The 2020 Black Archive Reviews – Part One (January to June)

This review block covers the set of Black Archives released in the first half of 2020. The stories covered by this set are Doctor Who and The Silurians, The Underwater Menace, Vengeance on Varos, The Rings of Akhaten, The Robots of Death and The Pandorica Opens/The Big Bang. At the end of the reviews, I pick out my personal favourite and explain why.

You can buy all of these from Obverse Books here.

The Black Archive #39: The Silurians by Robert Smith?

Key Themes: Technology, the 1970s energy crisis, the military, land rights, animal testing, science and ethics, and whether the Silurian plague could’ve killed us all.

Mathematicians typically review each other’s work. Whether it’s checking calculations or peer reviewing a new research paper, mathematics is very much a subject about teamwork and collaboration. Perhaps this goes against the prevailing stereotype that mathematicians are reclusive souls who solve hard problems on their lonesome, but the more common reality is that you need to work with others to ensure your arguments are communicated clearly and precisely; that we’re all singing from the same hymn sheet so to speak. This is the norm when it comes to mathematics, but it’s pretty rare when it comes to Doctor Who. And since Black Archive scribe Robert Smith? and myself are both mathematicians, this is one of those rare occasions.

Smith?’s specialism is mathematical biology, so it’s no surprise he’s opted to write about the second outing for Jon Pertwee’s incarnation. This entry by Smith? specialising in science and the spread of plague contains seven succinct chapters on seven separate themes over a seven-episode serial called Doctor Who and The Silurians, first broadcast in the year 1970, which makes it the most sibilant book in the series so far. Not content with last month’s controversial decision to omit Utopia (2007) from the analysis of the Series 3 finale, this Black Archive pretends that the initial three words of this serial’s title were never there, as the book predominantly refers to the story as “The Silurians”. I can however understand the latter decision a lot more given it was an in-house production error that led to this unusual title occurring.

The themes covered are diverse, ranging from the links to the 1970s energy crisis, morality in science, and the role of technology in the story. I strongly felt that the book developed in strength as each chapter went by, which gives it a nice crescendo in quality. The particular highlights were when Smith? enters his specialisms, providing unique and informed insights into questions on whether Doctor Who is a science show and whether the Silurian plague could have actually killed us all, a topic that has become surprisingly prescient with the current coronavirus outbreak happening right now. The book is also beautifully and thoroughly referenced, as is evident by the surprisingly lengthy bibliography on display.

However, by structuring the book around some rather broad questions, the analysis does sometimes lead to some rather general conclusions, such as those in the book’s initial two chapters saying that technology both can and can’t solve all our problems and that a Doctor Who story should be as long as it needs to be. The discussions had about these topics were certainly good reads, and I was particularly intrigued by Smith?’s passionate defence about the story’s exceptional length. But I really did feel these could have led to more interesting results. For example, I would have suggested that the book’s second chapter should really have been framed as “Does The Silurians really need to be seven episodes long?” instead. What I’m trying to say here is, I think there should have been another way.

In a fair number of my reviews I have neglected to mention the cover art and icon design by both Cody Schell and Blair Bidmead respectively. I’m actually quite the fan of this entry’s cover, which features the cave drawings of a Silurian with woodland creatures as it’s icon, brilliantly captured by Bidmead, as seen in the serial’s first episode. The choice by Schell to then overlap parts of the three creatures using white, brown and green outlines is inspired. It quite neatly represents the overlap of science and nature presented in the story here as well as the harmonious coexistence between the Silurians and the animals billions of years ago.

Concluding Thoughts

Smith?’s Black Archive entry breaks exciting new ground by looking at the themes of science and ethics in The Silurians, bringing unique and specialist insight on this particular serial. The discussions on morality, animal rights and pandemic plagues are well worth your time here and shows Smith?’s pedigree as a long-time critic of the show. I also do hope this encourages more scientific takes on the show in future entries. After all, “science leads” according to Kate Stewart, Head of Scientific Research at UNIT. She learnt that from her father, but did her father learn it from reflecting on this story’s events? Perhaps, but who knows?

 

The Black Archive #40: The Underwater Menace by James Cooray Smith

Key Themes: How does surviving material influence fan perception, should we even be allowed to take this story seriously, and is traditional fan wisdom bollocks?

There’s no doubt about it – The Underwater Menace (1967) is one of the strangest televised adventures in the entirety of Doctor Who’s 50+ year history. Its setting is mythical, taking place in the lost underwater city of Atlantis. Its science is ropey, with absurd ideas of draining the ocean into the Earth’s core. And its villain is utterly preposterous, a near-contemporary scientist, whom the Doctor is already aware of by reputation I might add, whose ideas of ‘supreme power’ will actually leave no-one in Atlantis alive to see the repercussions of his actions. But it does score highly on originality.

