(n-1)-thoughts, n=5: Freedom of speech, university statement on free speech, the late Steven Weinberg, and delayed autism research

Freedom of speech

Outside of science, one of my favourite things to study as a hobby is history. I also deeply enjoy and appreciate philosophy. One thing I’ve learned in my time studying history and philosophy is that, when judged alongside the human character (insofar that we may establish such a generalisation), democracy is a system that perhaps shouldn’t work but somehow functions in miraculous ways. The miraculous part of democracy is that, as a system, it is generally stable despite or, perhaps, because of multiple competing forces. How it stablises despite so many pressure points, is a very interesting question of political theory and systems theory. Admittedly, it is naive to think in the following way, but there are times when I am pulled to consider a newtonian, mechanical view of social systems and their configuration. In the context of social discourse, think of how a view or movement based on certain ideas and arguements often seems to evoke an equal, opposite view. Look at the social world as a distant observer might, and notice the pattern that oftentimes there is a movement and then a reaction. In conditions of increasing polarisation, concepts and ideas – viewpoints – can become extremised and so too do their opposite. If a person is not left, then they must be right. There are a number of books on political polarisation, including some that take a science view of bias, and they all hint toward combinations of structural, cognitive, and psychological factors.

I often look at the social world as the absence of reason. This might be a bit too classical and critical enlightenment, but in many ways I think we’ve lost touch with the concept of subtlety in the rational process: that there is nuance and subtlty to concepts and to formulating rigorously researched ideas about complicated topics. For example, am I a ‘climate denier’? No. But am I skeptical of a lot of the hysteria around climate change? Yes. (I think, for example, of anti-modern movements or those that organise themselves under the notion of Deep Ecology). Does this mean I completely reject climate science, or that I completely reject the notion of climate change, although in places I may be sceptical? No. It seems that in the world of concepts and of human ideas, more often than not views become extremised and concepts are taken to their ideological boundaries where irrationality transforms into unreason. We see it all the time, not just in politics where formally it is accepted that designations of left and right, along with their associated bias, may clash in debate without much objectivity. To me, it is an absurdity. But one thing that history has taught me, and, certainly, the history of science, is that it is important to constantly resist getting tied down to bias, prejudice, and the type of knowledge formation that comes with ideology in all its guises. Much of what the history of science teaches is about our utter stupidity as a species in thinking that, in whatever historical period, we may belive to possess all of the answers or have a complete grasp on the truth. It is thus only a matter of pure comedy that we may engage in politics in such a way as thinking ours is the righteous view.

If I may speak honestly, I find a lot about modern politics – by which I mean the nature of its structure and engagement – irrational. I’ve never understood why in modern British democracy we assign the role of secretary of education, for example, to a professional politician with no experience in the field of education. Why is evidence-based, expert driven governance made to seem like a concept associated with some alien-rational, futuristic, scientific utopia? I suppose when contrasted to the system of competing echo chambers known as party politics, the idea of evidenced-based policy appears futuristic. Given that we do not live in anything like a scientific society, I’m not sure an actual scientific society would be structured in such a way that non-experts are allocated important roles in the practice of democratic governance. I mean, what does it say about the prospect of a society predicated on, or at least hoped to be informed by evidence based policy, when professional politicians with pre-established agendas preside both over the evidence and the policy? To me, the hard truth seems to be that all of politics is based on subjectivism and, in some sense, with the loss of the rational process that strives to seek the objective. Discourse instead seems to manifest in ways that formalise false equivalence or the categorical fallacy of inconsistency. For any issue, at least two sides are portrayed as equally valid when there may in fact be asymmetry. In some or many cases, perhaps no two political reductions are even capable of capturing the total complexity of the matter at hand. But with the loss of the objective as a concept that ought to be strived toward, debate is reduced to subjective bias and political prejudice that is symbologic of the postmodern vacuum in which we find ourselves.

Maybe I am just pessimistic. Then again, think of Brexit. Rub away all of the dross and antics, all of the extremisms and prejudiced ideologies that sought to exploit the situation, one will see that there were logical arguments from both sides of the debate. There were arguments from both the left and right-wing to leave the EU, with the former emphasising democratic control and participation in a similar way as the sovereignty argument on the right. Likewise, arguments to Remain were not just a left versus right issue, although, as it is so often today, simplistic narratives tend to rule public discourse and political slogan design. What was most striking about the entire process is that, rarely if ever, one observed a politician or public intellectual change their mind. It’s as though people didn’t engage in debate, but instead focused on shutting the other down. Maybe it is a matter of polarisation in which two sides often emerge as set against each other, and then from there discourse seems to shut down. Or maybe there is something to that old Newtonian idea. What is clear is that there was no collective encircling of an issue (or it was an exception to the rule), no process of gathering information from all sides – taking in new evidence and data – and constantly working through rational arguments (often through a process of changing one’s mind or outlook). This is how a civilised democratic society, armed with science and modern technologies, was meant to function. Or, at least, that’s how I like to imagine it.

This brings me to another thing that history has taught me: a democratic society based on core liberal and enlightenment values is one that requires citizens in deeply fundamental ways to be able to disagree. But the concept of the enlightenment requires something still much deeper – and this relates directly to democracy – that individuals enter into a debate, or disagree, within the frame of reason. Think of it this way: If I disagree with someone about a mathematical matter, it doesn’t make sense that I debate with them outside of mathematics. I pick up a dry wipe marker and explain mathematically why I don’t agree. Debates about freedom of speech in modern western society seem to lose sight of key content within the concept: what gives it so much fundamental import as a social concept is that it is intrinscially rational. If, at my university, an individual was invited to give a talk on why they are sceptical about the interpretation of climate science data, I may or may not agree; but given that their argument is rigorously constructed, well-researched, and rationally presented I support the freedom to present the view. If I don’t agree, and if I think that their argument is logically inconsistent or wrong, then it is up to me to disprove their case. This, to me, is what freedom of speech means. Yes, on some simplistic and practical level one may deduce their right to say anything, as so often this is what the popular debate on free speech seems to imply: for example, I may in this moment conjour some fanciful theory about why alien hamsters control all of human society, and I may provide a provocative argument for why this is true. But freedom of speech isn’t freedom to be unreasonable or freedom to not engage rationally in the arena of rational ideas, should one wish to engage at all; and although one might conflate their right to free speech with an imagined right to be taken seriously, such a view is in fact tantamount to utter stupidity.

Freedom of speech requires responsibility – it requires that one be normatively critical of one’s own view and be capable of exploring openly the thoughtful argument of the other – and it seems we have somehow lost sight of this fact just as we have lost sight of the meaning of constructive debate.

Stephen Fry, one of my favourites, had a fantastic line recently which is paraphrased below: ‘on one side is the new right, promoting a bizarre mixture of Christianity and libertarianism; on the other, the “illiberal liberals”, obsessed with identity politics and complaining about things like cultural appropriation. These tiny factions war above, while the rest of us watch, aghast, from the chasm below. […] It’s a strange paradox, that the liberals are illiberal in their demand for liberality. They are exclusive in their demand for inclusivity. They are homogenous in their demand for heterogeneity. They are somehow un-diverse in their call for diversity — you can be diverse, but not diverse in your opinions and in your language and in your behaviour. And that’s a terrible pity.’

University of Nottingham statement on free speech

As mentioned in a past post, since the start of term I have struggled to keep up with my blog. One thing I meant to write about was the recent statement by my university on freedom of speech. It may have been updated since I read it in the summer, as the university was seeking collaboration and feedback at the time. I should go back and read it again, but my assessment at the time was that it seemed well-balanced. It struck me that, as written, it conveyed the intention to genuinely realise the meaning of inclusivity, diversity, openess, and respect. This is what should come from an institution that seeks to foster learning, intellectual exploration, rational debate, and the wonderful process of formal inquiry in the collective pursuit of truth.

A thought of existential variety

The late Steven Weinberg had a wonderful comment about life and the human condition in his book, The First Three Minutes: ‘The more the universe seems comprehensible,’ he wrote, ‘the more it also seems pointless.’ I’m sympathetic with his view about the god-of-the-gaps. Truth be told, I consider myself agnostic; I don’t know for certain that there isn’t a God and if there is I would be inclined revolt in typical Camus fashion. That needless suffering should exist under the watch of some supreme being is detestable, in my view. So, although not an atheist in the extreme, I’ve always found Weinberg’s reflections reasonable when talking about the absence of God and how science may contribute positively to human meaning. Speaking in an interview, he once reflected: ‘To embrace science is to face the hardships of life—and death—without such comfort’. Pertinently, he continued: ‘We’re going to die, and our loved ones are going to die, and it would be very nice to believe that that was not the end and that we would live beyond the grave and meet those we love again. Living without God is not that easy. And I feel the appeal of religion in that sense.’

