Friday, 19 August 2016

Ross Ashby and Educational Research

I'm very pleased to get a paper on Ross Ashby's work accepted for this year's Society for Research in Higher Education conference (see http://www.srhe.ac.uk/conference2016/) in collaboration with colleagues at the University of Liverpool. I always enjoy the SRHE conference and it's a good scholarly place to get Ashby onto the educational research agenda.

The majority of pedagogical theories have their roots in cybernetics or General Systems Theory, from Piaget and Vygotsky onwards. The provenance of the ideas is forgotten, and with it, opportunities to develop and critique theory by examining its origins is also lost. Piaget is covered in educational courses everywhere, but nowhere is there a critical engagement with Bertalanffy and General Systems Theory which inspired him (apart from a few like Maggie Boden or Ernst von Glaserfeld who make the cybernetic connection explicit). This is important because the epistemological and methodological territory is obscured - and the deep work is to be done in uncovering it. I was interested to discover that this is perhaps starting to change: Margaret Archer, who's contributed a lot to the sociology of education, has recently been discussing Ross Ashby, and I've been to talking to Mark Carrigan (who's currently completing a book of collected essays by Archer) about the extent of her understanding. There's a discussion to be had here.

So here's my contribution for the SRHE. If Archer misrepresents Ashby in criticising his concept of "variety", then it may be because only a portion of his work is in the wider public discourse. In fact, Ashby was a pioneer of cybernetics who developed his own epistemology of what a cybernetic science was. This is what I'm interested in. The picture below is from Ashby's notebooks (in the British Library, but available online at http://www.rossashby.info/journal/page/6741.html) where he was exploring his idea of Constraint Analysis, or 'cylindrance' - a concept which I think is critical to understanding education and educational research methodology.


Intersubjectivity and Teaching: Analysing constraint in online and face-to-face engagement through the cybernetic lens of Ross Ashby

Abstract
Ross Ashby’s work is little known in education, although his concepts of Double Loop learning, Ultrastability, Requisite Variety and Self-organisation have had a profound effect on educational theory. We focus on his work on Constraint Analysis which, we argue, has application in understanding educational relations, addressing concerns arising from recent critique around sociomateriality, critical realist educational theory, and assessment practices. We provide an overview of these techniques and demonstrate their applicability through case-studies. We argue that Ashby’s cybernetic approach occupies a unique position by opposing analysis of causal mechanisms, and instead articulating a dynamics of constraint. Arguing that “the cyberneticist observes what might have happened but didn’t” he deployed Shannon’s Information Theory, which he saw as analogous to his own relational theories, developing sophisticated techniques for measuring relations. In conclusion, we argue that intersubjective relations in education become available for analysis - with implications for new approaches to assessment.

The analysis of relationality and intersubjectivity in education underlies recent critiques concerning the objectification of learning (Ashwin, 2015), the technocratisation of education (Barnett, 2013), sociomaterial approaches to online education (Gourlay and Oliver, 2013) and critical realist accounts of education which draw attention to absence and constraint (Kahn, 2015; Donati and Archer, 2015). Our aim in this paper is to draw on an older tradition of examining relations through the analytical techniques of “Constraint analysis” as they were developed by cybernetic pioneer Ross Ashby (Ashby, 1965). Ashby’s Constraint analysis presents a negative epistemology which, we argue, when applied to education is necessarily intersubjective.

A psychiatrist who became a seminal figure in cybernetics, Ashby’s ideas of requisite variety, ultrastability, double-loop learning and self-organisation have become profoundly influential in education although the provenance of the concepts has become obscured.  In distinguishing causation and constraint, he argued that cybernetics was a science of constraint where “the cyberneticist observes what might have happened but did not”. Modelling was a tool for exploring ideal logical possibilities; experiment gave rise to knowledge by revealing the constraints of nature that bore upon logical possibility. It is an approach which stands in contrast to better-known realist methodologies which focus on identifying causal mechanisms (Pawson and Tilley, 2002). At its heart was an attempt to understand learning as process whereby a self-organising system could become self-directing.
Beyond his epistemology, Ashby asserted an approach to measuring constraint drawn from Shannon’s Information Theory (1948). He saw Shannon’s work and his own as expressing the same basic principle: for one system to control another required its complexity to be at least as great as the system to be controlled. Often this balance requires constraining complex systems – for example, the teacher-class relationship is constrained by the rights and obligations of the classroom. Shannon explored how constraints operate within everyday communication in grammars: the general term he used to describe this patterning was ‘redundancy’ – latent rules which generate superfluous information to aid communication. Fundamentally, Ashby suggested that the background of communication – the redundancy – was more important than the foreground. So how might we analyse the background of education?

