The Movie Arrival and Remembering the Future

(Film Spoiler alert)

“Praised be to God Who made the Point to be outstretched within the Book of Origination, an Ornament through which is the Genesis of Creativity. From it He differentiated the knowledge of what hath been and what will come to pass. He made it to be a manifestation of the mysteries of what distinguished the [Arabic letter] “K” and the [Arabic letter] “N”! He ennobled it [the Point] …..”[1] -Baha’u’llah (provisional translation Stephen Lambden)

The idea’s of language presented in the recent film “Arrival” have been bouncing around my mind for a while. In the film, knowledge of the alien language so rewires the protagonist’s mind that she can ‘remember’ the future like one remembers the past. On first blush it would seem a ridiculous violation of all we know about physics to “remember the future”. But when I think about it more, I must confess it takes a bit more thought to understand why we don’t remember the future in the way we can remember the past. If we suspend for a while what we ‘think’ we know about causality, it is not immediately obvious why this is the case.

Arabic “K” and “N” Be!

I found when I started to pull on this thread, that it was connected to many other concepts about order, information, life, and attraction. To me these ideas are encapsulated by the above quote from Baha’u’llah. Here the Arabic letter “K” and “N” together make the word “Be” in Arabic. This is in reference to God’s creative command “Be!”. Judging by this statement of Baha’u’llah’s, the break in symmetry of past and future knowledge might hold the key to the primal creative act itself.

So if you are so are feeling like punishing your mind a little today. This is just the thing for it. I forewarn you this will be painful and is not a pleasurable read. In what follows I will try and take you down the logical path this thread takes me and see where we end up. I will hopefully avoid too many errors in logic on the way. While I draw heavily on the writings of the prophet founder of the Baha’i Faith, Baha’u’llah and his son and successor Abdu’l-Baha, these are just my flawed personal thoughts and don’t represent any official position.

If we reflect on the difference between future and past knowledge there does seem to exist some kind of symmetry. To begin, let’s consider a simple classical system of non interacting moving particles (i.e. ideal gas). They are well mixed (representing the highest state of entropy) and confined to a box. In this case, the past and future are actually equivalent. If the system is truly in a maximal entropic state, as defined by our ability to measure its state, the past and future states are indistinguishable.

particles in a box

The difference between past and future only emerges when the symmetry of the distribution is broken. For example if all the particles are forced to initially reside in one location in the available space, a point, then the distinction between past and future states becomes evident. This is because now one has a reference to distinguish future from past.

Still even in this system of non-interacting particles where the future and past can be distinguished, both are equally knowable. One can calculate and predict to arbitrary times in both the past and future states, based on knowledge of the existing state (all the particles positions and velocities). This is because the equations of motion are very simple, linear and can be integrated to any arbitrary time in the past or future.

When the possibility of interaction is introduced, this added complexity makes the system much more difficult to integrate. Depending on the nature of the allowable interactions, the system can at times become very sensitive to the initial conditions. This shortens the length of time in either temporal direction which one can accurately estimate. An example would be if one considers the trajectory of two particles with nearly identical velocities and positions. Under certain types of dynamics their paths will diverge wildly. This is one of the reasons its very hard to predict the weather. The time scale at which you can predict accurately is sometimes called the correlation time scale. At this point, however it appears to be symmetric with respect to future and past time. Both would seem to equally suffer from the inability to predict to far into the past or future.

So the question remains why is it in practice it still far easier to ‘predict’ the past than the future? What key thing is necessary to add to this system so that the past becomes easier to calculate than the future? It seems to me that this thing is related to measurement or memory. If you think about it for a bit, it becomes clear that there is essentially no difference between measurement and memory other than some implied notion of the time duration that recorded data is held.

Fast (white) and slow (black) particle in equilibrium (top). Maxwell’s Demon opens door to sort particles of different speed (bottom).

The connection of this difference between future and past knowledge to measurement is rather interesting for several reasons. First it is now understood that the Maxwell Demon paradox is resolved by referencing the process of measurement and data storage (Landauer’s erasure principal [2]). Briefly, the Maxwell Demon paradox was an attempt to expose a problem with the second law of thermodynamics. For those unfamiliar with the second law of thermodynamics, a very simple way to understand it is that it tells us, isolated systems tend towards mixing or disorder. The genesis of the second law was during the 19th Century, when scientists were trying to understand how to extract work from a heat engine. To model this they would invoke a thought experiment involving hot (fast) and cold (slow) particles in a box. It was understood that an engine could be driven (work extracted) using a differential between hot and cold ‘baths’ of gases. However the process of extracting work required ‘mixing’ of the hot and cold ‘baths’. After they were mixed, it was observed no more work could be extracted. The second law quantified this observation and stated that no work could be extracted from a system of fast (hot) and slow (cold) particles which were mixed (highest state of entropy).

