Geometeer
Context:  I wrote this article in the mid-1990s, while Chief Scientist at the Centre for Information-Enhanced Medicine at the National University of Singapore (NUS), for the annual student journal of the Pharmacology Department — hence the pharm-specific intro. Someone asked me to make it more available, so here it is.

The Joy of Ignorance

"I seem to have been only a boy playing on the shore of knowledge, diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, and throwing them inaccurately at the mermaids."               Sir I**** N****


Do you ever worry, as you sit over those heavy books late at night, learning to chant the whole pharmacopaeia in the right order, that you may be losing your most precious resource?

Your ignorance.

True and tested knowledge encrusts your brain:  2mg will kill a dog, 7mg will kill a human, 13mg will kill a professor.   There's more to know, but you will know it bit by bit.   It is only in graduate school that they tell you "In the present state of our knowledge of the action of drugs, it is premature to practice medicine":  right now, they are stuffing you with Knowledge.

Your ignorance cowers in the corners of your battered imagination

The first paper I wrote after leaving Warwick Maths Institute, where I did my PhD, was about electronic vibrations of crystals, based on quantum calculations of lattice interactions which I still do not understand.   My co‑author had built a subtle model that said which combinations of frequency, direction and energy were possible; his problem was to compute which energies were in more combinations, and which were in less.   (Knowing that graph, the 'spectrum', a physicist can calculate many other interesting quantities like specific heat.)   He was loaded to the ears with math techniques for doing that calculation.   The very first crystal models handled this way, with far simpler interactions, had led to elliptic integrals of both the first and the second kinds — a dirty job, but some people have to do it.   More complicated models quickly forced the physicists to retreat to numerical methods; great FORTRAN IV programs that took hours or days… and couldn't cope with my friend's new model.   A key step, given a wave frequency and direction to find the energies possible, had become too hard.

I looked at his equation, and saw what his years of training had blocked him from:  choose an energy level, and we could easily find the possible frequencies and directions.   That led to a far neater, cheaper and more adaptable way to compute.

All the specific knowledge I had, he had too.   What he was missing was partly my geometrical point of view (I think more in pictures, he thought more in formulae), but my perception turned easily into formulae, or we could not have computed with it.   Much more crucially, he was missing my enormous ignorance of the problem, and the methods that had been used before.   Those were so rich and powerful that surely some subtle modification could solve his problem?   He was trapped by his lack of ignorance.

Of course, ignorance alone is not enough.   I could no more have worked on electronic lattice vibrations using my own training than I could fly to Budapest on my own wings.   I had to be part of a team, where skills and ignorances could mesh to create something of professional quality, and could satisfy people who knew the classical tools far better than either of us; people who had built those tools.   I had to severely damage my ignorance of FORTRAN IV (mostly repaired now, thanks).   I had to learn to listen to physicists — not easy for a mathematician.   Since then I have worked with and listened to people from archaeology, psychology, engineering, medicine, ecology, and recently ophthalmology; a blessed area of clarity.

You need to listen closely, to get good use of your ignorance.   I know nothing about Uighur folksong, but that ignorance is dead ignorance.   Without an Uighur singer or musicologist to stir life into it, it remains a lifeless sea in my ignorance ocean.   I cannot ask dumb questions, or even clever ones.   The dumb ones are the most important.

Clever questions can seal away your ignorance as securely as specialist training.   If you ask questions to prove how well you understand the other person, you're thinking about that proof… and not about what she is saying.   Stay in touch with your ignorance, do not hide it.   Ask about what you truly do not understand, however dumb you fear the question sounds.   Honesty brings faster understanding, and greater respect.   You cannot fool a subject specialist that you understand, when you don't.   The specialist can clear up puzzlements for you if, and only if, you ask.   (A good one can hear in your questions what you need to know, and build an answer to fit what honest questions have revealed about your understanding.   Mediocre experts, insecure, will make answers hard, to prove their own cleverness in grasping this hard stuff.  Avoid such people, and hope they soon move from research to a job where they can be useful.)

At the Centre for Information-enhanced Medicine, one day, we interviewed two job candidates.   Candidate A knew a lot about medical images, which we work with in most of our projects.   B knew parts of signal theory which would not directly apply to any current project.   By a knowledge test, A was the obvious choice; we hired B.

B was fascinated by the thought of adapting what she knew to questions she knew nothing about.   When language was a problem (we have a wide mix of accents and vocabularies, between us) she never saved face by pretending to understand.   She forced us to find words she could follow.

A never asked an unexpected question.   His knowledge was impressive, but his ignorance was not the kind needed for interdisciplinary research.

A/P Ngiam said to the Pharmacy Congress (Pharmaceutica 95/96) that "we will be needing less pharmacists but very good ones, and these pharmacists must be well schooled in information technology, robotics, biotechnology, pharmacoeconomics".   If that is not too much for your knowledge to cover, I could threaten you with nanotechnology, chaos theory of the immune system, cell membrane biomechanics…  Whatever you are schooled in, you are not schooled enough; and a school sets exams, and exams can only test your knowledge.   What will matter is the quality of your ignorance in these fields, the openness of it.   How well can you work with someone who breathes robotics as you breathe pharmacokinetics?




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