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.

 

The Maths of Doctor Who #4.2 – “There’s an awful lot of one, but there’s an infinity of the other.”

“Saving the day through a heartfelt sing song and the illogical powers of an emotional leaf felt like a distinct cop-out.”

– Mark Snow, IGN.1

“I caught the sound of a man airing the preposterous notion that the sum of all primes approaches infinity.”

– A complaint to BBC Radio 4 regarding an episode of More or Less.2

Infinity makes people cross. The very idea itself asks us to the imagine the most impossible of notions, that something can goes on forever. Fans of Doctor Who are likely to say that it is a show that will ‘go on forever’, but what they probably more accurately mean is that ‘Doctor Who will go on for the rest of my life and many, many years after’. If Doctor Who were to run for 100,000 years, then yes that might seem like a very, very long time indeed, but 100,000 years is just the teeniest tiniest drop in the ocean when compared to the all-encompassing enormity of infinity.

How then can we even begin to comprehend something like that using only our finite and comparatively tiny lived experiences? And when presented with rational arguments and logical conclusions on the consequences of such an idea, why do we intuitively decide to reject these answers as preposterous and absurd? Perhaps it is because it’s unlike anything else we know. Perhaps it has something to do we how we feel about infinity instead. This blog I hope will unravel the mysteries and shed some light on our understanding of infinity itself. But why have I actually brought up the idea of infinity? Because of The Rings of Akhaten (2013), of course.

The Rings of Akhaten and The Notion of Infinity

Judging by the Readers’ Poll conducted by Doctor Who Magazine in 20143, it would seem that The Rings of Akhaten is one of the most unpopular episodes among fandom at-large. This idea is examined in considerably more depth within William Shaw’s entry in The Black Archive range on The Rings of Akhaten, but Shaw has observed that “nearly all of the [contemporary reviews] were quite positive, or only mildly negative. The only strongly negative review from the time was in Doctor Who Magazine. Something about this episode seemed to hit differently with hardcore Doctor Who fans”4. One of the main points of critique is the episode’s climax, which not only involves the notion of infinity but also what Mark Snow of IGN has described as “the illogical powers of an emotional leaf”. So first off, let’s quickly recap the dialogue from that climatic moment:

CLARA: Well, I brought something for you. This. The most important leaf in human history. The most important leaf in human history. It’s full of stories, full of history. And full of a future that never got lived. Days that should have been that never were. Passed on to me. This leaf isn’t just the past, it’s a whole future that never happened. There are billions and millions of unlived days for every day we live. An infinity. All the days that never came. And these are all my mum’s.5

Upon Clara’s successful resolution to the problem, the Doctor then decides to come back to the fore and act like he knew this was the answer all the time:

DOCTOR: Well, come on then. Eat up. Are you full? I expect so, because there’s quite a difference, isn’t there, between what was and what should have been. There’s an awful lot of one, but there’s an infinity of the other. And infinity’s too much, even for your appetite.

This dialogue suggests a rather intriguing question: are we to accept that the Doctor’s past memories offered here are merely finite, whereas the lost future of Clara’s mum, symbolised by “the most important leaf in human history”6, represents an infinity of unlived days? What perhaps makes this even more unintuitive and radical a conclusion to the story here is that we generally perceive the Doctor as this immortal hero, who stars in a show that we like to think will go on forever. Yet here, in this particular moment, it actually pales in comparison to the seemingly finite, and tragically cut-short, lifespan of Clara’s mother. Allow me then an exciting digression into the ideas and consequences of infinity itself, in the hope that I will be able to answer this question more comprehensively. I do hope it’s not too much for your appetite.

ClaraLeafAkhaten
Pictured: Clara, the Doctor, and the Most Important Leaf In Human History.

“Hey, do you mind if I tell you a story?” – The Early Days of Infinity

The earliest recorded mention of infinity is widely regarded to be from the philosopher Anaximander (c.610-546 BC) who used the word ‘apeiron’, which more literally means “unbounded” or “indefinite”, though many philosophers such as Heidegger and Derrida have debated the translation of this term. However, the Ancient Greeks were seemingly terrified by the notion, a fear which has since been termed as a “horror of the infinite”7. This is especially notable in the works of mathematician Euclid who, by using a clever recursive argument, first proved the existence of infinitely many prime numbers. Yet he deliberately avoids the word ‘infinite’ altogether. Instead, his proof in Book IX of The Elements translates into English as “Prime numbers are more than any assigned multitude of prime numbers”8. The Ancient Greeks may have been among the first to entertain the notion of infinity, but they certainly refused to take it seriously.

Perhaps the most well-known use of the infinite in philosophical pop culture is Zeno’s Paradox about a hypothetical race between the hero Achilles and a tortoise. The tortoise is given a head start on Achilles and the race begins. By the time Achilles has reached the starting position of the tortoise, the tortoise has moved some distance ahead. Once Achilles has reached that position, the tortoise will have moved ahead some more, albeit a shorter distance. This process continues ad infinitum and so the argument here is that Achilles will never overtake the tortoise to win the race. Intuitively though, we know that in real life a man would easily overtake a tortoise in a running race and herein lies the paradox. What makes this paradox of infinity somewhat inadequate is that it does not explicitly recognise that an infinite sequence of events can still lead to a finite result. This is the entirely logical result of summing up sequences of numbers that converge towards a particular value and in mathematics we call that a ‘limit’.

Infinity, however, was still slow to catch on in the minds of mathematicians and doesn’t get its iconic ‘figure-of-eight’ symbol (∞) until 1665 when John Wallis first described an infinitesimal as the fraction 1/∞9. His idea caught on with the likes of Newton and Leibniz who would go onto independently discover calculus (formerly known as infinitesimal calculus) during the latter half of the 17th Century. By this point, it seems that infinity was here to stay.

“I’ve seen bigger.” – Are Some Infinities Bigger Than Others?

So far then, we’ve talked about the origins of infinity and things getting infinitely smaller, but what about when things get infinitely bigger? In fairness, mathematicians didn’t tackle that one head on until towards the end of the 19th Century. The principle figure behind this area of work was Georg Cantor, who introduced the radical new notion of cardinality, which essentially is a way to count the magnitudes of infinity. Rather than treat infinity as some flimsy piece of philosophical conjecture or just as an impossibly large number, Cantor decided that infinity should now be regarded as an entirely separate concept, complete with its own set of rules. Some of his contemporaries went as far as to describe this as ‘heretical’, which unfortunately led to him having a series of nervous breakdowns over his lifetime. David Foster Wallace has even identified this historical event as the origin of a stereotype he termed ‘The Mentally Ill Mathematician’ (with the most famous example of course being John Forbes Nash Jr., the pioneer of game theory, as the subject of the Oscar-winning film A Beautiful Mind (2001)) alongside others including the ‘Tortured Artist’ and ‘Mad Scientist’10.

To understand Cantor’s idea of cardinality, consider the set of all whole numbers, also commonly known as the natural numbers, and the set of all even numbers, which are all the numbers wholly divisible by two. If I asked you how big the set of all whole numbers is compared to the set of all even numbers, I would reasonably expect you to say that it is double the size. This seems intuitive because whilst both the sets of whole numbers and even numbers are infinite (as they both go on forever), the even numbers appear half as frequently throughout the whole numbers. Yet I can draw a one-to-one mapping of the whole numbers to the even numbers by pairing each whole number with the double of that number. This one-to-one mapping means they are in fact the exact same size and so have the same cardinality. Infinity then has now been repurposed to more precisely describe the size of any collection of objects and can be used to compare the relative sizes of infinity.

Picture2
Pictured: A one-to-one mapping of the natural numbers N to the even numbers E. This illustrates the idea that both sets have the same cardinality and so are ‘equivalent’ in size.  They are both countably infinite. Image take from https://en.wikipedia.org/wiki/Cardinality.

Since mathematicians had run out of Greek letters to borrow, Cantor instead borrowed the Hebrew letter ‘aleph’ (ℵ) and so the cardinalities of infinite sets are written as ‘aleph numbers’ with ‘aleph null’ (ℵ0) being the smallest, and refers to the size of the natural (or counting) numbers. This cardinality of infinity, and any sets of identical magnitude are also known as ‘countable infinities’, with any higher cardinalities known as ‘uncountable infinities’. From this, you can identify the sets of integers and rational numbers as countable infinities, whilst the sets of all irrational numbers and real numbers are uncountable infinities. Whilst this might sound like a lot of work just to get a grasp on what infinity means, these ideas can help us with some more tangible problems ranging from the number of possible ways to slice a pizza to the number of possible chess games that can be played.

As I said earlier, Cantor was criticised by some mathematicians at the time but some came staunchly to his defence. One of those was David Hilbert who described Cantor’s work as “the finest product of mathematical genius” and defiantly exclaimed that “no-one shall expel us from the Paradise that Cantor has created”11. No sensationalism detected whatsoever. Hilbert is expressing Cantor’s work on infinity here in terms of a state of afterlife, a place of eternal happiness, yet it may be worth noting that Hilbert himself was agnostic (he was raised as a Protestant though). In this moment, infinity is not so much what it actually is, mathematically speaking, but rather what you actually believe in.

“There are billions and millions of unlived days for every day we live.” – How Does The Rings of Akhaten Handle Infinity During Its Climax?

We can clearly divide the climax into two key events: the Doctor’s speech that fails to resolve the situation and Clara’s speech that manages to succeed instead. The Doctor offers to the Sun God12 his memories but this fails to satisfy its appetite. His passionate speech conjures up these incredible, awe-inspiring and seemingly impossible imagery such as watching “universes freeze and creations burn” and “universes where the laws of physics were devised by the mind of a mad man”. The Doctor’s strategy here then appears to be to overload the Sun God with these extraordinary tales. But this is a massive oversight on his part. Whether a story is short or long, probable or impossible, factually accurate or entirely fiction, it doesn’t matter: it is still a story. What will end the Sun God’s existence is not the nature of these stories, but the number of them.

But surely the Doctor has an infinity of stories to tell? Indeed, if we are to take all of the licensed expanded universe stories (and, just for good measure, all the unlicensed fan fiction as well) then we can see gaps between adventures that can contain an uncountable infinity of adventures, even in places where logically there shouldn’t be more adventures (otherwise known as The Law of Big Finish). One could suggest a multitude of reasons to get around this, ranging from the television show not considering these canonical to perhaps the Doctor having a finite capacity to his memory, but I think the most reasonable answer is also the simplest one: the Doctor is selecting a finite set of memories to offer. His adventures may take an infinity of forms but his chosen memories are a finite number. In fact, throughout the entire story, he is unwilling to sacrifice anything of his, whether it be his sonic screwdriver, Amy’s glasses, or his entire past, and so he continues to fail at understanding the situation at hand13.