I often think that I could be diagnosed with cancer next week and be dead within a month. There is an innate indifference about the human condition, and with that I think a deep human fear of death, as Ernest Becker noted, governs a lot of human social systems. We can of course speak on the grandest scales and describe the precise nature of our cosmic insignificance – that we are not even a speck of dust on the scale of the universe. But even on a microbial and biochemical level, there is much that dictates the course of our lives over which we have no control. We can of course do our best to limit the probability of contracting some horrible disease or illness, and therefore play the percentages. And yet, really good people by the best moral standards, who eat right and live healthy, can contract the most awful of illness. These thoughts may appear morbid, but they describe reality. We’ve each known this indifference and fundamental arbitrariness from birth – catapulted into existence with no choice as to our geography or time in human history, we set forth with the conditions of our lives quite plainly and starkly defined. We can of course choose to fill the gaps – what some philosophers call the god of the gaps – but I’ve never found that a helpful or reasonable idea.

What I have found really important in philosophy, is that one can think in this way and acknowledge the gap without succumbing to nihilism. In an odd way, there is also hope to be found. Human beings are meaning makers, if nothing else. One can discover a cool new mathematical object and dedicate the rest of his/her life to studying it. Why? Because it is interesting, exciting, and contributes to knowledge. Of course an asteroid could crash into the earth and wipe out that knowledge completely, but that doesn’t mean that such knowledge shouldn’t have existed in the first place. There is a fine line between recognising and embracing the arbitrary and meaningless nature of life on the grandest scales, and also creating meaning and enjoyment and pursuing interests – to take care of one another and provide better conditions for those of the future – in revolt of that very reality. I often come back to this thought, because within it is a deeply lovely lesson. As Weinberg put it, the deeper idea is ‘to make peace with a universe that doesn’t care what we do, and take pride in the fact that we care anyway.’

Autism genetic project paused

One last thought. Actually, on this issue there is much to say, but I will limit this entry to a simple expression of disappointment.

It was recently announced that an autism genetics study was paused due to backlash. From what I understand, criticism includes a failure to consult the autism community about the goals of the research and there are concerns that the research could be misused, which I assume to be a concern about eugenics. This is obviously a very complicated issue, and always there are ethical points that need to be considered; but I think the latter is a bit misunderstood and this is probably a failure of scientific communication. The genetics of autism is complex. For example, cystic fibrosis involves a single gene, so it easier to screen for it. And, when screen is done, it is has nothing to do with eugenics. In the case of autism, it is likely that there are multiple genes, if not thousands, such that prenatal screening seems incredably unlikely – not that this was an intended outcome of the research anyway. Furthermore, while I understand some have concerns about eradicating autism as though it were an illness, when, in fact, it also contributes many positive traits, from what I have read the proposed research has no such intentions.

As a person diagnosed with ASD, I am very much supportive of the research. I think that, as with anything, it is best to study and understand a phenomenon as deeply as possible. Indeed, we should strive to have more of a scientific understanding of autism. At the same time, I understand that some may have ethical concerns. In science, we always have to proceed cautiously and thoughtfully. It is important to hold all scientific research to the highest ethical standards, which should be a normative process, and to also think about all possible outcomes and potential future (mis)use; but, in this case, it seems mistrust was largely down to a failure in scientific communication.

*Edited for grammar and clarity.

(n-1)-thoughts, n=4: A return to the North Sea, new string papers, and Strings 2021

Our return to the North Sea

Beth and I frequently talk about how we miss the North Sea. We lived on the coast and I think it is our nature that we both prefer its unique countryside. But now that we’re living in East Midlands, landlocked and busy at university, we haven’t been back for a couple of years. So for our summer holiday we’ve travelled to North Norfolk, a place that for many reasons became an adopted home for both of us, to smell the sea again and enjoy the beautiful sights.

It may perhaps sound a bit mawkish, but in many ways North Norfolk provided an opening for discovery, not just in a literal sense but also in a philosophical sense as a space to reflect on the world of ideas. There is a line by John Berger that speaks of a place from which the world can be discovered – that is, a foundation from which one can venture forward but always return if needed. I think this is what the North Norfolk countryside came to represent for us: at the time a much needed place of peace and calm, but also a place of thought and reflection, where time runs slow and where we could gather ourselves, find our footing in life, and sometimes spend entire afternoons contemplating life. If for Plato and Socrates our true home is the eternal world of ideas, the North Sea, with the calm and quiet nature of the hills, valleys, woodlands, and beaches unfolding alongside it, is the continuum from which philosophy and mathematical realism can be pursued. Its the total landscape, the geography, and the open horizon that is grounding.

The little cottage where we used to live, just off the main road which the Romans would have similarly ventured when travelling to the coastal towns, was our first proper home. It was maybe the first place where we both found lasting comfort, coming from difficult situations and experiences. It was modest accommodation – a flintstone cottage, with an old fireplace, pinewood shelves, and steep narrow stairs sharply turning from the kitchen at the back up to the bedroom facing the main road. It was a tiny dwelling, perhaps a bit too cramped at times. But with our library of books, regular philosophical discussion, and no shortage of slow days of reflection, maths, and hobby, it was the perfect place at the right time. On the most difficult days, we could just listen to the birds in the back garden, find peace in our thoughts, or write to our contentment.

The main town, Holt, the origin derived from the Anglo-Saxon word for ‘wood’, is a place defined very much by its surrounding line of trees and small forest areas. It is situated on a hill, and, although a couple miles from the coast, a fresh sweeping wind from the North Sea can often be felt. Out here, the air is fresh. Space is wide and open.

One of my favourite places was, and remains to be, the woodland and heath not far from where we lived. It’s not marked on the map, so it is truly a hidden place to be discovered. Beth and I would take regular walks and spend many afternoons sitting among the heather – purple flowers of Calluna vulgaris – and yellow flowers of Ulex gallii. One year, I remember wild ponies were introduced to help maintain the land, and often we would see them hanging out by the brook or underneath a tree on a hot summer day. Upon our return this week, it was a joy to visit this place again.

A trail through the heath.

I’m not very good at creative writing, although I’ve tried to learn and experiment with it. One thing that we used to do is, during our walks in the heath or through the many wonderful nature reserves, we would treat them like field expeditions. And, like a keen biologist or natural scientist, we would take our time for the finer inspection of all species of plant and animal. I would practice writing in my journal in an observational and documentative way. Being back here, I was inspired to dig up one such piece of writing. At the time I was experimenting with phenomenological-style notetaking, trying to intricately describe my experience of the countryside. I think I also took inspiration from the structure of a number of writings by various authors that I was reading back then.

To the left of me dense thicket carries into the distance, a rolling plain of healthy evergreen and intricate pathways of rotting needle, brown and dank, align in close order row upon row upon row. To the right, at the nearest edge of the forest, golden rays of sunlight spray across an open valley. Its radiating warmth and all-consuming light illuminate the young grasses breaking into the soil, filling the land with a rich, unfolding spectacle of colour. Looking beyond these trees, it is readily noticeable that there is an abundance of wildflower and bracken, a diverse quality of dazzling tones and subjects, which harmonize in a single unified phenomenal pallet like one massive, entanglement of earth. Ramshackle and unexpected, diverse and revealing, from endless rills and rivulets, from ditches to dells, from hedgerows to underbrush, with each new experience pressing deeper into this landscape and, ever from the background of this vast horizon of rolling hills before me, entire swells of breathing life continuing to reveal themselves. From the rabbits and wood pigeons who rather be hidden; the swaying fields are a thoroughfare for creatures of various kinds, from field mice to deer and the odd passing fox; song thrush, jays, long-tailed tits, and spotted woodpeckers - what grows and lives in this place is truly possessed of a beauty all its own.

As for the very belly of the forest, off the heath, there is a rich vision of evergreen, each swirling pine looks entirely similar to the other. But upon closer inspection we see that each particular pine tree is distinguishable and, indeed, of unique character. The pine itself is of course home to many things. Birds, insects, a peering squirrel; all find comfort in these dense woodlands. But row upon row, with its dwarf shoots that spiral from off the axils of scaly bracts, such a dense growth of pine, whose intricate branches are like a massive conic arrangement of narrow needles bundled together by both bark and sap, is a marvel in itself.  Occasionally stepping on fallen seed or the coned fruit, my senses are overwhelmed by the spatially sweet and particular fragrance that lingers throughout the air.

