Thomas Pynchon’s novel

‘What resources do we have to understand the world around us?’ In answer to this question, N. Katherine Hayles identifies three categories: mathematical equations, simulations modelling, and discursive explanations. She immediately dismisses the first category for her project, admitting: ‘I have little to say, other than to note […] the limited usefulness of mathematics in describing complex behaviors’ (

A log cabin and c (homophone of ‘sea’) equal a house on the water or a houseboat. As Lance Schachterle and P. K. Aravind explain, ‘[t]he pun seems to have no grander purpose than to provide some passing amusement – amusement enhanced precisely to the degree to which the reader appreciates the underlying mathematics’ (

Pynchon’s Second Equation is the most intricate and puzzling of the three passages in mathematical notation in

It is introduced as ‘describ[ing] motion [of the Rocket] under the aspect of yaw control’ (GR 284), with yaw being a sideways rotational movement with which a rocket can veer from its prescribed path. Apart from this, readers learn little about the Second Equation. Given that it appears between a mathematical joke and the Poisson distribution, we might first ask if Pynchon’s Second Equation is real. Or is it made up, like the ‘hilarious graffiti’? A second question concerns its function in the novel: if the joke warns readers not to take intimidating mathematical notation too seriously and the Poisson distribution points to a pattern in a large number of unpredictable individual events, what role does the Second Equation have for interpretations of

In his wide-ranging guide to

Is Pynchon’s equation of motion a standard differential equation used by specialists to calculate the path of a rocket’s flight or to control its yaw? No: Pynchon’s equation does not resemble anything one might reasonably expect. […] Not only are most of the symbols in Pynchon’s equation obscure, but the general structure of the terms in the equation also makes it impossible to identify with one or other of the equations describing the position and orientation of a rocket in flight. This equation, then, is not a genuine mathematical expression in this context. It may appear authoritative to the layperson, but it is unlikely to fool a rocket scientist. (

Schachterle and Aravind draw out the literary implications of inventing a formula: the forbidding notation plays with mathematics as a form of authority; those in the know can use it to impress and control the uninformed majority. The Second Equation would accordingly have different effects on mathematical laypersons than on experts able to question its authority: ‘curiously, on closer inspection […], the equation does not stand up to physical/mathematical analysis. Will the reader in the know about the equation recognize its inner hollowness, its inability as presented to do what it purports to control motion?’ (

The consequences of Schacherle and Aravind’s interpretation are significant: according to their view, the Second Equation makes mathematics a tool of the Elect rather than a common resource to understand the world. Yet, where they describe the symbols in the equation as ‘obscure’, another interdisciplinary team tried to explain some of the symbols. Thomas Moore enlisted ‘a fellow amateur, reputed to have majored in mathematics’ for his book

Θ is the desired yaw angle, present as a ‘control.’ ϕ is the missile’s range; the differential

The mathematician at work seems not to have doubted the reality of the equation and saw sense in the terms. The disagreement between the interdisciplinary research teams on this point leaves open the question of whether Pynchon’s Second Equation should be considered invented or real. Given the relevance of this answer for interpretations of authority, control, and the power of the elect few over the uninformed majority, we – a literary scholar and a mathematically-inclined biologist – took another look at the Second Equation and at sources that might prove its either real or made-up nature.

Since our examination of literary sources in Pynchon studies did not reveal a definitive proof of the either real or imagined nature of Pynchon’s mathematical description of rocket control, we turned to scientific material. When revisiting the previously considered texts, we realised that neither the book by Kooy and Uytenbogaart from

You come in – just hit town, here in the heart of downtown Peenemünde, hey, whatcha do for fun around here? hauling your provincial valise with a few shirts, a copy of the

The 1935 Volta Conference in Rome addressed the topic ‘High Velocities in Aviation’, and the scientists mentioned in the quotation above contributed papers on supersonic flight that might have been relevant to the later development of the V-2 (

It’s a blueprint of a German parts list, reproduced so crummy he can hardly read the words – ‘Vorrichtung für die Isolierung, 0011-5565/43,’ now what’s this? […] Flagnote on the flagnote sez ‘Geheime Kommandosache!’ (GR 287-88)

The text gives details here, for example the blue colour of the paper, the code number of an original document concerning the V-2, and the stamp ‘Geheime Kommandosache’ – secret command (see appendix, Figure

Screening the reports on the theory and development of rocket steering reveals a set of basic formulas that refer to the calculation and control of the rocket’s flight path: the path equations, the equation of moments, and the steering equation (see appendix, Figure

Instead of using the elaborate notations _{1}, and c_{2} seem to be very different from the expressions in Pynchon’s formula. But these factors only stand for more complex parameter equations that consist of physical functions and coefficients. We find clues as to what these equations look like and what the components mean in other original documents (ARCH 86.59, ARCH 86.65, ARCH 87.79) and articles (e.g. _{1}, and c_{2} are abbreviations:

It is not necessary to go into the physical details here, but what we can readily see is that all three parameter equations are divided by the value Θ. This means that we can revert to a previous version of the equation by multiplying all components with Θ. Then, using the mathematical rather than the physical notation of the differentials and moving the fourth term to the other side of the equal sign where it becomes negative, we obtain the following variant of the equation of moments:

If we now replace the parameter c_{2} with its detailed expression (see above), the equation shows a first term that is identical to Pynchon’s formula and a fourth term that is almost identical:

Even without substituting the remaining parameters d and c_{1}, it is clear that Pynchon’s Second Equation resembles – and in fact is – the equation of moments that the Peenemünde physicists and engineers used to calculate and control the angular motion (yaw) of the V-2 rocket.

