(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.

Introduction to category theory

This is the first entry in my notes on category theory, higher category theory, and, finally, higher structures. The main focus of my notes, especially as the discussion advances, is application in string / M-theory, concluding with an introduction to the study of higher structures in M-theory. We start with basic category theory roughly following the book ‘Category Theory in Context’ by Emily Riehl (online version here), as well as the perspective of a selection of other texts and lectures cited throughout. For the engaged reader, I recommend reviewing the respective pages on nLab for further references.


There is a line by Wilfrid Sellars: ‘The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term’. The things we must come to know ‘in the broadest possible sense’ – at its most abstract, a type of conceptual modelling – must in some way be classified such that we may distinguish the type of thing, the relation between thing of similar and dissimilar class, and its particular properties or attributes. For example, think of basic biological nomenclature going back to Aristotle. Another example would be the standard model of particle physics. (For the time being, we will put aside philosophical issues going back to Hegel, Russell, and others, as well as broader debates having to do with process vs. substance metaphysics, and so on).

From a mathematics and physics point of view, if we take Sellars’ statement seriously, then, at the highest level in the conceptual hierarchy what we begin to contemplate is a way to think about what Peter Smith describes in his notes on category theory as, ‘structured families of structures’. That is to say, we naturally come upon the need for some systematic framework for the study of abstract structures, how we may define a family of such structures, and their interrelation. We take as a starting point in these notes motivation from both foundational mathematics and fundamental physics.

A simple example of a structure is a topological space. Simpler still, take an example from group theory. Any group may be described as a structure, which comprises a number of objects equipped with a binary operation defined on them that obeys well-defined axioms. Now, what of a family of groups? We can of course also define a family of groups with structure-preserving homomorphisms between them (for a review of groups and sets leading up to the basic ideas of category theory, see Chapter 2 in the above notes by Smith). This gives an example of a structured family. This reference to groups is apt, because as we will see later in these notes: classically, a group is a monoid in which every element has an inverse (necessarily unique). A monoid, as we will review in a future entry, is one of the most basic algebraic examples of a category.

More generally, when looking at a family of structures along with the structure-preserving maps between them, our goal will be to reach an even higher level of abstraction that takes the form of a further structure: i.e., a structure-of-structures. We can then continue this game and ask, what is the interrelation of this structure-of-structures? From this question we will look to climb to another level and speak of operations that map one functor to another in a way that preserves their functorial properties.

When I think of the idea of a category, this increasing picture of generality and of climbing levels of abstraction is often what I like to picture. To use the words of Emily Riehl [1], ‘the purview of category theory is mathematical analogy’. While some give it the description, however affectionately, of ‘abstract nonsense’, I prefer to think of category theory – and, more broadly, the category theoretic perspective – as very much akin to the geologist constructing a topological map containing only vital information. This notion of climbing levels of abstraction, is, in many ways, simplifying abstraction. What use would it be to perform analysis within the framework of these increasing levels of simplifying abstraction? In foundational mathematics, the motivation is quite clear. In fundamental physics, on the other hand, it may at first seem less obvious. But as we will discuss in these notes, particularly in the context of quantum field theory and string / M-theory, there is quite a lot of motivation to think systematically about structured families of mathematical structures.

What is a category?

One way to approach the idea of a category is to emphasise the primacy of morphisms. In the paradigm view, in contrast to set theory, category theory focuses not on elements but on the relations between objects (i.e., the (homo)morphisms between objects). In this sense, we may approach category theory as a language of composition.

Let us build toward this emphasis on composition in a simple way. Consider some collection of objects A, B, C, D   with a structure preserving morphism f  from A  to B  , another structure preserving morphism g  from B   to C  , and, finally, a structure preserving morphism h  from C  to D  . (In a handwavy way, this is how we motivated the idea of a category in a previous post). In diagrammatic notation we have,

\displaystyle A \ \xrightarrow[]{f} \ B \ \xrightarrow[]{g} \ C \ \xrightarrow[]{h} \ D  .