The countryside here is in many ways a place of Tolkein description. It has been nice sitting again by the cliffs and walking through the overgrown footpaths. As I tried to capture, it is Shire-like in its beauty. With its salt marshes; winding roads lined by hedges, wild flowers, sedges, and rushes; and rolling hills demarcated by broad leaved woodland, towering at times with veteran oaks, birch, and, my favourite, Scotch pines – there is so much to be admired in this part of the country. Down by the sea, fishermen sit with lines cast, birds circling overhead. Again, it is perhaps more than a bit mawkish, but it is for me one of the places in our beautiful country that speaks a bit to old Romanticism, with every brook and winding turn outlined by hedgerows evoking a scene from a classic Keats poem.

It is my nature to be reclusive. No doubt, there are many other reasons why I find home by the sea and in the countryside. But as I write from the cottage where we’re staying, I remember why North Norfolk represents more than a place of stillness and beauty. With a cup of tea and some maths by the window, in the quiet thoughtfulness, the appearance and seeming order of the world of phenomena, mental idealisations or not, rushes forth some profound reality.

New string papers

As I was preparing to leave for holiday, three papers appeared of significant interest. I haven’t had a chance to work through them all yet, between being strict with my holiday time and with String 2021 ongoing, but I felt motivated over a cup of tea to take note:

Heterotic duels of M-theory

A nice paper by Bobby Samir Acharya,  Alex Kinsella, and David R. Morrison on the non-perturbative heterotic duels of M-theory was released. This is of particular interest to me as it relates to the wider study of the non-perturbative aspects of M/heterotic duality.

This duality was discovered in the mid 90’s in which one can take M-theory compactified on a K3  and find it relates to the E8 \times E8  heterotic theory compactified on a three-torus. When you look at the 4D picture, we may instead compactify M-theory on a G2  manifold (equipped with a K3 fibration), which is a seven-dimensional Riemannian manifold that is special because it comes with the holonomy group in the exceptional simple Lie group G_2  . For the E8 \times E8  , it gets compactified on a Calabi-Yau threefold equipped with a three-torus. I haven’t had a chance to read through and consider the paper in any great detail, but it is noticeable that it starts with a similar set-up, taking low-energy M-theory with G2  orbifolds as the choice of compactification, with choice of equipped K3-fiberation to enable comparison with the dual heterotic string spectrum. A key observation, I take it, is that for the heterotic background there is a subtlty with the gauge bundle on T^3  such that, when it comes to the non-perturbative physics, there are point-like instantons on orbifold points of the geometry. This is where things get both interesting and complicated, and I’m not sure in what way these instanton effects in the spectrum relate to M-branes. I am keen to read the second half of the study.

Higgs mass in string theory

Another paper that appeared looks at calculating the Higgs mass. It’s by Steven Abel and Keith R. Dienes. This paper is quite the joy, and I’m sure anyone with interest in string theory will enjoy it over a cup of tea. Abel and Dienes harnesses the powers of the world-sheet theory to perform some proper stringy calculations, developing a framework that presents a relationship between the Higgs mass and the cosmological constant. What is neat about the computation is that this connection is generic for all closed string theories and provides a bit of a platform for future studies on gauge hierarchy problems.

Double sigma models and geometric quantisation

With a rush of papers leading up to my holiday, this one immediately caught my attention and got me excited. Luigi Alfonsi and David Berman study geometric quantisation in double field theory and double sigma models. From what I have seen, it is grand.

I was actively thinking about quantisation of double sigma models, as this is one area in which I have been working. In fact, I recall a few discussions a year or more ago about a project looking into the quantisation of the doubled string. In parts, from working in the area, what we see in this paper is kind of what one would expect in that, to start, the zero-mode sector for the closed string is intrinsically non-commutative. This alone is an interesting fact with some deep implications. Commonly, in the set-up where the target-space is treated as a phase-space, one will also equip a symplectic form \omega  , and one will can construct a theory with an action following Tseytin (we talked about this in a past post). What is found with the inclusion of \omega  is an interesting connection with Born geometry (maybe I’ll write about this in a future post) and, furthermore, one will often find discussion on symplectic structures as it relates to Poisson geometry which has some deep relation with T-duality.

In short, in the quantisation procedure there is a choice of polarisation, and the authors want to make a choice of polarisation in conjunction with the strategy for geometric quantisation. What happens, in any case, is that T-duality will give polarisations. And then what one wants to study is the noncommutative algebra associated to the doubled phase space. What the paper shows is that there are, in essence, two types of quantisations going on, because there is one coming from the usual phase space and then another from the duality frame (i.e., what in the formalism is understood in terms of the Lagrangian submanifold).

A deeper idea here has to do with the doubled phase space and para-Hermitean geometry, which I think I’ve mentioned a wee bit in the past. On that note, it is also interesting to think about the findings in this paper as it relates to the idea of metastring theory and quantisation.

As an aside, I’ve been working on a draft essay about a series of papers by Luigi. I wanted to write a bit about double sigma models and double field theory before finishing this essay, with a mind toward giving the reader some reference. They are fantastic papers on the global double space of double field theory, among other things. I also have Luigi’s PhD thesis on hand, which I think is great. There is a lot to discussed here in the context of the doubled geometry of double sigma models and higher structures.

Strings 2021

The annual string conference, Strings 2021, is ongoing (21 June – 2 July). It’s always an event that I look forward to, as it brings together the entire string theory community. Among a large list of great and usual names, my eye immediate caught an anomalous speaker amongst the expected and anticipated: namely, Roger Penrose. I will be most eager to hear what he has to say during his presentation on Friday 2, July. The topic is on gravitational singularities. There are of course a number of talks that I am looking forward to – too many to list! For now, here is the schedule with list of speakers, including links to notes and recordings. If I find the time and motivation, I’ll write a summary of my favourite talks next week.

Institute of Physics scholarship award and full interview

I’m proud and honoured to share that I’ve been awarded a PhD research scholarship by the Institute of Physics. An announcement by my university can also be found here.

As I’ve written about elsewhere on this blog, my PhD research focuses on M-theory and the question of string theory’s non-perturbative completion. To be a recipient of the Bell Burnell Graduate Scholarship Fund on the basis of my planned research in mathematical physics, which included having to deliver a presentation on my topic and an interview with the physics panel, is quite satisfying. Admittedly, I was a bit nervous knowing that I can be maths heavy and that this might not be recieved too well in-front of a well-distinguished panel comprised mostly of experimental physicists! But I am delighted that the wonderful physics content of my research was acknowledged.

In conjunction with the announcement of my scholarship award, I was invited to participate in a more personal interview designed for the non-physics reader. Within I answer a variety of questions, including about my current research. I also share a bit more about myself, my upbringing, and other personal stories and reflections.

Below is the complete version of the interview I gave for the Institute of Physics. There is also a shortened, edited version that can be found here.

***

1. Tell us about your work – and what drives you (We want to know about your area of physics and why you’re passionate about it. What does it mean to you? Why is it important? Imagine the reader is not a physicist).

Firstly, thank you for inviting me to answer questions.

The situation today in fundamental and high-energy physics is incredibly interesting. A lot has happened since the 1950s or so, with many great successes. Just think: essentially all observable phenomena are well described, on the one hand, by quantum field theory and the Standard Model of particle physics, and also by Einstein’s theory of general relativity on the other. We have established tremendously accurate descriptions of the very small – quantum theory – and the tremendously massive – cosmology and astrophysics. Modern physics has made some remarkable achievements, both in advancing human knowledge, and in supporting how we may apply the laws of nature to develop important technologies. Having said that, it is almost certain that these fundamental theoretical frameworks are incomplete. For example, general relativity and quantum field theory break down when we start to study situations at the centre of a black hole or close to the big bang. Many readers will likely also have heard of concepts like dark energy and other things, which also currently remain unknown.

A big question in fundamental physics, perhaps the deepest and most important, has to do with what we call quantum gravity. This represents the unification of general relativity with quantum field theory. I work in mathematical physics, and, in particular, my research is focused in string / M-theory. Today, this is the most promising and indeed leading theory of quantum gravity.

One of the great successes of string theory is how, in a single consistent mathematical framework, we have a theory that combines gravity with the quantum laws of nature. This means that at very large scales, we find gravity as Einstein described it in his general theory of relativity. But on very small scales, in which space-time is discretised, we have a theory that captures the idea of quantised units of gravitational energy. We think of these quantised units as particles that we call gravitons. In practical language, string theory describes how the curvature of space-time emerges from the existence of gravitons. Thus, we have a quantum theory of gravity.