Clara, however, doesn’t just offer her past memories but “a whole future that never happened”, all the uncountable possibilities of the days she could have shared with her mother, “passed on to [her]”. I would argue here that it’s entirely intuitive that she figures this out given that she has already made one sacrifice earlier on in the story, her mother’s ring – in order to gain access to the space moped. Unlike the Doctor, Clara is willing to offer everything, willing to demonstrate the unbounded sentimental value she holds of her most treasured possessions, and this is why she succeeds. It would be impossible to map all the days that could have happened to the days Clara expected her mum to live out with her; an uncountable infinity of days. Just like Hilbert proclaiming that Cantor had created a ‘Paradise’ from his work on infinity, and just like Clara’s mother’s ring, a never-ending circle representing a union that lasts forever, it’s actually the sentiment of infinity that truly counts here. And infinity is too much, even for the Sun God’s appetite.

This emphasis on sentimentalism over mathematical rational is not just present here in The Rings of Akhaten but in Neil Cross’s other work too. In an episode of Luther, Alice Morgan tells John Luther about the size of the observable universe:

MORGAN: Did you know that the observable universe just got bigger? […] Last time I saw you, we assumed there were about 200 billion galaxies. The revised estimate puts it at two trillion, so what we believed to be absolutely everything was basically just a round error. Closer to zero than the true number.14

Yes, Alice. That’s how scale factors work.

The intended effect here is imply that our place in the universe is so much smaller than we had previously thought, but anyone with some sense of mathematical intuition would realise that on such a large scale, even though the absolute difference of nearly two trillion seems a gargantuan number, it is actually relatively tiny. Two trillion is still nowhere near everything, not a scratch on infinity. The emphasis here yet again is not on understanding what it actually means, but on what it makes you feel.

Whilst it may be disappointing to see that the Eleventh Doctor fails to understand what is taking place during The Rings of Akhaten, he does learn his lesson eventually. In The Time of the Doctor (2013), he sacrifices the remainder of what he believes is his thirteenth and final life to defend the town of Christmas on the planet Trenzalore. And just like Clara’s sacrifice of “the most important leaf in human history”, it manages to change their future. Perhaps then that is why we hear a reprise of The Long Song just before the Eleventh Doctor regenerates.

The Borromean Rings of Akhaten – A Conclusion

I have one last piece of mathematics to bring up in this discussion: Borromean rings. The Borromean rings consist of three interlocking circles forming what is known in knot theory as a Brunnian link. What this simply means is that if one of the circles were removed, then all remaining circles would become unlinked. If you inspect the picture closely you may realise that this is a geometrically impossible shape; no-one could physically construct such an object using real rings. It does become possible once you make the rings elliptical but then these aren’t proper rings, are they?

Picture1
Pictured: The Borromean Rings. Image taken from https://www.ancient-symbols.com/symbols-directory/borromean-rings.html

The name itself comes from the coat of arms of the Borromeo family, an Italian aristocratic family from around the 17th Century. They certainly weren’t the first to use the symbol as it dates back to the Vikings of Scandinavia, who called it ‘Odin’s triangle’ or a ‘walknot’. Besides Viking runes, it has also been found in early Buddhist art and Roman mosaics. It frequently appears in religious scripture as a symbol of strength in unity and to represent sacred trinities, groups of three-into-one, such as the Holy Trinity of the Father, the Son and the Holy Ghost, for example. These Borromean rings then are not just a symbol of unity, but also of faith and belief. In the final scene of The Rings of Akhaten, the Doctor returns to Clara her mother’s ring:

DOCTOR: They wanted you to have it.

CLARA: Who did?

DOCTOR: Everyone. All the people you saved.

Whilst I think it’s a great shame that we don’t get to see the people of Akhaten do this in person, it nevertheless shows that they greatly value what she has done for them. The return of her mother’s ring then is a symbol of their belief in Clara. But Clara was not alone. She was also supported by Merry, the Queen of Years, and by Ellie Ravenwood, her own mother, symbolised here by “the most important leaf in human history”. In his recent Black Archive, William Shaw argues that it is these three characters who can provide an alternative positive, feminist version of the future in response to the Doctor’s patriarchal assumptions that are present in The Rings of Akhaten14. Here then I propose a new trinity, one that symbolises unity in sisterhood all across the “Seven worlds orbiting the same sun” and beyond. I shall call it the Trinity of Akhaten, and it consists of Clara, Merry, and the Most Important Leaf in Human History. Long may they continue to be with us, now and forever more.

 

References

Whilst all internet references have been highlighted throughout, my primary sources of inspiration and reference points were the following three books:

  • Alex’s Adventures in Numberland by Alex Bellos.
  • Things to Make and Do In The Fourth Dimension by Matt Parker.
  • The Black Archive #42: The Rings of Akhaten by William Shaw.

 

Footnotes

1 Snow, Mark, ‘Doctor Who: “The Rings of Akhaten” Review, IGN, 6 April 2013, https://www.ign.com/articles/2013/04/07/doctor-who-the-rings-of-akhaten-review.

2 Parker, Matt, Things To Make And Do In The Fourth Dimension, p403.

3 Griffths, Peter, ‘The Results in Full!’, DWM #474, cover date July 2014.

4 Maleski, Sam, ‘INTERVIEW – William Shaw, the Leaf and “Rings of Akhaten”’, Downtime, 25 April 2020, https://downtime2017.wordpress.com/2020/04/25/interview-william-shaw-the-leaf-and-rings-of-akhaten/.

5 All transcripts are taken from http://www.chakoteya.net/DoctorWho/33-8.htm and edited for clarity at the author’s discretion.

6 All quotes are taken from The Rings of Akhaten unless otherwise stated.

7 Hutten, Earnest H., The Origins of Science: An Inquiry into the Foundations of Western Thought, George Allen & Unwin Ltd, p. 135. Why not have a listen to this BBC Radio 4 programme to learn more about the Ancient Greeks and the ‘Horror of the Infinite’?

8 Heath, Sir Thomas Little; Heiberg, Johan Ludvig, The Thirteen Books of Euclid’s Elements, The University Press, p. 412 (Book IX, Proposition 20).

9 Bellos, Alex, Alex’s Adventures in Numberland, p400.

10 Bellos, Alex, Alex’s Adventures in Numberland, p400.

11 Parker, Matt, Things To Make And Do In The Fourth Dimension, p404.

12 Or is it a Planet God? See Appendix 1 of William Shaw’s Black Archive on The Rings of Akhaten for more discussion on whether Akhaten is a planet or a sun.

13 For more on how the Doctor misunderstands the events of the episode, see Chapter 1 of William Shaw’s Black Archive on The Rings of Akhaten.

14 Luther, Series 5, Episode 2 (2019). I have never actually seen an episode of Luther but this quote is referred to on pg92-3 in the Black Archive on The Rings of Akhaten.

15 For more on how these three offer a feminised vision of the future, see Chapter 2 of William Shaw’s Black Archive on The Rings of Akhaten.

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

Key Facts:

  • Story No. 32. Written by Geoffrey Orme. Directed by Julia Smith.
  • Episodes 1 and 4 are missing. They are survived by episodes 2 and 3.
  • Key Themes: How does surviving material influence fan perception? Should we even take this story seriously? Is fan wisdom bollocks?
Screen Shot 2020-04-11 at 15.30.21
The Underwater Menace: I’d planned to include more fish puns in this review but later decided to scale back on them.

The Review

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 certainly 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 even 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 how does missing material affect fan reception, taking full advantage of the rediscovery of Episode 2 back in 2011, as well as 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. Just take a look below at some of the questions this book presents well-informed and dutifully researched answers for you:

  • 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 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 60s serial The Sensorites (1964)) and Lennie Mayne (Director of four 70s Who serials). It is truly an excellent capstone to the book itself.

under1
The Fish People: Far from being background characters, they actually rose up and seized the means of food production.

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 by James Cooray Smith 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 Maths of Doctor Who #3 – “We would have to consult our top scientists”

Doctor Who has always been recognised as science-fiction show and its earliest serials used time travel as a narrative device in order to tell stories set on either far-distant planets or in the long-distant past that not only aimed to entertain families between Grandstand and Juke Box Jury but also teach children about both science and history. But by 1966, this approach to the show’s production shifted significantly, abandoning history in favour of science. This coincided with the introduction of writer Kit Pedler and script editor Gerry Davis. For this blog entry, I want to have a look at how Pedler and Davis’ serials brought a surge in STEM representation in the show’s format, looking at how mathematics and, more broadly, science, is used in their storytelling. But first, a bit of background.

Christopher Magnus Howard “Kit” Pedler was born on 11 June 1927 and initially worked as a British medical scientist at the University of London, where he was head of the electron microscope department. His first contribution to British television was, perhaps unsurprisingly, Tomorrow’s World and would later go onto co-create and co-write Doomwatch (1970-72). However, he is arguably best known for his work on Doctor Who, for which he has three credited scripts (The Tenth Planet (1966), The Moonbase and The Tomb of the Cybermen (both 1967), provided initial ideas for three further stories (The War Machines (1966), The Wheel in Space (1968) and The Invasion (1969)) and generally acted as the show’s unofficial scientific advisor under Innes Lloyd’s tenure as producer, who wanted to inject more hard science into the show’s format.

Kit’s frequent collaborator was television writer Gerry Davis, who was Doctor Who’s script editor for over a year (running from episode 4 of The Massacre (1966) to episode 3 of The Evil of the Daleks (1967)) and so was part of the production crew that oversaw the transition from William Hartnell to Patrick Troughton. He too was a co-writer for The Tenth Planet and The Tomb of the Cybermen but also contributed The Highlanders (1966-67), which introduced long-serving companion Jamie McCrimmon, as well as Revenge of the Cybermen (1975) during Tom Baker’s first season, though this was heavily re-written by the then-script editor Robert Holmes. The original version, now entitled Return of the Cybermen, will be released as a Big Finish audio drama in November 2021. Together then, it seems we have a duo whose primary skills complement each other: Pedler having the cutting-edge scientific ideas that he wants to fashion into stories but lacking in television experience, whilst Davis has such experience writing TV soaps and drama but can use such scientific ideas to make socially and culturally relevant stories for BBC broadcast. But how did that translate into Doctor Who itself?

kit-pedler-and-gerry-davis-doomwatch
Pictured: Doctor Who writers Kit Pedler (left) and Gerry Davis (right). There seem to few photos of them together, with this being the most common by far.

The War Machines and STEM Representation in Late-1960s Who

Kit Pedler’s first story idea for Doctor Who to get made became The War Machines, written by Ian Stuart Black, and at one stage had the working title of “The Computers”1. Not only is it one of the few complete serials from Season 3, it is also the only entirely complete serial to feature companions Ben and Polly, which also happens to be their debut story. The story is set in contemporary time, which is highly irregular for the show at this point, and the plot mainly revolves around a highly advanced supercomputer called WOTAN (which stands for Will Operating Thought ANalogue) who turns out to be surprisingly malevolent.

Episode 1 sees the Doctor meet WOTAN’s creator, Professor Brett, before later attending a meeting of the Royal Scientific Club, immediately presents scientists as members of the upper echelons of British society, hanging around with the likes of aristocrats such as Sir Charles Summer and security figureheads such as Major Green. It also establishes a link between science and the military that would be become a lot more prominent during the first few seasons of Jon Pertwee’s tenure2. You only have to look as far as Summer’s coining of the term C-Day for Computer Day, which naturally invokes thoughts of the D-Day landings during the Second World War, to further cement the link.