It is fairly intuitive that we should be able to define a composition of these maps. All we need, as an axiom, is associativity. For example, we may compose f  and g  such that we obtain a map from A  to C  . We may write such a composition as g \circ f   . Similarly for all the other ways we may compose the maps f, g  , and h  . This means that we ought to be able to then also compose a map for the entire journey from A  to D  . Diagrammatically, this means we obtain:

One sees that we can apply the structure preserving map f  followed by the composite g-followed-by-h. Alternatively, we may just as well apply the composite f-followed-by-g and then afterwards apply the map h  . This very basic picture of a collection of objects A,B,C,D  , the maps between them, and how we may invoke the principle of composition for these maps already goes some way toward how we shall formally define a category. One will notice below that we need a bit more than associativity as an axiom, and along with the objects of a category we will speak of morphisms simply as arrows. From now on, if A \in \text{Ob}(\mathcal{C})  we write A \in \mathcal{C}   .

Definition 1. A category \mathcal{C}  consists of a class of objects, and, for every pair of objects A,B \in \mathcal{C}  , a class of morphisms, \text{hom}(A,B)  , satisfying the properties:

  • Each morphism has specified domain and codomain objects. If f  is a morphism with domain A  and codomain B  we write f: A \rightarrow B  .
  • For each A \in \mathcal{C} , there is an identity morphism id_A \in \text{hom}(A,A) such that for every B \in \mathcal{C} we have left-right unit laws:
  1. \displaystyle f \circ id_A = f \text{for all} f \in \text{hom}(A,B)
  2. \displaystyle id_A \circ f = f \text{for all} f \in \text{hom}(B,A)
  • For any pair of morphisms f,g  with codomain of f  equal to codomain of g  , there exists a composite morphism g \circ f  . The domain of the composite morphism is equal to the domain of f  and the codomain is equal to the codomain of g  .

Two axioms must be satisfied:

  • For any f: A \rightarrow B  , the composites 1_B f  and f1_A  are equal to f  .
  • Composition is associative and unital. For all A,B,C,D \in \mathcal{C}  , f \in \text{hom}(A,B)  , g \in \text{hom}(B,C)  , and h \in \text{hom}(C, D)  , we have f \circ (h \circ g) = (g \circ f) \circ h  .

Further remarks may be reviewed in [1, 2, 3]. We emphasise that for any mathematical object there exists a category with objects of that kind and morphisms – i.e., structure-preserving maps denoted as arrows – between them. The objects and arrows of a category are called the data. The objects of a category can be formal entities like functions or relations. In many examples of a category, the arrows represent functions, but not all cases of an arrow represents a morphism. These subtleties will be saved for future discussion.

An important notational point is that one should keep close attention on morphisms. Often categories with the same class of objects – e.g., a category of topological spaces compared with another category of topological spaces – may be distinguished by their different classes of morphisms. It is helpful to denote the category as \text{hom}_{\mathcal{C}}(A,B)  or \mathcal{C}(A,B)  to denote morphisms from A  to B  in the category \mathcal{C}  .

Importantly, to avoid confusion, we speak of ‘classes’ or ‘collections’ of objects and morphisms rather than ‘sets’. One motivation is to avoid confusion when speaking of \text{Set}  , which is the the category of all sets with morphisms (as functions) between sets. If a set of objects were required, instead of a class, then we would require a set of all sets. As it will be made clear when we reach the discussion on how to consider categories of categories, we may speak of sets of sets but, as Russell’s Paradox implies, there is no set whose elements are ‘all sets’. So we cannot speak of a set of all sets or a category of all sets. Likewise, it is conventional when we consider categories of categories to avoid the notion of a category of all categories (see Remark 1.1.5. in [1]). Instead, we speak of a limit in the form of a universe of sets and, in more advanced discussion, we will come to consider categories as universes.

Related to this concern about set-theoretical issues, it is important to note that we work with an extension of the standard Zermelo–Fraenkel axioms of set theory, allowing ‘small’ and ‘large’ sets to be discussed. In category theoretic language, we invoke similar terminology:

Definition 2. A category \mathcal{C}  is finite iff it has overall only a finite number of arrows.

A category \mathcal{C}  is small iff it has overall only a ‘set’s worth’ of arrows – i.e. the class of objects is a set such that the arrows of \mathcal{C}  can be put into one-one correspondence with the members of the set.

A category \mathcal{C}  is locally small iff for every pair of \mathcal{C}  – objects A,B  there is only a ‘set’s worth’ of arrows from A  to B  , i.e. those arrows can be put into one-one correspondence with the members of some set.

Examples of categories

What follows are a few examples illustrating the variety of mathematical objects that assemble into a category:

  • Set, the category of sets where morphisms are given by ordinary functions, with specified domain and codomain. There is a subtlety here in that the view of Set as the category of all sets becomes paradoxical, so, typically, we limit to a universe of sets (more on this in a separate entry).

