UOA10-13: Cycles of Time; Public engagement with conformal infinity
Submitting InstitutionUniversity of Oxford
Unit of AssessmentMathematical Sciences
Summary Impact TypeSocietal
Research Subject Area(s)
Mathematical Sciences: Pure Mathematics
Summary of the impact
This case study describes public engagement with the University of
Oxford's research in Mathematical Physics via the popularization of
science through the writings, public lectures and media appearances of Sir
Roger Penrose. Published in 2010, Penrose's book Cycles of Time
deals directly with the research contributions and has reached broad
audiences via books, public lectures, TV appearances, and YouTube
postings. The impact has been to engage large numbers of the public with
modern theories of the origin of the universe in a mathematically
In 1999, Professor Paul Tod, faculty member at Oxford University,
published [1,2] a mathematical study of Penrose's Weyl curvature
hypothesis as described in , giving a rigorous analytic treatment of
solutions to the partial differential equations at an initial singularity
and an optimal geometric framework for their study. Tod gave a definitive
statement of the Weyl curvature hypothesis and showed that it could be
re-framed as the condition that the conformal structure of space-time can
be smoothly continued through an initial singularity. This gives a clear
mathematical meaning to `the universe before the big bang' and underpins
Penrose's subsequent proposals for the nature of physics before the big
The singularity theorems imply that there must have been an initial
singularity, the big bang, approximately 14 billion years ago, in which
the universe that we see started essentially from a point. This is now an
integral part of the standard modern view of our universe. The existence
of the big bang invites questions such as: What controlled the big bang?
Did anything precede it? If so, what? A theme emphasized by Penrose is
that the second law of thermodynamics provides overwhelming evidence for
special initial conditions for the evolution of the universe; he proposed
the Weyl curvature hypothesis, namely that the `Weil curvature' should
vanish as the initial singularity is approached. With this assumption,
Tod's work demonstrated that it is meaningful to continue the conformal
geometry of the universe back in time to before the big bang .
Penrose's concept of conformal infinity gives a geometric realization to
those events that occur at infinitely late times, exploiting an analogy
with the perspective ideas of projective geometry as a surface at infinity
whose conformal structure again has a smooth continuation through
infinity. More recently, Nobel prize winning studies of observational data
showed that the universe is controlled by a positive cosmological constant
(also known as accelerated expansion or dark energy). Penrose observed
that with such a positive cosmological constant, conformal infinity has
the same conformal geometry as the big bang in Tod's work. This led him to
propose that the big bang is conformally glued to the future infinity of a
previous aeon or epoch of the universe with positive cosmological constant
, answering the question as to what precedes the big bang. Two
consecutive aeons are separated by infinite time and massive particles
cannot communicate from one aeon to the next. However, massless particles
such as photons or gravitational waves continue through from one aeon to
the next leading to observable consequences. The paper  was the first
announcement of the new conformally cyclic cosmology proposals.
Key researchers from the University of Oxford
K.P. Tod: University Lecturer at the Mathematical Institute, 1985-date.
R. Penrose: Rouse-Ball Professor at the Mathematical Institute 1973-1998,
subsequently retired but working in the Mathematical Institute as an
References to the research
* K. Anguige and K.P. Tod, "Isotropic cosmological singularities. 1.
Polytropic perfect fluid space-times,'' Annals Phys., 276 (1999)
257 [gr-qc/9903008], 29 citations. DOI: 10.1006/aphy.1999.5946
* K. Anguige and K.P. Tod,"Isotropic cosmological singularities. 2.
The Einstein-Vlasov system,'' Annals Phys., 276, (1999) 294
[gr-qc/9903009], 16 citations. DOI: 10.1006/aphy.1999.5947
 S Hawking and R Penrose, the Nature of Space and Time, New Edition,
Princeton University Press (April 01, 2010) ISBN: 9780691145709.
Originally published in 1997.
* K.P. Tod,"Isotropic cosmological singularities in
spatially-homogeneous models with a cosmological constant," Class.
