A Profusion Of Place | Part I: Of Unity And Philosophy

by Steven Gussman


            ¹Physicist Max Tegmark's Our Mathematical Universe is a hodge-podge, part popular astronomy book, part memoir, and part creative playground for exploring new ideas. His account of mainstream physics and astronomy sheds light on the subject in a unique way, and I appreciate that he is willing to directly recognize the obvious big questions.² The book ultimately revolves around Tegmark's unlikely idea of the most expansive multiverse imaginable, and several arguments from fundamental physics to cognitive psychology are employed to get there. Like many of us, Tegmark is dissatisfied with standard quantum physics, but he (and increasingly his colleagues in physics) embraces a cure that's worse than the disease in the Everettian “many worlds” multiverse interpretation, which simply moves the central problem without answering it.³ By taking advantage of the most simple models of recent scientific ideas in need of more empirical evidence (such as quantum foundations and inflationary cosmology), Tegmark is able to assume an unimaginable proliferation of worlds.⁴ The namesake of the book is Tegmark's hypothesis that the physical universe is nothing but bare mathematics, an argument he makes by playing a bait and switch with the two terms.⁵ Given the ever-increasing number of universes this book argues in favor of, I see my role as culling things back down. In the present essay, I will be addressing the general arguments for the existence of a multiverse.

            Our Mathematical Universe is really a book about multiverses, as every argument that Tegmark makes leads to another multiverse. Tegmark has come up with a very useful taxonomy of multiverses. The level-I multiverse is what most of us simply call the universe (albeit modified by the rather premature assumptions of both an infinite volume of spacetime and infinite matter to fill it, all seeded with different initial conditions by quantum-random fluctuations just prior to the big bang). Here, anything that can occur according to the ordinary laws of classical physics does occur somewhere because given infinite matter, space, and time, even the rarest events must happen. The level-II multiverse comes from the premature assumptions that inflation occurred before the big bang (rather than immediately after, as the theory originally intended) and that inflation is an eternal event, constantly spawning off new level-I multiverses such as our own, separated by an exponentially expanding field of meta-space called the inflaton.⁶ The level-III multiverse is the multiverse associated with quantum physicist Hugh Everett's many worlds interpretation of quantum physics—the idea that since quantum physics only ever yields probabilistic (rather than classically deterministic) solutions to physics problems, it is actually telling us that each of the possible outcomes does occur somewhere. Finally, most hypothetical of all, the level-IV multiverse is Tegmark's own contribution to the proliferation of worlds, and it is related to his idea that he calls the mathematical universe hypothesis, which states that physical reality is itself nothing but abstract mathematics, and so the level-IV multiverse emerges from the fact that Tegmark cannot explain why only some math seems to describe our universe, which Tegmark takes as a prediction that all mathematical structures exist as separate universes governed by those maths. Needless to say, many level-IV universes contain level-II universes (as long as they contain eternal inflation—indeed, they may contain much worse!), all level-II universes contain a level-III multiverse, and all level-III universes contain a level-I multiverse.⁷ Tegmark seems almost religiously in awe of this infinitude of worlds, which may say more about what makes him tick than the Cosmos. Indeed, Tegmark writes, “... we may find ourselves inhabiting a reality grander than our ancestors imagined in their wildest dreams.”⁸ One has to wonder if that wasn't for good reason—as Carl Sagan warns, “Imagination will often carry us to worlds that never were. But without it, we go nowhere.”⁹
            To start with, I will note that semantic arguments aren't based on deep philosophical disagreements, and so I will spend little time on the debate between whether there can be more than one “universe”, by definition. What is interesting is whether reality really looks like several (or infinitely many) copies of what we now think of as our “universe”, or just the one as was classically thought. The “universe” is already known to be bigger than the observable universe (which consists of a spherical particle horizon with us at the center, and is always “expanding” in the sense that photons from further and further away are always finally reaching us from out in the universe as time permits).¹⁰ Any universe with a finite speed limit for information to travel will only be partially detectable to an observer based on where they are located and how old their universe is. Thus, a multi-observable-universe is trivially true, though no one would consider this an actual multiverse, just a limit on the interactions between any sufficiently far away portions of a single universe (that is to say that observable universes are just infinitely many overlapping particle horizons—nothing but reference frames—not distinct structures or objects).¹¹ Astronomer and philosopher of science, Carl Sagan preferred the singular use of “universe”, but in truth, it wouldn't be the first time a scientific concept had outgrown its literal meaning by being too presumptuous—“atom” is famously Greek for “indivisible”, and yet it turns out that the atoms of the periodic table are not elementary particles, but are instead made up of (and mediated by) lower level objects such as electrons, quarks, photons, and gluons.¹² Tegmark writes, “... some... use the phrase... 'the universe,' to mean everything that exists, in which case, by definition, there can't be any parallel universes.”¹³ Yet semantically, I can't help but think that it would only be in keeping with tradition to have multiple “universes” just as we have divisible “indivisibles”.

            The assumption that our universe consists of infinite space and time, containing infinite matter-energy is on surprisingly weak footing considering how well-subscribed it seems to be among cosmologists. Quantum Engineer Seth Lloyd (a collaborator of Tegmark's) claims, “The same observations that establish the detailed history of the universe imply that the observed cosmos is a vanishingly small fraction of an infinite universe... Beyond the horizon of our observation lies more of the same—space filled with galaxies stretching on forever... All but an infinitesimal fraction of the universe is unknowable.”¹⁴ But he doesn't explain what that theory which predicts the infinities is—it looks to me like the best (indeed one of the only) arguments in favor of it seems to be that it's a simple assumption in lieu of evidence pointing in any particular direction (and in place of much theoretical motivation towards a serious answer at all).¹⁵ This is a situation in which astronomers' Copernican Principle (a heuristic, not a physical law), which states that local observations should be taken to be ordinary, runs awry.¹⁶ It is true that historically, cosmology and physics were marred by the idea that we were special—the heavens above were supposed to have followed different, more perfect laws than our lowly, secular Earth, and it was assumed that Earth was the center of the solar system which was assumed to be the center of the universe. It turns out that the laws of physics are the same everywhere in the universe and that Earth isn't the center of the solar system, which isn't the center of the Milky Way galaxy, which isn't at the center of the universe. But replacing one dogmatic assumption with its reverse isn't the right solution—the solution is to always apply scrutiny and follow the evidence. Assumptions, hypotheses, and conjectures should be taken with a grain of salt when they have little to no empirical confirmation behind them. We know our universe is either flat, or very large if it is another geometry which curves back on itself. For the universe to be flat, it almost certainly must be infinite, but there is little reason to think that the universe is flat and infinite rather than large, curved, and finite to allow for the flatness observed on scales we have already confirmed).¹⁷ In fact, Tegmark admits that the minimum size of a non-flat universe given our cosmic microwave background (CMB) measurements only requires 100 level-I universes!¹⁸ If this is true, his level-I multiverse is dead in the water. A universe 100 times the size of our observable universe is very different than his normal level-I argument–it merely increases our universe's known number of galaxies, stars, and planets by a factor of 100, which can scarcely be called a “multiverse”. It is indeed just a universe with completely distinct galaxies, stars, and planets with no expected doppelgangers, uncanny similarities, or 'loss of determinism' (it is exactly what one ordinarily pictures deep space to be like).¹⁹ It seems Tegmark's best evidence is the claim that the infinity assumption is the “simplest” model; as in all such cases, it seems we lack enough information to leave equipoise and construct grand ideas around weak foundations. Infinite flatness filled with uniform matter is a fine assumption to make in the meantime, given it may simplify our models and calculations, but taking it so seriously as to assume that it actually means there is an infinite level-I multiverse is going too far. In fact, one of the ways in which Tegmark contradicts himself is to lean on arguments such as this, while at another point arguing that he doesn't think infinity exists at all, even in mathematics—he thinks that there is some maximum quantity and precision. Tegmark claims to both believe in the cosmological infinity-assumption and that infinity doesn't exist (even pointing out that this will tame much of the outlandish ideas I'm opposing in the present work).²⁰ I will add to his skepticism a strange contradiction in mainstream physics: when infinite quantities show up as the results of physics calculations (such as the infinitely curved spacetime / infinite density at a black hole singularity), it is typically understood as a sign that the theory is “breaking down” (that this is an approximate theory being used outside of its effective domain).²¹ Yet in cosmology, Tegmark makes it seem fairly customary to nonchalantly assume infinite spacetime and matter in the simplest models. Considering this infinity didn't even come out of an equation, but is simply an assumption, it ought to be taken even less seriously by comparison. Given that the big bang is often considered the mechanism for birthing our universe, it's worth wondering how realistic it is to suppose that not only a whole lot of matter occupied the same subatomic spot, but infinite matter, most of which subsequently expanded away. It all smacks of attempting to take unfinished theories further than they can reasonably be expected to go, of pretending all scientific progress ends right now, and so we have to make due with only our current equations and observations. Strangely, Tegmark insists that multiverses are the predictions of theories.²² But predictions are based on precise mathematical solutions—the extent to which these theories can be made to speak of multiverses are just tantalizing little hints at best ('maybe quantum superpositions correlate to entire doppelganger universes', 'maybe inflation goes on forever and gives rises to many universes', 'maybe the reason we haven't yet explained the values of physical constants is because there exist all sorts of universes with all manner of physical constants', etc.). These are not what we traditionally call scientific predictions: they're hand-waving possibilities. Strangely, Tegmark says that the scientific method is in part about making “... predictions from assumptions...”, and even calls theories “... a collection of assumptions...”. While he may have been simply speaking to the provisional nature of knowledge, it is interesting when juxtaposed with the fact that he sees mulitverses as “predictions of theories”, when he's actually making the prediction from an empirically verified theory plus an entirely un-empirically verified assumption (like that of infinite space and matter).²³ While it may be fun to think about doppelgangers of oneself in a far away patch of spacetime, there is very little reason to think it is actually the case. We ought to remain agnostic as to whether the universe is truly flat at the largest scale, is infinite in scale, and contains infinite matter-energy until better evidence comes in, and that means refraining from taking the more outlandish consequences of an infinite multiverse too seriously.²⁴
            Tegmark employs general arguments in favor of multiverses on multiple occasions. The first such case that I want to address, which one might call the historical induction argument, is simply the observation that we have historically thought the universe were smaller than it would later turn out to be (first our solar system, then our galaxy), and so perhaps we are making this mistake once more.²⁵ However, it's difficult to see how this could have historically been any different—conservatism grounds things in what is currently known and progress shows finally that there really is something new. Strange indeed it would be if historically, things significantly shrank, because one needs a reason to believe there are more things and needn't one to think that there exists only what already meets the eye. Even so, this is a flimsy argument, as a trend such as “the Cosmos turns out to be larger than we expected” needs to terminate somewhere. Indeed, this argument could even be used against Tegmark's meager four-tiered multiverse (though barely, as we shall see) to say, why not more?

