It’s the end, but the moment has been prepared for…

12th Doctor, The
Character played by Tom Baker in Doctor Who. It was established in the story The Brain of Morbius that the Doctor was in his twelfth life, and in The Deadly Assassin that a Time Lord only has thirteen lives in total. The first of these was later retconned in The Five Doctors.

A character introduced in the 1980/81 series of Doctor Who, played by Matthew Waterhouse. His name is an anagram of Dirac, after P.A.M. Dirac, the Nobel Prize-winning physicist. Originally intended as an ‘artful Dodger’ figure, he was quickly reconceived as an audience-identification figure.

As such, he was portrayed as a sullen, anti-social teenager, with flat affect, who was terrified and resentful of women, thought fascism wasn’t as bad an idea as people made out, had no social skills whatsoever and spent much of his time boasting about how good he was at mathematics in a desperate attempt to make people like him. We will see in future essays if this assessment of Doctor Who fandom in the 1980s was an accurate one.

Strangely, Doctor Who fandom didn’t take to the character, and he was killed off halfway through series 19.

The belief that the world can be represented in a symbolic form, and that by manipulating those symbols, while following a strict set of rules, one can both understand and manipulate the world itself.

One of the odder things about the Doctor Who production office in the early 1980s, and one that apparently stems from the fascination with symbol manipulation, is that there developed a mild obsession with anagrams. These would appear in the names of characters (q.v. Adric, but see also Brotadac, a character from the story Meglos), as well as in the cast list (with surprise reappearances of characters being disguised by the actors’ names appearing in anagram form).

Baker, Tom
Actor who portrayed the 12th Doctor. Regularly resigned from the role, but had his bluff called when the new production team of script-editor Christopher Bidmead and producer John Nathan-Turner took over.

Bidmead, Christopher
Script-editor for series 18 of Doctor Who, which he intended to take in the direction of hard science. Also the writer of Logopolis and Castrovalva. While Logopolis is Bidmead’s first credited script for the series as writer, his interests can be seen throughout series 18 — in particular, he is fascinated by Platonism, recursion, entropy, and representing people’s internal states as external landscapes.

Black hole
A star which has collapsed in on itself and no longer shines. Within the event horizon of a black hole, the direction of gravity is actually equal to the direction of time (and entropy) — movement toward the singularity is inevitable, and the same thing as movement forwards in time. Once inside, you can’t escape your destiny, which is to fall, helplessly.

Block transfer mathematics
A fictional form of mathematics, invented by Christopher Bidmead for Logopolis. While it was named after an operation that was performed by Bidmead’s own home computer, in the Doctor Who universe it is the name for a type of calculation that can only be performed by organic brains, and not by computers. This suggests that the Church-Turing hypothesis does not hold in the Doctor Who universe.

Block transfer mathematics actually brings solid objects into being as a result of its calculations — this is how TARDISes are created, for example — and as such may better be characterised as a form of magic(k) than of mathematics.

The second story to be written by Christopher Bidmead, this follows directly on from Logopolis, and explores many of the same ideas. It takes its title — and location — from an engraving by M.C. Escher.

Chameleon circuit
The circuit which is supposed to make the outer form of the TARDIS change (while leaving its inner form the same) to fit its surroundings. This broke in the very first ever Doctor Who story, and it is the Doctor’s decision to fix this founding event of the series that leads to the events of Logopolis, including the destruction of uncounted billions of planets.

Church-Turing Hypothesis
The claim — accepted by a majority of today’s computer scientists, though unproven and unprovable — that any computable mathematical function can be computed by a Turing machine (a type of idealised computer). The class of functions that can be computed by a Turing machine is proven to be equal to the class of functions that can be computed by recursion.

Cloister Bell
A warning bell sounded by the TARDIS when something truly disastrous is about to happen, it is heard for the first time in Logopolis. It is located in the TARDIS’ Cloister Room, which appears here for the first time.

Cloister Room
A room in which, it is later established, the TARDIS’ copy of the Eye Of Harmony, a black hole, is kept. In Logopolis, though, it is just portrayed as a normal cloister. The word cloister, of course, is normally used to describe places inhabited by Monks.

Computer programming
The belief that the world can be represented in a symbolic form, and that by manipulating those symbols, while following a strict set of rules, one can both understand and manipulate the world itself.

A measure of disorder, the amount of entropy in a system is a measure of how chaotic that system is. Another way to look at it is as a measure of the amount of missing information — the more information it takes to specify something’s state, the higher its entropy is.

In a closed system, entropy always increases. This increase is actually what gives rise to time — things becoming more chaotic, more disorganised, winding down, is precisely what time actually means.

Escher, Maurits Cornelis
An artist whose works were (and are) very popular among people who were also interested in computer programming and mathematics. His work generally revolves around recursion, and the idea of effects being their own cause.

Godel, Escher, Bach
A book by Douglas Hofstadter, which postulates that the nature of intelligence can be found in recursion (what Hofstadter refers to as ‘strange loops’). One of the best popular books on mathematics ever written, this book had a much bigger influence on popular culture than one might realise. In particular, Christopher Bidmead seems to have taken many of the ideas for his Doctor Who work from it. A high-school level course from MIT, covering many of the ideas in the book, can be found at .

