Boltzmann’s brain

Ludwig Boltzmann developed a statistical explanation of the second law of thermodynamics by defining entropy as being proportional to the logarithm of the number ways in which we can arrange a system [see ‘Entropy on the brain‘ on November 29th 2017].  The mathematical expression of this definition is engraved on his head-stone.  The second law states that the entropy of the universe is always increasing and Boltzmann argued it implies that the universe must have been created in a very low entropy state.  Four decades earlier, in 1854, William Thomson concluded the dissipation of heat arising from the second law would lead to the ‘death’ of the universe [see ‘Cosmic heat death‘ on February 18th, 2015] while the big bang theory for the creation of the universe evolved about twenty years after Boltzmann’s death.  The probability of a very low entropy state required to bring the universe into existance is very small because it implies random fluctuations in energy and matter leading to a highly ordered state.  One analogy would be the probability of dead leaves floating on the surface of a pond arranging themselves to spell your name.  It is easy to think of fluctuations that are more likely to occur, involving smaller systems, such as one that would bring only our solar system into existence, or progressively more likely, only our planet, only the room in which you are sitting reading this blog, or only your brain.  The last would imply that everything is in your imagination and ultimately that is why Boltzmann’s argument is not widely accepted although we do not have a good explanation for the apparent low entropy state at the start of the universe.  Jean-Paul Sartre wrote in his book Nausea ‘I exist because I think…and I cannot stop myself from thinking.  At this very moment – it’s frightful – if I exist, it is because I am horrified at existing.’  Perhaps most people would find horrifying the logical extension of Boltzmann’s arguments about the start of the universe to everything only existing in our mind.  Boltzmann’s work on statistical mechanics and the second law of thermodynamics is widely accepted and support the case for him being genius; however, his work raised more questions than answers and was widely criticised during his lifetime which led to him taking his own life in 1906.


Paul Sen, Einstein’s fridge: the science of fire, ice and the universe.  London: Harper Collins, 2021.

Jean-Paul Sartre, Nausea.  London: Penguin Modern Classics, 2000.

On being a leader

Decorative photograph of a sunrise in CornwallLast week I was a part of a team delivering an intensive one-day course on leadership and ethics to a small group of technologists from industry as part of our CPD programme [see ‘Technology Leadership‘ on January 18th, 2017].  It was the first time that I had interacted face-to-face with a group of students for more than eighteen months.  We are being cautious on campus and so all of the delegates wore face masks and I wore a visor.  It can be hard to hear what people are saying in a group when they are wearing masks but we managed to have some useful discussions about ethical dilemmas [see ‘Engineers, moral compasses and society‘ on October 21st, 2015], leadership styles [see ‘Clueless on leadership style‘ on June 14th, 2016] and the meaning and development of self.  Wilfred Drath tells us that as individuals we are engaged in a life-long activity of constructing meaning with respect to our self and others.  I described some of my reflections on being and leadership in an effort to encourage the delegates to reflect on their own sense of being.  Being is a process and human being is the process of organising meaning or making sense of oneself, the world and one’s place in the world.  Robert Kegan has described the process of making sense of the world in terms of self and others using six states through which we progress from birth and childhood to adulthood. These states are: State 1 – Incorporative in which an infant sees the world as an extension of itself; State 2 – Impulsive in which an infant recognises objects as separate to itself but believes objects change with its perception of them; State 3 – Imperial in which a child recognises that others have perceptions and needs but sees its own needs as paramount.  In adulthood, there are three further states: State 4 – Interpersonal in which you recognise that you are one amongst many with whom you have relationships leading to a strong desire to conform; State 5 – Institutional where we have a sense of personal identity which leads to autonomy; and State 6 – Inter-individual, one who is capable of holding many identities and embracing paradoxes.  We never quite lose old meanings and the differences between states are subtle but important.  Research suggests that about 60% of adults are predominately in State 4, about 35% in State 5 and 1% in State 6.

Drath suggests that most management structures have been designed by and for people in State 5 who are self-possessed, self-regulating and autonomous managers that see with and not through their identity.  This leads to two major weaknesses: they find it difficult to handle interpersonal relationships objectively which leads to difficulties in being empathetic and resolving conflicts; and they are blind to the demands of their internal system of self-regulation which drives them towards workaholism and impedes their ability to be reflective [see ‘Wading in reflections‘ on October 31st, 2018].  These weaknesses hinder their progression towards becoming leaders who can maintain and enhance the processes of a collaborative community, using for example the ‘fair process’ of procedural justice described by Chan Kim and Renee Mauborgne [see ‘Advice to abbots and other leaders‘ on November 13th, 2019].  A primary reason for resisting progression from state 5 to 6 is the fear of losing effectiveness by tampering with a winning formula.  This is something I realised that I suffered from when I first started teaching leadership and was unwilling to define my successful approach [see ‘Clueless on leadership style‘ on June 14th, 2016].  I found that Goleman’s model of leadership styles allowed me to identify retrospectively the different approaches I have used in various roles.  The transition from state 5 to 6 requires relinquishing a deep personal meaning and a fundamental way of understanding self and its relationship to the world. Ultimately, these are replaced by a deeper understanding of life, a celebration of diversity, a willingness to accept that things will go wrong, and an ability to enhance the processes and share the fruits of collaborations.  These are rewarding at a personal level but also lead to your teams being happier and more successful [see ‘Leadership is like shepherding‘ on May 10th, 2017].