Categories of Constraint and their measurement
There are clearly many constraints bearing upon teachers and learners. Beyond the personal constraints which form the hinterland of every individual (for example, personal histories, attachments, values, social class, etc), there are specific constraints which learners are subject to, including:
  • The constraints of a course structure, the medium through which it operates, the timetable, the temporal dimension of lectures, assessments, discussions and presentations.
  • The constraints of the social or professional environment bearing upon learners - particularly as they relate to the activities of the course.
Equally, for teachers there are a different set of constraints including:
  • The institutional context of education – the need to engage students, the need to meet quality requirements
  • The constraints of scholarly discourse and academic ambition – the need to publish, maintain political position within academic environments and academic communities
As with a grammar, there are discernible patterns of behaviour which may be taken as indicative of particular constraints: from a learner’s lack of engagement or plagiarised assignments, a teacher’s favourite pedagogical tricks, through to verbosity (or not) in online forums, or the asking of powerful questions. What do these patterns of behaviour – by both teachers and learners – tell us about the interactions between different kinds of constraint? This question forms the basis of an analysis of a number of case studies from online and face-to-face education.

Constraint, Uncertainty and Information Theory: Some examples
We present three examples from medical education with a combination of purely online engagement, blended and face-to-face courses. The analysis provides a simple way of characterising the differences between online and face-to-face interactions by considering the dimensions of constraint operating in each case. For example, in the online case, data is available concerning the patterns of student engagement as set against the formal constraints of the course (lectures, assessments, timetable). Analysis of this data reveals a “counterpoint” between different kinds of redundancy: for example, repeated themes that occur in forum discussions, particular patterns of exchange between individuals, the asking of questions, or the coordination of understanding about assessment requirements or broader rules of the course.

Whilst face-to-face engagement is less data-rich, some constraints remain similar (for example, timetable and assessments), whilst others are identifiable as part of what Alfred Schutz calls the “pure we-relation” of face-to-face engagement (Schutz, 1960) – for example, the shared passing of time through being in lectures together. There are also dynamics of transition as shifts occur between face-to-face situations with their multi-layered constraints of embodied co-presence, and online situations with more limited sets of constraints surrounding online utterances. In each case, these analysable constraints combine with latent issues of individual background, social and professional context. We suggest that some indicators of these latent issues can be determined from learner utterances and their expression of values. In each case, the constraints applied by teachers is considered, from the organisation of learning activities, through to the explanation of assessment criteria. We explore how the analysis can be broadened to embrace the constraints bearing upon the teacher.

Conclusions
Ashby’s techniques provide a range of analytical tools which can be used to cut through confusion which can become exacerbated through attempts to identify causal mechanisms or other forms of ‘variables-based sociology’ (Smith, 2010). By focusing on the background of education, attention is placed on relations, not individuals. By seeing differences between educational media as relational differences, we can explore the ways in which relations might be managed according to the constraints exercised by agents within an educational medium, and make judgements about effective practices which fluctuate constraints in educational processes. Online media afford very different constraints than do face-to-face media although as yet a coherent and empirically investigable paradigm for understanding teaching and learning across any medium does not exist. Enticingly, since Ashby’s constraint analysis is relational, exploring how it might overcome objectivist assessment strategies presents an intriguing challenge for future work.