Another interesting and perhaps quite alarming statement from Sir Charles Summer is that WOTAN “is merely a brain which thinks logically without any political or private ends. It is pure thought. It makes calculations, it supplies only the truth.” The complete disassociation between science and logic from politics and ethics here is later demonstrated to be spectacularly misjudged when WOTAN starts hypnotising people to construct the eponymous War Machines and attempt to take control over London, unless one considers total conquest of the world to be an unquestionable truth about how life should be. As Commander Millington remarks about computers in 1989’s The Curse of Fenric, “Whose thoughts will they think?” With plans to link WOTAN to computers around the world, the story presents science not only as a subject that will shape the future of our society, but also one that will be highly influential in the unfolding geopolitical landscape, with Parliament, the Kremlin and the White House all name-checked in the background of Summer’s press conference.

WOTAN’s presence in the story not only brings science into the show but also mathematics. Later on in Episode One, we have the very first maths problem to feature in Doctor Who when the Doctor asks:

DOCTOR: Er, what is the square root of 17422?

(The machine whirrs, then prints a number on a piece of paper.)

BRETT: Correct?

DOCTOR: One moment please. 131 point 993. Yes, that’s near enough.3

I hope I’m not the first person to have actually checked this but if you type that question into your calculator you should get an answer of 131.992424, which to three decimal places would round to 131.992, not 131.993. With this in mind then, the Doctor’s comment of “near enough” lends an alternative reading of the scene. Rather than being in awe of WOTAN’s computational speed and accuracy, the Doctor is actually aware of the machine’s slight calculation error beyond the second decimal place and that he now realises Summer’s complete faith in its calculations are misplaced. It would also imply that the Doctor has superior mental maths skills to the villain.

The plot’s resolution involves the Doctor using his own scientific knowledge to reprogram a captured War Machine and then gives it new orders so that he can use it against WOTAN; the War Machine firing repeatedly at it until WOTAN is destroyed. Far from bringing world peace as was intended, it seems the technology of WOTAN is just yet another new tool that can be used in warfare and is also capable of destroying itself. Only when science and technology are used, not in isolation as intended by Summer, but in conjunction with the Doctor’s ethics can they be used to prevent the invasion of London and so subsequently bring peace.

first-doctors-accessories-war-machines-black-fez
Pictured: Sir Charles Summer (left) and Dr. Who (right) arguing whether or not the show was political back in 1966. The apolitical War Machine is required.

STEM Representation After The War Machines

Far from being an outlier in Doctor Who’s cavalcade of serials during the 1960s, The War Machines presents a decisive shift in the characters and themes used in the show’s storytelling. Judging by the progression of serials under Innes Lloyd as producer, he seems to have declared that historical ones are now out and scientific ones are firmly in. Scientists would now feature as key characters in the majority of stories. Starting from Hartnell’s swansong, The Tenth Planet, we would get the introduction of the Cybermen, who would become Doctor Who’s second villain after the Daleks, as well as the trope of teams of scientists being in space stations or other remote locations, extending all the way until the end of the 1960s.

Communities of scientists working together and facing some form of mechanical menace feature in every story where Kit Pedler is credited, clearly showing it is a staple of his storytelling within the show. Pedler would also revisit the ideas of international communications (and magnetic forces) from The War Machines in his final story contribution to the show, The Invasion, which features the remarkable rise of International Electromatics (or International Electromatix if you’re reading the novelisation) and it even features a Head of Security figure called Packer, again linking science with national security.

As for mathematics, Episode One of The Moonbase is the first Doctor Who episode to feature mathematicians as named supporting characters when Hobson says “Nils, our mad Dane, is an astronomer and mathematician as is Charlie here.” The show would also go on to get its first mathematical companion in the form of Zoe Heriot, who introduces herself in The Wheel in Space by saying “I’m an astrophysicist. Pure mathematics major.” However, the juxtaposition of these two sentences is quite striking to a mathematician like myself. The two areas mentioned here could not be further apart. Astrophysics is a subdomain of physics that involves the study of planetary bodies and would involve substantial applied mathematics such as the mechanics of celestial bodies, whereas pure mathematics is generally used to describe the study of mathematics devoid of any context or application, including areas such as geometry, analysis and number theory. Perhaps GCHQ aren’t hiring anyone in 2079?

Whilst the use of scientific ideas in the stories by both Pedler and Davis can be at times wishy-washy and at worst just plain inaccurate, their consistent and topically relevant inclusion in the show’s format was arguably a good thing. It provided the show one of its most iconic villains in the form of the Cybermen as well as several memorable stories that viewers and fans have enjoyed over the years. All but one of Kit Pedler’s six contributions are available to buy on DVD either because they are fully intact or have been completed with animation, and I suspect The Wheel in Space is not far off being animated itself – though that’s just a personal hunch. However, I do have one bone to pick with Pedler and Davis, and it really is a rather petty one, but there’s a certain scene in one of their stories that I find just absolutely atrocious. I doubt most people will find it as annoying as I do, but there’s no harm in trying to explain why. So, let’s talk about Episode One of The Tomb of the Cybermen.

The Tomb of the Cybermen and Appropriating Mathematics as Technobabble

Thought to be yet another long-lost Troughton classic, the serial The Tomb of the Cybermen (1967) was recovered from a TV station in Hong Kong in 1991, and then quickly released by BBC Enterprises on VHS in 1992. With a gap of almost twenty-five years between its initial broadcast and initial commercial release, Tomb has now been available for fans to view longer than it had been lost4. It has received wide acclaim from the fandom, with some proclaiming it as “quite simply, the best [Cyberman] story”5 and “one hundred minutes of sheer magic”6. It was even the first Troughton-era serial to be released on DVD back in 2002, later getting its own Special Edition in 2012. Simply put, it is a highly-regarded serial among fans, coming in at number 23 in a 2014 DWM Poll7, that perhaps, I might dare to suggest, are being a bit too generous towards it. But I digress…

Screen Shot 2020-04-05 at 17.34.52
Pictured: Troughton (centre) may not know what he’s talking about but he certainly knows how to look smart with just a notepad and pen.

For those who need a quick reminder, the opening of Tomb sees the Doctor and co. arriving on the planet Telos at the same time as an archeological expedition. They have discovered an ice tomb which they believe contains the last remains of the Cybermen and, somewhat concerningly, the Doctor keeps drip-feeding them the answers to all the puzzles and traps set for anyone who tries to enter. One such person he assists is Eric Klieg, who delivers this quite remarkable line of dialogue:

KLIEG: But take this mathematical sequence, for example. I’m really no nearer to its solution. I’ve tried every possible combination. You’d hardly call that easy!

At this point in the story, it has already been established that Klieg has helped financed the expedition (so he’s probably very well-off) and we later learn he is a member of the Brotherhood of Logicians, though we never learn what this actually means beyond having sympathies towards the Cybermen. However, the aforementioned line of dialogue suggest quite positively that Klieg is no expert in mathematical logic. In fact, he seems to have a flimsy grasp of the basics of maths itself.

A sequence can be defined as a set of numbers that follow each other in a logical pattern: all we need is a starting point (or first term) and a pattern (or term-to-term rule). Arithmetic sequences involve adding the same number each time and we can use this to generate our times tables (For example, the three times table is 3, 6, 9, 12, 15, 18, 21, 24 …). Geometric sequences involve multiplying by the same number instead, and this can generate the powers of two for example (1, 2, 4, 8, 16, 32, 64, 128…). Other sequences are more playful, such as the Fibonacci numbers, where you get the next number by adding the previous two (1, 1, 2, 3, 5, 8, 13, 21, 34…) or one of my personal favourites, “say-what-you-see” sequences, where the next number is a numerical description of the previous number (1, 11, 21, 1211, 111221, 312211…)8.

We can see that sequences have starting points and rules, but they don’t have solutions, unless perhaps you’re trying to get the next number? But then if you don’t know the next number, how do you know you have a sequence? Furthermore, what are these combinations that Klieg is using to try and solve it? Combinatorics is the area of mathematics that looks at possible outcomes or combinations of events, such as shuffling a pack of cards or rolling a set of dice. It’s certainly not the sort of maths I would use to solve an unknown sequence. I can only begin to understand what he means by his bold claim of trying every possible option by thinking he must be highly incompetent. And to be fair, that’s probably what he’s supposed to be. The arrogant fool who overestimates his intellectual abilities, and requires a much smarter character to help him, who somehow thinks he can become the new leader of the Cybermen. So maybe the writers had intended this all along then… except then the Doctor opens his mouth:

DOCTOR: You see, if you take any progressive series it can be converted into binary notation. If you take the sum of the integrants, and express the result as a power series, then the indices show the basic binary blocks. Only I wouldn’t do it if I were  you. Oh no, I really wouldn’t do it!

If you listen to the DVD commentary of this scene, you will hear Frazer Hines talking about how terrible he was at maths and I’m not surprised as this is what is must sound like to those who don’t understand. Never mind the remarkable logical leap that expects you to convert your numerical sequence into binary numbers (unless we are to believe that Cybermen think entirely like simple computers?), what firmly put this into the realm of nonsense is the word ‘integrants’ – there are no such things in mathematics. You can have integrals, integrands and integration, but not ‘integrants’. However, integrant is a word in the OED relating to something that is integral. This then I would conjecture is a classic case of Patrick Troughton learning an approximation of his lines, rather than what was on the script. Or maybe he did just misremember? Perhaps it was even a typo? We can’t know for sure, but it does seem to fit a wider observation about Troughton’s overall performance.

Even if we substitute it with a near-sounding replacement like integrals or integrands, it doesn’t help elicit any understanding. Why would you consider taking the terms of a sequence and turn them into a sum of integrals or integrands? I should probably clarify these terms first. An integral is an equation that invokes the process of integration, in much the same way that a sum invokes the process of addition, so it’s basically a fancy sum. Integrands are the functions that you are wanting to integrate, like how in a sum you have numbers you want to add. As for integration, well Klieg starts blabbing on about it some more straight after the Doctor’s not-so-subtle hints:

KLIEG: Look! Sum between limits of one and nine one integral into power series. Yes! Yes! Then you differentiate…

At this point, Klieg seems to be your stereotypical mad scientists having some eureka moment, but my final curious observation here is that he has an integral and then… differentiates? This makes little sense since. Differentiation is the process used to find rates of change of mathematical functions, usually the gradients of curves, whilst integration allows you to find the area under the curve. The Fundamental Theorem of Calculus shows us that differentiation and integration are the inverse processes of each other, meaning if you were to integrate a function and then differentiate it you will get back to where you started. If Klieg manages to solve anything here, I haven’t got the faintest idea how.

Whilst one might consider commending the use of mathematics within a popular children’s TV show, for those who understand the language being used may be frustrated by the lack of any coherent logic to it. And as for those who don’t, like Frazer Hines’ comment stated earlier for example, it brings back school day memories of mathematical anxiety, where people remember have frustrated and confused feelings about not understanding what is happening in the lessons. I would therefore be inclined to draw the conclusion that such representation does more to hinder than to help the subject’s image. I have already highlighted some instances where Pedler and Davis’ representation is much more, shall we say, integrated into the stories they tell, but this scene falls below the mark in my opinion.

