(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.


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).