However Maxwell proposed another thought experiment. In his system, he imagined the existence of a ‘demon’ who would sort the fast and slow particles via opening and closing a trap door. Once sorted a heat engine could be run, extracting work from the system in violation of the second law of thermodynamics. This troubled physicists for a long time, many tried to claim that energy would be consumed in opening and closing the trap door thus introducing new energy into the closed system. But it was shown that lossless (or mostly so) sorting was possible. Finally, Landauer resolved this apparent paradox by accounting for the data storage needs of the demon in performing the measurement necessary to sort the fast and slow particles. In this way the act of measurement necessarily raised the entropic state of the memory or recording device, thus preserving the second law.

This represents another way in which the recording of data is intimately related to entropy, the other being Shannon’s classical definition of information as entropy. We however will later discuss how Shannon’s interpretation requires some adjustment. A second interesting thing about the act of measurement is of course that this act famously ‘collapses’ the Quantum wave function. Often in describing the process of collapsing the wave function, the term ‘observation’ is used. However I think that this word has lead to some unfortunate confusion on the part of many who should know better. This is because for many the word ‘observation’ presumes a consciousness to receive the observation. Strictly speaking this is not true, only the act of measurement is necessary which doesn’t presuppose any sort of consciousness to receive the data. It does raise another interesting question, which inverts the relationship. It would seem that measurement and memory is a necessary but not sufficient condition for consciousness.

Returning to the original question, why are there not ‘memories’ of the future? Let’s first examine how common systems typically exhibit memory. One way is if the system has certain types of dynamics with dramatically different levels correlation times than the bulk of the system. These can act as memory or record keeping agents. They can encode initial conditions for a past state. So an example would be mud which records the foot print of a hiker or a fossil. The dynamics of mud or the fossil have extremely different time scales with in it. When the footprint or fossil are first imprinted, the time scale is very rapid and very sensitive to the state of the system. Later after the mud drys the time scale for any further changes could be millions of years. Thus they can be used to record the state of the hiker or fossilized animal long beyond the standard ability to estimate the ‘past’ based on the current state.

If it is due to the existence of dynamics of differing time scales, then what permits forward time able to encode data in a way that backward time cannot? I think this is related to the fact that we define forward time relative to the evolution direction of the symmetry or mixing of the system. So in the case where we set the particles to be initially confined to a point in space this defines time zero and future time is measured relative to the progress of mixing. This of course is a description of the progress of entropy or the rule of the second law of thermodynamics. Indeed the second law is commonly invoked as a candidate for the arrow of time. This is because progress of irreversible processes such as the shattering of a glass appear to proceed only in one direction. One doesn’t observe the shards of glass collecting themselves spontaneously to form a glass. Only if one changes the direction of time’s procession could this be observed.

These irreversible processes are tied up with the formation of memories for several reasons. First irreversible processes are usually highly sensitive to initial conditions. They encode to a high degree of precision the initial state which preceded the irreversible process. So for example if say a burglar enters a home and doesn’t break any thing, (irreversible process) reconstructing his path would be very challenging. If on the other hand a clumsy burglar who enters the home, breaks and knocks over many things, then reconstructing his motion would be far easier. So in the example of the foot print the mud must undergo a thermodynamically irreversible process to encode the data about the hiker. This by definition of the direction of time can only occur in forward time.

Three configurations at different Newtonian times t of a typical solution of the N-body problem. The time symmetry of the law is reflected in qualitative symmetry about the central region in which the distribution of the particles is maximally uniform. The direction of time indicated by the arrow of the time axis is purely conventional. Either choice of direction gives contraction with structure destruction through uniformity at minimal size followed by expansion and structure formation, mainly in the form of Kepler pairs (shown as loops). Internal observers must be on one side of the central region and would regard it as their past ( Figure from [3]).