Example. In this category the objects are sets, morphisms are functions between sets, and the associativity of the composition law is the associativity of composition of functions.

We may define the category Set (The category of sets): \mathcal{O}  (Set) is the class of all sets, and, for any two sets A,B \in \mathcal{O}  (Set) define \text{hom}(A,B) = f: A \rightarrow B  as the set of functions from A  to B  . The composition law is given by the usual composition of functions. Since composition of functions is associative, and there is always an identity function, Set is a category. This ends the example.

Other categories of note:

  • Grp, the category of groups where morphisms are given by group homomorphisms.
  • Vect_k, the category of vector spaces over some fixed field k, where morphisms are given by linear transformations.
  • Ring, the category with rings as objects and ring homomorphisms as morphisms
  • Top, the category of topological spaces where morphisms are given by continuous maps
  • Met, is the category with metric spaces as objects and continuous maps as morphisms.
  • Meas, is the category with measurable spaces as objects and measurable maps as morphisms.
  • Graph, the category of graphs as objects and graph morphisms (functions carrying vertices to vertices and edges to edges, preserving incidence relations) as morphisms. In the variant DirGraph, objects are directed graphs, whose edges are now depicted as arrows, and morphisms are directed graph morphisms, which must preserve sources and targets.
  • Man, the category of smooth (i.e., infinitely differentiable) manifolds as objects and smooth maps as morphisms.

All of the above examples are concrete categories, whose objects have underlying sets and whose morphisms are functions between these underlying sets (what we have called ‘structure-preserving’ morphisms). We will speak more about concrete categories, including formal definition, in a later note. For the sake of introduction, it is also worth noting that there are also \textit{abstract categories}. One example is as follows:

BG, the category defined by the group G  (or what we will describe as a monoid in the next entry) with a single object. The elements of G  are morphisms, with each group element representing a distinct endomorphism of the single object. Here composition is given by multiplication. There is an identity element e \in G  that acts as the identity morphism.

Closing comments

In the next post, we will review some other category definitions, review diagrammatic notation, and discuss in more detail the important role and subtlety of morphisms. In a closely followed entry, we will then finally turn our attention to monoids, groupoids, pre-ordered collections, and other related concepts, as well as start discussing examples in string theory.


These notes primarily follow a selection of lectures and texts:

[1] E. Riehl, Category theory in context. Dover Publications, 2016. [online]

[2] S. Mac Lane, Category theory for the working mathematician. Springer, 1978. [online].

[3] P. Smith, Category theory: A gentle introduction [online].

[4] J. Baez, Category theory course [lecture notes].

(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.

The US election and my holiday reading list

It is reasonable to wait for confirmation; however, as things stand, it appears Donald Trump is about to get walloped in the election, losing both in terms of the electoral college and the popular vote. One might indeed take a moment to say, ‘good riddance!’. But it will take a lot more than a Biden victory to defeat the prejudiced, often anti-science, and certainly contra-enlightenment views that have been amplified in the past years, not to mention the shady funding behind them.

What is super interesting, I think, is that when looking at the numbers the definitive nature of the urban / rural divide in the United States is made explicit. It is old sociology, to be sure, and I can think of no better description than how there seems a complete contradistinction of views. It is a rigid contest, and it is certainly not as simplistic as designating the young, educated urban dweller against the opposite in the country bumpkin. For example, it is noticeable that in some circles the right-wing voices in support of Trump have expressed anti-globalisation views in almost identical ways as some circles on the left, the difference primarily being in the framing. Although this doesn’t factor ideological residues, the point is that the split seems rather nuanced with as much economic as cultural import, not so different than what we have also witnessed here in the UK. For many reasons, I have been reminded also in recent years of Stephen Bronner’s analysis of anti-modernism movements. It will be interesting to read in the coming months new studies on these socio-economic and cultural dynamics, as no doubt a few books are already in the works.

One last comment before moving onto other things: it is hopefully telling that Biden’s first speech as president-elect made explicit mention of the need to reconnect with science. Rebuilding trust in scientific impartiality is imperative, after much opportunism that subordinated key scientific institutions to political bias and ideological ends. Surely, also, such a rebuilding effort coincides with the demand to strengthen evidence-based approaches to policy. Philosophically, such approaches are still not completely without their problems, but it is a project we ought to work toward.

