Explanation in mathematical conversations:An empirical investigation

Analysis of online mathematics forums can help reveal how explanation is used by mathematicians; we contend that this use of explanation may help to provide an informal conceptualization of simplicity. We extracted six conjectures from recent philosophical work on the occurrence and characteristics of explanation in mathematics. We then tested these conjectures against a corpus derived from online mathematical discussions. To this end, we employed two techniques, one based on indicator terms, the other on a random sample of comments lacking such indicators. Our findings suggest that explanation is widespread in mathematical practice and that it occurs not only in proofs but also in other mathematical contexts. Our work also provides further evidence for the utility of empirical methods in addressing philosophical problems

A methodology to estimate the potential to move inpatient to one day surgery

BACKGROUND: The proportion of surgery performed as a day case varies greatly between countries. Low rates suggest a large growth potential in many countries. Measuring the potential development of one day surgery should be grounded on a comprehensive list of eligible procedures, based on a priori criteria, independent of local practices. We propose an algorithmic method, using only routinely available hospital data to identify surgical hospitalizations that could have been performed as one day treatment. METHODS: Moving inpatient surgery to one day surgery was considered feasible if at least one surgical intervention was eligible for one day surgery and if none of the following criteria were present: intervention or affection requiring an inpatient stay, patient transferred or died, and length of stay greater than four days. The eligibility of a procedure to be treated as a day case was mainly established on three a priori criteria: surgical access (endoscopic or not), the invasiveness of the procedure and the size of the operated organ. Few overrides of these criteria occurred when procedures were associated with risk of immediate complications, slow physiological recovery or pain treatment requiring hospital infrastructure. The algorithm was applied to a random sample of one million inpatient US stays and more than 600 thousand Swiss inpatient stays, in the year 2002. RESULTS: The validity of our method was demonstrated by the few discrepancies between the a priori criteria based list of eligible procedures, and a state list used for reimbursement purposes, the low proportion of hospitalizations eligible for one day care found in the US sample (4.9 versus 19.4% in the Swiss sample), and the distribution of the elective procedures found eligible in Swiss hospitals, well supported by the literature. There were large variations of the proportion of candidates for one day surgery among elective surgical hospitalizations between Swiss hospitals (3 to 45.3%). CONCLUSION: The proposed approach allows the monitoring of the proportion of inpatient stay candidates for one day surgery. It could be used for infrastructure planning, resources negotiation and the surveillance of appropriate resource utilization