11institutetext: Verity Allan 22institutetext: Battcock Centre for
Experimental Astrophysics, Cavendish Laboratory, University of Cambridge
22email<EMAIL_ADDRESS>
# The Cavendish Computors: The women working in scientific computing for Radio
Astronomy

Verity Allan

###### Abstract

A discussion of the history of scientific computing for Radio Astronomy in the
Cavendish Laboratory of the University of Cambridge in the decades after the
Second World War. This covers the development of the aperture synthesis
technique for Radio Astronomy and how that required using the new computing
technology developed by the University’s Mathematical Laboratory: the EDSAC,
EDSAC 2 and Titan computers. This article looks at the scientific advances
made by the Radio Astronomy group, particularly the assembling of evidence
which contradicted the Steady State hypothesis. It also examines the software
advances that allowed bigger telescopes to be built: the Fast Fourier
Transform (FFT) and the degridding algorithm. Throughout, the contribution of
women is uncovered, from the diagrams they drew for scientific publications,
through programming and operating computers, to writing scientific papers.

##  1 Introduction

The years following the Second World War were a time of massive scientific and
technological innovation in the University of Cambridge. The University’s
Mathematical Laboratory was set up prior to the War to investigate numerical
methods, and after the war, Maurice Wilkes became its director. Having visited
the United States and seen the ENIAC (Electronic Numerical Integrator and
Computer) computer, he started building EDSAC (Electronic Delay Storage
Automatic Calculator), putting Cambridge at the forefront of the computer
revolution (Ahmed, 2013, p. 41). In the same post-War years, the Cavendish
Radio Astronomy group assembled, with Martin Ryle at its head. The Cavendish
Laboratory of the University of Cambridge had been doing fundamental physics
research for decades, and staff had won Nobel Prizes Cavendish Laboratory
(2021, Cited 30 Sep 2021). The Radio Astronomy group would add to this
collection, as Ryle and Tony Hewish won the Nobel Prize for Physics in 1974
for their innovative telescope design and the discovery of pulsars — work that
relied on the computers of the Mathematical Laboratory Nobel Media AB (1974
Apr 7 [cited 2021 Apr 7]).

This reliance on computers is exemplified by Ryle’s request for a bigger
computer:

> One day, Ryle came to me to say that he was planning the erection of a much
> larger telescope and to ask whether the Mathematical Laboratory could
> undertake to provide the computing support required. (Wilkes, 1985, p. 193)

This paper will explain why Radio Astronomy needed a bigger computer, and will
elucidate the role of other members of the Radio Astronomy group and the
Mathematical Laboratory beyond the relatively well-known names of Ryle,
Hewish, and Wilkes.

It has become more widely known in recent years that a lot of early computing
relied on women — thanks to work by Janet Abbate and Mar Hicks and Margo Lee
Shetterly Abbate (2012), Hicks (2018), Shetterly (2016). Women were clearly
involved in the early years of computing at Cambridge, as can be seen from the
archives of the Department of Computer Science and Technology, which is a
successor to the Mathematical Laboratory. A photograph of staff from 1949
shows 20 staff, of whom 8 were women Computer Laboratory (1999). In this
paper, we will uncover some of the contributions of women to science and
scientific programming in Radio Astronomy in the years from 1950 to 1963.

The University computers that the Radio Astronomy group used during this
period were EDSAC, the first electronic digital stored program computer in the
world, EDSAC 2, which led to many innovations in microprogramming, and Titan,
which led to advances in computer graphics and computer aided design (CAD)
(Ahmed, 2013, p. 72). Titan was the computer requested by Ryle, which was
needed for the One-Mile telescope.

##  2 The Women In Radio Astronomy Computing

The Radio Astronomy group became reliant on computing, and by 1965, over 40%
of all papers produced by the group had required the use of a computer to
process data (Leedham and Allan, 2021, p. 14). Women were extensively involved
in this endeavour. Around 50% of people acknowledged in papers for their
contribution to the programming and operation of computers were women (Leedham
and Allan, 2021, p. 14). These women were employed in a variety of roles.