            Another general argument in favor of multiverses is The Anthropic Principle which is invoked so as to explain so-called “fine-tuning”, which Tegmark defines as “Physical constants in the effective laws having values in a very narrow range allowing life...”.²⁶ In general, The Anthropic Principle simply states that if life occurs rarely in the universe, then we are in that rare region, for as unlikely as it is, we're clearly alive! One can extend that argument in favor of a multiverse by arguing that if the (seemingly) fundamental physical constants are narrowly tuned to be conducive to life, then there must exist a multiverse of universes with different physical constants (most of these not conducive to life), and we only find ourselves in a rare life-bearing universe because, again, we're clearly alive.²⁷ Putting aside the irony that most physicists who buy into these kinds of arguments also pay lip-service to The Copernican Principle (the assumption that there is nothing special about our place in the universe), the problem is that one could make this argument for anything —and if they did, it would probably have kept us from some discoveries we have made.²⁸ In fact, all questions we have historically answered could have been instead answered the same way. Why doesn't retroactively doing so suffice? Doesn't it become a mystery why we should have ever been able to come up with singular answers to any scientific questions, if an inference to infinite variety without special evidence suffices? As long as you postulate that everything exists, you can argue that it's not so strange that what you are currently observing exists. It's not a deeply clever idea like Darwinian evolution, because it's missing the selection and mutation portions.²⁹ Historically, allowing this kind of explanation would have stalled out scientific understanding a long time ago—for example: the answer to “why do people generally enjoy sex?” cannot be “because there exist both people who do and don't enjoy sex, but we've only tended to meet the former”.³⁰ Put this way, it's clear that the “answer” is simply a restatement of the observation, not an explanation of it! Having not accepted such answers, Darwin,Wallace, and their disciples eventually realized that people generally enjoy sex because those who do are more likely to produce kin and those kin are in turn more likely by inheritance to enjoy sex.³¹ This example does invoke a diversity of kinds of organisms (though mechanisms needn't generally), but with two crucial components which change it from a casual restatement of the question: a mechanism for generating variation (genetic mutation during replication) and a selection pressure biasing the proliferation of some outcomes rather than others over time (natural / sexual / artificial selection). Most multiverse ideas have neither—they simply state infinite variation with no mechanism for generating such a plethora of worlds and no selection of some over others to produce a non-random outcome.³² Evolution is a far-cry from attempting to explain the diversity of life by saying that all imaginable life-forms exist somewhere, and so the fact that we see these ones just means we're near these ones.³³ This kind of thinking gets rid of the need for any mechanism at all—if my friend gets an A on a test, rather than posit that he studied hard or cheated and adjudicate between the likelihood of these with empirical evidence, I can just assume he took the test infinitely many times, got every possible grade, and I must have just happened to have been around for one of the times where he got an A.³⁴ Even if we allow this kind of theoretical reasoning, it's not obvious why, in the absence of adjudicating empirical evidence, we should choose to interpret it as statistical (all possible universes exist, and we are in a rare life-supporting one by The Anthropic Principle) rather than as probabilistic (many possible configurations for our one universe could have existed, and a relatively unlikely life-supporting one is the one that happens to, by The Anthropic Principle).³⁵ On top of all of this, it is not unlikely that a true theory of everything would be inherently much more restrictive on the allegedly turn-able knobs that are (or aren't?) the fundamental physical constants.³⁶ Why is it thought that particles' masses and interaction strengths could be otherwise (surely something in our universe must be foundational)? This would seem to throw induction out the window.³⁷ The idea that if the mathematics of our equations doesn't explicitly limit the domain of input, then those situations with those inputs must exist somewhere is not logical, particularly when we know we don't have a fundamental theory, only approximate theories of different facets of some grand underlying theory of everything.³⁸ We simply don't look at Newton's law of gravitation, F = GMm/r² and think of the universal gravitational constant G as a variable without serious evidence that this is the case.³⁹ In short, I'm not really bothered by the idea that everything that's physically possible doesn't necessarily occur, or hasn't, or won't—why should it all? This is the difference between the actual and the possible. It's not obvious why it's not the case that certain relationships and ratios are true physical constants and so turning one knob adjusts the others to compensate and yields the same universe (this is like the difference between shrinking an object by having it be made of less matter versus shrinking the size of the constituent particles themselves). Tegmark compares the classical physicists' idea of constrained fundamental constants to older physicists' ideas that certain values in our solar system were fundamental in the sense that they required deep explanations (such as planetary mass or radii).⁴⁰ But while it's true that the discovery that there are many planets throughout the universe (of many different orbits, masses, and radii) disabuses us of any suspicion that our solar system's particular orbital properties are universally foundational, our understanding of physics does actually provide some understanding as to the realistic ranges of masses, radii, and orbital distances of bodies of certain materials.⁴¹ Furthermore, fine-tuning arguments assume we know what the values of physical constants ought to be ahead of time (from common-sense, not theoretical prediction), and that changing those values by a small amount should not have big consequences if there is a single universe. I would like to invoke chaos theory as a possible alternative explanation for the fact that small changes in fundamental constants seem to predict the vanishing of biology.⁴² If the roll of a die of certain common materials against surfaces of other certain materials can be found to yield quite sensitive results, why shouldn't cosmological evolution be sensitive to even subtle changes in fundamental constants?⁴³ The universe is by definition the most complex system—it is the sum total cause-and-effect of all of reality—would it be any wonder that facets of this system turned out to be “chaotic” in this sense?⁴⁴ Why should we test any ideas against observations as a measurement of theoretical success if we thought that any approximation shouldn't matter much to the evolution of the universe? No one thinks that finding such “chaotic” systems as the die-roll mentioned above requires hypothesizing a multiverse, so why should it be invoked for a universe that is “chaotic” in this sense, when we already know many of its isolated constituent subsystems to be?⁴⁵ Why should we even predict, measure, and use physical constants in our equations (not to mention check predictions from theories of cosmological history) if changing the fundamental constants should be assumed not to have much effect on cosmic evolution (the output of the equations)?⁴⁶ And all of that is without even asking the question of what is meant by a “small” change to a fundamental constant. Concepts such as large and small are subject to spatial relativity (they only make sense in a particular reference frame; “smaller” than what?). I would argue that when it comes to physical constants, we have no such reference frame. It is not obvious why a range of 1-34% (which is itself naively imprecise) should be considered “small”, let alone why the same percentage of change would be considered “small” for all constants.⁴⁷ Note, too that speaking in terms of percents does not actually normalize the problem: there is no reason that 150% or -25% ought to be considered anymore unrealistic an alternative version of the value than 0% to 100%; this is just a way of speaking about any arbitrary value in terms of the observed value. In fact, the only way I can think to propose to scientifically figure out what constitutes a “small” change to a physical constant would be to define it by the largest change that doesn't have large ramifications for predictions (such as the impossibility of life), which completely turns the idea of “fine-tuning” on its head. Could it be that properties of the universe now considered fundamental aren't? Sure. But that doesn't tell us that any of them actually aren't, much less which. At the end of the day, calling these values “fine-tuned” begs the question that The Anthropic Principle purports to answer; it may be that such things can't be fine-tuned which were never “tuned” in the first place.⁴⁸ The Anthropic Principle / fine-tuning multiverse is possible, in that it is a coherent hypothesis, but short very extraordinary empirical evidence, this kind of cop-out should be the last place we look to hang our hats, because it's so convenient as to leave one prematurely satisfied. In short, Tegmark's plethora of arguments in favor of multiverses can seem like a case of quantity over quality, particularly in the case of general arguments.

