Tag Archives: second law

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.

Sources:

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

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

An expanding universe

I attended a workshop last month at which one of the speakers showed us this graphic.  It illustrates that the volume of information available to us has been approximately doubling every year.  In 2005, the digital universe was 130 Exabytes (billions of gigabytes) and by 2020 it is expected to have grown to about 40,000 Exabytes.  The second law of thermodynamics tells us that entropy or disorder of the physical universe is always increasing; so, is this also true for the digital universe?  Claude Shannon proposed that information is negentropy, which implies that an increasing growth in information represents a decrease in entropy and this seems to contradict the second law [see my post ‘Entropy on the brain‘ on November 29th, 2017].  Perhaps the issue is the definition of information – the word comes from the Latin: informare, which means to inform or to give someone knowledge.  I suspect that much of what we view on our digital screens does not inform and is data rather than information.  Our digital screens are akin to telescopes used to view the physical universe – they let us see what’s out there, but we have to do some processing of the data in order to convert it into knowledge.  It’s that last bit that can be stressful if we don’t have some control mechanisms available to limit the amount of disorder that we ask our brains to cope with – we are back to Gadget Stress [see my post on April 9th, 2014] and Digital Detox [see my post on August 10th, 2016].

Source: Atsufumi Hirohata, Department of Electronics, University of York www-users.york.ac.uk/~ah566/lectures/adv01_introduction.pps

Image: http://japan.digitaldj.network.com/articles/9538.html

 

Entropy on the brain

It was the worst of times, it was the worst of times.  Again.  That’s the things about things.  They fall apart, always have, always will, it’s in their nature.’  They are the opening three lines of Ali Smith’s novel ‘Autumn’.  Ali Smith doesn’t mention entropy but that’s what she is describing.

My first-year lecture course has progressed from the first law of thermodynamics to the second law; and so, I have been stretching the students’ brains by talking about entropy.  It’s a favourite topic of mine but many people find it difficult.  Entropy can be described as the level of disorder present in a system or the environment.  Ludwig Boltzmann derived his famous equation, S=k ln W, which can be found on his gravestone – he died in 1906.  S is entropy, k is a constant of proportionality named after Boltzmann, and W is the number of arrangements in which a system can be arranged without changing its energy content (ln means natural logarithm).  So, the more arrangements that are possible then the larger is the entropy.

By now the neurons in your brain should be firing away nicely with a good level of synchronicity (see my post entitled ‘Digital hive mind‘ on November 30th, 2016 and ‘Is the world comprehensible?‘ on March 15th, 2017).  In other words, groups of neurons should be showing electrical activity that is in phase with other groups to form large networks.  Some scientists believe that the size of the network was indicative of the level of your consciousness.  However, scientists in Toronto led by Jose Luis Perez-Velazquez, have suggested that it is not the size of the network that is linked to consciousness but the number of ways that a particular degree of connectivity can be achieved.  This begins to sound like the entropy of your neurons.

In 1948 Claude Shannon, an American electrical engineer, stated that ‘information must be considered as a negative term in the entropy of the system; in short, information is negentropy‘. We can extend this idea to the concept that the entropy associated with information becomes lower as it is arranged, or ordered, into knowledge frameworks, e.g. laws and principles, that allow us to explain phenomena or behaviour.

Perhaps these ideas about entropy of information and neurons are connected; because when you have mastered a knowledge framework for a topic, such as the laws of thermodynamics, you need to deploy a small number of neurons to understand new information associated with that topic.  However, when you are presented with unfamiliar situations then you need to fire multiple networks of neurons and try out millions of ways of connecting them, in order to understand the unfamiliar data being supplied by your senses.

For diverse posts on entropy see: ‘Entropy in poetry‘ on June 1st, 2016; ‘Entropy management for bees and flights‘ on November 5th, 2014; and ‘More on white dwarfs and existentialism‘ on November 16th, 2016.

Sources:

Ali Smith, Autumn, Penguin Books, 2017

Consciousness is tied to ‘entropy’, say researchers, Physics World, October 16th, 2016.

Handscombe RD & Patterson EA, The Entropy Vector: Connecting Science and Business, Singapore: World Scientific Publishing, 2004.