Why Don’t We Remember the Future?

Or: Why Do We Perceive Time as Flowing in One Specific Direction? Whence the Directionality of Time?

What the Problem Is

Dear visitor,

In an earlier page, in which I introduced myself as the great magician Harry Foudini, I discussed the view of our world as a “frozen” four-dimensional world, a “block world” as others call it, in which time does not flow, but simply “is” — whatever that means. Time is just another spatial macro-dimension in that view, very similar to the other three spatial dimensions, barely distinguishable from them. However,... there is a problem.

The problem is that, as you and I and everybody knows, we have memories of the past; and no one — that I know of — claims to have memories of the future.

Now how do you explain that, Mr. Foudini?

See what the problem is? No? Sorry, my fault, I didn’t explain things well. OK, let me try again:

If the universe is a chunk, i.e., a block of four macro-dimensions, then time, which is one of those dimensions, shouldn’t have any preferred direction. Notice that the universe is time-wise asymmetric, because it was little and uniform shortly after the Big Bang, and it appears much larger and grainy (full of clusters of galaxies) now. But I’m not talking about the temporal asymmetry of the universe; I’m talking about its directionality: why does the universe contain some gray matter that has memories of its past, but not of its future? If I can’t explain that, then there is, after all, something inexplicable in the 4-d block world view of the universe, and so perhaps that view fails. Maybe the fact that brains remember the past and not the future points to an inherent directionality in the universe, which is evidence for the correctness of the conventional view that sees time as something very different from space, and us experiencing the world time-slice after time-slice. Thus, one might claim that the directionality of time is not a problem at all for the conventional view. Even though I argued in the above-mentioned page that the conventional is a flawed view (specifically here), still, that view has nothing to explain regarding the directionality of time, because it takes it as a given, as an “axiom”. It is I, Foudini, who has to answer what appears in my view as a conundrum.

But it’s not just me. Physicists, too, find the directionality of time puzzling, because they can’t see it anywhere in their formulas of physics. Although their formulas are time-symmetric, physicists can still explain the asymmetry of time as a result of the second law of thermodynamics. But the directionality? “Who ordered that?” Here is what Brian Greene says in The Fabric of the Cosmos:[1]

“Eggs fall, cracking and splattering, but we never see splattered eggs and eggshells gather together and coalesce into uncracked eggs. The compressed carbon dioxide gas in a bottle of Coke rushes onward when we twist off the cap, but we never find spread-out carbon dioxide gas gathering together and swooshing back into the bottle. [...] Perhaps the most pointed example of all is that our minds seem to have access to a collection of events that we call the past—our memories—but none of us seems able to remember the collection of events we call the future. [...] There seems to be a manifest orientation to how an enormous variety of things unfold in time.” (pp. 143–144.)

Now, the truth is Greene uses the above examples to question the origin of temporal asymmetry, but he is equally at a loss when it comes to the directionality of time. Unfortunately, he doesn’t make a clear distinction between the two notions. Others, however (mainly philosophers), do. Later in this page I give the analogy of a cone to illustrate this distinction: a cone is asymmetric, because it’s pointed on one end and blunt on the other; but it doesn’t have any predetermined direction along its central axis: we can trace the cone from tip to base, or from base to tip, whichever way we want. The universe seems to be both asymmetric and have a preferred directionality: events appear to come to us from the future and are left behind in the past, as if we are passengers in a train that travels along time from the past and into the future. Why?

In what follows, I explain where the directionality of time comes from. My explanation states that the directionality is not a physical but a cognitive phenomenon. (By that I don’t mean that cognition is not physical; only that the explanation cannot be understood by recourse to the laws of physics, because it rests outside the scope of physics, just as biology does, for example.) So let’s see the explanation in detail.

1. Why Is There Asymmetry in the Macro-world?

First, we must fully understand the explanation of a very common phenomenon of our everyday experience; or rather, of a large number of related phenomena. The phenomena I’m talking about are things like these:

  • You’ve seen a piece of glass fracturing into smaller pieces, but you never saw small fragments of glass joining back and making the original, whole piece.

  • You’ve seen improperly maintained houses acquiring cracks and losing pieces, but you never saw a house turning into a shining refurbished gem of the neighborhood by pure chance, without people actually working to refurbish it.

  • You’ve seen people growing old, getting dehydrated skin, wrinkles, and organs that malfunction. Eventually they die. But never did you see anyone turning into a youngster as the years go by, improving the functions of his or her body and its general condition.

  • You’ve seen smoke coming out of chimneys and cigarettes, dispersing in the air, but never any smoke condensing back into some location in space.


Figure 1.1: A derelict church at Methoni, Greece.
Churches cannot be pulled down in Greece, so the only way to have them demolished is by letting time run its excruciatingly slow course of destruction. This church has been deteriorating since the Medieval times.

