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

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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

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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

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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

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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

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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

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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

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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

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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

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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!

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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.

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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.

Review: The Black Archive #32 – The Romans by Jacob Edwards

Key Facts:

  • Black Archive Entry: No. 32, written by Jacob Edwards
  • Based on the Story: The Romans (No. 12).
  • Writer/Director: Written by Dennis Spooner. Directed by Christopher Barry
  • Key Themes: The introduction of comedy in Doctor Who; the representation and accuracy of Roman history; the counterculture of the 1960s; an episode-by-episode analysis of the writing, production and execution of The Romans.
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The Romans: If music be the food of comedy, play on. Or some words to that effect.

The Review

For me, Dennis Spooner taking over from David Whittaker is as important as Patrick Troughton taking over from William Hartnell within the history of Doctor Who. In each case, the successor had to go beyond the style of their predecessor, to redefine what the show and the character were about respectively, otherwise it would not stand much chance continuing once they had long gone. As such, I am particularly fond of The Romans and The Time Meddler by Dennis Spooner, as this is where I can start to recognise the roots of the show that I know and love today. With this in mind, I had high hopes for Jacob Edwards’ critical monograph on The Romans. It did not disappoint.

Many of the strongest entries in The Black Archive range I have encountered so far open with a short introduction that encapsulates why their chosen episode is of particular interest to them and hence ripe for analysis; this one is no exception. Edwards’ astute observation that Rome wasn’t built in a day but The Romans more or less was, and yet it still endures to this day really sets the tone for the analysis to come. Over a respectable nine chapters, he explores the episode’s use of comedy and whether it endures to this day, its use of history and whether it’s entirely accurate, the episode’s relationship with 1960’s counterculture (covering race, class, gender, sexuality, second-wave feminism and disability), and finally an episode-by-episode critique of the finished product.

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Inferno: We didn’t start the fire. It was always burning, since Nero was gurning.

The analysis is strong, providing a great deal of insight into the influences upon the scripting process, the production decisions that forever changed the direction of the show, and the varying attitudes to the text over a period of fifty years. Edwards’ pool of reference points is also comprehensive, drawing upon a wide range of media that depicts Ancient Rome (I, Claudius, A Funny Thing Happened on the Way to the Forum, Quo Vadis, Carry On Cleo, Gladiator and the Asterix books!). He also makes ample references to the works of Tacitus and Suetonius who both reported on the morally reprehensible behaviours of the emperor Nero, yet also highlights the reasonable possibility that these were exaggerated or malicious lies (though I hardly find this comforting). There are also once again the seemingly compulsory references to Elizabeth Sandifer’s TARDIS Eruditorium and Tulloch and Alvarado’s The Unfolding Text.

I only had a few minor critiques of the finished work, all regarding the structure of the text. Firstly, the last chapter provides Edwards’ personal viewing analysis of The Romans and whilst he does provide good commentary… It felt like a ‘cheat’ chapter. If all the other Black Archive entries wrote thirty pages commenting on their episode’s writing, direction, production and execution in such a standardised format then the overall range would I feel suffer as a result. The sudden change from matter-of-fact subheadings (e.g. Acting and Characterisation) in the first half of this chapter to far more witty and thematic subheadings (e.g. Ashes to Ashes, Farce to Farce) in the second half is also jarring.

This brings me to the book’s overall structure where the first seven chapters combined are as long as the final two chapters.  I personally would have collected these first seven as two broader chapters examining the comedy (1-3) and then the history (4-7) within the episodes, allowing for a more consistent pace of chapters and potentially provide more opportunities for the witty subheadings that help punctuate each chapter, though perhaps this is more subjective. As I said, these are minor critiques.

Concluding Thoughts

To paraphrase the second episode title from The Romans itself, all reviews lead to a conclusion. This is a delightful entry in The Black Archive series of monographs and it comes highly recommended, even to those who may even not be too fond of the episodes themselves. Edwards’ analysis is unafraid to critique the episodes’ shortcomings on racial and disability representation but also quite successfully argues that The Romans was indeed a key turning point in the Doctor Who’s unfolding history and recognises why its quality has endured long past its production sell-by date. The Great Fire of Rome was set alight thousands of years ago, but it is The Romans that still burns bright to this day.

