Back in March, to commemorate Pi Day, I decided to treat you dear readers to a discussion on the number pi in Doctor Who, particularly focussing on Flatline. I know, I spoil you! But today, if you are reading on publication day, is Tau Day, so I’ve decided to talk some more about mathematics in Flatline. Enjoy!

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Are the Boneless proper aliens?

Over the course of Flatline, the term ‘aliens’ is used just three times: once by Clara and twice by Rigsy. None of these are direct references to the Boneless, so the Boneless are never actually identified as aliens during the episode. And rightly so, in my humble opinion. The Boneless did not arrive on Earth from outer space either before or during the story; they have always been here.

This isn’t unheard of within Doctor Who. For example, we have seen Earth-based monsters such as the Silurians and Sea Devils as well as the sea creature from Thin Ice. What the Boneless share with these monsters is that they all inhabit a previously undiscovered space. But rather than living underground or underwater, the Boneless instead live within the two-dimensional space of our everyday world. It seems pretty clear then that the Boneless are not aliens as they’re not extraterrestrials; they don’t come from outside planet Earth. They would instead fall under the more generic classifications of monster or creature.

And yet most, if not all, of the officially licensed reference material on Flatline would have you think otherwise! Doctor Who Magazine Issues 493 and 494, pages 14-30 of Doctor Who: The Complete History – Volume 79, and even pages 28, 29, 34 and 38 of the novelisation of Flatline belonging to the Pearson English Readers series. Even Jamie Mathieson calls them ‘aliens’ a couple of times on his own blog here and here.

But I think there are two likely reasons for this.

The first is that Mathieson originally intended the Boneless to be ‘true’ aliens. According to pages 17-19 of Doctor Who: The Complete History – Volume 79, Draft 1.0 of Flatlinehad the Boneless originate from a flat 2D spaceship that takes the form of a graffiti tag. This same tag is referenced multiple times throughout the draft script, appearing not just on the walls of the train tunnels but also on the bodies of their victims, like they are marking their territory.

However, you might also argue that the term spaceship here is actually a form of pun. This would mean that it doesn’t transport the Boneless across outer space in our three-dimensional universe, as is the conventional definition, but rather it transports them across the boundary between 2-D space and 3-D space. This detail was omitted in subsequent drafts of the script, but that doesn’t enable us to rule out the explanation entirely.

But the second reason is perhaps for the simpler one: that all Doctor Who monsters are referred to as aliens, even those that explicitly originate from Earth. The third Doctor and Liz Shaw repeatedly referring to the Silurians as aliens throughout Episodes Four to Seven of Doctor Who and The Silurians. The television script is written by Malcolm Hulke, who created the Silurians, and he is evidently aware that they are not extraterrestrials, given that he devised the story specifically as a response to the worry of script editor Terrance Dicks that the new earthbound format would mean writers could only tell two kinds of story: mad scientists or alien invasions.

In this sense, the word alien means something strange and unfamiliar to us humans, rather than something originating from beyond planet Earth. This can be illustrated by considering the Doctor. Whilst yes, they technically are an alien as they originate from another planet, they can sometimes be considered to be human-surrogate since they are humanoid in appearance and familiar with life on Earth. The Twelfth Doctor even asserts this himself in In The Forest of The Night.

DOCTOR: This is my world, too. I walk your earth. I breathe your air.

So whilst it is somewhat ambiguous whether the Boneless are extraterrestrial in origin, we can meaningfully consider the Boneless to be aliens due to their relative unfamiliarity with our own world. The Doctor treats them as such and, in a moment of pure inspiration, decides to use mathematics as a way of communicating with the Boneless. This shows him trying to think about their perspective by considering their relationship with dimensional space. It demonstrates a great level of empathy towards them, presuming they are an intelligent race who might not be as hostile as they first seem.

The Doctor often uses talking as a first line of defence, which is apt given that they travel around in a time and space machine that has telepathic circuits that can translate almost every language they encounter (although there are exceptions like the ancient scripture on Sanctuary Base Six in The Impossible Planet/The Satan Pit). Perhaps that’s why strangers are quick to trust this wandering traveller? Because the Doctor speaks their language.

But Flatline sees the TARDIS unable to translate on this occasion, with the Doctor concluding this must be “because their idea of language is just as bizarre as their idea of space.” He turns his efforts towards the most universal of languages: mathematics! The idea of mathematics as a universal language has been bandied about for a long time, supported by the likes of Galileo Galilei, Issac Newton, Richard Feynman and Ian Stewart over the centuries. But there isn’t a widely accepted definition.

