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future have very different ontological statuses; one has happened, the other
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hasn’t.
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From the Laplacian point of view, where information is present in each
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moment and conserved through time, a memory isn’t some kind of direct
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access to events in the past. It must be a feature of the present state, since
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the present state is all we presently have. And yet there is an epistemic asym-
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metry, an imbalance of knowledge, between past and future. That asym-
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metry is a consequence of the low entropy of the early universe.
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Think of walking down the street and noticing a broken egg lying on the
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sidewalk. Ask yourself what the future of that egg might have in store, in
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comparison with its recent past. In the future, the egg might wash away in
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a storm, or a dog might come by and lap it up, or it might just fester for a
32
few more days. Many possibilities are open. In the past, however, the basic
33
picture is much more constrained: it seems exceedingly likely that the egg
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used to be unbroken, and was dropped or thrown to this location.
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We don’t actually have any direct access to the past of the egg, any more
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than we do its future. But we think we know more about where it came
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from than where it might be going. Ultimately, even if we don’t realize it,
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the source of our confidence is the fact that entropy was lower in the past.
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We are very used to unbroken eggs breaking; that’s the natural way of
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things. In principle, the set of things that could befall the egg in the future
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is precisely the same size as the set of ways it could have arrived in its present
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condition, as a consequence of conservation of information. But we use the
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Past Hypothesis to rule out most of those possibilities about the past.
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past histories
future histories
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compatible with
compatible with
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present information
present information
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low-entropy
actual past
beginning
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current state
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of the universe
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The Past Hypothesis of a low- entropy beginning breaks the symmetry between the past, 21
on the left, and future, on the right.
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The story of the egg is a paradigm for every kind of “memory” we might
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have. It’s not just literal memories in our brain; any records that we may
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have of past events, from photographs to history books, work on the same
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principle. All of these records, including the state of certain neuronal con-
27
nections in our brain that we classify as a memory, are features of the cur-
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rent state of the universe. The current state, by itself, constrains the past and
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future equally. But the current state plus the hypothesis of a low- entropy
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past gives us enormous leverage over the actual history of the universe. It’s
31
that leverage that lets us believe (often correctly) that our memories are reli-
32
able guides to what actually happened.
33
•
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Back in chapter 4 we highlighted how Laplace’s conservation of informa-
36N
tion undermines the central role that Aristotle placed on causality.
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Concepts like “cause” appear nowhere in Newton’s equations, nor in our
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more modern formulations of the laws of nature. But we can’t deny that the
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idea of one event being caused by another is very natural, and seemingly a
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good fit to how we experience the world. This apparent mismatch can be
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traced back to entropy and the arrow of time.
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It might seem strange to describe the world as operating according to
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unbreakable physical laws, and then turn around and deny causality a cen-
07
tral role. After all, if the laws of physics predict what will happen at the next
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moment from what the situation is now, doesn’t that count as “cause and
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effect”? And if we don’t think that every effect has a cause, aren’t we un-
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leashing chaos on the world, and saying that basically anything can happen?
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The strangeness evaporates once we appreciate the substantial difference
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between the kind of relationship of the past to the future that we get from
13
the laws of physics, and the kind we usually think of as cause and effect. The
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laws of physics take the form of rigid patterns: if the ball is at a certain po-
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sition and has a certain velocity at a certain time, the laws will tell you what
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the position and velocity will be a moment later, and what they were a mo-
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ment before.
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When we think about cause and effect, by contrast, we single out certain
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events as uniquely responsible for events that come afterward, as “making
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them happen.” That’s not quite how the laws of physics work; events simply
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are arranged in a certain order, with no special responsibility attributed to
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one over any of the others. We can’t pick out one moment, or a particular
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aspect of any one moment, and identify it as “the cause.” Different moments
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in time in the history of the universe follow each other, according to some
25
pattern, but no one moment causes any other.
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•
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Understanding this feature of how nature works has led some philosophers
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to advocate that we eliminate cause and effect entirely. As Bertrand Russell
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once memorably put it:
31
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The law of causality, I believe, like much that passes muster
33
among philosophers, is a relic of a bygone age, surviving, like the
34
monarchy, only because it is erroneously supposed to do no
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harm.
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It’s an understandable reaction, but perhaps a bit too extreme. After all,
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it would be hard to get through the day without appealing to causes at all.
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Certainly when we speak of the actions taken by human beings, we like to
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assign credit or blame to them; that won’t work if we can’t even say that
05
their actions caused any particular outcome. Causality provides a very use-
06
ful way of talking in our everyday lives.
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As with memory, the emergence of everyday causality from the underly-
08
ing rigid pattern of the laws of physics can be traced to the arrow of time.
09
Think of an example very much like that of the broken egg: a glass of wine
10
spilled on the carpet. There are many future and past histories of the atoms
11
that make up the wine and the glass that are compatible with what we can
12
see about its current state. Now let’s add a “mini Past Hypothesis”: that five
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minutes ago the glass of wine was sitting on the table, not moving.