The Maths of Doctor Who #1 – “I don’t mean edible pie, I mean circular pi.”

Dissecting The Narrative

As I recall, Flatline (2014) was the first episode of the Capaldi era that I didn’t watch on the live broadcast. Rather than tune into the Doctor and Clara’s latest adventure, I was too busy having an adventure of my own in a restaurant, somewhere in Exeter, with three Daleks (who were terrifically friendly) and Polly Wright herself (who was terrifically bonkers). A few hours earlier we’d just wrapped on a very successful mini-convention event that I helped organise at the university and we’d decided to go out for a meal to celebrate. It remains possibly the best excuse I’ve ever had for missing an episode of the show.

Naturally, the episode that I missed had to be a really good one. Jamie Mathieson quickly established himself as one of my favourite writers of the revived era with his first two episodes, Flatline and Mummy on the Orient Express (2014), both of which are full of inventive ideas, memorable characters and some pretty good jokes along the way. No wonder he topped the Doctor Who Magazine poll for the best writer of Series 8 then. There are numerous ideas and themes to dissect (much like the monsters themselves did) in Flatline, but there’s one scene in particular that I’d like to dissect myself.

Around the halfway point in the episode, whilst Clara and her newfound gang are trapped inside the train shed, the Doctor, who himself is trapped inside the shrunken-down TARDIS, suggests that the creatures are “reaching out, attempting to talk… Trying to understand.” Perhaps the situation unfolding is not an alien invasion but all a big misunderstanding because there is no way for them to communicate with the humans, besides flattening every unfortunate person that crosses their path. Even when Clara remarks that usually the TARDIS translates alien languages, the Doctor reasons that “their idea of language is just as bizarre as their idea of space. Even the TARDIS is confused.”

It’s at this point the Doctor attempts to communicate with the creatures, which he will later refer to as the Boneless, and he starts by using the number pi (π). For those who need a refresher of their GCSE maths, pi is the constant value you get when you divide the circumference (C) of a circle with its diameter (d). We can also write this as an equation, C/d = π. This statement is true no matter how great or small the circle is; the ratio between the circumference and the diameter is always the same. It’s also used to calculate the area of any circle – just multiply pi by the square of the radius (Area of a circle = π x r2).

The Doctor makes this sound like a reasonable choice – after all circles exist in two dimensions (“Even in a flat world they would have circles”) and so pi could in theory be a recognisable constant to them. But pi is also arguably one of the strangest and most baffling numbers we have in mathematics. It belongs to three rather unusual groups of numbers: the irrational numbers, the transcendental numbers, and the non-constructible numbers. Put simply, it is not a very nice and easy number to understand.

In fact, in the Pearson novelisation of Flatline, the dialogue referencing pi is entirely absent from the book. Instead, the author has decided to replace this with the rather fabulous line “Let’s start with some numbers. Even in a flat world, they’ll have numbers.” Such is the complexity of the number pi that they felt it was necessary to censor it from young teenage readers, though it’s probably more likely that they wanted to make the text itself more widely accessible to an audience learning to read and analyse literature.

Therefore, whilst borrowing from the rhetoric style of the Twelfth Doctor himself, I suggest the following statement…

Proposition: The Doctor actually antagonised, and perhaps even declared war on the Boneless, using the number π.

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Attack Eyebrows: Presumably this is how the Twelfth Doctor would react to the argument being proposed here.

An Irrational Choice?

Pi is probably the most famous example of an irrational number. This is when a number cannot be expressed as the ratio of two integers (that means any whole number – positive, negative or zero), and so cannot be written in decimal form using a finite or repeating set of digits after the decimal point.

For example, one third can be written as 0.333333… where the 3 digit just repeats forever, and so is a rational number. Whilst one seventh can be written as 0.142857142857… where the set of digits ‘142857’ also repeat forever, and so is also rational. In contrast, pi in decimal form starts with 3.1415926535… and then just keeps going – it will never loop back round and start regularly repeating any set of digits. There just simply is not enough time in the universe (or indeed any other universe) to write it out in full.

