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putationally cumbersome. There tends to be a trade-off between compre-
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hensiveness of a theory and its practicality.
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Our ability to construct two different theories about the air in your
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room, once as a fluid and another time as a collection of molecules, is an
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especially concrete and vivid example of emergence, and more generally of
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the poetic- naturalist idea of telling multiple stories about the same underly-
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ing reality. There are, as you might guess, some subtleties worth exploring.
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•
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One of the features of the molecules/ fluid example is that we can derive the
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macroscopic fluid theory from the microscopic molecular theory. That is,
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we can start with the molecules, assume that there is a high density of mol-
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ecules at every point in space, and then “smooth out” the distribution to
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obtain explicit formulas for fluid properties such as pressure and tempera-
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ture in terms of what the molecules are doing. This is what is meant by
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“ coarse- graining” above.
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Sneakily, however, we have taken advantage of a very special feature
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of kinetic theory, one that doesn’t readily extend to other situations we
32
might be interested in. At heart, the molecules in the air are simple objects,
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mindlessly bumping into one another when they pass through the same
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point in space. All we’re really doing to derive the fluid description is
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calculating the average properties of all the molecules. The average number
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of molecules gives us the density, the average energy gives us the tempera-
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ture, the average momentum moving in different directions gives us the
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pressure, and so on.
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We can’t take such features for granted. Quantum mechanics, in par-
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ticular, features the phenomenon of entanglement. It’s not possible to spec-
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ify the state of a system by listing the state of all of its subsystems
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individually; we have to look at the system as a whole, because different
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parts of it can be entangled with one another. To dig a bit deeper, when we
10
combine quantum mechanics with gravity, it is widely believed (although
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not known for certain, since we know almost nothing for certain about
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quantum gravity) that space itself is emergent rather than fundamental.
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Then it doesn’t even make sense to talk about “a location in space” as a
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fundamental concept.
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We needn’t ascend to esoteric realms of quantum gravity to find situa-
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tions in which a straightforward smoothing- out process isn’t enough to
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take us from a microscopic theory to an emergent one. Perhaps we want to
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have a theory of the human brain that emerges out of the behavior of many
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neurons. Or a theory of a single neuron that emerges out of the interactions
20
of the molecules of which it is made. The problem is that both neurons
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and the complicated organic molecules in each neuron are pretty complex
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in their own right; their behavior depends in subtle ways on the specific
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inputs they are receiving from their environments. Simply averaging over
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all of them in some region isn’t going to capture all of that subtlety. That’s
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not to say that there can’t be a useful emergent theory, with a many-to-one
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map from neuron states to brain states, or molecular states to neuron states;
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it’s just that obtaining it is going to be a bit more indirect than it was for the
28
air in our room.
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The molecular and fluid descriptions of air in a room provide an inno-
30
cent, uncontroversial example of emergence. Everyone agrees on what is
31
happening and how to talk about it. But its simplicity can be misleading.
32
Seeing how relatively easy it is to derive fluid mechanics from molecules,
33
one can get the idea that deriving one theory from another is what emer-
34
gence is all about. It’s not— emergence is about different theories speaking
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different languages, but offering compatible descriptions of the same under-
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lying phenomena in their respective domains of applicability. If a
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macroscopic theory has a domain of applicability that is a subset of the
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domain of applicability of some microscopic theory, and both theories are
02
consistent, then the microscopic theory can be said to entail the macro-
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scopic one; but that’s often something we take for granted, not something
04
that can explicitly be demonstrated. The ability to actually go through the
05
steps to derive one theory from another is great when it happens, but not at
06
all crucial to the idea.
07
08
•
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As systems evolve through time, perhaps in response to changes in their
10
external environment, they can pass from the domain of applicability of
11
one kind of emergent description to a different one— what’s known as a
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phase transition. Water is the most familiar example. Depending on the
13
temperature and pressure, water can find itself in the form of solid ice, liq-
14
uid water, or gaseous water vapor. The underlying microscopic description
15
remains the same— molecules of H O— but the macroscopic properties
16
2
shift from one “phase” to another. Because of the different conditions, the
17
way that we talk about the water changes: the density, hardness, speed of
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sound through the medium, and other characteristics of the water can be
19
completely altered, and our vocabulary changes along with them. (You
20
wouldn’t talk about pouring a block of ice, or chipping a cup of liquid water.) 21
22
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Heat being added
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gas
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boiling
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perature
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mTe
liquid
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melting
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solid
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Time
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How water changes phase from solid to liquid to gas, as heat is added to it and the temperature rises. The melting and boiling points exhibit plateaus; here the internal structure S35
of the molecules is being rearranged, even though the temperature remains fixed.
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The way that phase transitions actually occur is a subject of endless fas-
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cination to scientists. Some transitions are rapid, some are slow; some
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change the substance utterly, others represent a more gradual evolution. The
04
figure illustrates one interesting feature of phase transitions: not all changes
05
are visible on the surface. As we add heat to water, it goes from ice to liquid
06
to vapor, and the temperature rises along the way. At the precise transition
07
point, there is a period where the temperature remains constant while the
08
molecular structure of the water is being rearranged. Entirely new physical
09
properties can come into existence as we change phases, such as solidity or
10
transparency or electrical conductivity. Or life, or consciousness.