Quant. Grav., 24, (2007) 2415 [arXiv:0704.2506 [gr-qc]].
The three asterisked outputs best indicate the quality of the
underpinning research and are contained in high quality internationally
Details of the impact
The impact is on society through public interest and engagement with
science and the stimulation of public discourse. The questions of the
`origin of the universe', `what happened before the big bang?', and `how
space-time might emerge from a more fundamental theory' are some of the
most frequently addressed issues in popular science and stimulate wide
interest (and controversy). Roger Penrose's writings have opened up new
avenues in this debate that have led to much interest outside academia.
The beneficiaries since 2008 have been the general public who gain an
understanding of current models for the evolution of the universe.
The research of Paul Tod demonstrated rigorously that the Weyl curvature
hypothesis gave mathematical sense to the question of whether the
conformal geometry whose existence is demonstrated mathematically has any
physical meaning. This underpinned Penrose's Conformally Cyclic Cosmology
proposal. His recent broad audience book Cycles of Time: An
Extraordinary New View of the Universe (published in 2010) explains
the conformal cyclic cosmology which is underpinned by the research
described in Section 2.
Cycles of Time has been hugely successful. More than 95,000 copies
have been sold worldwide since 2010 [A], it has been translated into
German, Polish, Italian and Russian, and released as an audio book. The
Nature of Space and Time has sold 10,502 copies in the period [B]
and the Road to Reality, another pre-cursor building on the themes
in the Nature of Space and Time, has sold nearly 120,000 copies since 2004
including 45,400 in the REF period [A]. The books are also promoted with
accompanying public presentations at large book fairs (e.g., 25/11/10 at
Toppings, The Paragon, Bath, Somerset or 26/3/12 Sunday Times Literary
Festival, Oxford). A new book by Penrose is an automatic choice for review
in quality media of all kinds.
Penrose's books are highly unusual among popular science books in
celebrating rather than obscuring the mathematical equations and
geometrical pictures that underlie the physical ideas. They take the
audience seriously as intellectuals and do not oversimplify. Readers
engage directly with Penrose's writing, as evidenced by a 2008 reader
review [C] of The Road to Reality on Amazon: "If you
assiduously go through every sentence until you understand its meaning,
if you consult outside references as necessary, if you really absorb
this material- it is phenomenal. Penrose will equip you with a visual
and intuitive comprehension of the advanced math necessary to really
understand the big theories of physics. [...] In terms of the
breadth and scope, I could compare this to the Feynman lectures.
[...] This is a book to live in for a long time. There is nothing else
quite like it. The rewards justify the large amount of reader time and
effort that will need to be committed. Five stars, absolutely".
Professional and reader reviews of Cycles of Time also attest to
Penrose's success in engaging with the wider public:
"The most influential person to develop the general theory of
relativity since Einstein" [D]
"A gifted popularizer of science [...] Roger Penrose has
attracted a popular audience with thought- provoking books on physics,
consciousness and the theory of computation" [E]
"Doing what most find impossible has long been Penrose's stock in
trade in mathematics and physics, even when it comes to publishing"
"One of the world's best science writers" [G]
"As usual, one gets a clear, simply, but new view of physics from
Penrose. The depth is much greater than many popular science books, but
I find I can grasp the ideas. I have wondered for a long time how to get
an understanding of metrics which seem all important in modern physics.
I looked at a collection of math books which would provide the knowledge
but felt that it would take the rest of my life to get there. Penrose
gave me as much knowledge of the ideas and usage of the methods as I
need in one page" [H]
This approach makes his contributions to the public engagement with
science particularly important as it allows the public to see scientific
debate as a rigorous evaluation of mathematical argument and empirical
data rather than as `anything-goes' speculation with one person's theory
being on a democratic footing with anyone else's.
Another unusual feature of Penrose's public engagement is that he is
rarely reviews other people's ideas except to counterpoint them against
his own. He engages people directly with his own research and that of his
close associates following the programmes that he has initiated. The
public engagement described in this study arises directly from the
research described here and not from that of others or older ideas. This
point is reinforced by his use of hand-drawn diagrams which have attracted
much favourable comment from readers of his books and online viewers of
his lectures, for example "He's probably the only world famous speaker
that draws his own slides with color marker pens! Not just a brilliant
mind but also a talented illustrator!" comments one YouTube watcher
in 2011 [I].