But this is just the start for the show’s relationship with mathematics, and more broadly science. Doctor Who will go on to have far more sophisticated representations of mathematics in stories like Castrovalva (1982) by Christopher H. Bidmead, which employs recursion and Escher’s art, Flatline (2014) by Jamie Mathieson, which sees creatures transcending between the second and third dimensions, and Extremis (2017) by Steven Moffat, which employs the not-so random nature of random number generators to help deliver a key plot revelation in that particular story. But I think it’s somewhat fair to say that it all got started back in 1966 when Pedler and Davis wanted to bring their interests and ideas into the stories of Doctor Who. Just so long as you don’t start peer-reviewing their work.

Footnotes

  1. Source: http://www.shannonsullivan.com/drwho/serials/bb.html
  2. For more on this, I would recommend Robert Smith?’s Black Archive on The Silurians (1970) which investigates further the link between science and the military.
  3. All quotes are taken from the transcripts provided on http://www.chakoteya.net/ with a few minor spelling and grammar edits by myself.
  4. Source: https://www.herocollector.com/Article/doctor-who-tomb-recovered
  5. Martin Day in Cloister Bell 10/11, dated March 1985
  6. Jeff Stone in TSV 29, dated July 1992.
  7. http://doctoroo.blogspot.com/2014/06/from-doctor-who-magazines-first-50.html
  8. If you haven’t quite understood this then here’s a longer explanation. The first number is 1, which can be described as one one, so the next number is 11. This can be described as two ones, so the next number is 21. This can then be described as one two and one one so the next number is 1211… and so on. Wikipedia calls them Look-and-say sequences but they are the exact same thing!

Ten Women in STEM I’d like to see in the next series of Doctor Who

If you’re reading this around the time of publication, then you’ll surely be aware that the latest series of Doctor Who has just finished, and now the long wait for a new special or series begins again. If you also happen to be reading this on the day of publication itself, then today, March 8th, is International Women’s Day, a day for celebrating the social, economic, cultural and political achievements of women around the world.

A personal highlight for me in Series 12 was the appearance of Ada Lovelace in Spyfall: Part Two, marking not only a rare positive portrayal of a mathematical figure within the show (certainly in comparison to the likes of Adric, the Sylvest twins and the Logopolitans), but also the first female historical STEM figure (that’s Science, Technology, Engineering and Mathematics) to feature in the TV show. Interestingly, Lovelace has already made an appearance within a Big Finish audio play, The Enchantress of Numbers (which I wholeheartedly recommend to you), alongside Tom Baker’s Fourth Doctor.

Alongside the other appearances of Nikola Tesla and Thomas Edison, it’s been a good year for STEM figures in the show and I hope Chibnall will continue this trend during his time as showrunner and executive producer. Should he happen to stumble upon this blog post, then perhaps he can use this as a starting point for finding other female STEM figures to include in a future episode of Doctor Who. Here are ten possible suggestions:

Marie Curie (1867-1934)

mariecurie3

Born as Maria Sklodawska, Curie was the first woman to win a Nobel prize and the only woman to have won two Nobel prizes to date (which were Physics in 1903 and Chemistry in 1911). A Polish chemist and physicist, she conducted pioneering work into the subject of radiation and radioactivity alongside her husband Pierre Curie, who was a French physicist. Curie also named two radioactive elements that she discovered: radium and polonium (which is named after her home country of Poland). She is undoubtably one of the most well-known female scientists in history. Perhaps we could have an episode where the Doctor is facing some sort of radioactive extra-terrestrial and she needs some expertise to help save the Earth?

Grace Hopper (1906-1992)

Screen Shot 2020-03-08 at 14.29.47

Why stop at Ada Lovelace when you can have another outstanding computer programmer? Born Grace Brewster Murray in 1906, Hopper (nicknamed “Amazing Grace”) invented the first compiler for a computer programming language as well as popularising the idea of machine-independent computer languages (“They told me computers could only do arithmetic.”). She has a PhD in mathematics from Yale, served as an Admiral in the US Navy and helped to popularise the term ‘debugging’ after removing a moth that had got stuck in a Mark II computer running at Harvard. Maybe she could help the Doctor out if she ever has a rematch with Daniel Barton, the CEO of VOR, a company more powerful than most nations, in the Series 12 opener Spyfall.

Rachel Carson (1907-1967)

 180419_carson_1951_banner2

Carson was an American biologist, conservationist and author of a trilogy books based around marine life. Her incredible work helped raised awareness of serious environmental problems, such as those caused by artificial pesticides, and inspired the global conservation movement. This eventually led to the creation of the Environmental Protection Agency (EPA) in America and President Jimmy Carter posthumously awarded her the Presidential Medal of Freedom. An appearance from her would not only continue post-2005 Who’s love of visiting historical authors, but also follow up the environmental themes seen in episodes like Orphan 55 and Praxeus.

Rosalind Franklin (1920-1958)

newrjy4ad

A prominent British Jewish chemist, Franklin is best known for her work on X-ray crystallography that has helped us understand and identify the structures of deoxyribonucleic acid (or DNA). Tragically, her contributions to science were only truly recognised after her premature death at age 37, caused by ovarian cancer. Her work led to the discovery of the double helix structure we all associate with DNA now but   she was sadly not recognised for this contribution by the Nobel Committee. An episode featuring her would certainly help draw more attention to her scientific contributions.

Maryam Mirzakhani (1977-2017)

Fields_Maryam_Mirzakhani

Mirzakhani was the first Iranian and the first woman to be awarded the Fields Medal, the most prestigious prize within the field of mathematics (it is awarded once every four years and only to people under 40). Her specialist region of research was on the symmetry of curved surfaces, an area of maths that blends dynamics with geometry. Tragically, she died aged 40 from breast cancer but her legacy has been profound: her birthday May 12th is now recognised as International Women In Mathematics Day, her international fame has significantly progressed the societal representation of Iranian mothers in her home country, and students at the University of Oxford set up a society in her name for women and non-binary students who study mathematics there. An ideal episode would not only recognise her excellent mathematical ability but also the social and cultural progress that she has inspired.

Caroline Herschel (1750 – 1848)

caroline_herschel

Herschel is most notable for being the first woman ever to discover a comet. A German astronomer, she worked alongside her brother William and took meticulous notes and records of her observations. She was also the first woman to be salaried as a scientist and the first woman in England to hold a position in government. Doctor Who has rarely seen older female scientists represented (such as Professor Rumford in The Stones of Blood) but Herschel would most definitely be a great choice to include in the TV show.

Florence Nightingale (1820-1910)

Florence_Nightingale_(H_Hering_NPG_x82368)

Arguably one of the more well-known figures on this list, Nightingale is perhaps best regarded as a social reformer and founder of modern nursing, becoming an icon within Victorian culture known as “The Lady of the Lamp”. But what is perhaps less celebrated is her aptitude for mathematics. She was a trailblazer in the art of data visualisation (indeed, she popularised the use of the pie chart) and used graphical representations of data to convince others of her observations. Her meticulous and comprehensive study of sanitation of hospitals during the Crimean War enabled her to effectively lobby the British Government for improved sanitation through the Public Health Acts of 1874-75. It is perhaps one of the earliest instances of evidence-based policy in the history of British Government. She truly was a badass statistician.

Rosalyn Sussman Yalow (1921-2011)

Screen Shot 2020-03-08 at 11.30.25

Yalow was the second woman to be awarded a Nobel Prize and the first in Medicine, for which she developed the technique of radioimmunoassay, which allows scientists to trace substances in the bloodstream. Despite its commercial potential, Yalow refused to patent the method. This kind of scientific innovation could certainly work in a story about alien infection, and would most definitely bring her work to the attention of a much wider audience. 

Jocelyn Bell Burnell (1943-)

p05tnb1g 

The first person to discover (the first four) pulsars, highly magnetized rotating neutron stars that emit regular pulses, Bell Burnell was denied the honour of a Nobel Prize for Physics years later on the grounds that she was a postgraduate student (She even went on record to say she believed such a recognition would demean the prize itself). Her discovery is regarded as “one of the most significant scientific achievements of the 20th Century” and she is the only person on this list who is still alive. She has since held distinguished positions such as president of the Royal Astronomical Society and the Institute of Physics.

Marie-Sophie Germain (1776-1831)

sophie-germain

Germain was a French mathematician, physicist and philosopher who persevered through considerable opposition (including her parents, male mathematical peers and just the patriarchal nature of society in general) to become one of the most influential polymaths of recent centuries. She would smuggle candles to her bedroom to allow herself to study through the night, and submitted academic work under the nom de plume Monsieur Le Blanc so that her male mathematical peers would take her seriously, yet despite recognition from distinguished figures like Lagrange and Gauss she was sadly unable to make a true career out of mathematics. She was a true pioneer in the fields of elasticity theory and number theory, and the French Academy of Sciences now has an annual mathematics prize named in her honour. Her final works, which were published posthumously, were on philosophy and she passionately argued that there were no differences between the humanities and the sciences. Put simply, she was brilliant.

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

Key Facts:

  • Based on the Story: Doctor Who and The Silurians (No. 52).
  • Written by Malcolm Hulke. Directed by Timothy Combe.
  • Key Themes: Technology, the 1970s energy crisis, the military, land rights, animal testing, science and ethics, how long should a Doctor Who story be, and whether the Silurian plague could’ve killed us all.

The Review

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 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 (and indeed science), 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 in fact 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 (1970), which perhaps 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 coronavirus outbreak happening right now. The book is also beautifully and thoroughly referenced, as it evident by the surprisingly lengthy bibliography on display.

However, by structuring the book around some rather broad questions does at times lead to some rather general conclusions, such 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 did feel these could have led to more interesting results. For example, I would suggest 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.

I have also so far in these reviews neglected to even mention the cover art and icon designed by Cody Schell and Blair Bidmead respectively (and if you haven’t seen the latest covers by them then go here and look at them!). 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 in the story here as well as perhaps the harmonious coexistence between the Silurians and the animals many 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 I 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? Who knows.

Review: The Black Archive #38 – The Sound of Drums/Last of the Time Lords by James Mortimer

Key Facts:

  • Black Archive Entry: No. 38, written by James Mortimer.
  • Based on the Story: The Sound of Drums/Last of the Time Lords (No. 187, or is it 188?).
  • Writer/Director: Written by Russell T Davies. Directed by Colin Teague.
  • Key Themes: The roles of the Saxons (Lucy and Harold), the roles of the heroes (Martha and the Doctor), and the reinvention of the Time Lord mythos.
Screen Shot 2020-01-18 at 18.11.34
The Sound of Drums/Last of the Time Lords: This cage doesn’t make me think of either of the episodes at all. It just makes me think of the Dead Parrot sketch.