References
Ashby, W. R.(1965) “Measuring the Internal Informational Exchange in a System.” Cybernetica 1, no. 1 Ashby, W.R (1956) An Introduction to Cybernetics
Ashwin, P (2015) Going global: Opportunities and challenges for HE researchers, available online at https://srheblog.com/2015/10/19/going-global-opportunities-and-challenges-for-he-researchers/
Barnett, R (2013) Imagining the University, London:Routledge
Donati, P; Archer, M (2015) The Relational Subject Cambridge: CUP
Gourlay, L. & Oliver, M. (2013) ‘Beyond ‘the social’: digital literacies as sociomaterial practice’, in Literacy in the Digital University: Critical Perspectives on Learning, Scholarship & Technology, eds R. Goodfellow & M. Lea, Routledge, London, pp. 79–94.
Kahn, P (2015) Critical perspectives on student engagement as ‘what students do’, Presentation to 2015 SRHE conference, available online at https://www.srhe.ac.uk/conference2015/abstracts/0138.pdf
Pawson, R; Tilley, N (2002) Realistic Evaluation New Delhi:Sage
Schutz, A (1960) Phenomenology of the Social World Northwestern University Press
Shannon, C; Weaver, W (1948) A Mathematical Theory of Communication University of Illinois Press
Smith, C (2010) What is a person? Rethinking Humanity, Social Life, and the Moral Good from the Person Up Chicago: University of Chicago Press


Thursday, 18 August 2016

Been successful with your A-levels? What Universities ought to offer you but don't....

There are a number of problems facing bright A-level students. First of all, education is horrendously expensive. It's possible that the brightest students will have the most powerful crystal balls to look into the future and think what a debt of over £60k means when they are trying pay absurd mortgages, child care which is more that half the average salary, ever increasing transport costs, all while the student load company will have the right to ramp-up interest rates with little anyone can do about it. All this against an economic backdrop of stagnant wages, employment insecurity and real difficulties in career progression.

Secondly, an undergraduate degree isn't enough. Undergraduate education has become an expensive extension of schooling and higher learning is on the retreat - both among the student body and amongst the institutional management. The business model of Universities has become about printing certificates in the same way that the business model of the pre-reformation Catholic church was printing indulgences. With 10% participation, a degree certificate marked you out. Now almost everyone's (ok, about 50%) got one, you'll need something else - masters? PhD? How much more?

So here's what you should do. It does not cost £9000 to teach an undergraduate student for a year, and part of what makes up the cost are institutional overheads - those grand buildings, the library, extortionate fees for publishers, the administration. That's not to mention the profiteering of property developers in turning cities into bijou student accommodations (and some of these developers are Universities - like this one: http://www.manchestereveningnews.co.uk/news/greater-manchester-news/revealed-how-new-40m-bolton-8636291) So find an option which charges the real cost. Online ought to be considerably cheaper (why isn't it?). £9000 could buy you a couple of personal tutors and someone to write your assignments for you (*joke*). But, you might worry, the important thing about university is the social aspect - going out and meeting people. Academics go out and meet people at conferences - they present papers, they increase their status by presenting their ideas. Why can't undergraduate students do this too? There are great opportunities like http://www.bcur.org/http://www.universitas21.com/article/students/details/4/undergraduate-research-conferencehttp://www.icurportal.com/https://utscaps.wordpress.com/conferences/conference/. If you attended 5 international conferences a year, the total cost would be far less that £9000. Companies like Expedia or AirBnB could also participate in the making of packages for nomadic undergraduates.

The really important thing about education is status. A degree used to be a status symbol. Now it often invites the question "why didn't you use it? What are you working in Aldi?". But to be published, to present at conferences, to collaborate in international teams, to be entrepreneurial - all of these things increase status too. With a really cheap way of accrediting learning episodes into a degree, then your graduation from your own bespoke online degree will give you far more than all those hours stuck in deathly lecture theatres. You will have travelled. You will have published. You will have networked. And you will be employable.

