Root Privileges

India and physics, sometimes together. Online since 2012.

  • Tech-bros are fully aware of what they’re doing

    (Optional reading before you begin: ‘The billionaires’ eugenics project: how Epstein infiltrated Harvard, muzzled the humanities and preached master-race science’, The Nerve)

    Science writer Philip Ball describes “nerd tunnel vision” as the rationalisation scientists who maintained ties with Jeffrey Epstein after his 2008 conviction for soliciting underage sex offer, hinting at something more calculated than just oversight. “Nerd tunnel vision is a defining feature of much of the Edge discourse,” Ball writes, referring to Epstein consort John’s Brockman’s salon for “third culture” intellectualism: “moral obtuseness; a determination to win the argument rather than to listen and ponder; a tendency to fabulate improbable futures from narrow ‘rational’ logic; ignorance of and contempt for other ways of seeing the world.” Ball is in effect describing not a people that’s unaware or who failed to notice but a people who deliberately, with eyes wide open, chose what matters to them.

    “But they were just socially awkward, you say, caught up in their work, unable to see the forest for the trees.” That’s the original description of what it meant to be a ‘nerd’. But when evolutionary biologist Robert Trivers emailed registered sex offender and human trafficker Jeffrey Epstein in 2012 about “a wonderful lunch, a REAL pleasure… quite apart from the bevy of beauties”, when cosmologist Lawrence Krauss persistently begged Epstein for legal advice on sexual harassment charges he faced or even when MIT Media Lab director Joichi Ito concealed funding from Epstein, are we really witnessing naïveté or are we watching sophisticated actors make sophisticated calculations about what they can get away with?

    As Epstein’s ties to more and more scientists, technologists, and venture capitalists become apparent, there’s also a diagnosis doing the rounds that Silicon Valley’s techno-elites, a.k.a. the “tech-bros”, are simply mistaken in their embrace of transhumanism, longevity research, and what increasingly looks like repackaged eugenics. This diagnosis flatters us — the diagnosticians — by positioning us as the clear-eyed ones who saw the cautionary tales from a bygone era for what they were. But I think the unscrupulous scientists and the tech-bros saw them too, and proceeded to run a different cost-benefit analysis from what others did.

    To see why, it’s important to see first that the story Silicon Valley tells about itself — of garage startups and disruption — obscures a more deliberate genealogy. Computer scientist Timnit Gebru and philosopher Émile Torres coined the label ‘TESCREAL’ as a critical construct (not a self-identification; many in Silicon Valley reject the bundling) to describe an overlapping cluster of ideologies: transhumanism, extropianism, singularitarianism, cosmism, (Bay Area internet) rationalism, effective altruism, and longtermism — many of which sank roots in the 1990s.

    Extropianism and organised transhumanism have been adjacent to the Bay Area for a while, with newsletters, salons, and institutes linking human enhancement and “self-transformation” to an explicitly technologist ethos liberated from worrying about limits, whether material or social. This worldview fit neatly with a Valley culture already comfortable with narratives of radical innovation and libertarian politics. In the 2000s, singularitarian ideas also moved from niche futurist conclaves into mainstream tech discourse via high-profile evangelists and Silicon Valley institutions. The 2010s saw rationalist and effective altruist networks overlap with AI labs, venture capital, and philanthropy, specialising in translating moral philosophy and speculative technical futures into funding priorities and institutional agendas. By the 2020s, once frontier AI became the Valley’s central product, these once-semi-separate strands of thought started to resemble a unified milieu.

    This baleful setup further has a prehistory that complicates any argument that contends it’s just been stumbling in the dark when it makes choices we won’t. One part of the prehistory is the mid-20th-century scientific elitism that shaded into eugenics. William Shockley helped invent the first semiconductors and transistors and is a  foundational figure tied to Silicon Valley’s early industrial formation. Shockley also later became publicly associated with racist and eugenicist claims while at Stanford University. While Shockley’s views were on the fringe even then, transhumanism’s closest antecedent is Anglo-American eugenics; the term was first used by British eugenicist Julian Huxley. So when Nick Bostrom — a central figure in these movements and whose work at Oxford University’s Future of Humanity Institute explicitly notes its pull on Silicon Valley elites and funders — was revealed in 2023 to have sent emails in 1996 stating his belief in racial differences in intelligence, should we treat this as an aberration or as a data point in a larger pattern?

    A second wave of the prehistory, from  the late 1980s to the 2000s, is the Silicon Valley’s own flavour of transhumanism, especially in the form of cryonics, what it called “morphological freedom”, brain-computer futures, garnished with the explicit belief that technology should let individuals redesign their bodies and minds. The Extropy Institute was an early node in this movement and its idioms fit Silicon Valley’s entrepreneurial culture of working without constraints. By the mid- to late-2000s, ‘singularity’ — the hypothetical moment in future when AI surpasses human intelligence and triggers rapid, uncontrollable technological growth — also became a popular rallying point. The third and final wave kicked on in the 2010s and is still surging: from just talking about living forever, the tech bros set up labs, biotech pipelines, and ecosystems for “consumer biohacking”, emblematised by Alphabet’s Calico Labs. In the 2020s, finally, conversations about reproduction and eugenics moved from being fringe rhetoric to ‘gray-zone’ products and venture-backed firms.

    Today there are companies marketing expanded embryo screening not just for severe disease risks but for probabilistic traits, including — controversially — cognitive outcomes. One October 2024 investigation by The Guardian described a US startup selling embryo screening framed around gains in IQ and “liberal eugenics” concerns. The product: making dubious genetic advantages selectable for those who could pay. A November 2025 report in the Wall Street Journal described another San Francisco startup pursuing embryo gene-editing research despite legal prohibitions, backed by prominent tech investors and looking for permissive jurisdictions.

    None of these are mistaken decisions, to be sure. The tech-bros may believe what appears dystopian through the moral lens of the 2020s could become normalised or even celebrated by society of the 2040s. Or they understand these are cautionary tales but believe the aspects warranting caution are either exaggerated or can be managed with better execution. Many of these figures are also staunch materialists and techno-determinists who don’t harbour the humanistic assumptions underlying most science fiction writing. When Aldous Huxley warns them about a society engineering away suffering using pleasure, surveillance, control, and punishment, they may genuinely see that as solving a problem rather than creating one. This is because the caution depends on valuing things like struggle, authenticity, and inefficiency, of which they’re usually dismissive. Which is why Mark Zuckerberg spending $10 billion to attempt to create the ‘Metaverse’ isn’t a failure of imagination but the success of a different imagination.

    Some tech-bros also recognise exactly where this leads and view the resulting instability, disruption, and concentration of power as features rather than bugs because periods of chaos create opportunities for those positioned to profit from it. The might also believe that by being aware of the cautionary tales they’ve inoculated themselves against the specific failure modes the tales came with. “We’ve read 1984,” you might hear them say, “so obviously we won’t make those mistakes.” This is of course hubris but importantly it’s not stupidity.

    Which brings us back to Jeffrey Epstein and the scientists who orbited him. Ball wrote that Epstein liked to surround himself with “a certain type of male scientific ‘intellectual’: arrogant, entitled, ‘anti-woke’ and often misogynist, typically late middle-aged and Ivy League and on the lookout for young women to impress and sleep with.” Many of Epstein’s pet scientists were supplied by literary agent John Brockman, who in the 1990s turned scientists into literary superstars that commanded large book advances and wrote authoritative-sounding op-eds. Brockman styled this crew as heralding a ‘Third Culture’ centred on the Edge Foundation, of which Epstein was the major funder.

    Some of those in Brockman’s orbit were and remain very insightful intellectuals and by no means all had Epstein connections. Others severed those links after Epstein’s first conviction. But we can’t ignore the overlapping themes as well as personnel between Edge and Epstein Island. As Ball put it:

    Celebrity culture always has a coarsening effect on scientific discourse itself. Flashy simplicity trumps thoughtful complexity: these ‘thought leaders’ often make claims that leave real experts with their heads in their hands. Considered views on history and ethics become distractions. And there’s a politicized element: Edge culture intersects with the technofascist futurism of Silicon Valley libertarians, and laments about #MeToo, wokeism, and pushy feminists are a constant refrain in the email exchanges.

    Epstein’s connections, the TESCREAL ideologies, investments in longevity and embryo selection startups,  the pronatalist conferences, the eugenicist discourse — none of them was a separate issue. They’re one and the same problem, or perhaps different manifestations of the same underlying orientation, which is to treat human ‘limits’ as engineering problems, then fund private bets to overcome them, with little regard for what social harms they accrue along the way.

    Critics have also argued that these philosophies have encouraged tech-bros to shift attention away from solving present humanitarian issues and towards speculative futures. This appeal works on Silicon Valley elites who fund institutes dedicated to this thinking because it allows them to frame their anxieties about death, intelligence, biological limits, and control as moral imperatives that transcend democratic deliberation. The longtermism of MacAskill of which Musk is so fond contextualises efforts in terms of billions of humans not yet born: how convenient, then, that those billions can’t vote, can’t organise, can’t contradict the projections made on their behalf.

    The pitfall in believing the tech-bros are making the choices that they are simply because they don’t know what you know is that it excuses us from confronting the possibility that Silicon Valley’s brightest minds have concluded that the engineered, surveilled, controlled, stratified future they envision is in fact not the entire point. Perhaps they’ve decided that when history is written by the posthuman victors, today’s cautionary tales will look like Luddite panic. Perhaps they’ve calculated that by the time the negative externalities become undeniable, they’ll already have captured enough of the gains to insulate themselves from the consequences. Or maybe they genuinely believe they’re doing good, that longer lifespans and enhanced intelligence and space colonies are moral imperatives, that anyone who can’t see this is simply thinking too small. In which case we’re not dealing with cynicism but with a totalising ideology that has convinced itself it holds the keys to human flourishing, and the fact that this ideology concentrates benefits among people who already have the most power is treated as a happy coincidence.

