Tag Archives: entropy

Psychological entropy increased by ineffectual leaders

Decorative image of a flowerYou might have wondered why I used ‘entropy’, and ‘psychological entropy’ in particular, as examples in my post on drowning in information a couple of weeks ago [‘We are drowning in information while starving for wisdom‘ on January 20th, 2021].  It was not random.  I spent some of the Christmas break catching up on my reading pile of interesting looking scientific papers and one on psychological entropy stimulated my thinking.  Psychological entropy is the concept that our brains are self-organising systems in a continual dialogue with the environment which leads to the emergence of a relatively small number of stable low-entropy states.  These states could be considered to be assemblies of neurons or patterns of thoughts, perhaps a mindset.  When we are presented with a new situation or problem to solve for which the current assembly or mindset is unsuitable then we start to generate new ideas by generating more and different assemblies of neurons in our brains.  Our responses become unpredictable as the level of entropy in our minds increases until we identify a new approach that deals effectively with the new situation and we add it to our list of available low-entropy stable states.  If the external environment is constantly changing then our brains are likely to be constantly churning through high entropy states which leads to anxiety and psychological stress.  Effective leaders can help us cope with changing environments by providing us with a narrative that our brains can use as a blueprint for developing the appropriate low-entropy state.  Raising psychological entropy by the right amount is conducive to creativity in the arts, science and leadership but too much leads to mental breakdown.


Hirsh JB, Mar RA, Peterson JB. Psychological entropy: A framework for understanding uncertainty-related anxiety. Psychological review. 2012 Apr;119(2):304

Handscombe RD & Patterson EA, The Entropy Vector: connecting science and business, Singapore: World Scientific Press, 2004.

We are drowning in information while starving for wisdom

Decorative image: Lake Maggiore from AngeraThe title of this post is a quote from Edward O. Wilson’s book ‘Consilience: The Unity of Knowledge‘. For example, if you search for scientific papers about “Entropy” then you will probably find more than 3.5 million. An impossible quantity for an individual to read and even when you narrow the search to those about “psychological entropy”, which is a fairly niche topic, you will still find nearly 500 papers – a challenging reading list for most people.  The analysis of the trends embedded in scientific papers has become a research activity in its own right, see for example Basurto-Flores et al 2018 on papers about entropy; however, this type of analysis seems to generate yet more information rather than wisdom.  In this context, wisdom is associated with insight based on knowledge and experience; however the quality of the experiences is important as well as the processes of self-reflection (see Nicholas Weststrate’s PhD thesis).  There are no prizes for wisdom and we appoint and promote researchers based on their publication record; hence it is unsurprising that editors of journals are swamped by thousands of manuscripts submitted for publication with more than 2 million papers published every year.  The system is out of control driven by authors building a publication list longer than their competitors for jobs, promotion and grant funding and by publishers seeking larger profits from publishing more and bigger journals.  There are so many manuscripts submitted to journals that the quality of the reviewing and editing is declining leading to both false positive and false negatives, i.e. papers being published that contain little, if any, original content or lacking sufficient evidence to support their conclusions  and highly innovative papers being rejected because they are perceived to be wrong rather than simply deviating from the current paradigm. The drop in quality and rise in quantity of papers published makes keeping up with the scientific literature both expensive and inefficient in terms of time and energy, which slows down acquisition of knowledge and leaves less time for reflection and gaining experiences that are prerequisites for wisdom. So what incentives are there for a scientist or engineer to aspire to be wise given the lack of prizes and career rewards for wisdom?  In Chinese thought wisdom is perceived as expertise in the art of living, the ability to grasp what is happening, and to adjust to the imminent future (Simandan, 2018).  All of these attributes seem to be advantageous to a career based on solving problems but you need the sagacity to realise that the rewards are indirect and often intangible.


Basurto-Flores, R., Guzmán-Vargas, L., Velasco, S., Medina, A. and Hernandez, A.C., 2018. On entropy research analysis: cross-disciplinary knowledge transfer. Scientometrics, 117(1), pp.123-139.

Simandan, D., 2018. Wisdom and foresight in Chinese thought: sensing the immediate future. Journal of Futures Studies, 22(3), pp.35-50.

Nicholas M Weststrate, The examined life: relations amoong life experience, self-reflection and wisdom, PhD Thesis, University of Toronto, 2017.

Edward O. Wilson, Consilience: the unity of knowledge, London, Little Brown and Company, 1998.

Meta-knowledge: knowledge about knowledge

As engineers, we like to draw simple diagrams of the systems that we are attempting to analyse because most of us are pictorial problem-solvers and recording the key elements of a problem in a sketch helps us to identify the important issues and select an appropriate solution procedure [see ‘Meta-representational competence’ on May 13th, 2015].  Of course, these simple representations can be misleading if we omit parameters or features that dominate the behaviour of the system; so, there is considerable skill in idealising a system so that the analysis is tractable, i.e. can be solved.  Students find it especially difficult to acquire these skills [see ‘Learning problem-solving skills‘ on October 24th, 2018] and many appear to avoid drawing a meaningful sketch even when examinations marks are allocated to it [see ‘Depressed by exams‘ on January 31st, 2018].  Of course, in thermodynamics it is complicated by the entropy of the system being reduced when we omit parameters in order to idealise the system; because with fewer parameters to describe the system there are fewer microstates in which the system can exist and, hence according to Boltzmann, the entropy will be lower [see ‘Entropy on the brain‘ on November 29th, 2017].  Perhaps this is the inverse of realising that we understand less as we know more.  In other words, as our knowledge grows it reveals to us that there is more to know and understand than we can ever hope to comprehend [see ‘Expanding universe‘ on February 7th, 2018]. Is that the second law of thermodynamics at work again, creating more disorder to counter the small amount of order achieved in your brain?

Image: Sketch made during an example class

Time at the heart of our problems

This week I started teaching thermodynamics to first year undergraduate students for the first time in twelve months.  I have had a break for a year because my course, which is only delivered once per year, was moved from first to second semester.  Although I have continued to teach postgraduate courses, it’s been like a sabbatical enforced by timetable changes.  Sadly, it’s over and I am back in the large lecture theatre in front of a couple of hundred of students – that makes it sound as if I don’t enjoy it which is not true but it does increase the intensity of the job because all of the other aspects of the role continue unabated.  So, for me time appears to accelerate as I attempt to jam more activities into a week.

Time lies at the heart of much of thermodynamics although we tend not to deal with it explicitly; however, it is implicit in our use of changes in the state of a system to understand it.  Quote Anaximander, the pre-Socratic philosopher & pupil of Thales of Miletus: ‘We understand the world by studying change, not by studying things’.  Time also lies at the centre of the tangle of problems found at the intersection of the theories of gravity, quantum mechanics and thermodynamics.  As Carlo Rovelli has remarked we are still in the dark about this tangle of problems; so, I will touch on it in my thermodynamics course but just to show students the limits of our knowledge and perhaps inspire one or two of them to think about tackling them in postgraduate studies.

Meanwhile, I plan tackle my challenges with time by slowing it down once a week with a walk in the Clwydian Hills where the landscape appears unchanging so that time stands still allowing me to relax.


Rovelli C, Seven brief lessons on physics, London, Penguin Books. 2016.

Wohllerben P, The hidden life of trees, London, William Collins, 2017.