In general, things seem to deteriorate if left to their own devices. Because of this deterioration, we observe an asymmetry between the “before” and the “after”. For example, the smoke was contained within a small volume before, and has expanded into a larger volume after. And because of this asymmetry of processes in the macro-world we can always tell which direction of time to label “past”, and which “future”.

But physicists have long observed that there is nothing in the laws of physics, as known since Galileo’s time, that points to some kind of asymmetry between the “before now” and the “after now”. Laws of physics are symmetric(*) with respect to time. For instance, let’s look at what Brian Greene writes in The Fabric of the Cosmos:[1]

“It turns out that the known and accepted laws of physics show no [temporal] asymmetry […]: each direction in time, forward and backward, is treated by the laws without distinction. And that’s the origin of a huge puzzle. Nothing in the equations of fundamental physics shows any sign of treating one direction in time differently from the other, and that is totally at odds with everything we experience.” (p. 13, emphasis in the original.)

Want to see temporal symmetry in action? Then watch the following figure (assume the moving circles are molecules of a substance jostling and bumping against some other, invisible molecules, thus performing random walks):

Figure 1.2: “Molecules” moving randomly

When we look at a microworld “movie” from up close (or a movie showing some object that moves according to Newton’s laws of motion), we can’t tell whether the movie is running forward or backward in time. For example, in the above figure, we don’t know whether I set the movie running forward, or in reverse. The symmetric treatment of the two temporal directions (past and future) in Newton’s laws of motion implies that whether time runs forward, or backwards, the laws will predict exactly the same outcome. But why are physicists puzzled?

I think what puzzles physicists like Greene is this: on one hand, they know that we, human beings, have some way of distinguishing between past and future by using our brains. On the other hand, they assume the brain is a physical device, abiding by the laws of physics. So they reason that there should be something in the laws of physics that hints at how a physical device, the brain, manages to distinguish between past and future. But there isn’t!(*) No physical law distinguishes between “before now” and “after now”, so that we could say, “Aha! Perhaps the human (or animal) brain uses this law, so that’s how it makes the distinction!” Isn’t this puzzling? Do we have to conclude that the brain is not strictly a physical device? Does the brain employ some non-physical, immaterial “magic” by which it perceives the asymmetry between past and future?

No, we don’t have to resort to such hocus-pocus. We should refrain from invoking a greater mystery (“immaterial powers”, “magic”) in order to answer a lesser one. The brain can indeed be considered a purely physical device, but what it manages to do is not necessarily describable by the discipline of physics; that is, physics is insufficient to describe the brain. What is required to explain the brain’s perceived properties of time is cognitive science; also, a tad of biology won’t hurt, to explain how brains evolved to acquire such abilities. That’s what this article is about.

But we need to consider things in order. First, we must understand why processes appear temporally asymmetric in the macro-world, because that’s where the long history of time starts.

1.1 The Second Law of Thermodynamics, and What Causes it

The law that causes the deterioration of structures in our familiar macro-world is known as the Second Law of Thermodynamics (2ndLoT) and, contrary to what its name suggests, it’s not a law of physics — strictly speaking — but a law of statistics and geometry. The 2ndLoT states, roughly, the following:

Physical systems tend to evolve toward states of greater disorder
(or of “higher entropy” in physics jargon).

The following figure is an example of the 2ndLoT in action. It shows a number of particles arranged in an orderly fashion, which start moving randomly in space (they perform “random walks”) as soon as you press on .

Figure 1.3: Particles dispersing in space, due to the 2ndLoT

Think of the particles as the pebbles and gravel that, once upon a time, made up the church of Fig. 1.1. As you can see, although they start at an initially ordered arrangement, they end up dispersed randomly and evenly in space, although there’s nothing in Fig. 1.3 that orders them to disperse away from the center. The particles merely move randomly in space, and will not return to the center “till cows come home”! (And, by the way, now you know why cows don’t ever come back home all by themselves.) The reason for this behavior will be explained in a minute. But first, please note the following.

There has been a lot of confusion about what the 2ndLoT really is, even among some scientists. Because it was first observed in the context of thermodynamics (whence its name), some professors of physics or chemistry might claim that what is depicted in Fig. 1.3 is not an illustration of the 2ndLoT. What they miss is that the notion “Second Law of Thermodynamics” is something deeper than what they observe in the context of thermodynamics, in which what disperses is energy (i.e., photons). But the deeper law concerns also the dispersal of mass, like the simulated particles of Fig. 1.3. I discuss this confusion in detail in this page. The law should be known by a more general name — perhaps something like “the Law of Dispersal” — but thermodynamics is its historic origin, so the name stuck with us.