    That doesn’t mean we must ban all life extension research or stop developing AI — but we should stop treating these as purely technical pursuits and instead recognise that every choice about what to study is also a choice about what kind of future we want and who gets to decide. We should insist that technological sovereignty isn’t just the capacity to build things but the capacity to deliberate together about whether we should build them at all. And, finally, we should stop giving these actors the benefit of the doubt. They’re not naïve. They’re not mistaken. They understand perfectly well what they’re building and they’re building it anyway.

  • A laser worthy of a nuclear clock

    The nucleus of the thorium-229 isotope has a special property: it has an excited state that’s incredibly close in energy to its ground state. The existence of such an isomer is remarkable because when nuclei normally get excited, they need enormous amounts of energy — hundreds of thousands or even millions of electron volts (eV). But the Th-229 nucleus’s excited state is only about 8.4 eV above its ground state. This is really small by nuclear standards and, importantly, it means light can excite the nucleus into this energy level.

    This in turn matters because scientists have developed very precise atomic clocks over the last few decades that work by using lasers to excite electrons in atoms and measure the frequency of the light required to do this. These clocks are so accurate that they’re used for GPS, keeping time on the internet, and in fundamental physics experiments. But they also have a limitation: electrons are relatively easy to disturb, so a stray external electric or magnetic field can shift their energy levels slightly but enough to make the entire clock less stable.

    Nuclei on the other hand are much smaller and are buried deep inside the atom, shielded by the electron cloud from the world beyond. So a nuclear clock based on a nuclear transition would potentially be much more stable and accurate than even the best atomic clocks.

    The Th-229 isomer is the only nuclear transition that’s low enough in energy for scientists to realistically build a laser to make happen. In fact they have been trying to make a nuclear clock based on this transition for years now. Recently, two research groups finally managed to create this transition using lasers and they determined that the wavelength of light needed is 148.4 nm. This is in the vacuum ultraviolet range — i.e. ultraviolet light with a very short wavelength. Such light gets absorbed by air so they need to operate in a vacuum. Thus the name.

    But here’s the catch: the laser sources that these research groups used to excite the transition were pulsed lasers, which means they only produced light in very short bursts, lasting just a few nanoseconds each.

    When you have such short pulses, the light inherently has a broad range of frequencies mixed together. Scientists say the linewidth is several gigahertz wide. But the natural linewidth of the Th-229 isomer transition is very narrow, only about 60 microhertz. That’s a difference of several orders of magnitude. It’s like trying to measure something with a 1-m-long stick when you need precision down to the width of a single atom. Nuclear clocks demand a much more stable laser with a really narrow linewidth — ideally continuous rather than pulsed.

    In a paper published in Physical Review Applied on February 11, researchers from Tsinghua University and the Chinese Academy of Sciences have proposed a way to generate a continuous-wave vacuum ultraviolet laser light at exactly 148.4 nm, with a very narrow linewidth, using a process called four-wave mixing.

    Four-wave mixing is a nonlinear optical process. Normally, when light passes through a material, it just passes through without the different colours of light affecting each other. But if you have intense enough light and the right kind of material, you can get nonlinear effects, i.e. where multiple photons of light interact with atoms in the material to create new photons at other frequencies.

    In four-wave mixing, you take three laser beams and send them through such a special medium. If everything is set up just right, they will combine to create a fourth beam at a new frequency. And the frequency of this new beam will be the sum of the frequencies of the three input beams.

    The authors have proposed using cadmium vapour as the mixing medium. Cadmium because it has many properties that make it perfect for this job. First, it has electronic transitions that can be exploited to make the nonlinear process very efficient. Specifically, the team plans to use a two-photon resonance, meaning two of the input laser beams will have frequencies that, when added together, will exactly match the energy needed to excite cadmium atoms to a particular excited state. This resonance will greatly enhance the efficiency of the process. Second, the wavelengths of the lasers required to produce the desired output are readily available (of wavelengths 375 nm and 710 nm).

    The two previous studies also used four-wave mixing but ended up with pulsed laser light because they used xenon as the mixing medium. Xenon is a generic choice because it results in light of a wide range of wavelengths. If researchers are exploring and don’t know exactly what wavelength they need or if they do want to use light of different wavelengths, xenon is great. On the flip side, it isn’t particularly suited to generating 148.4 nm light. Rather, it can if researchers can supply the input light at enormous power. 

    Pulsed lasers help with this requirement using a trick. Imagine you’ve a water hose: if water flows out continuously at a steady rate, you might get a gentle stream, but if you put your thumb over the end and suddenly release it, you get a powerful jet that can spray much farther even when the total amount of water per minute is the same. Pulsed lasers work like this: at the brief moment when the laser emits light, the intensity is very high even though the average power is low. And four-wave mixing is much more efficient with this intense light — enough to generate enough vacuum ultraviolet light to detect the nuclear transition.

    To this end, the paper went into considerable technical detail about calculating how efficient using cadmium vapour would be, including assessing the element’s atomic structure. The authors also calculated something called the nonlinear susceptibility, which said how strongly the cadmium atoms would respond to the light.

    They also had to worry about phase-matching. For the four-wave mixing process to work efficiently, the different light waves need to stay synchronised as they travel through the medium. This is tricky because different wavelengths of light travel at slightly different speeds through cadmium vapour (a phenomenon called dispersion). However, the authors showed that carefully controlling the temperature of the vapour and tightly focusing the laser beams could result in good phase-matching.

    Overall, their calculations suggested that with input laser powers of 3 W at 375 nm and 6 W at 710 nm — both very achievable using current technology — they could generate more than 30 µW of vacuum ultraviolet light at 148.4 nm. While 30 µW may not sound like much, it’s actually a lot for spectroscopy experiments. More importantly, because this is a continuous-wave process rather than a pulsed process, and because it’s essentially just a frequency multiplication of stable input lasers, the output light should have a very narrow linewidth. The team estimated it could be below 1 kHz, which is orders of magnitude better than the pulsed sources currently in use.

    A narrow linewidth is so important because then scientists can observe something called Rabi oscillations in the nuclear transition. This is when you can coherently drive the nucleus back and forth between its ground state and excited state, which is essential to build a nuclear clock. The researchers showed that with their proposed laser system, the linewidth would be narrow enough to observe these oscillations, opening the door to much more precise measurements of the Th-229 transition and eventually to building an actual working nuclear clock.

    Such a clock could have applications beyond just timekeeping. The Th-229 transition is particularly sensitive to changes in fundamental constants of nature, so it could be used to test whether these constants actually stay constant over time; scientists could also use it to search for certain types of dark matter. The proposed laser system thus represents a crucial technological step towards all these applications.

  • A bad Sprite ad

    One of the advertisements during the ongoing T20 cricket World Cup on Star Sports India has been for Sprite, the carbonated beverage from the Coca-Cola Company. In the ad, it’s a hot day, two people are irritated by the heat and humidity, and they beat it by taking a swig of chilled lime-flavoured Sprite.

    It should be obvious by now but in case it isn’t — in fact the manufacturer and the advertiser are either unaware of this or they know but don’t care — a sugary carbonated beverage is a terrible thing to consume on a hot, humid day in order to feel better.

    The chill alone can feel quite relieving. However, carbonation doesn’t meaningfully improve hydration and in some people causes bloating and burping and/or induces a full feeling that can prevent the person from drinking other fluids, especially water. Ingesting carbonated fluids can also worsen heat-stress or nausea.

    The sugar of course makes it all worse. This is Sprite’s sugar content according to Coca-Cola:

    A large quantity of sugar — not unlike the amount in a 200 ml bottle or larger — can for many people slow the rate at which the stomach empties and exacerbate thirst, especially if you drink a lot at once. If you’re sweating heavily already, a sugary drink sans enough electrolytes is far from ideal for replacing what you lose.

    When pushed on such unhelpful advertisements, these manufacturers, advertisers, and promoters have typically replied saying their food products’ contents are within the FSSAI limits. They’re right — but the FSSAI’s limits are based on the contents being safe while assuming all other conditions ideal. They’re not based on you consuming Sprite on a hot and humid day.

    Featured image credit: Rasmus Andersen.

  • The Birch and Swinnerton-Dyer conjecture

    On Monday night, I kid you not, I dreamt of the Birch and Swinnerton-Dyer conjecture. It was only by name, a fleeting mention in a heated conversation I was having with a friend. I’m not sure who spoke it or why.

    When I woke up, I looked it up, and found that it’s one of the Millennium Prize problems — one of seven unsolved mathematical problems for each of whose correct solutions the Clay Mathematical Institute offers an award of $1 million.

    I’m vaguely familiar with these problems’ names, and the substance of only three, so after the dream, I resolved to understand the conjecture and why it remains unsolved. Here goes.

    Let’s start at high-school maths.

    The equation y = 2x + 1 is a straight line on a graph.

    For any given value of x, there’s only one corresponding value for y.

    Similarly, in high school, you’d have learnt that the equation for a circle is: x2 + y2 = 1.

    If you look for points on this circle where x and y are fractions, i.e. where they’re rational, you’ll find plenty.

    For example, (⅗, ⅘) is such a point on the circle because (⅗)2 + (⅘)2 = 1.

    The Birch and Swinnerton-Dyer conjecture is about elliptic curves rather than circles.

    Despite the name, these curves aren’t ellipses. An elliptic curve is defined by an equation that looks like this:

    y2 = x3 + Ax + B

    Let’s say A = -1 and B = 1. The equation becomes: y2 = x3 – x + 1

    If you plot this equation on a graph, you’ll get a smooth, flowing curve.

    Mathematicians are obsessed with finding the rational points on these curves, i.e. points where both x and y are fractions.

    For some elliptic curves, there are only a few rational points. For other elliptic curves, there are infinitely many.