Some were hired as Computors in the 1950s and 1960s,111Source: Cavendish
Laboratory Archive Personnel Records. initially to do calculations, and then
later to assist with programming. Computor or Computer as a job description
was common in the 1940s, first to describe someone who was hired to do
calculations by hand or with a mechanical or electro-mechanical computer, and
then to describe a worker who used a computer in some capacity Light (1999).
The Cavendish records also show that people (often women) were hired as
scanners for High Energy Physics: their job was to analyse photographic plates
from cloud chamber experiments. Women were also hired as Research Assistants:
Elizabeth Waldram was hired as such (Ahmed, 2013, p. 63). Judy Bailey, who
later became Deputy Director of the University Computing Service (another
successor to the Mathematical Laboratory) worked for Radio Astronomy as a
Technical Officer University of Cambridge (2008 [cited 2021 Apr 7]).

Women were also hired to prepare diagrams for scientific papers, drawing
graphs and contour diagrams, as it was not yet possible to prepare these with
computers. While preparing this paper, because of the Covid-19 pandemic, it
was not possible for me to look at University records to get a sense of the
number of people in these roles, nor of how many of them were women. They were
known as the girls in the attic Clifford, F. E. (1964), p. viii.

Some of the women involved in scientific computing were PhD students and
researchers themselves. Ann Neville, one of Ryle’s PhD students, did a
considerable amount of programming. She had to program for EDSAC 2, and to
save space, many constants had to be combined into one constant, just to shave
a few bytes off the size of the program.222Donald Wilson, Personal
Communication, 22 April 2021.

##  3 The first forays into scientific computing

While Charles Wynn-Williams was a pioneer of electro-mechanical computing for
the Cavendish Wynn-Williams (1931), the Radio Astronomy group did not leap
straight to digital computing for all their papers. We can trace the use of
computers and the contributions of programmers primarily through the
acknowledgements section of papers. They published their first paper using
EDSAC in 1953, and use through the 1950s was fairly sporadic (Leedham and
Allan, 2021, p. 14).

The first women we encounter in the acknowledgements probably were the
computers. In 1951, a Mrs A. C. Hollis-Hallett is credited as having analysed
a large proportion of the records (Smith, 1951, p. 963). It’s not possible to
verify this, as no records survive. Similarly, a Mrs Moore is credited in a
paper by Scheuer and Ryle from 1953, for help in the computation of results
(Scheuer and Ryle, 1953, p. 17). It’s likely that Mrs Moore was the computer,
not EDSAC, as EDSAC was not listed in the acknowledgements (which was the
common practice at the time).

However, the development of a new technique in Radio Astronomy was going to
change the group’s relationship with computers: the technique of aperture
synthesis.

The basic principles were sketched out by Ryle in a 1957 paper Ryle (1957),
and implemented by John Blythe. Aperture synthesis, as the name suggests,
allows for the synthesis of a larger aperture. By using two or more smaller
telescopes, one can achieve the resolution (but not the sensitivity) of a
telescope with diameter equivalent to the longest spacing between
antennas.333The distance between a given pair of antennas is known as a
baseline: the length of the longest baseline dictates the resolution
achievable by the telescope. However, when measuring a signal with a
particular pair of antennas, only part of the signal is observed – the
measurement is of a Fourier component of the signal Christiansen and Högbom
(1985), Chapter 8. To reconstruct the complete signal, the other Fourier
components must be measured, which can be achieved by moving the antennas
around to fill in the aperture. The Fourier components then need to be
combined and transformed into a useful measurement of sky brightness.

Thus the Fourier Transform must be calculated for aperture synthesis
telescopes, and this is not really feasible to do by hand. So the Radio
Astronomy group was forced to turn to computers. Blythe’s papers from 1957,
where he implemented this technique, used EDSAC for the calculations (Blythe,
1957a, p. 651), (Blythe, 1957b, p. 659). One of these papers used EDSAC to
perform 15 hours of computation, performing over 2 million operations, to
output data in a form suitable for making contour maps Blythe (1957a). In both
papers, Blythe credited a Mrs J. Sandos who performed most of the analysis.
No-one in the Radio Astronomy group can recall Mrs Sandos (who may have been a
member of the Mathematical Laboratory), but she undoubtedly helped with the
complex data preparation process: error-free punched tapes were required as
input, and all the data had to be arranged in a particular way in order to
compensate for EDSAC’s lack of storage space.

