Preference to freshmen. The mathematization of natural science originated with Galileo and Newton in the 17th century. Today, known laws of nature can account for every observation made over a vast length scale, from the frontier of elementary particle physics (PHIL 10-PHIL 17 cm) to the extent of the observable universe (1029 cm). While technologies do not currently exist, and possibly will not for the foreseeable future, to allow probes of nature below and above these limits, the tie of mathematical theory to observation, however tenuous a connection that may be, remains the test of any physical theory. Yet theorizing continues to push beyond, positing entities and structures that may never be confronted with observational challenge. In short, fundamental physical theory is at a fork in the road, where the only way forward seems to lie in mathematical speculation (string theory at the smallest scales, multiverse cosmology at the largest). Our goal in this seminar is to step back from this scenario, and to remind ourselves that the successful application of mathematics in natural science since the 17th century shows that mathematics is an invaluable tool for science, providing concise frameworks for organizing and simplifying human interactions with the world. The remarkable fact that this tool has proven so successful should not be misunderstood, the map should not be mistaken for the territory. Known laws of nature, the most empirically successful physical theories, remain our laws, and our theories, rendering those parts of nature within their domain comprehensible to us.
3 units · Letter (ABCD/NP)
Preference to freshmen. The mathematization of natural science originated with Galileo and Newton in the 17th century. Today, known laws of nature can account for every observation made over a vast length scale, from the frontier of elementary particle physics (10-17 cm) to the extent of the observable universe (1029 cm). While technologies do not currently exist, and possibly will not for the foreseeable future, to allow probes of nature below and above these limits, the tie of mathematical theory to observation, however tenuous a connection that may be, remains the test of any physical theory. Yet theorizing continues to push beyond, positing entities and structures that may never be confronted with observational challenge. In short, fundamental physical theory is at a fork in the road, where the only way forward seems to lie in mathematical speculation (string theory at the smallest scales, multiverse cosmology at the largest). Our goal in this seminar is to step back from this scenario, and to remind ourselves that the successful application of mathematics in natural science since the 17th century shows that mathematics is an invaluable tool for science, providing concise frameworks for organizing and simplifying human interactions with the world. The remarkable fact that this tool has proven so successful should not be misunderstood, the map should not be mistaken for the territory. Known laws of nature, the most empirically successful physical theories, remain our laws, and our theories, rendering those parts of nature within their domain comprehensible to us.
Offered in Winter 2027 at Stanford University.