    The question is: how can we tell, just by looking at the equation, how many rational points it has?

    A fascinating property of elliptic curves is that you can add points together.

    If you take two rational points on the curve, called P and Q, draw a line through them, and see where that line hits the curve a third time, that third point — after reflecting it across the x-axis — will also be a rational point.

    Mathematicians call this point P + Q.

    This is how elliptic curves have a ‘rank’.

    If a curve has rank = 0, there are only a finite number of rational points on the curve. You can add them all day but you’ll keep finding the same few spots again and again.

    If a curve has rank ≥ 1, it has infinitely many rational points. You can generate them by adding the rational points together to travel all over the curve.

    The Birch and Swinnerton-Dyer conjecture an attempt to calculate this rank using a completely different part of maths.

    To solve a difficult problem, mathematicians often try a simpler version first.

    For example, in order to calculate the rank of an elliptic curve, mathematicians looked for solutions in modular arithmetic.

    Consider a clock, whose numbers are modulo 12. In normal counting, 10 + 5 = 15. But on a clock, 10 + 5 = 3. This is because once the count hits 12, it resets. Since 10 + 5 = 10 + 2 + 3 = 12 + 3, you’re left with 3.

    This is what modulo 12 means.

    You can do the same thing with an elliptic curve equation.

    You pick a prime number p (like 2, 3, 5, 7, 11…) and ask: how many integer solutions are there if we only care about the remainder when divided by p?

    For instance, let’s use the elliptic curve y2 = x3 – x + 1 with p = 5.

    We want to find all solutions (x, y) where the values of x are picked from the set {0, 1, 2, 3, 4} — since these are the possible remainders when divided by 5 — and the equation holds modulo 5.

    This means:

    1. Pick a value of x from {0, 1, 2, 3, 4}

    2. Calculate y2 = x3 – x + 1 using normal arithmetic

    3. Find the remainder when you divide that result (y2) by 5

    4. Now find a y from {0, 1, 2, 3, 4} such that y2 has that same remainder when divided by 5

    So let’s check each possible value of x:

    • x = 0 so y2 = 1. Is there a y in {0, 1, 2, 3, 4} whose square equals 1 mod 5? 1 or 4
    • x = 1 so y2 = 1. Is there a y in {0, 1, 2, 3, 4} whose square equals 1 mod 5? 1 or 4
    • x = 2 so y2 = 7. Is there a y in {0, 1, 2, 3, 4} whose square equals 7 mod 5? None.
    • x = 3 so y2 = 0. Is there a y in {0, 1, 2, 3, 4} whose square equals 0 mod 5? 0
    • x = 4 so y2 = 61. Is there a y in {0, 1, 2, 3, 4} whose square equals 61 mod 5? 1 or 4

    So when p = 5, the elliptic curve y2 = x3 – x + 1 had seven solutions.

    Now, let Np be the number of solutions for a specific prime p. Because there are only p possible values for x and y in this scenario, finding Np is easy.

    Let’s use the same example.

    Since we’re working with modulo 5, both x and y can only be from {0, 1, 2, 3, 4}. That’s only five possible values each.

    And for each x, we only had to check at most five values of y. That’s at most 25 checks in all — which is very easy for a computer.

    Studying the curve modulo p, for many different values of p, yields information about the original curve over the rational numbers.

    Specifically,finding all the rational points on the curve y2 = x3 – x + 1, e.g. (0,1), (1,1), (-1,-1), etc., is extremely difficult. There could be infinitely many and they could involve large numerators and denominators.

    But for each prime p, counting how many solutions exist modulo p is easy: you just need to check all p2 possibilities.

    Notice also how for any given p, there are also around a p number of solutions on average.

    The number of solutions per possibility contains information about the rank of the elliptic curve.

    This connection happens via the L-function.

    In the 1960s, Bryan Birch and Peter Swinnerton-Dyer had a radical idea. They wondered if the number of solutions Np for various values of p could reveal the rank of the curve.

    They created the L-function to hold this information, written L(E, s). This is a complex function built using all the Np values for every prime number p.

    If a curve has many rational points, i.e. a high rank, we’d expect it to also have a high value of Np. If the curve has few rational points, Np should also be low.

    L(E, s) is a function of the variable s.

    Birch and Swinnerton-Dyer used a computer — then a room-sized machine called EDSAC 2 at the University of Cambridge — to calculate these values.

    They noticed a stunning pattern.

    Recall that for a given p, there are around a p number of solutions on average.

    If Np ​> p, the curve was said to have more solutions than average for that prime.

    If Np < p, the curve was said to have fewer solutions than average for that prime.

    Birch and Swinnerton-Dyer checked what happened when they multiplied these results together for thousands of primes. Their product looked like this:

    ∏p≤XNpp\prod_{p \leq X} \frac{N_p}{p}

    In words, this formula asks: across all the prime numbers up to a certain limit X, is the elliptic curve consistently producing more solutions than average or fewer?

    When they plotted this formula on a graph, they noticed a clear divergence based on the rank of the curve.

    If a curve had only a finite number of rational points, the product fluctuated a bit but remained relatively small and stable.

    If the curve had infinite rational points, the product started to grow. The more primes they included in the calculation, the larger the product became.

    Here’s a visual.

    In the top graph, the blue curve has rank 0, so you see the product fluctuate but stay relatively small and bounded. The red curve has rank 1, so the product grows significantly larger.

    The bottom graph shows the same curves on a logarithmic scale, revealing the pattern over a larger range of values. The blue curve stays relatively flat with small oscillations while the red curve continues to surge upwards.

    Overall, Birch and Swinnerton-Dyer noticed that curves with finite rational points, i.e. rank 0, had a relatively bounded product. And curves with infinite rational points, i.e. rank ≥ 1, had a boundless product.

    Ergo, higher rank means faster growth.

    The product that Birch and Swinnerton-Dyer computed is closely related to the L-function.

    How?

    For each prime number p, they defined a variable ap = p + 1 – Np

    ap measures how Np differs from the expected value p + 1.

    If Np = p + 1, then ap = 0, i.e. it’s exactly average.

    If Np > p + 1, then ap < 0, i.e. there are more solutions than average.

    If Np < p + 1, then ap > 0, i.e. there are fewer solutions than average.

    The L-function makes use of the ap value thus:

    L(E,s)=∏p(1−ap⋅p−s+p1−2s)−1L(E, s) = \prod_p (1 – a_p \cdot p^{-s} + p^{1-2s})^{-1}

    In sum, the behaviour of the product as X grows is mathematically related to whether L(E, s) has a zero at s = 1.

    If you plug s = 1 into the L-function and get 0, the corresponding elliptic curve E has at least some infinite points.

    But if the L-function hugs the zero very closely, the rank of the elliptic curve E is higher.

    Thus, Birch and Swinnerton-Dyer conjectured: the rank of an elliptic curve is equal to the order of the zero of its L-function at s = 1.

    When a function equals zero at some point, the ‘order’ says how strongly it touches zero.

    If the order is 0, the function doesn’t actually equal 0 at that point. If the order is 1, the function crosses through 0 normally. If the order is 2, the function touches 0 and bounces back (e.g. y = x2 when x = 0). If the order is 3 or more, the function hugs zero closely before leaving.

    If the function L(E, s) has a zero of order r at s = 1, it means:

    • L(1) = 0
    • L‘(1) = 0 (the first derivative is also zero)
    • L”(1) = 0 (the second derivative is also zero)
    • … continuing through the (r-1)th derivative
    • But Lr(1) ≠ 0 (the r-th derivative is not zero)

    The conjecture states that this order r equals the rank of the elliptic curve.

    So if the L-function has a zero of order 2 at s = 1, the curve should have rank 2 — meaning it has infinitely many rational points that can be generated from 2 independent base points (like P and Q earlier).

    While the rank is generally the most interesting part of the conjecture, the full version goes further to provide an exact formula for how the function behaves when s = 1.

    Here’s the conjecture in mathematical terms:

    L(r)(E,1)r!=ΩE⋅Reg(E)⋅#Ш(E)⋅∏cp(#Etor)2\frac{L^{(r)}(E, 1)}{r!} = \frac{\Omega_E \cdot \text{Reg}(E) \cdot \#\text{Ш}(E) \cdot \prod c_p}{(\#E_{\text{tor}})^2}

    The terms on the right side represent different properties of the curve:

    Reg(E)\text{Reg}(E)

    — called the regulator, it measures how spread out the rational points are

    #Ш(E)\#\text{Ш}(E)

    — the Shafarevich-Tate group, which measures how much the curve ‘cheats’ by having solutions that look real but aren’t (this is a very hard part to calculate)

    ΩE and cp\Omega_E \text{ and } c_p

    — factors related to the shape and size of the curve.

    In effect, the right side of the conjecture is about analysis because it’s concerned with the analytic property of the L-function at s = 1.

    The left side of the conjecture is about algebra and geometry because it depicts the rank of the elliptic curve.

    Mathematically, these are such different types of objects that proving they’re always equal is extraordinarily difficult.

    There’s currently no algorithm that’s guaranteed to find the rank of an arbitrary elliptic curve.

    Mathematicians can find some rational points and make educated guesses but proving “that’s all of the points” or that “these points will generate all the rest” is very difficult.

    The L-function is defined as an infinite product over all prime numbers.

    Proving that it even converges to a particular value or that it behaves in a predictable way requires some heavy-duty mathematics.

    While mathematicians know that counting the number of solutions an elliptic curve equation has modulo p can determine the structure of rational solutions, they don’t know why.

    This is called the local to global principle and it’s an unsolved problem in its own right.

    Mathematicians have proven the conjecture for specific families of elliptic curves — but proving it for all possible elliptic curves requires many techniques that mathematicians don’t even possess.

    It’s like finding that the number of ways you can rearrange furniture in your house is secretly determined by the prime factorisation of your door number. You could check millions of houses and see the pattern holds, but why would such different things be related?

