recommend few if any to the general reader. That’s because they aren’t just technical, but only technical. They are “dry”, not just because they demand the reader deal with sophisticated nuances, but because they introduce their subject matter as their subject matter.

Now, there’s nothing wrong with this. In fact, it’s very hard to write a book about something, especially an academic monograph, without talking almost exclusively about that something. Of course, most books on methods in the sciences, certain kinds of reasoning or logics, epistemology, etc., give plenty of examples. But they are of the kind that we find e.g., in Bostrom’s 5th chapter “The self-sampling assumption in science” where there are sections on SSA in thermodynamics or evolutionary biology. Few books are able to recognize how far two related subjects (in this case, fine-tuning and the anthropic principle), both the main topic of countless popular books, can serve to introduce and cover in no small detail something like a specific kind of abstract reasoning. Bostrom not only found such a perfect way to thoroughly introduce the reader to so abstract a topic, he proceeds to cover it in more detail with a variety of interesting examples, and then uses a popular and fascinating probability paradox (the doomsday argument, one of the paradoxes in Eckhardt’s Paradoxes in Probability Theory, which cites Bostrom here) as yet another way to flesh out still finer points of his approach.

Thank you, and please help yourself to our complimentary gift on your way out

To embarrass myself by quoting the children’s television show Reading Rainbow, “but you don’t have to take my word for it.” If you think that fine-tuning, multiverse theory, the anthropic principle, and scientific reasoning might be interesting topics, but you don’t want to spend the money, another great thing about this book is that it is available in FULL for free and LEGALLY (well, I think legally, as it is available from the book’s website). So please, help yourself:

Anthropic Bias – complete text

Dictionaries don’t define words, and words don’t really make up language

There are many academic topics which most people not in a related field know little or nothing of. There are others, such as astronomy, quantum physics, climate science, brain sciences, etc., that are interesting enough to be discussed (mostly inaccurately) in blogs, popular science magazines, newspapers, YouTube, TV, and so on. Then there are fields like linguistics. Most linguists (and often those who aren’t linguistics but study language as neuroscientists or cognitive psychologists) have had the experience of telling others what their field is only to be met with an initially positive, receptive audience that expects to hear one thing and, upon hearing something quite different behaves quite differently (sometimes even a bit hostile, at least in a few accounts I’ve heard). This reaction is because brain research or quantum physics require watching or reading about to get an inaccurate view of, and diligent study to get something more,  but everybody speaks and most people can read too. Most also either speak more than one language or have at least taken some foreign language classes.

It turns out that knowing more than one language often translates into knowing less about language. Worse still, wide-spread literacy (especially for languages with a long tradition of dictionary use) also creates rather fundamental misconceptions. So fundamental, in fact, that it took linguists a long time to realize how much even they were misled about the nature of language thanks to dictionaries and a long tradition of grammar schools and grammarians (yes, you can blame all of your problems on anybody who tried to teach you “proper” grammar, especially those who responded to “Can I go to the bathroom?” with “I don’t know, can you?” or introduced you to participles).

But let’s start with something simpler than whether or not Georgian has gerundives. Let’s start with words and simple structures, because this is really about language, words, and meaning. It would seem natural to suppose that a great part of language consists of words and a kind of mental “dictionary” of their meanings. It was so natural that linguists like Chomsky tried to understand language this way, thinking that meanings could be relegated to this mental “list” of dictionary-like meanings (called the “lexicon”) and the rest consisted of purely formal (syntactic) rules for manipulating the words of any given language to produce grammatically “correct” sentences. So, for example, linguists (even before Chomsky) produced tree diagrams in which sentences were broken down into smaller and smaller chunks within larger chunks. The main chunks were noun phrases (NPs), verb phrases (VPs), and prepositional phrases (PPs), familiar to those who were tortured…uh, I mean taught, traditional grammar in school.

