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Time Dilation Time dilation stems from Einstein’s theory of special relativity, which says that moving clocks tick more slowly by a factor (called the Lorentz factor). At everyday speeds, the Lorentz factor is approximately one, so the effect is negligible. Near light speed, it becomes dramatic. Here’s the Lorentz factor formula showing how the factor increases with speed: $$ \begin{aligned} &\gamma = 1/\sqrt{1 - v^2/c^2}\\ &\text{where}\\ &\hspace{1em}\gamma = \text{Lorentz factor}\\ &\hspace{1em}v = \text{relative velocity between two objects}\\ &\hspace{1em}c = \text{speed of light} \end{aligned} $$Project Hail Mary The ship in Project Hail Mary (the Book and Movie) travels at about 92% of light speed, so the Lorentz factor is approximately 2.55. In reality, the ship would most likely accelerate for half the trip and decelerate for the rest, but let’s keep it simple using constant velocity. One year on the ship corresponds to about 2.55 years outside it. That’s why a journey that feels like a few years to Grace can become more than a decade for Earth. ...

Life is not a game, but there sure are a lot of games in it. Game Theory Game theory is a branch of mathematics that studies the behavior of individuals in situations where their decisions impact one another. It has applications in parlor games as well as broader contexts. Nash Equilibrium Do you remember the movie “A Beautiful Mind”? It’s based on a true story about John Nash, a mathematician who developed the concept of Nash equilibrium. In game theory, Nash equilibrium is a situation where no player can benefit by changing their strategy, assuming the other players’ strategies remain unchanged. It’s a fundamental concept in understanding strategic interactions between individuals or entities. ...

The fastest path between two points is a straight line, unless everyone follows the same line. Latency vs. Bandwidth vs. Throughput In computer networks, two metrics are critical to determining performance: Bandwidth: the maximum things you can get done at once. Latency: how long each thing takes. It feels obvious to optimize bandwidth. Theoretically, you can get everything done at one time and not worry about how long it takes, but the impact of latency multiplies. ...

Ironically, the best solutions for hard problems often involve taking shots in the dark. Everyone loves control, but the problem is you can’t do everything at once. You can’t count the grains of sand on a beach, because even with the utmost determination, the grains are constantly being moved to and from the beach as you count. But one person could easily use randomness to sample a variety of places on a beach to calculate about how much sand in a fraction of the time. ...

Relax everyone, if you ever feel stuck just… no, that’s all, that’s the answer. If you ever feel stuck, relax. Constraints are often the first thing you should question, not the first thing you should obey. For example, imagine you’re optimizing an event seating chart based on the compatibility of people sitting next to each other. The real question is not “How do we compute the perfect seating chart?” It is “How do we reframe the problem so that we find the best solution for the things we actually care about?” ...