    And how do you prove that this must always be true?

    This is why the Birch and Swinnerton-Dyer conjecture remains unsolved.

    Bryan Birch (left) and Peter Swinnerton-Dyer. Credit: William Stein and Renate Schmid

    Elliptic curves are a backbone of modern security. They’re used to secure websites, cryptocurrency transactions, app-based messaging, and so forth.

    Remember that ‘adding’ two rational points P and Q could lead you to a third rational point R? Elliptic curve cryptography exploits this fact.

    Choose a public elliptic curve, i.e. an elliptic curve whose equation is public, and a point G on it.

    Pick a random secret number k — your private key.

    Compute k.G, i.e. add G to itself k number of times. Let’s call the result Q. This is your public key.

    As with all cryptography, you can share the public key (Q) but you must protect the private key (k).

    Given G and Q, the task of finding k is called the elliptic curve discrete logarithm problem.

    Even extremely powerful computers struggle to crack it. There’s no known efficient algorithm to solve it.

    This is why understanding the distribution of rational points on elliptic curves is the foundation of how we’re keeping secrets in the digital age.

    The same difficulty that makes the conjecture so hard to solve is what makes elliptic curve cryptography secure.

    Mathematicians have proven the conjecture for when the rank is 0 or 1 and only for certain curves. For rank 2 or higher and for all curves, the Birch and Swinnerton-Dyer conjecture remains one of the greatest unsolved problems in mathematics.

  • Developing Tamil Nadu

    “If the National Democratic Alliance (NDA) comes to power, it will ruin the developed State of Tamil Nadu” — Tamil Nadu Chief Minister M.K. Stalin said this in his address to a local conference organised by the Indian Union Muslim League in Kumbakonam on January 28.

    While Stalin’s claim relies on aggregate metrics like the GSDP and the GER, economic development is really a culture. True development means rising incomes as well as expanded human freedoms and better quality of social systems — which are areas where Tamil Nadu still faces an uphill task. For instance while the DMK government launched ambitious initiatives like the ‘Green Tamil Nadu Mission’ and the ‘Tamil Nadu Climate Change Mission’, enforcement on the ground remains reactive. The State Pollution Control Board suffers from regulatory capture and its focus is on granting clearances to aid industrial GSDP growth rather than penalising non-compliance.

    Pollution hotspots like Ennore and the Cooum River have seen little qualitative improvement in water and air quality indices despite four years of rhetoric. A culture of development would require TN to shift from managing pollution, e.g. clearing oil spills after they happen, to preventing it through strict liability, which the state has been reluctant to enforce to avoid spooking investors.

    In fact noise pollution has become so pervasive that most residents have simply become accustomed to it. After I lodged a complaint with the SPCB over an offender in my neighbourhood last year, an official from the board reached out just to say, “That’s how it is, there is nothing we can do.”

    The Dravidian Model is often lauded for high access to education, as seen for example by the high gross enrollment ratio, but what of learning outcomes and employability? The need for the ‘Naan Mudhalvan’ scheme Stalin launched in 2022 is itself an admission of systemic failure: it acknowledged that most of the engineering and arts graduates the state produces are unemployable sans remedial skilling. Similarly a developed state wouldn’t just have children in school, it would have them performing at global standards, yet Tamil Nadu’s public education system still struggles to compete with private counterparts.

    But perhaps the strongest  reason to disagree with Stalin’s ‘developed’ tag for Tamil Nadu is the persistence of caste-based atrocities, which points to a failure in social development. The 2022 incident in Vengaivayal, where human faeces were found in a water tank meant for Scheduled Caste residents, comes to mind, as does the inability of the state apparatus to swiftly identify and punish the perpetrators. Sociologists have argued that economic growth without eradicating caste spatiality is incomplete modernisation, so not being able to swiftly deliver justice in such a high-profile case undermines the claim that TN offers a “safe” or “developed” social environment for minorities and marginalised groups.

    Finally, even from a fiscal standpoint, a ‘developed’ economy should run on sustainable revenue models rather than consumption funded by debt. According to recent CAG reports and fiscal analyses (2023-2024), Tamil Nadu continues to run a revenue deficit, meaning the government is borrowing money just to pay for daily expenses such as salaries and subsidies rather than investing in capital assets. The current administration has also doubled down on populist welfare, including cash transfers, without fixing the structural revenue leaks, e.g. electricity board losses, creating a sort of fragile development where the state is one or two fiscal shocks away from crisis. Truly developed economies on the other hand maintain revenue surpluses to fund welfare.

    I’m rooting for the DMK to win the impending Assembly elections, which is why I’m concerned that by engrossing the anti-Hindutva space while leaving socio-economic fractures unhealed, comments like Stalin’s may till the soil for the very ideology his party claims to resist — by pushing groups that remain disenfranchised despite claims to development to seek solutions in the opposition’s counter-narratives.

  • From the Heisenberg cut to the Copenhagen interpretation

    The following post was motivated by this exchange (on X.com), which prompted me to write out my understanding of the Copenhagen interpretation of quantum mechanics and the part the Heisenberg cut plays in it. I haven’t gone into the variants of the interpretation that Maria Violaris brings up; I only focus on understanding what the interpretation does and doesn’t say to begin with, and its history.

    There are many interpretations of what quantum mechanics says about reality. This is unlike classical physics, where theory and reality converge almost perfectly. If using Newton’s laws of motion you determine that a ball flying through the air will have some speed at some point, you’ll find that to be the case when you take measurements. Quantum mechanics on the other hand has some uncertainty baked into the outcomes of certain measurements; there’s no escaping it. That means the mathematical formalism describes only the probability of the outcomes of measurement rather than the event itself, creating a fundamental gap between the theory and observations that different interpretations have tried to bridge with competing philosophical explanations.

    Perhaps the most popular among them is the Copenhagen interpretation: a small 2016 survey found it enjoys the most agreement among physicists; it also holds sway in the popular imagination thanks to Erwin Schrödinger’s thought experiment involving a cat that’s both dead and alive. However, Schrödinger came up with that idea to illustrate his belief that the Copenhagen interpretation of quantum mechanics paints an absurd picture of reality. The interpretation has been refined over time and is more complicated than that, and certainly not absurd.

    In Schrödinger’s thought experiment, the cat is a metaphor for an observable property of a quantum system. That the cat is both dead and alive — a statement that the wavefunction of the property is in a superposition of two (or more) states. When you open the box to see if the cat is dead or alive (but not both) in the metaphor, the description of the system updates from a superposition to a single outcome.

    Note that this is a simplified picture. For a more thoroughgoing account, I recommend Jim Baggott’s post ‘The Copenhagen Confusion’. Here’s a line from the operative passage: “The ‘collapse of the wavefunction’ was never part of the Copenhagen interpretation because the wavefunction isn’t interpreted realistically. The only thing that happens when an electron is detected on a screen in the context of Copenhagen is that we gain knowledge of the position of the electron.” In this post, however, I’m going to flatten these details for simplicity’s sake where necessary.

    Werner Heisenberg (left) and Niels Bohr. Credit: Bundesarchiv, Bild 183-R57262 and public domain

    A useful entry point to the interpretation is the Heisenberg cut, which is a conceptual boundary within the interpretation. It draws the line between the quantum system, i.e. the wavefunction and probabilistic laws, and the measuring apparatus or the observer, described by classical mechanics and deterministic laws. And these two parts of the overall system share a foundational relationship: the Copenhagen interpretation uses this cut to bridge the gap between the mathematical formalism of quantum mechanics and the empirical reality of what scientists observe in a lab.

    In Niels Bohr’s view, the cut is required because humans are macroscopic entities who communicate using classical language. (“It’s very hard to talk quantum using a language originally designed to tell other monkeys where the ripe fruit is”: Terry Pratchett.) Bohr argued that we don’t have a choice but to describe experiments in terms of everyday physics, including positions, momenta, and times, because these concepts also define our cognitive and linguistic capabilities. This means even though the subatomic world is quantum mechanical, the instruments we use to measure it, like photographic plates and our eyes, must be treated as classical objects. The Heisenberg cut is an imaginary boundary in our description of experiments where we stop using quantum concepts and start using classical ones.

    An important feature of the cut is its mobility, i.e. that a person can draw it anywhere in their description of the thought experiment: when a photon of light hits the cat, when a photon reflected by the cat reaches your eye, when you first open the box or somewhere else. According to the Copenhagen interpretation, the physical predictions of quantum mechanics don’t change based on where you make the cut, as long as it is placed somewhere along the chain of measurement. And the cut must exist if you’re to be able to ‘measure’ the system.

    The Heisenberg cut is also intimately tied to the measurement problem. On the quantum side of the cut, the system will evolve according to the Schrödinger equation, which is deterministic and preserves superpositions, i.e. it allows a particle to be in two states at once. On the classical side of the cut, you observe definite outcomes: the particle is either here or there.

    In effect the cut marks the point where multiple possible outcomes give way to a single recorded result. And in the Copenhagen interpretation, this transition isn’t a physical process that can be derived from the Schrödinger equation itself; instead it’s a non-dynamical event that occurs whenever a quantum system interacts with a classical measuring device. This leads to the somewhat paradoxical conclusion that quantum mechanics is a complete theory of the microscopic universe yet it banks on classical concepts (that it can’t make sense of) to make sense of its predictions.

    While both Bohr and Werner Heisenberg, for whom the cut is named, agreed that this cut should exist, they arrived at it for different reasons. Heisenberg treated the cut as a moveable mathematical boundary that separated the object from the subject, highlighting the subjective nature of observation. He was interested in how the observer’s knowledge changed the state of the system. Bohr on the other hand viewed the cut as an epistemological necessity fixed by the experimental arrangement. In other words for Bohr the cut wasn’t about a subjective observer disrupting nature but about the objective impossibility of separating the observer from the observed in the quantum realm (a.k.a. the uncertainty implicit to quantum mechanics).