With all that in mind, why should a range like The Black Archive, which delivers thoughtful and serious critiques of any and all Doctor Who stories, dare to take it seriously? The idea that recurring contributor (and former editor of the range) James Cooray Smith would decide to hang his hat entirely around this premise initially seems a rather silly one, yet it actually achieves remarkable results. Much like his last contribution to the range, which examined The Ultimate Foe (1986), Cooray Smith delivers a sublime blend of analysis, document-based research and behind-the-scenes history, with its 110-or-so pages just flying by.

Given the frivolous nature of the story’s ideas and plotting, it is perhaps unsurprising that each of the book’s nine chapters are fairly short ones (about ten pages each) but what brings it all together is the use of a few key over-arching themes. Namely, these are how does missing material affect fan reception, taking full advantage of the rediscovery of Episode 2 back in 2011, and how collective fan wisdom can at times be sorely misplaced, which leads not only to some superlative myth-busting but also a few finger wags at the fandom-at-large. This even extends to the author himself who slaps himself on the wrist in a delightfully cheeky footnote.

The questions covered are an eclectic mix that honestly speak for themselves. Here are just some of the questions that this book presents well-informed and dutifully researched answers for your reading pleasure:

  • Why does fandom universally hate a story they’ve probably never seen?
  • What exactly happened at the BFI in 2011 when Episode 2 showed up?
  • Why was this story filmed despite being formerly abandoned?
  • Why do fans keep writing badly accented versions of the episode’s third cliffhanger?
  • Whatever happened to the Doctor’s hat in this story?
  • How does this story ultimately shape Troughton’s portrayal of the Doctor?

For me, there were two undisputed highlights during this read and both are towards the very end of the book. First, there’s a substantial appendix based on the Doctor’s note to Professor Zaroff signed “Dr. W”, which looks at whether the main character of the show is called ‘Doctor Who’ and whether the character is referred to as ‘Doctor Who’ both within and outside the fiction itself. The appendix doesn’t so much as cover but utterly annihilate the discourse surrounding these related questions, and with considerable aplomb too. Although, I must say the complete omission of the opening scene from World Enough of Time (2017) is a little baffling. I also sincerely hope his ‘Dame Shirley Bassey’ argument just catches on in general.

The second highlight was the book’s final chapter looking at the life, work and collaborators of its author, Geoffrey Orme. Little is known about the life of Orme as he was never interviewed about his work, not even by a single Doctor Who fan, and he died in 1978. The search into the archives detailed in this chapter in the hope to the reveal hidden depths about the story of The Underwater Menace is commendable and reveals subtle and astute observations. This chapter is the literary equivalent of an astounding new Toby Hadoke documentary, such as those which have looked into the previously shrouded lives of Peter R. Newman (Writer of The Sensorites (1964)) and Lennie Mayne (Director of four 70s Who serials). It is truly an excellent capstone to the book itself.

Concluding Thoughts

Despite perhaps being as utterly mad as Professor Zaroff’s plan, this book manages to be a resounding success. This entry takes full advantage of the story’s poor fan reception and partially missing status as an opportunity to re-examine the serial with fresh eyes. Covering a diverse range of topics surrounding its troubled production, obscure cult status, and its mysteriously disappearing hat, The Underwater Menace comes highly recommended to those who want to discover whether it has hidden depths. But if it should happen that fan historiography isn’t to your literary tastes then don’t worry, because there’s plenty more Fish People in the sea.

 

The Black Archive #41: Vengeance on Varos by Jonathan Dennis

Key Themes: Orwellian literary influences, capitalist realism, depictions of violence in 1980s television and “video nasties”.

There’s a certain footnote in this book that I think quite neatly encapsulates the experience of reading of this Black Archive. On page 95, there’s a lone sentence which clarifies that 1982’s The Running Man takes place in the fictional totalitarian United States of America in the year 2019 and not the actual totalitarian United States of America in the year 2019. Dennis is here to talk to you about 1985’s Vengeance on Varos, and he ain’t pulling no punches.

The contents page of this entry looks exactly like what you’d expect if you were to identify the central ideas of Philip Martin’s first Who serial: Orwellian literature and dystopias, the portrayal of rampant capitalism, sadistic violence and “video nasties”. A light introduction on the garish nature of the Sixth Doctor’s coat gets things underway and neatly sets the style and tone for the analysis that follows. I can’t quite figure out how but this book manages to just feel so eighties, which is odd considering I don’t actually remember them – I was born in the decade that came after!

