Crystal Mathematician

Recall from the 17 August 2013 post that Luis Bettencourt, David Kaiser, Jasleen Kaur, Carlos Castillo-Chavez, and David Wojick had constructed and tested a model of emergence, and the results suggested that for an emerging field, recruitment of new participants is critical.

When recruiting, there are two audiences one may have in mind.

• Of course, there are students. Students are energetic, ambitious, and have yet to develop that conservatism that keeps middle class academics in their own fields.
• There are also colleagues. Colleagues usually do not change fields unless impelled to do so (by necessity or by wanderlust). Colleagues know how the game is played, and they bring expertise.

These are two different audiences. I don’t know how much is known about recruitment of students versus colleagues (perhaps very little, as “emerging fields” as a branch of the sociology of science is itself an emerging field), so all I can do is engage in armchair theorizing. The advantages and disadvantages of joining an emerging field can be assessed differently by students and researchers.

• A new field is an opportunity. Economists and ecologists have long observed that when individuals find a new environment they can exploit, they can more readily succeed than they would in established terrain. In a new field, there is less competition, there are basic and tractable problems to be solved – and considerable rewards for doing so.
• A new field is a gamble. Most new businesses fail, most revolutions fail, and probably most new academic fields implode; we remember the successes while the failures are quietly forgotten and rarely make it into the history books. Some do succeed, but fail to deliver on their promises. Even successful ventures may not produce timely success, and the original revolutionaries may not live to see the success of their revolution.

Let’s consider two issues: attraction and access.

Mathematical crystallography faces the same problem that small-town boosters have: how to attract new enterprise. We are all familiar with Chamber of Commerce boosters (the old-fashioned non-ideological kind) who appeared in the business section of the newspaper, talking up the potential of the town. That’s us. So how do we attract enterprise?

It pays to advertise, or so the poem goes. In academia, one can advertise with accessible, semi-popular works. The power of advertising may be over-rated: in assessing the impact of Richard Feynman’s 1959 speech, There’s Plenty of Room at the Bottom in inspiring nanoscience, Chris Toumey found that while many people later remembered Feynman’s article being discussed, there was little documentable evidence of impact prior to the 1980s.

Still, books like Herman Weyl’s Symmetry, Marjorie Senechal and George Fleck’s Shaping Space, and John Conway, Heidi Burgiel and Chaim Goodman-Strauss’s Symmetries of Things may be useful in attracting students to the field.

Papers might also be useful advertising, although the ones that come to mind look more like materials for recruiting colleagues. For example, in 2003, Omar Yaghi et al published a manifesto, Reticular synthesis and the design of new materials, advocating the development of a design process to facilitate the synthesis of novel crystals. On the other hand, in 2008, Massimo Nespolo published a manifesto, Does mathematical crystallography still have a role in the XXI century? which introduced readers to some of the active research areas. And I have just published an article, Prospects for mathematical crystallography, allied to postings in this website.

One possible selling point is that mathematical crystallography is an interdisciplinary field. Unfortunately, this could be a liability. Interdisciplinary fields have been all the rage for some time, but institutional support tends to be a bit thin. In 1995, the National Research Council issued a report on Mathematical Challenges from Theoretical / Computational Chemistry, which addressed institutional obstacles to recruiting for a closely related interdisciplinary field:

• For faculty, the institutional support and reward structures are designed for within-disciplinary efforts. For example, faculty are evaluated by departments, which often focus on their own disciplines. In addition (though the report did not go very much into this), internal funding is often made available through departments, and credit for external funding is usually assigned to departments.
• For students, the curriculum is often determined by departments, usually independently of each other. A student in one department could face a long sequence of prerequisites before being prepared to take a relevant course in another department.

The NRC did not mention another problem: external funding agencies like their grant proposals to go into the correct pigeonhole, which is a problem for interdisciplinary programs. So by all means, talk up the interdisciplinary aspects of mathematical crystallography. But we may have to support some institutional reform.

This brings us to a major obstacle: access. Chemists who want to join need to learn physics and mathematics, physicists who want to join have to learn chemistry and mathematics, and mathematicians who want to join need to learn chemistry and physics. I am most familiar with problems learning mathematics, so let’s look at those.

In 1992, Mattel’s Barbie doll said that Math class is tough. Mattel got in trouble with the American Association of University Women because Barbie’s audience was little girls, but there is a feeling that mathematics is an unusually difficult subject. There are a number of theories as to why.

