Friday, August 9, 2013

Is there an optimal periodic table and some bigger questions in the philosophy of science.

Eric Scerri,
Department of Chemistry & Biochemistry, UCLA.

Until recently I believed that there was such a thing as an optimal periodic table and that it was the business of philosophers of chemistry to try to discover what this form might be.  More recently a couple of developments have caused me to change my mind in a rather radical way.  
         Before discussing this change of mind let me backtrack a little.  In my 2007 book on the periodic table, I not only claimed that there was one best possible form but also suggested that it consisted of the left-step or Janet form of the periodic table which places helium among the alkaline earth elements (Scerri, 2007). 
         In my more recent “A Very Short Introduction to the Periodic Table”, I modified my view, although still maintaining that an optimal form was a viable proposition.  In this book I wrote that it was not yet possible to decide between two candidates for the optimal table (Scerri, 2011).  In addition to the very elegant left-step table I proposed a new form which places hydrogen at the top of the halogen group in order to introduce a new atomic number triad consisting of H(1), F(9) and Cl(17).  Given that perfect atomic number triads crop up in about half of all possible vertical groups of three elements in the periodic table it seems reasonable to assume that the placement of a troublesome element like hydrogen can be settled by moving it in order to create a new triad rather than keeping it at the top of the alkali metals where it does not form a triad.    
         Returning to my first book, one of the things I did there was to highlight some of  ‘little people’ in the history of science, by which I mean intermediate and lesser known personalities whose work was nevertheless very important in advancing our knowledge of chemistry and physics.  I am referring to the likes of Anton Van den Broek, a Dutch economist who first conceived of the idea of an atomic number for each element, which became the basis for Henry Moseley’s famous experiments on this subject. 
         Another case is the British physicist Edmund Stoner, who was the first to apply the newly discovered third quantum number to the assignment of electronic configurations of atoms. This was soon adopted and taken further by the enormously more famous Wolfgang Pauli, who introduced yet a fourth quantum number that eventually became associated with electron spin.    
         My third, and most recent book published by OUP, is called “A Tale of Seven Elements”, in which I delve into the way that the last seven elements were discovered among the original 1-92 of the old periodic table (Scerri, 2013).  But why precisely seven? 
         This is because after Moseley had consolidated the concept of atomic number it became clear that just seven elements remained to be discovered.  But this fact does not seem to have lessened the number of priority disputes as well as claims and counter claims that were made during these years which roughly speaking span the two World Wars. 
         I also tried to think about the causes of priority disputes among scientists and whether there is any underlying significance to this phenomenon.  I suggested that, whatever the causes might be, the important thing is that science as a whole makes progress while the fact that individual scientists involved in priority disputes might have their egos bruised is of secondary importance.  I began to think about science as one unified whole, perhaps as a kind of living organism analogous to James Lovelock’s Gaia which evolves while adapting to its environment.  In the case of science as a whole the environment would be the data that needs explaining and even the elements that have yet to be discovered.  This process I suggest is a gradual one, rather than one which experiences sudden revolutions in the way that Thomas Kuhn famously proposed (Kuhn, 1962). 
         The intermediate figures and lesser known little people matter just as much as their better known counterparts like Bohr, Einstein and Schrodinger.  Science is a seamless evolving process and this is better appreciated by including the important intermediate steps that the little people provided. 
         Appreciating the nature of science requires a view from afar which focuses on the overall evolution of ideas, experiments and even entities like elements rather than on individual famous scientists or their theories.  Moreover, theories should not be considered as being ‘right’ or ‘wrong’ just as the various steps that occur in the biological evolution of a species are not right or wrong but simply vary in terms of their adaptation to their environment. 
         According to this view science does not develop towards some truth that lies beckoning ahead of us, but it just develops in order to better cope with the environment or situation that science finds itself in at any particular epoch.  All of this amounts to a rather pluralistic view of science in which we consider and value the work of the little people who may only have made transitional contributions, or even some that may appear to have been wrong-headed ideas. 
         At the same time as these ideas were starting to occur to me I traveled to Uruguay and Argentina to give some lectures at a couple of international conferences.  I met up with an old friend and colleague, Hasok Chang, who is now at the University of Cambridge and who gave an interesting lecture in which he argued in favor of pluralism in science.  Chang stressed the need to hold alternative approaches to one and the same scientific problem at any given time.  He criticized the monist view that it is important to weed out all but one viable approach or theory in any given situation.  He too does not believe that there is one objective truth.  Chang believes that the concept of phlogiston should not have been abandoned as rapidly as it was at the time of Lavoisier’s chemical revolution (Chang, 2012).  Coming to the contemporary situation, he does not believe that Steven Weinberg’s “dream of a final theory” is ever going to materialize.
           Rather than dwelling too much on Chang’s views let me get back to the periodic table with which this blog began.  What do all these ideas imply about the notion of an optimal periodic table that I have been so keen to support in the past?  I now think that I was wrong to expect there to be one best table, as though there is one Platonic form that science is striving towards. 
            Rather than just pointing out the pros and cons of a couple of candidate forms of the periodic table, as I did in my VSI, I now want to go on record as renouncing altogether the idea of an optimal periodic table.  My growing view of the gradual evolution of science and the fact that it involves the whole scientific community, whether competing individual scientists realize this or not, is telling me that science does not progress towards an external ‘truth’. 
         I no longer see science as being teleological and again this reflects its essentially biological nature, since evolutionary biology we have long realized does not have a telos or end point.  Developments in science, including the development of the periodic table grows from within while looking at past science and not at some magical external goal.  And here I believe that Kuhn had it right, in his influential book, by insisting that scientific development is ‘pushed from behind’ rather than having a teleological nature (Kuhn, 1962). 
         This will not stop me from debating the relative virtues of various forms of the periodic table, nor will it blunt my critical faculties when confronted with what I consider to be an inconsistent system.  But I will finally drop the monistic insistence on there being one best periodic table. 