The first main chapter strikes while the iron is hot, swiftly drawing allusions between the political system found on Varos and the political mess we in the UK and those in the USA currently find themselves in. The second covers neoliberalism and Doctor Who’s unfolding relationship with capitalism as both theme and setting, drawing natural comparisons to both Oxygen (2017) and Kerblam! (2018). In my review of the Black Archive on the latter story I suggested that those interested in the story’s politics would be disappointed but now it seems there’s a book for those people as well.

The next chapter was my personal favourite as it helped contextualise the social and political zeitgeist around television violence in the 1980s and the relatively short-lived anxieties surrounding “video nasties”, which are excessively violent films that eluded classification from the BBFC due to a loophole and these caught the attention of a certain Mary Whitehouse. The chapter’s title “They also affects dogs” initially left me mystified until I subsequently learnt within the prose that this was a quote from a Tory backbencher who on national TV claimed there was research that shows “video nasties” not only caused children to become more violent, but dogs as well. This certainly made me feel that we live in a more enlightened age, albeit for a few precious seconds. A short discussion on how television is nothing without somebody to observe it brings the book to a sublime conclusion.

Concluding Thoughts

Other entries in the range do all the hard work of researching their themes and topics in depth, before leaving the reader to come to their own conclusions. You won’t get that with this one. Dennis is pretty blunt when it comes to his perspective on politics, economics and the media but he puts in such clear crystal prose that you are left in no doubt why he thinks that way and he’ll leave you wanting more. It’s a thoroughly recommended read and it confirms in my eyes that the somewhat underappreciated Sixth Doctor is getting some of the strongest critique in the range to-date.

 

The Black Archive #42: The Rings of Akhaten by William Shaw

Key Themes: The Doctor as New Atheist, feminist and post-colonial theory, the episode’s critical reception with fans, and the story’s engagement with ‘anniversary anxiety’.

I’ve personally always been a fan of The Rings of Akhaten; it’s far from my favourite Doctor Who story but I wouldn’t hesitate in telling you that it’s a pretty good one, with many charming aspects, and probably the strongest episode in an otherwise maligned series. To see it land in the bottom ten of DWM’s story poll in 2014 was somewhat baffling, and so I did hope that this episode would be critically reappraised one day soon. Not only then am I delighted that William Shaw has stood up to bat for The Rings of Akhaten as part of the Black Archive’s first foray into Series 7, but I’m also terribly surprised that someone else who rather likes the story has such radically different reasons for doing so. It seems that Doctor Who is once again a broader church than I had previously conceived.

Shaw frames the episode as a critical reflection of the show during its fiftieth anniversary year, highlighting numerous aspects that have previously been underappreciated, looking back at its flaws and shortcomings, whilst also looking ahead towards its future of as-yet unrealised potential. I could have easily predicted that such a book would examine the episode’s religious and patriarchal overtones as well as the poor critical reception among vocal fans; I just didn’t expect New Atheism.

Chapter 1 provides a fresh, exciting and radical viewpoint on the episode never-before-seen, arguing the episode is a subtle critique of the New Atheist movement. Those who remain unconvinced by the inspired introductory section linking Dawkins to post-2005 Who will have to be very patient. An early subsection entitled ‘Doctor Who and the New Atheist Movement’ runs for around seven pages without a single actual mention of Doctor Who itself. But I feel my patience was rewarded, Shaw’s introduction of several key texts manages to bridge the gaps between the episode and his reading, shedding light of the show’s broader relationship with the movement. It is by far the book’s most substantial chapter that could have been hastened by getting to its Doctor Who analysis more snappily.

The second chapter examines the episode through feminist and post-colonial theory. It kicks off with a fantastically astute observation of the post-titles opening scene of Clara waiting for the Doctor with her book ‘101 Places To See’. It’s a much stronger engagement with the episode than the first but a short section focussing on the episode’s ‘Long Song’ knocked its stride, telling the reader what the music is doing and when, with little how and why. Some reference to the music’s emotion and how this is achieved would benefit the musical analysis. This is a minor nitpick though.

Chapter 3 then seeks to rationalise why the episode did not have a good critical reception among fans, notably highlighting that most public reviews were actually quite positive. It comprehensively looks at multiple lines of inquiry including the show’s format, on-screen representation, thematic shortcomings and even the divorced popularity of the episode’s ‘Long Song’ speech on YouTube (don’t forget to subscribe to the Official Doctor Who YouTube channel), providing an ample set of reasons for the story’s arguably muddied execution.