One potential definition is that it means mathematics appears in everything, hence it must be universal. Mathematics can be found in all sorts of places, including the calculation of taxes (The Sun Makers), cracking secret codes (The Curse of Fenric), solving pub quiz riddles (42) and developing the world’s first computer program (Spyfall: Part Two). The Doctor even suggests that every subject is connected with every other in The Pilot, arguing that physics and poetry are the same thing “because of the rhymes.” Perhaps mathematics just rhymes with the universe?

Another take is that mathematics is the ‘only’ language that can truly describe the universe, ranging from the trajectories of the largest cosmological bodies to the slightest oscillation of quantum phenomena. This is the stance taken in Logopolis, a story that presents us with the notion that without mathematics there would be no universe for us to live in. Moreover, mathematics doesn’t just hold the universe together but rather mathematics IS the universe. This is captured in the alleged famous doctrine of Pythagoras that “All is number.” You remember Pythagoras (c.570 – c.490 BCE) from school, right? Weird fella, had his own cult. He’d certainly fit in among the other Logopolitans with his beard and toga.

The Doctor appears to reason that any form of intelligent life surely must have some form of mathematics and so decides to use the number pi to make contact with the Boneless.

The 1985 hard science fiction novel Contact, writtenby renowned scientist and cosmologist Carl Sagan, primarily deals with the theme of communication with extraterrestrials. The story is grounded in many real-life concepts from mathematics and the sciences. One of these is the notion of prime numbers. A prime number is any whole number with exactly two factors, with these factors being one and itself. I’ve already discussed them in more depth within a previous blog. They can be considered the building blocks of all numbers in mathematics, much like how the periodic table of elements can be considered the building blocks of all chemical compounds.

The scientists in Contact receive a pulse transmission that contains a sequence of prime numbers encoded in binary. One of the main characters comments that “prime numbers are very specific, very artificial… The prime numbers are to attract our attention.” This is an important observation since prime numbers have to be identified by checking they pass a primality test; they are difficult to predict and cannot be generated by a simple formula.  Prime numbers have actually helped inform the real-life Search for Extraterrestrial Intelligence, known as SETI. Prime numbers already have an established role in the real-life search for extraterrestrial intelligence so they seem a more obvious choice than the Doctor’s selection of pi.

(You might also be interested to know that one of the earliest known suggestions for searching for extraterrestrials came from Nikola Tesla in 1896, who suggested using a wireless transmitter to make contact with Mars. This actually informs some of the plot in Nikola Tesla’s Night of Terror.)

Another notable work of fiction centred around making contacting with extraterrestrials is Ted Chiang’s 1998 novella Story of Your Life, later adapted into the 2016 film Arrival. Both of these stories see a linguist (Louise Banks) and a physicist (Gary Donnelly; renamed Ian in the film adaptation) attempt to communicate with alien heptapods using their knowledge of language and science. Both versions of the story make reference to the Sapir-Whorf Hypothesis, a controversial theory in linguistics first conceived in the 1920s, which posits the notion of linguistic relativity, the idea that ‘language influences thought’. In other words, the boundaries of your imagination are constrained by the language that you understand. This idea does have its critics as well.

This goes against the idea that mathematics is a universal language since it would be constrained by cultural boundaries. Gary suggests that “their entire system of mathematics may be topsy-turvy compared to ours”. It shares similar ground with Contact, in which one character remarks that “we are trapped by our time and our culture and our biology, how limited we are, by definition, in imagining fundamentally different creatures or civilizations.” Louise and Gary eventually learn that the heptapods use language for purposes beyond pure communication, an idea which they had never considered initially, and this changes Louise’s perception of her own life as she learns that their language is not constrained by linear time.

Both Contact and Story of Your Life use methods of extraterrestrial communication that have strong foundations in the realms of mathematics, science and linguistics. This at least affirms the Doctor’s general approach to contacting the Boneless but not the specifics. The heptapods of Arrival use circular logograms to form their own language that transcends the barrier of linear time, and that’s arguably not dissimilar from the circular Gallifreyan symbols used by the Time Lords. Maybe that’s why the Doctor chose the circle constant pi as a basis for first contact with the Boneless?

But I still think this decision should be widely regarded as a bad move.

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“And incidentally, a Happy Tau Day to all of you at home!”