Auhtors: Samantha Lawler, Associate Professor, Astronomy, University of Regina and Aaron Boley, Professor, Physics and Astronomy, University of British Columbia

 

A giant mirror to create “sunlight on demand” was just approved by the United States Federal Communications Commission (FCC), despite opposition from astronomers and the public, and real safety concerns.

The FCC approved the company Reflect Orbital to test one satellite, named Earendil-1, as a means of reflecting the sun’s rays back to Earth for extra solar energy and wide-area lighting. The light is expected to cover an area about five kilometres wide, and will require repointing every four minutes.

And this is just the start. Reflect Orbital plans to have more than 50,000 satellites in action by 2035, which they claim will be used across agricultural, emergency response and other industrial sectors.

There are many problems with this proposal, including impacts these satellites will have on human health and safety, as well as on astronomy and the low-Earth environment.

Flashes during mirror repointing could disrupt pilots and drivers. The light could also disrupt circadian rhythms of plants, animals and humans. Sensitive detectors in research telescopes, as well as star-tracking cameras on lower altitude satellites, could be overloaded and fried.

The FCC said that the “risks of harm raised on the record regarding Reflect Orbital’s solar reflector are unrelated to the Commission’s role in authorizing use of radiofrequency spectrum.”

‘Weird space stuff’

Satellite proposals for “emergent space activities” in low-Earth orbit are becoming increasingly outlandish. The proposals have become so weird, in fact, that the FCC recently published a document called “Spectrum Abundance for Weird Space Stuff.”

“Once the province of science fiction,” this document states, “American companies are now upgrading, relocating and servicing satellites; manufacturing pharmaceuticals in space; building private inhabitable spacecraft; and conducting private robotic missions to the surface of the Moon.”

Millions of orbital AI data centres are also planned. Corporations seem to be scrambling to launch anything that might persuade investors throw money at them: space advertising, hotels for billionaires, artificial meteor showers, space burials for cremated remains, solar-powered infrared beams to power data centres and a variety of orbital missiles.

The phrase “weird space stuff” is refreshingly truthful. So, how did we get here?

SpaceX controls orbit

There are close to 11,000 SpaceX Starlink satellites currently in orbit above our heads. Anyone who wants to launch into low-Earth orbit needs to carefully consider SpaceX operations, or directly co-ordinate with them.

Otherwise they risk collisions, like the near-miss between a Starlink and Chinese satellite in December 2025.

Even the Artemis I launch in 2022 and Artemis II launch in 2026 had small “cutout” windows in their launch timing to avoid satellites, including those belonging to Starlink.

Co-ordination is good. Forcing it because one corporation has effectively occupied low-Earth orbit is not. Indeed, the 1967 Outer Space Treaty, which was signed by more than 100 countries including the United States, China and Russia, states that, “outer space is not subject to national appropriation by claim of sovereignty, by means of use or occupation.”

Whether SpaceX’s extensive use of Earth orbits violates this principle is now being tested in real time.

Copycat megaconstellations

In February, SpaceX filed with the FCC for one million more satellites, for “AI data centers.”

One million. That is 40 times as many satellites as have ever been launched — for a single megaconstellation consisting of completely untested technology that may not even work in space.

Not only did the FCC accept SpaceX’s filing, but they did so at ludicrous speed. Scientists worldwide then had just 30 days to model the effects with woefully incomplete information on masses, sizes, compositions and orbital distributions.

At the time of writing, four other copycat AI data centre proposals have been filed by rival companies, for tens of thousands of satellites each. And SpaceX just proposed another 100,000 satellites to interface with the million AI data centres that it already asked for.

Solar energy from space

The U.S. Federal Communications Commission was originally set up to regulate radio broadcasts. But it is now being asked to evaluate many non-radio effects, including orbital safety, which it may not have the required expertise for. It would make sense to move some of this evaluation to the U.S. Office of Space Commerce. However, recent budget cuts make that infeasible.

Consequently, the FCC will soon be asked to judge a daunting range of satellite proposals. They include a cluster of proposals to gather solar energy from space.

One idea is to send solar power down to earth through high energy beams. These could change atmospheric chemistry and kill birds and other wildlife that stray into the beam.

They would also require no-fly zones around receiving stations for airplanes and also satellites on lower altitude orbits (such as the orbits SpaceX just requested for 100,000 more Starlink satellites).