• One theory is that mathematics is a foreign language many people are too impatient to learn. Learning any language takes time and effort. (It doesn’t help when popular culture decrees that a person either has the math gene – in which case everything is easy – or they don’t, and no amount of work will help.)
• There is a theory that mathematics is an eccentric activity our savannah ape ancestors felt no adaptive pressure to master (although Keith Devlin argues that our ancestors felt a strong adaptive pressure to develop linguistic capacities that evolved into mathematics).
• There is a theory that vast numbers of people suffer from mathematical deficiencies due to poor education, poor parenting, or (of course) television
• There is a theory that mathematics is an alien landscape that excites phobias in susceptible people.
• And there is the theory that the primary (or most readily addressed) problem is how mathematics is taught.

There are even a few people who claim that math is not hard, or at least shouldn’t be. But considering that mathematics has a reputation that chemistry and even physics does not, participants in a mathematical field need to think about how to make their field accessible to novices.

Meetings (like the upcoming IUCr 2014 meeting; see the previous entry for details) are invigorating and fun and provide opportunities to meet and recruit people, but the work of learning a new field is a more lonely business and it involves a lot of reading. We have a strong interest in having a lot of accessible material. And accessibility is a problem in academia.

Etymological dictionaries tell us that arcane is a descendent of the Latin arcere, to contain or maintain, to keep or ward off, and perhaps to the Greek arkein, to keep off. It is associated with the Latin arcana, or mysterious secrets. These are all members of the family of words led by the Latin arca, or ark, as in Noah’s Ark and the Ark of the Covenant.

As a new word, arcane bubbled up in the Sixteenth century, in the midst of the explosion of books created by Gutenberg’s press. Books on just about everything suddenly appeared, and they sold. Just as the Internet not only made everything available to everyone, and made a virtue of universal access, so the Gutenberg revolution made all knowledge available to any plowman able to afford a book.

But some works seemed to remain out of reach, hence the notion of arcane works. Perhaps the printing press was partially responsible for the Plato boom that inspired Renaissance scientists: Plato was a natural novelist (see, e.g., his great literary invention, Atlantis). Perhaps the printing press was partially responsible for Aristotle’s poor reputation in that era: the Complete Works are a jumble of often unintelligible notes and fragments of dubious provenance. And Aristotle was hardly unique. As Great Works became available to the Common Man, common men found many of them inaccessible.

Communication theorists tell us that arcana can serve a purpose. I don’t mean unintentional arcana, like a bunch of moldy papers somehow associated by a major philosopher. I mean (often unconsciously) intentional arcana, like books by German metaphysicians we could name. Consider this grumpy passage by the greatest of them all, Immanuel Kant. In his Prolegomena to Any Future Metaphysics, a sort of Kant-for-Dummies-by-Kant-Himself, Kant writes that his major work, the Critique of Pure Reason

Some communication theorists might detect a little pride in that sentence. Still,

There are two interesting points about this passage. First, Kant was irritated that philosophers, much less educated laymen, were unwilling to invest the vast amount of time and energy required to read the Critique. But second, he did write the Prolegomena after all, and that was consistent with what some commentators have claimed about Kant: he had an agenda, and that agenda required readers and students. Kant started his introduction to the Prolegomena with the words, “These Prolegomena are destined for the use, not of pupils, but of future teachers …”; perhaps concerned by the criticism of his colleagues, he wanted to make sure that teachers, at least, understood what he was trying to say.

Academics aren’t the only ones who make the difficulty of the material into a gatekeeper, but that is one of our bad habits. Especially when our goal is accessibility. It all boils down to who the audience is. New Yorker archivist Joshua Rothman compared journalists, whose text is relatively undemanding because it is intended for a mass audience, to academics.

But mathematical crystallographers are not trying to fill a niche. We are trying to get people involved (or if you prefer, we are trying to create an array of niches). That means that we should be writing papers and books for as wide an audience as possible. So here are some “best practices” we probably should engage in:

• Papers should be self-contained. In an interdisciplinary field, one’s readers may be unfamiliar with some jargon and some concepts. It may be useful to define them in the paper if that does not take up too much space. Of course, sometimes that would be distracting, so another thing one needs is:
• Papers should have primary references. Where does the novice reader go to find out what actions, entropy, and carboxyl groups are? It takes very little space to give a citation to a general reference known to be accessible.

It may be a good idea to imagine a graduate student when writing a paper.