### Fundamental Lenses

A compilation of things that Harvard faculty have told me
they found formative in shaping their worldview, life and academic philosophies.
In their words, a "fundamental lens" is something that
shapes how one think about many fields and how
you approach *and choose* problems to begin with,
rather than an interesting factoid or method in a specific field.

#### What school can teach

- Understanding the notion of absolute proof
- The power of abstraction and studying structure divorced from context

- Limitations of empiricism, and associated philosophy
- Comparing the formal study of mathematical probability to probability calculations done by real-life practitioners who live under opacity and uncertainty
- Learning epistemic humility, and when to avoid calculating probabilities in the first place

- To appreciate the bluntness of words as tools to describe the world, and how a trained writer can sidestep such limitations
- To appreciate the joy and beauty that words can bring into the world

- Game Theory
- Contextualizing deviations from game-theoretic optimality using psychology
- Appreciating when psychology is (reproducibility) and is not (reproducibility) a Mickey mouse subject
- Economics as the study of incentives and allocation under scarcity
- Epistemological limitations of social science
- And those of mathematical modelling of complex systems in general

- Hardcore programming that teaches patience and diligence
- Seeing similarities between the cult of systems programmers to guilds of craftsmen in ages past
- A dose of humility for theorists, making clear the distinction between theory and practice (debugging, etc)

- Seeing financial markets, biological organisms and evolutionary systems as Turing machines

#### What school cannot teach

- It's easy to be blindly contrarian, and instinctive to take expert evaluations as gospel
- It's harder (and necessary) to correctly calibrate error bounds on expert commentary, knowing what sort of predictions are likely to be reliable, and which are likely to be marred by the experts' personal biases
- Developing a visceral appreciation for how easy open problems can be
- Many open problems are just problems someone stumbled upon, couldn't immediately solve, lost interest, and moved on to something that they had more interest in, branding the problem "unsolved" when in reality it isn't as difficult as it might seem
- If you have extremely strong fundamentals (understanding of undergraduate-level and beginning graduate-level material) in a field, you can get up to speed with world "experts" on open problems in many fields in a few focused weeks of study
- There are exceptions to this, of course, like pure mathematics