Environmental costs

While many of these projects claim to solve environmental problems by creating clean energy or capturing it in space, they function as a form of greenwashing.

The solar energy generated is only clean if you ignore the environmental costs of building, launching, maintaining and burning satellites up in Earth’s atmosphere. The daily operations of all these proposed systems will have huge environmental consequences.

There are companies that have tested plans for removing space debris from orbit. This is helpful for avoiding Kessler Syndrome — a runaway chain reaction of collisions. But where will the debris go once removed from orbit?

It will fall into Earth’s atmosphere, where it will deposit metal and possibly impact Earth’s surface. It is unclear who is responsible for any resulting damage or deaths.

For all humankind

The majority of satellites in orbit today are American, and the main federal agency regulating satellites is not set up to do that well. We are now seeing the consequences.

While outer space is effectively infinite, low-Earth orbit most definitely is not. Satellites orbit the Earth around once every 90 minutes. This means the collision potential between two objects in orbit is large.

The many satellites and rocket bodies that have burned up in Earth’s atmosphere over the last few years have already measurably altered it. Preliminary studies show that using Earth’s atmosphere as a crematorium for tens of thousands of satellites will have devastating effects on ozone and other atmospheric chemistry.

Astronomy is also under threat from some of the “weirder” ideas like space mirrors, solar sails and diffuse sky brightening from orbital debris.

An innovation challenge

We are not here to argue against satellites. Indeed, they provide a wide range of beneficial services to science and society. But each satellite comes with a cost that must be taken into account.

Ultimately, this is an innovation challenge. Unfettered growth and exploitation of any environment comes with serious consequences, including to the long-term sustainability of the operations that depend on that environment.

Doing more with less is the engineering challenge that needs to be met if we want to continue to use satellites in orbit.

 

This article is republished from The Conversation under a Creative Commons license. Original article.

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Author: Marta Irigoyen is a postdoctoral researcher at CIC bioGUNE

Chimeric antigen-specific receptor (CAR) T-cell immunotherapy targeting B-cell maturation antigen (BCMA; BCMA-CAR T cells) has produced remarkable clinical responses in advanced multiple myeloma (MM), with a substantial fraction of patients achieving complete remission ¹. However, many patients relapse within months, largely due to insufficient CAR T-cell persistence, a recognized mechanism of acquired resistance ². A major barrier to durable responses is the tumor microenvironment (TME), which is profoundly reshaped by tumor metabolic reprogramming ³. In fact, many tumor types, specially MM, are highly dependent on glutamine (Gln) metabolism for cell survival and proliferation ⁴. Thus, Gln “addiction” depletes local Gln levels and availability, impairing antitumor T-cell effector functions and promoting immune escape.

Based on these observations, a team of researchers hypothesized ⁵ that Gln deprivation within the TME limits the efficacy of CAR T-cell therapies. Indeed, antigen-specific T cells fail to proliferate and to produce interferon gamma (IFN-γ) under Gln-restricted conditions. They therefore investigated whether enhancing Gln uptake via overexpression of the Human SLC1A5 (ASCT2) amino acid transporter could improve the metabolic fitness and the antitumor activity of BMCA-CAR T cells in MM.

To assess the functional impact of ASCT2 overexpression in T cells, the authors infected CD8⁺ and CD4⁺ T cells from mice with an expression vector containing Asct2. To assess the impact of enhanced Gln uptake on T-cell function, CD4⁺ and CD8⁺ T cells from mouse spleens were stimulated with anti-CD3/CD28 beads at varying Gln concentrations. Interestingly, Asct2 overexpression significantly improved T-cell proliferation and IFN-γ production. Similar enhancements were observed in CD8⁺ OT-I (these cells contained a transgenic TCR designed to recognize ovalbumin (OVA) peptide 257-264 on MHC class I, modeling thus cytotoxic T-cell responses) and CD4⁺ OT-II T cells (these cells contained a transgenic TCR designed to recognize OVA peptide 323-339 on MHC class II, modeling the helper T-cell responses). Thus, Asct2-overexpressing OT-I T cells showed increased cytotoxicity against B16OVA cells. B16OVA cells are a well established in vitro model for cancer immunotherapy, expressing ovalbumin in order to facilitate strong immune responses to tumor antigens. The authors found that, even at low Gln levels, Asct2-overexpressing CD4⁺ OT-II T cells were more efficient lysing B16OVA cells.