Now, what causes the 2ndLoT? What kind of “force” is it that “orders” particles to disperse from their original location? It is actually quite easy to see why a particle, on average, will distance itself from its original location. (“On average” means that a single particle in a single observation might be seen to return to its original location at some time, but if we average out a large number of observations — of “walks” of the particle — then the average position of the particle will increase from the origin as time goes by.) Consider the following figure:

Figure 1.4: Geometric justification of the 2ndLoT

Suppose the particle shown with the purple dot started off at location O, is now at location p, and is “contemplating” to jump to a new location on the xy-plane at a distance r from its present one at p. Therefore, it will end up anywhere on a circle centered at p, having a radius of r (the full circle shown in the figure). Now, of all these “next locations” on that circle, which ones are closer to the origin O, and which ones are farther? The ones that are farther belong to the arc of the circle that is marked in bold, whereas the ones that are closer to O are on the thinner arc. Clearly, the bold arc is slightly longer than the thinner one. This means that particle p has a slightly greater probability to end up on the bold arc (farther with respect to the origin) than on the thinner arc (closer with respect to the origin). This is the reason why, according to probabilities and simple geometry, the particle will find itself at a greater distance from its original location, on average. A mathematical derivation of the speed by which the particle will distance itself from O is given in the previously referenced page (at this point), where it is proven that the speed is proportional to the square root of t, where t is the elapsed time. That’s exactly the formula computed by Einstein in his 1906 paper on Brownian motion.[2]

So we see that the asymmetry of processes in the macro-world is a consequence of the 2ndLoT, which in turn is a consequence of statistics (or probabilities) and simple geometry. Thus, if there are particles in a universe, and these particles extend along the dimension of time,(*) then there will be macroworld temporal asymmetry in that universe. This is a mathematical conclusion, as certain as the Pythagorean theorem, or the statement that 1 + 1 = 2.

Can mathematical results cause the emergence of structures in the macro-world, independently of the known laws of physics, as the latter appear in textbooks of physics? But of course! Consider the situation in the following figure:

Figure 1.5: Shape formed due to statistics only

Here, balls drop from the top of Fig. 1.5, and upon meeting one of the Λ-shaped obstacles they fall randomly either left or right, with equal probability. The result is the bell-shaped (Gaussian-like) curve formed at the bottom. This is a real-world object, and its shape cannot be predicted by the laws of physics, but only by the laws of probabilities. (Unless, of course, we extend the notion “laws of physics” to include all of known mathematics.)

Caveat emptor: the 2ndLoT, although it explains the macro-world temporal asymmetry, does not explain the overall temporal “asymmetry of the universe”, i.e., the fact that the universe started small at the Big Bang and continues growing in size for billions of years. The universal temporal asymmetry requires some other, extra-physical (cosmological) explanation. The fact that the asymmetry of the universe is unrelated to the 2ndLoT becomes clear if we consider a hypothetical situation in which the universe is in the process of a “Big Crunch”: in that case, the 2ndLoT would still hold (material structures would still disintegrate), but the 3D-space of the universe as a whole would be in a process of shrinkage, which would eventually force particles to follow not random, but biased walks, being continually restricted in 3D-space; but this would be an “add-on”, a property “on top of ” the 2ndLoT.

Let’s pause for a moment and ponder over what we have so far: we concluded that the macroworld ought to be asymmetric along time as long as there are particles in it — there is no escape from this conclusion. But an asymmetry is not the same as a direction. Okay, we could say we distinguish past from future because of their asymmetry, because they look different from each other, but why do we feel as if we move from the past toward the future? Couldn’t we feel we move from the future toward the past? Why do events seem to be coming from an unknown future and relegated into a known past? What causes the direction we feel is there? To see the difference between asymmetry and directionality, consider the shape of a cone (next figure):

Figure 1.6: A cone is an asymmetric object, but it lacks a built-in direction

The cone in Fig. 1.6 is asymmetric along a horizontally-running axis, since it’s thin at its tip, and thick at its base, so tip and base are different, we can tell them apart. But the cone has no preferred direction: we may scan it from tip to base, or from base to tip, or we might as well not scan it at all! What is it that causes us to feel that time is scanned in one particular direction throughout our lives? The answer has to do with what memories are, and how they are formed. This is discussed in the next section.


2. Why Do We Feel There Is a Direction in Time?

Hard questions can sometimes be answered by supposing that the opposite of what the question asks is true. In math, too, often a statement of the form “Prove that P is true” is tackled by saying: “Suppose P is false.” Then one proceeds to conclusions assuming the falsity of P, and reaches some logical contradiction, which leads the thinker to conclude that P must be true.


Something analogous will be attempted here. Normally, we perceive a direction in time that goes from order to disorder according to the 2ndLoT, and the question is: “Why do we feel there is that particular direction and not the opposite, or the absence of any direction?” Well, then suppose we don’t perceive the familiar direction in time. What are the consequences of that? That’s how our discussion will develop. But before we can think of abandoning the familiar direction of time, we better think first of a situation with the familiar direction (so we can later reverse it). An all-too-common incident from the world of nature between a gazelle (left) and a lion (right)will help us do just that.