Unification was also a key message, and quite understandably. Whatever one may think of French President Macron, last week he gave what I thought was a nice talk on the principle of enlightenment in the form of communicative reason (it reminded me very much of Habermas): to continue to work to create a public space structured in such a way that rational dialogue and debate may be achieved. This runs completely counter to demonisation and intense polarisation – the old habits of tribalism. Objective reason doesn’t commute, or is not compatible, with ideology in as much that analysis should work continuously to free itself from bias. It is unfortunate to see that it has become a tenet of general discourse to succumb to irrational worldviews in which their political and cognitive biases overshadow the normative process of reason. Biden spoke the other night of the battle between our better angels and our darkest impulses, which I interpreted in these terms – an expression that gives description to the enlightenment project. From a systems view, I am sceptical; but I am also open to seeing what he does. As with an incredibly difficult calculation or when probing an important proof, it is about incremental steps.


Now that I have submitted my thesis on double sigma models and field theory, I have two months holiday before I am due to return to university. During my break, I plan to catch up on a lot of reading. I would also like to finish a number of essays and potentially start drafting several more. For example, I am currently finishing an essay on braneworlds from my studies in autumn 2019. I also have a long essay being polished on deriving general relativity from string theory, among a list of others in my current area of the doubled string, generalised geometry, and de Sitter. So I look forward to my holiday where I can be in my own space a bit and enjoy writing on these fantastic topics.

I also have some others essays that I would like to write in other fields. For example, one essay that I have been working on for some time concerns the epistemology of the early medieval university in which Aristotleanism was formally introduced to Europe. For that purpose, I have added Nicholas Orme’s book on Medieval Schools to my holiday reading list.

There is another book at the top of my reading list. It’s Vincent Azoulay’s acclaimed ‘Pericles of Athens‘. I’ve been thinking of Pericles lately, perhaps partly to do with the experience of a year marked by a global pandemic. Indeed, the collapse of Periclean Athens was instigated in no small way by its own terrible malady – a rather vile plague that proved catastrophic for what was one of the earliest of egalitarian and democratic experiments in human history. (A nice discussion between historians was recently presented here). The intent here is in no way to draw analogies with our contemporary times, although with current trends it is not completely outlandish to suggest that contemporary democracy – and certainly present economic models in which it is housed – is facing a challenge. Indeed, and furthermore, it’s not just the pandemic but many trends in behaviour, not least what we have been seeing politically in the past years, that have highlighted the utter idiocy capable of human beings in a test of democracy at its very foundations. Isaac Asimov once wrote, ‘The great anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that “my ignorance is just as good as your knowledge“‘. In a similar vein, there is a great passage by Bertrand Russel that strikes the same point, and similarly a most famous passage by Walt Whitman comes to mind. Considering that some would argue that the prospect of enlightenment has not been fully realised, nor the prospect of democracy completely fulfilled, it will be interesting to read more about the struggles of Periclean Athens. An inspiration to some prominent enlightenment thinkers, often engagements with Pericles are dominated by the same old question that Socrates once asked: has philosophy made citizens (and, I would add, the life of citizens) better? History can often serve as a magnifying glass, and if philosophy’s remaining relevance is tied to asking the question of the existence of needless (social) suffering, maybe there is still something in Pericles to write about.

As a fun read, I’ve picked up Stephen Brusatte’s celebrated title exploring the latest research on the history of dinosaurs. It is a book that I have been desperate to read since the summer. I can’t wait to dig into its pages!

Finally, I was thinking of Brockman’s cross-field collection ‘Life’, with a contribution by Dyson on the garbage-bag-model followed by Ackerman’s ‘The Genius of Birds’. This was actually one of the first on my lists as it relates to my interests in mathematical biology (and plus, I enjoy studying birds in my spare time).

If there is time, I’ve been wanting to read Edward Wilson’s ‘Consilience: The Unity of Knowledge’. In addition to his now dated ‘On Human Nature‘, these books will certainly inspire a number of essays (his book ‘The Diversity of Life’ is also worth mentioning) because I have studied epistemology to great lengths and I am always keen to delve with nuance into evolutionary psychology and its issues. But they will likely have to wait until my summer holidays, along with a list of others (it is an ever-growing list!).

These mostly comprise my general academic reading and don’t really get into some of my ongoing non-academic books. I’ve been reading through a lot of the Star Wars canon recently. For my holiday, I picked up the new Marvel Kylo Ren comic series as well as the new Darth Vader series, and so far I have been enjoying both.