    Second, let’s look at how the Copenhagen interpretation treats the maths of quantum mechanics. The theory postulates that a quantum system evolves according to the Schrödinger equation. However, our human experience is obviously discontinuous: we see definite outcomes, not superpositions. The ‘collapse’ is the instant when the system switches from its smooth quantum evolution to a single, definite state.

    Without the Heisenberg cut, on the other hand, there’s no logical place for the wavefunction to collapse. If you treated the entire universe — including a subatomic particle, a microscope, a scientist, and the scientist’s brain — as one giant quantum system, everything would just keep evolving according to the Schrödinger equation forever. Eventually you’d end up with a universe in a massive, complex superposition but you’d never arrive at a specific measurement or result. This is actually the premise of the many-worlds interpretation of quantum mechanics, which removes the collapse and thus removes the need for a cut.

    In the Copenhagen interpretation, however, because you eventually arrive at a definite result (and which you need to do for science to be science), you’re forced to draw a line: “Everything on this side is quantum and describes probabilities and everything on that side is classical and describes facts”. The wavefunction ‘collapse’ is defined as the point at which the quantum description gives way to a single, definite experimental outcome. When the quantum system crosses the Heisenberg cut and interacts with the classical side, the wavefunction is said to have collapsed.

    Thus to discuss the Heisenberg cut is essentially to discuss the mechanism of collapse and highlights the implicit dualism of the Copenhagen interpretation: the universe is divided into the observer and the observed. The wavefunction describes what’s being observed and the collapse ensures the observed entity matches the observer’s reality.

    The concept of the cut originated in a few intense months leading up to Heisenberg’s publication of a paper in March 1927. At the time, Heisenberg had been working at Bohr’s institute in Copenhagen on rescuing the concept of particle trajectories, e.g. the tracks of particles recorded in a cloud chamber, which seemed to contradict the (then) new quantum mechanics.

    In 1925, Heisenberg formulated matrix mechanics, the first logically consistent mathematical framework for quantum mechanics. (This invention was an important first step of the ‘new’ quantum mechanics, whose centenary physicists celebrated worldwide last year.) Among other things, matrix mechanics predicted that certain physical quantities, such as energy, take on discrete values. However, this raised questions about reconciling the theory with physicists observing apparently smooth, continuous particle tracks in cloud chambers.

    The scattering of an alpha particle in a cloud chamber. Credit: Qwerty123uiop (CC BY-SA)

    Heisenberg resolved this contradiction by redefining what a ‘path’ actually is in a cloud chamber. This is a device filled with alcohol vapour that’s supersaturated, meaning it’s cooled to the point where it’s just about ready to turn into liquid. When a charged particle moves through this gas, it knocks electrons out of the alcohol molecules, creating a trail of ions. The vapour rapidly turns into liquid droplets around these ions, forming a visible white track that traces the exact path of the subatomic particle through the chamber.

    But Heisenberg argued that we never actually see a continuous path in a cloud chamber — only the sequence of individual droplets formed by ionisation. Solving the problem of the particle’s trajectory in matrix mechanics would never spit out a continuous path but it could determine the probability of an electron’s state transitioning from one discrete droplet to the next.

    When we say an object transitions from point A to point B in everyday life, we mean it moved through the space in between them. But in matrix mechanics, an electron state transitioning between droplets means a discontinuous update of reality rather than movement. In the context of this post, the state of the electron is a mathematical list of properties the electron possesses at the exact moment it hits a gas molecule and creates a droplet.

    So say when it hits droplet 1, the electron has energy Ehigh, momentum P1, and is roughly at position X1. At droplet 2, scientists find the same electron has energy Elow (because it lost some energy when it smashed into the first atom), momentum P2, and is roughly at position X2. In Heisenberg’s telling, the laws of physics don’t describe this journey so much as the probability of state 2 happening given state 1 just happened.

    This description resolved Heisenberg’s problem because his maths only handled the energy levels and transitions; it had no variable for the particle’s location at each instant in time. In other words by looking at the cloud chamber and saying, “Aha! This track is just a pile of separate water droplets”, he could claim that the physical world also works like his maths. Which means the path we see in the cloud chamber is just our human brains drawing a line between the dots. The electron itself only becomes classically describable when it hits something.

    In other words, in classical physics, the particle has a path regardless of whether we look at it, and the droplets merely reveal it. In Heisenberg’s view, the particle has no defined position or path in the empty space between the droplets. Instead a path as such comes into view only because the cloud chamber is performing a rapid series of measurements: each droplet represents an observation that forces the electron to take a stand on its position while the eventual smooth line is a mental construct we create by connecting these dots.

    Continuing from this idea, in a famous letter to Wolfgang Pauli and subsequently in his March 1927 paper, The Actual Content of Quantum Theoretical Kinematics and Mechanics, Heisenberg introduced a thought experiment involving a gamma-ray microscope. He argued that to observe an electron, one must hit it with a photon. This interaction would disturb the electron. He initially framed the measurement problem as a physical interaction between the electron (the system) and the photon (the probe), where the act of measurement mechanically disturbed the system.

    Bohr’s critique of Heisenberg’s draft then reforged the cut as a central tenet of the Copenhagen interpretation. When Heisenberg showed Bohr his paper, Bohr tore into it arguing that Heisenberg was wrong to focus on the disturbance because he assumed the electron had a definite position and momentum before the measurement and which the measurement then messed up. Bohr insisted on the more radical view that the properties of the electron aren’t well-defined until the experimental arrangement itself is fixed. For Bohr, the cut wasn’t just where a disturbance happened but the line where the observer switched from using quantum concepts to classical concepts to describe the experiment.

    The conversations on this point between the two men in February and March 1927 were intense, protracted, and emotionally exhausting. Heisenberg was 25 years old at the time and convinced he had solved the riddle of quantum mechanics with his paper whereas Bohr was relentless in his criticism, insisting Heisenberg’s fundamental premise was logically flawed.

    According to historical accounts, including Heisenberg’s own recollections later in life, the discussions would go on for hours, often late into the night. At one point, the combination of mental exhaustion and Bohr’s stubborn refusal to accept Heisenberg’s interpretation caused Heisenberg to break down in tears of frustration. But Heisenberg eventually capitulated, though not entirely: he didn’t rewrite the entire body of his paper but he did add a postscript to the end of the published version where he acknowledged that his explanation of the gamma-ray microscope had been too simplistic and that Bohr’s view regarding the electron’s indefiniteness was the deeper truth.

    The tears were the physical manifestation of the painful process of aligning the two different viewpoints into what became the Copenhagen interpretation. In fact, and at the risk of repetition, let’s treat this interpretation as the peace treaty that reconciled Heisenberg’s idea of uncertainty with Bohr’s idea of complementarity. Heisenberg’s view was initially very mechanical and focused on the observer’s limitations; he held that the fuzziness of the quantum world was a result of our clumsiness: i.e. the reality existed but our clumsy hands destroyed the data every time we tried to touch it. To him the Heisenberg cut was the place where this mechanical disturbance happened.

    Bohr however worked with the concept of complementarity: that the electron has a dual nature, wave and particle, and that these two natures are mutually exclusive, meaning we can’t see both at the same time. And the uncertainty isn’t because we hit the particle but because the electron literally doesn’t have a defined position and momentum at the same time. If you build an experiment to measure its position, the wave nature would vanish, and vice versa. He was saying in effect that the experiment itself defined what reality was allowed to exist at all in that moment.

    The Copenhagen interpretation loosely synthesised these two views, though it leaned heavily toward Bohr’s. It stated that we must accept two contradictory truths: the mathematical formalism (Heisenberg’s matrix mechanics and the Schrödinger equation) that predicts probabilities and the classical world of our measuring devices. The interpretation is the agreement that we can’t speak about what the electron is doing when we aren’t looking. We can only speak about the results of the interaction between the electron and the machine.

    In effect, the Copenhagen interpretation asserts that physics isn’t about the ontological nature of the electron, i.e. what it is, but about the epistemological nature of our knowledge, or what we can say. And the Heisenberg cut is the necessary border where the indefinite, contradictory quantum world based on Bohr’s idea of complementarity is forced to collapse into a single, definite fact.

    If Bohr and Heisenberg provided the philosophical foundation for the Copenhagen interpretation, the Hungarian-American physicist John von Neumann gave it its formal mathematical form in his 1932 book Mathematical Foundations of Quantum Mechanics. Von Neumann was also the one to show that the mathematics of quantum mechanics allowed the cut to be placed anywhere in this chain without changing the final calculated probabilities.

    Where’s Schrödinger’s cat in all of this, then? As it happens, the famous thought experiment in which the cat is both dead and alive is often misunderstood as a quirk of quantum physics; it was actually a scathing piece of satire Schrödinger designed to show that the Copenhagen interpretation was absurd. Schrödinger in fact didn’t believe a cat could be simultaneously dead and alive. His point was that if you followed Bohr and Heisenberg’s logic to its ultimate conclusion, you’d end up with such a nonsensical reality.

    In fact, the thought experiment, published in 1935, targeted the concept of the Heisenberg cut. In the Copenhagen view, a quantum particle like an atom doesn’t have a defined state: it exists in a superposition of all possible states until an observer measures. Schrödinger could accept this for atoms but couldn’t digest the prospect of applying the idea to macroscopic objects.

    In his mental argument, Schrödinger described a radioactive atom placed in a sealed steel box. If the atom decays in a random quantum event, a Geiger counter nearby would push a hammer, which would smash a vial of cyanide and kill a cat. If the atom doesn’t decay, the cat would live. According to the strict logic of the Copenhagen interpretation, this system remains in a superposition until an observer opens the box to check the cat’s existential status. But until the measurement itself, because the atom is both decayed and not decayed, the Geiger counter is both triggered and not triggered, and the cat is simultaneously dead and alive. Schrödinger’s question was about where the quantum ends and the classical world begins. In other words, where’s the Heisenberg cut?