By 1960, we see EDSAC 2 appearing in paper acknowledgements. However, the
workflow still retains a number of manual steps, as one paper notes:

> It would be possible to record such information directly in digital form,
> but it has been found relatively easy to transfer the present records to
> punched tape in a record reader and manual perforator. (Costain and Smith,
> 1960, p.412).

The acknowledgements are silent about who did this, but it’s quite likely to
be either PhD students or Computors.

##  4 Earth Rotation Aperture Synthesis and the Steady State Hypothesis

In 1961, an extension of the aperture synthesis technique was developed: using
the rotation of the Earth to help fill in the aperture of a telescope, thus
performing Earth Rotation Aperture Synthesis. This technique was prototyped
using the Cambridge 178MHz telescope and EDSAC 2 — the new, more powerful,
computer in the Mathematical Laboratory. This telescope and others were used
to collect data that seriously undermined the Steady State hypothesis.

In 1961, Scott, Ryle and Hewish performed earth-rotation aperture synthesis
for the first time Scott et al (1961). This paper has a number of interesting
features. Firstly, this paragraph:

> The processes of filtering and convolution are basically equivalent and in
> this case where the output of the receiver was already recorded in digital
> form it was convenient to carry out a direct convolution with a time
> function whose Fourier transform provides the required polar diagram. (Scott
> et al, 1961, p. 100).

This is an early use of a digital filter rather than a piece of electronics;
the work is moving from hardware to software. Note also that the digital form
is paper tape!

To record the data, a sample and hold electronic circuit was implemented
electro-mechanically, using photo-electric cells, to output two columns of
5-hole tape for each data point (giving ten bits of precision).444Thanks to
B.J. Harris for spotting that they were building a sample and hold circuit.
Each tape started at the same sidereal time: at the same time with respect to
the fixed stars in the sky, which is most useful to astronomers, so non-local
astronomical bodies can be located easily. The sidereal time arrangement meant
that the data could be efficiently processed — while EDSAC 2 had more storage
space than EDSAC, programmers still could not afford to be profligate. During
the data input phase, the data were convolved with a function which allowed
for error correction, and which also allowed the extraction of the sine and
cosine components which were required for the main computation. At this point,
the data were sorted into a more convenient order before being written onto
magnetic tape. This magnetic tape was used as the input data for the main
calculation, in which the data were put through the Fourier Transform. The
final outputs were effectively a 2-dimensional map of the sky, sampled at
discrete intervals. The probability distribution of the measured intensity was
also calculated and output. The final values for the sky map needed to be
interpolated, but this was done manually, possibly by the girls in the attic
or junior members of the group.

As well as being the first practical demonstration of aperture synthesis using
the earth to fill in the aperture, this paper also was important for providing
evidence against the Steady State hypothesis. The authors note:

> there is no evidence for a reduction in the density of radio sources… this
> observation implies an isotropy which extends to at least 10,000 sources
> steradian. (Scott et al, 1961, p. 111).

This isotropy in extra-galactic faint sources conflicted with predictions from
the Steady State model, which predicted that there should be many fewer faint
sources, and that there should be no difference between galactic and extra-
galactic sources. Once again we find a woman tucked away in the
acknowledgements: Mrs R. Feinstein. Ruth Feinstein was employed by the
Mathematical Laboratory of Cambridge Computer Laboratory (1999, [cited 2021
Apr 7]), and was an assistant to Dr Lucy Slater, who became Head of Computing
in the University’s Department of Applied Economics Andrews (2013, cited 2021
Apr 7), p.6. Ruth Feinstein assisted her husband, Charles, with calculating
and typing for his PhD thesis (Offer, 2008 Jun, [cited 2021 Apr 7], p. 4).
Unfortunately, she left the Mathematical Laboratory shortly after marriage of
Cambridge Computer Laboratory (1999, [cited 2021 Apr 7]), and she seems to
play no further part in computing for Radio Astronomy. She was, along with Dr
David Wheeler,responsible both for the running and design of the programme
(Scott et al, 1961, p. 111).555Note that at this time, the UK still used
programme to refer to computer programs.

###  4.1 The Steady State Hypothesis

A summary of the steady state hypothesis is that the universe is expanding,
but has no beginning and no end, and that its appearance does not change over
time. In contrast, the Big Bang theory states that the universe expanded from
an initial state of high density and temperature, and thus its appearance
changes over time.

