Einstein’s blackboard and the Friedman-Einstein model of the cosmos

The Einstein biographer Andrew Robinson, author of Einstein: A Hundred Years of Relativity , recently reminded me of the saga of Einstein’s blackboard. The blackboard, a well-known exhibit at the Oxford Museum for the History of Science, was used by Einstein in the second of three lectures he gave at Oxford University in 1931.


An image of the blackboard used in Einstein’s 2nd Rhodes lecture at Oxford in April 1931 (reproduced by permission of the Hebrew University of Jerusalem). The analysis is taken from Einstein’s 1931 model of the cosmos.

I came across Einstein’s blackboard during the course of our first Einstein study, a translation and analysis of Einstein’s 1931 paper on cosmology. Although the paper is not very well known in the English-speaking world, it is a work of historical importance, as it constituted the first scientific publication in which Einstein formally rejected his static model of the universe and embraced the possibility of a cosmos of time-varying radius. In the paper, Einstein adopts Alexander Friedman’s 1922 analysis of relativistic cosmic models of time-varying radius and positive curvature, but sets the cosmological constant to zero, predicting a cosmos that expands and contracts over time (the model is sometimes known as the Friedman-Einstein model and should not be confused with the later Einstein-deSitter model of the cosmos). With the use of Edwin Hubble’s redshift/distance graph for the spiral nebulae, Einstein extracts estimates from his analysis of ρ ~ 10-26 g/cm3 , P ~ 108 light-years and t ~ 1010 years for the density of matter, the radius of the cosmos and the timespan of the cosmic expansion respectively. However, our analysis indicated that Einstein’s estimates contained a systematic numerical error.

Before submitting our paper on this to a journal, I discovered to my great surprise that Einstein’s 1931 paper is neatly summarized on the Oxford blackboard (see above). Although the blackboard is quite well known as an intriguing museum exhibit, it seems no-one had made the connection with a published paper. Even better, one extra line on the blackboard, not included in Einstein’s published paper, makes clear the source of the numerical errors in the paper.

The analysis is quite easy to follow: for a cosmos of radius P, the quantity D is defined on the top line of the blackboard as D= (1/c). (1/P).(dP/dt): essentially the Hubble constant divided by the speed of light. From his earlier analysis, Einstein has developed two independent relations from the Friedman equations that relate D to the radius and density of the cosmos respectively:  D~ 1/P2  and D2  ~ 1/3 , shown as equations (1a) and (2a) on the blackboard. Using the contemporaneous Hubble constant of 500 kms-1Mpc-1, he thus extracts estimates of cosmic density, radius and timespan of expansion respectively,  displayed in the last three lines on the blackboard. However, these estimates contain errors as noted above, and the fourth line on the blackboard (not shown in Einstein’s published paper), makes the source of his error clear. Where Einstein obtains a value of 10-53 cm-2 for the quantity D2, simple calculation shows that this quantity should have been D2 ~ 10-55 cm-2 (or 10 -51 m-2). It appears that Einstein stumbled in converting the Hubble constant to his customary cgs units, resulting in a density of matter that was too high by a factor of a hundred, a cosmic radius that was too low by a factor of ten, and a timespan for the expansion that was too high by a factor of ten (although the units of measurement are not specifically stated for the density estimate, cgs units are implied by the other calculations).

Thus Einstein’s blackboard helped us to solve the riddle of the anomalous estimates of his 1931 paper! Our paper on this made the cover of the European Physical Journal and you can read more about Einstein’s blackboard on this blog here and on wikipedia here.


All of the above was interesting and good fun. However, I should say that our translation and analysis of Einstein’s 1931 paper yielded another, rather more serious result – namely that the 1931 paper is NOT a cyclic model, although it is often cited as the first cyclic model of the expanding universe. Einstein specifically rules out this possibility, pointing out that the model breaks down at the endpoints of the single ‘cycle’.







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A celebration of Sir Fred Hoyle at the Royal Astronomical Society

The birth centenary of the noted British astrophysicist Sir Fred Hoyle was celebrated on Friday at the Royal Astronomical Society with a one-day meeting of talks describing Sir Fred’s many contributions to 20th century physics. While he is chiefly remembered in some quarters as the physicist who was ‘wrong on the big bang’, Sir Fred in fact made a number of seminal contributions to modern physics in several fields. Indeed, it was a treat to witness former collaborators and students recall his contribution to stellar evolution, stellar nucleosynthesis, astrobiology and cosmology, to name but a few.