References / links

Chang, 2012, Is water really H2O? Dordrecht, Berlin, Springer. 

Kuhn, 1962, The Structure of Scientific Revolutions, Chicago University Press.

Scerri, 2007, The Periodic Table, Its Story and Its Significance, New York, OUP.

Scerri, 2011, A Very Short Introduction to the Periodic Table, Oxford, OUP.

Scerri, 2013, A Tale of Seven Elements, New York, OUP.


  1. I disagree. There is an optimal periodic table based upon valence and it is called The Rota Period: . There were more than 20,000 installs of the iPhone App in its first year:

  2. If this table is indeed a good candidate it should be published in a peer reviewed journal should it not?

    eric scerri

  3. While I loves me own PT tetrahedra, I have to agree wholeheartedly with Eric. Limitations of perception on the one hand and methods of representation on the other in 4D spacetime preclude this. Maybe the problem lies even deeper- if something can be a wave and/or a particle, or if conjugate variables disallow simultaneous readings, perhaps something similar pertains to the PT. Grow up. Live with it. Luckily the math behind it all, the numerological (better number theoretical) underpinnings, doesn't give a hoot about representational conventions or our abilities to cogitate.

    Jess Tauber

  4. I agree Eric. Can you help me achieve that goal?

  5. I am happy to read and comment on any draft you might send me.
    But I cannot argue your case personally since I am not convinced of the virtues of your table.


  6. Hi Eric, I have not a background in science/chemistry, But in the last couple of years have found myself drawn to science, I have come to believe that not just the elements are building blocks but also the "periodic table", Would be interested to know if you think there is any merit to my simple attempts at extending the periodic table, Which can be found here
    Regards Mark.

  7. Dear Eric Scerri,


    In late July 2015, I discovered the following formula for, what I call, Janet's extended periodic table.

    z(x, y) = x + y*(y^2 + (3*(-1)^y + 1)/2)/6

    Where z is the number of protons.


    x = 0 corresponds to the beryllium group
    x = -1 corresponds to the lithium group
    x = -2 corresponds to the neon group
    x = -3 corresponds to the flourine group
    x = -9 corresponds to the copper group

    x can also be a positive integer


    y = 2 corresponds to the row containing hydrogen and helium
    y = 3 corresponds to the row containing lithium and beryllium
    y = 4 corresponds to the row containing boron, ..., magnesium

    y can also be any other integer


    Please note, that z(-3, 3) = 1, or corresponds to hydrogen! That is, z(-3, 3) = 1, z(-3, 4) = 9, and z(-3, 5) = 17, form the hydrogen, flourine, and chlorine triad!


    I would say, that hydrogen's most natural placement is above lithium, and that hydrogen's second-most natural placement is above flourine.

    Sincerely, Madjid Simon Esmaili