The Review

The series 3 finale has always seemed to have something of a mixed reputation in my eyes. On the one hand, it saw the spectacular return of one of Doctor Who’s longest-serving villains: the Master, portrayed by John Simm for the duration of these episodes. It also continued RTD’s trend of continually upping the stakes for each subsequent series finale; it’s first half styled as an urban-based politically-themed thriller before leading into plans of total world domination in the second half is strikingly different from the other RTD-era finales that all revolved around Dalek invasions. However, its resolution of the Doctor becoming a messianic figure and its sidelining of abused female characters like Lucy Saxon and Francine Jones whilst the two Time Lords battle it out draws routine criticism towards the story. The question here is: how will first-time Black Archive scribe James Mortimer work his way through all this?

Mortimer divides his analysis into three distinct themes: The Saxons, The Heroes and The Mythos. What makes Mortimer’s book stand out from previous entries in the range is his strongly focussed and close reading of the text; his three chapters rarely stray from the episodes at hand here. I honestly found this quite refreshing on the whole, but the relative absence of comparative texts means it can seem lacking in, what I will term, the ‘bounce of ideas’ within the analysis. For example, Niki Haringsma’s Black Archive on Love and Monsters uses the narrative theories of Bertolt Brecht to discuss its atypical storytelling style and it has dramatically influenced my understanding of the episode. By comparing and contrasting the episode with these ideas, the arguments made felt all the more robust. I hasten to add that this is not so much a missed opportunity by Mortimer, but rather he has chosen a path less travelled by contributors to the range.

Nevertheless, he provides clear analysis on Lucy Saxon’s agency within the narrative and the portrayal of the Master as symbolic of toxic white masculinity. The observation that the kiss on the cheek by Rose to Mickey mirrors the kiss on the cheek by Martha to the Doctor was one of multiple inspired observations. I liked the observations of similarity in character beats (and even straight-up lifts in dialogue!) between this particular story and RTD’s other TV shows, such as Bob and Rose and Years and Years. The subtitle game here is also strong (Arc of Affinity and The Finite Quest are just two) and Mortimer’s clear deferral to the views of POC writers in order to discuss Martha’s representation is progressive and important, especially in light of that recent Question Time clip doing the rounds on social media. It at least gives me hope for the future.

Concluding Thoughts

Mortimer’s debut Black Archive is an enjoyable and recommended read for fans wishing to delve deeper into the series 3 finale or even RTD’s tenure as a whole. His analysis is thoughtful and focussed and he combs the text for every detail he can find. Some further comparative texts may have bolstered his arguments but it functions just fine without them. I would also add that I’d like to see James Mortimer return to the range, if he so wishes, as I’d like to read more of his Doctor Who thoughts. And he doesn’t need a signet ring to ensure that he can come back either.

The Maths of Doctor Who #2 – “Don’t they teach recreational mathematics any more?”

The Ambassadors Of Math (twang!)

Over its long and varied history, Doctor Who has had a few mathematically minded writers producing scripts for the show. Perhaps you would say that the most prominent of these is Christopher H. Bidmead, who served as script editor during the show’s eighteenth season, the last to feature Tom Baker as the incumbent Doctor, and also produced three scripts for the show: Logopolis (1981), Castrovalva (1982) and Frontios (1984). The first of these concerns itself with a society of mathematicians holding the universe together (indeed, Toby Hadoke has jokingly referred to this serial as ‘The Maths of Death’ on his Who’s Round podcast), whilst the second one draws upon the mathematically themed artwork of M.C. Escher. The third one has some funky gravity shenanigans. A near hat-trick then.

Looking more recently at the revived era of the show, Stephen Thompson (sometimes credited as Steve Thompson) also has a background in mathematics, as he himself was a former maths teacher before entering television writing. He has previously talked to the media about how the plotting of Time Heist (2014) was somewhat based around the River Crossing Problem, a classic logic problem involving the transportation of a fox, a hen and a bag of grain, and the movie-style poster specially made for Journey to the Centre of the TARDIS (2013) also has strong M. C. Escher vibes (or Castrovalva vibes, if you prefer).

However, I would actually argue that the most mathematical writer is none other than the current showrunner himself, Chris Chibnall. Three of the episodes penned by him so far have made reference to three distinct groups of numbers: happy primes in 42 (2007), cube numbers in The Power of Three (2012), and pentagonal numbers in The Tsuranga Conundrum (2018). Even more curiously, if you look at the order of solo-penned Chibnall episodes (meaning we ignore Rosa (2018) here) then each of these episodes is separated by three episodes without a numerical reference.

Should this pattern continue into the next series of the show, then that would mean Spyfall: Part Two (2019) should be the next Christ Chibnall episode to have a numerical reference. Will this trend continue to hold? Watch this space. I am also willing to propose another conjecture on the back of this here:

Chris Chibnall is actually the most mathematical writer in the history of (televised) Doctor Who. So far.

In order to examine this suggestion, let’s travel back in time and have a look at each of these mathematical references from the aforementioned Chibnall-penned episodes in turn and see if we can learn anything along the way. After all, Doctor Who has its very roots in educating the kids about science and history during Saturday teatime viewing, but why stop at those subjects? Why not keep the learning streak going? Why break the habit of a lifetime? (Or is it several lifetimes?) I’d like to think one more lesson wouldn’t hurt anyone. I’ll start with the most recent of the three…

Count on a Bomb, It’s Fifty-One!

16711579-low_res-doctor-who-series-11
The Tsuranga Conundrum: Or How I Stopped Worrying And Love the Pting.

In the climatic moments of The Tsuranga Conundrum, the Thirteenth Doctor and Yasmin plant a bomb in an escape pod as part of a trap for the Pting, who has been menacing them throughout the episode by eating parts of the spaceship. It’s at this particular point that the Doctor decides to utilise Yaz for a bit of Random Number Generation (RNG)1:

DOCTOR: Pick a number between 1 and 100.

YASMIN: 51.

DOCTOR: Pentagonal number. Interesting.

DOCTOR: Get in that corner.

YASMIN: What was the number for?

DOCTOR: Number of seconds before the bomb goes off. I moved it forward a bit.

YASMIN: What? I would’ve gone higher!

Humans aren’t particularly random when it comes to picking a ‘random’ number, with some numbers being far more preferable than others. A reddit user asked people to pick a random number between 1 and 100 and after thousands of responses the top three responses (in third, second and first respectively) were 7, 77 and 69. People appear to have a fascination with the number seven as ‘the most random number’ (and indeed, some appear to have a juvenile sense of humour).

It also seems that more often than not people go for odd numbers rather than even numbers, and prime numbers rather than composite (non-prime) numbers. Here we can see that Yaz has also picked an odd number but it isn’t prime since 51 = 3 x 17, though it can be mistaken for being prime given that similar-looking numbers like 11, 31, 41, 61 and 71 are all prime. I hope to write more on random number generators and their use in the episode Extremis in a later blog post, but let’s get back on track here.

Perhaps frustratingly for a mathematician like myself, the Doctor never actually defines what a pentagonal number is within the episode. Whilst Chibnall in Series 11 could be seen to be harking back to the William Hartnell days with a triage of companions and alternating the adventures between sci-fi and historical (if you ignore the episodes set in the present day), he could go one step further by including such definitions to strengthen the ‘educating the kids’ part that here. But no matter, this is where I come in!

Before we actually get onto pentagonal numbers, let’s start off with a simpler but related group of numbers: the triangular numbers. Triangular numbers are the number of dots needed to make an equilateral triangle of increasing side length. This is more easily seen using a diagram so below here is one I’ve borrowed from Wikipedia. The first triangle (T1) has just the one dot for each side, the second triangle (T2) has two dots for each side so it needs three dots altogether, the third triangle (T3) has three dots for each side so it has six dots altogether, and so on. You may have also noticed that you can predict these by counting the first n whole numbers (1 = 1, 1 + 2 = 3, 1 + 2 + 3 = 6, 1 + 2 + 3 + 4 = 10, 1 + 2 + 3 + 4 + 5 = 15, etc).

First_six_triangular_numbers.svg
The first six triangular numbers. Source: Wikipedia.

Naturally, we can extend this to other shapes. The square numbers are similarly the number of dots needed to make a square of increasing side length, though you may also recognise them as the numbers you get when you multiply every whole number by itself (1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25, etc). And then we get to pentagonal numbers which are, as you’d expect, the number of dots needed to make a pentagon with increasing side length. Unfortunately, the general formula is not quite as straightforward as the previous groups; the nth pentagonal number is actually equal to (3n2 – n)/2. The first six of these are 1, 5, 12, 22, 35 and 51, so we now know that 51 is not just any pentagonal number; it’s the sixth pentagonal number.

Pentagonal_number
And the first six pentagonal numbers – Source: Wikipedia

This has left me somewhat annoyed because The Tsuranga Conundrum was the fifth episode broadcast but it was the seventh episode to enter production, though I suppose it’s the sixth appearance of Jodie’s Doctor if you include Twice Upon A Time. If you can find some other possible hidden meaning as to why it’s the sixth pentagonal number, then leave me a comment down below.

That’s The Power of Three

doctor-who-the-power-of-three.jpg
The Power of Three: Did you know… the BBC tried to see these cubes at £39.99 a piece!?!

Next up we have The Power of Three, an episode from 2012 that features the “invasion of the very small cubes”, as the Doctor quite succinctly puts it. Whilst the story is largely concerned with this unusually slow invasion and the Doctor having to spend time living on Earth with Amy and Rory, the maths reference here comes in right at the end of the episode’s final scene:

AMY: So that was the year of the slow invasion, when the Earth got cubed, and the Doctor came to stay. It was also when we realised something the Shakri never understood. What cubed actually means. The power… of three.

 

If you listen very carefully, you can still hear the audible groans of people who witnessed that last line to this day…

We’ve already talked about square numbers, the sequence of numbers where each integer is raised to the power of two, and similarly you can get the sequence of cube numbers, sometimes referred to as just ‘cubes’, by just raising to the power of three instead (13 = 1 x 1 x 1 = 1, 23 = 2 x 2 x 2 = 8, 33 = 3 x 3 x 3 = 27, etc). Given that the world we live in consists of three dimensions (at least, it did the last time I checked), an understanding of cube numbers helps us to understand space and volume as well, so it’s certainly handy stuff.

Mathematicians have been fascinated for centuries by what we can and cannot do with cubes. For example, it is a proven fact that there is no cube number that can be written as the sum of two other cube numbers. This is in accordance to Fermat’s Last Theorem, a maths problem that was only solved relatively recently in the history of maths by Sir Andrew Wiles in 1997, around 358 years after the problem was first proposed by Pierre de Fermat himself! This precise theorem was also referenced by the Eleventh Doctor during his Skype conference in The Eleventh Hour in order to demonstrate how intelligent he is by claiming to have ‘the real proof’ for it.

ByAFcZPIAAAHZ4e.png
The Eleventh Hour: A prime example of how an impromptu maths conference can save the world.

This in itself is a reference to the proposed existence of a more straightforward proof that Fermat could have potentially conceived, as he once famously claimed to “have discovered a truly marvellous demonstration of this proposition that this margin is too narrow to contain” – a hilariously outrageous statement for someone who hardly ever bothered to rigourously prove his mathematical discoveries (perhaps I’ll cover his biographical life in more detail within a future blog post – stay tuned!). Anyway, the proof devised by Wiles at the end of the twentieth century used mathematics far beyond what was known hundreds of years ago and so it seems that his rather simple proof either never existed (which is my personal belief) or it is indeed forever lost to the mists of time…

Unless you’re an alien time traveller from the planet Gallifrey, of course.