Next, to assess the potential of Asct2 overexpression to enhance ACT therapy in vivo, B16OVA tumor-bearing mice were treated with either control or Asct2 CD8⁺ OT-I T cells. Interestingly, 14 days after tumor injection they found lower levels of Gln in the interstitial fluid, confirming a Gln-deficient TME. Then, mice were subcutaneously injected with B16OVA cells and, 7 days later, treated with control or Asct2 CD8+ OT-I T cells. Remarkably, mice treated with Asct2 CD8⁺ OT-I T cells exhibited a delay in tumor growth as evidenced by tumor weight and survival rate analysis. Moreover, mice treated with Asct2 CD8+ OT-I T cells showed a higher number of IFN-γ–producing antigen-specific T cells in the spleen compared with control T cells.

Given the well-established Gln “addiction” of MM ⁶ and the consequent Gln depletion in the bone marrow (BM), the authors next evaluated whether Asct2 overexpression in BCMA-CAR T cells could improve Gln uptake and potentially benefit CAR T-cell immunotherapy in MM. Because MM expresses BCMA, they generated a murine anti–Bcma-CAR T-cell therapy effective against MM in vivo. They tested whether Asct2 overexpression could improve their efficacy in vivo and observed that Bcma-CAR cells exhibited robust proliferation and high IFN-γ secretion when stimulated with Bcma. Besides, subsequent co-culture experiments with Bcma-expressing MM cells confirmed that Bcma-CAR T cells selectively secreted IFN-γ, and displayed cytolytic activity against MM cells. Replacement of the GFP reporter with ASCT2 yielded BCMA-CAR/ASCT2 T cells with enhanced Gln transport capacity. In coculture assays, ASCT2-expressing BCMA-CAR T cells exhibited superior cytolytic activity against MM cells, particularly under low-Gln conditions.

To evaluate if Asct2 overexpression could enhance ACT immunotherapy with Bcma-CAR T cells in vivo, they used a murine model in which mice were challenged with MM cells and treated IV with CD8⁺ and CD4⁺Bcma-CAR T cells (1:1 ratio) or Asct2 Bcma-CAR T cells. Interestingly, Asct2 Bcma-CAR T cells significantly improved overall survival (OS) in mice challenged with tumors, achieving 90% survival at day 100 after treatment. Besides, fourteen days after CAR T-cell transfer, there was a significant reduction in tumor cells in the BM of both CAR T-cell–treated mice groups, being more significant in the BM of mice treated with Asct2 Bcma-CAR T cells compared with those treated with Bcma-CAR T cells. Moreover, there was a higher number of infiltrating CAR T cells in both the spleen and BM of mice receiving Asct2 Bcma-CAR T cells. Then, they next evaluated the antitumor effect of the Bcma-CAR T cells in a genetic MM preclinical model that closely mimics common genetic alterations observed in human MM and, similarly, treatment with Asct2 Bcma-CAR T cells significantly enhanced OS compared with conventional Bcma-CAR T cells.

Finally, the authors explored the clinical relevance of ASCT2 expression in MM. RNA-seq analysis of BM aspirates of untreated patients with MM compared ASCT2 expression levels in various B-cell subtypes obtained from healthy donors as previously described, showed a marked upregulation in MM cells compared with normal B-cell subsets, suggesting a potential prognostic relevance of ASCT2 expression in MM. Next, to explore the clinical relevance of ASCT2 overexpression in human CAR T cells, they created 2 lentiviral constructs encoding an antihuman BCMA-CAR. They prepared a conventional BCMA-CAR and the ASCT2 BCMA-CAR construct coexpressing ASCT2. Notably, ASCT2 BCMA-CAR T cells showed greater proliferation and higher IFN-γ production upon BCMA stimulation at various Gln concentrations, and they had a higher proportion of naïve stem cell memory and central memory subsets. To further demonstrate the importance of ASCT2, they performed cytotoxicity assays with BCMA-CAR T cells against tumor cells with different ASCT2 levels. Silencing ASCT2 in MM cells reduced Gln uptake and confirmed the functional importance of this transporter in tumor–immune metabolic competition.

In summary, Asct2 overexpression enhances T-cell and CAR T-cells metabolic fitness and effector function under Gln-restricted conditions. In both B16OVA melanoma and MM in vivo tumor models, this strategy improved antitumor immunity and increased overall survival. These findings support metabolic engineering of CAR T cells as a rational approach to overcome nutrient deprivation in the TME an to enhance durable tumor control.