Not content with one radical concept about The Rings of Akhaten, Shaw delivers us another one in his final chapter on ‘Anniversary Anxiety’. It’s easily my favourite of the book, lucidly realising that the subtext of Clara as a proto-Doctor was always there from the get-go and makes her subsequent development in Series 8 and 9 all the more expected. It also grapples with tedious yet recurring internet arguments of Clara as a Mary Sue and Manic Pixie Dream Girl. Whilst the episode may not be perfectly executed, Shaw does establish how it pointed to the show’s narrative trajectory of Series 7 and beyond, again linking it to the story’s denouement of unrealised potential.

A set of three appendices makes the book all the more substantial with an examination of whether Akhaten is a sun or a planet, an interview with director Farren Blackburn, and a previously unseen production document for the episode; all providing key talking points in the book’s wider analysis. I find it difficult to imagine what else could be added to this book. A real-life autumnal leaf? Perhaps not, for I fear it may radically alter the entire projection of my life.

Concluding Thoughts

It is rare to find an entry in the Black Archive range that is simultaneously this comprehensive, holistic and unconventional in its take on a story. Shaw reframes The Rings of Akhaten as a story with radical and reformatory politics that fell short in the execution of delivering its message. Perhaps you won’t be as taken by its viewpoints as I was, but you’ve got to admire its sheer ambition and endeavour alone. The continuous introduction of bold, new ideas is what keeps discourse about the show fresh and exciting. Shaw’s conclusion points to an episode about listening and learning from others. I certainly learnt a few things reading it myself and I hope to follow through on its message in the years to come.

 

The Black Archive #43: The Robots of Death by Fiona Moore

Key Themes: Development from script to screen, Modernist and Expressionist influences, the character of D84, themes of class and power, diverse casting and the serial’s legacy.

With the recent release of Season 14 on Blu-ray, a lot of fans will have been rewatching The Robots of Death (1977). So, with the release of this Black Archive by writer and academic Fiona Moore (which would have been out in the same month were it not for a short delay), it seems like excellent timing to re-examine one of the most beloved Classic Who serials within the fandom-at-large.

First airing in early 1977, The Robots of Death was broadcast during one of the most popular eras in the show’s history. Furthermore, it was also one of the first Doctor Who stories to be made available for purchase on videotape, and then it was the very first Doctor Who story to be made available on DVD. The Robots of Death then is a serial that has enjoyed an exceptionally long shelf-life, especially for a forty-year-old piece of cheaply-made television. It has also probably been examined by fandom a lot more than other serials as well, so the question here really is whether there’s anything more that can be said about The Robots of Death. The answer, rather delightfully, turns out to be yes.

Moore’s monograph opens with a chapter contextualizing the conception and development of the serial, suggesting that a perfect storm of ingredients and individuals involved helped the story achieve its renowned status. It also takes the opportunity to bust some long-touted myths about the serial such as being an ‘Agatha Christie-style’ murder mystery and a story about ‘robot rebellion’. It then swiftly moves onto an analysis of the rehearsal and camera scripts to see how Taren Capel’s backstory became obscured between drafts as well as what happened to ‘Jan’, the crew member that never made it to screen!

The middle three chapters were what held my attention the most with an examination of the serial’s influences from Modernism and Expressionism, a character analysis of D84 and a discussion of the themes of class and power in the works of writer Chris Boucher. I particularly enjoyed how Moore delves much deeper into the collected works of Isaac Asimov and Frank Herbert in order to uncover more than just the usual surface-level links typically mentioned in reference material. It is precisely this kind of discourse that keeps me returning to the Black Archive range. All three of these chapters delighted me with new pieces of context and points of reference that allowed me to appreciate the story a bit more, in spite of me not being a huge fan of the serial.

The final two chapters have a more compilatory feel to them with a chapter on diverse casting followed by a concluding chapter on the serial’s legacy in the TV show and expanded media. The former has little to say specifically about the serial in question and so quickly spills over into the show’s broader casting history as well as the portrayal of Leela more generally, a topic that has been covered more comprehensively in The Black Archive #27: The Face of Evil by Thomas L. Rodebaugh. Meanwhile, the latter is an exercise in gathering all the bits of various continuity in novels, such as Corpse Marker (1999), TV stories, like Voyage of the Damned (2007), and of course the Big Finish audio dramas, such as Robophobia (2011).

Concluding Thoughts

The primary challenge with this Black Archive entry was to find new things to say about a serial that is much-loved, well-documented and oft-discussed in the Doctor Who fandom, and to that end it has succeeded admirably. It’s clear that Moore has a deep appreciation for the serial being discussed and this shines through in the writing of this monograph. This comes recommended to those who want to learn about the serial’s literary influences, the blurred line between man and machine, and how Boucher develops his ideas of class and power within his other works. You can throw your money for this at Obverse Books right away, but please do not throw hands at them.

