[Question] Should I Pursue a PhD?

Introduction

I’m currently flirting with the idea of trying for a math PhD 2 − 3 years down the line.

I’m currently on a Theoretical Computer Science Masters program at the University of [Redacted] in the United Kingdom.

(My program is 2 semesters of teaching (7 − 8 months) followed by a 9 − 12 month industrial placement starting in June 2023. [I might forego the 1 - year industrial placement if I can’t get a suitable placement [I.E. theoretical research that feels like it would be valuable experience for the kind of career I want to pursue] and graduate after one year by completing a masters project over the summer instead.)

After graduation I’m considering taking a gap year to fill in the gaps in my maths knowledge/​prepare for the PhD, maybe see if I can contribute to the research agendas I think are interesting/​promising).

I might also pursue a PhD in Theoretical Computer Science instead of mathematics (maybe applications for a TCS PhD would be looked on more favourably with a TCS Masters/​recommendations from my current lecturers).

Why A PhD?

I currently plan to learn a lot of (especially abstract) maths to (upper) graduate level for alignment theory (I want to do theoretical alignment work that is basically just applied maths), and I think I would benefit from the opportunity to study the relevant mathematics under a “guru”/​the dedicated mentorship a PhD provides. I expect the first few years of my career in alignment research would be mostly spent on deconfusion/​distillation, and I expect high levels of mathematical sophistication to be very valuable for that.

I find abstract maths and mathematical modelling “fun”, and really enjoy being a student.

My Alignment Theory of Change

I am operating under/​optimising for long timelines (transformative AI is decades away [20+ years]), and this influences what kind of research I believe to be most promising.

I expect theoretical (especially foundational [especially in our current pre paradigmatic stage to be the most promising]) and am persuaded by agent foundations agendas. The extant research agendas I’m most excited for and could see myself working on someday:

  • John Wentworth’s Natural Abstractions Hypothesis and Selection Theorems

  • Vanessa Kosoy’s Learning Theoretic Alignment Agenda

    • Other agendas that take a desiderata first approach to alignment

  • Garrabant and Demski’s Embedded Agency

My basic plan for alignment is something like:

  1. Study subjects that seem relevant to alignment theory

    • Mathematics: a fuckton

    • Theoretical Computer Science: likewise, a fuckton

    • Statistics (and its theory)

    • Learning Theory (Algorithmic and Statistical)

    • Information Theory (Algorithmic and Statistical)

    • Physics: Thermodynamics

    • Optimisation

    • Evolutionary Theory

    • Analytic Philosophy: ontology, epistemics, ethics, etc.

      • Develop executable/​computable philosophy for the above

    • Decision Theory

    • Game Theory

  2. Grapple with concepts that bear on agent foundations until I understand them better (“Deconfusion”)

    • Information and entropy

    • Computation (especially as an information dynamics phenomenon)

    • Abstractions, ontology, modelling/​map making

    • Optimisation

    • Causality/​dependencies and counterfactuals (including logical)

    • Epistemics (including for ideal agents)

    • Decision Making (including for ideal agents; especially in multi-agent environments)

    • Emergent behaviour in multi-agent environments (e.g. competition, coordination vs conflict, evolution)

    • Systems (especially complex) and their emergent behaviour

    • Embedded Agency more generally

    • Anthropics?

  3. Distill my learnings and understandings to make them more widely accessible (“Distillation”)

  4. Iterate #1 - #3

  5. ...

  6. Formulate an adequate theory of robust agency

  7. ...

  8. Solve alignment

Of course, I don’t expect to make it all the way to step 8. Mostly, I expect that deconfusion and distillation would be where most of the value from my “career” will come from.