For most of my life during which my grandfather was alive, I knew him as a professor of classics and linguistics at Cornell and then professor Emeritus. The books of his I received during his life (only a few) and those after his death were mostly about languages and were mostly language textbooks or grammars on e.g., Old Norse, Welsh, Cornish, Sanskrit, Old Church Slavonic, Greek Romany (he wrote that one, actually), etc. The only actual linguistics textbook I have of his—the first I read and what made me decide (wrongly) that linguistics wasn’t for me—was An Introduction to the Principles of Transformational Syntax by Akmajian & Henry (MIT Press, 1975). It was filled with tree diagrams in which a sentence S would be broken into two sub-branches NP & VP which were in turn broken into further sub-branches until at the bottom were the words of some sentence. The point was to describe the ways in which certain rules could transform or generate these grammatical structures (generate/manipulate the branches) using combinatorial methods (mathematical/formal rules that could be programmed into a computer). Once these rules were discovered, all one would need to generate or parse grammatically correct sentences would be these rules and access to an external dictionary like those thought to be in everybody’s head.

This failed. Time was when basically all natural language processing (NLP) and AI/machine learning more generally was based on generative linguistics (Chomskyan-based linguistics like that described in the aforementioned linguistics text), which was also the foundation for cognitive scientists’ understanding of language. Nowadays, NLP and related areas in machine learning/AI use advanced statistical methods and specialized databases like FrameNET rather than generative linguistics, and lots of different linguists with varying approaches and theories came to subscribe to an umbrella category of linguistic theories called cognitive linguistics (NOT generative linguistics). Meanwhile, even generative linguists increasingly had to admit that the “lexicon” wasn’t just a list of words if it existed at all, and studies of languages with radically different structures than those long known to scholars (Greek, Latin, Hebrew, German, French, English, etc.) posed significant problems even when it came to identifying whether languages had things like nouns and adjectives, and if so what empirical means there might be to determine such parts of speech.

Other than the problems posed by languages in which e.g., it seems as if everything is a verb (there are examples more extreme than Navajo, but I haven’t studied them and given the structure of Navajo I would be scared to), the big issue and the one which ultimately became central to the model of grammar cognitive linguists employ was that it seemed no matter how many rules which linguists added for a given languages, most actual speech consisted of exceptions to these rules. A landmark study was Nunberg, Sag, & Wasow’s paper “Idioms.” They challenged the view of “many linguists…[who] have been implicitly content to accept a working understanding of idioms that conforms more or-less well to the folk category” which essentially was content to regard idioms as idiomatic: a small part of any given language that could be ignored or at worst require entries in the “lexicon” that were larger than one word. In the paper, the authors showed that not only are idioms not so idiomatic as thought, but also possess rules & structures internal to them. The authors categorized idioms by these internal rules and structures, which we won’t cover, but it is important to talk a bit about their nature, as idioms were the basis for constructions and these are the basic unit of language (which we’ll get to shortly).

The easiest type of idiom to understand follows the “folk category” understanding, such as “birds of a feather flock together.” Despite its length, this idiom is basically like a single word. Even trying to change the tense is “ungrammatical” (*birds of a feather flocked together” is ungrammatical). Other idioms can be “decomposed” into meaningful parts which can be analyzed individually but only in the context of the whole idiom. Consider “spill the beans”. Clearly “Jack spilled the beans on the whole affair” is different from the (non-idiomatic) “Jack spilled the beans on the floor”. The idiom means “divulge information”, but we can split it into “spill=divulge” and “information=the beans”. This is not true of an idiom like “kick the bucket”, which is not as fixed as the “birds of a feather” metaphor (we can say “kicked the bucket”, for example), but can’t be decomposed into meaningful components. However, both “pull strings” and “kick the bucket” aren’t syntactically idiomatic in that we have a regular VP structure; the main problem with these “grammatical” idioms is that we can’t expect to regulate to the “lexicon” because “kick” in “kick the bucket” has no decomposable meaning and while “pull” in “pull strings” does, it only does in this idiom.

Other idioms are even worse. The division of idioms into “grammatical” and “extragrammatical” comes from the even more groundbreaking work with idioms by Fillmore, Kay, & O’Connor in a paper that basically founded Construction Grammar (and therefore construction grammars). Extragrammatical idioms don’t even follow predictable syntactic structures, including e.g., by and large, all of a sudden, believe you me, easy does it, be that as it may, first off, so far so good, make certain, no can do, etc.