 

The Black Archive #44: The Pandorica Opens/The Big Bang by Philip Bates

Key Themes: The Epic and the Intimate, Pandora’s Box and other fairytales, anomalies, the trouble with time travel, the story’s relationship with time, and the beginning and the end of the universe.

Steven Moffat’s first series finale remains one of the most popular episodes he ever wrote for Doctor Who. On its tenth anniversary, and just after a fairly recent re-release on Steelbook Blu-Ray (with the most glorious artwork by Sophie Cowdry), the Black Archive has given us its take on The Pandorica Opens/The Big Bang (2010) looking at how it deals with the grand and small scales, fairytales, time travel and, quite naturally, the Big Bang itself. Penned by first-time scribe Philip Bates, this book is a passionate and emphatic celebration of what Bates describes as his personal favourite Doctor Who story.

Bates opens with a sketch of the universe, asking us to consider its various perspectives. Ranging from expansive far-off galaxies to the movement of quantum particles, from the giants of history to the ordinary unknown faces of society, from the epic and the extraordinary, to the small and the intimate, wherever we look we are part of the universe and we are all stories in the end. Perhaps Bates can apply for the role of lecturer at St Luke’s University in Bristol, now the Twelfth Doctor has left a vacancy?

The first chapter looks at the storytelling devices in Moffat’s box of tricks to help convey the scale and complexity of the narrative here. It may shock you to read this but it never actually occurred to me that the fez in The Big Bang and The Name of the Doctor (2013) serve precisely the same narrative function and disappear as soon as their work is complete! It was great to read how Bates broke it all down, illuminating the connections and themes with Series 5 as a whole as well as Moffat’s other scripts. Chapter 2 looks at, perhaps unsurprisingly, at the legend of Pandora’s Box as well as the broader fairytale motifs on display in this story too.

It’s from chapter 3 onwards where things start to get a bit knotty as the remaining chapters look at anomalies, the rules of time travel, the various representations of time and how the universe is thought to have started and later how it might end. This, in my mind, was always going to be the trickiest part of analysing a story that plays fast and loose with the typical rules of the show without much of a rational or scientific basis to go off. Consequently, Bates goes for a defence arguing why the episode is entertaining, emotionally satisfying and earns the right to break some of the standard rules.

Whilst the overall book is certainly an easy read for Doctor Who fans, I would like to have seen more points of comparison with other time travel stories, like the Back to the Future films, to strengthen the analysis on the rules of time travel rather than solely relying on Doctor Who for reference points. Furthermore, the book’s latter chapters provide some sound insight into current scientific understanding on matters ranging from black holes, neutron stars and even 10-dimensional string theory, and I felt this was a remarkable improvement on the range’s previous entry covering The Impossible Planet/The Satan Pit (2006). Yet I was personally frustrated that the two lines of inquiry, those being the narrative and the scientific, didn’t seem to intersect. Why put the two together if they don’t seem to connect?

The back of the book has a brilliantly thought-out appendix, providing us with not one but six different reasons for why the TARDIS exploded in the finale, trying to reconcile the loose threads and thematic connections across the entire Matt Smith era. Will a subsequent novelisation confirm one of these theories or provide an entirely different one? Who knows!

Concluding Thoughts

The Black Archives come in many shapes and forms; some allow readers to re-contextualise the serial during the original time of broadcast, whilst others provide subject-based lenses to examine a particular story. However, Bates’ entry on The Pandorica Opens/The Big Bang is a celebration of one of Who’s most popular stories, helping us to better understand the ideas that made it resonate with fans in the first place, and an ideal jumping on point if you haven’t started the range already. I’m not convinced it will persuade others who don’t see it as one of the greats but otherwise I have no hesitation in recommending, should this one take your fancy. Now where did I put my fez…?

 

My Top Pick – #42: The Rings of Akhaten by William Shaw

If I had to, I could bat for any of these Black Archives for being the best one of the set – they’re all worth a purchase if you fancy them and they are all brilliantly different. But I’m going for #42: The Rings of Akhaten for its sheer level of ambition and originality. It even inspired me to write my own piece on the episode, helping to bridge the gap between my enjoyment of mathematics and the story itself. Clearly, it struck a chord with me, and I hope because of that I’ve managed to help someone else learn something about the episode, in much the same way that I did from Will’s book. I do hope there are many more places to see.

You can buy all of these from Obverse Books here.

The Maths of Doctor Who #5 – “It’s like it’s some kind of game, and only you know the rules.”