Review: Bertrand Russell’s ‘In Praise of Idleness’

In Praise of Idleness and Other EssaysIn Praise of Idleness and Other Essays by Bertrand Russell
My rating: 4 of 5 stars

View all my reviews

To some, or perhaps to many, it may seem a radical idea: idleness. But for the great British logician, mathematician, and Nobel laureate Bertrand Russell, idleness is seen as a historically rooted concept which ties intimately together the bonds of labour, leisure, and the prospect of human rationality. Or, at least that is my reading of his famously titled composition, ‘In Praise of Idleness’.

So, what does Russell mean by ‘idleness’? In some sense, it infers a socially organised definition of time that is economically independent of professional labour, in which one may instead expend their energy to fulfil personally meaningful pursuits. This could be, for example, a time for a person to explore painting or to explore a scientific pursuit or any number of interests. In some bodies of literature, such projects are called ‘existential projects’ to convey the personalisation of their meaning in one’s life. One may also call them ‘special interests’. In this sense, one can think of idleness simply as being the economically independent pursuit of a subject, activity, or quality for no other reason than it evokes the state of personal interest. Study for study sake, or a painter to paint without the pressure of starving – these are the sorts of examples that Russell evokes.

Russell_In Praise of Idleness

Idleness should thus not infer or be confused with one’s being disinclined to work or with simplistic views pertaining to individual laziness. Idleness should also not be seen as ‘the root of all evil’, as the idiom would have it. If we are to follow Russell’s arguments, idleness has substantial roots in positive human traits, such as curiosity, exploration, and invention. We also read how the notion of idleness is based on ethical, moral and empirical economic arguments. For Russell, social consumption can mean something very different, both existentially and socially, and thus humanistically. He also speaks of economic production and the way in which work and leisure cycles could generally mean something altogether more philosophically transformed in conception, particularly in terms of the meaning of leisure and its tradition and practical cultural configuration.

It is interesting to consider, on that note, how for thousands of years human beings have established traditions of celebrating different sorts of festivals – Judeo-Christian, Pagan, and so on. Think, for instance, of midwinter festivals based on the solstice or on religious themes. With these traditions follows also a deep historical relation between festivity and work. The festival represents, to frame it in terms of economic history, an interruption of daily labour cycles, with its concept rooted primarily in principles of free time for enjoyment [1]. Thinking of this, it is also interesting to recall that, using Christmas as an example, it was during the Victorian era that a formal socioeconomic relation developed between festivity, worker rights, and the commercial profit motive, particularly as middle-class families were afforded time off work with the financial means for surplus consumption. But if festivity and leisure – or idleness – are intricately related with labour by their very definition, and thus with economics, Russell’s account would seem to carry a certain diametric opposition to work patterns that exhaust the possibility of what he describes as energetic leisure.

In this sense, I read Russell’s essay as having some classical enlightenment motivation. Thoughtfulness – indeed, the time to practice thought and to explore intellectually – this seems a theme to Russell’s social philosophical view of which an advanced and aspiring rational society should strive to achieve. In other words, if idleness is a positive human experience, one which supports or fosters the individual subject to flourish rationally and, perhaps, self-actualise existentially, Russell ties this concept with the possibility of continued self-education and self-betterment, among other things. At the same time, while he celebrates the concept and experience of idleness, he also laments the loss of its broader social-economic and cultural realisation. It is argued that leisure time is expunged of idleness much as in the present-day example of Christmas, which is hyper-commercialised and seemingly increasingly filled with passive entertainments, as active energies are instead exhausted by work, intensely driven consumer cycles, and various other contemporary social behavioural patterns rigidified in such a way to maintain systemic mores. Russell’s arguments are based on traditional views of social-economic class structures, and he seems to suggest that the logic of social economy has been skewed; contemporary societies have in some ways lost sight of the meaningful idea of social production and the social purpose of consumption that may foster a more enlightened and rational society.

For these reasons, we read how with more energetic and thoughtful leisure one would then be better able to enjoy pleasures in which it was possible to take an active part. The central thrust of Russell’s argument in this regard is not so different than in present-day concepts of economic democracy and automation, in which in advanced technological society it is argued individuals should be increasingly afforded the freedom from necessary labour in order to pursue the many positive possibilities that life has to offer, including education and learning.