I hadn’t been to the RAS before although I was elected a Fellow a few years ago, and I was stunned by its fantastic location in central London. It is housed in the famous Burlington House on Piccadilly, sharing the premises and courtyard with the Linnean Society, the Geological Society and the Royal Academy of Arts, a stone’s throw from Piccadilly Circus. As luck would have it, the Royal Academy are currently hosting a show of the work of the Chinese artist Weiwei, and his striking ‘Tree Sculpture’ filled the Burlington courtyard.

Burlington house on Piccadilly, housing five learned London societies, including the Royal Academy of Arts

Weiwei’s exhibit ‘Tree Sculpture’ in the Burlington courtyard. The RAS is located on the west wing of the courtyard.

The meeting opened with an introduction by Lord Martin Rees, who gave a comprehensive overview of Sir Fred’s works in a short, a ten-minute talk. This was followed by a description of Hoyle’s contribution to accretion physics by Professor Andrew Fabian of the Institute for Astronomy (IOA) in Cambridge, and talks on Hoyle’s work on nucleosynthesis by Professor Lynden-Bell (IOA) and Professor Malcolm Longair, Director of the Cavendish laboratory.

Professor Jayant Narlikar of the Inter-University Centre for Astronomy and Astrophysics (Pune, India) then gave the talk ‘Fred’s theories and ideas about gravity’. This was a rare treat – as a long term collaborator, Jayant made several important contributions to the development of Hoyle’s steady-state model of the universe (including the development of a new version of the model based on the principle of least action, and the development of the later ‘quasi-steady-state’ model), so it was most interesting to hear his take on the genesis of the steady-state cosmologies of Hoyle and Bondi and Gold.

Hoyle and Narlikar in 1966

Another treat was a talk by Professor Chandra Wickramasinghe of the University of Buckingham, ‘Fred Hoyle and the foundation of astrobiology’. This presented interesting insights into Chandra’s long collaboration with Sir Fred, from their early work on interstellar dust to their famous hypothesis that life on earth was seeded by comets. The latter work essentially founded the modern field of astrobiology, although they are not always credited for this.

Jayant’s talk was followed by a talk on Hoyle’s cosmology by Professor John Barrow of the Department of Applied Mathematics and Theoretical Physics at Cambridge. John gave a superb overview of Hoyle’s steady-state model of the universe, and of the battle royale between Hoyle’s theory group and Martin Ryle’s astronomy group at Cambridge during the 1950s. Most members of the audience were familiar with this story, but John brought out many points that are not well known – not least that the widespread skepticism concerning Hoyle’s hypothesis of the continuous creation of matter was something of a moot point. As demonstrated by Bill McCrea in 1951, a viable steady-state model can be constructed without this assumption. John also reminded the audience that today’s models of cosmic inflation are effectively steady-state cosmologies, and, if the eternal inflationary scenario is right, it is possible that the observed universe is a locally evolving patch in a global ensemble that is in a steady state!

Eternal inflation could give rise to evolving universes embedded in a global steady-state ensemble

I touched on both these points in my own talk ‘Steady-state cosmologies in context‘, although my main aim was to remind the audience that Hoyle’s steady-state model was a reasonable hypothesis at the time – and that the notion of a steady-state universe surfaced in cosmology on many occasions, from Arrhenius to Nernst, from Holmes to MacMillan. Further, not many people know that soon after the emergence of the first evidence for an expanding universe, several physicists considered the possibility of an expanding universe that remains in a steady state due to a continuous replenishment of matter, from Tolman to Einstein, from Schroedinger to Mimura. That said, my main focus was to discuss Einstein’s abandoned attempt at a steady-state model , an unpublished work discovered 2 years ago. (You can find more on Einstein’s attempt at a steady=state model here and here).