A force that acts on any two bodies, attracting them to each other in proportion to their masses and in inverse proportion to the distance between them. This means that, for example, if you place a Time Lord with an approximate mass of 70kg at the top of a radio telescope, say Jodrell Bank, 89m above a planet with mass 5.972×10^24kg, and then have him let go, he will hit the planet a little over three seconds later.

Gravity, as a universal law, was first understood by Isaac Newton as a result of his researches into alchemy.

Hard science
What Christopher Bidmead wanted to reintroduce to Doctor Who. Judging from the script to Logopolis, hard science consists of millions of chanting monks in a city made to look like a brain, chanting block transfer mathematics codes in order to counteract entropy, while the ghost of someone’s future self tells him the future in order to cause it.

Jodrell Bank
An observatory near Alderley Edge in Cheshire, the main radio telescope of which was used to represent the Pharos Project in Logopolis. The Doctor’s regeneration thus took place near the legendary burial site of King Arthur, a hero who died but will be reborn when the need for him is greatest.

“Jodrell” is also a euphemism for masturbation, which I am increasingly worried is what this essay amounts to.

1) A TV serial, part of the series Doctor Who, written by Christopher Bidmead.
2) A portmanteau word, made up from the Greek Logos (word) and polis (city).
3) A city, shaped like a brain, on an unnamed world, in which various monks perform block transfer mathematics calculations in order to stave off entropy.

A Greek word, most often translated as ‘word’, but which can also be translated as ‘thought’, ‘logic’, ‘tao’ or ‘idea’. Most famously, this word turns up in the first sentence of the Gospel of John — Ἐν ἀρχῇ ἦν ὁ Λόγος, καὶ ὁ Λόγος ἦν πρὸς τὸν Θεόν, καὶ Θεός ἦν ὁ Λόγος. (“In the beginning was the Word, and the Word was with God, and the Word was God”). To quote Marvin R. Vincent, Word Studies in the New Testament, vol. 2:

This expression is the keynote and theme of the entire gospel. Λόγος is from the root λεγ, appearing in λεγω, the primitive meaning of which is to lay: then, to pick out, gather, pick up: hence to gather or put words together, and so, to speak. Hence λόγος is, first of all, a collecting or collection both of things in the mind, and of words by which they are expressed. It therefore signifies both the outward form by which the inward thought is expressed, and the inward thought itself, the Latin oratio and ratio: compare the Italian ragionare, “to think” and “to speak.”

It is also the word from which we get the word English word ‘logo’, and around this time John Nathan-Turner was attempting to make the Doctor more of a brand, by, for example, having him sport question-mark logos on his clothing.

The belief that the world can be represented in a symbolic form, and that by manipulating those symbols, while following a strict set of rules, one can both understand and manipulate the world itself.

The belief that the world can be represented in a symbolic form, and that by manipulating those symbols, while following a strict set of rules, one can both understand and manipulate the world itself.

Monks have always represented something a bit like the Doctor, but also a bit different, in Doctor Who. Whether it be the Meddling Monk of the early Hartnell stories, the first other Gallifreyan we ever meet, or Kanpo Rimpoche, the Buddhist monk from Gallifrey who helped the Pertwee Doctor regenerate into Tom Baker, or the monks here, or I.M. Foreman in the novel Interference, they seem to turn up at times of great stress and be involved in the changing of time.

Tom Baker himself was a Catholic monk in his early days, before he became an atheist.

Nathan-Turner, John
The producer of Doctor Who from 1980 through to its cancellation, by far the longest tenure of anyone in the production team of the show. Terrance Dicks has been known to use the phrase “people like Hitler, or Himmler, or Nathan-Turner”, and it’s fair to say that Nathan-Turner is not the most well-regarded of people, but in retrospect while the failures of his period on the show are different failures from those of previous years, they are not necessarily worse ones.

Roughly, the belief that physically existing objects, in the real world, are merely shadows of ideal, perfect versions of those things that exist in the realm of ideas.

The process by which the Doctor escapes the effect of entropy — rather than dying, like everything else, he can renew himself. From an internal BBC memo before the regeneration from William Hartnell into Patrick Troughton:

The metaphysical change which takes place over 500 or so years is a horrifying experience – an experience in which he re-lives some of the most unendurable moments of his long life, including the galactic war. It is as if he has had the L.S.D. drug and instead of experiencing the kicks, he has the hell and dank horror which can be its effect.

Recursion, in mathematics or computer programming, is a process which has a function be part of its own definition. A simple form of recursion would be when a function takes its own output as a new input — thus the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13… takes the last two numbers of the sequence and adds them together to create the next number.

Another example of this would be pointing a camera at a monitor to which it is connected, to get a ‘howlround’ visual, or a future incarnation of a character going back in time and instigating the events which caused that character to exist.

q.v. recursion

TARDIS Eruditorum
A sometimes-wonderful, sometimes-infuriating blog about Doctor Who. I mention it here because that blog’s essay on Logopolis makes this one look staid and normal in comparison.

q.v. entropy

Watcher, The
A future incarnation of the Doctor, from between his twelfth and final regeneration.

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