Universities used to be the gatekeepers to powerful technologies. Now these technologies are everywhere and they are very cheap. You may learn more from a Raspberry Pi or an Arduino than you would have ever learnt in a computer lab. It's not difficult to hack together kit which would otherwise cost thousands (I love this vital signs kit for the Raspberry Pi - https://www.cooking-hacks.com/documentation/tutorials/ehealth-biometric-sensor-platform-arduino-raspberry-pi-medical.

Then, you might think, "what course do I study?" It's a question which is framed by the traditional university - and it's the wrong question. A better question is "What assessment framework do I want?" The best answer is "the one that gives you the greatest flexibility to do the things you are interested in - and change your mind". The worst answer is "the one that makes you do loads of stuff you are not interested in." It may be that you want to work or do an apprenticeship, and study your work or your apprenticeship. Why not? Or you want to write and publish poetry, and study your own journey. Again, why not?

Finally, a question for the more adventurous... "Do I need an institution involved in this at all?". That's an important question. The institutional degree works because it is trusted. If some other mechanism of establishing trust is available - like, for example, peer recognition, or perhaps in the future, Blockchain - then no, you don't need an institution - you can enhance your status with a portfolio of activities and be assured of that this will be trusted in the same way as a degree.

Whatever you choose, and whatever those in power tell you, £60k is a lot of money, and in most cases, it will not deliver flexibility, publication, status enhancement, higher qualifications, travel, entrepreneurship, international networks, or technological experimentation. Universities are too stiff to change. They have become rather like the Maginot line: too busy defending themselves from what they see as the most likely threat, only to miss the fact that the world and its students may eventually choose to bypass them.

Friday, 12 August 2016

Jupyter Notebook as a Peer-to-Peer Learning Environment?

Tony Hirst's recent exploration of the properties of Jupyter Notebooks (see his blog https://blog.ouseful.info/) got me experimenting with Jupyter and thinking about its possibilities. I've not really taken much notice of Python until fairly recently (playing with Raspberry Pi is a great introduction), and so the IPython thing (which is the precursor to Jupyter) passed me by. But clearly a lot has been happening - and Jupyter is a very interesting environment: see http://jupyter.org/

The Jupyter notebook is basically a programming environment which is a little bit like the mathematical software 'workbooks' which have become the common interface for users of Maple and Mathematica. They present interactive cells into which code can be typed and executed inline, where new cells can be added to create a melange of different aspects of exploratory programming. Into these cells can be inserted coding from a wide variety of languages: python (obviously) but also R, javascript, html (markdown), ruby, and so on. The cells can be re-represented using a presentation tool which works a bit like an interactive Powerpoint. It's different and impressive: I found the editing facilities excellent - great auto-formatting for most language which makes it a fantastic environment for rapid PHP and Javascript development. But its interactive presentation features make it a potentially powerful e-learning platform.

Jupyter (or IPython) notebooks can be shared - so whole exploratory interactive instances can be shared between peers in a class. The notebook is a very rich kind of learning package, which can be experimented with, extended, forked, etc. The extensions are particularly interesting, because each notebook can run on an individual's machine, there are no problems with permissions to install new tools. This overcomes the greatest obstacle that now faces e-learning: the centrally-controlled VLE will no longer let us do anything because the institutional computer service department locks it down. Overcoming this was one of the drivers behind the Personal Learning Environment, and was a fundamental part of the thinking which led to the creation of the only true peer-to-peer VLE, Colloquia (http://colloquia.net)

A few years ago it was fashionable to advocate that institutions abandon their VLEs in the interests of learners. I was sceptical that the time wasn't right to do this given that there were still significant issues with staff engagement with technology. That situation has significantly improved, and now I think we should abandon the VLE. Institutions must find a different way of delivering learning because with their current centralised systems, they are impeding innovation. There are some fascinating experiments going on with Jupyter which could make it a proper peer-to-peer learning system. I was particularly interested in the attempt to integrate the block-chain inspired Interplanetary File System (IPFS) into Jupyter (see https://github.com/ipfs/apps/issues/29) - this could be very exciting.

For all working in e-learning today, there are some fundamental principles we should be reminding ourselves of.