The Seventh Doctor likes to play games. Not little ones mind, but really big ones. He likes to challenge opponents to games of strategy, like chess, but mix it in with the high-stakes winnings of gambling games, like poker. He’s not afraid to use real people as the game pieces, including his closest friends and allies, and the outcome of his games will ultimately determine the fate of entire worlds and cause the toppling of empires. Like he once said, quoting the former British Prime Minister Benjamin Disraeli, “Every great decision creates ripples…”1.

Arguably there is no story that makes this on-screen characterisation of the Seventh Doctor clearer than 1989’s The Curse of Fenric, a story which sees him do battle once again with an ancient and terrible evil known as Fenric. The Doctor challenges Fenric to a chess problem and Ace, along with us the audience, learns that the story’s unfolding events are all part of a real-life chess game being played between them. A game within a game, if you will, one an abstract representation contained within the other.

This story then employs the ideas of an area in mathematics known as ‘game theory’, and the serial itself explicitly invokes these ideas with the Doctor’s reference to the Prisoners’ Dilemma, perhaps the most well-known problem within game theory. We can even see, as we are told, a logic diagram for the Prisoners’ Dilemma on one of the blackboards in Dr. Judson’s offices. Whilst these ideas are present in the background of the story, they are never expanded upon or explained fully within the serial, which is unsurprising given how much is already going on – they were certainly pressed for time as it was when it came to the broadcast edit!

However, I feel that these ideas of game theory and the Prisoners’ Dilemma have stronger thematic relevance to the story than has been realised among fans, and that these ideas are remarkably suited to a story set during the height of the Second World War. So then, without further ado… Guys, it’s time for some game theory.

Game Theory and the Mathematics of War

“Real mathematics has no effect on war. No-one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems very unlikely that anyone will do so for many years.”

– G. H. Hardy, 1940.2

Mathematics had a considerable effect on bringing about the end of the Second World War in 1945. Not only had number theory been used by the cryptographers working at Bletchley Park to crack the Enigma Code and potentially shorten the war by around two years, but also the mathematics of relativity assisted with the development and subsequent testing of the first atomic bomb. Whilst Hardy, a highly regarded mathematician of his time, provides an emphatic defence about the pursuit of mathematical studies for its own sake in his landmark essay A Mathematician’s Apology, his aforementioned quote is perhaps one of the finest examples of Things That Have Aged Poorly. At times, his thoughts even stray into blatant misanthropy (“most people can do nothing at all well”3) and I would consider such an attitude against the narrative ethos of Fenric as well as Doctor Who more generally (e.g. “We’re all capable of the most incredible change”4).

However, Hardy was known to detest the militaristic applications of mathematics and so naturally did not play a considerable role in the efforts of the Second World War, but had he known about the highly secretive work of his contemporaries then he may have sooner revised his earlier statement. One such contemporary was John Von Neumann, a Hungarian-born mathematician from a wealthy Jewish family who emigrated to America comfortably before the outbreak of the Second World War. Writer Alex Bellos describes Neumann as “the mathematician who shaped the modern world”5. Whilst not a cryptographer like Alan Turing, he played a central role in the development of the modern computer, designing the fundamental internal architecture of the electronic device you are currently using to read this blog, as well as working on the Manhattan Project which developed the first nuclear bomb. He was also the central figure behind the field of game theory.

Game theory is “an area of mathematics concerned with modelling how participants behave in situations of conflict and cooperation”6. Neumann coined the term ‘game theory’ himself in 1944 when he co-wrote the book The Theory of Games and Economic Behaviour. However, his ideas weren’t simply used for recreational purposes but to predict the behaviour of competitive market forces in economic scenarios as well as develop military strategies for US intelligence during the Cold War. As Simon Singh notes, generals were now “treating battles as complex games of chess”7. This is precisely what the Doctor is up to in The Curse of Fenric when he arrives at the secret military base near Maiden’s Point.

But more than that, the story presents us with a dramatic representation of game theory in motion, set at the point in history when it first came into formal existence. Because in the year 1943, as the Doctor is masterminding a plan to prevent Fenric and the Ancient One detonating a set of devastating chemical bombs that will poison and pollute the entire world, Von Neumann is taking up his post on the Manhattan Project, pursuing the development of a weapon that will have similar consequences.

Perhaps it’s unlikely that writer Ian Briggs knew this detail within the history of mathematics, but nevertheless the inclusion of game theory in a story set at this exact point in history is extremely pertinent. As Una McCormack observes in her Black Archive, “The wartime setting of The Curse of Fenric is very far from being window dressing, and the moment in the war is crucial.”8 Neumann’s choice to apply his knowledge of mathematics to military warfare, in what can be read as an attempt to re-lay the global chessboard, creates the very future that we inhabit today. Just like in The Curse of Fenric, the history of the past continues to unfold within our present moment.