Reading his essay, I was reminded of a few historical examples. Think, for instance, about the development and evolution of writing and of our early mathematical ideas – a history that is intimately entwined with the genesis of civilisation. A good example comes from the ancient Babylonians. To Russell’s larger point, the early development of mathematics, much like writing, can be seen to be owed to the economic development of agriculture; because with agriculture one result was increased freedom from the precariousness of sustenance living in which people were then allowed more free time, with greater access to resources. As new technologies were conceived, and human pursuit was increasingly freed from the limits of basic survival to expand beyond that which was unavailable to hunter-gathers, the time available to explore, experiment with, and create things like writing became possible. The study of mathematics could also be pursued and formalised.

Indeed, to offer another example, the entire history of physics is riddled with such stories, like Michael Faraday playing with his magnets on a park bench in London or Issac Newton watching apples fall from trees, contemplating the nature of gravity. To the point of anthropologists and biologists who study human play, as another example that we may interpret in the frame of idleness, there is an argument to be made that what Russell is describing is in fact a fundamental biological and cognitive feature of universal human experience that is very much tied to inventiveness.

At this point, we may enter into various complex social, economic, and political arguments. Instead, as there are already many terrific reviews of Russell’s essay, both positive and critical, to close this discussion I instead want to focus on two things that struck me when recently rereading ‘In Praise of Idleness’. One playful thought was the potentially interesting applications in relation to a physics of society and of human beings, particularly regarding energetics. This has to do with the study of energy under transformation, and one may think of such transformation particularly between the individual and their labour under the fairly universal economic notion of the work-leisure trade-off. For the author, he argues that there is a sort of fetishisation of labour, especially manual labour, and he seems to want to argue that how we use labour energy is not efficient or optimised in the best ways. From the standpoint of a physics of humans and of society, it would be fascinating to see if some of his ideas are quantitatively grounded.

There are also many interesting economic points of consideration. First, it is worth noting that the contents of ‘In Praise of Idleness’ remain quite relevant today, given the resurgence of the idea of a shortened work week, especially in the UK and Europe. Some would argue that there is empirical evidence and many qualitative arguments about why the current configuration of work hours is not optimised for the benefit of both productivity and well-being [3, 4], supporting his view. Take a quantitative and qualitative view: work hours, commuting time, modern pressures of digital communication in which it is well studied that people also now routinely answer work emails in their leisure time – all of this and more matches data that substantiates the claim of an emerging culture of longer working hours [5]. Are the effects, psychological or otherwise, just as Russell observed or predicted?

On the other hand, inasmuch that the philosophical idea of idleness is tied with the economic argument of a shortened work week, how economically substantiated and viable is his argument? Some examples are as follows. If as a general rule of labour economics working more hours correlates with higher hourly rates of pay, and if as a general rule from a behavioural perspective higher rates of pay are one motivation for people in their social and economic life, then one may ask whether an economic conception of idleness is realistic. For instance, if the introduction of a shortened work week were to correspond to a cut in pay, would people be dissuaded to pursue the possibility of increased free time for the benefit of obtaining greater earnings? As this is a question about human behaviour and behavioural regulators, and hence agency, it is not so easy to model. Having said that, we observed major strikes by German steel workers in 2018 that saw them secure the right to work less at the cost of a drop in weekly earnings – although this also came with flexibility where workers may work longer hours if they choose. Perhaps agency and choice matter in this discussion.

Another point one may consider is that some economists argue that a shortened work week will likely result in an increase in earnings differentials and inequality. If, in general, those who work longer hours have higher hourly earnings than those who work shorter hours, then one would expect increased disparity in the earnings structure. Additionally, in a UK study of the public sector, a shortened work week was approximated to cost upwards of £45 billion, depending on some modelling assumptions including no increase in productivity [6].

For these reasons, when it comes to recent debates in the UK, should a shortened work week be considered some studies have shown that this reduction in time would need to be matched with an increase in productivity during work hours. There are some empirical examples where businesses that trialled shortened work hours saw productivity remain as it was or effectively increase. Although the sample is small, the argument here is that work hours – maximal output of energy during those hours – is better optimised and maintained when shortened and focused. This ties into arguments about the inefficiency of work hours within the current model – that, in the sense of Russell’s energy economics, maximum productivity and the maximum time of energetic labour – i.e., maximum labour hours – do not contradict an increase in leisure. This is partly why I think a physical theory would be interesting, if we could even construct the appropriate Hamiltonian. In empirical sociology, observations of phenomena like ’empty labour’ may also serve as an illustration of what some interpret as the outdated nature of present economic values and of modern conceptions of work [7]. Do these types of studies offer clues or evidence as to how and why economy may be reconfigured in ways in which Russell seems to indicate? It would furthermore be interesting to learn, in using separation theorem or something similar in the study of labour economics [8], whether energetic leisure serves as a positive argument in the utility function of the individual.