  1. Learners and teachers should be in control of the tools they use for learning
  2. They should be able to install, remove, amend any tool which they find useful without the say so of central IT departments
  3. IT departments have found themselves in the unfortunate position as gatekeepers to student data, and consequently fearful of data loss and legal action - this situation is unsustainable - Universities are not Facebook, and not even Ashley Madisson (!) - they will eventually be overwhelmed with the complexity of protecting data.
  4. Data should follow the student - it is their property, not an institution's.
  5. The coordination of learning is not the same as coordinating access to systems (but these have become confused): it is an intersubjective process mediated through communication of all kinds (online, face-to-face, etc) 
  6. Educational Personalisation is simply reorganisation so that education remains viable and sustainable.
Jupyter notebooks, or something like them, may not be the complete answer - but it seems to me a real advance on what we have become used to in educational technology. We now need some imagination to make it really inspiring, and able to do things that a central system could never do.

Sunday, 7 August 2016

E-learning and the Vita Activa/Vita Contemplativa distinction

The distinction between the Active life and the Contemplative life goes back to Aristotle and later the scholastic philosophy of Augustine and Aquinas. It is through the 20th century interpretation of Hannah Arendt that it has become more widely-known. A few years ago, when considering the potential impact of Personal Learning Environments, I wrote a paper where I drew on Arendt's arguments about the priority of the 'active life' (Aquinas, like most scholastics, argued for contemplation) and I considered whether social media participation was 'active' in the way she meant. I upheld a (perhaps hopeful) view that active engagement with online tools could become a kind of nexus between action and contemplation. Whilst I think the issue is critical to understanding the phenomenology of social media, I think it is now clear that my hope for a balance between action and contemplation was misplaced. As so many religious leaders try to remind us, contemplation is disappearing from our lives as we are increasingly sucked into a surrogate digital world which is fundamentally driven by money. The departure from contemplation is not new - societies have done this periodically over history. The consequences are always disastrous.

There is a central question about what 'agency' means in the context of Arendt's 'Vita activa'. Would she recognise what her mentor Heidegger would have seen as the 'fallen' (verfallen) behaviour not only with social media tools, but academic publication, bibliometrics and analytics as agency? I doubt it. The whole point about Arendt's agency was that it was thoughtful: she was thinking about the agency of Marx, of political revolutionaries, protest, sacrifice for a cause. The fallen 'unthinking' behaviour of social media is no different from the fallen, unthinking behaviour of all the "Eichmanns" that she saw surrounding her - not just Eichmann in the dock, but the Eichmanns in the witness stand. The confusing way in which the word 'agency' gets used today emphasises the point: Actor Network Theorists will argue, for example, that computers have 'agency'. But for Arendt, agency was moral: it goes to heart of the human condition, and it comes from the heart.

Universities have become very active places. Thinking is surprisingly rare - usually occluded by personal ambitions, ego and the pursuit of academic celebrity status. Universities used to be places where society did its thinking. If they no longer do that, where do societies now think? There is another more disturbing question. Universities have stopped thinking because political agendas have determined that they ought to stop thinking and do 'useful' things instead - like innovation (despite the fact that universities have often been obstructive to innovators who end up having to leave in order to succeed!).

In whose interests is it that society ceases to think? Perhaps Google, Facebook or Twitter might not complain too much - although they themselves were the product of thinking at one point. But conservatism, by its nature, is threatened by new thinking and new kinds of action. If Universities wish to rescue thinking (which they should), they should turn on the forces of their own conservatism. 

Thursday, 4 August 2016

#Elearning perspectives: Documents, Transactions and the question about learning

One of the critical issues which has emerged from the debate about #blockchain is the distinction between documents and transactions. Blockchain technology is a technology for storing transactions - something for which MIT have recently released some software for credentialing (see https://medium.com/mit-media-lab/what-we-learned-from-designing-an-academic-certificates-system-on-the-blockchain-34ba5874f196#.t3r9eiimo). Transactions themselves are effectively references to documents, or hashes of documents. This has led to some spin-offs from blockchain to explore ways in which the web - which is effectively a set of relations between servers and filesystems - might be instead a list of hashed documents. This is the approach of IPFS (see http://ipfs.io) - which offers a serverless way of addressing and storing documents.

