A Research Genealogy Project? (2)

I circulated the idea of a Research Genealogy Project among a few colleagues, who have offered some comments, giving me a bit more to ponder, particularly the basic question of what is this is really for? What purpose does it serve?

My tentative response to this at the moment is that the long term goal is to understand about higher levels of knowledge, understanding and insight and how they can propagate, flourish and advance. At a more mundane level, it might offer clues into the kinds of conditions that are more likely to lead to successful research activities based on a large body of genealogy data, perhaps useful for funding bodies.

In terms of a genealogy project based on formal research qualifications, I would focus initially on the relationships rather than the objects. There are many kinds of relationships and a standard each-way link without any meaning is usually not appropriate: the existing Maths Genealogy project already has some a sense of ordering or direction in which the Professor generally is the one who imparts to the student until the student absorbs and understands.

There are other inputs that could be modelled: ranging from formal instruction to collaboration, to influence. Looking back at my own Ph.D. (Use of Formal Methods for Safety-critical Systems), apart from my supervisor, I was given guidance by a few other staff and learnt from quite a number of researchers in the field. For instance, at the start I had to learn from those who had developed the formal theoretical foundations (e.g. the theory of testing equivalences of processes), whilst others provided certain contextual background (the application domain of medical device communications). When it came to applying some new theory, I used some methodologies (that applied safety analysis techniques) that adapted or built on the work of contemporary Ph.D students. All these informed and influenced me in my own research, but in different ways.

I corresponded with some of these by email, but although it might be interesting to model correspondence between researchers (nice graph theory applications), I can't see how you can dig into these emails in practice and in any case they were just a small proportion of authors that influenced my work.

It's going to be easier if you can work with what has been freely published, which brings us back to the thesis. What if they could be marked up in such a way that you can extract meaning? So you could know in a particular thesis whose work had provided the foundations, who was doing similar work. This is a task for experts in knowledge representation, retrieval and analysis. Patterns might emerge that show coalesence among some theses, where a lot of researchers tackle a popular topic and related issues; further some theses may show a lot of interconnectivity not only within subject areas but across subject areas, which might suggest making more explicit particular areas for co-operation and joint conferences. On the other hand, some research may be shown to go off on a limb and have little to do with others. Some nice visuals will make this much easier to see!

A Research Genealogy Project?

The Mathematics Genealogy project provides a field to categorise dissertations according to the Math Subject Class. Seeing how the selection is very broad, e.g. covering computer science, I was prompted to wonder what about genealogy projects for other subjects? There appear to be a few ideas and initiatives, including Thomas Witten's proposal for a Physics PhD Genealogy project, the High Energy Physics directory, the Software Engineering Academic Genealogy, the Theoretical Computer Science Genealogy and the Notre Dame University academic genealogy, that covers current members of its departments of Chemistry & Biochemistry and Physics.

It's a very fragmented picture, with independently developed systems, very partial coverage of researchers and yet already some duplication. It will become even more so as subject disciplines keep growing...

So it makes sense to me to take a fundamentally more integrated view that incorporates research in any field, one that can also have a richer model, taking into account different kinds of research qualifications, not just PhDs; and different kinds of relationships, not just formal supervisor-student; thereby responding to issues raised in the Mathematics PhD in the United Kingdom.

The findings yielded on this broader base will be fascinating, showing among other things how disciplines evolve over the generations, shedding light on questions such as: What happened to descendants of those who studied classics? What did the ancestors of computer scientists research? Many trends can be observed. There's a lot of talk in the UK about lifelong learning, so how about considering lifelong and generational research?

Another aspect that needs attention is the quality of entries. It's a tall order for just one central team responsible for verifying information received and compiling the database, which is the current arrangement at the Mathematics Genealogy Project. It would be better to distribute the workload and make use wherever possible of local expert knowledge, suitably authorised to update data in the areas with which they are familiar, whilst allowing for as wide public participation as possible.

So what's the solution?

I'm quite sure that the biggest consideration is organisational, not technical. It's probably a workflow problem and perhaps can be addressed by appealing to other international networks, most likely business networks. The quality control needs to rest with academic departments and it seems sensible that they should deal with information relating first to their department, then their institution and then neighbouring institutions. So I envisage an international network of genealogy research nodes where public contributions would be submitted though their nearest research node rather like, "contact your nearest reseller."

A few days ago I attended a presentation by someone who has done work for the World Wide Web consortium and he re-iterated the point that if there's one technical issue affecting software above all others it's scalability. So any proposal probably ought to design and develop a system that distributes the processing (cpu and resources) as well as the administration, though the computing power need not be distibuted per site (big companies typically use a few data centres containing large numbers of rack-mounted PCs). This suggests an application for a parallel computing grid.