The problem when it comes to these sorts of economic ideas and debates is that, in many cases, we require much more accurate modelling. Current mainstream economics is quite inept at understanding the reality of human behaviour. If one considers the likes of Paul Romer’s contentions on macroeconomics (as well as notable research by many other contemporary economists), it is not controversial to say that the current economic model and its established ideas may be challenged quantitatively and qualitatively [9]. From what I can see at the present time, some arguments are emerging about the need for an interdisciplinary theory. Much like a physics of society, in which it has been suggested that a physical theory of society will not achieve systematic and objective clarity without an interdisciplinary form of research [2], in economics agent-based models are issuing similar demands. If the challenge of an objective economics is to look for the cause of instabilities inside the system, some argue that this means that what one inevitably comes up against are the details of human decision making, which, in principle, drives one toward the randomisation of decisions based on both rational and irrational processes. But it also seems more than that: it’s about thinking systemically – not just about economic models in the abstract sense but also the incentive structure and the problem that economics faces in terms of an orientation of ethics. A trivial example is as follows: if a model fosters the pathology of a simplified self-preservation worldview, and if I am one of the only two bakers in town, am I not incentivised in some way to run the other baker out of town by whatever means justified by that very principle of my own preservation? The point to be drilled into is that in social-economic modelling, simplified arguments and narratives about agents engaging in free or purely voluntary trade can, and often do, end up moralising what are otherwise deeply systemic issues. I think, in certain respects, this takes us some way toward the message in Russell’s essay about realistic economic models.

Given the transformation of the incentive structure, perhaps energetic and thoughtful leisure would be realised as an important feature of a healthy system. In terms of Russell’s arguments, framed in a systems way, the benefits would be in reducing the social deficit of reason by maximising the subject’s energetic capabilities to reason, in which education may then be ‘carried farther than it usually is at present’, fostering the provision of ‘tastes which would enable a man to use leisure intelligently’. As I read it, his argument implies the enlightenment ideal that the individual would be better scientifically informed (eg., against myths); they would potentially be better politically informed about policies and more engaged when fulfilling their democratic duties; they would make thoughtful economic decisions; and, perhaps ideally, they would approach social debates with greater consideration and in greater awareness of their own biases.


[1] Josef Pieper, 1999, ‘In tune with the world‘. St. Augustines Press.

[2] Guido Caldarelli, Sarah Wolf, Yamir Moreno, ‘Physics of humans, physics for society’. Nature Physics Volume 14, p. 870. DOI:10.1038/s41567-018-0266-x.

[3] Will Stronge and Aidan Harper (ed.), ‘Report: The Shorter Work Week’ [http://autonomy.work/wp-content/uploads/2019/01/Shorter-working-week-final.pdf]

[4] Lord Skidelsky, ‘Report: How to achieve shorter working hours’ [https://progressiveeconomyforum.com/wp-content/uploads/2019/08/PEF_Skidelsky_How_to_achieve_shorter_working_hours.pdf]

[5] Peter Kuhn and Fernando Lozano, ‘The Expanding Workweek? Understanding Trends in Long Work Hours among U.S. Men, 1979-2006’. Journal of Labor Economics, 26 (2) April 2008: 311-43.

[6] Centre for Policy Studies, ‘The Costs of a Four-Day Week to the Public Sector’ [https://www.cps.org.uk/research/the-costs-of-a-four-day-week-to-the-public-sector]

[7] Roland Paulsen, 2014, ‘Empty Labor: Idleness and Workplace Resistance’. Cambridge University Press.

[8] Daron Acemoglu and David Autor, ‘Lectures in Labour Economics’ [https://economics.mit.edu/files/4689]

[9] Paul Romer, 2016, ‘The Trouble with Macroeconomics’. [paulromer.net/the-trouble-with-macro/].

**Cover image: ‘Woman Reading in a Landscape’ by Jean-Baptiste-Camille Corot.