Between the two talks on Sir Fred’s cosmology, Nicola Hoyle gave a fascinating description of her personal recollections of her grandfather. It included many intriguing photos and pieces of information I hadn’t seen before. The meeting ended with a talk by Professor John Faulkner of the University of California at Santa Cruz on Sir Fred’s contribution to our understanding of stellar structure and evolution, after which we all trooped off to the beautiful library of Geological Society on the other side of the square for coffee.

All in all, a superb conference in memory of a superb physicist. The meeting was organized by Simon Mitton of Cambridge University. You can find the programme here and slides for my own talk on the ‘Seminars’ page of this blog.

After the meeting, speakers were treated to dinner at the famous RAS Dining Club, and I rolled back to my hotel through the gardens of Buckingham Palace. On Saturday, I took a hop-on hop-off open bus tour of London and it was a great success. In particular, I caught a young string orchestra rehearsing Correlli and Vivaldi concerti in St Martin in the Fields, and a superbly talented string quartet playing Brahms’s Hungarian Dances in Covent Garden, not to mention a relaxing stroll  along the Embankment in the afternoon sun. I’d forgotten what London can be like on a Saturday afternoon, must visit the RAS more often!

The best way to see London


There is a detailed summary of the meeting in this month’s issue of Astronomy and Geophysics


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Robert Boyle Summer School 2015

Last weekend, I attended the Robert Boyle Summer School, an annual 3-day science festival in Lismore, Co. Waterford in Ireland. It’s my favourite annual conference by some margin – a small number of talks by highly eminent scholars of the history and philosophy of science, aimed at curious academics and the public alike, with lots of time for questions and discussion after each presentation.

Born in Lismore into a wealthy landowning family, Robert Boyle became one of the most important figures in the Scientific Revolution, well-known for his scientific discoveries, his role in the Royal Society and his influence in promoting the new ‘experimental philosophy’ in science.


The Irish-born scientist and aristocrat Robert Boyle   

As ever, the summer school took place in Lismore, the beautiful town that is the home of Lismore Castle where Boyle was born. This year, the conference commemorated the 350th anniversary of the Philosophical Transactions of the Royal Society by considering the history of the publication of scientific work, from the first issue of  Phil. Trans. to the problem of fraud in scientific publication today.


Lismore Castle in Co. Waterford , the birthplace of Robert Boyle

The summer school opened on Thursday evening with an intriguing warm-up talk on science in modern novels. Jim Malone , Emeritus Robert Boyle Professor of Medicine at Trinity College Dublin, presented a wonderful tour of his favourite novels involving science, with particular emphasis on the novels of C.P. Snow , Ian McEwan and the Irish satirist Flann O’Brien. I must admit I have not read the novels of C.P. Snow (although I am familiar with his famous essay on the two cultures of science and literature). As for Flann O’ Brien, we were treated to a superb overview of the science in his novels, not least the wonderful and surreal novel ‘ The Third Policeman’. Nowadays, there is an annual conference in memory of Flann O’ Brien, I hope Jim gives  a presentation at this meeting! Finally, I was delighted that the novels of Ian McEwan were included in the discussion. I too enjoyed the novels ‘Saturday’ and ‘Solar’ hugely, was amazed by the author’s grasp of science and the practice of science .

Turning to the core theme of the conference, the first talk on Friday morning was ‘Robert Boyle, Philosophical Transactions and Scientific Communication’ by Professor Michael Hunter of Birkbeck College. Professor Hunter is one of the world’s foremost experts on Boyle, and he gave a thorough overview of Boyle’s use of the Phil. Trans to disseminate his findings. Afterwards, Dr. Aileen Fyfe of the University of St Andrews gave the talk ‘Peer Review: A History From 1665′ carefully charting how the process of peer review evolved from Boyle’s time to today. The main point here was that today’s process of a journal sending papers out to be refereed by experts in the field is a relatively new development. In Boyle’s day, a submitted paper was evaluated by either the Secretary of the Royal Society or by one of the Fellows. However, it seemed to me that this ‘gatekeeper’ approach still constituted review by peers and was, if anything, more restrictive than today’s peer review.