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Author: Jaume Navarro is an Ikerbasque Research Professor at the University of the Basque Country

A few weeks after the invasion of Ukraine by the Russian army, many scientific institutions felt the need to issue public statements against that war. At the time, I was president of the Commission for the History of Physics within the International Union of Pure and Applied Physics (IUPAP) and, as such, I took part in the discussions leading to the final declaration. The timing could not be better for historians of science to make a significant, albeit small, contribution: my commission was working on a project to seriously study the origins and development of IUPAP, which was about to celebrate its centenary. Paying attention to history was important so as to articulate a statement that would avoid past mistakes and incorporate positive experiences of the Union in its one-hundred-year history. Because, like other scientific international unions, IUPAP was born with an idea of peace in mind, yet it had to maneuver through times of war, both hot and cold.

It was after the tragedy of the Great War (1914-1918) that a new wave of internationalism in science took shape. If excessive nationalism had drawn Europe to its worse carnage in history, so the argument went, it was time for international institutions to collaborate in the construction of peace. And scientific research, understood as a cultural enterprise, was one such area in which collaboration rather than competition was to play a key role. In hindsight, one of the ironies of this search for peace was that the losers (Germany, Austria, Hungary, Bulgaria, and what remained of a now highly unstable Ottoman Empire) both collectively and individually, were banned from taking part in the new international order. That meant not only that their national academies could not join the new international unions, but also that individual scientists from those countries were excluded from meetings and collaborations sponsored by the unions. This was particularly poignant in the case of physics.

Indeed, international collaboration had a somewhat long tradition in fields like astronomy or geodesy due to the global scale of some of their research projects. But physics, while the “king of the sciences” in the nineteenth century, had not seen the international cooperation of national academies in the same way. That partly explains why, with the creation of the International Research Council (IRC) by delegates of twelve nations in July 1919, the International Unions of Astronomy (IAU), Geodesy and Geophysics (IUGG) and Pure and Applied Chemistry (IUPAC) immediately approved their initial statutes, soon to be followed by the Mathematical Union (IMU) and the Union for Scientific Radio Telegraphy (URSI); yet, a union of physics would have to wait, both in form and, especially, in practice.

In 1922, a number of physicists from France, Belgium, Britain, the USA and a few other countries met in Paris and came up with a first draft of statutes for an International Union of Physics. It was the young American experimentalist, Robert A. Millikan, who pushed for a name that included both pure and applied physics. The main goals of the Union were the promotion of up-to-date scientific bibliographies, the coordination of fundamental units, and the organization or sponsorship of international conferences. Those present at the meeting to celebrate the fiftieth anniversary of the Société française de physique (SFP) in Paris in December 1923 finally approved the statutes of IUPAP nominating the British and Nobel prize winner William H. Bragg as president, and Henri Abraham, professor of physics at the École Normale Supérieure, as secretary general. But it was informally agreed that the Union would remain basically dormant until it could be fully international; i.e., include German physicists.

By 1924, the vindictive philosophy of the IRC against the Central Powers was being challenged. The Council had grown and now included national academies from up to twenty countries, mostly neutral during the war and who did not see the need for such exclusionary policy. Also, an increasing number of individual scientists were pushing towards a more reconciliatory and inclusive internationalism. French and Belgian representatives were the most reticent to amend the statutes of the IRC and lift the foundational ban. So much so that real changes only came in 1931 when the IRC dissolved and the new International Council of Scientific Unions (ICSU) took its place. From then on, not only was internationalism a real possibility but also each individual scientific union was freer to organize itself as they saw fit.

In the 1920s, however, internationalism in physics materialized in other forms. Two are the best-known and most influential institutions on this aspect: the Solvay Conferences and Niels Bohr’s Institute for theoretical physics in Copenhagen. The former were the initiative of the Belgian industrialist Ernest Solvay to promote relatively small, truly international, by-invitation-only conferences to address pressing issues in both physics and chemistry. After the success of the first two meetings in physics in 1911 and 1913, the third and fourth Solvay meetings in 1921 and 1924 took part in the boycott against the Germans. But, by 1927, the mood had changed and the fifth Solvay conference in Brussels, which eventually became one of the most influential events in shaping the transformation of the early quantum physics into the new quantum mechanics, saw the presence of five German physicists: Max Planck, Albert Einstein, Wolfgang Pauli, Werner Heisenberg and Max Born. In a way, that success was partly due to the tradition that Bohr had managed to create in his institute in Copenhagen. Indeed, Denmark had been a neutral country during the war and the Carlsberg Foundation had generously funded a research center for theoretical physics to keep Bohr in the country. Thanks to both elements, Copenhagen became the central point for physicists and mathematicians to meet and freely exchange ideas on the new quantum physics.

