But why should we belong to one of these special systems? For the same reason that apples grow in northern Europe, where people drink cider, and grapes grow in the south, where people drink wine; or that I was born where people happen to speak my native language; or that the sun which warms us is at the right distance from us—not too close and not too far away. In all these cases, the “strange” coincidence arises from confusing the causal relations: it isn’t that apples grow where people drink cider, it is that people drink cider where apples grow. Put this way, there is no longer anything strange about it.
Similarly, in the boundless variety of the universe, it may happen that there are physical systems that interact with the rest of the world through those particular variables that define an initial low entropy. With regard to these systems, entropy is constantly increasing. There, and not elsewhere, there are the typical phenomena associated with the flowing of time: life is possible, together with evolution, thought, and our awareness of time passing. There, the apples grow that produce our cider: time. That sweet juice that contains all the ambrosia and all the gall of life.
INDEXICALITY
When we do science, we want to describe the world in the most objective way possible. We try to eliminate distortions and optical illusions deriving from our point of view. Science aspires to objectivity, to a shared point of view about which it is possible to be in agreement.
This is admirable, but we need to be wary about what we lose by ignoring the point of view from which we do the observing. In its anxious pursuit of objectivity, science must not forget that our experience of the world comes from within. Every glance that we cast toward the world is made from a particular perspective.
Taking this fact into account helps to clarify many things. It clarifies, for instance, the relation between what a geographical map tells us and what we actually see. In order to compare the map with what we see, it is necessary to add a crucial piece of information: we must identify on the map our exact location. The map does not know where we are, at least when it is not fixed in the place that it represents—like those maps in mountain villages showing routes that can be walked with a red dot next to which is written: “You Are Here.”
A strange phrase: how can a map know where we are? We might be looking at it from afar, through binoculars. Instead, it should say “I, a map, am here,” with an arrow next to the red dot. But there is also something curious about a text that refers to itself. What is it?
It is what philosophers call “indexicality”: the characteristic of certain words that have a different meaning every time they are used, a meaning determined by where, how, when, and by whom they are being spoken. Words such as “here,” “now,” “I,” “this,” “tonight” all assume a different meaning depending on who utters them and the circumstances in which they are uttered. “My name is Carlo Rovelli” is true if I say it, but untrue if someone else not also called Carlo Rovelli uses the same phrase. “Now it is September 12, 2016” is a phrase that’s true at the moment that I am writing this but will be false just a few hours later. These indexical phrases make explicit reference to the fact that a point of view exists, that a point of view is an ingredient in every description of the observable world that we make.
If we give a description of the world that ignores point of view, that is solely “from the outside”—of space, of time, of a subject—we may be able to say many things but we lose certain crucial aspects of the world. Because the world that we have been given is the world seen from within it, not from without.
Many things that we see in the world can be understood only if we take into account the role played by point of view. They remain unintelligible if we fail to do so. In every experience, we are situated within the world: within a mind, a brain, a position in space, a moment in time. Our being situated in the world is essential to understanding our experience of time. We must not, in short, confuse the temporal structures that belong to the world as “seen from the outside” with the aspects of the world that we observe and which depend on our being part of it, on our being situated within it.95
In order to use a geographical map, it is not enough to look at it from the outside: we must know where we are situated in relation to what it represents. In order to understand our experience of space, it is not enough to think of Newtonian space. We must remember that we see this space from inside it, that we are localized. In order to understand time, it is not enough to think of it from outside: it is necessary to understand that we, in every moment of our experience, are situated within time.
Universal man at the center of the cosmos, in Liber Divinorum Operum by Hildegard of Bingen (1164–70).
We observe the universe from within it, interacting with a minuscule portion of the innumerable variables of the cosmos. What we see is a blurred image. This blurring suggests that the dynamic of the universe with which we interact is governed by entropy, which measures the amount of blurring. It measures something that relates to us more than to the cosmos.
We are getting up dangerously close to ourselves. We can almost hear Tiresias, in Oedipus, saying: “Stop! Or you will find yourself” . . . Or Hildegard of Bingen, who in the twelfth century seeks the absolute and ends up by putting “universal man” at the center of the cosmos.
But before getting to this “us,” another chapter is required, to show how the growth in entropy—perhaps only an effect of perspective—might give rise to the entire, vast phenomenon of time.
Let me summarize the hard ground covered in the last two chapters, in the hope that I have not already lost all my readers. At the fundamental level, the world is a collection of events not ordered in time. These events manifest relations between physical variables that are, a priori, on the same level. Each part of the world interacts with a small part of all the variables, the value of which determines “the state of the world with regard to that particular subsystem.”
A small system S does not distinguish the details of the rest of the universe because it interacts only with a few among the variables of the rest of the universe. The entropy of the universe with respect to S counts the (micro)states of the universe undistinguishable by S. The universe appears in a high-entropy configuration with respect to S, because (by definition) there are more microstates in high-entropy configurations, therefore it is more likely to happen to be in one of these microstates.
As explained above, there is a flow associated with high-entropy configurations, and the parameter of this flow is thermal time. For a generic small system S, entropy remains generally high along the entire flow of thermal time, perhaps just fluctuating up and down, because, after all, we are dealing here with probabilities, not fixed rules.
But among the innumerable small systems S that exist in this extraordinarily vast universe where we happen to live, there will be a few special ones for which the fluctuations of the entropy happen to be such that at one of the two ends of the flow of thermal time entropy happens to be low. For these systems S, the fluctuation is not symmetricaclass="underline" entropy increases. This growth is what we experience as the flowing of time. What is special is not the state of the early universe: it is the small system S to which we belong.