            Then there is the measure problem.⁴⁹ In mathematics, it is sometimes argued that there are differently sized infinities—the most famous example being that there is a larger infinity of integers than there are odd integers (as only half of all integers are odd).⁵⁰ In multiverse cosmology, thinkers are wondering how to count the different universes, as they contain no inherent order, and order matters when approximating the convergence of an infinite sum.⁵¹ There is a hope that the measure problem can be solved in such a way as to yield the same probability distribution as in quantum physics superpositions.⁵² Some cosmologists consider this number a sort of “amount” of reality (where universes of “greater measure” are in some sense “more real”).⁵³ Call me classical, but I think that real or fake is entirely the same as true or false, physical or un-physical, natural or supernatural, actual or actually not—whether or not something is real is a completely binary property. What this says to me is that if there really is a relationship between classical multiverses and the quantum multiverse, then because each universe's measure is a rational number (because each universe exists in some integer number of duplicate universes divided by some integer number of total universes, both of which may be different infinities), then quantum probabilities must also be rational numbers and therefore this continuous facet of quantum theory must be quantized. In other words, if this relationship were true and the measure problem solved, quantum mechanics would be due for an upgrade to only allowing rational probabilities assigned by its probability distributions.⁵⁴ Something about this jives nicely with Tegmark's later arguments against infinity and the continuum. In the meantime, considering how speculative these ideas are, it seems more likely that the fact that our current well-motivated idea of probability densities allows the prediction of irrational probabilities for measurement outcomes is telling us that it probably can't be the same thing as the rational value of the “measure” of a universe in a multiverse.

            On falsifiability, I am only partially persuaded by Tegmark's arguments against pure Popperian epistemology. A common argument against any scientific hypothesis is that it isn't actually a scientific hypothesis (falsification is Karl Popper's strict idea that a scientific hypothesis must be falsifiable—it must make clear predictions which can be shown to be false based on empirical observation through experiment).⁵⁵ I agree with Tegmark that this is perhaps too narrow in the sense that we should be defining scientific hypotheses as ideas which could describe reality (imposing any other restrictions would be, to borrow a term from Tegmark, “human baggage”).⁵⁶ There is a fear in any philosopher of science: what if there actually existed two physical phenomena which always cancel each other out in every single case, and so never have any observable effects; in what sense can it be said that they really are, or really are not happening? The most I can do to console you is to say that this is no different than the realization that every time you say “3”, you're actually saying “3 + (0 * x)” (among many other equations), that is to say that they are isomorphic (totally equivalent).⁵⁷ But I suspect something more is true about physical reality—most (and I would ultimately conjecture all) different hypotheses / theories have some different prediction (and at the very least, even if there are unobservables, we don't yet have criteria for deciding which phenomena are in that class). Call it the exclusivity conjecture in philosophy of science.⁵⁸ This is to claim that differences in explanation will always make different predictions in some way (another way of putting this is that different real mechanisms will always leave some unique information signature on the universe). This trivializes the whole argument because while I prefer Tegmark's definition of a scientific hypothesis (science is the description of reality, not the strictly falsifiable description of reality, though we hope that this is the case for epistemology's sake), I still emphasize the need for empirical evidence in support of a theory or predicted phenomenon. I take Tegmark's point that if a theory makes 10 predictions, one of which is in principle unobservable, and the other nine are confirmed by empirical evidence, then we ought to take the 10^th seriously.⁵⁹ But that does not mean believing this phenomenon as strongly as the others—all scientific knowledge is provisional—it may be that some new theory will predict the same nine observable phenomena, and not the 10^th unobservable one (and perhaps new observable phenomena that are themselves confirmed).⁶⁰ For this reason, the only way the certainty of an unobservable prediction could grow is slowly as time goes on with no new theory to supplant the one which makes that prediction. My sympathy with both Tegmark and his falsifiability critics comes from different directions than those factions; it's a conjecture about nature (that may be wrong), not a statement on what scientists are allowed to consider. Tegmark is right ontologically (we don't know for sure that reality actually follows such rules that everything that exists is observable in principle to us), and his critics are right epistemologically (it is unfortunately just a fact that we cannot have a good reason to believe we're in possession of a true ontological description without the concept of falsifiability testing). By example, Tegmark tries to argue that General Relativity's successes in empirical prediction leads it to be taken seriously where we don't yet have empirical confirmation—but I would rebut that it is crucial that we don't yet have it, and that we therefore have only probabilistic knowledge. For example, gravitational waves were taken more seriously after Nobel-prize winning circumstantial evidence was shown that co-orbiting pulsars lost energy in just the way this phenomenon predicted.⁶¹ Then in 2015 (verified and announced in 2016), when gravitational waves were at last directly detected, despite most physicists already believing they existed, the team at LIGO was also awarded the Nobel prize in physics (it's worth mentioning that Einstein never even got a Nobel Prize for either theory of relativity, though there is more to that story).⁶² Apparently something about directly observing this phenomenon we were all totally sure about was of particular importance. Perhaps multiverses are something we can believe in, but simply not something we can award Nobel prizes for. Puzzlingly, Tegmark specifically mentions black hole interiors as an example of an unobservable prediction to take seriously, but most think General Relativity breaks down at these singularities and doesn't help describe it, much!⁶³ How a theory breaks down can be telling, but it's not making a strong prediction, much less one that can be believed without empirical evidence. Nevertheless, I remain only a soft-Popperian because the central problem here is that while I suspect that there is no such thing as an unobservable phenomenon, there may well be, and I do not want to restrict our scientific understanding of the world—science ought to describe reality as best we can, with whatever reliable tools we can, and with no arbitrary restrictions. That said, I am on the side of the Popperians in practice, as I am extremely skeptical of anyone claiming an unobservable phenomenon.⁶⁴ Any phenomenon should be assumed to be in principle observable unless a lot of time and work goes by without anyone being able to figure out what kind of a signal it might leave for us to measure. Any time an observation “can be interpreted as evidence of” multiple different competing hypotheses, it's just not a specific enough observation to be empirical evidence for any of them.⁶⁵ One needs evidence that can differentiate between multiple competing explanations. This new idea that multiple explanations are going to be equally compatible is wrong-headed, and is creating confusion throughout physics all the way down to quantum foundations. Despite all of the anti-Popperians' claims, many experimentalists (and even theoreticians) have indeed been attempting to come up with possible observations and experiments which could shed light on whether or not a particular multiverse exists. In this light, the theoreticians who claim unobservable multiverses (and this almost only happens with multiverses) seem to be hiding from the challenge that everyone else in history's ideas have been subjected to: empirical evidence. I am in agreement with the Popperians that there is something deeply defeatist with assuming any scientific hypothesis is unobservable in principle, right out of the gate (especially if one is not an experimentalist anyway!).

            At this time, I will segue from the topic of physics to that of the sociology of physicists, for a hypothesis of my own: I predict that, absent obvious evidence (as is the current situation with most data pertaining to multiverses), more politically conservative physicists will tend to favor the tight economical view that a better understanding of fundamental physics will constrain the fundamental constants more apparently, and that politically liberal (and especially progressive) physicists will tend to favor large, expansive, and diverse multiverses. The assumption here is that political orientation is downstream from general philosophical orientation, which is likely at least statistically true; really, the reason that the same physicist is predicted to be more likely than his counterparts to favor multiverses and vote for Barack Obama (or favor a singular universe and vote for Ronald Reagan) is because they are philosophically conservative or liberal / progressive. That is, I'm arguing that it is a common cause (philosophical orientation) that leads to both political and physical orientation (in the absence of evidence one way or the other on a given physics question), not political orientation that directly causes physical orientation. Without making specific predictions about the correlation between a physicist's politics and multiverse preferences, Brian Greene seems to recognize the philosophical conflict of visions beneath the debate, writing, “... the anthropic principle... is a perspective that is diametrically opposed to the dream of a rigid, fully predictive, unified theory in which things are the way they are because the universe could not be otherwise. Rather than being the epitome of poetic grace in which everything fits together with inflexible elegance, the multiverse and the anthropic principle paints a picture of a wildly excessive collection of universes with an insatiable appetite for variety.”⁶⁶ Furthermore, coupling this hypothesis with the fact that there are more Democrat academics than Republican academics in every field (in physics, the ratio is 6.21), we are expected to get a skewed popular opinion (that may masquerade as a “scientific consensus” rather than an ordinary consensus), which will reflect in polls like those Tegmark has informally gathered at at least one conference.⁶⁷ Further yet, because left-leaning people tend to be more creative and I assume are likely more interested in educating the public, I suspect that this effect will be amplified further among popular book and column writers (and science popularizers, more generally). Both Becker and Carroll have cited a sort of “ick factor” as a lame counterargument they see to the idea of multiverses, which could be interpreted as a sort of conservative reaction (and both Becker and Carroll are quite left-of-center, politically).⁶⁸ A lack of philosophical diversity in an academic field (always leaning left in contemporary times) is usually understood to be leading higher-level social sciences (with direct connections to, and implications for, politics) such as psychology and sociology astray from dispassionate science, but it is interesting to wonder whether the discrepancy may have smaller effects even on as objective, direct, and austere a discipline as physics.⁶⁹

            I claim that much of the arguments in favor of multiverses boil down to instantiations of the philosophy-of-the-gaps fallacy: just because we don't know all of the limits of our current understanding now, doesn't mean that we never will, and that we can assume a naive interpretation of our current theories' mathematical solutions as all being manifest in a multiverse.⁷⁰ Ignorance can be temporary, but it doesn't have to be.