But let us go back to the early history of IUPAP because, while Bohr had played a significant role in bringing together physicists from both sides of the war, he was also partly responsible for the failure of IUPAP to take off. In 1931, Bragg resigned and Millikan was appointed president. His plan was to use his tenure as a springboard for American physicists to become more and more internationally relevant, as well as to materialize the inclusion of the German physical society into IUPAP. He expected to achieve both goals with the organization of a major international physics conference in Chicago in 1933, year in which the wind city was celebrating its centenary. With the presence of a large number of invited physicists IUPAP might finally formalize the German membership.

Millikan’s grand plan did not succeed. First, the recession after the crash of 1929 affected the organization of events during the “Century of Progress” celebrations and money to invite scientists from abroad was short. Second, IUPAP and all other unions had one national scientific institution representing the country. But Germany had two such societies, the Deutsche Physikalischer Gesellschaft (DPG) and Gesellschaft für Technische Physik (GTP), and the attempts by Millikan and, especially Abraham, who was still serving as secretary, in correspondence with Planck and other German representatives could not settle the question as to which German society was to represent the country in the Union. And, third, the political climate in Germany was changing and the nazi ideology taking hold of the country was certainly not keen on internationalism.

Chicago did finally organize a minor scientific meeting, but it was far from being the major event Millikan had envisaged to expand and consolidate IUPAP. Promoters of the Union did not, however, give up and decided to use a major physics conference organized by the British Institute of Physics and the Royal Society in both London and Cambridge in October 1934 as the place to formalize German membership. And as a sign to underline the true international character of the Union, they offered the presidency to Bohr as icon of internationalism. The correspondence between Millikan, Abraham, Bohr, Schrödinger and a few other physicists show an amusing yet sad chain of misunderstandings: Abraham and Bohr thought Millikan had accepted the presidency by misreading a telegram of the latter; but Bohr did not want to get involved unless the German membership was fully signed, not simply promised. And that never happened.

So, Millikan having resigned and Bohr having rejected the presidency, the soul of the dormant union was its long-serving secretary, Abraham, who worked hard to find a candidate to act as president while things were clarified. In 1937, the Swedish physicist and Nobel Prize winner Manne Siegbahn agreed to be the president of IUPAP, but the Union was still short of activities, cohesion and a clear goal. It was also the indefatigable Abraham who continued his search for ways to keep the Union alive. He proposed a conference in Copenhagen in 1938, with the support of Bohr, or in Stockholm, organized by Siegbahn or, even as late as late as May 1939 he was thinking of a conference in Paris for 1940. None of them ever materialized and World War II not only destroyed the hopes and dreams of having a fully functional and international Union of Pure and Applied Physics, but even more poignantly, ended with the life of its most ardent defendant: Abraham was murdered in Auschwitz in 1943. As we shall see in the next installment, the Union reinvented itself after the war and had to learn how to navigate the new peace of the Cold War.

Further reading:

Lalli, R. and Navarro, J. (2024). Globalizing Physics: One Hundred Years of the International Union of Pure and Applied Physics. Oxford University Press. [Available in open access: https://academic.oup.com/book/58182]

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Authors: Sergi Muria Maldonado, Professor de Didàctica de les Matemàtiques, Universitat de Barcelona; Anton Aubanell Pou, Professor de l’Institut de Formació Continuada i professor jubilat de Didàctica de les Matemàtiques, Universitat de Barcelona, and Jordi Font González, Professor de Didàctica de les Matemàtiques, Universitat de Barcelona

 

2026 marks 100 years since the death of Antoni Gaudí, the architect of the Basilica of the Sagrada Familia in Barcelona. While the temple’s beauty is extraordinary in its own right, it becomes even more profound when we explore the numerical patterns that lie behind its striking forms.

By contemplating the mathematical principles that underpin its structure, the visual harmony of the whole takes on a new dimension, endowing it with a renewed functionality, balance and coherence.

