Dear visitor,
In an earlier page of mine, in which I introduced myself as the great magician Harry Foudini, I discussed the view of our world as a “frozen” 4-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, 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 this, then there is, after all, something inexplicable in the 4-d block worldview of the universe, and so perhaps this view fails. On the contrary, one might claim that the directionality of time is not a problem at all for the conventional view, in which we experience the world time-slice after time-slice. Even though I argued in that page that the conventional is a flawed view (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. In my page (the one I referenced above) I gave the analogy of a cone to clarify 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.
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?
No, a “memory” of things past 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 in their evolution 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!
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 these 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 forms its stars, and, consequently, the formation of some stars that are larger than nine solar masses, which will 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.
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 non-existence of them in South America, but if you think about it you’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 a human mind, the compression of information in it 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?
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 exerting the force 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).
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 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 at 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.
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.
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, this 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:
A “movie” showing particles moving randomly, and thus dispersing in space
Each of the purple particles in the figure above moves randomly to a neighboring location at the next time-step. There are eight neighboring locations for each particle: up, down, left, right, and diagonally; if the location is occupied by another particle, the particle moves to a free location; and if all eight locations are occupied, the particle simply doesn’t move at that time-step. Each particle chooses to move to one of its free neighboring locations with equal probability. By virtue of these very simple rules of motion (which are essentially telling each particle to perform a “random walk”), we observe that although the particles start off at a condensed state (at frame 0 — see the frame number at the upper-left corner of the figure), they end up dispersed (at frame 30), and they would continue their dispersal if the frames could be generated without end. There is nothing that tells the particles “You have to disperse from each other!” Their dispersal in space is a simple consequence of elementary mathematics, as I explain in this page, and it exemplifies what is known as the informational version of the second law of thermodynamics.
Now, pieces of the universe do not disperse due to random walks in space, of course. In this case, space itself expands (in the direction from past to future), and causes the universal parts to increase their distance from each other. But within a single galaxy, for example, which is immune to universal space expansion, we can say that the second law of thermodynamics is at work, and so activity in the galaxy gradually dwindles, if observed over many billions of years. Information disperses in a galaxy, so fewer stars are created over time, more stars die and some of them explode as supernovas, more black holes are formed, and so on. Therefore, seen in the opposite temporal direction (from future to past), information in a galaxy appears to be condensing. Is a “memory” formed in that direction? Let us set up the frames of the previous figure in reverse order, play the movie backwards, and think about whether a memory is formed:
The same “movie”, but played backwards
Why do the particles in the above figure seem to 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 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.
What we observed about a galaxy, holds for the universe in its entirety as well. There is no force that causes the universal parts to come together toward the Big Bang event if we “play the movie backwards”. It is only our arbitrary decision to scan the temporal dimension along the particular direction from future to past that results in the universal condensed state. So I conclude that the early universe does not constitute a memory of its future stages.
 |
By the way, the same reasoning explains why we perceive causality in one direction and not in the other, i.e., why causality has the specific directionality that we ascribe to it. When an apple falls toward the surface of the earth (see figure), we say “gravity caused the fall of the apple”. That’s our simple, shorthand explanation for describing the fact that the earth and the apple were at a given distance before, and are at a shorter distance after the event of the fall (and thus occupy slightly different locations in space). The “before” and “after” events form an asymmetric overall picture, which we understand by constructing the relation “causes”. Thus, causality is asymmetric. Its directionality is a feature imposed on it by our memories, which are able to recall sequences of causally connected events. |
Note, 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 memories to perceive causality and impose on it a directionality, the same directionality they impose on the temporal dimension of the universe.
Footnotes (clicking on the caret (^) brings back to the text):
(^) 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.
References (clicking on the reference number brings you back to the text where the reference is made):
[1] Greene, Brian R. (2004). The fabric of the cosmos: space, time, and the texture of reality. New York: Knopf.
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Created: February 2008