The distinction between transactions and documents has also become more prominent with the rising importance of analytics. Learning analytics counts transactions on a web server (for example, one running a VLE). It can also count words in the documents which comprise those transactions - for example, the words in an essay. Various forms of combinatoric algorithms (like, for example, Shannon entropy calculations) produce automatically-generated descriptions of user activity. The level of sophistication of the algorithms and the amount of data to process has led to a belief that such automatic analysis can identify causal explanations for things that happen. The analysis combines documents with transactions where sometimes there are many transactions and very short documents (for example, forum posts - on social media, Twitter), and other times there are very few transactions and a very long document (an essay).

In education the production of a long document (on time) with few transactions is unreliable. Students who have few transactions with the institution - whether it is not attending lectures (and signing the register) or not logging on to the VLE - are unlikely to produce the 3000 word essay assignment at the end of it. A lack of transaction data is usually a sign that the student has dropped off the course. Few transactions in most walks of life is usually a sign of a system about a break down - whether it is a company or a marriage. Some sociologists (e.g. Coase's New Institutionalism, Luhmann's social systems theory) have gone so far as to say that social institutions only exist because of the transactions that are made with them. If the transactions stop, the institution dies. 

On social media, the drive of the company strategies of Facebook, Twitter, Google and Microsoft have been to increase the number of transactions users have with the services. If fewer people tweet, or send fewer tweets, Twitter has less data to exploit, whilst it is threatened by the possibility of a shrinking body of users to keep it going. So it has to find ways of getting people to interact in small transactions more: 'likes', 'retweets', 'pokes' and other minimal transactions are one strategy. Much more important however is the exploitation of mobile technology. Users staring at their screens endlessly on trains or even at the dinner table are sending transactions regularly - even when they aren't consciously aware of it: simply scrolling down the timeline now returns data to the service operators: these are tiny transactions which can be aggregated and analysed. 

The latest technologies only increase the trend of more rapid transactions and more detailed documents contained in those transactions. Facebook's acquisition of Oculus Rift has enabled it to potentially exploit every head (and maybe every eyeball) movement at users immerse themselves in virtual worlds. At the same time, the rise of Bots is also focused on increasing transactions through the creation of conversation agents which are designed to prompt responses from users (these too are documents). Whilst most of the world will be fascinated by the Bot's 'intelligence', the whole purpose of the Bot from the service provider's point of view is to maintain engagement: it's not a Turing test where an end user cannot distinguish a human from a machine; it's a game aimed at maintaining the engagement of the user. Finally, games themselves are also transaction generating.

When it comes to education, there has also been a rise in importance of mobile, and this too has been focused on increasing the regularity of transactions. Mobile-based e-portfolio systems for example, have tools for capturing information in as lightweight a way as possible. Games-based learning, when done well, has also had this effect. But one of the critical things is the importance and potential of the documents which are produced by machines in response to user input. 

The process of engagement and increasing transactions depends on the machine producing a document which constrains user behaviour in such a way that they continue to submit transactions. Seen this way, Bots are automatic document-producing machines. In fact, so is Google search: a user query is a short document, to which the machine responds with another document. 

If teaching and learning is seen as a 'viable system' between a teacher and their learners, the principal way in which this system is viable can be measured in the transactions which are exchanged. If the teacher wants to increase the number of transactions (and therefore make the relationship more viable) they need to find ways in which learner interactions are 'rewarded' with documents which constrain future behaviours to continue to submit transactions. 

Recently, I've been experimenting with automatically-produced documents to do just this. Effectively these are analytic reports which are sent to learners summarising their recent activity. The reports are all sent out at the same time, so learners tend to talk about them when they arrive (this is using time as an additional constraint). The reports indicate in a simple way where learners might need to increase their activity - and very often, it seems, this gentle 'nudge' has the effect of changing their behaviour (reported in the following week's report). There are many kinds of automatically-produced documents which are possible - many kinds of creative analysis which can serve to get learners talking to each other. And there are reports that can be created of learners' interactions with each other in the light of the reports. 