Another quite interesting fact is that it is impossible to ‘double the cube’, that is to geometrically construct a cube that has precisely double the volume of another cube, since the cube root of two is not a ‘constructible’ number. If you’d like to learn more about constructible numbers as well as the tragically ignored mathematician who discovered this truth, check out my previous maths blog post on Flatline and the number pi here.

Platonic Relationships

Cubes also belong to a rather select group of objects known as the Platonic solids. A Platonic solid is defined as ‘a regular, convex polyhedron’. To put this more plainly, that means any 3-D solid where every side is the same regular polygon (so the square sides on a cube for example) and that all the sides around the solid and all the angles within the solid are ‘congruent’, meaning simply that they are just the same size.

The precise origin of this concept is unknown as it can be traced as far back as to several ancient civilisations, and even authorship of the idea within Ancient Greek society is disputed, with some sources suggesting they should be referred to as Pythagorean solids rather than Platonic. There are only five Platonic solids: the cube (or hexahedron), the tetrahedron, the octahedron, the icosahedron, and the dodecahedron.

4634757632_8174c6db41_b.jpg
The Gang’s All Here: The Five Platonic solids as dice.

Any fans of board games or role-playing games might recognise these shapes as the shapes of dice used when playing these games: a tetrahedron is a four-sided die, a cube is a six-sided die, an octahedron is an eight-sided die, a dodecahedron is a twelve-sided die, and an icosahedron is a twenty-sided die. Their natural geometric properties make them ideal for games of chance where the probability of rolling each number should be equally likely, and also you might find them quite aesthetically pleasing to look at!

The mention of a dodecahedron also brings up an unexpected connection to the 1980 Tom Baker serial Meglos, a story that sees a shape-shifting cactus from Zolfa-Thura attempting to steal the power source of the planet Tigella, which happens to take the shape of a dodecahedron. The power source was originally meant to be in the shape of a pentagram according to the writers Flanagan and McCulloch, but was changed at the insistence of the then-script editor Christopher H. Bidmead.

It is perhaps worth observing that a pentagram is a star with five points which itself has symbolic links to the societies of Ancient Greece, and this may have then prompted the mathematically-literate Bidmead to suggest a Platonic solid instead. He also chose the dodecahedron; the only Platonic solid made up of five-sided shapes, those being regular pentagons. Arguably, this is his way of keeping to some of the writers’ original idea whilst still changing it to something he much more preferred.

The story of Meglos also concerns the ongoing dispute between two opposing groups: the scientific Satants, who utilise the Dodecahedron as a source of energy for the society, and the religious Theons, who believe the Dodecahedron is a crystalline gift from the great god Ti. This may also have further stimulated Bidmead to choose a Platonic solid for the shape that acts as a power source but also an object of worship since archaeologists and anthropologists have referred to the Platonic solids as “sacred geometry”.

The group of Platonic solids are recognised by cultures throughout history as having ‘divine properties’, and were well known amongst famous scientific societies, like the Ancient Greeks and Babylonians, as well as famous scientific thinkers such as Leonardo da Vinci. The five solids were believed to represent the four major elements and the universe: the tetrahedron represents fire, the cube represents earth, the octahedron represents air, the icosahedron represents water, and the dodecahedron represents the universe2. It seems unsurprising yet again that Bidmead chose this particular solid over the other four candidates.

29c77111d77c7d55eae9285ddca60ef8
The Sacred Texts: Da Vinci’s drawings of the five Platonic solids, and a sphere.

This observation actually rather neatly brings us back to The Power of Three once again, which started the discussion of this entire subsection. Here, the plot in this story involves the Shakri using cubes to gather knowledge about planet Earth and the behaviour of the human race before using this information to invade more tactically. Could it be that the Shakri themselves knew about the history of Earth civilisations that led them to choose the cube as the symbol of their invasion of Earth, or does the cube represent something entirely different to them? And could it be that the writer Chris Chibnall consciously chose the shape of the cube here, given that it symbolises the earth, further cementing my theory that he is in fact Doctor Who’s most mathematical writer?

The Answer To Life, The Universe, And Also The Pub Quiz

13966980461_22846b733e_b
School of Hard Suns: The pub quiz trivia knowledge here is absolutely on point.

Lastly, we come to what is probably the most overt maths reference in the history of modern Who so far (at the time of writing this Series 12 has yet to broadcast so this could well change in the near future), and it comes from Chris Chibnall’s Doctor Who writing debut. The episode 42 (2007), which incidentally is the only Doctor Who episode title to consist of solely just a number3, takes place in faux real time (oxymoron much?) as the Tenth Doctor and Martha have just 42 minutes to help a cargo spaceship called the SS Pentallion avoid crashing into a nearby sun.

To do this, Martha teams up with crew member Riley to work their way through thirty deadlocked doors in order to reach the ship’s controls, and each door will only open if they correctly answer a pub quiz question set by members of the crew. Almost nine minutes into the episode’s 45-minute runtime and we get the following dialogue exchange that has been immortalised, if not quite correctly transcribed, by this selection of GIFs on the Official Doctor Who Tumblr page4 .

RILEY: Find the next number in the sequence: 313, 331, 367, …? What?

MARTHA: You said the crew knew all the answers.

RILEY: The crew’s changed since we set the questions.

MARTHA: You’re joking.

DOCTOR: 379.

MARTHA: What?

DOCTOR: It’s a sequence of happy primes. 379.

MARTHA: Happy what?

DOCTOR: Just enter it.

RILEY: Are you sure? We only get one chance.

DOCTOR: Any number that reduces to one when you take the sum of the square of its digits and continue iterating until it yields one, is a happy number. Any number that doesn’t, isn’t. A happy prime is a number that is both happy and prime. Now type it in! I don’t know, talk about dumbing down! Don’t they teach recreational mathematics anymore?

At last, we have an episode that provides the definition of a mathematical concept mentioned within the actual dialogue – hurrah! Education is back on the agenda. But perhaps you still find this a little too technobabble for your tastes, so let’s expand a bit on the explanation given by the Doctor. And since I’ve already covered what prime numbers are back when I discussed The Tsuranga Conundrum earlier so I’m going to focus exclusively on happy numbers here.

The best way to see how happy numbers work is to go through an example so I’m going to pick the number 28. To check if 28 is happy, I need to add the square of each digit in 28 in an iterative sequence and see if we reach the number one. You should already know what square numbers are because I’ve covered those earlier in the blog as well (Isn’t planning a wonderful thing?).

22 + 82 = 2 x 2 + 8 x 8 = 4 + 64 = 68

It is clear that 68 is not the number one, so we have to repeat the process again:

62 + 82 = 6 x 6 + 8 x 8 = 36 + 64 = 100

Again, this isn’t the number one so we try one more time:

12 + 02 + 02 = 1 x 1 + 0 x 0 + 0 x 0 = 1 + 0 + 0 = 1

This shows not only that 28 is a happy number, but also every number along this sequence is also happy, meaning 68 and 100 are also happy numbers. And since the order of the digits does not matter when calculating these, it is also clear that 82 and 86 are also happy numbers. Below I’ve borrowed a handy tree diagram from the STEM Learning website that shows all of the happy numbers between 1 and 100.

happy_numbers_graphic
Happiness Will Prevail: All of the happy numbers between 1 and 100.

But what about the unhappy numbers, such as 2, 16, and 89? Well if you try this iterative process of adding the squares of digits with them, you will end up in a never-ending sequence of numbers, as you will never reach the number one. I’ve also included this other handy tree diagram from the STEM Learning website that shows all the unhappy numbers between 1 and 100. Notice that all the numbers pictured below all eventually end up in a cyclical loop shown by the dark blue numbers at the centre: 145, 89, 58, 37, 16, 4, 20 and 42. Rather tragically, it seems that 42 is in fact an unhappy number5. We can cap off this explanation by recalling that “a happy number is a number that is both happy and prime”.

unhappy_numbers
Side by side with sadness: All the unhappy numbers between 1 and 100, and a few greater than 100 too.

And as if that wasn’t enough, Chibnall’s scripting of episodes entitled 42 and The Power of Three perhaps pre-empted a previously undiscovered link between the two ideas, that is until 2019. Since 1954, mathematicians have been able to write every number between 1 and 100 as the sum of three cubes, except for one particular number – 42. Whilst some have conjectured (starting with Roger Heath-Brown in 1992) that every whole number can be written as the sum of three cubes this has yet to be proven, but a recent discovery has brought some hope. A computer algorithm in September 2019 found the first ever set of three cube numbers that sum to 42, as if you look at the thumbnail below you can see they are pretty large ones as well – no wonder it took us so long to find! There’s still much work to be getting on with in the world of number theory but for a small group of mathematicians on that day of discovery, 42 was indeed the answer to Life, the Universe and Everything.

Teaching Recreational Mathematics In A Fun But Irreverent Way

By examining three episodes penned by Chris Chibnall, we have ended up discussing triangular, square and pentagonal numbers, cube numbers, as well as happy numbers and prime numbers. We have also talked about the importance of the cube as one of the five Platonic solids, linking it to the 1980 serial Meglos, which also features a Platonic solid and was script-edited by a writer with a penchant for science and mathematics, and then discovered that the cube itself is an ancient symbol for the earth element. All of this has led us to the lament of the Tenth Doctor, and the title of this very blog: “Don’t they teach recreational mathematics anymore?”

It’s hard to be sure what he exactly means by the term ‘recreational mathematics’ here; some would even argue this is an oxymoron. I am somewhat amused by the definition for this term given by Wikipedia: “Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity”. Evidently whoever wrote this had not really considered the likes of Fermat who, despite becoming one of the big names within mathematics, largely played around with numbers in order to pass the time. The term ‘recreational’ seems to allude to an idyllic notion that maths can be an enjoyable pastime and/or something done for non-academic purposes6, like trying to solve BBC Radio 4’s Puzzle For Today, or just simply finding unusual number patterns and sequences, such as happy primes for instance. I personally rather enjoy thinking and learning mathematics, but it sadly seems rare that other people feel the same way.

Nevertheless, while the definition of ‘recreational mathematics’ seems to leaves us in ambiguity, I feel the definition of Chris Chibnall as a ‘mathematical writer’ for Doctor Who is actually far from being ambiguous, most certainly when stood in comparison to the pantheon of writers throughout the show’s 56-year history (and counting!). If you still doubt my claim that Chibnall is indeed the most mathematical writer, rather than the likes of Bidmead or even Thompson, then consider my one final point on the matter.

Perhaps when, as the SS Pentallion hurtles towards an all-consuming sentient fireball, the Tenth Doctor cries out about the lack of recreational mathematics in the education of those from either the 21st or 42nd centuries, it isn’t actually the vain, pompous and arrogant voice of the Tenth Doctor speaking here. Perhaps instead, it is the vain, pompous and arrogant voice of the then future Doctor Who showrunner Chris Chibnall bleeding into the script right here, as he tries to bring the show back to its early educational roots7. I hope he hasn’t changed his mind.

