The Big Picture
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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
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few more days. Many possibilities are open. In the past, however, the basic
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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-
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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
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that leverage that lets us believe (often correctly) that our memories are reli-
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able guides to what actually happened.
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Back in chapter 4 we highlighted how Laplace’s conservation of informa-
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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-
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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
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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
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pattern, but no one moment causes any other.
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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:
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The law of causality, I believe, like much that passes muster
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among philosophers, is a relic of a bygone age, surviving, like the
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monarchy, only because it is erroneously supposed to do no
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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
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their actions caused any particular outcome. Causality provides a very use-
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ful way of talking in our everyday lives.
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As with memory, the emergence of everyday causality from the underly-
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ing rigid pattern of the laws of physics can be traced to the arrow of time.
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Think of an example very much like that of the broken egg: a glass of wine
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spilled on the carpet. There are many future and past histories of the atoms
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that make up the wine and the glass that are compatible with what we can
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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-
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strains the possible histories of the wineglass over the course of the last five
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minutes. But notice a crucial feature about this constraint: we know that
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the evolution of the glass of wine was not what it would have been had it
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simply been left alone, undisturbed. In that case, with overwhelming prob-
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ability, the glass would simply have stayed there. Glasses of wine don’t hop
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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
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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
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falling.
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All of which sounds innocent enough, but what is really going on here?
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There’s certainly a sense in which the current state of the wineglass can be
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attributed to “the prior state of the entire universe, plus the laws of physics.”
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Anything that happens can be explained in that way. But we also have ac-
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cess to a more useful way of characterizing the situation, which relies cru-
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cially on the context in which we are speaking. In this case, it relies on the
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fact that we know something about wineglasses and their environments,
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and this particular situation specifically. Left to their own devices, glasses
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of wine that are sitting peacefully on tables tend to continue doing so. If our
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glass of wine had been floating in zero gravity on the International Space
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Station, our analysis would have been quite different.
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Understanding context becomes important because our invocation of
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causality relies on comparing what actually happened to what could have 06
happened, in a different hypothetical world. Philosophers refer to this as
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modal reasoning— thinking not only about what does happen but about
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what could happen in possible worlds.
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One master of modal reasoning was David Lewis, one of the most influ-
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ential twentieth- century philosophers whom non- philosophers have never
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heard of. Lewis suggested that we could make sense of statements like “A
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causes B” by thinking of different possible worlds: in particular, worlds that
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were essentially the same except for whether the event A actually occurred.
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Then, if we see that B occurs in all the worlds where A occurred, and B does
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not occur when A does not occur, it’s safe to say “A causes B.” If the wine-
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glass falls and breaks when Sally swings her elbow around, but stays on the
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table in a closely related world in which she does not, then Sally’s elbow
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swinging caused the glass to fall.
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There is one worry about this kind of account. Why can we say that A
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causes B, rather than B causes A? Why don’t we think that the reason why
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Sally swung her elbow is because the glass was going to be knocked off the
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table?
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The answer has to do with the leverage that different events have on one
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another. When we’re thinking about memories or records, the idea is that
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the later event (say, a photograph of you at your senior prom) absolutely
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implies the existence of the former event (you at your senior prom). But not
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vice versa; we could imagine you going to the prom and avoiding having
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your photograph taken. Causes are the other way around. Given the wine-
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glass on the ground, we can imagine things other than a stray elbow that
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could have knocked it down, but given the location of the glass to start, the
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swinging elbow absolutely implies that the glass will topple. When a later
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event has great leverage over an earlier one, we call the latter a “record” of
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the former; when the earlier event has great leverage over a later one, we call
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the latter a “cause” of the former.
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“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
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concepts that we invent in order to provide useful descriptions of the mac-
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roscopic world. The arrow of time plays a crucial role in how those contexts
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relate to the underlying time- symmetric laws of physics. And the origin of
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that arrow is that we know something specific and informative about the
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t (it had a low entropy), but there is no corresponding statement we can
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make about the future. Our progress through time is pushed from behind,
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not pulled from ahead.
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Learning about the World
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n
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ot much is known about Rev. Thomas Bayes, who lived during the
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eighteenth century. Serving mostly as clergyman to his local par-
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ish, he published two works in his lifetime. One defended New-
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ton’s theory of calculus, back when it still needed defending, and the other
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argued that God’s foremost aim is the happiness of his creatures.
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In his later years, however, Bayes became interested in the theory of
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probability. His notes on the subject were published posthumously, and
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have subsequently become enormously influential— a Google search on the
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word “Bayesian” returns more than 11 million hits. Among other people, he
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inspired Pierre- Simon Laplace, who developed a more complete formula-
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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.