Ryle’s group was building up to attack the Steady State hypothesis. There are
two papers from Harriet Tumner and Patricia Leslie, both PhD researchers in
the group Leslie (1961); Tunmer (1960). Neither paper mentioned using EDSAC 2,
though both used data from the Cambridge surveys that were processed using
that computer. These papers look at the brightness, density, size, and
clustering of extra-galactic radio sources — where the Steady State and Big
Bang hypotheses generated different predictions.

Then there is a 1961 paper from Paul Scott and Martin Ryle Scott and Ryle
(1961). This looks at the relationship between the number of radio sources,
and their flux density (essentially their brightness. The Steady State
hypothesis assumes that there is a particular relationship between the
brightness of the source, and how many sources of that brightness there are.

The acknowledgements in this paper read:

> We should like to thank Dr Hewish and Miss Patricia Leslie for useful
> discoveries, and Miss Ann Neville and Mr DR Marks for assistance in the
> reduction of observations. (Scott and Ryle, 1961, p. 397)

Ann Neville was one of Ryle’s PhD students, and she will appear as an author
on later papers.

Next there’s a paper by Hewish. He modelled the source number–flux density
relationship, and used EDSAC 2 to do it. This is one of the earliest uses of
the Monte Carlo method in Radio Astronomy: successors to this method are being
used today as as key modelling technique Feroz et al (2019). Hewish doesn’t
credit anyone else, so he most likely did a lot of the programming himself.
This contrasts with Ryle, who didn’t program at all, even though Ryle was well
aware of how essential computers were for aperture synthesis.666Dr Elizabeth
Waldram, personal communication 4 May 2021.

Finally, there is a Ryle and Clarke paper of 1961 in which they showed that
extra-galactic radio sources have no variation in density in different parts
of the sky — the only variation comes when observing the Milky Way galaxy
(which is nearby in astronomical terms Ryle and Clarke (1961). The observed
source number-flux density relationship doesn’t match the steady state
hypothesis. They conclude:

> These observations do, however, appear to provide conclusive evidence
> against the steady state model.

Any last hopes that the Steady State theorists had of salvaging their model
was blown away conclusively in 1964 when Penzias and Wilson detected the
Cosmic Microwave Background Penzias and Wilson (1965).

##  5 A radio survey of the North polar region

We now turn to analyse in some detail a paper from 1962, in which major
advances were made in both computing and Radio Astronomy Ryle and Neville
(1962).

There are two major computational innovations in this paper. The first is
Wheeler’s Fast Fourier Transform (FFT) algorithm, tersely described in a
single paragraph, plus an equation. From this, we can glean that the data from
the sky needs to be placed onto a Cartesian grid with $(x,y)$ co-ordinates.
This means data must be converted from spherical co-ordinates that are most
naturally used for observing objects on the sky into Cartesian co-ordinates.
While the mathematician Gauss developed the theory of FFT, this practical
implementation pre-dates the one by Cooley and Tukey in 1965, which is usually
credited as the first practical implementation Heideman et al (1984).

The other programming innovation was the map degridding algorithm, which
enables conversion back from Cartesian co-ordinates into spherical co-
ordinates, so the radio sources are correctly located on the sky, which also
ended up producing some of the world’s first computer graphics. The output
from the computer was plotted on a CRT (Cathode Ray Tube monitor, where it
lasted for a few seconds, just long enough to be photographed (Ahmed, 2013, p.
63). This work was done by Elizabeth Waldram, then a Research Assistant in the
group. This degridding algorithm (and its successors) were used for all
subsequent interferometers built by the group.777Dr Elizabeth Waldram,
personal communication 04 May 2021.

With the FFT and the degridding algorithm, it was possible to build a map of
the northern radio sky. It’s very likely that the final construction of the
map from the photographic plates was made by the girls in the attic. This kind
of mapping was a large part of their job. They weren’t working directly with
computers themselves, but they were a vital part of the scientific workflow,
often alongside secretarial staff who would type up manuscripts. We can see a
rare acknowledgment for the women doing such work in a 1962 paper Turtle and
Baldwin (1962):

> We are grateful to Miss C. Dunn and Mrs M. Warren for helping with the
> analysis and the preparation of the contour maps.