The last dimensionality/category we’ll cover (and we’ve already introduced a lot of the notions in construction grammar) is schematicity. This is a fancy way of referring to the ways in which some idioms are actually more like grammatical rules. Syntactic structures like PPs or NPs are highly schematic (they were treated as meaningless structures that applied to basically all possible grammatical sentences). That’s what makes them grammar as opposed to part of the “lexicon”. But there are idiomatic constructions like “the X-er, the Y-er” that are almost as purely syntactic: the higher they climb, the harder they fall; the more you practice, the better you’ll be; the more you act like that, the less likely I am to give you what you want; etc. The “the” part in front of the X-er & Y-er structures is actually distinct from the definite article “the”; it’s from the Old English instrumental demonstrative. Also note that this idiom is so “syntactic” that we have to use variables to describe it, just the way we describe syntactical structures. That’s how schematic it is.

Now we can easily describe construction grammar in its barebones form. There are actually many such grammars, from the original Construction Grammar to Radical Construction Grammar or Cognitive Grammar and even Word Grammar, but they all share a fundamental property that separated them from the models of grammar before them: that the lexicon and grammar are not distinct components but lie along a continuum and that therefore constructions are the basic units of language, not lexemes (which is pretentious-speak for “words”). Some constructions correspond or can correspond to traditional parts of speech like nouns or to words. But the realization that grammatical structures, not just words, were meaningful and that this lexico-grammatical continuum existed showed us that even when we can say that a word is a construction and part of another construction like a noun phrase, it’s still true that meaning comes not from some idealized mental dictionary but are internal to the constructions in which the words appear. It turns out that about half of language consists of “prefabricated constructions” in which structure and/or meaning are internal to units that are larger than words. Put differently, about half the time we use words the meaning can’t be understood as additive (i.e., the sum of the parts of the phrase/sentence). Moreover, even if we idealize words as having independent meaning, this meaning isn’t like a dictionary entry but an encyclopedia entry.

There is one last nail in the coffin of the traditional understanding of language (at least that I’ll cover). It is related to (and involves) the encyclopedic nature of lexical meaning. Simply put, meanings are flexible. Period. Not just because they might occur in some idiom or because they might act like the modal verb “might”, but also because of things like novel usages in which phenomena like metonymy come into play. One very broad category of ways in which meanings are extended regularly and “on the fly” so to speak (I deliberately used to prefabs/idioms there) is via metaphor. My favorite example comes from a linguist who overheard part of a conversation in a pub. A member of a group of friends had left for a while, and upon returning discovered that a female member of the group had left. After asking his friends where she was, he received the answer “she left about two beers ago.” Now, normally when we wish to indicate units of time, we don’t use beers. But here the ability to comprehend novel metaphorical extensions allowed the hearer (and the linguist) to understand that “two beers” referred to the (approximate) amount of time it takes to drink two beers.

So, to wrap up, I’ll summarize the key points. Language isn’t a bunch of grammatical rules we apply to atomic elements that linguists call lexemes and most people call words. It’s vastly more complex, dynamic, convoluted, and most of all inherently and thoroughly meaningful. Not only do words lack any “dictionary” like meaning or even more generally meaning apart from the constructions in which they appear, the “structures” in language convey meaning as do various linguistic (and/or cognitive) mechanisms like metaphor. Hence debates over what a word means that rely on dictionaries aren’t just subject to the quality of the dictionary, but are fundamentally problematic. Words don’t have dictionary like meanings, and debates over what atheism means or what hypotheses are or any number of topics discussed here and elsewhere that are based on disagreements over what certain terms mean can’t be resolved by quoting dictionaries. Sometimes the terms may be technical enough that there exists among specialists an agreed upon definition. Sometimes other facets of language and linguistic use can help resolve disputes which are based on lexical semantics. Sometimes logic helps. But quoting dictionaries your average dictionary is only one step up from simply defining your personal definition to be the definition, and there is never a THE definition of any word (words are inherently polysemous).

Multi-worlds and many-universes: On the universes of the multiverse

As I just addressed dimensions in physics, it seems natural to address universes next. Like misinterpretations of dimensions, people frequently conceptualize a multiverse with alternate universes that are essentially “higher dimensions” in the mystical/spiritual sense, science fiction writers imagine travelling to other universes in e multiverse, and finally it is only natural to suppose that by “multiverse” physicists mean that our universe isn’t the only one (despite the prefixation).
But the truth is that there is so much more (and less) to multiverse theory and it doesn’t usually involve any actual other universes (at least not in the sense often thought). Let’s begin at the beginning (it seems an à propos place).