    An illustration of the Schrödinger’s cat thought experiment. Credit: Dhatfield (CC BY-SA)

    If we make the cut at the Geiger counter, the cat would be a classical object and thus either dead or alive, not both. However, Bohr, Heisenberg, and von Neumann had shown that the cut was mobile. If we moved it to the human observer opening the box, the cat itself would become part of the system’s overall wavefunction — and Schrödinger had contended that treating a living organism as a probability wave was ridiculous. He used the cat to argue that there must be something missing in the theory, some hidden variables or physical reality, that would determine the state of the cat before an observer looks at it.

    For Schrödinger, the cat proved that the Copenhagen interpretation’s refusal to define objective reality between measurements was a philosophical failure. It showed that while the cut could work mathematically, as von Neumann had proved, it led to macroscopic impossibilities in the physical domain.

    The Copenhagen interpretation in turn didn’t surmount Schrödinger’s critique by answering the riddle but by dismissing Schrödinger’s question as unscientific. Bohr argued that Schrödinger was ‘illegally’ extending quantum concepts beyond the point where a classical description would be required. In his view a Geiger counter is a macroscopic measuring device so the cut between the quantum and classical worlds would occur the moment the particle interacts with the Geiger counter. And by the time the signal reaches the hammer, let alone the cat, the quantum description would already have yielded a definite outcome at the measuring device, so the cat would never have had to be described as being in superposition.

    There was also a powerful sociological narrative at the time that painted Schrödinger and Albert Einstein as an ‘old guard’ that was too stuck in classical determinism to accept the radical new truths quantum mechanics was throwing up. By 1935, the Copenhagen interpretation was the dominant orthodoxy among the younger, more productive generation of physicists like Pauli and (to a lesser extent) Paul Dirac, who viewed the cat and the Einstein-Podolsky-Rosen paradox not as genuine physical problems but as the confusion of men who couldn’t let go of the past. The proponents of the interpretation essentially declared that if the theory predicted the results of experiments correctly, then any philosophical discomfort about cats that were both dead and alive was the philosopher’s problem, not the physicist’s. And quantum mechanics perfectly predicted the results of experiments.

    Historical timing also played an important part in cementing the Copenhagen interpretation’s dominance. Shortly after Schrödinger published his paper, physics shifted dramatically from the philosophical debates of the 1920s to the pragmatic urgency of the 1930s and 1940s. The rise of fascism and World War II turned the focus of the community towards nuclear energy and The Bomb. In this environment, the “shut up and calculate” approach — a phrase coined later to describe this attitude — took over and physicists shelved questions about the reality of the cat as irrelevant metaphysics.

    The interpretation was also shielded by von Neumann’s mathematical authority. His 1932 book also claimed to show that ‘hidden variable’ theories, i.e. which would restore a specific reality to the cat independent of observation, were mathematically impossible. While Grete Hermann and John Bell later found this proof to be circular, for decades it served as a brick wall that convinced the physics community that there was literally no alternative to the Copenhagen interpretation.

  • That humans quest for cosmic dawn

    From ‘Cosmic dawn: the search for the primordial hydrogen signal’, Physics World, November 18, 2025:

    The EDGES instrument is a dipole antenna, which resembles a ping-pong table with a gap in the middle. It is mounted on a large metal groundsheet, which is about 30 × 30 m. Its ground-breaking observation was made at a remote site in western Australia, far from radio frequency interference.

    The “observation”:

    Hydrogen is the most abundant element in the universe. As neutral hydrogen atoms change states, they can emit or absorb photons. This spectral transition, which can be stimulated by radiation, produces an emission or absorption radio wave signal with a wavelength of 21 cm. To find out what happened during that early universe, astronomers are searching for these 21 cm photons that were emitted by primordial hydrogen atoms. … In 2018 the [EDGES collaboration] hit the headlines when it claimed to have detected the global 21 cm signal (Nature 555 67).

    It will always be fascinating that a setup as deceptively simple as this one enables Earthlings to acquire information from distant reaches of the cosmos — the cosmos!— and from a time called the cosmic dawn. This is to me one of the great achievements of science, in particular scientists’ ability to link some information to specific sources in definitive ways. When you learn more, you realise where the lines between what you do and don’t know lie, at increasing resolution; about how you can and can’t interpret knowledge; and how to acquire more knowledge of increasing quality. That’s how a simple setup, one that can be transported on a small truck on a small planet in one galaxy in some part of the universe, allows us to learn about the universe as a whole.

    I’ve been awed by certain advances in materials science and quantum technologies for the same reason. A good example is nitrogen vacancy centres. Take four carbon atoms, link them together in a tetrahedral shape, make millions of copies of this ‘unit cell’, and you get diamond. If in some of the tetrahedra you replace one carbon atom with a nitrogen atom and dislodge one of the neighbouring carbon atoms, you get a nitrogen vacancy centre. And in this centre, thanks to the relative arrangement of atoms around it, the electrons have a quantum spin that’s extremely sensitive to magnetic fields. For added measure the centre responds with red light if you shine green light on it when the quantum spin is excited by a field. Et voila: you have a powerful magnetic field detector that’s already miniaturised and with a convenient optical readout. But how did physicists get here?

    They did by starting off studying why diamonds are different colours. They found that when they took a clear, transparent diamond and hit it with high-energy electrons or neutrons in a particle accelerator, the diamond would turn green or bluish. Then when they heated the irradiated diamonds to 600º C, the green colour shifted into a pinkish purple or deep red. Just as scientists could interpret data collected by the ping-pong-table-sized antenna to possibly be radio waves from the early universe, scientists understood these tests to mean the carbon atoms in the diamond lattice could be knocked off and replaced with nitrogen atoms. In 1965, a South African researcher named L. du Preez found that when his team irradiated a diamond with nitrogen in it and heated it, the material seemed to emit radiation of 637 nm wavelength. In the 1970s, Gordon Davies and M.F. Hamer in the UK found that when they squeezed this diamond, the light it emitted split and shifted, proving the defect had a specific axis. Finally, in the 1990s, Jörg Wrachtrup and others found that these ‘defects’ had a magnetic property that could be controlled with microwaves and ‘read’ using laser light.

    You learn something, you learn how to apply it to make a tool, use the tool to develop a technique, use the technique to detect something that you couldn’t before, use what you learn to hone the next tool, develop new techniques, and discover even more. Computer scientist Étienne Fortier-Dubois’s ‘Historical Tech Tree’ visualisation offers a captivating view of this knowledge loop through history. However, what it doesn’t depict, and what most histories of science and technology focused on the technic don’t depict, is crucial: the value of the knowledge loop is determined almost entirely by how it interacts with societies and vice versa.

    As technologies mature, some discoveries seem to become almost inevitable but which ones do see the light of day depends on power. In a 1922 article in Political Science Quarterly, the sociologists William Ogburn and Dorothy Thomas described 148 major inventions and discoveries that two or more people had made independently, arguing that culture and technology actually co-evolve. Some famous examples from history include calculus (Isaac Newton and Gottfried Wilhelm Leibniz), evolution by natural selection (Charles Darwin and Alfred Russel Wallace), the discovery of oxygen (Carl Wilhelm Scheele, Joseph Priestley, and Antoine Lavoisier), and the telephone (Elisha Gray and Alexander Graham Bell). On the other hand, scientists worked out public-key cryptography inside Britain’s signals intelligence establishment in the early 1970s but remained officially unacknowledged for that until the government declassified it in 1997. Similarly and effective antiretroviral therapy for HIV existed by the mid-1990s but for years remained concentrated among richer countries and elites in practice because patent, pricing, and political pressure choked off generic competition and access.

    Some of the most consequential technical systems were also incubated in secrecy and under pressure, showing that states and firms can concentrate talent and money in ways that a ‘republic of letters’ can’t — exemplified by the military-industrial complex in the post-war US — and still have the same outcomes. These settings have the same knowledge loop but the state has fenced it off from society at large, whether by classifying it or, as is often the case in India, by structurally weakening the means to access it. To use a different example: the American writer Charles Fort famously said, “A steam engine comes when it is steam engine time”. The more important question however is how “steam engine time” itself arises: when the corresponding supply chains, capital, geopolitical competition, profit, surveillance, and labour regulations, among other things, are in place.

    (Aside: Fort’s comment also reveals a well-known problem with world-building in the sci-fi and fantasy genres of literature. The British writer M. John Harrison called it the “great clomping foot of nerdism”, an expression with which I’ve taken offence more than once, but over time I’ve come to discern a particular problem — one that this post allows me to articulate clearerly: if you world-build a world in which steam engines appear without the requisite social and cultural conditions, you’re not doing it right. That, for all its focus on the technic, would indeed be a great clomping foot.)

    In order to facilitate such scientific and technological progress, then, a human society needs to get itself on and then stay on the path of learning, investing, researching, and maturing knowledge and technologies. It needs to facilitate that combination of availing scientists the freedom to ask questions and the resources to answer them, over and over — and it needs to develop the social, economic, and political conditions to apply the outcomes of that loop efficiently for the better of society, without entrenching existing inequities or creating new ones. The latter is very important because societies generally don’t stay on that path by consensus but by so using coercive instruments like budgets, patents, labour policing, and bargaining with other countries.

    In the end a potent technique can be born in a cramped corner of human society — whether a lab or a monopoly — but culture matters most for whether it spreads, who controls it, who gets to benefit from it, and, eventually, what kind of change it leads to in turn. It’s difficult not to return to what now seems like the absurdity of the ping-pong-table-sized antenna bolted to a groundsheet in a quiet patch of Earth, a modest platform from which humans are trying piece back together a time when there were no planets, no eyes, no archives, just hydrogen and the universe’s first pinpricks of light. The achievement isn’t only that we can sense something so ancient but that we can justify that we’re hearing it, step by step, against noise as much as self-deception.