Due to its never-ending nature, there is no precise way to express it numerically but there are also several robust methods for calculating these digits of pi with increasingly greater accuracy. The computation of pi is something of a mathematical badge of honour for applied mathematicians and computer scientists, requiring them to combine the most advanced computing power they have with the most efficient algorithms they can write. In fact, at the time of writing, the world record for approximating pi is currently held by Emma Haruko Iwao, a software engineer at Google, who on Pi Day 2019 (that is the US date of 3.14.19) calculated the value of pi to 31.4 trillion digits. How neat!

I do, however, wonder what method the Doctor used to calculate pi in the episode. Perhaps the TARDIS has access to more powerful mathematical methods developed far in the future or from a far more advanced civilisation. I would also ask whether or not he could even communicate to the Boneless what he was precisely trying to calculate; bearing in mind communication was already the key barrier to begin with. Without any sense of forewarning, sending a never-ending number could be interpreted as a way of antagonising the Boneless by trying to overload their senses as they try to grapple with our dimensional space and interpretation of number.

Transcending All Understanding

Next up, we have the fact that pi is also a transcendental number. The concept of a transcendental number is quite a modern one given that it was only first defined in the 18th Century by a well-known mathematician called Leonard Euler (who incidentally also has an irrational number named after him – the number e).

Transcendental numbers are briefly mentioned in a Big Finish Main Range audio drama starring the Sixth Doctor called  …ish (2002), written by Phil Pascoe, who incidentally has also recently published The Black Archive entry on the Sixth Doctor serial Timelash. The script itself is quite a verbose one and is sure to appeal to any budding lexicographers as the plot itself involves a character trying to discover the ‘Omniverbum’, a word that is infinitely long and transcends all meaning. Anyone who uncovers its existence would then cease to exist as they fall victim to, and I mean this quite precisely, a literal black hole. However, Phil’s script rather unfortunately gets the definition… not quite correct. Here’s what one of the characters states near the beginning of Part Three:

“A transcendental number, such as pi, can only be approximated since it is impossible to write down as a finite or repeating sequence of digits.“

Those of you following along so far will have noticed that this matches the aforementioned definition of an irrational number. It’s a common misconception, since not only is pi both irrational and transcendental, but also because transcendental numbers are a subset of irrational numbers. This just means that all transcendental numbers are irrational but not all irrational numbers are transcendental. I strongly suspect Phil included this idea in …ish because of its use of the phrase transcendental, rather than the actual concept behind it. It’s actually not too uncommon for mathematical terms to mean something entirely different to a similar sounding concept from another discipline. For example, mathematical induction is not the same as inductive reasoning in philosophy; it’s actually a form of deductive reasoning! But nevertheless, I still have huge respect for Phil including the idea within the script and would recommend you give his audio a listen.

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Omninumerum: Does this Big Finish audio drama have an incorrect definition of transcendental numbers? Well, …ish.

A Crash Course in Algebra

So ‘what is a transcendental number?’ I hear you all crying out. Well before I define it, I think it would be best to introduce another concept to you first, which is algebraic numbers. Algebraic numbers are simply all the numbers that are solutions to an algebraic equation. So for example, if I had the equation x – 6 = 0, then the solution here is x = 6, and so we can say that 6 is definitely an algebraic number. It is easy to see that any whole number is algebraic. If you pick any whole number and call it a, then that number solves the equation x – a = 0.

This also works for any fractional number, though mathematicians more typically call these rational numbers. If I have the number two-fifths (or 2/5) then that number solves the equation 5x – 2 = 0, hence two-fifths is an algebraic number. In this example, the five is an integer coefficient, which just means a whole number in front of any x terms. Similar to the whole numbers, if you pick any fraction and call it a/b then that number solves the equation bx – a = 0, hence all the rational numbers are algebraic.

Now here’s where it gets interesting. Consider the equation x2 – 2 = 0. Then the solution to this equation is the square root of two (or √2). If you type √2 into a calculator you will get a never-ending set of digits after the decimal point. Just like pi, the square root of two is another well-known example of an irrational number. Hence, we can see that there are at least some irrational numbers that are also algebraic numbers. Hopefully you are feeling fluent with the concept of an algebraic number now!