Suppose that an unsuspecting gazelle is wandering in a region where a lion is resting, and at time t1 the gazelle comes and stops some 100 yards away from the lion (see diagram in Fig. 2.1), grazing the grass, completely unaware of the danger. At first, the lion is also unaware of the gazelle’s presence. However, the smell of the gazelle starts spreading in the environment (time t2), and at some point it reaches the sensitive nose of the lion (time t3). At that time the lion, alerted by the smell, starts moving stealthily toward the source of the smell (time t4). We will let nature decide what will happen from that time on, because what concerns us is what happened up to that time.

Figure 2.1: Successive stages in a natural drama

What was just described is the normal sequence of events, with time running in the forward direction. Notice that the gazelle is a source of information, because its odor particles disperse in the environment according to the 2ndLoT, inform the lion of the gazelle’s presence, and cause the subsequent event of the lion approaching the gazelle.

Now imagine that you see the same “movie”, but running backwards. What would you see?

At time t4 you’d see the lion backstepping and moving away from the gazelle. Once at a maximum distance at t3, the lion would stop and “rest” on the ground. At the same time, the odor particles that were in the air and which had been marching miraculously toward the gazelle from all directions, would abandon the vicinity of the lion, whose nose would stop detecting(*) anything interesting. The odor particles would all find their way to their common destination, the gazelle, as if guided by a magic hand. The gazelle would soon depart from the region backstepping, and that would be the end of the story. Or would it?

Something doesn’t pan out in this story. Hm... why were those smelly particles directed toward the gazelle? Who, or what force directed them there?

Naturally we, knowing that the previous story originated from the reversal of the forward-playing movie, realize that the reason the particles ended up at the gazelle is that the movie was played backwards, because “normally” the particles disperse. But now we are trying to see if the backward-running movie could ever be the normal one. We cannot rely on the naturalness of the forward-running movie because our working assumption is: “Suppose we don’t perceive the familiar direction in time; instead, suppose we perceive as normal the opposite direction (the one against the 2ndLoT).”

2.1 The Loss of Causality

So, in a world of time running backward we’d be confronted with the conundrum of the “odor-particle conspiracy”: particles would end up at a common destination, like pilgrims on their way to Mecca. However, real pilgrims have a purpose, plans, and volition that directs them wherever they must go; what do mere particles have that directs them to the same location? That would remain a mystery. But, alas, the world would be full of such mysteries:

  • Molecules of SiO2 (silicon dioxide, or silica) and various other chemicals would gather up from “the four corners of the world” to form first some tiny broken pieces of glass, which would join and keep forming ever larger pieces, until the pieces would, in one final act of pure magic, all gather up seamlessly together and form the single rectangular glass of a now-unbroken window.

  • The brown and yellow leaves of trees would miraculously sort themselves out, each according to its kind, and find their way up into the right kind of tree (never-ever ending up on the wrong type of tree), becoming greener after several days.

  • Speaking of leaves, photons would be emitted from their chloroplasts, and would all eventually be directed toward a nearby star, the Sun, as if photons “knew” which way to go, working against the randomness of the quantum world.

And these magical acts would be only the tip of an iceberg. For you would also see objects act as if they defeated gravity all the time, miraculously jumping with just the right momentum so as to end up at a higher altitude: those would be all the objects that simply fell down from a higher to a lower place in the normal, forward-running movie of the world. For instance, suppose that in “forward time” you hold a stone in your hand, and then you release it, letting it drop to the ground. In “backward time” this stone comes to your hand, but how does it manage to defy gravity? Because an astonishing number of quantum events on the ground conspire to give the stone just the right kind of kick so that it ends up in your palm. So we see that the magic wouldn’t concern just some gazelles and their odor particles; it would be part and parcel of our experience in the everyday world. Indeed, that kind of “magic” would be so prevalent that we wouldn’t be able to explain nature. We feel we have a natural explanation when we say that X happened because of Y. But In our back-running world, most of our “because” statements would be incomplete:

  • We say the plain flooded because there was a lot of rain and the nearby river overflowed. But in the back-running world, the plain was drained. Fine, now why did that happen? What forced copious quantities of water back into the river? Further, what caused the water of the river to form dropplets of rain that were kicked skywards forming clouds, “helped” throughout their entire skyward trek by infinitesimal conspiring kicks of air molecules? The “because” is lost; it’s that magical power at work again.

  • Or, consider a landslide in reverse: large quantities of soil would first become wet and muddy, then the mud would be withdrawn, without cause and explanation, collecting on the slope of a nearby hill, perhaps simultaneously revealing houses, livestock, and people — who would magically become alive. Why did that happen? Who knows.