  • To be Indian is to set records

    For all the ways in which the Indian people are divided these days, they’re seemingly united in their desire to set records. On January 22, a tinkerer named Sohan Rai, a.k.a. “Zikiguy”, said on Instagram that he and his team “are planning to do India’s highest ever flag hoist in near space for this Republic Day”.

    What is it about setting records? The national BJP government itself, which — from the day Prime Minister Narendra Modi was first elected — has tried repeatedly to extend the record books backwards into mythology, asserting ancient Indians piloted interplanetary aircraft and performed plastic surgery millennia before the advent of modern science. But recasting religious metaphors like the elephant-headed god Ganesha as literal medical feats only reveals the ideology’s own neurosis to validate Indian heritage using the yardstick of modern Western empiricism. It’s practically a retroactive attempt at record-setting where the leadership, admitting it can’t dominate the prevailing global hierarchy, simply imagines India to have been the original superpower.

    The 2016 Tamil film Joker brought the same pathos to clearer light through its protagonist, Mannar Mannan (Tamil for “king of kings”), who abandons democratic petitioning and other mechanisms in favour of performing absurdity — much as farmers from Tamil Nadu did when they protested in Delhi in 2017 by holding dead rats and snakes in their mouths — to draw the state’s attention. The state, the thinking seems to be, has become inured to ‘normal’ poverty and will only react to spectacular embarrassment.

    The Limca Book of Records is a symbol of this syndrome. The then Parle-Bisleri chairman Ramesh Chauhan conceived of the book in 1986 and first published it in 1990 as an extension of the ‘Limca’ brand, as a tool of “soft” marketing. That it exists at all is because Indians alone are setting so many records, even those bordering on the facile. Today the Limca Book is the second-oldest of its kind in the world, after the Guinness Book, and accepts applications from Indians worldwide provided they hold an Indian passport — a requirement that reveals how both citizenship and record-setting are equally emblematic of being Indian.

    A ‘record’ is an event that documents primacy through some extreme act, and the extremum can take different forms depending on what sort of primacy one wishes to establish. Prime Minister Narendra Modi built the world’s tallest statue in Gujarat and Maharashtra responded by promising a taller one because the BJP was engaging in a pissing contest and the other was furthering the same stunted logic by contending that one didn’t have to be a nationalist to piss higher, for instance.

    More recently, when astronaut Shubhanshu Shukla first went to space onboard the Axiom-4 mission, various media outlets reported that he’d set a record by becoming the first Indian to conduct an experiment in space. By that measure, Indians have scores of records left to set, including becoming the first Indian to cough in space, the first Indian to get out of the right side of bed in space, and the first Indian in space whose name starts with ‘M’. But hey, it’s technically a record, and it’s printed, and if it’s printed it must be true.

    In his work, the historian Vinay Lal has argued that the Indian obsession with the Guinness Book is rooted in a deep-seated postcolonial disquiet. He’s posited that the colonial experience left India with a sense of “historical incompleteness” because the West had come to be seen as the world’s standard-bearer of modernity and ‘hard facts’. In his telling, Indians also have a “fetish for numbers” because in a chaotic and often unmanageable democracy, precise numbers — e.g. “typing 103 characters in 47 seconds with a nose” — offer the comfort of certainty and empirical truths, and which also feel scientific.

    Records also allow these ordinary persons to be heroes. While achievements like Olympic gold medals and Nobel Prizes require state funding, favourable (and arguably arbitrary) social conditions, political stability, and training/research hardware, the Guinness and Limca records often demand only time and a high tolerance for discomfort. This is why many Indian records are feats of endurance or body modification, such as “longest fingernails” or “most time spent standing on one leg”, rather than exercises of athleticism or brilliance.

    The Indian state itself isn’t immune to the same tendencies. For example, the sociologist Shiv Visvanathan has written that the state uses such records to replace complex historical narratives with crude statistics. Thus we have a prime minister focusing on the number of people simultaneously doing yoga rather than engaging with its philosophy in any meaningful sense. The Union health ministry advanced a similarly pathetic claim during the COVID-19 pandemic when it said it was conducting the “world’s largest vaccination drive”, betraying its real design: to create a spectacle to unify the mob and to project an image of power and efficiency to mask infrastructural and social weaknesses.

    Of course when the people themselves take advantage of their numbers to set records, it’s just quaintly saddening. As Samanth Subramanian reported for The New York Times in 2015:

    The first time Nikhil Shukla adjudicated a Guinness world record, two million people turned up. Standing on a makeshift dais just before dawn in January 2012, Shukla gazed with bleary, incredulous eyes; he was 28, and he had never seen such a mammoth crowd in his life. Tolls on the national highway from the nearest city, Rajkot, had been suspended to accommodate the traffic, and Shukla had to trudge 20 minutes from his V.I.P. parking spot, squeezing through dense thickets of bodies, to approach the stage. The throng that gathered in this patch of dusty farmland in western India to watch the event came from villages and towns across the district. They had responded to a call from a Gujarati community organization that, with a vague aim of promoting public harmony, wanted people to pair off and shake hands with one another, setting a world record for the most simultaneous handshakes.

    All this is to say that the Indian affinity for records isn’t benign or innocent but is nurtured by an unresolved postcolonial identity that still looks to the West, or Western ideals, to certify its own reality. In this universe the Indian citizen resorts to obscure feats of endurance as a desperate attempt to become visible even as an increasingly authoritarian state exploits this pathos to its own ends.

    As for what Sohan Rai is going to attempt: he’s bypassing the elite barriers to the space programme, since he can’t yet be an astronaut himself; he’s internalised the state’s performance of power by enacting in miniature the quest for legitimacy using gigantism (thus rendering himself very visible in the process); and by attaching an altitude number to the hoist he’s seeking to convert the abstract sentiment of national pride into an empirical ‘truth’ that can be recorded.

    Sure, there are some reasons to be optimistic: in the course of attempting this record, Rai will (I assume) step beyond simply enduring discomfort and solve important problems in atmospheric physics, telemetry, the behaviour of materials in the stratosphere, and so on. The problem is I’m not sure what all that could amount to other than also legitimising the state’s own devices to distract the people from their anxieties.

  • Normalising deviance

    When a rocket launches, we usually only care about one thing: did it work? We cheer if it reaches orbit and we gasp if it doesn’t. The French philosopher Bruno Latour called this “black boxing” because when a machine is successful we stop looking at its complex inner parts, we just see an input, which is the launch, and then a satellite in orbit. The box becomes sealed by its own success. But Latour also found that a black box must crack open when things break: when a car stalls you need to open the hood. You can no longer ignore the engine and figure it out by working on the chassis.

    ISRO has yet to release the Failure Analysis Committee (FAC) report for the PSLV-C61 mission. For PSLV-C62, a short statement on its website says “a detailed analysis has been initiated”; I’m not sure if this is the same as a new FAC. If the organisation is opening the “black box” only for itself, investigating failures internally while keeping the results secret from the public and independent peers, it’s falling into a trap Latour expected: that objectivity doesn’t come from a single person or a single agency looking really hard at a problem but from having as many different people as possible, with different viewpoints and biases, looking at it.

    For years, NASA engineers knew that foam insulation was falling off the external fuel tank and hitting the Space Shuttle. They looked at it constantly and they analysed it. They did open the hood but they also  only talked to each other, and in the process they managed to convince themselves it wasn’t a safety risk. The American sociologist Diane Vaughan called this the ‘normalisation of deviance’: when small departures from conservative practice become routine because of the idea that “nothing bad happened last time”. If they’d released those internal reports to external aerodynamicists or independent safety boards before Columbia lifted off, they likely wouldn’t have had the disaster they did.

    Today ISRO risks the same ‘normalisation of deviance’: without external eyes to challenge its assumptions, its experts are at risk of convincing themselves that a recurring PS3 stage glitch is manageable — right up until it isn’t.

    Latour also often spoke of the ‘parliament of things’, the idea that technologies like rockets are part of our political and social world rather than simply being technical objects. If ISRO solves the problem internally, it might fix the specific valve or sensor or whatever but it won’t fix the institutional pressure that caused the quality control to slip in the first place. Only public scrutiny, i.e. the assembly of MPs and citizens asking irritating questions like “why?”, can force an agency to fix its hardware as well as its culture.

    Then we have institutional memory as well: when you fix a problem in secret you’re also withholding the lessons you’ve learnt from young engineers. Public reports are effectively a permanent, searchable archive of mistakes.

    In the 1979 book Laboratory Life: The Social Construction of Scientific Facts he coauthored with the British sociologist Steve Woolgar, Latour defined an “inscription” as any visual display produced by a lab setup, no matter how large or expensive, whose final output is a piece of visual information. For instance, a bioassay might start by pipetting chemicals and shaking tubes but it ends with a sheet of paper with numbers or a jagged line on a graph. That paper is the inscription. And at this point the scientists discard the physical substances (the chemical compounds) and retain the inscription.

    According to Latour, science is almost never a single ‘eureka!’ and almost always a series of inscriptions. This narrative is useful to understand that objectivity in science is often a myth: because scientists don’t just passively observe nature but are writers and craftworkers in their own right and draw on the corresponding skills to make sense of nature. A statement becomes a ‘fact’ only when the inscriptions supporting it are so clear and numerous, so that dissenting voices are silenced, and to challenge a fact you need to produce counter-inscriptions of a similar or greater calibre.

    But when there’s no inscription, when the FAC reports are invisible, what do you challenge if you need to? How do you achieve progress in a rational way?