How split-ends create universes: The Many-Worlds Interpretation of Quantum Mechanics

A long time ago (the 50s) in a galaxy far, far away (the milky way, which is still far, far away, just not from our perspective), there lived an individual by the name of Hugh Everett III. As you can imagine given this pretentious name, Dr. Everett retired from physics early in order to make millions. However, this wasn’t his plan. In his doctoral thesis (written under the supervision of the great J. A. Wheeler), Everett proposed the basics of what is now called the many-worlds interpretation (MWI) of quantum mechanics. He proposed a way of dealing with the so-called “collapse of the wave-function.” Put as briefly as possible, quantum mechanics is statistical/probabilistic in nature, but the equations that define how quantum systems “evolve” in time (such as the famous Schrödinger equation) are deterministic. So our math tells us that the system behaves one way, but when we try to measure the system it acts quite differently: The state of the system “jumps” or “collapses” upon measurement in a very unsatisfactory way (it’s wayyy more involved than this but I’m massively simplifying for brevity). One big problem with this mysterious “collapse” notion is that it doesn’t do a good job of explaining how the quantum realm, which is supposed to be the foundation for reality, yields the classical world we experience. Everett proposed we resolve this by understanding that the possible outcomes are really “actual”, and that our classical world is constantly emerging from infinitely many realized outcomes of infinitely many quantum interactions, and each outcome is a “branch” realized by this infinite splitting of universes into others.

So, when you get split ends, the universe splits. But this multiverse theory isn’t really different universes (or rather, it’s more like different histories of the same universe). It’s not like there’s “our” universe which is just one among many. After all, “our” universe is constantly splitting too, so there isn’t really even a single “us” (granting the MWI is true, of course). Another way to think about it that won’t help you is that the “wave function” never collapses because there’s only one wave function that encompasses all reality. The possible outcomes of quantum mechanics aren’t possibilities, they’re just “branching worlds” of this wave function. If it were possible to travel to one of these alternate “universes”, there would be no point to MWI. Everett (who didn’t use the term “many-worlds”, which was coined by DeWitt), didn’t really even go as far as suggesting there exist alternate histories in which e.g., World War I remained “The War to End All Wars” (i.e., no WWII).

Not a multiverse, just a universe with some really deep pockets

The next “multiverse” theory is even less like a multiverse. The good news is it’s much simpler. It’s well-known that the universe is expanding. It’s even more well known that a very widely (although not universally) accepted theory (the Big Bang theory) posits that this expansion began a while ago (probably even before the 50s!) from a “point” out of which the entire universe emerged. It’s not very widely known how problematic the nature of this “bang” is. Obviously, the laws of physics breakdown at the “bang” itself, but they continue to fail after the initial moments of the universe (expansion faster than light, no atoms, immensely high temperatures and pressures, etc.). With some fairly minimal assumptions, the Big Bang theory also gets us a multiverse (it’s a “buy one get one free” sort of thing). Simply put, as the universe expanded you can think of it as sort of “ripping” into various pieces. Our piece is bounded by our particular cosmic horizon-a sort of limit that prevents us from observing anything beyond it. These pieces are often called universes, and this is (an incredibly simplified) version of the multiverse theory: a set of universes originating from the same cause, with the same laws of physics, impossible to “reach” or “travel to”, and fairly boring. In fact, some physicists don’t like to call these pieces “universes” at all:
“Some refer to the separate expanding universe regions in chaotic inflation as ‘universes’, even though they have a common causal origin and are all part of the same single space–time. In our view (as ‘uni’ means ‘one’) the Universe is by definition the one unique connected¹ existing space–time of which our observed expanding cosmological domain is a part. We will refer to situations such as in chaotic inflation as a multidomain universe, as opposed to a completely causally disconnected multiverse.”
Ellis, G. F., Kirchner, U., & Stoeger, W. R. (2004). Multiverses and physical cosmology. Monthly Notices of the Royal Astronomical Society, 347(3), 921-936.

