(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, it requires a lot of concentration and thought. 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 via Landauer’s erasure principal [2]. (see my other article for a more in depth discussion of Maxwell’s Demon and its connection to information)

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.