The renowned Boyle scholar Professor Michael Hunter of Birbeck College, UCL, in action

On Friday afternoon, we had the wonderful talk ‘Lady Ranelagh, the Hartlib Circle and Networks for Scientific Correspondence’  in the spectacular setting of St Carthage’s Cathedral, given by Dr.Michelle DiMeo of the Chemical Heritage Foundation.  I knew nothing of Lady Ranelagh (Robert Boyle’s elder sister) or the The Hartlib Circle  before this. The Circle was clearly an important  forerunner of the Philosophical Transactions and Lady Ranelagh’s role in the Circle and in Boyle’s scientific life has been greatly overlooked.


St Carthage’s Cathedral in Lismore


Professor DiMeo unveiling a plaque in memory of Lady Ranelagh at the Castle. The new plaque is on the right, to accompany the existing plaque in memory of Robert Boyle on the left 

On Friday evening, we had a barbecue in the Castle courtyard, accompanied by music and dance from local music group Sonas. After this, many of us trooped down to one of the village pubs for an impromptu music session (okay, not entirely impromptu, ahem). The highlight was when Sir John Pethica,  VP of the Royal Society, produced a fiddle and joined in. As did his wife, Pam – talk about Renaissance men and women!


Off to the Castle for a barbecue

On Saturday morning, Professor Dorothy Bishop of the University of Oxford gave the talk ‘How persistence of dead tree technology has stifled scientific communication ; time for a radical rethink’, a presentation that included some striking accounts of some recent cases of fraudulent publication in science – not least a case she herself played a major part in exposing! In the next talk,‘ The scientific record: archive, intellectual property , communication or filter?’ Sir John Pethica of Oxford University and Trinity College Dublin made some similar observations, but noted that the problem may be much more prevalent in some areas of science than others. This made sense to me, as my own experience of the publishing world in physics has been of very conservative editors that err on the side of caution. Indeed, it took a long time for our recent discovery of an unknown theory by Einstein to be accepted by the physics journals.

All in all, a superb conference in a beautiful setting.  Other highlights included a fascinating account of poetry in science by Professor Iggy McGovern, a Professor of Physics at Trinity College Dublin and published poet, including several examples from his own work and that of Patrick Kavanagh, and a guided tour of the Castle Gardens, accompanied by Robert Boyle and his sister. You can find the full conference programme here.

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Robert Boyle and his sister Lady Ranelagh picking flowers in the Castle Gardens

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A day out (and a solar eclipse) at Maynooth University

I  had a most enjoyable day on Friday at the mathematical physics department of Maynooth University, or NUI Maynooth, to give it its proper title. I was there to attend an international masterclass in particle physics. This project, a few years old, is a superb science outreach initiative associated with CERN, the European Centre for Particle Physics particle in Geneva, home of the famous Large Hadron Collider (LHC). If you live on planet earth, you will probably have heard that a famous particle known as the Higgs boson was recently discovered at the LHC. The idea behind the masterclasses is to give secondary school students the opportunity to “become a particle physicists for a day” by performing measurements on real data from CERN.


The day got off to a great start with a lecture on “Quarks, leptons and the forces of nature” by Dr. Paul Watts, a theoretical physicist at Maynooth. An excellent introduction to the world pf particle physics, I was amused by Paul’s cautious answer to a question on the chances of finding supersymmetric particles at the LHC. What the students didn’t know was that Paul studied under the late Bruno Zumino, a world expert on supersymmetry, and one of the pioneers of the theory. Paul’s seminar was followed by another lecture, “Particle Physics Experiments and the Little Bang” , an excellent a talk on the detection of particles at the LHC by Dr Jonivar Skullerud, another physicist at Maynooth. In between the two lectures. we all trooped outside in the hope of seeing something of today’s solar eclipse . I was not hopeful, given that the sky was heavily overcast until about 9.30. Lo and behold, the skies cleared in time and we all got a ringside view of the event through glasses supplied by Maynooth physics department! Now that’s how you impress visitors to the college… images IMG_20150320_101922