Despite the many successes of string theory, we still face some open problems and challenges in formulating the complete theory. It is not possible, at this point, to speak of such challenges without a degree of technicality as this is a highly technical subject. What I will say is that, in keeping to practical language, one of the biggest and most important questions we face concerns what may be described as the non-perturbative completion of string theory. This is what my PhD research is focused on understanding.

To explain this, allow me to share a bit of history. As late as 1995, we had five perturbative string theories – type I, type IIA, type IIB, and the two flavours of heterotic string theory (SO(32) and E8 × E8) – and these were seen to be distinct. Much of modern physics is built using tools and approaches that deal with what we may describe here as local, approximate, perturbative descriptions of reality. And these perturbative theories of fundamental physics – the five string theories – are remarkably successful and beautiful. Just from the humble idea of the extended of object of the string, which is a generalisation of point particle theory (which one may have some familiarity with going back to undergraduate or A-level physics), we can generate some brilliant results like Einstein’s gravity. But just think of the situation in the mid-1990s: in quantum gravity, we had five theories without a way of knowing how to select the correct one. This is quite a messy situation! But one of the amazing qualities of string theory is that it comes with a wealth of symmetries.  And it was following a very important proposal by Edward Witten that the five perturbative string theories were found to be deeply related by a number of non-trivial dualities, or, for the sake of practicality, what we may describe here as symmetry relations. So rather than being distinct, the five string theories were found to represent different limits of an overarching theory.

This is quite an evocative idea, namely that there is some deeper underlying structure to quantum gravity, from which things like space-time may even emerge! This overarching theory is known as M-theory, and the non-perturbative completion of string theory to M-theory is specifically what my PhD research seeks to investigate.  M-theory is truly remarkable for several reasons. Although the five perturbative string theories exist in ten space-time dimensions, M-theory exists in 11 space-time dimensions. So it is a higher dimensional theory. Given that one can think of it as the parent theory to string theory – i.e., as a single mathematical structure that unifies the zoo of perturbative string theories, with its low-energy effective action being what we call supergravity – it represents a unique theory of quantum gravity. More than that, M-theory is, in every sense, the leading candidate for a Theory of Everything (ToE). It is also the mathematical theory that makes sense of the dynamical physical objects we call branes (objects that, again, emerge in higher dimensions as a generalisation of point particle theory), which propagate through space-time according to the rules of quantum mechanics.

However, although there presently exist many hints and plausibility arguments in support of the proposed existence of M-theory, a systematic formulation of the non-perturbative theory remains an open problem. There are many reasons why a fundamental and rigorous formulation of M-theory is important. Not only do we expect to find new physics and new mathematics – in fact, it has been described as a great unexplored ocean in this regard – it will also help provide a final say on things like fundamental string cosmology.

As you may be able tell, it is an area of research I find to be incredibly exciting, not least because it is potentially so fundamental. In recent years a number of especially exciting developments have begun to crystalise in how we may attack the question of a rigorous formulation of M-theory, including the study of what we call higher structures. The presence of higher structures – or what we may summarise as higher homotopy theory – in fundamental physics is in and of itself a super interesting fact. And, as I mentioned at the outset, a lot of what we talk about and study also has to do with combining spacetime geometry and quantum field theory defined as generalised geometry. As I have alluded, some of the implications are grand, including the extension of spacetime itself, with a further consequence being the possibility that geometry and gravity – indeed, space and time – are emergent concepts.

As I work in mathematical physics and find great interest in both foundational maths and fundamental physics, I enjoy this area of research because there is a wonderful interplay between the two. My PhD research is positioned at this interface.

2. What drew you to this area of physics? (Tell us a little about your physics journey and how you ended up focusing on this area. When did you first become excited about physics? What was it that excited you? What led you to where you are now?).

By most accounts within the formal parameters and constraints of mainstream education, my physics journey up to this point has been described as highly unconventional. This is certainly largely owed to the fact that I have Asperger’s, and as a person with autistic spectrum disorder (ASD) I experience a lot of difficulties and unique challenges. Formal education environments are certainly something that I did not cope with well in the past, and something I continue to struggle participating in today.

Due to the challenges that come with my Asperger’s and also the difficult conditions I experienced growing up, I was often in and out school for many years. To be completely honest, there were a lot of times when I tried to go to school or participate at a university, and it was just never sustainable for me. The classrooms or lecture halls were too overwhelming; the curriculum was too slow or uninteresting; time pressures were too difficult to manage; the lectures or lessons were not fundamental enough or too restrictive for my interest. It was often, I suppose, the case that I would rather be given the textbook and left on my own to work through and derive everything. I am much more comfortable with that independence. I have also grown used to being in my own space, with all of my books, with my maths and physics, working and studying on the things I find meaningful. So, I think there are a lot of reasons, from my perspective, as to why formal education has always been in some ways inharmonious or discordant.

In truth, without the right support, I probably wouldn’t have successfully joined the University of Nottingham and still be working at the university today. It was a massive personal step for me, one that we worked up to over a couple of years, and once I arrived at university it was incredibly challenging on so many levels. It required a lot of support, patience, and understanding. But I was also incredibly fortunate to have landed at such a fantastic school, with great support staff for people like me with ASD. The same can’t be said in all cases, and there are a lot of brilliant people out there with ASD that don’t receive the right support, or who don’t have the opportunity or foundation to pursue a formal university education for social, economic, or cultural reasons. I think I am decent at maths and physics, capable enough to teach myself string theory for example, and I was super close to not being a university student because, in a multitude of ways, I generally don’t ‘fit’ in the way that is expected.

Needless to say, and to return to the question, so much of my life so far has been outside of formal education. As a result, I have self-studied almost everything I know. When I was younger, I taught myself calculus and eventually expanded my self-learning to higher mathematics. The same with much of physics, from classical mechanics through to quantum field theory – I had already taught myself a lot of this prior to entering university as a first-year undergraduate. This is why my physics background may be described as unconventional. But to be honest, from my perspective, teaching myself maths and physics without relying on a teacher or sitting a class, seems like quite a normal and reasonable thing to do. I work at my own pace and ask my own questions. I can explore and enjoy maths and physics in my own way, giving myself as much time as I deem necessary to explore a topic fundamentally. You know, I think in a lot of ways maths and physics have become some of the only things in the world that truly make sense to me.

When I joined the University of Nottingham, I had been developing a lot of interest in general relativity, quantum field theory, and quantum gravity. I read about a number of different theories of quantum gravity, many of which I found to suffer mathematical inconsistency among other things. This is how I found my way to string theory, also with the encouragement and support of my professor Tony Padilla, who is now also my supervisor.

During the first weeks of my undergraduate, I took my string studies very seriously, and around this time my interest in non-perturbative theory began to crystalise. In that first year, the School of Physics obtained permission from the university to accelerate me to a Master of Research degree. My thesis involved the study of double sigma models in string theory. I am now looking forward to studying for my PhD within the Particle Theory Group at the University of Nottingham.

3. What does winning the scholarship mean to you – and what difference will it make? (How do you feel about winning? How do you feel about taking on a PhD? Would you be able to take on a PhD without it? In what ways will it help/make a difference?)

I’m both proud and honoured to have been awarded the scholarship for the duration of my PhD. I’m also incredibly proud to have affiliation with the Institute of Physics and to take on an ambassadorial role, something I take very seriously.

Coming from where I do, outside of formal education, I used to sometimes sneak into university lecture halls and, well, there were times when I would think to myself that perhaps I could do a PhD in physics or be a good researcher in a formal academic environment. I don’t always think about it so explicitly these days, but it truly means everything to me to be doing my PhD in mathematical physics. One could speak to the depth of the notion of existential meaning here, in terms of one’s projects and interests in life. But it is more than that for me. I would be working on my maths and physics no matter what, because it is what I know and it is what interests me; but now I have the opportunity to do so within a formal environment without financial concern, social judgement, or other pressures and worries.

To formally pursue a PhD at such a wonderful university and as part of a very cool research group, to get to continue working with Tony Padilla and to talk strings every day, and really to be able to study my maths and physics in an encouraging environment, is kind of life-changing. I am very grateful and I look forward to the future, where, hopefully, after a good PhD I can continue to contribute quality work and carve out a formal research career, maybe even teach strings one day. The scholarship has helped provide a good foundation in pursuing these ends.

4. What challenges have you faced to get to this point? (Any barriers/challenges that you have had to overcome that you feel comfortable talking about. Has anyone discouraged you? Have your personal circumstances made it harder? Have societal barriers/conditions had an impact? How have you overcome these challenges?).