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That hypothesis breaks the symmetry between past and future, and con-
15
strains the possible histories of the wineglass over the course of the last five
16
minutes. But notice a crucial feature about this constraint: we know that
17
the evolution of the glass of wine was not what it would have been had it
18
simply been left alone, undisturbed. In that case, with overwhelming prob-
19
ability, the glass would simply have stayed there. Glasses of wine don’t hop
20
right off the table and onto the floor of their own accord.
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Therefore, we can say with confidence that something must have dis-
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turbed the glass of wine— a stray elbow, or someone trying to fit a cheese
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plate onto an already- crowded table. With the information we have we
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can’t say precisely what it was, but we know that something intervened to
25
alter how the wineglass would have behaved had it been left untouched.
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That something, whatever it was, we justifiably label the “cause” of the glass
27
falling.
28
•
29
30
All of which sounds innocent enough, but what is really going on here?
31
There’s certainly a sense in which the current state of the wineglass can be
32
attributed to “the prior state of the entire universe, plus the laws of physics.”
33
Anything that happens can be explained in that way. But we also have ac-
34
cess to a more useful way of characterizing the situation, which relies cru-
35S
cially on the context in which we are speaking. In this case, it relies on the
36N
fact that we know something about wineglasses and their environments,
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M E M O R I E S A n d C Au S E S
and this particular situation specifically. Left to their own devices, glasses
01
of wine that are sitting peacefully on tables tend to continue doing so. If our
02
glass of wine had been floating in zero gravity on the International Space
03
Station, our analysis would have been quite different.
04
Understanding context becomes important because our invocation of
05
causality relies on comparing what actually happened to what could have 06
happened, in a different hypothetical world. Philosophers refer to this as
07
modal reasoning— thinking not only about what does happen but about
08
what could happen in possible worlds.
09
One master of modal reasoning was David Lewis, one of the most influ-
10
ential twentieth- century philosophers whom non- philosophers have never
11
heard of. Lewis suggested that we could make sense of statements like “A
12
causes B” by thinking of different possible worlds: in particular, worlds that
13
were essentially the same except for whether the event A actually occurred.
14
Then, if we see that B occurs in all the worlds where A occurred, and B does
15
not occur when A does not occur, it’s safe to say “A causes B.” If the wine-
16
glass falls and breaks when Sally swings her elbow around, but stays on the
17
table in a closely related world in which she does not, then Sally’s elbow
18
swinging caused the glass to fall.
19
There is one worry about this kind of account. Why can we say that A
20
causes B, rather than B causes A? Why don’t we think that the reason why
21
Sally swung her elbow is because the glass was going to be knocked off the
22
table?
23
The answer has to do with the leverage that different events have on one
24
another. When we’re thinking about memories or records, the idea is that
25
the later event (say, a photograph of you at your senior prom) absolutely
26
implies the existence of the former event (you at your senior prom). But not
27
vice versa; we could imagine you going to the prom and avoiding having
28
your photograph taken. Causes are the other way around. Given the wine-
29
glass on the ground, we can imagine things other than a stray elbow that
30
could have knocked it down, but given the location of the glass to start, the
31
swinging elbow absolutely implies that the glass will topple. When a later
32
event has great leverage over an earlier one, we call the latter a “record” of
33
the former; when the earlier event has great leverage over a later one, we call
34
the latter a “cause” of the former.
S35
“Memories” and “causes” aren’t pieces of our fundamental ontology
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describing our world that we discover through careful research. They are
02
concepts that we invent in order to provide useful descriptions of the mac-
03
roscopic world. The arrow of time plays a crucial role in how those contexts
04
relate to the underlying time- symmetric laws of physics. And the origin of
05
that arrow is that we know something specific and informative about the
06
pas
t (it had a low entropy), but there is no corresponding statement we can
07
make about the future. Our progress through time is pushed from behind,
08
not pulled from ahead.
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P A R t t W O
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Learning about the World
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n
13
ot much is known about Rev. Thomas Bayes, who lived during the
14
eighteenth century. Serving mostly as clergyman to his local par-
15
ish, he published two works in his lifetime. One defended New-
16
ton’s theory of calculus, back when it still needed defending, and the other
17
argued that God’s foremost aim is the happiness of his creatures.
18
In his later years, however, Bayes became interested in the theory of
19
probability. His notes on the subject were published posthumously, and
20
have subsequently become enormously influential— a Google search on the
21
word “Bayesian” returns more than 11 million hits. Among other people, he
22
inspired Pierre- Simon Laplace, who developed a more complete formula-
23
tion of the rules of probability. Bayes was an English Nonconformist Pres-
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byterian minister, and Laplace was a French atheist mathematician,
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providing evidence that intellectual fascination crosses many boundaries.
The Big Picture Page 11