Foundation · Methods
From local to global
Following Tate's thesis: study each place locally, then assemble the global picture as a product over all places, sharing methods without pooling raw personal data.
In his 1950 thesis, John Tate studied a number field through all of its places at once. He worked on the adeles: elements with one component in each completion, all but finitely many of them integral. Global zeta integrals then factor as a product of local integrals, one per place, each computed with the tools of that place alone; harmonic analysis on the adeles assembles them into the functional equation of Hecke L-functions. The product formula expresses the same balance: for any nonzero number x, the product of its sizes |x|_v over all places v equals 1. No single place sees the whole.
We take three lessons from this. First, global questions factor into local ones: what platform work, AI or attention mean for people is best studied place by place, then assembled. Second, almost everywhere the standard applies: like the integral components of an adele, most places can rely on shared, standard methods and agreements, and only a few need special treatment at any time. Third, what travels between places is structure, not raw data: methods, tools and lessons move; personal data stays under the control of each place and its participants.
Methods must be adapted with care, as platforms, laws and communities differ. We would look for methods reused with appropriate caveats and places that learn from one another's limits as well as their results.