The Big Picture

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The Big Picture Page 17

by Carroll, Sean M.


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  Reality Emerges

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  ith our Bayesian knowledge- building tool kit in hand, we can

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  return to fleshing out some of the ideas behind poetic natural-

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  ism. In particular, the innocuous- seeming but secretly pro-

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  found idea that there are many ways of talking about the world, each of

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  which captures a different aspect of the underlying whole.

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  The progress of human knowledge has bequeathed to us a couple of in-

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  sights that, taken together, suggest a world that is profoundly different from

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  the picture we construct from our everyday experience. There is conserva-

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  tion of momentum: the universe doesn’t need a mover; constant motion is

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  natural and expected. It is tempting to hypothesize— cautiously, always with

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  the prospect of changing our minds if it doesn’t work— that the universe

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  doesn’t need to be created, caused, or even sustained. It can simply be. Then

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  there is conservation of information. The universe evolves by marching from

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  one moment to the next in a way that depends only on its present state. It

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  neither aims toward future goals nor relies on its previous history.

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  These discoveries indicate that the world operates by itself, free of any

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  external guidance. Together they have dramatically increased our credence

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  in naturalism: there is only one world, the natural world, operating accord-

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  ing to the laws of physics. But they also highlight a looming question: Why

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  does the world of our everyday experience seem so different from the world

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  of fundamental physics? Why aren’t the basic workings of reality perfectly

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  obvious at first glance? Why is the vocabulary we use to describe the every-

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  day world— causes, purposes, reasons why— so different from that of the

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  microscopic world— constant motion, Laplacian patterns?

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  T H E B IG PIC T U R E

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  This brings us to the “poetic” part of poetic naturalism. While there is

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  one world, there are many ways of talking about it. We refer to these ways

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  as “models” or “theories” or “vocabularies” or “stories”; it doesn’t matter.

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  Aristotle and his contemporaries weren’t just making things up; they told

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  a reasonable story about the world they actually observed. Science has dis-

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  covered another set of stories, harder to perceive but of greater precision and

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  wider applicability. It’s not good enough that the stories succeed individu-

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  ally; they have to fit together.

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  One pivotal word enables that reconciliation between all the different stories:

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  emergence. Like many magical words, it’s extremely powerful but also tricky

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  and liable to be misused in the wrong hands. A property of a system is “emer-

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  gent” if it is not part of a detailed “fundamental” description of the system,

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  but it becomes useful or even inevitable when we look at the system more

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  broadly. A naturalist believes that human behavior emerges from the complex

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  interplay of the atoms and forces that make up individual human beings.

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  The Starry Night. (Painting by Vincent van Gogh)

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  R E A l I t y E M E R g E S

  Emergence is ubiquitous. Consider a painting, such as van Gogh’s The

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  Starry Night. The canvas and paint constitute a physical artifact; on one

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  level, it is just a collection of certain atoms in certain locations. There is

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  nothing to the painting other than those atoms. Van Gogh didn’t infuse it

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  with any form of spiritual energy; he put the paint onto the canvas. If the

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  atoms making up the paint had been put in different locations, it would

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  have been a different painting.

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  But it’s obvious that specifying an arrangement of atoms isn’t the only way

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  of talking about this physical artifact, and it’s not even the best way for most

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  purposes. When we talk about The Starry Night, we refer to the color palette,

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  the mood it evokes, the swirling of the moon and stars in the sky, and perhaps

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  to van Gogh’s period in the asylum at Saint- Paul de Mausole. All of these

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  higher- level concepts are something in addition to a dry (but accurate) list of

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  all the atoms that make up the paint. They are emergent properties.

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  The classic example of emergence, one you should constantly return to

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  whenever these things get confusing, involves the air in the room around

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  you. That air is a gas, and we can speak of it as having various properties: a

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  temperature, a density, a humidity, a velocity, and so on. We think of the

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  air as a continuous fluid, and all of those properties take on numerical val-

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  ues at every point in the room. (Remember that gases, like liquids, are flu-

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  ids.) But we know that the air isn’t “really” a fluid. It we look at it very

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  closely, down at a microscopic level, we see that it’s composed of individual

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  atoms and molecules— mostly nitrogen and oxygen, with trace bits of other

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  elements and compounds. One way of talking about the air would simply

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  be to list every one of those molecules— perhaps 1028 of them— and specify

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  their positions, velocities, orientations in space, and so on. This is some-

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  times called kinetic theory, and it’s a perfectly legitimate way of talking.

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  Two ways of thinking about air: as a collection of discrete molecules, or as a smooth fluid.

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  T H E B IG PIC T U R E

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  Specifying the state of each molecule at every moment in time is a consistent

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  and self- contained description of the system; if you were as smart as Laplace’s

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  Demon, that would be enough to determine the state at any other time. In

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  practice it’s incredibly cumbersome, and nobody ever talks that way.

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  Describing the air in terms of its macroscopic fluid properties such as

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  temperature and density is also a perfectly legitimate way of talking. Just as

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  there are equations that can tell us how the individual molecules bump into

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  one another and move over time, there are separate equations that tell us

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  how the fluid parameters evolve over time. And the good news is, you don’t

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  need to be nearly as smart as Laplace’s Demon to actually find the solution;

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  real computers are completely up to the task. Atmospheric scientists and

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  aeronautical engineers solve such equations every day.