Footnotes

1. Funny enough, while looking for citations for this essay, I came across passages I had read and forgotten, and inside of them I found astrophysicist Adam Becker writing about a, “profusion of worlds”, What Is Real? by Adam Becker (2018) (pp. 256), and evolutionary biologist Richard Dawkins writing, “a plethora of universes,” The God Delusion by Richard Dawkins (2006 / 2008) (pp. 175). I had recently been deciding whether to entitle this collection of essays “A Profusion Of Place” or “A Plethora Of Place”, I believed independently.

2. I am inspired here by Economist Eric Weinstein having had the courage to point out that the following is an obvious question (that is often neglected by teachers): “What is the universe expanding into?”, “Joe Rogan Experience #1203 – Eric Weinstein”, uploaded by PowerfulJRE (2018) (42:28) (https://youtu.be/X9JLij1obHY?t=2548). Thanks to PodScribe for helping me locate this passage (https://podscribe.app/feeds/http-joeroganexpjoeroganlibsynprocom-rss/episodes/664ea75440dc4ec486a4e72d852a51ad#00:48:44 ).

3. Quantum foundations will be the specific topic of Part III of the present work.

4. Inflationary cosmology will be the specific topic of Part II of the present work.

5. The relationship between physics and mathematics will be the specific topic of Part IV of the present work.

6. Our Mathematical Universe by Max Tegmark (2014) (pp. 100-101, 103, 111-113). To be fair, Tegmark does admit that inflation still may not be correct or may not be eternal, Our Mathematical Universe (pp. 126).

7. This Russian-stacking-doll quality is mentioned by Tegmark, Our Mathematical Universe (pp. 328).

8. Our Mathematical Universe (pp. 152). Tegmark even describes the previous expansion of our understanding of the scale of the universe by saying it “pales in comparison” to those he will describe, Our Mathematical Universe (pp. 6-7).

9. Cosmos by Carl Sagan (1980) (pp. 2).

10. This kind of “expansion” of the observable universe is not to be confused with the real (or metric) expansion of the entire universe as a whole (the idea that space itself is stretching ever more). The “expansion” of the particle horizon is a simple consequence of the fact that we exist in a particular location at a particular time and that there is a finite speed of light. Light traveling at this maximum speed from far enough away in the universe hasn't reached us yet, but every moment that ticks by, more of it does reach us than before, Our Mathematical Universe (pp. 126). This just means that more of the universe (that already exists) can be observed by us as we move into the future.

11. Astronomer Sir Martin Rees points out that the “observable universe” is simply a reference frame inside of the universe itself in his essay, “Multiverse”, This Idea Is Brilliant edited by John Brockman (2018) (pp. 136).

12. On the (in)divisibility of atoms, Cosmos (pp. 188, 233). “... I prefer to use 'Cosmos' for everything, and 'Universe' for the only one we can know about.”, Pale Blue Dot by Carl Sagan (1994) (pp. 36). Physicist Leonard Susskind calls the whole of reality, the “megaverse”, The God Delusion (pp. 173).

13. Our Mathematical Universe (pp. 120).

14. From Lloyd's essay, “The Universe”, This Idea Must Die edited by John Brockman (2015) (pp. 12).

15. Tegmark admits the infinities are just an assumption of the Big Bang model, and that space may be finite, but also suggests theory predicts infinite space, Our Mathematical Universe (pp. 17, 33, 97, 126).

16. It has become tradition (at worst, an arms race) for astronomers to invoke The Copernican Principle and admonish humans for thinking themselves particularly special in this universe. This is put best by Sagan, in which it is simply a poetic warning against anthropocentrism, but coming from Tegmark and many others, it feels a bit on-the-nose and as though it's simply ticking off a box. The Copernican Principle is also known as The Principle Of Mediocrity, Science In The Soul by Richard Dawkins (2017) (pp. 193, 195), which is a re-printed essay entitled “Intelligent Aliens” from Intelligent Thought: Science Versus The Intelligent Design Movement edited by John Brockman (2006) (though I have not read this book). Tegmark notes that some see the assumption of an infinite universe as justified by The Copernican Principle, Our Mathematical Universe (pp. 129).

17. Tegmark tries to claim the CMB data points to an infinite space-time because it points to a flat space-time, but in reality, it doesn't necessarily point to either—cosmologist Andrei Linde (a father of inflationary cosmology) only even mentions the theory as solving why the universe is uniform (though to be fair, it's a short essay whose core thesis is in favor of infinite multiverses) in his essay (against the idea of), “The Uniformity And Uniqueness Of The Universe” in This Idea Must Die (pp. 44-45).

18. Our Mathematical Universe (pp. 127).

19. Tegmark mentions the purported 'loss of determinism', Our Mathemaitcal Universe (pp. 123). By Tegmark's calculations, one would be expected to need a level-I multiverse containing somewhere around 10¹⁰²⁹ universes to have a doppelganger of oneself out there, Our Mathematical Universe (pp. 119).

20. Namely, that, “... Despite their seductive allure, we have no direct observational evidence for either the infinitely big or the infinitely small. We speak of infinite volumes with infinitely many planets, but our observable universe contains only about 10⁸⁹ objects (mostly photons). If space is a true continuum, then to describe even something as simple as the distance between two points requires an infinite amount of information, specified by a number with infinitely many decimal places... we don't need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow's weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too—in a way that's more deep and elegant than the hacks we use for our computer simulations.”, which comes from his essay “Infinity”, This Idea Must Die (pp. 50-51). I would only push back on this by wondering if the assumption of infinity inherent to calculus isn't still hiding somewhere in our logic of “limits” as variables approach certain values, even inside of the approximation methods used in computers. To put a point on the internal contradictions in the present book, Tegmark also mentions that he doesn't believe there are infinitely many objects (despite spending most of the book arguing in favor of just this), Our Mathematical Universe (pp. 316). Like any good scientist, I suspect he is able to hold mutually exclusive possible hypotheses branching in different directions until one becomes evident, but it is strange to hear him forcefully argue that contradictory sides are already evident, say that he believes these mutually exclusive claims, or say that he would place huge bets on some of these claims, only to contradict them, seemingly without noting the tension, Our Mathematical Universe (pp. 194, 196, 220, 319, 343, 361).

21. The Elegant Universe by Brian Greene (2003) (pp. 118, 344).

22. Our Mathematical Universe (pp. 119, 124, 361).

23. He does also mention the step, “Compare observations with predictions, update assumptions.”, Our Mathematical Universe (pp. 300).

24. I use “agnostic” as synonymous with “equipoise” (not yet known), and not in the classical mysterianism sense as to mean unknowable in principle, as in physician and social scientist Nicholas Christakis' essay “Equipoise”, This Idea Is Brilliant (pp. 303-305). That said, I don't necessarily use either to mean that I judge the different possibilities to be truly equally likely; that's what long-form argument is for.

25. Our Mathematical Universe (pp. 19, 33, 138). Astrophysicist Neil deGrasse Tyson entertains similar appeals, Astrophysics For People In A Hurry (2017) (pp.89, 205). As does Rees, though to his credit, he admits it would simply be an “intellectual and aesthetic upside” to a separately proven multiverse, not a strong argument in its favor a priori, in his essay, “Mutliverse”, This Idea Is Brilliant (pp. 138).

26. Our Mathematical Universe (pp. 139). Tegmark notes that physical cosmologists (“... Paul Davies, Brandon Carter, Bernard Carr, Martin Rees, John Barrow, Frank Tipler, Steven Weinberg...”) first argued for fine-tuning in the 1970's and 1980's, Our Mathematical Universe (pp. 142). The earliest recordings of an infinite universe hypothesis that I know of (with an understanding of the attendant consequence that everything possible actually occurs somewhere in this universe) and a primitive type of Anthropic Principle (unless I am reading too much into philosopher and historian Anthony Gottlieb's editorializing) come from ancient Greeks Leucippus and Democritus around the fourth or fifth century, B.C., The Dream Of Reason by Anthony Gottlieb (2000 / 2016) (pp. 64, 109).

27. Our Mathematical Universe (pp. 352). The Anthropic Principle is also known as The Self-Selection Principle, Science In The Soul (pp. 193, 195), which is a re-printed essay entitled “Intelligent Aliens” from Intelligent Thought. He also notes it is originated by “... mathematician Brandon Carter in 1974, and expanded by physicists John Barrow and Frank Tipler... ”, and that Carter ultimately preferred it be called The Cognizability Principle, The God Delusion (pp. 162, 440), further citing “The anthropic principle and its implications for biological evolution” (1983) by Brandon Carter and The Anthropic Cosmological Principle by John Barrow and Frank Tipler (1988) (though I have read neither work). There exists a distinction between a weak (the naked statement that living beings must find themselves in a region of the Cosmos conducive to life) and strong (justification for a multiverse) version of The Anthropic principle; the latter is the one I complain about in the present work, A Brief History Of Time by Stephen Hawking (1988 / 1996) (pp. 128-129) and Pale Blue Dot (pp. 30-31). Dawkins (and Tegmark) further make a distinction between “planetary” and “cosmic” versions, as we already know about the near-infinite variety of planets in the universe (whereas I am presently arguing that a variety of universes is far from evident)—this means that The Anthropic Principle is trivially true in the planetary case (in fact, the strong and weak Anthropic Principle are one and the same for the planetary version), The God Delusion (pp. 162-164, 169-170, 172, 174), and Our Mathemaitcal Universe (pp. 145). As a less anthropocentric example of The Anthropic Principle (linguistic irony noted), Tegmark claims the masses of fermions look random, and therefore if you demand a deep explanation of these physical constants, you must assume that they're a random sample from other realities, Our Mathematical Universe (pp. 147).