  • Sunken ships would come out of the abyss of the ocean, pushed upward by the water molecules, currents, and small and large eddies in just the right ways, while the sea would become turbulent. The ship would emerge out of the water in the storm, acquiring sailors either through boats or directly from the water. Again, no explanation.

If you’d prefer to watch things instead of imagining about them, then take a look at the following entertaining video:

Figure 2.2: Which song is this?

In the first half of the above video, a guy does various things that are understood normally with time running forward, while he sings a known tune backwards. In the second half, the same video is played backwards. Most likely, the guy produced this video to show to his audience that he can sing backwards. But of particular interest to us are the various time-reversed events in the second half of the video. Watch them, and try to see how many of them start completely unpredictably, and proceed utterly mysteriously, ending up in structures or in situations for which there is no rationale, no way to claim that “X happened because of Y”.

Those examples show that the backward-running world would be inexplicable, which means, causality as we understand it would be gone. Instead, the mentioned “magic” would prevail.

Still, one might think that we might be able to form new laws of physics, based on our empirical observations of just what happens in that world. Unfortunately, even that would be impossible. The reason is that we have and use the known laws of physics because they explain events, and such explanations are based on causality. Think of the earlier example of the gazelle and the lion. In the familiar, forward-running movie, we can answer the question “Why did the lion start moving toward the gazelle?” (i.e., what caused it to behave like that?) by pointing to the odor-carrying particles and noticing that they have a single source: the gazelle. There is a single source (the gazelle), and potentially multiple receivers (all lions in the region, including the one of our example, other gazelles, flies, etc). The idea of “single source, multiple receivers” is what allows causality to work. However, in the backward-running movie, the opposite is true: there are multiple sources and a single receiver (the gazelle), or “sink” of information, as it is called. When there are multiple sources we can’t point to a single one of them and say: “The event happened because of that”, because there is no rational reason to single out one of the multiple sources, since they are indistinguishable for explanatory purposes. The case of “multiple sources, single receiver” is what kills causality, and won’t allow us to formulate any rational set of laws of physics.

Actually, in a world without causality it’s not just that there would be no rationally formulated laws of physics. Something much stronger would be true: there wouldn’t be any sentient beings to think about anything — let alone formulate laws. The following section explains why.

3. The Loss of Cognition

The act of thinking, which is probably the most essential task of human cognition, requires memory. It’s impossible to conceive of human-like thinking without memory, either short-term, or long-term. The reason is that a thought is based on some things already existent, and these existent things reside in memory. For example, consider the thought: “It’s cold today.” In entertaining this thought, you are able to think it’s cold because you have a memory of recent past temperatures and an expectation of what the temperature should be according to them; the word “today” shows you’re comparing the present temperature with the past, and the past exists in your memory. Or, consider the thought “I’m feeling fine”: the mere act of saying “I” implies access to an internal symbol in memory that stands for your self, which is connected to (associated with) a vast collection of past events and objects in your memory. The totality of those associations allow you to identify the symbol with what you perceive as your “self”.[3] Subtract memory, and you wouldn’t “know thyself”, quite literally.

But what is a memory?

We have memories of the past and not of the future — that’s the one fact we know for sure. But are we alone in the universe with this ability? I am not talking about aliens, but about things here-and-now, around us: are human minds — and perhaps even a few animal minds to a much reduced degree — the only entities that remember things past? Well, now we have computers, you might say, which also manage to remember, and even more accurately than biological minds. But consider the world as it was for example before World War II, with no computers. What about then?

But, a “memory” of past events exists in the universe even without the aid of minds. Consider planets like the Earth, Mars, Venus (terrestrial planets, as they are called): the matter out of which they are made, the zillions of heavy atoms that form their masses, are a sort of “memory” of a large number of supernova explosions that happened in our galaxy before the formation of our solar system, because atoms with nuclei heavier than carbon can only be formed in the depths of stars that eventually undergo supernova explosions. (As is well known, even the atoms that form the molecules of our bodies have been manufactured in the depths of cosmic explosions.) Supernovas came first, terrestrial-like matter came later, as a consequence; the latter is a memory (of sorts) of the former events.

Or, take the asteroid belt in our solar system; it can be seen as a “memory” of a past event: the event of the collision of two astronomical bodies in the early stages of our solar system. Take the existence of mammals: it’s a “memory” of another catastrophic event, the event of the asteroid (or meteor) that stroke the Earth 65 million years ago and wiped out the dinosaurs (along with a large number of other species), thus paving the way for mammals to “radiate” evolutionarily and become the new conquerors of the “large terrestrial animal” niche. (The memory I am talking about is not in the mammalian brain of course, but in the fact of the existence of the mammals themselves.) Similarly, the existence of marsupials in Australia is a “memory” of the break-off of Australia from Antarctica, around 90 million years ago (actually from the super-continent Gondwana), thus protecting the marsupials from the invasion of placental mammals. Contrariwise, the existence of placental mammals in South America (and the near-extinction of marsupials there) is a “memory” of the joining of the two Americas at the isthmus of Panama, some 3 million years ago. (And so is the opossum, the only marsupial in North America, which migrated from south to north when the Panama land bridge was formed.) Our world is full of memories!