Mathematician Claudi Alsina i Català deeply studied the mathematics of the Sagrada Família. He undertook his initial studies in this field at the University of Barcelona, and supervised the doctoral thesis of Jordi Faulí, the architect currently in charge of the temple’s ongoing construction.

In his memoirs, Alsina stated:

Many had wondered whether the design of the Sagrada Família contained some module or system of proportions that guided the building’s metric relationships. (…) One Saturday afternoon, sitting at my desk at home, with all the data and documents on this mysterious proportional system – if indeed it existed – I discovered it. The 7.5-metre module and the ratios between the divisors of 12 (1:4, 1:3, 1:2, 3:4, 2:3, 1) seemed to explain a great deal.

12: the magic number

It is no surprise that the number 12 plays a prominent role in the structure of the church. Gaudí conceived the Sagrada Família as a synthesis of architecture and religious symbolism, and the number 12 features heavily in the Bible: Jacob’s 12 sons, the 12 tribes of Israel, the 12 apostles and the crown of 12 stars in the Book of Revelation are just a few examples.

But its significance is not merely symbolic. From a mathematical point of view, 12 is a number particularly well-suited to establishing proportions, as it has many divisors. According to Alsina, the relationships between these divisors account for much of the basilica’s proportional system.

The 7.5-metre module

Drawing on Alsina’s work, we invite you to take a brief mathematical tour of the Sagrada Família.

The temple’s dimensions are based on the number 12 and a module of 7.5m. It is 90m long (7.5 × 12) and 60m wide (7.5 × 8). The width of the main nave is 45m (7.5 × 6).

In terms of height, the highest vault is that of the apse, at 75m (7.5 × 10), followed by the vault of the transept at 60 metres (7.5 × 8). The nave vault is 45m high (7.5 × 6), the side aisle 30m (7.5 × 4), and the choir 15m (7.5 × 2).

The Tower of Jesus Christ is the central and tallest of the cathedral. It stands at 172.5 metres (7.5 x 23), close to the height of the landmark hill of Montjuïc. It is crowned by a four-armed cross, 17m high and 13.5m wide. Surrounding this are the four Evangelist Spires, which reach a height of 135m (7.5 x 18).

The 138-metre high Tower of the Virgin Mary is the second tallest in the basilica. It is crowned by a 12-pointed star, which rests on three supporting arms. This star has a diameter of 7.5m, and is made up of a regular dodecahedron, with pyramid-shaped pentagonal points rising from each face. Its reflections of daylight and night-time illumination lend this star a unique beauty.

Polyhedral towers

Polyhedrons also feature prominently in the towers of the Sagrada Família. The four towers of the Glory façade are topped by dodecahedrons, the four towers of the Nativity façade by truncated irregular octahedrons, and the four towers of the Passion façade by truncated cubes.

On each of the 12 towers, a spire rises above these polyhedrons. Those dedicated to the evangelists are crowned with regular icosahedrons containing spotlights that illuminate the large cross that sits atop the Tower of Jesus Christ. Just above each icosahedron is a sculpture that symbolically depicts each evangelist. There are numerous star-shaped polyhedrons throughout the church, particularly on the Nativity façade.

A forest of towers

Catenary arches feature prominently as key structural elements of the church, as they are a highly effective way to transfer loads to the ground without the need for additional support. They can be seen in the system of sloping columns that support the vaults of the interior naves, the vaults and ceilings themselves, and the Nativity façade.

Inside the Sagrada Família, there are four different types of column. All are double-helix torsion columns – each has a rounded, star-shaped polygonal base, and is formed by the intersection of two opposing Solomonic columns. Above each one is a knot from which different branches emerge, similar to those of a tree, which very efficiently support the towers and the roof of the church.

The skylights in the roof are also one-sheet hyperboloids. Made up of straight lines, they are easy to construct, and optimise the capture and projection of light.

The symbolism of 7 and 33

The church has other deeply symbolic hidden features. Take, for instance, the canopy above the high altar, which forms a regular heptagon 5 metres in diameter, whose seven sides symbolise the seven gifts of the Holy Spirit.

On the Passion façade there is a magic square in which the sum of all rows, columns and diagonals is 33. It appears to be inspired by the magic square featured in the engraving Melancholia I by Albrecht Dürer.

The mathematics that underpins the Sagrada Família makes it all the more beautiful. While the building itself is a sight to behold, a deeper understanding of the principles behind it inspires even greater admiration for the enduring genius of Antoni Gaudí.

