The science at the end of the Whoniverse

Yes that’s right, Doctor Who is back on our screens, spitting himself out of dinosaurs’ mouths and into our hearts where he belongs. On this week’s episode, the first of Series 8, a homicidal android is stalking the streets of Victorian London, mutilating golden-hearted cockneys for their fleshier organs and turning the remains into donor kebabs in order to conceal the evidence of his crimes.

Slap bang into the middle of this mess lands the Tardis, lodged inside the throat of an exceptionally irritable tyrannosaur. Trapped on board are the wide-eyed Clara Oswald and the new and improved Time Lord Peter Capaldi – whose saurian features make the aforementioned reptile look positively cuddly.

The Doctor’s arrival is greeted with a clash of symbols.


A dense network of complicated mathematical symbols that he sketches onto Madame Vastra’s floorboards in an attempt to repay his host with a unique range of decorative graffiti. Either that or he’s trying to work out something timey-wimey while making himself look clever.


Now, most of these CaCO3-based scribbles are indecipherable to the average human being. On his right, for example, there’s a question mark drawn inside a circle, and on his left there’s what looks like a shooting star that’s been pierced by an arrow.

Most of the equations that can be interpreted by our primitive brains, however, would clearly be crucial to a Time Lord trying to get a jetlagged dinosaur back to her rightful time zone.

Take these two equations, for example:


I don’t see how you could be expected to navigate the manifold complexities of multi-dimensional geometry without an understanding of the binomial expansion. Or, for that matter, an awareness that


While csch may seem like the sort of noise a disgruntled physicist would make when reviewing an episode of Doctor Who, it is actually a representation of the hyperbolic cosecant – a trigonometric function equivalent to one over the hyperbolic sine. This complicated-looking formula that the Doctor has taken such pains to spell out is actually no more than a textbook definition. What would perhaps have been more helpful was to let viewers know that csch(x) also equals inline-equation, an expression more might have been able to understand.


That being said, I can totally understand why the Doctor would need to remind himself that


I don’t know why he didn’t just write it equals ±8, but hey, he’s a busy man. Places to go, faces to spectacularly change into.

It’s also good to know that everyone’s favourite Time Lord has a steely grip on the physics of electromagnetism. Why else would he jot down the Biot-Savart law, which describes the magnetic field B generated by an electric current I flowing through a wire?


Rather sloppily, however, the good Doctor has forgotten to integrate both sides of the equation. The right-hand side of the equation is still expressed in terms of dl – which is to say the current flowing through an infinitesimally small length of wire – while the left-hand side reads B instead of dB, implying that the whole magnetic field can be deduced from just one infinitesimal slice instead of the entire length.

Biot and Savart, incidentally, carried out their experimental collaborations around about the year 1820, so it’s likely that any practicing physicist stepping into the Doctor’s room towards the end of the 19th century would have instantly known what was being discussed.

While this is the only set of squiggles with any meaningful physical significance, there’s a rather interesting little calculation going on in the top left-hand corner. Here the Doctor appears to be trying to find a point M (with coordinates Mx, My) on the circumference of a circle whose centre is at (p/2, 0)


The natural equation to use here would be the well-worn technique for determining the radius of a circle, namely:


That would make sense.



Most definitely do not.

And I’m afraid that things only go downhill from here. This next equation,


While impressive, represents little more than an opportunity to rev up the BODMAS-mobile, and


Indicates a rapid decline into senility.

This next equation, by the way, is almost total gibberish,


and unless I’m missing something dramatic,


Is hardly the revelation of the millennium.

But maybe I’m being too harsh. This is all just entertainment, you say. What does it matter if a fun children’s show gets some silly mathsy thingamajigs wrong?



I actually believe it matters a great deal.

Equations, especially the big complicated ones you see on television and in movies set at NASA or MIT or some weird mathematician’s dorm room, are meant to be pretty fricking cool. Whether it’s statistical analysis or chaos theory or quantum mechanics or astrophysics, those numbers and symbols are meant to represent a control over the physical world that will thrill the pants off Joe and Jane Audience.

Anybody capable of reproducing these equations off the top of their head is therefore not only very intelligent but also tremendously powerful. The numbers guy or girl in these films may well be a wet blanket – a quivering mass of self-interested insecurities unable to conduct a normal conversation without straining any of their pitifully underdeveloped muscles – but when the chips are down and an answer needs to be found, they absolutely steal the show.

So if we’re going to be responsible for equating knowledge with power in this way, we’d better make sure that in the first place we get the knowledge right. What’s funny is that so much of what we see on the screen is clearly and unashamedly fake – from the sound to the lighting, the visual effects to the make-up, and from the idealised backdrops to the characters’ flawless, silky-smooth hair.

Science is pretty much the one thing that doesn’t need any help to be made either more interesting or more complicated than it already is. God knows there’s no shortage of mind-bending equations and symbols for a set designer to tap into. Given enough chalk, most of the theoretical physicists I know could cover the walls, floorboards and ceilings of a good-sized room while on their first coffee break of the day. And trust me, they would be cheap.

Now please don’t get me wrong: I delight in the surrealist mayhem of Doctor Who, and would never seek to reduce the show to a string of inaccurate observations and misrepresentative clichés.

All I ask in return is that nobody does the same to science.

Gilead is a martyr to scientific accuracy who bears his cross product with stoic fortitude over @gileadamit.

5 thoughts on “The science at the end of the Whoniverse

  1. (x, why?)

    Is it senility and gibberish or has his 2000-year-old mind, filled with the knowledge of the entire universe maybe a little beyond your ken? Then again, the Doctor lies.

  2. TM

    “Now please don’t get me wrong: I delight in the surrealist mayhem of Doctor Who, and would never seek to reduce the show to a string of inaccurate observations and misrepresentative clichés.”

    Liar – you just misrepresented something shown on our screens for no more than about ONE SECOND as something seemingly (and inaccurately) vitally important to the rest of the 75 minutes of footage.

    You say it’s important to get it right, but let’s be realistic: no-one – not even one of these scientists you basically claim are near-on ripping their hair out right now – even got past SEEING the first equation, let alone bothered to work it out.

    One person screencapping it and getting a wee bit too obsessed with going through each and every one of the sums is absolutely misrepresenting how everyone else took it in. And that in itself is a geek cliche.

    “All I ask in return is that nobody does the same to science.”

    So in your own words, you’re as guilty as they are, so no, you can’t ask the same in return.

  3. Pingback: Getting the science right | Proof Communication

  4. Thaddaeus

    I would say the simple stuff was him taking a mental inventory of his new brain, and what are described as errors or gibberish were either false starts as he tried to reboot all his subsystems, or else expressions of mathematical principles unknown to humanity.


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