James Berkeley Larsen

James Berkeley Larsen

UMich PhD student in Applied Math & Scientific Computing, interested in simulating quantum systems

New Year, New Me

1 minute read

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Trajectory

With the arrival of the arbitrarily chosen day set aside by our society as the first of the year comes the ritualistic resolutions meant to change our behavior. One such resolution of mine was to revive Computational Catharsis as a sandbox for my thoughts. Here goes nothing.

Beyond that simple goal (coupled with a minimal habit of the James Clear variety) and a few others, I was thinking more abstractly about who I am, who I want to become, and what it takes to bridge the gap between the two. My mind kept gravitating towards the idea of a trajectory. The fundamental idea behind calculus is that dynamics of a system are best understood through a study of rates of change. If I want to predict or modify my own personal trajectory, perhaps I need to take a personal derivative of sorts: I propose that the derivative of who I am with respect to time is who I am becoming–the bridge to who I want to become. This state of being changes smoothly, hence the inevitable failure of overly ambitious goals.

Why We Remember

I finished Charan Ranganath’s debut pop-science book, and was quite pleased with it. Beyond reinforcing my habit of regularly discounting my own recollections as “false memories”, Ranganath provided a medium for me to marvel at the remarkable computational abilities of our biological hardware. I found it similar in vibe and scientific rigor to Matthew Walker’s Why We Sleep, but maybe not as life changing for the simple reason that sleep studies inform behavior modification more naturally than memory studies. Embarrassingly, my biggest takeaway might be the brief introduction to the idea of cryptomnesia, something I’ve needed a word for since hearing the similarities between the openings of Leon Bridges’ Coming Home and Taylor Swift’s Lover.

Miscellanea

Other curiosities I spent time with this past week:

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Minesweeper as a Markov Process

As promised two weeks ago, I’ve started my attempt to formulate Minesweeper in the language of reinforcement learning (RL). The mathematical backbone of RL is a Markov decision process (MDP), consisting of a state space $\mathcal{S}$, an action space $\mathcal{A}_s$ for each state $s \in \mathcal{S}$, transition probabilities $P_a(s,s’)$ for states $s,s’\in\mathcal{S}$ and action $a \in \mathcal{A}_s$, and the reward functions $R_a(s,s’)$. The goal of the MDP is to find the policy $\pi$ that determines the best action $a$ from any given state, i.e., \begin{equation} \pi^* = \arg\max_\pi \mathbb{E}_{s \sim \pi, a \sim \pi(s)} \left[ \sum_{t=0}^\infty \gamma^t R_a(s_t, a_t) \right] \end{equation} for some discount factor $\gamma \in [0,1]$.

Rich Sutton Plays Minesweeper

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Month Two

Turns out, a new year’s resolution to blog every week is too ambitious. Maybe I can update that to once a month? Here goes a simple February blog post, coming back into the CompCath sandbox to see what I can put together.

Hello World

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Genesis

With November quickly fading away, I am thinking ahead to future iterations of the universe. Why not include a personal online blog/CV in such future iterations? Hence, the birth of Computational Catharsis.