So if irreversible processes are necessary for the formation of ‘memories’ are there ‘irreversible-like’ processes which flow against the direction of time? At first one might be inclined to say, ‘no,’ however there are several natural things which exhibit a similar type of behavior. One involves the dynamics of particles operating under a self-attractive force like gravity. Recent work by Barbour[3] and his colleagues seem to show that there is something unique about systems under the operation of an attractive force. In this paper they say, “self-gravitating systems exhibit “anti-thermodynamic” behavior that is not fully understood.” Thermodynamics as it was originally conceived didn’t take into account gravitation. Indeed the operation of self-attractive forces leads to symmetry breaking and clustering which is very different from how ideal gases behave. Further when they studied systems of particles under the influence of Newton’s gravitational law, they found an interesting thing. This type of system would evolve naturally into three distinct states. One diverging from a center, another converging towards a center and a singularity type where all the particles are coalesced to a point.

Artist’s conception of a protoplanetary disk

Let’s consider the example of the formation of our solar system. We have initially an amorphous rotating blob of gas and dust which over time coalesce into a Star and planets. Because this system is very sensitive to initial conditions, density perturbations will have a profound impact on the subsequent form. As a result one might consider them as ‘reverse’ memory functions. That is the imprints of the future solar system should be observed in the density perturbation of the dust cloud. Another system with a kind of ‘reverse’ time behavior are living things. So for example with the planting of a seed into soil a subsequent form is constructed pulling together the soil, water and air to generate a new structure. Both these cases are almost the exact opposite of what happens when a glass breaks.

These two candidates for a reverse memory function, the attractive force and life, might in fact be related in a way. There is this idea which Abdu’l-Baha expresses in many places, where he identifies “Love” with the power to bring forth life. “Love is the very cause of life”.We declare that love is the cause of the existence of all phenomena and that the absence of love is the cause of disintegration or nonexistence.”[4] He then goes on to make an interesting definitional shift and relates the physical “attractive force” to a primitive form of love.

On another level, there is a lot of recent theoretical work [5] which suggest that gravity might be due to quantum entanglement. However quantum entanglement is itself a manifestation of a correspondence or correlation between particles. In this case information about the state of the distant entangled partner particle is obtained from a measurement performed on the local particle. Thus allowing one to predict the state of the sister particle before it is measured (though no real ‘information’ is transmitted). This brings us back again to information and prediction.

Seeing life as a kind of manifestation of future memory might not be so ridiculous. I recently wrote a short article which suggests that that action of creating models to predict the future might be definitional for life. That this process of refining better and better models of the universe, which describe the actions of science, is really the apex of the evolutionary process. This activity can also be described using the ancient idea of a ‘Talisman’.

These thoughts were motivated by a new definition of information put forward by Adami [6]. He offers a correction to the standard Shannon definition of information which equates it with entropy. Adami claims that true ‘information’ should be defined as that data which enables you to make a prediction better than chance. He also links this information to evolution, since this kind of data becomes the valued commodity in the process of evolution. We could actually apply Adami’s predictive criteria to past knowledge as well. So ‘information’ is anything which tells you better than chance the state of something regardless of its temporal position. Part of the reason that future knowledge is more ‘valuable’ might be due to its involvement in the generation of ‘future’ order. This is implied by its connection to life. It is also more clearly seen when reflecting on the Maxwell Demon problem. In that system the ability of the Demon to sort the particles required some ability to ‘predict’ the trajectories of the fast and slow particles in order to sort them. However past knowledge also implies the existence of past order.

There is also this idea that, “the words of God” have a kind of creative and predictive power inherent in them. The creative aspect is expressed by Baha’u’llah in the following manner:

“(the) Word of God which is the Cause of the entire creation, while all else besides His Word are but the creatures and the effects thereof. Verily thy Lord is the Expounder, the All-Wise. Know thou, moreover, that the Word of God — exalted be His glory — is higher and far superior to that which the senses can perceive, for it is sanctified from any property or substance. It transcendeth the limitations of known elements and is exalted above all the essential and recognized substances. It became manifest without any syllable or sound and is none but the Command of God which pervadeth all created things. It hath never been withheld from the world of being.”[7]

Since we now see that there is an intimate link between predictive power and the rise of order, it is interesting to consider the effect of the words of God in this light. Might its creative and organizing power be due in part to its predictive power? Perhaps these words, the love and life it spawns, represent some kind of memories of the future.