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  So the fluid description and the molecular description are two different

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  ways of talking about the air, both of which— at least in certain

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  circumstances— tell very precise and useful stories about how air behaves.

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  This example illustrates a number of features that commonly appear in dis-

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  cussions of emergence:

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  • The different stories or theories use utterly different vocabu-

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  laries; they are different ontologies, despite describing the

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  same underlying reality. In one we talk about the density,

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  pressure, and viscosity of the fluid; in the other we talk about

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  the position and velocity of all the individual molecules.

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  Each story comes with an elaborate set of ingredients—

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  objects, properties, processes, relations— and those ingredi-

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  ents can be wildly different from one story to another, even

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  if they are all “true.”

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  • Each theory has a particular domain of applicability. The fluid

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  description wouldn’t be legitimate if the number of mole-

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  cules in a region were so small that the effects of particular

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  molecules were important individually, rather than only in

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  aggregate. The molecular description is effective under wider

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  circumstances, but still not always; we could imagine pack-

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  ing enough molecules into a small enough region of space

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  R E A l I t y E M E R g E S

  that they collapsed to make a black hole, and the molecular

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  vocabulary would no longer be appropriate.

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  • Within their respective domains of applicability, each theory

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  is autonomous— complete and self- contained, neither relying

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  on the other. If we’re speaking the fluid language, we describe

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  the air using density and pressure and so on. Specifying those

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  quantities is enough to answer whatever questions we have

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  about the air, according to that theory. In particular, we don’t

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  need to ever refer to any ideas about molecules and their

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  properties. Historically, we talked about air pressure and ve-

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  locity long before we knew it was made of molecules. Like-

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  wise, when we are talking about molecules, we don’t ever

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  have to use words like “pressure” or “viscosity”— those con-

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  cepts simply don’t apply.

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  The important takeaway here is that stories can invoke utterly different

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  ideas, and yet accurately describe the same underlying stuff. This will be

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  crucially important down the line. Organisms can be alive even if their

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  constituent atoms are not. Animals can be conscious even if their cells are

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  not. People can make choices even if the very concept of “choice” doesn’t

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  apply to the pieces of which they are made.

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  If we have two different theories that both accurately describe the same

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  underlying reality, they must be related to each other and mutually consis-

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  tent. Sometimes that relationship is simple and transparent; other times we

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  just have to trust that it’s there.

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  The case of fluid dynamics emerging from molecules is as simple as it

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  gets. One theory can directly be obtained from the other by a process

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  known as coarse- graining. There is an explicit map from one theory (mole-

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  cules) to the other (fluid). A particular state in the first theory— a list of all

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  the molecules, their positions, and velocities— corresponds to some par-

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  ticular state in the second one— a density and pressure and velocity of the

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  fluid at every point.

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  T H E B IG PIC T U R E

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  Moreover, many different states in the molecular theory get mapped

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  to the same state in the fluid one. When this is the case, we often call

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  the first theory the “microscopic” or “ fine- grained” or “fundamental” one,

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  and the second the “macroscopic” or “ coarse- grained” or “emergent” or “ef-

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  fective” one. These labels aren’t absolute. To a biologist working with an

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  emergent theory of cells and tissue, the theory of atoms and their interac-

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  tions might be a microscopic description; to a string theorist working on

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  the quantum theory of gravity, superstrings might be the microscopic enti-

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  ties, and atoms are emergent. One person’s microscopic is another person’s

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  macroscopic.

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  We want our theories to give physical predictions that are consistent

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  with each other. I
magine that a state x in the microscopic theory evolves

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  into some state y. And imagine that the “emergence” map sends x and y to 14

  states X and Y in the emergent fluid theory. Then it had better be the case 15

  that X evolves to Y under the rules of the emergent theory, at least with very 16

  high probability. Starting with a microscopic state, the process “evolve for-

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  ward in time, and see what that corresponds to in the emergent theory”

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  should give the same answer as “see what it corresponds to in the emergent

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  theory, then evolve forward in time.”

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  states in the

  states in the

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  microscopic theory

  emergent/effective theory

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  evolution

  through

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  time

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  x

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  X

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  emergence

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  Emergence of one theory from another. Boxes in each image represent different possible 32

  states the entire system could be in, as described by each theory. Time evolution and emer-33

  gence should be compatible: microstates that map to the same emergent state should

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  evolve into microstates that also map to the same emergent state. Several microstates map 35S

  to each emergent state.

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  R E A l I t y E M E R g E S

  Coarse- graining goes one way— from microscopic to macroscopic— but

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  not the other way. You can’t discover the properties of the microscopic

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  theory just from knowing the macroscopic theory. Indeed, emergent theo-

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  ries can be multiply realizable: there can, in principle, be many distinct

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  microscopic theories that are incompatible with one another but compati-

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  ble with the same emergent description. You can understand the air as a

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  fluid without knowing anything about its molecular composition, or even

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  if there is a description in terms of particles at all.

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  The reason why emergence is so helpful is that different theories are not

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  created equal. Within its domain of applicability, the emergent fluid theory

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  is enormously more computationally efficient than the microscopic mo-

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  lecular theory. It’s easier to write down a few fluid variables than the states

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  of all those molecules. Typically— though not necessarily— the theory that

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  has a wider domain of applicability will also be the one that is more com-

 

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