28. Sagan makes (perhaps too) much of the uneasy relationship between The Copernican Principle and The Anthropic Principle, and laments that The Anthropic Principle is too presumptuous, Pale Blue Dot (pp. 33-34). By contrast, Rees sees multiverses generally (as regarded in eternal inflation models, The Anthropic Principle aside) as the next step in The Copernican Principle playing out (see footnote 16, above), in his essay, “Multiverse”, This Idea Is Brilliant (pp. 138). Physicist Lawrence Krauss is sympathetic to multiverses hypotheses motivated by something other than fine-tuning / The Anthropic Principle, seeing these as violating The Copernican Principle in his essay (against the idea that) “The Laws Of Physics Are Predetermined”, This Idea Must Die (pp. 54). As Tegmark points out, physicist George Ellis actually both warned that proponents of The Anthropic Principle / fine-tuning may be making too many assumptions, and that multiverse arguments could be a slippery slope to more and more multiverse “explanations” (which Tegmark seems to have taken as a challenge), Our Mathematical Universe (pp. 361, 363), which further cites “Does The Multiverse Really Exist?” by George Ellis (2011) (https://www.scientificamerican.com/article/does-the-multiverse-really-exist/) (though I have not yet read this). For this reason, that one can “explain” anything with The Anthropic Principle, cosmologist Paul Steinhardt calls these, “Theories of Anything,” This Idea Must Die (pp. 56). Mathematical physicist Peter Woit shares this sentiment, claiming too many physics ideas now follow a paradigm of “anything goes” in his essay (against the idea of), “The 'Naturalness' Argument”, This Idea Must Die (pp. 70). Tegmark notes that for his work on the eternal inflationary multiverse, physicist Eddie Farhi calls father of inflationary cosmology, Alan Guth, “The Enabler”, Our Mathematical Universe (pp. 150). For his part, Tegmark thinks that figuring out how to retire the idea of infinity from mathematics may tame the unwieldy consequences of these infinite multiverses in his essay, “Infinity”, This Idea Must Die (pp. 48). Mathematical physicist Roger Penrose laments the laziness of the Anthropic Principle standing in for real progress, as well, Fashion, Faith, and Fantasy by Roger Penrose (2016) (pp. 322). Cosmologists Neil Turok and Paul Steinhardt also make the complaint that The Anthropic Principle / fine-tuning multiverse both makes too many assumptions and sets a bad precedent for failing to actually answer questions, Endless Universe by Neil Turok and Paul Steinhardt (2007) (pp. 222, 232, 235-236, 250). Mathematician Marcus du Sautoy makes fairweather remarks about The Anthropic Principle being “... a bit of a cop-out.”, The Great Unknown by Marcus du Sautoy (2016) (pp. 222). Although astrophysicist Stephen Hawking bought that the physical constants appear “fine-tuned”, he nevertheless appears to have thought that strong Anthropic Principle multiverses were an unsatisfying explanation, A Brief History Of Time (129-131, 137). Dawkins claims Susskind buys the fine-tuning / Anthropic Principle multiverse (and Dawkins himself is sympathetic to it), The God Delusion (pp. 171-173).

29. Incidentally, Dawkins criticizes a movement in the history of evolutionary biology he calls “mutationism”, which neglected the importance of selection (somehow imagining that the variety provided by mutation was enough to explain biological observations on its own), Science In The Soul (pp. 119, 143), which was originally published as the chapter, “Universal Darwinism”, in Evolution From Molecules To Men edited by D. S. Bendall (1983 / 1985) (though I have not read this latter book).

30. To be fair, evolutionary psychologists use the similar heuristic assumption that at some point in the deep past, there existed both those who did and didn't enjoy sex, but that over time the asexual types were naturally bred out for obvious reasons, Cosmos (pp. 29). But evolutionists do not usually hold that this is literally true, just that something like that happened; some kind of selection among variety herded the gene pool to today's observation being the norm, but it could have been upstream from this particular trait, and without empirical evidence, one cannot be sure which competing alleles actually happened to manifest and be selected in or out. (Incidentally, in this case, it is quite likely that the selection for the enjoyment of sex did not occur on humans at all, but on some long ago species that each species it evolved into inherited, much like how our five fingers originated in the five-boned-fin of an ancestral fish), Cosmos (pp. 298). It suffices to say that, assuming infinite time (as geological timescales are quite large), the traits we observe today, about four billion years since evolution began, should be quite adaptive among possible alleles indeed, as there was a lot of time for mutation to create variety and selection to cull out the lesser traits (although there was also significant time for the environment, and therefore the selection pressures, to change)–Sagan mentions the date since life began in Cosmos (pp. 27) and Pale Blue Dot (pp. 84). But this is not the same thing as claiming that every possible organism with every possible allelic trait exists at the same time, and we just happen to be looking at the ones we happen to be looking at.

31. Cosmos (pp. 29).

32. To be fair eternal inflation has an incredibly speculative and hand-waving mechanism for the creation of multiverses in the 'Big Bang phase transitions of parts of the inflaton into universes with quantum random differences in their physical laws', but still lacks any selection mechanism; every kind of universe is generated, Our Mathematical Universe (pp. 111-113, 118, 134-136). Physicist Lee Smolin is an interesting exception: he has the idea that black holes may contain a kind of offspring-universe with slightly different laws of physics than its parent-universe (mutations). Sometimes, those offspring-universes lack the physical laws and constants required to form their own black holes (reproduce), and this is the equivalent of being selected out, The God Delusion (pp 174-175) and Our Mathematical Universe (pp. 151-152). The result is much more universes with black holes than without, and one can think of those universes with more black holes as being more prolific, and their kinds of physical law (phenotype) as being more common among universes by inheritance. One wonders what the equivalent of death would be (cosmologists have spent a lot of time pondering the possible ends of the universe, and it is likely that different universes would embody different ends that took different amounts of time to arrive). One obvious issue is the question of what happens to the child-universes when their parents die (they are in some sense contained within their parents, unlike biological organisms)? The phenomenon of Hawking Radiation tells us that on a long enough timeline, black holes are losing mass into their (parent) universe and will eventually evaporate altogether. This seems to break the biology analogy; why are younger children dying instead of older parents, and being subsumed by those parents? And The Law Of Conservation Of Energy tells us that a closed system (such as a universe) does not create nor destroy energy / matter. But if there were a multiverse, why might we not see a singular universe as an open subsystem, and the multiverse as the closed system, in which apparent violations of the conservation law (which have not been observed) are actually squared by the excess or missing energy being accounted for in some other universe (in the case of Hawking radiation, one expects the mass of the child universe to be reducing over time, being added back into the parent—this happening would be an in-principle testable prediction of Smolin's hypothesis if I am not mistaken). Another question is whether the original common ancestor to all universes is also a black hole. If so, inside of what? If the outermost universe is a black hole, how is it Hawking radiating, and again, into what—if it is into nothing, isn't this violating The Law Of Conservation Of Energy and The Law Of Conservation Of Information? Isn't all energy and information in the universe leaking away, being slowly destroyed until there is capital-N nothing? As we go further and further down the cosmic rabbit hole, this seems to be a good time to point out how highly speculative this hypothesis is: there is relatively little actual reason to think that a universe can exist inside of a black hole thus far, let alone any idea of how or whether the laws of physics would be different inside of these. Still, its inclusion of reproduction and mutation mechanisms for variety, and a selection mechanism for the probability of finding yourself in a given type of universe makes it a better model for The Anthropic Principle applying than most popular multiverse hypotheses (but then we still need totally separate evidence to see if it is true, meaning that even here, The Anthropic Principle can basically only live as a post-hoc observation, not support for a multiverse as it has tended to be used).

33. In fact, given the number of possible genetic combinations, it is known that not every possible human genome has come into existence, and the theoretical ability to count such combinations has caused nobody in the field of biology to take seriously the idea that this is a prediction that each such person exists somewhere—Sagan mentions the immensity of the number of possible human genomes in Cosmos (pp. 33-34). Of course, this argument only gets worse when you take into account all species (and possible species), which appear to be effectively innumerable. Evolutionary biologists will sometimes argue that individuals with genes for trait X out-competed those with the allele for trait Y, but they're not actually sure exactly which Y-trait alleles existed in competition in pre-history (without empirical evidence for populations with competing traits that go away when the new trait shows up, from, say, the fossil record), only that X-trait genes proliferated at the cost of some competing allele because they functioned so as to increase fitness well enough to be present, today.

34. “The Philosopher John Leslie uses the analogy of a man sentenced to death by firing squad. It is just possible that all ten men of the firing squad will miss their victim. With hindsight, the survivor who finds himself in a position to reflect upon his luck would cheerfully say, 'Well, obviously they all missed, or I wouldn't be here thinking about it.' But he could still, forgivably, wonder why they all missed, and toy with the hypothesis that they were bribed, or drunk.”, The God Delusion (pp. 173).

