PrePostFacto

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The Luke anecdote may not be the best example, but the general idea is sound. Hermann Hesse in Siddhartha said, "Wisdom cannot be passed on. Wisdom that a wise man tries to pass on to someone always sounds like foolishness." That's slightly too categorical and strong, but still broadly correct and consistent with the point of the original post.

Following up on gjm's comment (sorry I'm a little late commenting on this post - I came to it via Scott Alexander's "Contra Hoffman" post), there was an interesting followup analysis of the cancer mortality effect in VITAL that concluded that "supplementation with vitamin D reduced the incidence of advanced (metastatic or fatal) cancer in the overall cohort, with the strongest risk reduction seen in individuals with normal weight." https://jamanetwork.com/journals/jamanetworkopen/fullarticle/2773074 

This study is interesting because, among other things, it bridges the cancer "incidence" and cancer "mortality" questions by looking closely at "incidence" of advanced / metastatic cancer as well as cancer mortality. To address the "data mining" concern, cancer incidence and cancer mortality were both preregistered outcomes of VITAL - those of us who follow Vitamin D research and lean toward (rather than contra) Hoffman with respect to Vitamin D had expected the VITAL researchers to preregister cancer mortality as a primary outcome and cancer incidence as a secondary outcome, not just because mortality seems more important than incidence - both are important, of course - but also because the leading theories of Vitamin D's physiological effects provide a mechanism for reducing cancer mortality whereas the mechanisms for reducing initial (not metastatic) cancer incidence are speculative if they exist at all. (Alas, in the VITAL preregistration cancer incidence was primary and mortality secondary. Still, they were both preregistered and not just something that popped out after looking for something of significance.) The discussion section in the JAMA article explains the issues in detail, and the studies cited in the "biological plausibility" section ("[a]n association between vitamin D supplementation and metastatic and fatal cancer is biologically plausible") are worth reviewing.      

David Metzler's "Ridiculously Huge Numbers" (YouTube)

Link: https://www.youtube.com/user/davidmetzler/playlists

Description: A comprehensive review of how mathematicians think about and notate huge numbers. 

Positives: 

  • Metzler starts with concepts and notation that most high school students and even precocious middle school students have seen and works "up" from there.
  • Each video is relatively short and covers a "huge number" topic or two that most mathematically-inclined people can follow.

Negatives:

  • It's a long series, and after the first few videos, the concepts and notation become quite esoteric.