[UPDATE: The episode Spyfall: Part Two featured an early counting machine, Charles Babbage and The Enchantress of Numbers herself, Ada Lovelace – I see this as an absolute win!]

All references are linked or specified throughout the article.

Footnotes

1 All episode quotes throughout this blog are my own transcriptions based on viewing them.

2 For more background on platonic solids as ‘sacred geometry’, have a read of this Mathematics Magazine blog post.

3 The next closest in my mind is 100,000 BC as an alternative serial title for An Unearthly Child, but this itself is a year rather than a number. Also, Chibnall is the only writer to have two episodes with a number in the title (42 and The Power of Three).

4 Don’t forget to click below to reblog the Official Doctor Who Tumblr page.

5 For a bit more background to happy and unhappy numbers, have a read of this STEM Learning blog post here.

6 For more content on recreational mathematics, have a read of this New York Times article.

7 If Chris wants to combine the show’s educational roots with the demands of a modern audience – is there Space For Chib ‘n’ All?

My Top Ten Games of 2019

We briefly interrupt your regular Doctor Who content on this blog for something entirely different. Simply put, I played a good number of quality video games in 2019 and so I wanted to share a selection of my favourites. The rules are very simple: any video game that I personally played and finished for the very first time in the calendar year 2019 is eligible, regardless of what year it actually first came out. Nothing else matters. Hence why it’s my own top ten. This should be obvious. However, I’ll start off with some honourable mentions…

Honourable Mentions:

  • Abzû – This is a short, sweet, serene swimming adventure where you save an underwater civilisation to the sounds of a symphony orchestra. It is also great for learning about different fishes and for some meditation on your telly.
  • Donut County – A wonderfully silly physics game where you move a hole in the ground around to solve puzzles, and then also swallow everything you see into the ground. And all because of a selfish racoon. Has ‘millennial humour’ written all over it.
  • Firewatch – I didn’t quite fall in love with this narrative thriller as the critics seemed to but it was certainly quite innovative and atmospheric, delivered some tense dramatic moments and Delilah was played beautifully by Cissy Jones – probably one of the best video game characters of the decade.
  • Ghost Trick: Phantom Detective – A hidden gem released late in the life of the Nintendo DS, but you can download it on iOS! Ghost Trick is a detective puzzle game that has you solving your own murder… as a ghost. You travel around locations by possessing various objects in the environment and have until sunrise to solve the murder mystery. This game also has a dog and his name is Missile and he is a Pomeranian and he is pure and wonderful and innocent and loyal and heroic and HE IS DEFENDED.

 

With those out of the way, onto the top ten…

#10 – Uncharted 2: Among Thieves

ac19838c1b3b16179096bfcee9512cca

How long have I ignored this: About ten years. First released in 2009.

What’s it about: You play as Nathan Drake, a rough-and-ready treasure-hunting everyman on his globe-trotting exploits, following in the footsteps of the world’s greatest explorers. Whilst the first game had you following Francis Drake’s long-lost treasures, the second here involves uncovering a secret that Marco Polo took to the grave. Future instalments in the franchise involve the travels of Lawrence of Arabia and Henry Avery (already we have two Doctor Who links!).

Why I like it: I grew up playing the Crash Bandicoot games in the late ’90s so I already have a lot of love for the developer Naughty Dog – I felt it was about time to investigate what games they had made more recently. I’m also not a huge fan of shooting games in general but the game surprised me with its variety of gameplay, strong pacing, and a  ripping yarn that seamlessly carries you from set piece to set piece. This one truly made me feel like I was living the action-adventure life of Indiana Jones: solving puzzles, scaling lost tombs and fighting bad guys. The entire sequence of events involving a certain train ride around halfway in is one of the most exciting and memorable action sequences I’ve seen in any video game too.

#9 – GRIS

ss_631d99cc6462cce94081032b7e600a6b87c3f7d3.0

How long have I ignored this: Less than a year. First released in 2018.

What’s it about: Gris is a linear-style puzzle-platformer where you play as a young hopeful girl (presumably called Gris) on a metaphorical quest to find herself after a traumatic experience. She repeatedly encounters an ever-shifting dark figure and the game has achievements that refer to The Five Stages of Grief. There is no dialogue and so the story is entirely conveyed through image and sound.

Why I like it: Despite its brief 3 to 4 hour runtime, I have not stopped thinking about this game all year. It looks like a watercolour painting has come to life and absorbed you into its world, and this coupled with a magnificent orchestral score utterly sells the beauty, torment and raw emotion of this narrative. Whilst I do think it could have also worked as animated short, the choice to make this a single-player game without any fail-state allows it to become a meditative experience, to think and reflect at largely your own pace; I think that’s really lovely. Any of those reviewers bemoaning “yet another indie game about mental health” can get in the sea to be quite honest.

To think that a studio primarily consisting of three guys from Barcelona produced one of the most visually striking video games of the decade is in itself a triumph and seeing it nominated for Artistic Achievement at the BAFTAs alongside Red Dead Redemption 2, God of War and Spider-Man was quite something. If you watch the trailer for this and like what you see, then it’s almost certainly a game for you as well.

#8 – Donkey Kong Country: Tropical Freeze

2018-05-12_ent_40764097_I1

How long have I ignored this: Five years. First released in 2014 on something called a WiiU. You may have heard of this obscure gaming device at some point in recent years.

What’s it about: Donkey Kong and his family are having a birthday party but then suddenly Arctic animals called ‘the Snowmads’ invade their island and you get blown off it by A Very Strong Wind. What follows is a traditional side-scrolling platformer adventure across six colourful islands in order to reclaim your homeland. It’s the fifth game in the franchise and was developed by Retro Studios, who are perhaps best known for the Metroid Prime games.

Why I like it: Right, let’s get this out the way first… Tropical Freeze is a stupid name. I do wish they had thought of something better. However, this may well be the finest traditional 2D platformer game I have ever played. And I’ve played a lot of those. A LOT. The art of a great platformer for me is to feel at one with the character on screen; to intuitively feel that the character responds to your controls, that every interaction feels logical and every mistake does not feel unfair. Tropical Freeze, in all these respects, handles beautifully.

It has an embarrassment of riches when it comes to ideas and every level introduces, develops and then masterfully synthesises these ideas before discarding them in favour of something else entirely in the next stage. That’s top tier game design, and this video by Game Maker’s Toolkit shows a specific example of what I mean here. This game is also challenging, to the point where repeated deaths nearly made me throw the controller across the room, only abated by the fact that I felt I was able to have prevented each mistake. The game is vibrant and colourful – you see sandy beaches, treacherous mine shafts, tropical savannahs and underwater kingdoms, all looking quite gorgeous. The accompanying soundtrack by David Wise, one of Britain’s best gaming composers, is superb. It heartens me to see that the rerelease on Switch has sold more copies that the original release on WiiU – more people playing this title is definitely a good thing.

#7 – Baba Is You

ss_9eadb1cdc09f574d49d32a722d7bda5813c96a64.1920x1080

How long have I ignored this: Came out this year. Got it at launch.

What’s it about: A puzzle game unlike anything you have ever seen. You play as Baba (at least to start with) and you have to get to the flag to win each level (at least to start with). Every level has blocks with words on them, and when these are pushed together they make rules. For example, WALL IS STOP means you can’t go through a wall. But you can move these blocks around the level in order to make and break rules that allow you to complete the level. What follows is a puzzle game that has you shifting the fabric of reality in order to reach your goal. If you are still unsure, watch the opening few minutes of this.

Why I like it: I’m always on the look-out for exciting and original indie games, and this fits the bill nicely. The game itself was the brainchild of a lone Finnish game developer who devised the concept from a game jam event, and now he’s developed it into a full game. It’s unique and clever and I have never ever seen anything like it. It is very challenging, and I found the difficulty curve of levels too steep at times, but that’s arguably part of the allure. I have shown it to a few friends and have been delighted when they solve a puzzle in a completely different way to myself; we all think differently. There is an abundance of levels, 10% of sales go to the developer’s charity and it’s just brilliant stuff. I expect this to sweep the awards for game design, innovation and debut game in the New Year.

#6 – Undertale

1_VqRHEkSrfkyjpVRmAL4n5A

How long have I ignored this: Four years. First released in 2015.

What’s it about: You are a human boy or girl who has fallen from the world of humans and into the world on monsters. What follows is a traditional SNES-era RPG à la Earthbound as you attempt to return back home. But will you fight the monsters you encounter on your journey, or will you show mercy?

Why I like it: From various avenues, I have been told that I need to play Undertale – I got around to it eventually. It was without question one of the funniest and most original games I have played in years. Honestly, some parts of this game had me crying on the floor with laughter. Its subversion of expectations and brilliant use of meta-humour are its greatest strengths. By designing an entire game around the concept of morality, where it is easy to make bad decisions and it is difficult to do the right thing is a stroke of genius and has ensured this game’s status as a cult classic. I also understand there are several things I never encountered in my first playthrough from researching online and I was a bit slow picking up on the whole morality motif so I intend to revisit the game soon to appreciate it that bit more. The thought of replaying it one day fills me with determination. And if you haven’t already played it, do. At least to experience the wonderful likes of Flowey, Papyrus and Sans.

#5 – Untitled Goose Game

Screen-Shot-2019-11-17-at-6.33.19-PM-e1574033818362

How long have I ignored this: Got it at launch. Came out this year.

What’s it about: It is a beautiful day in the village, and you are a horrible goose. A comedy slapstick puzzle game where you go around completing your list of tasks that aim to annoy just about every person you meet. And why not, they probably voted for Brexit anyway. 

Why I like it: The memes. SO MANY MEMES. For around a month you couldn’t go anywhere without seeing some meme about the eponymous Untitled Goose causing havoc to people, both real and fictional. But also, more seriously, it’s another really good indie game from 2019. Comedy in video games is hard, since you don’t always have control of timing, delivery or pace, and to successfully engineer multiple slapstick moments that depend upon the behaviour of the player is a commendable achievement. There aren’t many games where you play as an annoying piece of poultry either so the entire premise is just inspired; the execution is also polished and sublime. It may be a short experience but I definitely see myself honking at Middle Englanders far into 2020 and perhaps even beyond.

#4 – What Remains of Edith Finch

what-remains-of-edith-finch-1

How long have I ignored this: Two years. First released in 2017.

What’s it about: You play as the titular Edith Finch as she returns to her family home for the first time in many years. What follows is three-hour narrative experience that unfolds like a Lovecraftian fairy-tale – highly innovative, surprisingly mature, and utterly unforgettable.

Why I like it: I saw some strong reviews for this title upon its release in 2017 but what really caught my eye was that in 2018 it received seven nominations at the video game BAFTAs (these included Game Design, Innovation, Original Property, Narrative, Performer and Original Music) and then proceeded to go home with one – the Best Game category. That makes it the first indie game and the shortest ever video game to take home the top prize; I was rather intrigued.

Edith Finch perhaps falls into a subcategory of games known as ‘walking simulators’, which typically involve walking around an environment, listening to dialogue, and sometimes interacting with objects. They are typically maligned for being disproportionately focussed on narrative over any substantial gameplay and using the banner of “This is Art” to deflect criticism at the game.