35. The latter comes from the classical notion of chance randomness arising from our ignorance of certain details (pseudo-randomness), whereas the former is the much more modern notion of chance as truly fundamental randomness, which, as I will argue in a later essay, is not even likely in quantum physics, the field that has delivered the biggest confusion of the last century. Tegmark rejects the probabilistic view, seeing it is a cop out to say 'we just got lucky' or “It's just a fluke”, even while supporting the arguably equally problematic statistical view, Our Mathematical Universe (pp. 140, 142-143, 362). The best defense I could make is that I don't believe in fundamentally random / probabilistic processes, as would seem to be required to give rise to a universe (whereas the multiverse could simply be the terminating starting point of the Cosmos, with no mechanism having created it). But those who argue in favor of the statistical view typically do believe in fundamentally probabilistic processes (in quantum physics), apply those principles to cosmology, and tend to believe in a mechanism for creating the multiverse (eternal inflation, quantum measurement, etc.), so they cannot really justify choosing a statistical interpretation over a probabilistic one; they do so because they already assume a multiverse through other means (which again, renders the fine-tuning / Anthropic Principle multiverse as trivially true, rather than an argument in favor of a multiverse in the first place).

36. Cognitive scientist Steven Pinker (referencing The Fallacy of Fine-Tuning (2011) by Victor Stenger) points out this possibility, Enlightenment Now by Steven Pinker (2018) (pp. 423). Dawkins also cites Stenger on the topic, The God Delusion (pp. 170), further citing God, The Failed Hypothesis by Victor Stenger (2008) (though I have yet to read either Stenger work). String theorist Brian Greene notes this possibility as well, The Elegant Universe (pp. 368-369). As does Dawkins, The God Delusion (pp. 173).

37. Ironically, most proponents of The Anthropic Principle rely crucially on both down-playing the importance of induction by empirical evidence (multiverses are often claimed to be un-observable in principle) and a need for a lame kind of almost-anecdotal empirical observation that one finds themselves in this kind of universe. This is the sum of a completely speculative multiverse married with a banal observation of one's surroundings. Typically, scientific explanation consists of a deeply vetted theoretical prediction married with careful, statistical observational evidence.

38. Tegmark explains how an underlying Theory Of Everything would tie current partially disparate scientific theories together, Our Mathematical Universe (pp. 257). Interestingly, he also points to the fact that mathematical equations usually have many different solutions, and does admit to essentially interpreting this quality in fundamental equations (which we do not have) as predicting those solutions really manifest somewhere, Our Mathematical Universe (pp. 362). This doesn't strike me as entirely obvious, even in the case of a fundamental equation (though I am sympathetic to the idea that this fundamental equation may unambiguously constrain to one solution corresponding to the universe we observe, I do not think this is necessarily required for there not to be a multiverse).

39. Keep in mind that when trying to evaluate these parallel universes with different fundamental constants, it is still usually assumed that they have the same fundamental laws, such as The Law Of Conservation Of Energy and The Second Law Of Thermodynamics (the law of increasing entropy). Why? If constants are turn-able knobs, why not laws? Tegmark takes this seriously when he goes ahead and predicts a (level-IV) multiverse where every possible mathematical law governs things, but most physicists who are okay with the former are probably not okay with the latter. This strikes me as inconsistent.

40. “Some questions were abandoned as naive or misguided, such as explaining the sizes of planetary orbits from first principles, which was popular during the Renaissance.”, Our Mathematical Universe (pp. 247).

41. So it is mostly, but not entirely true when Tegmark writes (citing physicist Eugene Wigner) that traditional physical laws “... give no information about why...” initial conditions have their values, Our Mathematical Universe (pp. 339-340). Flying in the face of both this idea and The Copernican Principle, data on exoplanets have shown our solar system to be fairly abnormal—most star systems are multi-star systems, and even our planets are somewhat abnormal: “Earth is an extreme world. Of the thousands of confirmed or candidate planets astronomers have discovered in our galaxy, the most common type is a world unlike anything in our solar system: an enigmatic ball of either rock or gas that is bigger than Earth, but smaller than Neptune... three quarters of the worlds [the Kepler telescope] has discovered are this gassy variety, a planetary type not found at all among our eight planets... The findings fit nicely with theories of planet formation, which suggest that planets above a certain size cannot be made of mostly rock. The more dense material you pile on to a rocky planet, the more it shrinks under its own gravity.”, “Neil deGrasse Tyson Explains Multiple Star Systems” uploaded by StarTalk (2013) (at 1:26) (https://www.youtube.com/watch?v=aQrtz2-XWHA), excerpted from “Cosmic Queries: The Sun and other Stars” (2013) (https://www.startalkradio.net/show/cosmic-queries-the-sun-and-other-stars/ ), and “Most Common Planets Are Weird 'Mini-Neptunes” by Victoria Jaggard (2014) (https://www.newscientist.com/article/dn24826-most-common-exoplanets-are-weird-mini-neptunes/), who in turn cites unspecified papers by astronomers Geoff Marcy and Yoram Lithwick (though of course I have not read these).

42. Chaos theory is the idea that there exist “chaotic systems”–systems which, even given perfect deterministic laws (and so perfect predictability in principle), nevertheless produce unpredictable outcomes in practice because small perturbations in inputs to these functions lead to drastically different outputs (small differences such as those inherent in any practical measurement of an initial condition). As a counter-example, in a non-chaotic system, inputting 1.000 and 1.001 might yield highly similar outputs—given f(x) = 2x, we would get f(1.000) = 2.000 and f(1.001) = 2.002: very similar answers (depending on what these numbers represent). For a great explanation of chaos theory, see du Sautoy, The Great Unknown (pp. 21-71). It is worth noting as well, that there may be many forms of alien life (and physically possible alien life) which we do not predict from our physical equations, and which might still (or only) exist as parts of astrobiology even after changing the tuning of physical constants; we do not have the tools to make much of the predictions of these knob-changes, Pale Blue Dot (pp. 33), A Brief History of Time (pp. 129), and Krauss' essay (against the idea that) “The Laws Of Physics Are Predetermined”, This Idea Must Die (pp. 54). Physicist Lisa Randall goes further, pointing out that without the direct observational evidence of biology and the abstraction of biological science, we would have never predicted Earth-biology from our current understanding of physics despite the fact that it must underlie biology, “Michael Shermer with Dr. Lisa Randall — Dark Matter & the Dinosaurs (Science Salon # 1)” uploaded by Skeptic (2015) (52:57 - 53:10). E. O. Wilson calls this difficulty consilience by synthesis (as opposed to consilience by reduction): the fact that it's easier to tie sciences downward towards lower levels such as physics after we've understood them in their own abstraction than it is to predict sciences upwards above physics, via lower abstractions (we know some scientific facts about sociology; try predicting those from the pure quantum physics of many particles), Consilience by Edward O. Wilson (1998) (pp. 73-78). Tegmark mentions this difficulty as well, Our Mathematical Universe (pp. 257).

43. The Great Unknown (pp. 65-68), which in turn cites “The Three-Dimensional Dynamics Of The Die Throw” by Marcin Kapitaniak, Jaroslaw Strzalko, Juliusz Grabski, and Tomasz Kapitaniak (2012) (which I have not yet read).

44. The obvious criticism of this is that the first-approximation of cosmology may be much simpler than other subsystems (say, human development) within it, because it is just such details that are ignored in the models (cosmologists tend to look at the blunt history of the universe only in terms of a few variables, such as temperature and entropy). The problem is that one cannot claim that chaos theory does not apply to these simplified models if they then make predictions about the emergence of biology (as biology was omitted from the simple model so that it would be simpler; complexity is being sneaked back in in the last minute!).

45. In fact, Tegmark concedes that some parameters don't require much luck at all, Our Mathematical Universe (pp. 354). Perhaps these are simply non-“chaotic” variables in the system.

46. The fact is that the large-scale emergence of (first chemistry, then) biology is far downstream from small differences in inputs to particle physics, meaning it might not be surprising that it is “chaotic”. In fact, mutations can be chosen by evolution by natural selection whose phenotype-mechanism acts early, as during embryology, so that the mutation can have an outsize downstream effect, The Extended Phenotype by Richard Dawkins (1982 / 1999) (pp. 262). It is sometimes exaggerated that given the same initial conditions, evolution by natural selection would turn out different forms if allowed to run again. Of course, there would need to be changes in initial conditions somewhere in the local universe, however subtle, for this to occur—and the “subtle” part starts to sound like chaos theory. See du Sautoy for a bit on a related debate in evolutionary biology, The Great Unknown (pp. 58-59).

47. “... the dark energy density... it's about sixteen orders of magnitude smaller than one might naturally expect, yet changing it by even a percent up or down dramatically reduces the amount of either carbon or oxygen produced by stars. Increasing it by 18% radically reduces fusion of hydrogen into any other atoms by stars, while reducing it by 34% makes hydrogen atoms decay into neutrons as their proton gobbles up their electron.”, Our Mathematical Universe (pp. 354).

48. “Hard-nosed physicists say that the six knobs were never free to vary in the first place.”, The God Delusion (pp. 173).