 

This article is republished from The Conversation under a Creative Commons license. Original article.

The post The mathematical secrets of Barcelona’s Sagrada Familia appeared first on Mapping Ignorance.

Author: Tamara Cruz Tena, strategy consultant, CIC  energiGUNE

When energy storage is discussed in the context of the energy transition, the conversation almost invariably turns to electricity. Solar and wind power have made the temporal mismatch between energy production and energy demand one of the defining challenges of low-carbon energy systems, and technologies capable of storing electrical energy have consequently become central to discussions about decarbonization.

Yet this emphasis on electricity raises an interesting question. If a substantial fraction of the energy ultimately consumed by modern societies is required not as electricity but as thermal energy, should future energy systems necessarily store energy in electrical form?

The question may appear deceptively simple. Electricity plays a visible role in modern economies, powering everything from communications and transportation to industrial equipment and domestic appliances. Thermal energy, by contrast, often remains hidden within industrial processes, heating systems and manufacturing operations. Nevertheless, many of the activities that sustain modern societies depend primarily on heat rather than electricity.

Steelmaking, cement production, chemical manufacturing, food processing, paper production and numerous other industrial activities require thermal energy delivered under specific conditions of temperature, power and duration. In many cases, fossil fuels have historically fulfilled this role not because alternative energy sources were unavailable, but because combustion offers a relatively direct means of producing high-temperature thermal energy where and when it is required.

As renewable electricity becomes increasingly available, this situation may encourage a different way of thinking about energy storage. Rather than focusing exclusively on how electricity can be stored and later returned to the grid, it may also be worth considering whether part of that energy could instead be stored in forms intended for later thermal use.

Such an approach would not eliminate the need for batteries, nor would it necessarily be appropriate for every application. It does, however, suggest that thermal energy storage may represent a distinct scientific and engineering problem whose requirements differ from those associated with conventional electrical storage technologies.

Storing energy for later thermal use

At the heart of the discussion lies a relatively straightforward physical observation. Electrical energy can be converted into thermal energy with high efficiency through a variety of heating technologies. Once this conversion has taken place, the resulting energy may be stored within a material or chemical system and later recovered when thermal energy is required.

Importantly, what is stored is not temperature itself. Temperature is an intensive thermodynamic property and therefore cannot be accumulated in the same way as energy. Instead, thermal energy storage systems retain energy through changes in the state of a material, whether by increasing its temperature, inducing a phase transition or driving a reversible chemical reaction.

The simplest of these approaches is generally known as sensible heat storage. In such systems, energy is stored through an increase in the temperature of a material. Water provides the most familiar example, although industrial applications may employ molten salts, rocks, ceramics, graphite or other materials capable of operating under more demanding thermal conditions. The amount of energy stored depends on the mass of the storage medium, its heat capacity and the temperature interval over which it operates.

A second possibility involves latent heat storage, where energy is absorbed or released during a phase transition. Because phase transitions may involve substantial enthalpy changes while temperature remains relatively constant, these systems can store significant amounts of energy within comparatively narrow temperature ranges. This characteristic has made phase change materials attractive for applications in which thermal energy must be supplied near a particular operating temperature.

Even more ambitious concepts involve thermochemical storage. In these systems, thermal energy drives reversible chemical reactions, allowing energy to be stored in chemical form and later recovered when the reverse reaction occurs. Under certain conditions, such approaches could potentially enable storage over much longer timescales than conventional thermal systems, although their practical implementation remains associated with significant scientific and engineering challenges.

At first sight, these approaches may appear to offer relatively straightforward solutions. However, as is often the case in energy research, the situation becomes considerably more complicated once practical constraints are taken into account.

Materials operating at elevated temperatures may experience degradation through corrosion, thermal fatigue, creep, phase instability or other mechanisms whose importance depends on the operating conditions and storage medium. Repeated thermal cycling can gradually alter material properties, while large-scale systems introduce additional challenges related to heat transfer, containment and long-term reliability. In thermochemical systems, reaction kinetics, cycling stability and reactor design may become equally important considerations.

As a result, the central question is not whether thermal energy can be stored. It clearly can. The more difficult question is whether such storage can remain technically reliable, economically viable and operationally robust under the conditions required by industrial applications.

