‘Ocarina of Time’ and the Bootstrap Paradox

Fans of Ocarina of Time might remember that fun questline where you have to travel to the Bottom of the Well to get the key item that lets you access the next temple. In order to drain the well and open the entrance, Link must first speak to the clearly irate windmill caretaker. In his rage, The Phonogram Man explains that seven years ago, some punk kid came into his windmill, played a mysterious song on his ocarina, and screwed everything up. He recites the song and Link learns the Song of Storms, one of the most iconic Zelda melodies.

Using the power of the Master Sword, Link travels back in time seven years and returns to the windmill as a child. He plays the song at the windmill, which drains the nearby well in the town square. The Phonogram Man learns the song which he then teaches to adult Link seven years in the future.

Notice anything strange about this sequence of events? Link learns the song as an adult from the windmill caretaker, travels back in time, and teaches it to the windmill caretaker as a child. Seven years later the caretaker teaches the song to adult Link. Link only knows about the song because of the windmill caretaker, and the windmill caretaker only knows the song because of Link. If so, then where did the song originally come from?

The Bootstrap Paradox

The above kind of situation is sometimes called a bootstrap paradox. A bootstrap paradox is a situation in which an object exists in a closed-loop and has no clear origin or explanation. The situation in Ocarina of Time with Link and the windmill caretaker is a bootstrap paradox as the Song of Storms seems to have no discernible origin. At each step in the time loop, the existence of the song is explained by learning it from someone else ad infinitum. The term “bootstrap paradox” is a reference to the phrase “pull yourself up by your bootstraps” in reference to some impossible or absurd task.

One way to think about the bootstrap paradox is in terms of cause and effect. In a bootstrap-situation, the cause of some effect is located in the future of the effect, and the effect itself is a cause whose effect is the initial cause. Bootstrap paradoxes seem paradoxical precisely because the relationship between cause and effect is inverted. In a bootstrap situation, the cause occurs temporally after and effect but is also explanatorily prior to that effect. The result is an infinite causal loop in which it seems like the bootstrapped thing has no ultimate cause or is self-caused.

Here is another example of a bootstrap paradox: A young man is walking down the road when an elderly woman gives him a pocket watch. Years later, the man creates a time machine and travels back in time. He gives the pocket watch to the woman’s younger self, who grows up and gives it to the young man. Again, this is a bootstrap paradox because the pocket watch has no clear origin. The man received it from the woman in the future, who received it from the boy in the past, who got it from the woman in the future…etc. The watch just seems to timelessly exist in a self-contained loop.

Philosophers sometimes refer to the bootstrap-situation as an ontological paradox because it relates to the lack of explanation for the existence of something. Bootstraps paradoxes can involve objects, like in the pocket watch example, or information, like the Song of Storms in the Ocarina of Time example. In either case, the main problem with bootstraps paradoxes is that some object or fact seems to have no ultimate explanation or explains its own existence.

Are Bootstrap Situations Possible?

Bootstrap paradoxes are a common plot device in fiction and have been used in a ton of media, such as The Terminator, Harry Potter, and Doctor Who. While they may be convenient in fiction, the question remains: are bootstrap situations possible in the real world?

Some might say that bootstrap paradoxes like the one in Ocarina of Time are logically impossible and contradictory. However, this criticism may not hit the mark. After all, the bare description of a bootstrap paradox does not seem inherently contradictory. Everything in the loop is perfectly self-consistent and has an explanation. The main difference is that the chain of causal influence seems to loop backward in time. Bootstrap situations seem paradoxical, but that is only because they present a situation that is counterintuitive to our everyday experience. Normally, we experience cause and effect flowing from past to the future, but does that necessarily mean it is impossible that the relationship could be inverted in certain circumstances?

Moreover, there are some scientific reasons to think that bootstraps situations might be possible. According to General Relativity, our best empirical theory on the nature of spacetime, closed time-like curves could exist. A closed timelike curve is a region of spacetime that twists back on itself such that an object traveling through it would intersect its own world line in the past. In other words, our best empirical science seems to suggest a mechanism by which some object or thing could bootstrap itself into existence. Theoretically, it should be possible for some object to reach back and interact with its past self, like a billiard ball that curves around in spacetime and strikes itself, initiating the original motion.

Does the Ocarina of Time Loop Work?

In the case of Ocarina of Time, the bootstrap paradox is a paradox of information. The information that is the song has no discernible origin and seems to just exist as a brute fact etched into the fabric of nature. But why should we think this is impossible? After all, from the standpoint of physics, information is just some particular configuration of matter. If we can accept, as physic implies, that regions of spacetime can exist in a timelike loop, then why couldn’t some piece of information meander its way around and effect itself in the past? The idea is counterintuitive no doubt, but just because it’s counterintuitive does not mean it’s impossible.

There is one possible solution to the bootstrap paradox in Ocarina of Time that does not involve a causal loop. In the sequel Majora’s Mask, Link travels to the parallel universe of Termina. In Termina, the Song of Storms was created by the composer brother Flat, whom Link meets in Ikana Canyon. The existence of Flat provides an explanation for the existence of the Song of Storms as he created it.

This does not solve the problem though. Introducing Flat into the equations makes things needlessly complicated for the sake of an explanation that is more in line with our common experiences. Besides, neither Link nor the windmill caretaker interacts with Termina’s Flat during the events of Ocarina of Time, so it is unclear how appealing to Flat in Termina is supposed to explain the existence of the song in Ocarina of Time’s universe.

A much more natural and simple explanation is that the Song of Storms in Ocarina of Time is a piece of information that is part of a consistent and closed causal loop. Information is a sequence of matter in spacetime and spacetime according to General Relativity can exist in a closed timelike curve. The single timeline explanation is much more elegant and logically consistent despite the fact that it is counterintuitive.

Bootstraps, Physics, and Video Games

Obviously, the bootstrap paradox in Zelda could just be a consequence of some divine magic and not really need a logical explanation. However, the fact that physics implies that some forms of time travel are possible means that discussions about the potential paradoxes of time travel are of interest to physicists and philosophers. Games like Ocarina of Time just happen to provide an excellent medium to investigate and think about the issue.

One thing I like about video games is when they use their setting, story, and plot elements to investigate unique and complex ideas. Whether it’s the narrative of parallel quantum universes in Bioshock Infinite to the questions raised about personal identity and memory in Soma, games that respect the intelligence of the audience and are not afraid to drop some mindblowing concepts are even more fun to play because you might learn something from them.