In addition to my lifelong struggle with my Asperger’s, which, clinically, has been diagnosed as severe, I also had a very difficult childhood and experienced a lot of bad stuff growing up. I grew up in an environment that was incredibly dysfunctional, hostile, and in many moments scary. There was a lot of abuse and neglect, periods in and out poverty, with no heat in the winter – just not very nice things for quite a long time. By the time I was 14 or 15, without the right support, I could barely function, let alone cope. And in these circumstances, the pursuit of one’s interests and intellectual passions were rarely permitted. Instead, there were many times in life that were largely about survival and trying to escape. These were times that were generally quite debilitating. For years I also struggled with my mental health. I still do, although there is always an aspect of that owed to my ASD.

I can talk about it all now because I’ve had a lot of time and support in working through the traumatic events and the terrible stuff I witnessed and experienced. Growing up, I moved to different families, which offered great reprieve, and there have been so many extraordinary people that brought me into their homes, sometimes for years, and supported me as I slowly found my feet in life. These are individuals and families who intervened to fill the gap and take on abandoned parental responsibilities. They did so much for me, helping enable a positive foundation to grow and develop in life, to self-actualise, and to be able to pursue my interests. So, despite having to face a lot of challenges in life, some of which are quite extreme, I am also very thankful today. My life could have turned out differently on many occasions. And partly why I share that here is because, well, maybe someone will read this and take something from it. There are a lot of people that have ASD or that grow up in bad conditions and are never given the proper support they need as human beings – a positive and healthy foundation to life from which one can then begin to move. It’s Maslow’s hierarchy of needs, which, while problematic in places, serves as a reminder that the meaning of society is to help foster the conditions in which all citizens can realise their full potential. As a society, I think from a fundamental humanistic perspective we ought to never stop demanding socio-economic, cultural conditions that give as broad a scope of people as broad of a horizon of opportunity as possible.

It is also the case for me that in growing up in incredibly difficult conditions, I have come to recognise that I owe a lot to my Asperger’s and my sense of personality. I think it enabled me in many ways to survive the incomprehensible by maintaining a presence of mind. I eventually learned to cope with and understand life through my studies. Not only did my books come to provide a welcomed and flourishing space, they offered explanation and detailed insight into all that I had observed: psychologically, sociologically, economically, and so on.  One way that it is described is that, for some people, they learn to manage their present experience by thinking of their past experiences as reference points; for me, this is how I use books. So, aside from my beloved physics and maths, I have studied everything with great interest: from the whole of psychology and human behaviour to our best current theories on social structures and relations, history, anthropology, economics, philosophy, and in many ways across the social and natural sciences. I have never been dissuaded by the challenges I have faced. As a young adult, outside of formal education, I spent my days alone at public and university libraries, or sitting at the back of university lecture halls that I had snuck into.

I’ll share a story that is quite personal to me. As a child, when times were especially difficult, I remember sneaking away to the far and unvisited corner of a local park. Lying there, on the opposite side of the hill that faced away from everything and everyone, I would stare at the clouds and contemplate existence. Particles, birds, planets, and stars. Why do clouds exist and why are they shaped the way they are? Why do they move as though they are moving through fluid, floating without support? This was a site of one of my first philosophical and scientific reflections. And, really, despite my many difficulties in formal education environments, some of which are ongoing, science and academics has played an incredibly important role in my life. It has become a natural extension of myself as a person with Asperger’s who is driven to understand in accordance with my life spent with my books. I learn about human relations and behaviour through their empirical study just as I learn about quantum fields through my physics. I think with that inquisitiveness, one of my earliest memories of being excited about physics was when I was no more than 6 or 7 years old. I saw a photograph of a professor standing in front of a chalk board, and written on the board was sigma notation. Looking back, it was likely generality relativity that was being taught, but the mystery of the language, the power of physics that we may describe the nature of reality, it always stuck with me.

As I said before my ASD also brings many of its own unique struggles and daily challenges. I require a lot of support. I can compute scattering amplitudes but struggle to manage a calendar or money. I sit here writing because I am fortunate to have received support with my Asperger’s, to have a stable home environment, and to have a loving and caring partner, Beth. There is a lot of well-defined research which, last I checked, showed that about 80% of people with ASD struggle to hold down a full-time job or be independent, and it was estimated that suicide rates are 10 times more than average. Not all autistic people can work, and, for sure, I know that struggle to maintain my own independence. There were times when I was ashamed or pressured because I couldn’t maintain a job or understand how to pay rent, because I couldn’t maintain independence, understand how to manage my bills, and organise my life. Prior to intervention, I was kind of just left to work it out. Now, of course, that is my experience – everyone will have their own. But the point is there are so many simplistic narratives about autistic people and even just about poverty in general. In education, I was once deemed a troublemaker! Another lost soul and statistic.

I think we need to do more as a society to understand the complexity of individual situations, and we absolutely need to do more to combat ongoing prejudices and to support people with ASD.

5. What would you say to those who have also faced barriers to following their dreams to pursue physics at university and beyond? (Any advice/encouragement would be great).

I don’t want to be naïve and just say “go for it”. The reality is that different people have different challenges with different barriers. If a person loves physics and it is their main passion in life, but at the same time facing homelessness or a precarious existence, it is not just a matter of saying “go for it” and “you can do anything”. Poverty and class can be barriers. Racism, too, can be a significant barrier. Disability, mental health, physical health – people face all sorts of different challenges.

What I am trying to say is that if someone dreams to study physics, that is amazing because physics can offer a person so much in life. They should do so regardless of age, gender, race, disability, class, and so on. Absolutely. But saying that is not enough. People also need support, and there is absolutely nothing wrong with that. It is up to our institutions – university, government, etc – and it is up to us as a physics community to identify where support may be lacking. If you are a person wanting to pursue your passion for physics but struggling with personal circumstances or barriers to doing so, don’t be ashamed to seek support. Universities have advice and support services who can often help you to find ways forward.

6. Why do you think diversity in physics is so important?

Unfortunately, I am not familiar with the data and the mathematics, so I can only present my personal thoughts which I don’t think have much or any value. What I can perhaps share, as a physicist who also has interests in biology, especially mathematical biology, and who enjoys thinking about life, is a broader or perhaps more fundamental perspective about the concept of diversity that I find inspiring.

Let me put it this way: when we speak of diversity, what are we actually (in a fundamental sense) speaking of? I find, for me at least, that discussion about diversity can sometimes result in confusion. The word is used in many contexts with many meanings. In political and sociological language, the structure of the language often implies an antonym of homogeneous groups, or, sometimes, as an antonym of a specific individual as a group: a white male with certain physical attributes, class distinction, and heterosexual orientation. From the dictionary definition of diversity, on the other hand, we find that it means difference or variance. I think science has an important perspective to offer in this precise sense.

From a genetic-centric view, and certainly also in other parts of biology, we have a concept called normal human variety. To that, I am not just speaking here of race and racial diversity. I am talking about differences in people of all kinds, including what today is called neurodiversity, which is meant to describe people like me with autism. My point is that, prior to the development of genome sequencing, people would use phenotypic characteristics (skin colour, bone structure, head size, etc.) to assess things like racial differences and even to attempt to define the concept of race, smartness, and so on. Indeed, still today cognitive bias and other prejudices are based on phenotypic characteristics of human beings and, at times, quite archaic ways of thinking. We see it every day.

I won’t get into here the debates between realism, anti-realism, and constructivists, although the limited attempts to argue the former in this context are like Swiss cheese while the latter can also be too one-dimensional. In any case, what I am driving at is how, in the past (unfortunately these attitudes still seem to manifest in the minority) what was thought of as different species or races among humans and other biological organisms was determined by phenotypic characteristics and as a result, phylogenetic trees and different groupings of humans and other organisms were often incorrectly constructed. But with technological advancements and our ability to sequence genomes quicker, more efficiently and cheaply, we have been able to compile larger genome databases with some powerful algorithms that can compare genomes more accurately. Thus, in biology, phylogenetic trees, the relationships between species, and divergences within species, can be more accurately assessed and drawn. What we find is that a lot of things that may have been thought to have been be related are not and vice versa. When comparing genomes of people from different parts of the world, we have found that although there are many minor variations between the genomes of humans as a whole, there is not enough difference to define different races. That is to say, there is no evidence for taxonomic delineation according to any definition of species or sub-species within humans, such that phylogenies inferred from mitochondrial DNA do not show any clear distinctions.