3.1 What is a memory?

What is the fundamental property that could characterize something as a memory of past events? What is the quintessential aspect of events like those I mentioned above by which we can lump them all into the category of “memory”? Here is a proposal:

A “memory” is condensed information that summarizes a large number of other pieces of information, all of which contributed to the formation of the “memory”.

Perhaps the first example among those I gave earlier, i.e., the formation of terrestrial matter out of supernova explosions, is the best one that exemplifies the notion of condensation and the loss of information in order to form a memory. Picture this: as supernova explosions occur all over the galaxy, they put protons and neutrons together in their extremely energetic factories of material condensation, and make the heaviest nuclei of atoms that otherwise would not exist. But for those heavy atoms to appear, a vast number of prior events must have happened in the universe: the formation of subatomic particles after the Big Bang; their condensation into lumps of matter that formed the galaxies; the condensation of matter within each galaxy that formed its stars, and, consequently, the formation of some stars that are larger than nine solar masses, which become candidates for supernova explosions; the formation of atoms such as carbon, neon, oxygen, silicon, nickel, iron, and more, in the “nuclear furnaces” of such stars; the evolution and short life of such stars that burn their material furiously; and eventually their explosion, which spews the already formed heavy elements in space and manufactures even heavier ones. Further, the released atoms that form interstellar matter condense in some parts of the galaxy and form other systems of stars with planets, one of which was our solar system. The following is a schematic depiction of the idea that matter condenses to form planets.

Figure 3.1: Terrestrial-like planets are nothing but condensed interstellar matter.
(Note: this is an abstract drawing made for mnemonic purposes only — it does not depict the way planets are formed!)

But every form of memory is, in some sense, condensed information. It’s harder to see this in cases such as the existence of marsupials in Australia, or the near-extinction of them in South America, but if we think about it we’ll realize that such events are the culmination of a vast number of other events that had to have happened before. Evidently, information is lost during the formation of a memory. An elephant in Africa cannot serve as a direct and accurate remembrance of the asteroid hitting the Earth and killing the dinosaurs, in the sense that we cannot reconstruct the event of the asteroid’s collision merely by looking at an elephant; but, if we know a bit about the history of evolution on Earth, the elephant serves to vaguely remind us of that event, because without it most likely there wouldn’t be elephants; instead, some like-sized reptiles might still be around, occupying the elephant’s niche. (Of course, it takes a human mind to interpret the existence of elephants as a vague memory of the asteroid’s collision; but elephants exist even without human minds, so the “memory” is there, no matter whether we are present to recognize it as such or not.)

Coming now to human minds, the compression of information in them becomes much more evident. Every piece of generalized knowledge, such as “babies learn to walk at around one year of age”, or “smoking is a health hazard”, or “buildings deteriorate if not maintained”, and so on, are condensed pieces of information that have resulted out of a large number of observations that have been made either by other people, or by ourselves. Scientific laws, such as the law of gravity, and mathematical conclusions, such as the Pythagorean theorem, are condensed information that has been produced by thousands of generations of human minds, who observed, threw away the particulars and the irrelevant details, and kept such laws as the most convenient summaries of those observations.

In short, memories are condensed information. But... what causes the condensation of the information?

3.2 Who is the culprit of informational condensation?

Gravity is (primarily; plus the other attractive forces). And the way to understand the condensation caused by gravity in the universe is very simple, but I prefer to explain it by way of an analogy first. Imagine a creamy liquid, such as hot flavorful coffee, rotating fast in a mug, as in the figure below on the left. During this time the texture of the liquid is relatively uniform, forming mainly concentric circles of similar constitution. Now suppose we stop turning the stirrer that causes the rotation and let the liquid slow down. Soon, the uniformity of the texture on the surface will decrease, and structures such as swirls and eddies will form (figure on the right).

Figure 3.2: Left: the texture of initially fast rotating coffee in a mug is relatively uniform. Right: swirls and eddies start forming as the rotation weakens.

We can say that “informational entropy” was initially low, or equivalently, that the order was high. This is because the strong forces that fast rotation created “drowned” any other forces that might work against uniformity. As the rotational speed dropped, forces such as surface tension and others that cause bubbles to form conglomerations started taking the upper hand, causing the formation of eddies and the loss of uniformity (increase of informational entropy, decrease of order). But note that the eddies actually represent local spots where order increases. Thus, while the overall order in the mug decreases, there are some “hot spots” where order increases, at least temporarily.