Viewing the eclipse

After lunch we had the workshop proper. Each student was assigned a computer on which software had been installed that allowed them to analyse particle events from the ALICE detector at the LHC (lead ion collisions). Basically, the program allowed the students to measure the momentum and energy of decay products of particles from the tracks produced in collisions, allowing them to calculate the mass of the parent particle and thus identify it. As so often, I was impressed how quickly the students got the hang of the program – having missed the introduction thanks to a meeting, I was by far the slowest in the room. We all then submitted our results, only to find a large discrepancy between the total number of particles we detected and the number predicted by theory! We then all returned to the conference room, and uploaded our results to the control room at the LHC. It was fun comparing our data live with other groups around Europe and discussing the results. Much hilarity greeted the fact that many of the other groups got very different results, and the explanation for that (but what many groups really wanted to know was  whether we got a good look at the eclipse in Ireland). IMG_20150320_154423

Uploading our results via a conference call with the contol room at the LHC, CERN

All in all, a wonderful way for students to get a glimpse of life in the world of the LHC, to meet active particle physics researchers, and to link up with students from other countries. See here for the day’s program.


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A Night at the Academy Awards

I spent a most enjoyable evening last week at the Royal Irish Academy. Ireland’s premier learned society, the Academy is an all-Ireland body that promotes excellence in the sciences and the humanities, fostering links between ‘the two cultures’. Membership of the Academy is considered a high honour amongst Ireland’s academics, and former members include eminent Irish intellectuals such as William Rowan Hamilton,  Ernest Walton, Seamus Heaney and W.B. Yeats.

I was there to witness the awarding of this year’s  RIA Gold Medals for outstanding research. The medals were presented to Professor Werner Nahm, for his seminal work in theoretical physics and to Professor Desmond Clarke, for his research in the history and philosophy of science in the 17th century.  I was pleased but not surprised at Werner’s award; his research has already been recognized with  several international prizes, not least the famous Planck Medal of the German Physical Society. As Director as the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS), Werner plays a key role in mathematics and physics in Ireland. (He also has a side interest in the history of science, and was one of the first people I turned to in our studies of unpublished Einstein manuscripts. In fact, Werner recently showed me a hardcopy of a little-known book at DIAS by Albert Einstein, published only in French, with annotation in the margins by the late Eamonn de Valera – all very much in keeping with the interdisciplinary spirit of the Academy!)


The main conference hall at the Royal Irish Academy


The library at the Royal Irish Academy

The evening was most enjoyable, with erudite professors of science and the humanities intermingling in the Academy’s beautiful premises on Dawson Street in Dublin – indeed part of the remit of the Academy is the promotion of links between the two disciplines. The ceremony included speeches from Jan O’ Sullivan , our Minister for Education, and  Tom Boland, director of the Higher Education Authority.

One surprise was that the event did not include acceptance speeches by the awardees. This seemed strange, given the prestige of the RIA medals (imagine a Nobel award without the speech). One would have liked to hear the recipients describe their research, thank colleagues, and comment on the challenges of academia. In particular, I thought it was a pity that there was no opportunity for two highly distinguished academics to respond to the speeches of the Minister for Education or the Director of the HEA. For example, I suspect Werner would have liked to comment on the current lack of funding for research in basic science and its impact on the study of mathematics and theoretical physics in Ireland (and on his Institute).  I have never met Professor Clarke, but it would have been most interesting to hear his views on the challenges faced by historians in Ireland.

All in all, a most enjoyable occasion. I was disappointed that the event attracted almost no media coverage afterwards, despite the presence of several press photographers on the night. Perhaps the occasion was deemed too intellectual by news editors –  what is a lifetime’s achievement in academia compared with latest adventures of Roy Keane…


There is a short article describing the event in the Weekend section of The Irish Times. However, it’s easy to miss as there are no  photographs and there doesn’t seem to be an online version.

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Academics and their holidays

Last week, I returned to the snow world for the first time in a long while. The college teaching semester starts on Monday 12th, and I managed to get my corrections done over Christmas, leaving a precious few days over. I had intended going to a conference on relativity and spacetime in Israel, but in the end I decided I was more in need of a few days holiday, not to mention some exercise!
‘Tis well for some,you might say, and indeed it is. For those who can, the week after New Year is a very good time for a snow holiday – cheaper and less crowded (and little danger of being stranded in airports). That said, I recently worked out that, during the teaching semester, I work an average 20 hours unpaid overtime per week in comparison with my previous 9-5 job . This isn’t particularly unusual for an academic involved in research but it’s important to take a break sometime to recharge the batteries.