Zero-Sum Games and The Prisoners’ Dilemma

JUDSON: You’re familiar with the Prisoner’s Dilemma, then?

DOCTOR: Based on a false premise, don’t you think? Like all zero-sum games. But a neat algorithm nevertheless, Doctor Judson.9

This quote gives us a nice insight to the Seventh Doctor’s moral philosophy here, as he states that all zero games are based on a ‘false premise’. Game theorists will assign a value, sometimes referred to as ‘utility’, to every possible outcome for each player in a game. A zero-sum game is one where if you add up all the possible values, the sum of all the utility, you get zero. This means that if one player gains some points then another player must lose an equal number of points; the sum total of points remaining constant. If you were to apply this idea to all real-world contexts, it would suggest that there must always be winners and losers in each game. The concept of a mutually beneficial outcome for all players doesn’t exist! There is significant research10 to suggest that people tend to have a cognitive bias towards zero-sum games. They believe, intuitively or otherwise, that this is how the world works.

Consequently, this suggests that the Doctor believes life more accurately reflects a non-zero-sum game, meaning that there exists at least one outcome where all the players can gain utility, that it is indeed possible for to achieve mutually beneficial outcomes. This remark then foreshadows the story’s conclusion where the British and Russian soldiers, Bates and Vershinn, join forces to fight the common enemy. This is a rejection by them of the ideology of zero-sum games as they embrace the possibility for the first time that both sides can win. Moreover, this is a rejection of Thatcher’s own political philosophy by the narrative, as is pretty much every other story produced under the tenure of script editor Andrew Cartmel. It also managed to pre-empt Geoffrey Howe in his resignation speech in 1990 (“The European enterprise is not and should not be seen like that – as some kind of zero-sum game”).

What about the Prisoners’ Dilemma then? How does that fit in with all this? Below I have presented the problem as formalised by Albert W. Tucker in 1950:

“Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:

  • If A and B each betray the other, each of them serves two years in prison.
  • If A betrays B but B remains silent, A will be set free and B will serve three years in prison.
  • If A remains silent but B betrays A, A will serve three years in prison and B will be set free.
  • If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).”11

We can more easily refine the description of this problem with a pay-off matrix, a grid which shows all the values in an easy-to-read layout, like so:

Criminal B remains silent Criminal B betrays
Criminal A remains silent [1, 1] [3, 0]
Criminal A betrays [0, 3] [2, 2]

For each set of outcomes, the first number represents the jail term of criminal A and the second number represents the jail term of criminal B. So if A betrays and B remains silent, then A spends 0 years in prison whilst B spends 3 years in prison, just as its stated in the second bullet point above. It is also not a zero-sum game, allowing the two prisoners to decide whether they want to cooperate or compete with each other.

What outcome might we expect if we let the two criminals play the game? Well, one way that a game theorist might predict this is to investigate whether there is a dominant strategy here. A dominant strategy is an action that a criminal can take that will always provide the better outcome, regardless of what the other criminal chooses to do. We can see that such a strategy is indeed present here.

If Criminal B expects Criminal A to remain silent, then they should choose to betray because they will spend zero years in prison instead of one. But if Criminal B expects Criminal A to betray them, then they should still choose to betray them because they will spend two years in prison instead of three. Whatever Criminal A chooses, it would seem the rational choice for Criminal B is to betray.

Another approach is to use the minimax algorithm, meaning here that each criminal wants to minimise their maximum sentence. A quick look at the pay-off matrix shows that the maximum sentence possible for each criminal is three years and this can only occur if they remain silent. So, in order to avoid the worst possible outcome for themselves individually, they will each choose to betray the other and so consequently end up with two years in jail each. Again, this reveals the dominant strategy of the game presented here.

This individualistic and supposedly rational mindset to decision making reveals the inherent tragedy of the Prisoners’ Dilemma, because whilst they have individually avoided the worst outcome for themselves (three years in prison) they have ended up in the worst-case scenario as a collective (four years combined in prison). If the prisoners had decided to cooperate instead of compete, by both remaining silent, then they would have collectively spent only two years in prison, which would have been the best-case scenario for the prison gang.

You can change the actions, the points and the context of the scenario, but if your pay-off matrix reveals this same basic conclusion as described here then it is yet another example of the Prisoners’ Dilemma. The tragedy then is that by choosing to avoid the worst-case scenario, the players of the game fail to achieve the best-case scenario.