Something analogous occurs in the universe, if we scan it along its temporal dimension in the direction from the Big Bang to our present and future. Originally, immediately after the Big Bang, the universe was in a supreme state of uniformity. But as time passed, gravity started making its effect felt, by forming galaxies (and clusters of galaxies), which are analogous to eddies on the surface of the coffee: galaxies are local “hot spots” where order and information increases, although overall in the universe order and information decreases, in accordance with the second law of thermodynamics (which applies to closed systems, such as the universe as a whole; galaxies, or any other sub-parts of the universe, are not closed systems).

So, galaxies are spots where information increases. Even within galaxies there are hotter spots: they’re the stars with their planetary systems, which are condensed interstellar matter, as I mentioned earlier. All this is the result of gravity. On at least one planet (ours) we become witnesses of an even hotter spot where information increases: it is the biological life, which keeps producing its own spots of complexity in the form of certain species of animals and plants.(*) The concentration of information due to biological evolution is the indirect product not only of gravity, but also of the other forces of nature that act in much shorter ranges (i.e., the electromagnetic and strong nuclear force), although the relationship is tenuous and hard to see. Finally, within biological life, brains have evolved to more and more complex kinds, with the human brain and mind being currently the most complex one of all. Thus, from an information-theoretic point of view, the average adult human mind is the hottest spot of condensed information that we know of in the universe. That’s why, when we talk about a memory, we usually associate the concept with the human mind; but any form of condensed information, even if not as condensed as in a human mind, constitutes a form of memory, which owes its existence ultimately to the matter-condensing ability of gravity and the rest of the forces of nature.

3.3 So why is the direction perceived as from past to future in a memory?

Because, by virtue of its constitution, a memory “reflects” (in an informationally lossy way) events in one direction along the temporal dimension (the one we call “past”), not events in the other direction (“future”). Future events do not have a causal connection with a memory, only past ones do. The “reflection” I am talking about is a result of the condensation (or concentration) of information, and it appears as such only when we trace time from past to future. If we trace time in the opposite direction (from future to past) then we do not observe informational condensation (locally, in a galaxy), but rather the opposite: we observe the spreading of information, which cannot be interpreted as memory (see also the next section). Because of the causal connection between past events and the configuration of information in a memory, memories can “look” toward the past, but they have no way of looking toward the future, being not causally connected with future events. As a result, memories perceive the particular directionality of time that we are all familiar with.

The conclusion is that if there are minds with memories in the world, then those minds are bound to impose a direction on time, due to the causal connection of events represented in their memories. Minds will call “past” the direction toward which the events in their memories are connected in causal chains.

Therefore, the directionality of time is a cognitive “add-on”, not a real feature of the physical universe. No wonder physicists search in vain to find it in the laws of physics.

Note that there is no circular reasoning in the above. I am not saying that causality causes memories (and human minds), and memories create in them the relation of causality (that would be circular). I am saying that gravity and the other forces at the same time both cause memories and arrange events asymmetrically in time, which allows our minds to perceive causality and impose on it a directionality — the same directionality we imposed on the temporal dimension of the universe later (when we learned about it).

3.4 Reverse Causality?

I wrote above that information condenses from past to future locally, e.g., in our galaxy. But what about the universe as a whole? If we look at the universe in its entirety, then we see that information condenses in the opposite direction: the one that goes from future to past. Can the universe at a given time be regarded as a memory that remembers events that belong to our future?

This is a tricky question. When we look at the universe in its entirety we cannot proceed from one time to the next in lockstep fashion. We could if its geometry were Euclidean; but it’s not, it is relativistic. So the “now” when we talk about the entire universe does not make sense in the familiar way. Still, some form of “now” can make sense if we allow it to propagate at the speed of light. If we do so, then we can conceive of times future, when large portions of the universe appear expanded, and of times past, when the same portions of the universe appear condensed. Then what? Is the early universe a “memory” of its later stages?

The trouble with this idea is that a memory is not merely information that used to be dispersed (as in the future universe) and ended up in a condensed state (as in the past universe). There is something more, already hinted at above: there must be a causal connection between the dispersed and the condensed state, i.e., some force must have acted to put the dispersed pieces together and form the condensed state. In the case of normal memories, that force is gravity (and the rest of the four natural forces). In the case of the universe as a whole, which we trace temporally in the direction from future to past, there is no such force, there is no reason that causes the parts of the universe to come together; the only “reason” they come together is that we decided, arbitrarily, to “play the movie backwards”, i.e., in the direction from future to past, and so of course we see parts coming together. The following animated figure will make this clear:

Figure 3.3: A “condensation movie” (or a dispersal movie but played backwards)

Why do the particles in the above figure travel (haphazardly) toward the center, until they all join at a perfectly square arrangement? Is there some force that causes them to act that way? No, there is no such force. The only reason they concentrate at the center is because I arranged the frames in reverse order, I forced them to do so; but of course mine is far from a natural force. (It is arbitrary; I could as well have arranged the frames in any order.) The lack of a natural force implies the lack of causality, hence the lack of the formation of a “memory”. In contrast, in the familiar past-to-future direction, the existence of the natural forces such as gravity imply the existence of causality, hence the formation of memories.