So let’s bring this back to the original idea of transcendental numbers and explain how they are related to this. Transcendental numbers are the opposite of algebraic numbers; they are all the numbers that are not a solution to any algebraic equation. This also means that every number that you can think of is either an algebraic number or a transcendental number – there are no exceptions. In general, mathematicians just love to partition things in two distinct groups such as positive and negative numbers, even and odd numbers, rational and irrational numbers. It’s just what they do!

A few of you might be thinking, well what about the equation x – π = 0? Surely that has pi as a solution? Well it does… but it’s not an algebraic equation. The unspoken rule of algebraic equations is that we can only use whole numbers, also known as integers, in them, and so the example given here is not an acceptable equation. This here is the crucial counterexample, which clearly demonstrates that the definition given in …ish doesn’t quite work. Irrational and transcendental numbers are not the same thing; the terms are not interchangeable.

If you managed to follow all this then very well done because this is something usually taught to those in the final year of their undergraduate maths degrees. Give yourself a  gold star!

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Badge of Mathematical Excellence: Found in the wreckage of a space freighter around 65 million years ago. Seeking new owner.

Simplicity In Complexity

As we have seen, showing that a number is algebraic is quite straightforward in that you just need to find an equation that it solves. But transcendental numbers are very hard to prove because you have to show that no such equation exists. When I studied algebraic number theory at university, we were simply allowed to state that pi was a transcendental number without further reasoning, due to the advanced nature of the concept. This certainly lacks rigour in approach to learning but it was still great when revising for the final exam.

But I was still curious. So I took out a book from a university library that contained the first proof that showed pi is a transcendental number by Ferdinand Von Lindemann in 1882. I have no qualms in saying that I hadn’t got the faintest idea what was happening on the page. In fact, it was much like that bit in the novelisation of Shada (2012) where Ship has to read out The Worshipful and Ancient Law of Gallifrey to his Lord Skagra: “Squiggle, squiggle, squiggle, squiggle… squiggle, line, squiggle, squiggle…” I have since found a more accessible text online that explains the proof pretty clearly, which you can read here if you so wish. It’s not for the faint-hearted.

People, and presumably other intelligent life, gain an understanding of the world around us, all of its systems and functions and processes, by using equations to model and predict their outcomes. However, the transcendental numbers are the group of numbers that do not solve ordinary kinds of equations. Why then would the Doctor try to solve a communication problem by sending a number that is known for its inability of being a solution to the most common kinds of mathematical equations? It seems that the Doctor’s strategy does not appear to add up. The plot thickens…

A More Constructive Approach

Lastly, we come to constructible and non-constructible numbers. Whilst transcendental numbers have only been around for the last two hundred years, constructible numbers have been around for about two thousand years, dating back to the ancient Greek mathematicians of old. Moreso, the ancient Greeks were clever enough to realise that the theory of constructible numbers was the key to solving several problems they had stumbled upon within their study of mathematics, even though they could not prove the answers for themselves.

So how do we know if a number is constructible? Constructible numbers are defined as all the possible lengths of line segments that can be created using a straightedge ruler and pair of compasses in a finite number of steps. In other words, imagine you have a piece of paper and a pen. Draw two dots on the paper and then join them with a straight line using the ruler – this is now a line of length one (and so one is a constructible number, obviously). But now you can only add new points on to the page, using your straightedge ruler and pair of compasses, as long as they follow these three rules:

  • Any new point you construct must be the intersection of two lines, two circles or a line and a circle.
  • All lines are drawn with the ruler (no measurements!) and must pass through two points you have already constructed.
  • All circles must be centred on points you have already constructed and their radius must be the distance between two points you have already constructed.

If you would like to see some proof that all the integers, rational numbers and square roots of numbers are in fact constructible numbers, have a look at this site here.

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A handy tree diagram that shows the relationship between the different number groups we’ve discussed here. Sadly, trees have no moving parts and don’t communicate.

However, for the purposes of this blog post, I am far more concerned with what the property of constructibility tells us about numbers. I’ll show you what I mean with a famous example. It’s an ancient maths problem first proposed by some ancient Greek geometers. You might have already heard of this as it gives us a well-known saying…

Squaring The Circle

People use the phrase ‘squaring the circle’ as a metaphor for doing the impossible, or perhaps something extremely difficult at least. In mathematics, it refers to the following problem: can you construct a square with the exact same area as a given circle in a finite number of steps using a straightedge ruler and pair of compasses? You can probably infer from the language used in this question that this has literally everything to do with constructible numbers.