This is what I find inspiring and what I think about when thinking of diversity. The story of human beings, of our evolution, and of the universality we all share on this rock in some isolated region of the universe – it is quite beautiful. The Homo sapiens lineage has relatively recent origin when compared to other evolutionary timescales, like the planet Earth we call home, and our cosmic insignificance couldn’t be more pronounced. The universality to this reality is one that I think supports a critical humanistic vision, a perspective that, from an objective standpoint, also celebrates the incredible genetic diversity among local populations. It gives us fundamental perspective about the arbitrary nature of geographic boarders, racist attitudes, tribalism, and the many needless wars and suffering that have been waged and inflicted throughout human history on the basis of such arbitrary identifications.

In other words, while there is this incredible universality to human beings, and the similarities among people is something to be celebrated, there is so much to also celebrate about our differences – what we can call the particular as it emerges from the general. So, for example, people with ASD and the different perspectives we may offer as individuals, which, currently, is described under the heading of neurodiversity. Or, for example, the different perspective we may all offer, given our geographies and our own psychological histories. Or the diversity in our skin colours and other phenotypic differences that have come about rapidly in our evolutionary history. One of the great things about humanity is owed to the fact that as human beings we come in different shapes and sizes, we have different facial characteristics, varying eye colour, different finger prints, and different skin colours. For me, it gives perspective on how irrational our social history has also been – the needless suffering that people have faced and continue to face as a result of grim prejudice. Recently, for example, the daily prejudice black people continue face has been a renewed subject of discussion in the media. I think also of people with autism or other disabilities.

When I think of modern science, like in my area of fundamental physics, I think of the conferences I’ve attended, and the wonderful diversity of perspectives that combine. Modern science can be a fantastic representative of a more rational world, where people from many different geographic regions and backgrounds work together to solve difficult problems and to contribute to the scientific body of knowledge.

7. The IOP is committed to encouraging participation in physics among people after the age of 16 – especially those from under-represented backgrounds. How do you think we can better support others from under-represented groups who are considering studying physics? Is there anything you want to do as an ambassador?

From the little I have shared about myself, it is obvious that I think education is important. Life-long learning, for me, is a process whose end is defined only by one’s mortality. It doesn’t matter if you’re 16, 25, 55, or 80 years of age, one can always decide to take up an interest in physics or whatever else. In fact, I would encourage anyone interested in studying science to take up physics, even if they don’t plan to pursue it as a career; because regardless of what area you find interest in, physics can offer an important perspective in life. But to anyone from an under-represented background considering studying physics, or who has a passion for studying physics, I would say keep trying, and ask for support. If you are facing challenges and barriers in life, think about who might be best placed to support you through these and contact them to ask for help. This might be a teacher at school, your local council or social services department, your GP or another healthcare professional, the Citizen’s Advice Bureau, charities and support groups set up for people like you, family or friends, or the university you would like to attend. There is support out there, and it can take time to find the right support and to work through challenges, so being patient with yourself and others can help. There will be better days and harder days, so take one day at a time. Try to learn from setbacks and if things don’t quite go to plan, try to rest, regroup, and get back up the next day and try again. This is after all what a scientist often has to do!

As someone from an underrepresented background, it can sometimes be hard to feel confident that you could go to university, or be a scientist, if you don’t see or hear about people who are similar to you doing the same thing successfully. Sometimes it can feel isolating, wondering whether others have experienced the challenges that you have in pursuing their interests and goals in science, and if so, how they might have overcome these, or even whether it is possible to overcome such challenges at all. Sometimes it can be difficult to find easy answers to questions about whether a particular environment (e.g. a university or workplace) will be welcoming and accessible to someone like you. In this respect, I think organisations like IOP can help by working with universities to make them more welcoming, accessible and supportive environments for people from underrepresented backgrounds. IOP can also work to increase the visibility of people from underrepresented backgrounds who are studying and working in Physics. This could include such individuals sharing both their successes (to show that success is possible!) and the challenges they have faced, including how they have worked through these challenges. These real-life examples can be much more helpful to people who may be facing challenges and barriers of their own in pursuing physics at university or as a career, than a rose-tinted success story that leaves out the challenges and bumps along the way.

As an ambassador this is something that I would like to contribute to, and I hope that by sharing my story, perhaps it might encourage others who have faced similar challenges to keep trying and working towards their goals.

8. What would you say to someone thinking about applying to the fund? (Would you encourage them to apply? If so, why? What advice would you offer?)

I would encourage anyone to apply. Unfortunately, I am not one to give advice about applications and things, because I tend to struggle a lot with these procedures. What I can say is make sure your application meets all of the criteria, and, if your application is not successful, don’t be discouraged. Take it as a learning experience – ask for advice about any areas in which you can improve your application for next time, and try again either with another funder and/or with the Bell Burnell fund at the next application round.

9. What message do you have for Professor Dame Jocelyn Bell Burnell – and other supporters who have made this funding possible?

I suppose I would just like to thank Prof. Dame Burnell and the others involved in the scholarship. It means a huge amount to me to be able to pursue my PhD, and I hope that my research in the next few years helps to repay the support and belief in me, and that, moving forward, I can be a good ambassador and help contribute a meaningful voice in the British scientific community.

(n-1)-thoughts, n=6: Asperger’s and writing, Lie 2-algebroids, linguistics, and summer reading

Asperger’s, studying, and writing

As a person with autistic spectrum disorder (ASD), I’ve learned that writing plays an important and meaningful role in my life. I write a lot. By ‘a lot’ I mean to define it as a daily activity. Sometimes I will spend my entire morning and afternoon writing. Other times I will be up through night because my urge to write about something has kept me from sleeping. Most often I write about maths and physics, keeping track of my thoughts and ideas, planning essays, or writing about my work. But I also make it a principle of life to read widely. Indeed, I enjoy reading – studying – as much as I enjoy writing, and this often motivates me to write about many other topics. The two go hand-in-hand.

One reason writing has become important for me has to do with how, as a person with Asperger’s, social communication (by which I mean verbal, but of course also entails other forms like sign) is a source of struggle. I don’t often write about my Asperger’s, mainly because I find it a difficult process. It is hard to organise my thoughts about it, and I am never sure what is appropriate to share. In formal language, my Asperger’s is described clinically as high-functioning but severe. A big part of my life is about learning new strategies to cope. Some of the strategies may even be familiar to others without ASD, like learning to talk in front of others in ways that minimise anxiety and stress, or without completely freaking out (what we call in my language ‘red card’ moments). Or, to give another example, we work on finding strategies for the times I am at the office, so my brain doesn’t go into hyperdrive and so I can focus on discussion and also things like writing on the whiteboard. Another thing about my Asperger’s is that it can be hard adjusting to new people and it can be very stressful acclimatising to new environments. I’ve been working with Tony, now my PhD supervisor, for two years or more and I have only recently started to acclimatise and find our engagement a bit easier to manage. Indeed, in the same time I’ve been at the University of Nottingham, it remains an ongoing process adjusting to this new environment and to being on campus. Like with my close friend, Arnold, who, even after seeing him everyday for years, it was often still a challenge for me to engage with him socially and to visit his house. There is a lot to my experience, not just the social aspect of experience, that can be difficult and demanding as well as overwhelming. I also struggle a lot with anxiety and other things, in addition to extreme sensory sensitivity. So I require a lot of time and space for stillness in my own environment, with my own structure and routine – usually in my own space with my books and other comforts – because sensory overload can easily overwhelm.

In my one attempt to write about living with ASD I expressed how it can be difficult to understand cultural meanings as another example. This is a way of describing orientation to many of the ‘codes’ or behavioural routines that normalise in society. For example, I remember when I was a teenager being pressured a lot to establish the same routine economic patterns as others, or blamed because I didn’t have a job or couldn’t maintain one. I find it difficult to compute things like why daily life is the way it is for most individuals or why people behave as they do. What motivates daily behaviour and routine? How do people make decisions or direct the future course of their lives? Science, textbooks, and studying fervently became, at least in part, a survival-based mechanism. There is no instruction manual about humans; or about why history has taken the path it has in the course of human and societal development; or why many arbitrary social customs have come to be the way they are; or why my father acted and behaved the way he did; among many other things that come to be a feature of life. Studying became my way to cope and to understand, and writing became an extension of that. For instance, I studied every aspect of psychology to help better understand my experiences growing up or why, at least in part, people act violently or use violent language. I’ve read and written across most of philosophy; the same for economics, certainly enough to understand the fundamental debates; and also a lot of sociology. At one point I read a lot of political history, with history one of my favourite subjects. While all of this has a purpose in aiding my attempt to try and understand the world I am a part of, it also supports my passion for studying, my focused interests, and provides the stimulation I need.