From Branches to Bubbles, Pieces to Pockets: Inflationary Cosmology Take 2

But the story of “universes” resulting from inflation doesn’t end here. In a similar multiverse theory, not only do the “pieces” or “pocket universes” differ more radically, but the “gaps” in the multiverse allow for “bubble universes” that not only have different laws of physics but perhaps the possibility of interaction (they can careen into one another, which isn’t exactly the kind of interactions between universes from sciences fiction). However, I’m not going to explain this one. I’m going to use it as an example to show that my explanations aren’t as bad as they seem by quoting another, fairly non-technical introductory piece on multiverse cosmologies:
“In the fashionable variant known as eternal inflation, due to A. Vilenkin and A. Linde, our “universe” is just one particular vacuum bubble within a vast–probably infinite–assemblage of bubbles, or pocket universes. If one could take a god’s-eye-view of this multiverse of universes, inflation would be continuing frenetically in the overall superstructure, driven by exceedingly large vacuum energies, while here and there “bubbles” of low-, or at least lower-, energy vacuum would nucleate quantum mechanically from the eternally inflating region, and evolve into pocket universes. When eternal inflation is put together with the complex landscape of string theory, there is clearly a mechanism for generating universes with different local by-laws, i.e. different low-energy physics. Each bubble nucleation proceeding from a very large vacuum energy represents a symbolic “ball” rolling down the landscape from some dizzy height at random, and ending up in one of the valleys, or vacuum states. So the ensemble of physical by-laws available from string theory becomes actualized as an ensemble of pocket universes, each with its own distinctive low-energy physics. The total number of such universes may be infinite, and the total variety of possible low-energy physics infinite, but stupendously big.”
Davies, P. C. W. (2004). Multiverse cosmological models. Modern Physics Letters A, 19(10), 727-743.

Naturally, you not only use the word “frenetically” in everyday discourse, but of course are more than well aware of the ways in which extra dimensions required by string theory are explained in terms of compactification to space-like regions in which they determine the physical laws for each particular region.

“As Above, So Below”: Combining the Multiverse with Many-Worlds

Certain physicists have decided that, as long as we’re admitting the possibility of infinitely many bubble universes eternally popping into existence and having differing laws of physics, and because this sounds a lot like the many-worlds interpretation of quantum mechanics, it would be a good idea to say that these quite independently developed theories formulated to address fundamentally distinct issues are nonetheless the same. I have no illusions about my inability to condense into a paragraph anything remotely resembling a clear account of how some physicists derive an equivalence between the MWI and multiverse cosmology. So I’ll leave this one with “nothing is possible, because every possibility is actualized”.

“I found God! He was hiding in a holographic anthropic multiverse”

Scientists may not be as objective as we’d like, but at least they rely on fairly minimal assumptions as opposed to e.g., historians of prehistory or theologians. Except when they don’t:
“Despite the growing popularity of the multiverse proposal, it must be admitted that many physicists remain deeply uncomfortable with it. The reason is clear: the idea is highly speculative and, from both a cosmological and a particle physics perspective, the reality of a multiverse is currently untestable…For these reasons, some physicists do not regard these ideas as coming under the purvey of science at all. Since our confidence in them is based on faith and aesthetic considerations (for example mathematical beauty) rather than experimental data, they regard them as having more in common with religion than science…To the hard-line physicist, the multiverse may not be entirely respectable, but it is at least preferable to invoking a Creator. Indeed anthropically inclined physicists like Susskind and Weinberg are attracted to the multiverse precisely because it seems to dispense with God as the explanation of cosmic design” (emphases added)
Carr, B. (2007). Introduction and Overview. In B. Carr (Ed.). Universe or Multiverse? Cambridge University Press.

I like the 2nd bolded portion, mostly thanks to

Amoroso, R., & Rauscher, E. (2009). The Holographic Anthropic Multiverse: Formalizing the Complex Geometry of Reality (Series on Knots and Everything Vol. 43). World Scientific.

What could this obscure sounding combination of cosmology, theoretical physics, and mathematics have to do with why some physicists like the multiverse because it “seems to dispense with God as the explanation” of the cosmos? Because Amoroso and Rauscher’s cosmology is (in their words) “a theistic cosmology”, despite being a multiverse cosmology and despite espousing the holographic principle (yes, it’s related to holograms; no, the world isn’t a hologram like the holograms we’re familiar with are).

Wrapping this up (finally)

I could keep going for some time and not scratch the surface. But the point is that invariably even the most exotic multiverse theories aren’t the kind described in everything from popular science to science fiction films. Even those which hold that some 10¹⁰²⁹ miles away there is an identical version of you are still really (if real, that is) part of this universe, and the very thing that seems to warrant calling them universes is that they are untestable, undetectable, and impossible to ever travel to or visit (even if you had a Delorean equipped with a flux capacitor AND a warp drive).