    The Soviet Union’s N1 rocket was its equivalent of the USA’s Saturn V,  designed to take cosmonauts to the moon. And it failed all four times it launched. An important reason was that, for all its other successes, the Soviet space programme was a sealed box. There was no independent press to ask why the rocket’s engines were exploding and no parliamentary questions about safety protocols — and inside this Matrioshka doll of secrecy its engineers were paralysed by political pressure. When data showed the rocket had a high probability of failure, managers simply massaged the numbers to please the Kremlin. And because the failures were state secrets, the collective intelligence of the scientific community was never brought to bear on the problem.

    Look at NASA’s Challenger disaster in 1986 on the other hand, which was also a tragedy born of a political pressure to launch at all costs. NASA managers had ignored warnings from engineers about the Space Shuttle’s O-rings failing in cold weather; they had, as with Columbia but 17 years earlier, normalised deviance and had accepted small failures right up until they added up to a big one. After the explosion the American system forced the black box open and the Rogers Commission identified the technical fault as well as interrogated the institutional culture. And by publicly airing these concerns — including ‘letting’ Richard Feynman dip an O-ring in ice water on live TV to prove a point — NASA was humiliated, yes, but it was also saved. The scrutiny forced it to rebuild its safety protocols, recover public trust, and allow an object as complex as the Space Shuttle to return to flight, until Columbia revealed this turnaround to have been incomplete.

    Because the Soviet state kept the failures of its N1 missions to the moon a secret, future Russian engineers couldn’t fully study those specific failures in open academic literature. On the other hand NASA’s failures are effectively public textbooks, with engineers in India, Europe, and China today studying its failure reports even today to avoid making the same mistakes. Likewise by hiding the PSLV-C61 report, and the PSLV-C39 FAC report and other reports of a similar nature, ISRO isn’t just hurting itself: it’s hurting the global knowledge base of rocketry. And like the Soviet Union of yore and unlike NASA in the late 1980s and the early 2000s, by shielding its findings from criticism, ISRO is ensuring its solutions are weak and at risk of failing again.

    If ISRO engineers know a failure will be hushed up to protect the prime minister’s image, they may be less likely to speak up about a faulty sensor or a cracked nozzle. If people can’t ask why the PS3 stage failed the pressure to fix it is essentially replaced by the pressure to just “make it look good” for the next launch. In the end by closing itself off ISRO risks becoming a fragile institution. It treats its rockets as matters of fact — unquestionable symbols of national pride — rather than as matters of concern, complex machines that need honest and sometimes harsh public maintenance. There’s a reason transparency is one of the ingredients of good engineering.

  • String theory and reconciliations

    According to particle physics, the fundamental building blocks of the universe are point-like particles, essentially small dots of energy with no dimension. String theory posits that these dots are actually minuscule vibrating loops of energy. A violin string vibrating at different frequencies produces different musical notes; similarly these filaments are said to be able to vibrate at different frequencies, each one creating a different particle of our universe. One note is an electron, another is a photon, and so on.

    String theory hasn’t been proven — it hasn’t made any testable predictions so far, in fact. Yet it exists because scientists are looking for a ‘theory of everything’: a single theory that can explain both gravity and quantum physics. At present these two theories together explain their particular domains very well but scientists don’t know how they fit together. String theory is one of a few theory programmes trying to reconcile them; others include loop quantum gravity and twistor theory.

    On January 7, scientists from Hungary, Israel, and the US published a curious paper in Nature. Stumped by the complex shapes of neurons, they reportedly found a solution in some arcane equations in string theory and, according to them, the equations also describe how blood vessels and neurons branch.

    If you were an engineer designing the wiring for a brain or a vascular system, you’d probably try to save money by using the least amount of wire possible. For a long time, biologists assumed nature ‘thought’ the same way. According to this paper, however, it doesn’t, at least not necessarily. The researchers analysed high-resolution 3D scans of neurons, blood vessels, and fungi and showed that biological networks don’t care about minimising length but about minimising surface area. And to figure out the complex geometry of how these tubelike structures connect, the researchers borrowed the maths of interacting strings.

    The scientific method says that if you can’t prove something with an experiment, it isn’t science. The problem for string theory is that it describes a part of space so small and so fleeting that no machine we can currently build could ever study it. Yet many physicists have stuck with it because, even though it remains entirely mathematical, they’ve glimpsed deep connections between its equations and structures and other branches of mathematics and physics. According to the physicists these connections are signs that string theory contains ‘truths’ worth exploring more and due to which it can’t simply be dismissed out of hand.

    On the other hand we also have scientists like Peter Woit who have lamented, repeatedly, that string theory is a dead-end, that despite all of its mathematical elegance and structure the fact that it hasn’t made a testable prediction, and doesn’t seem like it will for the foreseeable future, it’s been a drain on physicists’ time and intelligence. Over the years however, neither side has been able to persuade or dissuade the other, and today many criticisms have hardened into denial and vitriol.

    Stockholm University philosopher Richard Dawid published a provocative book in 2013 that, despite its seemingly reconciliatory premise, entrenched these divisions. In the text, titled String Theory and the Scientific Method, based on a small conference he’d conducted a short while earlier, Dawid argued that the history of science is witness to a revolution in how scientific truth can be redefined. (American philosopher and biologist Massimo Pigliucci’s essay in Aeon on the conference and how philosophy can help with science’s demarcation problem is also worth a read.) He proposed that in the absence of empirical data, experts must rely on non-empirical evidence, like the sheer mathematical elegance of a theory or the fact that no one can find a better alternative. That is, he seemed to say, a theory could be true because it’s too ‘good’ to be wrong.

    I’m partial to criticisms of the book, especially those advanced by George Ellis, Joe Silk, Sabine Hossenfelder, and Carlo Rovelli, rather than the book itself.

    Ellis and Silk, both cosmologists, argued that Dawid’s push for “non-empirical theory assessment” (which he prefers to “post-empirical science”) is dangerous for suggesting that a theory can be validated by its ‘elegance’ or its power to explain something post facto. The danger here is that if you move these goalposts you also let in pseudoscience. Hossenfelder, a physicist, took aim at Dawid’s argument that string theory must be true because scientists haven’t found another option that’s equally good. According to her, claiming there are no alternatives is a sociological observation rather than scientific proof, i.e. that scientists can’t imagine an alternative today doesn’t mean one doesn’t exist. It may simply be a lack of imagination, of funding for rival approaches or even of groupthink within the academic community.

    Third, Rovelli, also a physicist and a cofounder of loop quantum gravity, argued that the history of science is littered with beautiful, mathematically coherent theories that turned out to be wrong. He also posited that Dawid’s “unexpected explanatory coherence”, i.e. when a theory solves problems it wasn’t built to solve, is often a result of confirmation bias and that once a community is deeply invested in a mathematical framework, it will inevitably find internal connections that look ‘miraculous’ but have no bearing on physical reality.

    Hossenfelder’s and Rovelli’s criticisms also help to see the problems with using the new Nature paper to claim it verifies or legitimises the pursuit of string theory in any meaningful way. Its authors show that the mathematics of string theory handles problems in which you need to minimise the surface area very well, but this shouldn’t be surprising, as Rovelli has argued. Complex maths is often useful in disparate fields but just because calculus describes both the orbit of planets and the marginal cost of gizmos doesn’t mean gravity holds the economy together.

    Similarly, that string theory describes the branching of neurons doesn’t mean the universe is fundamentally made of vibrating strings. The only way to know the latter is if the theory unifies the principles of quantum mechanics with gravity and makes a testable prediction.

    The paper’s authors themselves, while taking care to temper their claims regarding the physical reality of string theory, have also expressed optimism about its mathematical necessity. They’ve called their finding a “formal mapping between surface minimisation and high-dimensional Feynman diagrams” and say they’re taking “advantage of a well-developed string-theoretical toolset”. They also clarify that they’re removing the fundamental physical properties usually associated with string theory as a ‘theory of everything’ and instead treating the matter at hand as a very difficult geometry problem. Then, however, they strongly imply that the mathematics of string theory is essential to solving this problem.

    Now, is it possible to reconcile the (demonstrated) usefulness of the string theory toolkit with Rovelli’s and Hossenfelder’s criticisms? Specifically, setting aside for a moment the fact that the new study treats the maths of string theory as a toolkit: while solving the problem doesn’t ‘prove’ string theory in any meaningful way, how does one reconcile the notion that string theorists indeed developed this mathematical toolkit with Rovelli’s criticism? Is it possible to argue that only string theory could have discovered this toolkit despite Hossenfelder’s criticisms or is it possible to conclude in a reasonable way that we simply use the complex mathematics and discard the rest?

    I think this entails distinguishing between the mathematical machinery and the physical claims. Rovelli’s position isn’t that string theory mathematics are ‘wrong’ or ‘useless’ but rather that internal consistency and mathematical elegance alone don’t constitute empirical proof of quantum gravity. So the fact that string theorists developed a toolkit that can solve problems in biology doesn’t contradict Rovelli, in fact it arguably supports his view that string theory has become a rich mathematical framework. The act of reconciliation lies here in accepting that string theorists spent decades exploring the geometry of interacting surfaces (which they call “worldsheets”).

    Second, vis-à-vis Hossenfelder’s pushback to Dawid’s argument that there are no equally good alternatives to string theory, it also seems physically as well as historically risky to argue that only string theory could have discovered these tools. A mathematician focusing purely on topology or differential geometry could likely have arrived at similar tools without positing 10 dimensions or supersymmetry. In this sense string theory has simply been a historical catalyst, an ‘engine’ that seems to have accelerated humans’ approach to the toolkit that they subsequently used to solve a particular problem in brain biology.

    I’m generally wary of non-empirical assertions, so perhaps a scientifically robust position for me to take is the instrumentalist rather than the realist view: i.e. to conclude we can use the mathematics and discard the physical dogma. This way I retain the formalism, which is the calculus of optimising 3D surfaces, because it works for the data, while rejecting the ontology, i.e. the idea that the universe is fundamentally composed of strings.