However, I have played a number of really good so-called ‘walking simulators’, such as The Stanley Parable, an ingenious satire on the narrative tropes in video games, guided by an omnipresent narrator voiced by Kevan Brighting (who, Doctor Who fans, was the uncredited voice of the Bank in Time Heist), as well as Gone Home, another brilliant game that sees you uncovering the mystery of your abandoned family home. The aforementioned Firewatch also fits into the category.

It is difficult to explain why I love it so much without spoiling what happens and I just honestly recommend you go in completely blind. All I can really say is that its magic lies in the use of the gameplay to communicate narrative, emotion and character. One of the latter parts of the game is certainly one of my favourite sequences ever in a video game, as it deftly describes something that I’d struggle to put into words. It truly is a powerful, surreal and sublime piece of art. I hope to share this one with as many people as I can because I really want to talk about this one more. It also somewhat incidentally stands on the shoulders of the next game on my list…

#3 – Journey

22ed9661fb7fa1bb59f0b57753f5d6b3

How long have I ignored this: Seven years. First released in 2012.

What’s it about: You are a nameless traveller, and you go on a journey. That’s pretty much all there is to it.

Why I like it: Okay I’m actually kinda cheating here because I first played this at a friend’s house years ago but I honestly don’t recall any of it. Why it never left any impression on me then but subsequently moved me on quite a personal level now I’m not entirely sure but this is a powerful and emotive experience and comes highly recommended to anyone, whatever your gaming background. Again, like with Gris, this is not so much a game but more of a space that absorbs you right in, a space you inhabit to close off the outside world and be at one with the experience. The whole design philosophy of this game is so ingenious you don’t even realise the game is providing you subtle visual and musical cues which are effectively communicating where you need to go and what you need to do, but not a word is spoken throughout. It is perhaps the first video game that can truly claim not just to be an entertainment product but a piece of interactive art. It was made to be experienced.

The awe-inspiring music here is composed and arranged by Austin Wintory, who has the distinct honour of producing the first video game soundtrack ever to be nominated for a Grammy. In fact, they had to rename the category to Best Soundtrack For Visual Media in order to include it (and sadly it lost to The Girl With The Dragon Tattoo). I have returned to this game multiple times this year whenever I have felt anxious or worried about things and it always been remarkably therapeutic for me, like it somehow clears away the leftover thoughts in my mind.

I also remember some uproar back when it swept the awards scene in 2013; most notably for winning the video game BAFTA for Online Multiplayer against several dedicated online action/shooter titles. The way you interact with other players is pretty special (I won’t spoil it here if you don’t know) but it rather cleverly circumvents the usual toxicity you find in most other online multiplayer titles. And it totally deserved all the recognition it got. One of the very best games of the decade.

Okay, this next one utterly surprised me.

#2 – The Last of Us

2014_06_09_TLOU_RemasteredE3Trailer_Blog960x540_eed770f71049a868341614cae060d37f

How long have I ignored this: Five to six years. The main game released in 2013 and the DLC titled Left Behind released in 2014.

What’s it about: You follow the post-apocalyptic adventures of Joel and Ellie, an unrelated father and daughter duo, as they travel across America trying to survive the harsh, infected worlds outside the main pockets of remaining society. There is much, much more to the story here, but I’ll leave that to the game itself. 

Why I like it: This game should be a textbook example of Games That I Do Not Like. It’s about the zombie apocalypse, even though the game never refers to it as such, instead using terms such as The Infected to refer to any zombies. The gameplay is largely focussed on combat, shooting and crafting, all of which don’t particularly interest me. And lastly, it firmly belongs in the genre of survival horror, and I personally hate almost anything to do with that – I am easily scared. So, what on earth happened here?

Well to start off, it’s developed by Naughty Dog, whom I’ve already discussed earlier regarding Uncharted 2: Among Thieves. It just goes to show that you should always look at who is creating your art, not just what it’s about and who’s in it. But whilst the Uncharted series is focussed on blockbuster action-adventure escapades, here The Last of Us delivers an entirely different experience, one in which the resources are scarce, stealth is essential, and the silence is deafening. At first, I found it okay, and then when the difficulty ramped and the horror had really settled in, I really didn’t think I was enjoying it, but I persevered through it regardless. And once the credits rolled, I suddenly found myself hitting New Game+. With the anxiety of what might happen next now gone away, I started to stop worrying and learned to love the game, its hauntingly beautiful world, its well-refined gameplay, its crescendo of character beats; I started to see the game more clearly.

The game rather effectively uses the all-consuming apocalypse to bring out big emotions within the characters you encounter – particularly with the relationship with Joel and Ellie. The performances given by Troy Baker and Ashley Johnson are true tour-de-forces and their interactions with one another are at the heart of this game. I would actually go as far to argue that Ellie is perhaps the greatest video game character of all time; loyal, fierce, vulnerable, a sarcastic wit, and curiosity for the society she never knew. She has a book of puns to bring levity to the situation, a no-nonsense attitude to Joel’s paternalistic bullshit, and a very real fear of being left on her own. At times, she perhaps seems more real than most people I have met.

This all comes down to the well-crafted narrative from the game’s creative director Neil Druckmann who, in a decade that has increasingly seen games focus on online interaction with peers, adding in-game monetisation and manufacturing more addictive gameplay, has instead focussed on crafting an emotionally resonant experience, one that covers the whole spectrum of emotions as well. You can never quite tell how things are going to turn out as you progress further and further. I recall him being presented the video game BAFTA for Story in 2014 by Steven Moffat, and now realise in retrospect that on that stage were two rather brilliant writers, who have each redefined their respective mediums.

As we head into 2020, Naughty Dog plan to release their long-awaited sequel to this game and it’s surely going to be one of the biggest games next year, certainly the most-anticipated. I can now see what the hype is all about, and I think I very much intend on picking up the sequel as soon as I possibly can. But for now, I think the line that sticks with me is the motto from Ellie’s favourite comic book series, Savage Starlight: “To the edge of the universe and back. Endure and survive.”

#1 – Chibi-Robo!

Chibi-Robo-Banner-1024x512

How long have I ignored this: First released in June 2006 for the Nintendo GameCube. That makes it thirteen years old this year. That’s basically retro.

What’s it about: You play as Chibi-Robo, a tiny robot purchased by the Sanderson family to improve the quality of their lives. You interact with the family and complete household chores, such as picking up litter and scrubbing muddy footprints, which rewards you with Happy Points. These can then be used to purchase tools and upgrades so you can explore more of the house. You help the family during day phases, and then at night, the household toys come to life à la Toy Story, all with their own problems for you to solve.

Why I like it: I first read about Chibi-Robo! in an issue of Official Nintendo Magazine (F to pay respects) covering their ‘100 Greatest Nintendo Games’, I’m think it came in at number 87 or something. I loved that magazine and read every issue cover-to-cover, and I’m sure a fair amount of my lexicon can be traced back to certain writers in ONM. Anyway, I was drawn to its unusual description as a game that was much more than housekeeping and noted that it was a first-party title published by Nintendo themselves. I acquired a copy many years ago, before my university studies in fact, and it has now become one of most rare and expensive collectables I own. But this year I finally sat down to find out what it was all about.

The start itself is wacky; you’ve been purchased as a present by a 1960s American household where the family unit consists of: a lazy, unemployed geeky father, an overworked, under-appreciated housewife, a daughter who only dresses and speaks like a frog, and a sassy dog. You also quickly learn that for some miraculous reason all the household toys come to life at night when no-one is watching. These include a stuffed caterpillar suffering from unrequited love, a landbound pirate who longs to search for buried treasure, and an egg-shaped toy soldier suffering from post-traumatic stress disorder, to name but a few. Like I said, it’s pretty wacky but also strangely charming. This game is full of charm and wit and soul.

As you accumulate Happy Points by completing chores and finding lost objects, you’ll gain new abilities like a helicopter to fly across ledges and a blaster to activate switches and attack spiders. Completing certain tasks allow access to new parts of the house and advance the overarching plot-line of the game. There also a considerable number of side-quests and mini-games to complete if you want to see everything there is within the game.

I’m not sure I can even coherently explain the plot here in less than 2000 words but over the course of the fifteen hours it took me to finish it the game’s storyline covered at least the following themes (in no particular order): the American Dream, childhood poverty, divorce, substance abuse, unrequited love triangles, death in childbirth, the responsibility of foster parents, contact with alien lifeforms, grief, loneliness, and time-travel in order to create a better future. And this game is rated 7+. The words ‘only in Japan’ spring to mind.

29143-menu-Chibi-Robo
This is Jenny, and she reaaaaaaally likes frogs. Like a lot. Ribbit.

But what holds the game together is the protagonist himself: the titular Chibi-Robo! He doesn’t speak a word, despite all the conversations he somehow manages to initiate, and any decisions he must make result in you selecting either a tick or a cross from above his head. Occasionally, the game would give you either two ticks or two crosses to choose from, hilariously preventing you from making narratively inappropriate decisions. But his willingness to help everyone he encounters and put himself at risk to evil robot spiders that seem to be lurking about the house, make him a brave and pure-hearted individual; despite being entirely metallic. Like I’ve said, he is utterly charming, and his adventure with the Sanderson family is a rollercoaster ride throughout.

The true tragedy of Chibi-Robo! is that it was unrecognised and unloved. Released in the dying months of the Nintendo GameCube, which was Nintendo’s least successful console to date, the game naturally sold poorly; around 100,000 copies across the entirety of Europe. The franchise got a spin-off title the following year on Nintendo DS called Chibi-Robo: Park Patrol but it never released here in Europe and sold poorly in America due to being a Wal-Mart exclusive. It then got a direct sequel to the first game in 2009 set in the house of frog-loving Jenny, now all grown-up, also on Nintendo DS, but unfortunately this was actually never released outside Japan.

A downloadable-only spin-off title called Chibi Robo! Let’s Go, Photo! for the Nintendo 3DS was released in 2014 but this strayed away from the series’ roots in favour of gimmicky camera-use and augmented-reality features. The most recent game in the franchise was Chibi-Robo! Zip Lash, released in 2015, which makes it the second game in the series to get a physical release in Europe over nine years after the first title came out. Frustratingly, it was a somewhat generic puzzle-platformer that simply used the title character. It didn’t do well with sales or reviews. The game’s producer said in an interview that this might be ‘the last chance’ for the franchise. Understandable, given all the effort they’ve put into releasing these games. Nintendo has evidently put a lot of effort into marketing the franchise to Western audiences whilst remaining true to the series’ roots.

This here then is why Chibi-Robo! takes my number one slot. For the great video games that pass us by unloved and unnoticed. For the franchises mishandled and misrepresented by those who simply don’t know what to do with them. And for the many, many games that people buy each and every year, only to remain upon their dusty forgotten shelves. Which I suppose not just goes for the games but equally the CDs, and the DVDs, and the books as well. Longing to be read, watched, heard and played; to be worn away from repeated use. Here then I hope that one day, eventually, these things will find their fans. After all, everyone wants to be fanatic about something.