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Jump Discontinuities

Generally when we think of a baseline for the future, we tend to assume it's a flat line from exactly where we are now. But this is almost never actually the case. If you're actively investing, net positive returns mean almost nothing. The actually useful question is whether you're outperforming the simple counterfactual: putting your money in an index fund and letting it compound.

This concept of comparing to a simple counterfactual generalizes surprisingly well to almost every aspect of life. It's easy to be complacent, seeing how far you’ve come and the obvious differences between you now and you in the past. But it's a lot harder to see which parts represented genuine changes beyond the trajectory you were already on. For example, graduating high school feels like progress, but a freshman version of me was on the path to do this.

The reason I’m writing this is because I have a mental list of things I've done that I’m proud of, and I realized that I’m most proud of these things because they fundamentally improved my life trajectory. I think there hasn’t been a long stretch of time where I haven’t ‘progressed’, so I always beat the flat baseline. In fact, this flat baseline makes almost everything look like success. But the things I’m proud of doing are things that I wouldn’t even have imagined a few months before. The bar goes from ‘Am I progressing?’ to ‘Am I doing things that change what is possible for myself?’ I think of these as jump discontinuities: moments where my trajectory doesn't merely improve, but jumps to somewhere I couldn't have reasonably predicted.

Take working for example. At the end of my first internship, I was exactly where I expected I would be. I largely went through the motions at work, and nothing I did had really changed the trajectory I was already on. But when I started working full-time, my approach changed, and I accomplished things that I didn’t think I would when I started. It literally felt like a jump discontinuity in my life trajectory. Looking at my experiences this way made me realize how complacently I took my first internship. I was proud because I made progress, but in reality that should’ve been the baseline, and I could have accomplished a lot more.

The goal isn’t to beat your baseline all the time, it's to make your old baseline irrelevant as often as you can. Don't just ask whether you're moving forward, or even whether you’re moving forward faster than you were before. Ask whether you're going somewhere you wouldn't have gone otherwise.

And yes, I realize the mathematical definition of jump discontinuity does not perfectly fit the metaphor, but I hope the point comes across :)

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