The material in the archive of the German Museum has allowed us to conclude that Pynchon did not invent his Second Equation and that the formula is plausible in the context of rocket steering. But we may have doubts about whether Pynchon arrived at the formula in the same way, by reading dozens of German reports, extracting the equation of moments, and then transforming it. While not questioning the relevance of the archival material for other features in

To shorten a long story of searching for sources: the essay ‘The Control System of the V-2’ by Otto Müller includes an ‘equation for control in yaw’ (

Next to the equation, Müller’s paper contains illustrations and explanations of its parameters, variables, and terms (

Our finding that Pynchon took his Second Equation from Müller’s paper in

The idea was always to carry along a fixed quantity, A. _{t}_{1}∗’

_{t} corresponding to _{1}∗_{1}∗. (

In the next case, the method is reversed: Pynchon condenses information from a section in a paper:

The Schwarzkommando use

Whilst the change-over from the HV method to the

This example shows how Pynchon uses the terminology he finds in the collected papers to equip characters working on the rocket, here Achtfaden, with authentic vocabulary:

No one wrote then about supersonic flow. It was surrounded by myth, and by a pure, primitive terror.

According to C.

Next to copying and adapting terms and phrases, Pynchon also draws on graphs and charts in

Boundary-layer temperature

In the quotation below, Pynchon draws on a diagram of the device for integration (Figure

So the Rocket, on its own side of the flight, sensed acceleration first. Men, tracking it, sensed position or distance first.

A final example shows that Pynchon’s processes of translation include images as well as more mundane translations from German to English. Talking about the rocket, engineers in the novel explain that ‘[i]t was

Determining the source of Pynchon’s Second Equation is the first step to better understand its role in

So was the Rocket’s terrible passage reduced, literally, to bourgeois terms, terms of an equation such as that elegant blend of philosophy and hardware, abstract change and hinged pivots of real metals which describes motion under the aspect of yaw control

The three elements of motion under yaw control – ‘preserving, possessing, steering’ – correspond to bourgeois values of stability, (material) security, and determinacy. With its characteristics of maintaining orientation and controlling a desired path, the Second Equation is presented as a tool of the Elect. The rocket’s feedback mechanism is ‘conservative’ in the sense of working towards retaining the initial path: a guidance device inside the rocket continually measures the orientation of the rocket, calculates the deviation from the expected values, feeds back the results of the calculation to correct the rocket’s path and to begin again the process of measuring and correcting. The control during flight is thus part of the rocket itself and no longer in the hands of the technicians on the ground. As Schacherle and Aravind note, the passage in which the Second Equation appears refers to many forms of controlling movement through feedback, so that ‘the control equation not only suggests the formalized dynamics of how the German engineers sought to stabilize the trajectory of the V-2, but also generalizes beyond the physics of flight to the far more shadowy attempts at control […] in this section’ (

The characterisation of the Second Equation in terms of bourgeois values connects the control of the rocket’s flight that the formula symbolises and the control of the privileged Elect over the life paths of the powerless majority. Associations between the rocket and the Elects’ domination pervade the novel, and Weissmann/Blicero brings the two aspects together: he dominates the young soldier Gottfried in sadomasochistic practices and, at the end of the novel, puts him into a rocket and launches it. Like the rocket’s path, Gottfried’s destiny is determined from the beginning: he is completely at the mercy of Weissmann, and his captivity is compared to the fairy tale ‘Hansel and Gretel’ when he is said to belong ‘in a way none of them can guess cruelly to the Oven… to

It is tempting to think that Pynchon came across this image in the Smithsonian Institution or another archive, and that it inspired the idea of a mysterious S-Gerät that is being built into the Rocket 00000 and that turns out to be a plastic shroud encasing a human being. Significantly, with the S-Gerät a human element becomes part of the rocket during flight. As explained above, the rocket controls its own path with the help of a guidance device using a feedback mechanism: once in flight, the rocket is out of human control. But with the S-Gerät, a human element becomes part of the rocket once again. In the book by Benecke and Quick, we find reference to a ‘“Steuergerät” (control device)’ (

Human beings and the rocket are connected in various ways in

Joseph Tabbi remarks on the difference between the rocket’s trajectory and the mathematics describing it: ‘The trajectory is mathematics, pure and transcendent; but the rocket is engineering; first and foremost it is “raw hardware”’ (

In Slothrop’s case, the reality of physical existence is ‘dissolved in the acid of mathematics’, a formulation that the historian of science Yves Gingras uses in his essay ‘What did Mathematics do to Physics?’ to describe how ‘mathematization led to the vanishing of substances’ once thought to be real, for example Cartesian vortices and the ether (

When asking what resources we have to better understand the world of

Page reference to Pynchon’s

The findings were first presented at the International Pynchon Week, 5–9 June 2017 in La Rochelle, France. We would like to thank the Pynchon community for helpful questions and suggestions and also thank the reviewers of

Access to the collection and archive on the V-2:

Many documents are accessible online via

In the following, all documents from the archive of the German Museum are marked with ‘ARCH’ and the code number.

Meaning of the physical values in the equation:

Θ: moment of inertia

C_{a}: draught coefficient

_{u}: force acting on the rudders (perpendicular to rocket axis)

ρ: air density

The authors have no competing interests to declare.