I don't know what the implementation itself should look like: it could well be underpinned by a relational database or might even be a special kind of wiki (thinking about how that can really grow rapidly). However, the data model should certainly be given careful consideration. How to deploy it on the Internet? How to authenticate and authorise? Lots of questions will pop up if one investigates further!

Mathematics Genealogy: Indexing

Exploring some of the entries in the Mathematics Genealogy project has led me learn about some interesting and unexpected connections, but it's also highlighted quite a number of limitations regarding accuracy and promptness of updates. Saying this is really just an indication that if you offer something good, then people will be looking for more!

One particular issue is that the total number of descendants requires a separate process to run as explained by the FAQ, which says:

Because of the time required to run the descendant counting program, it is only run once per week (early morning US Central Time on Sundays), while our data is updated nightly.

That surprises me somewhat as with around 100,000 people with not very many details stored per user and few relations, it's not a big complex database. The issue here is probably that it's a relational database and the advisor-student relationship is hierarchical, somewhat like a tree structure. However, it's not a tree because of having multiple parents (multiple advisors), but rather a directed graph, where the nodes represent the mathematicians and the edges correspond to the advisory relationship. [I'm taking definitions from MathWorld, an encyclopaedia that provides clear and nicely formatted explanations with diagrams]. Further, I think there is a fair chance that it would be more general than a simple directed graph from the scenario of the same supervisor supervising a candidate in more than one thesis - although it might sound unlikely today, it is quite plausible a few centuries ago, when a researcher could be at the forefront in a number of fields. I'd also expect it to be an oriented graph, in that supervision is expected to go in one direction, but it's not inconceivable that a student produces a thesis separately in two fields under two supervisors and then shares the knowledge back across.

Returning to the problem of counting, hierarchical relationships are easy to model in a relational database, but retrieving even summary counts may mean a lot of spidering through the hierarchy, which can be very slow. The key consideration is how to index the database. I'm not a database expert, but have seen this issue in the daily work I undertake as an administrator of WebLearn an e-learning system based on software called bodington, which is essentially a web database application. The system contains various resources, arranged hierarchically, in trees, so more specific than the genealogy case.

Jon Maber, the original developer, had started work on Bodington in the mid 90s and had thought about the issue of efficent queries about resources within a given branch; he reviewed approaches to indexing and decided to adopt the tree visitation model devised by Joe Coelko. Celko had given consideration to this graph theory problem and came up with SQL for Smarties: A Look at SQL Trees, an article that appeared in DBMS, March 1996 . Basically, each node or vertex has two indices - left and right - that are numbered according to a complete tour of all the nodes, visiting each twice. It means that selecting the number of descendants of a resource a simple SQL statement that subtracts one index from another at the given node. However, there is a trade-off in that every time you update the database you need to update the index, so if lots of changes are being made it can be a major performance issue.

Celko's solution may not be appropriate in this case, but it looks like the of approach that may lead to a suitable index that will allow real-time queries of how many descendants. The article was published more than 10 years ago, so I expect research has progressed a fair bit since then.

Mathematics Genealogy

I recently came across the Mathematics Genealogy project, which offers a fascinating view of how guidance in doctoral research in maths is passed down from supervisor to student. It's a service currently hosted by North Dakota State University and supported by the Clay Foundation. It's quite a simple idea that can reveal fascinating details about the evolution of subjects studied and 'lineages' of famous mathematicians.

I have an entry, but it's wrong! I did indeed submit a thesis with that long title and study under the guidance of the late Prof. Robert Odoni, but only obtained an M.Sc., having decided after about a year not to continue for the doctorate. The Prof's record is far from complete - he was previously at Exeter University for quite a few years, so I expect he would have had doctoral students there. Also not there yet: he was supervised mainly by Harold Davenport and then towards the end by Alan Baker, both distinguished number theorists.

I do have a Ph.D. in theoretical computer science on 'The Use of Formal Methods for Safety-critical Systems,' for which my supervisor was Dr Kate Norrie, but there's no link shown. That lineage goes through Frobenius, whose work was fundamental to my M.Sc. and before him Gauss, one of the most prolific mathematicians known, and as I write almost 1/3 of all people in the database are his descendants!

It's noticeable that via Odoni, one traces back a UK line of researchers that only goes back as far as the 20th Century, whereas the line via Norrie is mainly German and goes back to the 17th Century. This apparently reflects the fact that in the UK, PhDs were only introduced in the 20th Century. This means that British mathematicians are poorly represented in the genealogy project as it stands, a situation discussed at length in 'The Mathematics PhD in the United Kingdom'. (Incidentally nice to see T. M. Fred Smith mentioned - he kindly acted as my main personal tutor for my B.Sc. at Southampton, even after I later changed my registration and dropped stats in favour of pure maths!)

I've filled in update forms over a week ago, but as yet there have been no changes in the entries of my supervisors or myself. So I'm wondering about improvements...