The wide impact of these ideas and Penrose's presentational style is
evidenced by regular invitations to give distinguished public lectures and
to appear on the media the world over. Penrose featured prominently in a
2010 BBC Horizon programme which attracted more than 1.8 million
viewers [J]. His public lectures typically pack out the largest available
auditoria, sometimes with overflow rooms equipped with video-links. For
example, a capacity audience of 477 saw him at the Royal Institution in
2010 [K], while an audience of more than 700 saw him lecture after
receiving the 2011 Fonseca prize. Of those who filled in a feedback
questionnaire following the Royal Institution lecture, 94% had come `to
find out more' and 82% wanted `to find out more following the event' [K].
He gave the Tagore, Bose and Chandrasekhar memorial lectures in Kolkata,
the Chandrasekhar lecture Delhi, the Neils Bohr lecture in Copenhagen, the
Trotter Public lecture after receipt of the Trotter prize at Texas
A&M, and the Copernicus Institute Lecture in Warsaw among many others
around the world.
The impact of Penrose's public lectures is not limited to the few hundred
people that attend each of them, as they are often filmed and posted
online. For example, YouTube lists 344 videos in response to a search for
`Roger Penrose'; not all of these feature him directly, but total views of
those that do, and were posted since 2008, number well over 500,000 [L]. A
good example is his 2009 Christmas Lecture Aeons before the Big Bang
with more than 52,000 views [M]; another is his 2010 TEDx lecture aimed at
encouraging young people to engage with STEM subjects, with more than
32,000 views [N]; and a third is a public lecture on Twistors and
Quantum non-locality, broadcast on TV in Ontario in 2011, with more
than 40,000 views [O]. Many of the posted videos generate comments
numbering in the hundreds and often stimulate online dialogues about the
content of the lectures.
These are outstanding impacts on a world stage. As can be seen, Penrose
is in great demand and has a worldwide following.
Sources to corroborate the impact
[A] Email from Literary Consultant, The Zeno Agency, confirming sales
numbers for the books of Roger Penrose, copy held by the University of
[B] Email from Executive Editor, Princeton University Press, confirming
sales numbers for The Nature of Space and Time, copy held by the
University of Oxford.
[C] Reader review at http://www.amazon.co.uk/review/R2SS0HKLRGGNT9/ref=cm_cr_pr_perm?ie=UTF8&ASIN=0099440687&linkCode=&nodeID=&tag=
[D] Review in Nature of Cycles of Time
[E] Review in The Wall Street Journal of Cycles of Time
[F] Review in The Guardian of Cycles of Time
[G] Review in The New York Journal of Books of Cycles of Time
[H] Reader review at http://www.amazon.co.uk/review/R1PWAJGLN1V1U6/ref=cm_cr_pr_perm?ie=UTF8&ASIN=0224080369&linkCode=&nodeID=&tag=
[I] Viewer review at http://www.youtube.com/watch?v=oBkOYQ02chs:
[J] Horizon, Before the Big Bang, 11 October 2010, BBC2, over 1.82
number of viewers found on www.barb.co.uk
[K] Email from Public Programme Manager at the Royal Institution. Contact
details held by the University of Oxford.
[L] Viewing figures for Penrose videos on youtube:
[M] Aeons Before the Big-Bang, Sir Roger Penrose Christmas Lecture,
[N] Space-Time Geometry and a New Cosmology, 6 March 2010 TEDx, Warwick
TEDX organisers. Contact details held by the University of Oxford.
[O] Twistors and Quantum Non-Locality, Public Lecture and broadcast on TV
Ontario, 6 April 2011, Ontario Canada, at http://www.youtube.com/watch?v=hAWyex1GKRU
[C]-[I] exemplify the significance of the public engagement activities;
[J]-[O] exemplify the reach.