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The village of Fieberbrunn in Tirol and neighbouring gondola

This year, I bought a last-minute package with Crystalski to Fieberbrunn, a little known resort in Tirol, Austria. The village is only a few kilometres away from the well-known resorts of St Johann and Kitzbuehel, but so far undiscovered by English-speaking tourists. I signed up for a few advanced sessions with the local ski school – skiing is a highly technical sport and one can always learn a great deal from Austrian ski instructors (not to mention hearing some German). Sure enough, we spent several days trying to absorb tips on posture from Ottmar F., a leading free-rider and scarily qualified instructor from these parts. Best of all, the course concentrated on some gentle off-piste skiing, always my weak spot.


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Off-piste with Ottmar- then back to the piste at last

It’s not the easiest of holidays – each day, I would return exhausted to the hotel and spend an hour recuperating in the pool, before doing some study in the evenings. I was happy enough to hand back transceiver and avalanche pack yesterday, that’s enough exercise for a while!
Best of all, I got the guts of my next paper written during the week – an essay on Einstein’s philosophy of cosmology for the upcoming Oxford/Cambridge compendium on the philosophy of cosmology. Not for the first time, I notice that I get more work done when I stay away from the office…

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Robert Boyle Summer School 2014

Last weekend saw the third Robert Boyle Summer School, an annual 3-day meeting in Lismore, Co, Waterford in honour of one of Ireland’s greatest scientists. Born in Lismore into an extremely wealthy family, Boyle  became one of the most important figures in the Scientific Revolution,  well-known for his scientific discoveries, his role in the rise of the Royal Society and his influence in promoting the role of the experiment in the ‘new philosophy’.


The Irish-born scientist and aristocrat Robert Boyle   



Lismore Castle, the birthplace of Robert Boyle

The summer school took place in the Heritage Centre in Lismore, the beautiful town that is the home of Lismore Castle where Boyle was born.  The talks covered a wide range of topics, from Boyle’s scientific legacy to the interplay of science and religion (like many figures of the scientific religion, Boyle was quite devout and extremely interested in the interface between science and religion). See here for the conference program.

This was the third such summer school, organised jointly by the CALMAST science outreach group at Waterford Institute of Technology  and the Lismore Heritage Centre. As the only such event on a major figure in the scientific revolution, it is beginning to attract some of the world’s top experts on this period of science (known as ‘early modern’). This year, the programme included talks by Lawrence Principe (Drew Professor of the Humanities at Johns Hopkins and author of The Scientific Revolution (OUP) and The Aspiring Adept: Robert Boyle and his Alchemical Quest); John Hedley Brooke (Professor Emeritus of Science and Religion and Oxford University , and author of Science and Religion: Some Historical Perspectives and Religious Values and the Rise of Science in Europe); and Terry Eagleton  (author of over forty books and Distinguished Professor of English literature at Lancaster University).


Lawrence Principe at Boyle 2014


John Hedley Brooke at Boyle 2014

It was the sort of conference I like best – a small number of inter-disciplinary talks aimed at curious academics and the public alike, with lots of time for questions and long breaks for discussion. On the last day, Boyle’s legacy was also celebrated by some talks concerning the science of today; we had a superb lecture on astrophysics from Professor Lorraine Hanlon of University College Dublin, and an outstanding seminar on inflammation and ageing by Professor  Luke O’ Neill, one of Ireland’s best known and most successful biochemists.  Other highlights were a lecture on fraud in modern science by Jim Malone, Emeritus Robert Boyle Professor of medical physics at Trinity College Dublin, and an open-air barbecue in Lismore Castle on Friday evening,including a re-enactment in costume of some famous Boyle experiments by Eoin Gill of WIT.


Eoin Gill aka Robert Boyle


Song and dance in the grounds of Lismore Castle

All in all, a superb conference in a beautiful setting.  The meeting was sponsored by Science Foundation Ireland, the Royal Society of Chemistry, the Institute of Chemisty (Ireland), the Institute of Physics (Ireland), the Robert Boyle Foundation,  i-scan, Abbott, Lismore Castle Arts and the Lismore House Hotel.


A late night music session with Luke O’ Neill  


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