Similarly, when we consider the universe as a whole, we see that there is no force that causes parts of the universe to come together toward the event of the Big Bang. It is only our arbitrary decision to “play the movie backwards”, i.e., to scan the temporal dimension from future to past, which results in the universal condensed state. So I conclude that the early universe does not constitute a memory of its future stages.

3.5 And why are things like that in our universe?

Last, but not least, one question might be: “Why do we live in a universe in which gravity and the other forces cause memories and the asymmetry in time?”

My best answer to this question is that this is another case of the “anthropic principle”; specifically, the “weak anthropic principle” as I believe. Follow the link to learn more about the subject, if you are not already familiar with it.


Footnotes (clicking on the caret (^) brings back to the text):

(^) Perhaps the reader wonders what exactly is meant by the phrase “the laws of physics are time-symmetric”. Here is an explanation: Suppose you observe an object moving from point A to point B, at speed v = 1 m/s. The object reaches B after 1 s. Therefore, the distance between A and B is 1 m. The formula that relates space s, time t, and speed (or velocity) v, is known since Galileo’s time and we learn it in high school: s = v·t (substitute v = 1 m/s and t = 1 s to find s = 1 m). Now, what would happen if this event was run “backwards”? That is, what if time was running in the reverse direction, like an old-fashioned movie in which the direction of the film has been reversed, showing people walking backwards? Nothing essential would change in the physical event. We would see the object going from B to A, instead of from A to B. To describe this we would use the same formula s = v·t, and we would have the option of putting t = -1 s, and v = -1 m/s, (since v comes with an arbitrarily set positive direction, which in this example we took it to be from A to B), yielding again s = 1 m. No essential change was made. To put it otherwise: if we see a movie showing an object going from A to B, and another one showing the object going from B to A, we have no way of knowing which of the two movies was shot in forward-running time, and which in backward-running time.

(^) The truth is there are some physical systems that break the time symmetry, but they are rather exotic. In particular, there are some particles, such as K-mesons and B-mesons, that show the so-called weak nuclear force does not treat past and future fully symmetrically. However, Greene, along with other physicists, thinks that since these particles play essentially no role in determining the properties of everyday material objects, they are unlikely to be important in explaining the puzzle of the asymmetry of time (Greene, 2004,[1] p. 495).

(^) That is, a hidden, underlying assumption in the 2ndLoT is that there be particles: there must be material entities that we can point at and claim they are “the same” entities in space-time. For example, suppose that a photon was absorbed by an electron of an atom, thus causing the electron to jump to a higher energy level. If later the electron dropped to a lower energy level emitting a photon in the process, we may assume that this was “the same” photon, conceptually. (In this way photons can be thought to perform random walks within the molecules of a hot material.) Similarly, an atom is “the same” atom, even if in the course of time it exchanged all its protons, neutrons, electrons, and other elementary particles with different ones. In the macroworld scale, we say a human being is “the same” one, even though almost none of the cells of a 20 year old person is the same as those with which the person was born.

(^) Actually the lion wouldn’t be detecting anything at any time, since the odor particles would be leaving from its nose, and information in its brain would be “undone” (de-structured, so to speak). In general, what we call “sentient beings” wouldn’t be experiencing anything, thus there wouldn’t be sentient beings as we know them, but that’s a problem that is examined in more detail in the following sections.

(^) In what sense does biological evolution produce greater complexity? For example, birds and mammals, which appeared in the last 200 million years, are more complex than bacteria, which are here since at least 3.5 billion years ago, in the sense that such large animals include bacteria in their bodies, whereas bacteria do not include other animals in their protoplasm. Thus, 3 billion years ago biological complexity had not reached beyond bacteria, but now it includes bacteria and more complex organisms. The interested reader might want to take a look at this page, where I discuss this idea further.

(clicking on the reference number brings you back to the text where the reference is made):

Greene, Brian R. (2004). The fabric of the cosmos: space, time, and the texture of reality. New York: Knopf. (^)

Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. This posthumous publication of Einstein’s five papers on Brownian motion is translated by A. D. Cowper, and edited and annotated by R. Fürth. Dover Publications. (^)

Hoftstadter, Douglas R. (2006). I Am a Strange Loop. Basic Books. (^)


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Created: February 2008