On top of it all, living with Asperger’s can be quite exhausting. Indeed, one thing that is common for people diagnosed with autism is the experience of a certain type of fatigue, or what, in my house, we call ‘crashes’. These are a daily experience, where I need to put on my headphones and sit in my own (still and comfortable) space for however long it takes to calm my brain. For these reasons, day to day life is often spent in controlled environments, because it helps ease the red card moments, reducing stress and anxiety, and thus also helps combat the amount of crashes.

I think it all adds up in some sort of complicated sum as to why I find writing an important outlet. But even writing has its own difficulties. I remember my teacher, when I was 6 or 7 years old, say that my brain runs faster than my pen. I think this is true. I think of the sluggish pen effect as the difficulty in converting the internal representations of whatever concept or idea into concise written form at the pace I wish to feed ink to paper. So even though I write everyday and have been practising for many years, the usual result of my writing is typically permeated with errors. The process can be disabling and discouraging, to be honest, with many moments of frustration and failure; but, I’ve also learned that when I battle through and produce something I am happy with, the moment of victory is worth so much.

For many personal reasons, I’ve been regularly encouraged to write more and share more on my blog, and this is something I’ve been working toward. I think that, over a couple of years, I’ve grown more and more comfortable sharing essays and technical notes, although perhaps that is especially true in recent months; but I am also practising writing in other ways, like more personally and less formally. Technical writing is much easier than informal discussion, although a definition of the latter still seems somewhat unclear.

So as one step, this is a new blog post format that I may start experimenting with over the coming weeks, in addition to my usual research entries, essays, and technical notes. Although I prefer to keep my blog focused on my maths and physics research, which of course is mainly string related, allowing from time to time the inclusion of the odd bit of academic diversion, I think this (weekly or fortnightly) format of (n-1)-thoughts may be a fun space that allows me to practice writing in different ways, to share disconnected thoughts or random interests, outside of the formal essay or technical structure.

Generalised geometry, higher structures, and some John Baez papers

Another gem by, Urs! In a recent post on higher structures and M-theory, I made a comment recommending that people read Urs Schreiber’s many notes over the years. In my own research, I’ve found them to be invaluable. The most recent example relates, in some ways, to what I also mentioned in that post about how we may motivate the study of higher structures in fundamental physics: namely, how the Kalb-Ramond 2-form can be seen as an example of a higher structure as it is generalised from the gauge potential 1-form. I won’t go into details here, but the other day I was thinking about such generalisations, and I was thinking about Hamiltonian mechanics in the process. As I’ve mentioned before, if I were to teach string theory one day I would take this approach, emphasising at the outset the important generalisation from point particle theory to the extended object of the string.

Thinking of higher structures, I knew there were many connections here, and I was wanting to fill out my notes, for instance from how in generalised geometry the algebraic structure on TX \otimes T*X is a Courant Lie 2-algebroid. Those who study DFT will likely be quite familiar with Courant algebroids, and, certainly from a higher structure perspective this line of study is interesting. I also knew there was an original paper, which I had seen in passing, talking about this and the relation to symplectic manifolds, but I couldn’t find it. Then, bam! As Schreiber notes in a forum reply, ‘Courant Lie 2-algebroids (standard or non-standard) play a role in various guises in 2-dimensional QFT, thanks to the fact that they are in a precise sense the next higher analogue of symplectic manifolds and thus the direct generalization of Hamiltonian mechanics from point particles to strings’.

The part ‘from point particles to strings’ was hyperlinked to an important paper, the very paper I was looking for! The paper is Categorified Symplectic Geometry and the Classical String by John C. Baez, Alexander E. Hoffnung, Christopher L. Rogers. I look forward to working through this.

I also want to highlight several other papers from around the same time by Baez, including one co-authored with Schreiber, that I think are also foundational to the programme:

Categorification co-authored with James Dolan;

Higher-Dimensional Algebra VI: Lie 2-Algebras co-authored with Alissa S. Crans;

Lectures on n-Categories and Cohomology co-authored with Michael Shulman;

and, finally, Higher Gauge Theory co-authored with Urs Schreiber.

Thinking about my summer reading list

My summer holiday is in June this year, as I have a conference in mid-July and then I am scheduled to return back to university 1 August. I think Beth and I are going to spend a week in a North Norfolk, one of our favourite places, which has also sort of become a home for both of us. In anticipation of my break, I’ve started putting together my summer reading list, as I do every year. To be honest, there are so many good books right now, it is difficult to choose.

Although my list isn’t complete, one book that I’m already looking forward to is Jennifer Ackerman’s ‘The Genius of Birds‘. I had this book on my Christmas break reading list but, unfortunately, I didn’t have enough time to get to it.

I recently purchased ‘Explaining Humans: What Science Can Teach Us About Life, Love and Relationships’ by Camilla Pang, and I think I will add this to my list. Camilla has a PhD in biochemistry and, as she also has ASD, my interest in this book is more so about her personal journey coming to grips with the complex world social around her through the lens of science. It sounds, on quick glance, that we’ve come to cope with the world in similar ways and share an interest in understanding human behaviour and development. Having said that, I think there is a bit of a risk that people might read this book and conflate it with some sort of autistic worldview, which is completely incorrect, or, equally incorrect, as a scientific view of human behaviour. Contrary to some reviews, I wouldn’t read Pang’s book looking for a strictly scientific view (else one will be disappointed). I could be wrong, but I think ‘Explaining Humans’ may have potentially been mispromoted, hence some of the confused feedback. I approach this book as I would when reading someone’s memoirs, like ‘Diary of a Young Naturalist‘ by Dara McAnulty, ‘Lab girl‘ by Hope Jahren, or ‘Letters to a Young Scientist‘ by Edward O. Wilson. With topics including the challenges of relationships, learning from mistakes, and navigating the human social world by finding tools in things like game theory and machine learning, my interest is in the fact that this is another author with autism and, for myself, I similarly use textbooks and my studies to understand and manage my experience the world. Even on a purely phenomenological level, it will be interesting.

Another book that I may add is of a completely different tone: namely, Saul David’s ‘Crucible of Hell’. I’ve been enjoying reading about WWII again, and, as noted in this post on Dan Carlin’s podcast series on the events in the Asiatic-Pacific theatre, the battle of Okinawa (and others) I haven’t read much about. A few more books I have been thinking about: Douglas R. Hofstadter’s ‘Gödel, Escher, Bach: an Eternal Golden Braid‘, ‘The Deeper Genome‘ by John Parrington, ‘King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry‘ by Siobhan Roberts, ‘Decoding Schopenhauer’s Metaphysics’ by Bernardo Kastrup, ‘Quantum Computing Since Democritus‘ by Scott Aaronson, Jared Diamond’s ‘Guns, Germs, and Steel: The Fates of Human Society‘, and Daniel Kahneman’s latest ‘Noise: A Flaw in Human Judgement‘. Tough decisions.

Linguistics

I’ve been short on time this week finishing some calculations and working on a paper, prior to receiving my second Covid jab. But the other afternoon I thoroughly enjoyed this article. It’s on the Galilean challenge and its reformulation, wherein discussion unfolds on why there is an emerging distinction between the internalised system of knowledge and the processes that access it.

As alluded a moment ago, a general theory of development has interested me for a long time. For my book published by Springer Nature, a lot of the study and references were originally motivated by this interest. When I last did an extensive read on the topic, there was a lot of progress in developmental models – biology, bio- and neuro-linguistics, child psychology, and so on. The summer when I was writing my book, I had already compiled all of my research and I was running short on time in terms of the writing process (I wrote the book in the span of two weeks). Around the time of my research, if I recall there was discussion in biolinguistics regarding the hypothesis of ‘[t]he fibre tract [as one reason] for the difference in language ability in adults compared to pre-linguistic infants’. I remember noting that interesting ideas were developing, and this is a nice article on that front. What is particularly fascinating, I would say, is how language design appears to maximise computation efficiency, but ‘disregards communicative efficiency‘ [italics mine].

This certainly runs directly counter to common belief, as mentioned in the article, namely the established view that communication is a basic function of language. For a long time, as I understand it, there was belief that there was an experiential component to early language formation; but what current research suggests is that, an experiential component is not fundamental at all. Of course an experiential component plays a role, in some capacity, when it comes to externalisation processes, such as in development of variances in regional accent here in England as an example. I mean, the subject is mediated (to whatever degree) by his/her sociohistorical-cultural circumstances, but, unless I am misunderstanding (I need to read through the research more deeply) language itself is not some purely social construct.