The interactive web confuses the distinction between documents and transactions: a dashboard, for example, is a document which invites transactions to produce a new variety of document. Yet the distinction between the two is simple: documents constrain transactions; transactions produce documents. E-learning is about manipulating these constraints in such a way as to encourage conversation between learners and teachers. 

Thursday, 28 July 2016

Learning is like...

Learning is like:
The growth of a plant
The movement of the eye over a painting
Wandering through the streets of an unfamiliar city
The development of a piece of music
Improvisation
Falling in love
Doodling
Falling out of love
Reading
Praying
An evolving ecosystem
The sensation of taste
a caress
Death
Silence
Dreaming
Relationships
Movement
War
Heat
A dying ecosystem
Sex
A drama
To say "it is like" is to invite a description. Learning is like many descriptions - put together - like poetry (which is another one).

The question is not what learning is like. It is what it means to be like anything else. 

We could talk about metaphors. A metaphor is a description, after all. But playing a game of identifying metaphors is like dividing "Der Ring Des Nibelungen" into its constituent Leitmotifs. The music gets lost.

Much better, I think, to ask about the dynamics of multiple descriptions. That goes to the heart of the question about learning and teaching.

Thursday, 21 July 2016

Deep perspectives on Education: Time, Entropy and Intersubjectivity

For physicists, entropy and time are concepts which are tied-up together. Eddington's "arrow of time" is most generally seen as an increase in entropy (see https://en.wikipedia.org/wiki/Entropy_(arrow_of_time))

Boltzmann's Entropy however, is a measure of uncertainty about the state matter at a particular location. It is statistically expressed in his famous probabilistic equation. Basically, beneath all the interpretations laid upon it, it is counting.

With Shannon's appropriation of Boltzmann's equation, the entropy measure could be used for counting the surprisal in communication: in the way that we might look for disorder among atoms, we can look for (and count) disorder among symbols. One of the key features of Shannon's approach is the idea of the 'selection' of symbols, where the greater the number of symbols selected is an index of the communicating system's complexity, and the capacity requirements of the communicating channel (this was Shannon's practical purpose in developing his theory).

When we come to talk about human communication, selection at the level of symbols invites a more sophisticated idea of selection at the level of meaning. In Sociology, Niklas Luhmann developed this idea into an elaborate and complex theory of society. From here, entropy might be seen to provide the root of a theory of meaning. More profoundly, might we count to reveal meaning?

We need to take a step back. What was assumed in the physicist's conception of time in the first place? Phenomenologists would question the initial assumption about entropy because it failed to account for the perceiving subject's experience of entropy and time. It would also question the emphasis (so strong within physics) of the individual perceiving subject, when physical observations and scientific discoveries are not just individual, but social and intersubjective. These phenomenological issues were explored by Husserl, Bergson, Schutz, Merleau-Ponty and Heidegger (to name a few). It's worth noting that Bergson had an intriguing but rather unfruitful meeting with Einstein in the 1922 (see this - which sees their dispute as partly political -  https://muse.jhu.edu/article/193244/pdf) which led to extended debate.

I find Schutz's account of time interesting because it sees time emergent not from the experience of emerging physical disorder, but from the intersubjective experience between human beings: time always flows in a world of others. What may be important here is that meaning and mattering become prior to information. Also important is that those activities we do together - learning, working, playing. Schutz gives an account of what these things might be which I find far richer that the formalism of information theorists because it suggests that educational practice is the most important thing that human beings need to understand properly. Schutz is also critical to the entropy debate because his work was of seminal importance to Talcott Parsons, whose work on "double contingency" was fundamental to the development of Luhmann's theory.

Is there a middle ground between the Einstein, Bergson, Schutz, Luhmann viewpoint? Well, entropy is counting. Counting produces descriptions. Descriptions are communicated between people. Communication entails a continual intersubjective apprehension of time. Is it this intersubjective apprehension of time that we call 'education'?