Chess Problems and Mind Games

“But the ‘great game’ of chess is primarily psychological, a conflict between one trained intelligence and another”

 – G. H. Hardy.12

This fundamental idea behind the Prisoners’ Dilemma appears in a number of ways throughout the story. Perhaps the most obvious of these is the chess puzzle presented by the Doctor as a challenge for Fenric to solve. The solution is revealed to be an unintuitive yet rather straightforward move involving opposing pawns uniting in order to reach checkmate, but logically this seems rather bizarre. As Sandifer duly observes, “the fact that the chess puzzle and its solution are completely non-sensical, that a mate-in-one puzzle that stumps an ancient god for ages is ridiculous”13.

However, thematically it ‘rhymes’ with the narrative at-hand. The Doctor’s chess puzzle is a mirror of the real-life game happening right now at the secret military base, and is used by him to showcase the flaw in Fenric’s strategic outlook; he cannot fathom the possibility that the pawns might not kill each other at the first possible chance, the clear dominant strategy, or to actively choose to work against the premise of the game itself. The pawns then, represented by Bates and Vershinn, choose to work together in order to achieve the best outcome for themselves rather than as individuals. Cooperation over competition.

Then there’s the Ancient One. For most of the narrative, he14 is used as a game piece by Fenric, who belittles and barks orders at him, in order for him to reach his desired outcome of the chemical pollution of the entire world. But I mentioned earlier that we witness a game within a game and this allows the Doctor to redefine the game being played. He persuades the Ancient One to stop being a pawn in Fenric’s game, essentially exiting the chessboard, and instead becomes a player in the game, substituting into the Doctor’s place. This entraps Fenric once again in a game where he cannot foresee the winning move, and now he must face the consequences of mistreating his own game piece. And since the Ancient One by this point already believes that mutual cooperation between them is no longer possible, they are left only with the option to betray each other: mutually assured destruction. This is the flipside to Bates and Vershinn. The Curse of Fenric’s resolution presents us with both ‘winners’ and ‘losers’ of the Prisoners’ Dilemma. Of course, this reading assumes that we actually witnessed the end of Fenric, but the expanded universe may have other ideas.15

Margaret Thatcher once famously said, “There is no alternative.” But unfortunately for her, there is. So what is it? The alternative is that we witnessed just one of many iterations in the ongoing battle between the Doctor and Fenric. Much like how in Heaven Sent (2015) we initially see one iteration of the Doctor running about the castle, in fact. What then does such a game look like? Let’s dare to imagine that we can even comprehend such a thing.

Consider then that the Seventh Doctor and Fenric are playing the most elaborate and extraordinary game. One with an impossibly large number of options for each of them to choose from, and perhaps not limited to a mere two-dimensional display of outcomes but many, many more. And the potential pay-offs are not just points on a scoreboard but the lives of countless individuals, people like you or me, and the continued existence of our world. The whole of reality as we know then is at stake here. A ‘rather neat’ algorithm, as the Doctor put it, that started so very long ago and will continue from now until the end of time. Making decision after decision. Iteration after iteration. Game after game.

The end of history? Far from it.

“We play the contest again, Time Lord.”

 

Bibliography

  • Alex Through the Looking Glass by Alex Bellos
  • A Mathematician’s Apology by G. H. Hardy
  • Fermat’s Last Theorem by Simon Singh
  • The Black Archive #23: The Curse of Fenric by Una McCormack
  • The Simpsons and Their Mathematical Secrets by Simon Singh

All internet references have been highlighted throughout.

Footnotes

1 Remembrance of the Daleks (1988)

2 Hardy, G.H., A Mathematician’s Apology, p44

3 Hardy, G.H., A Mathematician’s Apology, p7

4 The Woman Who Fell To Earth (2018)

5 Bellos, Alex, Alex Through The Looking Glass, p261

6 Singh, Simon, The Simpsons and Their Mathematical Secrets, p99

7 Singh, Simon, Fermat’s Last Theorem, p167

8 McCormack, Una, The Black Archive #23: The Curse of Fenric, p41

9 The Curse of Fenric: Special Edition (2019)

10 For example, see “Belief in a Zero-Sum Game as a Social Axiom: A 37-Nation Study” and “Your gain is my loss”: An examination of zero-sum thinking with love in multi-partner romantic relationships and with grades in the university classroom.

11 I’ve quoted this as presented on the Wikipedia page on the Prisoner’s Dilemma. Accessed 3rd August 2020.

12 Hardy, G.H., A Mathematician’s Apology, p30

13 Sandifer, Elizabeth, Take Hitler and Put him in the Cupboard Over There (The Curse of Fenric)

14 The television story identifies the Ancient One as male with he/him pronouns but the novelisation tells us that the Ancient One is female and uses she/her pronouns. I do not agree with TARDIS Wiki insisting on referring to the Ancient One as “it”.

15 See Gods and Monsters by Alan Barnes and Mike Maddox.