11
When we’re talking about simple molecular systems, it’s often possible
12
to pinpoint precisely what kind of theoretical vocabulary is appropriate, as
13
well as where we transition from one phase to another. The boundary lines
14
become fuzzier when we start discussing biology or human interactions,
15
but the same basic ideas apply. We’ve all witnessed phase transitions in the
16
mood of a roomful of people, when someone says the right (or wrong)
17
thing, or when a new person enters the dynamic. Here is a partial list of
18
important phase transitions in the history of the cosmos:
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• The formation of protons and neutrons out of quarks and
21
gluons in the early universe.
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• Electrons combining with atomic nuclei to make atoms, sev-
23
eral hundred thousand years after the Big Bang.
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• The formation of the first stars, filling the universe with new
25
light.
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• The origin of life: a self- sustaining complex chemical reaction.
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• Multicellularity, when different living organisms merged to
28
become one.
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• Consciousness: the awareness of self and the ability to form
30
mental representations of the universe.
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• The origin of language and the ability to construct and share
32
abstract thoughts.
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• The invention of machines and technology.
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There are phase transitions in the realm of ideas as well as that of mate-
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rials. Philosopher of science Thomas Kuhn popularized the idea of a
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“paradigm shift” to describe how new theories could induce scientists to
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conceptualize the world in starkly different ways. Even an individual per-
02
son changing their mind about something can be thought of as a phase
03
transition: our best way of talking about that person is now different. Peo-
04
ple, like water, can exhibit plateaus in their thinking, where outwardly they
05
hold the same beliefs but inwardly their mental gears are gradually turning.
06
07
•
08
The fact that each theory or way of talking works only within a specified
09
domain of applicability is absolutely crucial. Again, the example of air is a
10
simple one, but perhaps so simple that it lulls us into a false sense of com-
11
placency.
12
Even though we think of the air in the room as “really” being made of
13
various molecules, that theory’s domain of applicability fails to include
14
some situations, such as when the density becomes so high that the air
15
would collapse into a black hole. (Not to worry, that’s far removed from the
16
physical situation in most rooms you will find yourself in.) But the fluid
17
description also fails in those cases. In fact, the domain of applicability of
18
the emergent fluid theory is a strict subset of the domain of applicability of
19
the molecular theory.
20
21
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The Universe
The Universe
The Universe
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Theory 1
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Theory
Theory
Theory
Theory
Theory
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1
2
1
2
2
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How domains of applicability of different theories could relate to each other.
29
30
That situation— two ways of talking, one of whose domain of applica-
31
bility fits inside that of the other— is by no means necessary. In the diagram,
32
we have shown various ways that domains of applicability might fit to-
33
gether. One might be a subset of the other; or the two might be distinct but
34
overlapping; or they could just be completely different, not sharing any
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situations in common. For example, in string theory, a leading candidate
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for a quantum theory of gravity, there are “duality relations” between theo-
02
ries that leave us in the middle situation, where we have two theories with
03
overlapping domains of applicability.
04
Another example— controversially— might be human consciousness.
05
People are made of particles, and we have a successful picture of how indi-
06
vidual particles behave, the Core Theory we’ll discuss more in chapter 22.
07
You might think that we could fully describe a person if only we knew the
08
complete state of all of their particles. We have every reason to believe that
<
br /> 09
the domain of applicability of particle physics includes the particles that
10
make up human beings. But it’s possible, however unlikely, that there is one
11
set of rules obeyed by particles when there are only a handful of them inter-
12
acting with one another, as studied by particle physicists, and a slightly dif-
13
ferent set of rules that they obey when they come together to make a person.
14
This is called strong emergence, which we’ll discuss in the next chapter.
15
There’s no direct evidence that this is true for human beings, but it might
16
help you avoid the ramifications of having all of human behavior described
17
in principle by the known rules of particle physics, if those are the kinds of
18
ramifications you find unpleasant.
19
These non- hierarchical domains of applicability are not the situation we
20
most often encounter in discussions of emergence. It is far more common
21
to find situations like the leftmost one in the diagram, where one theory is
22
appropriate in a subset of the domain of another theory, perhaps in a nested
23
chain of multiple theories. Indeed, this is closest to the notion of a “hierar-
24
chy of sciences,” introduced by French philosopher Auguste Comte in the
25
nineteenth century. In this view, we start with physics at the most micro-
26
scopic and comprehensive level; out of that emerges chemistry, and then
27
biology, and then psychology, and finally sociology.
28
It is this hierarchical picture that leads people to talk about “levels”
29
when they discuss emergence. Lower levels are more microscopic, fine-
30
grained descriptions, while higher levels are more macroscopic and coarse-
31
grained. That can be convenient when it happens, but what matters is not
32
the existence of a hierarchy but the existence of different ways of talking
33
that describe the same underlying world, and are compatible with each
34
other when their domains of applicability overlap.
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02
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04
What Exists, and What Is Illusion?
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A
13
uguste Comte helped coin the term “sociology,” and put it at the
14
top of his pyramid of science; he thought of the study of societies
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The Big Picture Page 18