Students and faculty have made Harvard University great, but why do the best people keep coming? Harvard's wealth certainly helps. Yet like age and location, which also work to Harvard's advantage, money can't produce excellence in the absence of some heritable spirit.
Harvard is driven forward by a kind of constructive confusion about its own usefulness. It values learning for its own sake, and also as a service to society. Harvard stays lively by arguing, but never reconciling the inconsistency.
Harvard naturally invites comparisons to the ancient universities of Oxford and Cambridge, where its Puritan founders studied. But they built Harvard for reasons more civic than scholarly. The governors were men of affairs, not academics. The college was part of an uncertain plan to civilise a wilderness; disinterested learning is a relatively recent innovation.
Unexpected coincidences remind us of our mixed heritage. A few years ago, Harvard installed plumbing in a colonial-era chapel now used for choral practice. The excavated earth contained human bones! Had we disturbed a Native American burial ground? No, when the student body outgrew the chapel in 1783, it became home to the medical school. The bones were the detritus of 18th-century dissections.
Today, the professional schools are so autonomous that Harvard sometimes seems less a university than a loose academic federation. The Faculty of Arts and Sciences teaches everything from Celtic language to engineering and 14 varieties of biology. The professional schools - of business, medicine, public health, education, law, divinity, design, government - are described as "fiefdoms" by sceptics of decentralisation, who mistakenly think it is a pre-modern anachronism.
The university's governors, who are still mostly businesspeople, have pressed for stronger central management. While he was wrestling with the Harvard octopus as the university's president, the economist Lawrence Summers quipped: "Academic freedom is wonderful, but it really doesn't have a place in the purchase of cement." Professors don't actually buy their own cement, but only this year have we adopted what our current president, historian Drew Gilpin Faust, calls "a common calendar for the common good".
Harvard's unity remains somewhat rhetorical; calendar reform notwithstanding, undergraduates cannot study in most of the professional schools. And yet, where connections make sense, they happen - many undergraduates do conduct research in medical school labs.
Frustrating as it is for central planners, disunity is one of the keys to Harvard's greatness. Because of Harvard's design - or evolution - local experts make most academic decisions. The administration decides whether a retiring Chaucerian scholar will be replaced or whether a professorship in systems biology will be created, but professors decide who should be appointed. Local academic control is inefficient, but it's hard to argue with the results.
The central administration also stays away from undergraduate admissions. Trained staff recruited almost 29,000 applicants from around the world last year - almost all admissible. Together with a faculty committee, admissions officers decide who will fill the 1,650 spots in the freshman class. The results are another key to Harvard's greatness. Incoming freshmen are so talented that professors occasionally wonder about their own "value added" - sometimes, less Harvard education seems to be more. Two of Harvard's most prominent former students, Bill Gates of Microsoft and Mark Zuckerberg of Facebook, dropped out shortly after taking my classes.
Also key to Harvard's success is money. Yes, wealth can produce hubristic ambitions, as evidenced when Harvard briefly considered rerouteing the Charles River to annex part of Boston to its Cambridge campus. And the $11 billion (£6.8 billion) that Harvard "lost" last year exceeds the value of most universities' entire endowment. Harvard can afford investments of which few other institutions can dream. Admission is decided without reference to financial need, and the university awards so much financial aid that students can graduate debt-free.
Still promoting literacy as it did in 1636, Harvard has the world's greatest university library, with incomparable collections of ephemera and archival material as well as books. But recent faculty growth has been mostly in science and engineering, alarming humanists who fear marginalisation. At the undergraduate level, Harvard is unapologetically anti-professional: its new general education programme defines liberal education as "undertaken without concern for topical relevance or vocational utility". Yet most of its graduates - many of them now from socio-economically disadvantaged backgrounds - pursue careers in medicine, law or business.
Far from resenting their lack of career training, alumni give back to Harvard generously, in time and money, for the scholarly riches and educational freedom they enjoyed. The old tensions remain unsettled, pervasive and productive.
• Times Higher Education-QS World University Rankings 2009: full coverage and tables