Drath WH, Managerial strengths and weaknesses as functions of the development of personal meaning, J. Applied Behaviorial Science, 26(4): 483-499, 1990.

Goleman D, Boyatzis R & McKee, The new leaders: transforming the art of leadership into the science of results, London: Sphere, 2002.

Goleman D, Leadership that get results, Harvard Business Review, 78(2):4-17, 2000.

Kegan R, The evolving self: problem and process in human development, Cambridge MA: Harvard University Press, 1982.

Kegan R, In over our heads: the mental demands of modern life, Cambridge MA: Harvard University Press, 1994.

Kim, W.C., Mauborgne, R., Fair process: managing in the knowledge economy, HBR, 3-11, January 2003.

Too much of a good thing?

I wrote a couple of weeks ago about ‘Our last DIMES’ meetings (on September 22nd, 2021).  They were hybrid meetings with about half the participants attending in person and the remainder on-line.  When the pandemic started we had to master the skill of conducting discussions via our laptops while sitting on our own.  Now, we are learning how to include everyone in a discussion when only half of the participants are in the physical room.  One of our first steps was to re-equip our meeting rooms with higher quality video conferencing facilities so that we can see and hear one another more clearly.  Unfortunately, our new equipment revealed the poor quality of the video clips we have produced during the DIMES project.  Nevertheless, if you have never been present during a wing-bend test or a fatigue test on a large composite panel then you might find these clips interesting (see also the video of ‘Noisy progressive failure of a composite panel’ on June 30th 2021).  We also produced an introductory video for the DIMES project which was to be first in a series of video shorts but the pandemic intervened and we have never been in the same place as our camera crew so we have not made anymore.  Maybe that’s a good thing because 500 hours of video are uploaded every minute to YouTube so you will not have time to watch our DIMES videos 😉.

For more short videos from our earlier projects see ‘Archive video footage from EU projects’ on June 5th, 2019.

The University of Liverpool is the coordinator of the DIMES project and the other partners are Empa, Dantec Dynamics GmbH and Strain Solutions LtdAirbus is the topic manager on behalf of the Clean Sky 2 Joint Undertaking.

Logos of Clean Sky 2 and EUThe DIMES project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 820951.


The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.

If you don’t succeed, try and try again…

Photograph of S-shaped plateYou would not think it was difficult to build a thin flat metallic plate using a digital description of the plate and a Laser Powder Bed Fusion (L-PBF) machine which can build complex components, such as hip prostheses.  But it is.  As we have discovered since we started our research project on the thermoacoustic response of additively manufactured parts (see ‘Slow start to an exciting new project on thermoacoustic response of AM metals‘ on September 9th, 2020).  L-PBF involves using a laser beam to melt selected regions of a thin layer of metal powder spread over a flat bed.  The selected regions represent a cross-section of the desired three-dimensional component and repeating the process for each successive cross-section results in the additive building of the component as each layer solidifies.  And there in those last four words lies the problem because ‘as each layer solidifies’ the temperature distribution between the layers causes different levels of thermal expansion that results in strains being locked into our thin plates.  Our plates are too thin to build with their plane surfaces horizontal or perpendicular to the laser beam so instead we build them with their plane surface parallel to the laser beam, or vertical like a street sign.  In our early attempts, the residual stresses induced by the locked-in strains caused the plate to buckle into an S-shape before it was complete (see image).  We solved this problem by building buttresses at the edges of the plate.  However, when we remove the buttresses and detach the plate from the build platform, it buckles into a dome-shape.  Actually, you can press the centre of the plate and make it snap back and forth noisily.  While we are making progress in understanding the mechanisms at work, we have some way to go before we can confidently produce flat plates using additive manufacturing that we can use in comparisons with our earlier work on the performance of conventionally, or subtractively, manufactured plates subject to the thermoacoustic loading experienced by the skin of a hypersonic vehicle [see ‘Potential dynamic buckling in hypersonic vehicle skin‘ on July 1st 2020) or the containment walls in a fusion reactor.  Sometimes research is painfully slow but no one ever talks about it.  Maybe because we quickly forget the painful parts once we have a successful outcome to brag about. But it is often precisely the painful repetitions of “try and try again” that allow us to reach the bragging stage of a successful outcome.

The research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK (see Grants on the Web).


Silva AS, Sebastian CM, Lambros J and Patterson EA, 2019. High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations. J. Sound & Vibration, 443, pp.397-410.

Magana-Carranza R, Sutcliffe CJ, Patterson EA, 2021, The effect of processing parameters and material properties on residual forces induced in Laser Powder Bed Fusion (L-PBF). Additive Manufacturing. 46:102192