49. This is not to be confused with the measurement problem in quantum physics, which is about why we seem to see a single random value from within a predicted probability distribution, upon observation, Our Mathematical Universe (pp. 177).

50. Our Mathematical Universe (pp. 313). This alone seems problematic to me, and again, Tegmark does go on to agree, making the plausible argument that the concepts of infinities and infinitesimals are only approximations of very large and very small values, not real quantities, Our Mathematical Universe (pp. 316-317). Sagan appears to implicitly take this view when he writes, “A googelplex is precisely as far from infinity as is the number one.”, Cosmos (232).

51. Our Mathematical Universe (pp. 313).

52. Our Mathematical Universe (pp. 220, 223-225). Becker also briefly mentions the possibility of unification between classical and quantum multiverse hypotheses, What Is Real? (pp. 256, 285).

53. According to Tegmark, Everett argued that the probability density of the wavefunction (its “square”, or the product of it with its complex conjugate) gave the measure / weight of a parallel universe, Our Mathematical Universe (pp. 222).

54. Please forgive me if I am wrong about this facet of quantum physics being continuous, as I am still extremely early on in my technical understanding of the subject. Tegmark does say that quantum physics' wavefunctions are continuous (though I am not sure if it necessarily follows that the probability distribution derived from the “square” of that wavefunction is also continuous) in his essay “Infinity”, This Idea Must Die (pp. 51). My understanding is that even in those situations in which the outcome itself is entirely discrete, say the spin of a particle which is binary (either spin-up or spin-down), an infinite number of “superpositions” (or probabilistic combinations) of these are allowed: (approximately) 0% spin-down and 100% spin-up, 100% spin-down and 0% spin-up, and all infinitely many rational and irrational possibilities in-between. Tegmark argues that if the quantum multiverse is related to the classical multiverse, then this means that there exist not just the two universes in which the particle is measured spin-up and spin-down, there actually exist (potentially infinitely) many in both states, but that the ratio between how many duplicates of the one outcome to the number of duplicates of the other outcome satisfies the quantum probability. For example, if the quantum probability is 25% spin-down and 75% spin-up, then there are three times as many duplicate universes with a spin-up outcome than those with a spin-down outcome. The problem I am trying to illustrate is that parallel universes come in integer numbers and the ratio of duplicate universes to overall universes is then a rational number—this can only tend to approximate the case of quantum physics making a prediction of a probability distribution with an irrational quantity as the probability—imagine a case where the theory predicts a π-percent chance of measuring spin-up and a 100 percent minus π-percent chance of measuring spin-down. It would intuitively seem that there could not exist an integer number of duplicate universes divided by an integer number of total universes (the definition of a rational number is that it is the ratio of two integers) that could satisfy this requirement (unless comparing the sizes of different infinities somehow allows for yielding irrational numbers, but this may be a problem for our method of comparing infinities, not support for the present multiverse idea). There appears to be another less elegant complication: for observables that have not yet been quantized, such as position, given there is a large infinity of possible positions for a particle to be in (most of them irrational), then how could one have enough rational numbers (the infinite set of rational numbers is smaller than the infinite set of irrational numbers) to assign probabilities to each of the possible positions? It is worth noting that there are many physicists who think that spacetime will be quantized, with the quantum being somewhere around the Planck-length, a theoretical small distance obtained by performing unit analysis arithmetic on physical constants. The most popular such group are probably the loop-quantum gravity (the current major competitor to string theory for a theory of quantum gravity) physicists.

55. This is probably the most common argument against multiverse hypotheses among physicists, including Ellis, Our Mathematical Universe (pp. 361), which further cites “Does The Multiverse Really Exist?”; Steinhardt in “Theories of Anything”, This Idea Must Die (pp.56); Turok and Steinhardt, Endless Universe (pp. 234, 250); Smolin in his essay (against the idea that) “The Big Bang Was The First Moment Of Time”, This Idea Must Die (pp. 33); and Sagan (characteristically more ginger than most), Pale Blue Dot (pp. 34). Du Sautoy is more hopeful that these multiverse hypotheses will eventually be realized to produce empirically testable predictions (though I think most detractors simply think these ideas should be taken less seriously unless and until they do make measurable predictions—someone like Tegmark holds that these parallel universes need not leave any observable signature for him to already believe, right now), The Great Unknown (pp. 220-221, 226). Physicist Joanne Baker echoes this sentiment, 50 Ideas You Really Need To Know: Quantum Physics by Joanne Baker (pp. 155). Becker puzzlingly insists that scientific hypotheses need not be falsifiable before maintaining that they do indeed need empirical evidence for confirmation (implying he may not fully understand how far the anti-falsifiability camp often goes in eschewing the need for observational verification—again, Tegmark claims to believe in these multiverses right now), What Is Real? (pp. 260-264). He also claims that even Popper wasn't completely happy with falsification, What Is Real? (pp. 260, 263). Along those lines, physicist Sean Carroll claims that it's forgotten that Popper understood falsifiability to be the case only “in principle” , and proposes that scientific hypotheses must be definite (making quantitative predictions) and empirical so that we can “fit models to data”, in his essay (against the idea of) “Falsifiability”, This Idea Must Die (pp. 126-127). I endorse this, but I do not see why he is so adamant that this is different from being falsifiable—if your theory makes a definite empirical prediction, then measurement during experiment will either be consistent with it, or falsify it (as currently formulated). I have trouble finding a definition for “falsifiable” that doesn't sound exactly like “makes definite empirical predictions”. Like Becker, Carroll, Tegmark, and myself (although I likely lean more in favor of needing direct empirical evidence than they do), Rees takes the view that unobservable objects may well be the real predictions of theories and cannot be dismissed out of hand in his essay, “Multiverse”, This Idea Is Brilliant (pp. 137). Astrophysicist Gregory Benford offers that indirect empirical evidence (such as interaction effects between multiverses) would suffice in the essay (arguing against) “The Intrinsic Beauty And Elegance Of Mathematics Allows It To Describe Nature”, This Idea Must Die (pp. 471).

56. Tegmark mentions “human baggage” (while I agree that language is a form of human baggage in this sense, I disagree with him that anything outside of the naked mathematics is, which I will expand upon in Part IV), Our Mathematical Universe (pp. 255-256, 258-259). “... science is all about understanding reality...”, Our Mathematical Universe (pp. 300). Similarly, “... scientific theories... need to give explanations, unify previously disparate concepts, and bear some relationship with the world around us.”, What Is Real? (pp. 264).

57. Tegmark explains isomorphism as the mathematical equivalence of models, Our Mathematical Universe (pp. 280).

58. Tegmark (who evidently doesn't like the idea much) calls it the omnivision assumption, though I am not fond of this terminology, Our Mathematical Universe (pp. 363-364). The opposite view, that there exist phenomena which cannot be observed even in principle has something in common with another (I think premature) idea: mysterianism (the idea that the human mind is physically incapable of understanding certain aspects of reality), “Michael Shermer with Colin McGinn — Mysterianism, Consciousness, Free Will & God (SCIENCE SALON #29)” uploaded by Skeptic (2018) (especially 13:40 - 16:45). Rees also makes an argument for this in his essay (rebutting the idea that), “We'll Never Hit Barriers To Scientific Understanding”, This Idea Must Die (pp. 167, 169). I am skeptical of the premature conclusion, but I must admit that it is a strong argument that other animals' brains clearly cannot understand certain truths about reality, and our brains were not specially designed for understanding the entire Cosmos (there is little reason to believe that even the smartest human has the smartest physically possible brain in the universe), “Michael Shermer with Colin McGinn — Mysterianism, Consciousness, Free Will & God (SCIENCE SALON #29)” (especially 13:40 – 16:45), and my cousin Frank Scales also mentioned this animal-brain analogy to me before. Greene explains the possibility of hard-mysterianism (that some facets of nature may be unknowable in principle, to any kind of mind, The Elegant Universe (pp. 385). Tegmark does not seem to go as far as mysterianism in his views, writing that the abilities of the human mind have been historically underestimated (though, similar to the historical induction argument that having tended to underestimate the size of the Cosmos suggests a multiverse, this is not evidence that our ability to understand will not terminate somewhere), Our Mathematical Universe (pp. 19). Psychiatrist and philosopher Jordan Peterson writes, “... it's not clear that [humans] have any real limits.”, 12 Rules For Life by Jordan Peterson (2018) (pp. 296).

59. Our Mathematical Universe (pp. 124).

60. Note that for me, simultaneously not yet believing something but taking it seriously only speaks to its likelihood of being absolutely true or false, given my knowledge. I invoke none of this poppycock about “amounts of realness” wherein some things are “realer” than others. Even Linde himself admits that the fine-tuning / Anthropic Principle multiverse cannot be directly proved or disproved as long as our best theory predicted unobservable universes, and he explicitly lays out what kind of theory would be needed to supplant such a prediction: “... (1) invent a better cosmological theory, (2) invent a better theory of fundamental interactions, and (3) propose an alternative explanation for [the uniformity of the universe and the particular values of the physical constants],” in his essay (against the idea of), “The Uniformity And Uniqueness Of The Universe”, This Idea Must Die (pp. 46-47). Tegmark relays that Ellis notes that the incompleteness of current theories may eventually discredit current multiverse research, Our Mathematical Universe (pp. 361), which further cites Ellis' “Does The Multiverse Really Exist?”.