We can actually simplify this problem even further using a handful of key facts we have discussed during the course of this blog post. First off, we know that the area of a circle is equal to π x r2. Suppose we want to ‘square’ a unit circle, which is a circle with a radius of one (r = 1). Then the area of this circle is equal to:

π x 12 = π x 1 = π

This means that in order to prove that we can square the circle, we need to construct a square that has the same area as this circle, which is an area of π. Squares are defined by as a quadrilateral shape that has the same length and width, and since the area of any quadrilateral is the length (l) multiplied by the width (w) then the area of the square is just l2, since l = w here. We want the area of the square to be π so this means that l2 = π and so l =π. Therefore, if we can construct a line that has length √π then we have solved the problem. But, we also know from earlier that we can construct square roots of numbers, and so this means we just need to construct a line with length π in order to prove you can square the circle.

What this line of mathematical reasoning has hopefully just demonstrated to you is that being able to square the circle and being able to geometrically construct a line of length π are actually equivalent statements. They mean the same thing. And so if we can prove or disprove either the statement about constructing a line of length pi, then we have equally proved or disproved the statement that you can or cannot square the circle.

The only question that remains unanswered here is whether or not π is indeed constructible. It isn’t. This is because all constructible lengths must be algebraic numbers, as was first proven by the much neglected French mathematician Pierre Wantzel in 1837. Wantzel was also the first to prove that it was impossible to ‘double the cube’ and ‘trisect any angle’ using his knowledge of constructible numbers; astounding results that were largely ignored by the mathematical community for nearly a century.

As an aside, I found out in my research that Wantzel died tragically young at only 33 years of age, apparently due to overworking himself and his abuse of coffee and opiates. There is very little biographical detail to be found about him, with perhaps several key documents still only available in French. His Wikipedia page fills just one screen and he doesn’t have an entry in any of the 27 volumes of the Complete Dictionary of Scientific Biography. He is regrettably yet another example of a mathematical prodigy who died quite young – see also Niels Henrik Abel, Évariste Galois, Srinivasa Ramanujan, and Maryam Mirzakhani. And whilst probably by coincidence, Doctor Who itself has not been immune to mathematical prodigies who die tragically young either.

Combining Wantzel’s result with the proof that pi is transcendental (von Lindemann, 1882) we can conclude that pi cannot be algebraic and, hence, cannot be constructible. Normally, this would be the point to wrap up the discussion on the constructibility of pi; we’ve solved the problem after all. It would be absolutely ridiculous to imagine that somebody could possibly be so stupid and ignorant as try and overturn this concrete mathematical fact. But naturally that didn’t stop the United States of America trying to pass the counterstatement into law.

A Potty Bill

In February 1897, the Indiana General Assembly were deliberating over House Bill No. 246 of that year, more easily identifiable as the Indiana Pi Bill. This frankly absurd bill was the brainchild of Dr. Edwin J. Goodwin, a physician by trade yet a crank by reputation. Within the text of his bill, Goodwin claimed to have ‘squared the circle’, a maths problem that we already know was rigorously disproved fifteen years prior (von Lindemann, 1882). His nonsensical reasoning for this incredible statement was the following line about the diameters of circles:

“… the fourth important fact, that the ratio of the diameter, and circumference is as five-fourths to four.”

This is a somewhat obtuse way of saying that pi is equal to four divided by five quarters, so that’s 4 ÷ 5/4, which is equal to 3.2, a number which is clearly not irrational, transcendental, or non-constructible. Given that pi is approximately equal to 3.14, this value of 3.2 doesn’t even round correctly to one decimal place! The only way I can begin to rationalise this behaviour is to imagine this is some sort of 19th century precursor to ‘shitposting’.

Understandably, the politicians were utterly baffled by the wording of this bill, leading it to be bounced from the House of Representatives, to the Finance Committee, to the Committee on Swamplands, and then finally to the Committee on Education, who then proceeded to pass the bill without any objection because none of them possessed the wisdom to fathom what it actually meant.