Regarding reference to the evolutionary record, I wonder how the developing view in the article relates to ongoing research concerning, for example, certain species of birds, their migratory paths, and the question of inherited or genetic knowledge. It’s an absolutely fascinating area of study, something I’ve been reading about with my interests in mathematical biology, and of course there is very apt analogy here also with broader developments in microbiology.

One last thing of note from reading the article, as I have written quite a bit about the enlightenment philosophes and the start of modern science, it is notable how they sought to ask the question of language. Descartes’ fundamental enquiry into language – the Cartesian question – remains interesting to this day, and I was delighted to see it referenced at the outset. I recommend reading Descartes’ meditations plus other contributions to the enlightenment philosophes – Kant, Spinoza, Hume, to name a few. There is so much here that remains relevant to our modern history and to the development of the contemporary social world. For a few years I’ve been writing a series of essays on Hegel’s science of logic and his epistemology, which is notably relevant today in my area of work in fundamental maths/physics.

Mental health awareness week

Finally, it’s mental health awareness week in the UK. Often these sort of campaigns can be incredibly superficial, failing to look at root causes or ask fundamental questions about well-being and support, but they don’t have to be. Mental health awareness is something that I’ve always taken seriously, not least because I have experienced many challenges with my own mental health throughout my life. The last time I did research and wrote on the subject, suicide statistics in many leading Western countries were significant. I know, too, that for people with autism, like myself, mental health can present a significant challenge in addition to the other challenges one may face. People with autism are much more likely to die by suicide than the general population, as many cause-specific analyses of mortality for people with autistic spectrum disorder (ASD) indicate. Sometimes these facts are overlooked when we talk about mental health as a society, and often I find it important to highlight. But mental health doesn’t discriminate, it affects all people from all backgrounds, and weeks like this one are a good time to help foster discussion, combat stigma, and to think about mental health in all of its facets.

*Image: ‘Streams of Paint‘ by markchadwickart (CC BY-NC-ND 2.0).

History of Japan from the Heian period through the Second World War

For readers who like to study history, whether rigorously or simply for the enjoyment of historical discussion, last week I finished listening to a series of podcasts – much more like a series of extensive lectures, with each entry spanning 4 to 5 hours in length – on the history of Japan and its involvement in the Second World War. The talks by Dan Carlin (see bottom) have been published over the course of the past two years, and serve almost as a narration of Japanese history (from Carlin’s view) beginning roughly from the Heian period through to the events of the Asiatic-Pacific theatre.

Carlin, it must be said, is not a historian (it is fair to say that he is an amateur historian). And while it is generally the case that many historians applaud his podcast and popular engagement with history, it is important to approach his presentation as a form of popular history, firstly. That is to say, I take it as history as a way of seeking and exploring lessons, and thus, too, as a way of speculative theorising connections of factual historical events. This is not to say that Carlin is not brilliant at presenting history. He is in every sense one of the best popular history presenters, who, as I see it, has a first-principle motivation to give context to historiography by highlighting the human experience of an event. History is bloody, absolutely; and the ‘human factor’ that Carlin ensures is not lost in history is deeply important, not least philosophically. It must also be said that he provides plenty of support for his views and never fails to provide his full list of references, which usually includes both primary and secondary sources; but, again, the insisted nuance is that rigorous historical study and popular history are two very different things. The point of discretion here is just to say that one must approach each talk critically, for example discerning when Carlin is presenting his own theory or views and when he is directly citing a primary or secondary reference.

In more ways than one, listening to Carlin’s historical presentations – especially his emphasis on the human aspect of history – reminds me of an allegory on history by Albert Camus. This is something I should maybe return to and write about sometime.

***

Admittedly, the history of Japan is something I know of in discrete, disconnected pieces. It’s just not something that has been a focus in my history studies. Like a puzzle picture, some parts I have filled in but mostly in passing or in unconcentrated ways. For example, I have some understanding of its pre-historic period, mainly from books covering our best known research on early human migration that happened to include the Japanese archipelago. Over time I have also picked up some bits on ancient Japan and things like Heian culture, famously the era in which the samurai emerged. I’ve also read bits on Japan’s involvement in World World II but, again, my focus has largely been on the European theatre. Both of my grandfathers, one on my Scottish side and the other on my English side, were involved in the war. I grew up with the Second World War being a regular topic of discussion, with the Battle of Britain and other notable events often a focal point. As a kid, I also studied planes and I really liked the old British war planes, like the Spitfire, and used to build models of them as a hobby. All of this is to say that I’ve never focusedly studied the Asiatic-Pacific theatre in the same way I’ve done the European.

This is perhaps one reason why I found myself thoroughly enjoying Carlin’s series. One can approach his telling of the history with the aim in mind being a study of Japan’s involvement in both world wars. For this reason the focus is narrowed on pertinent historical and cultural developments preceding the great wars, before finally covering the events in the Pacific theatre. There is far too much to comment on, as the range in subject matter is vast. One thing that I found interesting is Carlin’s emphasis on colonialism as it relates to Japan’s motivation, military emergence, and ultimately resource-focused campaign in Asia. But before this, there were so many pertinent socio-cultural and historical developments in Japan’s history, as Carlin tells it, which contribute to what is described as a certain cultural and behavioural fanaticism. This fanaticism is expressed, in one way, through the eyes of the Japanese soldier of the time and finally culminated in an extreme barbarity that very much defined the Asiatic-Pacific theatre.

Carlin starts by first examining the phenomenon of Hiroo Onoda, the last Japanese soldier to come out of hiding from a Philippine jungle and surrender in 1974. What drove Onoda to behave in a way that, in one frame, may be described as going beyond the valour of duty, or in another frame may be described as fanatical and delusional, is a driving question in Carlin’s thesis. It is what shapes his telling of the history, because it leads Carlin, in the prologue, to introduce the observation – very much as we observe across all societies, I would argue – that human beings are malleable for better or for worse, and the ways in which we may be shaped or perhaps even deformed in extreme ways are based on our sociohistorical-cultural circumstances. So what were these circumstances? How did they develop? And what are the deep historical roots, not least related to Japan’s foray into imperialism?

Again, there is much to say, given the range of Japan’s history covered. I encourage the reader to listen to the series, because, while at times Carlin seems to make some drastic theoretical connections, the way he tells the story is absolutely gripping and, no doubt, within his recounting of many first-hand accounts, there are kernels of truth disclosed that are overwhelmingly moving in the sense that the Asiatic-Pacific theatre, in its sometimes unrelenting barbarity, was a deeply human tragedy.

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I will leave the reader with this comment, as it is particularly on my mind. The prologue to Carlin’s series, described above, and much of how he traces key developments in Japan’s history – it reminded me very much of Edgerton’s study on social pathology, in which it is argued that a society may be more or less pathological, with the degrees of variance characteristic of the particular sociohistorical-cultural moment. This was also the thesis of my book, Society and Social Pathology, published a few years ago. Within it I argued, if we are to understand social pathology in a critical way, conceptualizing the complex interconnection between the individual subject and his/her social conditions is the first place to start. In studying the relation between one’s sociohistorical-cultural conditions and the impact those conditions have on the individual subject, my thesis argued toward a more comprehensive, systems view of society, its development, its pathology, and its discontents. As a matter of perspective, if nothing else, a number of questions that Carlin asks – for instance, what leads to the development of the sort of behaviour displayed by Onoda – reminded me of similar questions when coming to study the importance of obtaining a well-defined and rigorous concept of social pathology. Below is an excerpt from when I was thinking about such matters:

One incredibly important argument that we will discuss […] concerns how […] all societies, just like individuals, can be pathological to greater or lesser degree (Edgerton, 2010). This is an important feature of my present thesis. In a survey of literature on the history of human society, it would appear fairly safe to conclude that social pathology as defined in this book is a reoccurring characteristic across cultures and epochs.  Overcoming the pathological development of human society is, to borrow the words of Kenan Malik (2014), “a historical challenge”. That is why although capitalism […] may take a central focus in the present study, due to the fact that capitalism as a particular social formation is what defines our present social world, this particular period of human social development is also part of a significantly broader history. For this reason if the intention is to look at the facts, the realities, the many social phenomena, which defines a large part of modern life, in attempt to understand why needless social suffering persists and why irrationality prevails, to accomplish this task we must also come to grips with […] a philosophy of history [that] intersects with and combines numerous disciplines, from anthropology and archaeology to psychology. And it will help us contextualize a framework for understanding both the ongoing process of pathological development throughout history, as well as the ongoing process pertaining to our present conditions.

Episodes:

*Image: Pacific Theater Areas, Wikipedia.