61. “Neil deGrasse Tyson Explains Gravitational Waves and Gravitons”, a clip from StarTalk's “Cosmic Queries: Gravity” episode (https://www.youtube.com/watch?v=EH70kTm25Es ) (2014) (3:17 – 4:03). “Gravitational Waves Detected 100 Years After Einstein's Prediction” from LIGO (2016) (https://www.ligo.caltech.edu/news/ligo20160211 ).

62. Our Mathematical Universe (pp. 5). “Gravitational Waves Detected 100 Years After Einstein's Prediction” from LIGO (2016) (https://www.ligo.caltech.edu/news/ligo20160211 ).

63. Rees makes the same argument as Tegmark in his essay, “Multiverse”, This Idea Is Brilliant (pp. 138).

64. Tegmark admits these multiverses are at least partially “untestable”, and spends little time on experimental proposals (yet does spend time on BICEP-2's experiment being evidence for a multiverse, though this famously and unfortunately turned out to be a measurement fluke), Our Mathematical Universe (pp. 110-111, 125, 151).

65. “... the discovery that a physical parameter seems fine-tuned to allow life can be interpreted as evidence of a multiverse where the parameter takes a broad range of values, because this interpretation makes it unsurprising that a habitable universe like ours exists, and predicts that this is where we'll find ourselves.”, Our Mathematical Universe (pp. 352).

66. The Elegant Universe (pp. 368). Greene goes on to point out that the conservative argument is poised to make a comeback even in the case of a multiverse, “... the conclusion that [a multiverse] compromises our predictive power is far from airtight... if we unleash our imaginations and allow ourselves to contemplate a multiverse, we should also unleash our theoretical musings and contemplate ways in which the apparent randomness of the multiverse can be tamed. For one relatively conservative musing, we can imagine that... we would be able to extend our ultimate theory to its full sprawling expanse, and that our “extended ultimate theory” might tell us precisely why and how the values of the fundamental parameters are sprinkled across the constituent universes.”, The Elegant Universe (pp. 368-369, 385). Rees also argues that some fundamental laws would still constrain the multiverse (with previously-thought physical laws being more like “local bylaws”) in his essay, “Multiverse”, This Idea Is Brilliant (pp. 136-137). To be completely fair, Tegmark seems to want to split the baby between the two views, sometimes emphasizing the unwieldy nature of multiverses, other times seeming to claim they're as austerely constrained as classical physics (also utilizing the term “by-laws”), Our Mathematical Universe (pp. 123, 138, 150, 320-321, 340).

67. For Tegmark's informal poll, Our Mathematical Universe (pp. 228). “It is no surprise that... professors lean left... One of the strongest personality correlates of left-wing politics is the trait of openness to experience, a trait that describes people who crave new ideas and experiences and who tend to be interested in changing traditional arrangements... Social conservatives tend to... prefer things to be orderly and predictable... and they are more likely to see the value of traditional arrangements.”, The Coddling Of The American Mind by Greg Lukianoff and Jonathan Haidt (2018) (pp. 110), who in turn cite McCrae (1996), and Carney, Jost, Gosling, and Potter (2008) (though I have not read these papers). Lukianoff and Haidt show that the left-to-right ratio in academia went from 2:1 in the mid-1990s, to 5:1 in 2011 (with at least a slight dip in the following few years), arguing that “The only field among the social sciences that is known to have enough political diversity to allow for institutionalized disconfirmation is economics, where the ratio... was... four to one.”, The Coddling Of The American Mind (pp. 110-111). One 2018 study (with data gathered in 2017, N = 8,688) found that the overall Democrat:Republican ratio was 10.4:1, with the lowest being Engineering at 1.6:1, Economics at 5.5:1, Physics in 6^th most politically diverse at 6.2:1, and Communications a whopping 108:0!, “Homogenous: The Political Affiliations Of Elite Liberal Arts College Faculty” by Michell Langbert (2018) (https://www.nas.org/academic-questions/31/2/homogenous_the_political_affiliations_of_elite_liberal_arts_college_faculty ) (note, I have not read this entire paper, and refer only to Figure 1, which is the chart of Democrat:Republican ratio per academic field). This “... particularly in fields that deal with politicized content, can undermine the quality and rigor of scholarly research... when a field lacks political diversity, researchers tend to congregate around questions and research methods that generally confirm their shared narrative, while ignoring questions and methods that don't offer such support.”, The Coddling Of The American Mind (pp. 112), which in turn cites Duarte et. al. (2015) (though I have not read this paper). In fact, even the students have become more left-wing over time, “... roughly 20% of incoming students identify as conservative, and that figure has held steady since the early 1980s. Self-described 'moderates' made up roughly half of all incoming students in the 1980s and 1990s, but that figure has been dropping since the early 2000s—it's now in the low forties—as the percentage of progressives (self-described 'liberals') rises into the high 30s.”, The Coddling Of The American Mind (pp. 113), which in turn cites “The American Freshman: National Norms Fall 2016” by Eagen et. al. (https://www.heri.ucla.edu/monographs/TheAmericanFreshman2016.pdf ) (2017) (though I have not myself read this).

68. Becker mentiones the ick-factor when he claims detractors find multiverses “unpalatable” and not to their “taste” (Becker claims he can dismiss any arguments from unfalsifiabilty as “ignorant” people succumbing to what I'm calling the “ick-factor”, but I clearly disagree), What Is Real? (pp. 260, 263-264). Carroll has lamented that some physicists' objections to a quantum many-worlds multiverse are as weak as, “... I just don't like all those worlds...”, “Episode 36: David Albert on Quantum Measurement and the Problems with Many-Worlds” uploaded by Sean Carroll (2019) (https://youtu.be/AglOFx6eySE at 50:31). They (literally) both agree that this is not a good counterargument, “Mindscape 59 | Adam Becker on the Curious History of Quantum Mechanics” (2019) (https://www.youtube.com/watch?v=em7dkYZTetE at 1:04:42). Tegmark made mention as well, claiming many see multiverses as “too weird to be real”, conveying either “this makes no sense”, or simply “I hate it”, Our Mathemaical Universe (pp. 152-153, 363). Lloyd wrote, “The promiscuous nature of the multiverse may be unappealing (Willam James, who coined the word, called the multiverse a 'harlot')...” (language that would traditionally be familiar in a socially conservative political conversation), in his essay “The Universe”, This Idea Must Die (pp. 13). I should note that I'm not aware of ever seeing so base an opposition to multiverses (even if I may feel it on some level), I mainly see opposition on the explicit grounds of unfalsifiability. On the topic of these physicists' political orientations, I think both would proudly agree they are left-of-center. Being a fan of work from both of these individuals, I have garnered my sense for their being left-wing from multiple occasions, but again, as I doubt there will be a disagreement about this claim, I will just provide a couple of examples. Becker has his pronouns “he/him” in his Twitter bio, originally a way for trans-people to assert their non-obvious pronouns, now used by sexually unambiguous individuals to signify solidarity with trans-people (and, I argue, a way of virtue-signaling one's politically progressive bona fides) (https://twitter.com/FreelanceAstro). Carroll implied that he is not conservative during a discussion in which he criticized both Fox News and the Trump administration on The Joe Rogan Experience, “Joe Rogan on Fox News & Sean Hannity”, uploaded by Joe Rogan and Anime (https://www.youtube.com/watch?v=GOnhCiUpumc), excerpted from “Joe Rogan Experience #1151 - Sean Carroll”, uploaded by PowerfulJRE (2018) (https://www.youtube.com/watch?v=ZtxzMb9CpTM ).

69. For more on the history of the politically left-leaning (even Marxist) bias of academics (of social scientists in particular), and the consequential flaws in the research of their fields, see the first third of The Blank Slate by Steven Pinker (2003 / 2016) (pp. 1-135).

70. I have named this as a more general version of the god of the gaps fallacy: the observation that many religious arguments rely on placing god just outside of current scientific understanding (presently, god might be invoked to “explain” consciousness)–ignoring that these types of arguments in the past have placed god in areas now understood by science (evolution by natural selection replaced biblical Genesis as the explanation for where people came from, for example), The God Delusion (pp. 151). In the case of multiverses, some physicists are placing multiverses in locations that are currently open questions in science (such as why the fundamental constants have the values they have). One might fairly defend this as one hypothesis among many, but there is a peculiarity about this particular hypothesis: physicists who endorse it regularly oversell the footing it is on, and many even claim to already “believe” it as the correct explanation (rather than remaining in equipoise until the evidence is in). Besides Tegmark, Carroll has been known to describes himself as a “partisan” of the quantum many-worlds multiverse, “Episode 28: Roger Penrose on Spacetime, Consciousness, and the Universe” uploaded by Sean Carroll (2019) (https://www.youtube.com/watch?v=DJADe-_dRB0 ) (at 1:14:53). When Tegmark briefly lists Ellis' problems with multiverse hypotheses, many of his main points boil down to the fact that these physicists' evidence is dubious because they are pretending all current theories are complete and can be trusted to give an accurate prediction to such extreme questions as whether or not there exist multiple universes, Our Mathematical Universe (pp. 361), which further cites “Does The Multiverse Really Exist?”.