However, rather fortunately, the then head of the Mathematics Department at Purdue University in Indiana, Professor C. A. Waldo, happened to be visiting the statehouse to discuss matters of academic funding when, by pure chance, someone mentioned this bill to him. The committee then offered to introduce Professor Waldo to Goodwin, but he simply replied he already knew enough crazy people. A quick lecture to the senators showed them the error of their ways and so after a second debate the Indiana Pi Bill was postponed indefinitely. It remains in a filing cabinet, somewhere in the basement of the Indiana statehouse to this very day, just waiting for the next idiot willing to revive it.

Teaching Maths in a Fun But Relevant Way

Whether the Doctor actually remembered, or considered, or even knew of any of this to begin with, is purely speculative. But I would like to think that in their many years travelling the universe the Doctor would have come across at least some, perhaps most, of this knowledge regarding pi. As a self-proclaimed maths tutor to the medieval people of Essex in The Magician’s Apprentice (2015), before going onto lecturing on just about anything he wishes in The Pilot (2017), I’d like to think the Doctor is an informed and well-educated individual about many things in the universe, and that most definitely includes mathematics.

Returning to that critical moment in Flatline, when the Doctor sends the number pi to the Boneless, which itself has led to this entire discussion about the nature of pi, perhaps the Doctor was being more optimistic here than I had initially expected? By trying to communicate with the Boneless using the language of numbers, trying to impart knowledge and understanding about the world they happen to find themselves in, he was really trying to save the world. He was trying to be a good man all along.

There are other aspects of the number pi that I haven’t had the time to touch upon, such as its surprising and unexpected occurrences in areas such as quantum physics and the natural world. Perhaps the most mind boggling of them all is this sliding block physics puzzle that can generate digits of pi without any (obvious) reference to circles.  These are arguably all things that would suggest that pi was a reasonable choice to establish communication, by thinking of it as a universally recognised constant that consistently appears throughout the universe, whatever level of it you may be operating on.

But as we have also seen, the irrational, transcendental and non-constructible nature of pi makes it a lot less friendly than you initially thought. Indeed, we see the Boneless trying to reinterpret and construct themselves in three dimensions, having previously existed in only two, and so sending them a number that isn’t geometrically constructible could be seen as a form of attack or challenge in their own terms. If the Doctor chose the number pi knowing about these properties then he would be party to antagonising the monsters of this story, and so facilitating himself to play the role of “the man that stops the monsters”.

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A good man: Did the Doctor try to antagonise the Boneless in Flatline?

This would then suggest that the Doctor is declaring war on the Boneless. To use the words of Danny Pink in the episode The Caretaker (2014), the Doctor is “an officer”, that “he’s the one who lights” the fire, whilst Clara and her gang of survivors are the soldiers fighting the battle on his behalf. Meanwhile, the Doctor is rather conveniently trapped inside the TARDIS console room, away from the main battlefield here.

However, perhaps the conclusion is even more straightforward than this. Perhaps the Doctor, whilst having the best of intentions, just doesn’t have a clue what he is doing. This itself is the resolution we get from the man himself at the very end of Series 8 in Death in Heaven (2014). He proclaims that is “not a good man”, “not a bad man”, “not a hero (nor) a president (nor) an officer.” After all his travels through time and space, this is who the Doctor thinks he is:

“I am… an idiot, with a box and a screwdriver. Just passing through, helping out, learning.”

I expect that, with reference to this case, he means passing through Bristol, helping out the locals, and learning more about the number pi. Well, we can only hope.

 

Appendix: Jokes About Pi

  • My friend decided to get a tattoo of the symbol pi. It was an irrational decision.
  • Did you know that 3.14% of sailors are pirates?
  • Teacher: What is the area of a circle?
    Student: Pi r squared.
    Teacher: No. Pie are round. Cakes are square.
  • Me: Doctor doctor, I keep having nightmares about the digits of π
    Doctor: Is it a recurring dream?
  • Don’t ever have an argument about pi. You’ll just go round in circles.

 

References

  1. The subsection ‘A Potty Bill’ which discusses the Indiana Pi Bill is largely based on material within Chapter 3: Are you π-curious? in The Simpsons and Their Mathematical Secrets by Simon Singh.
  2. All online references are linked to at the relevant points throughout this blog post.
  3. The links to Phil Pascoe’s work are not references but unpaid advertising.