The contour maps were drawn from EDSAC 2 output (Turtle and Baldwin, 1962, p.
476).

With this paper, we have the foundations for modern radio astronomy computing.
The FFT saves a lot of computational effort compared to the Direct Fourier
Transform which works with spherical co-ordinates. However, the use of the FFT
also necessitates the use of gridding and degridding algorithms, which we need
to first transform our data into the right shape for the FFT, and then put it
back into spherical co-ordinates afterwards. FFT and gridding algorithms
remain an important part of Radio Astronomy research Ye et al (2020), Veenboer
et al (2019), Nishimura et al (2021).

It’s clear from Wheeler’s inclusion in the acknowledgements rather than as a
co-author that the exclusion of women programmers from authorship wasn’t
purely a result of sexism. Sexism may still have played a part, as a majority
of those acknowledged for programming in Radio Astronomy papers were women
(Leedham and Allan, 2021, p. 14). Mar Hicks has shown how work done by women,
especially in the computing field, was devalued, which may also have been a
contributing factor (Hicks, 2018, passim). Wheeler was acknowledged in Ryle’s
Nobel Prize lecture for his Fast Fourier Transform algorithm Ryle (1992); none
of the women get mentioned.

##  6 Discussion

It’s clear from the preceding sections that women were deeply involved in the
production of scientific papers in the 1950s and 60s, and that they were also
involved in doing much of the programming and a good deal more of the science
than is usually recognised. The programming also required good mathematical
skills and an understanding of Radio Astronomy, so that programmers could work
with sidereal time and Right Ascension and Declination (the spherical co-
ordinate system used by astronomers) and their conversion into Cartesian co-
ordinates for use in the FFT — something that mathematics undergraduates often
struggle with. Perhaps the girls in the attic didn’t require such advanced
understanding, but they were expected to work to the highest standards of
accuracy.

It is extraordinarily difficulty to get a picture of many of the computational
methods used. Programs were not routinely recorded at the time, though there
are some contemporaneous program booklets stored in the archive of the
Department of Computer Science and Technology.888See for example, shelfmark
V75-58, which lists programs used by the Department on Geology on Titan.
However, none of these survive for Radio Astronomy. The information presented
in papers is minimal — usually just enough to allow for some mathematical
recreation, but not enough to understand the algorithms. This may have been
the result of the culture of the research group at the time; Ryle may have
maintained more of a war-time culture of secrecy than we find desirable as
scientists today.999Donald Wilson, personal communication 22 April 2021.

It is also worth noting that, while women may have left the Mathematical
Laboratory on marriage, this wasn’t true for members of the Radio Astronomy
group. Indeed, programmers were in such high demand that they could work part-
time and flexibly, many years ahead of this becoming widely available. Dr
Waldram recalls working 10-15 hours a week in the early 1960s, to accommodate
her childcare needs.101010Elizabeth Waldram, personal communication 4 May
2021.

##  7 Conclusion

The acknowledgements to papers provide one of the few ways of finding out
about the work done in early scientific computing, as they often indicate that
work was done using a computer, and who did that work. We can get tantalising
glimpses of what that work was, and the people behind it. This could usefully
be supplemented by more archival work within the University, once this is
possible again.

###### Acknowledgements.

My thanks go to Dr Elizabeth Waldram, one of the Cavendish’s computing
pioneers, who has given her time very generously, to Dr Donald Wilson, who
provided many valuable insights into this period, to Dr David Green, who
helped me with my LaTeX, to J. Nevins, who helped proof-read, and to Professor
Malcolm Longair, who has supported this project.

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Gelfand–Dickey hierarchies. For many of these hierarchies this is the first
time a pluri-Lagrangian structure has been given. The success rate of our
method suggests that it is a useful tool to study connections between discrete
and continuous integrable systems. Nevertheless, there are lattice systems to
which the continuum limit procedure does not seem to apply, an issue which
deserves additional investigation. Previously, only a few examples of
continuous pluri-Lagrangian 2-form systems were known. The multitude of new
examples given in this work contributes to the evidence that a pluri-
Lagrangian structure is a relevant attribute of integrability.

### Acknowledgments

This research was supported by the DFG through the SFB/TRR 109,
‘Discretization in Geometry and Dynamics’. The author is grateful to the
anonymous referees for their insightful comments.

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