A maturity paradox

Interestingly, many of the technologies that could contribute to this objective are no longer at an early stage of development. Electric heat pumps, electric boilers, electric resistance heaters and several forms of sensible and latent thermal energy storage have reached relatively high levels of technological maturity. From a purely technological perspective, the challenge is therefore not always one of invention. In many cases, the relevant technologies already exist.

Yet this observation introduces a different question. If a number of these technologies are already mature, why does their future role remain difficult to assess?

Part of the answer may lie in the complexity of modern energy systems themselves. The behaviour of a heat pump, an electric boiler or a thermal storage unit can often be described in considerable detail. However, energy systems contain thousands of interacting components operating across multiple spatial and temporal scales. Incorporating detailed representations of thermal technologies into large-scale energy models may therefore become computationally challenging, particularly when such models are intended to optimize entire electricity, heating and industrial sectors simultaneously.

This creates an interesting tension. The physical behaviour of thermal technologies is often governed by complex thermodynamic processes, yet large-scale energy planning frequently requires simplified mathematical representations that remain computationally tractable. Determining how much detail can be removed without losing essential information remains an active area of research and may influence how the future role of thermal energy storage is assessed.

This distinction may help explain why thermal energy storage has attracted increasing scientific interest in recent years. A significant fraction of industrial energy demand is thermal rather than electrical, and many industrial processes require heat directly. Under such circumstances, converting electrical energy into thermal energy, storing it, and subsequently using it as heat may sometimes prove more practical than repeatedly converting energy between different forms.

Beyond storage

The implications extend beyond individual storage technologies. Some researchers have suggested that thermal energy storage could also contribute to system flexibility by partially decoupling heat demand from the instantaneous availability of renewable electricity. During periods of abundant renewable generation, electrical energy could be converted into thermal energy and stored for later use. If such approaches prove technically and economically viable at scale, they could potentially help reduce some of the temporal mismatches that arise in renewable-dominated energy systems.

Whether this possibility ultimately becomes significant remains uncertain. Industrial sectors differ substantially in their temperature requirements, operating schedules and process constraints. Storage technologies that appear promising in one context may prove less suitable in another. Likewise, systems that perform well under laboratory conditions may encounter unexpected limitations when deployed at industrial scales.

For this reason, thermal energy storage may be best understood not as a single technology but as a broad collection of approaches aimed at addressing a common problem. The details differ from one system to another, but the underlying question remains remarkably simple: if much of the energy consumed by modern societies is ultimately required in thermal form, what is the most effective way of ensuring that such energy remains available when it is needed?

Viewed from this perspective, the challenge is not simply one of storage. The objective of an energy system is not merely to retain energy for later use, but to ensure that energy remains available in a form compatible with the process that ultimately consumes it. In some cases that form may be electrical. In others, it may be thermal. Determining when each option is preferable remains an active area of research.

Whether any particular thermal energy storage technology ultimately becomes a major component of future energy systems remains unclear. What already appears increasingly difficult to ignore, however, is the observation from which the entire discussion emerges. A substantial fraction of the energy consumed by modern societies is required in thermal form. This fact alone may justify a closer examination of how such energy can be stored, transported and recovered efficiently. As researchers continue to investigate the materials, mechanisms and constraints involved, thermal energy storage may offer a useful reminder that decarbonization involves more than replacing one source of electricity with another. It may also require a deeper understanding of how energy itself is used.

The BRTA is a consortium that remains a step ahead of future socio-economic challenges worldwide and in the Basque Autonomous Community; it addresses them through research and technological development, thus projecting itself internationally. The BRTA centres collaborate to generate knowledge and transfer it to Basque society and industry so as to make them more innovative and competitive. The BRTA is an alliance of 17 R&D centres and cooperative research centres with the support of the Basque Government, the SPRI and the Chartered Provincial Councils of Araba, Bizkaia and Gipuzkoa.

References

1. Maruf, M. N. I., Morales-Espana, G., Sijm, J., Helistö, N., and Kiviluoma, J. (2021) Classification, potential role, and modeling of power-to-heat and thermal energy storage in energy systems: A review. arXiv. Available at: https://arxiv.org/abs/2107.03960
2. CIC energiGUNE (2022) Thermal energy storage: a key factor in energy transition. Available at: https://cicenergigune.com/en/blog/thermal-energy-storage-key-energy-transition
3. International Energy Agency (2024) Energy Efficiency 2024. International Energy Agency. Available at: https://www.iea.org/reports/energy-efficiency-2024

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