Joel Quiñones

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Bayes’ theorem is probably the single most important thing any rational person can learn. So many of our debates and disagreements that we shout about are because we don’t understand Bayes’ theorem or how human rationality often works. Bayes’ theorem is named after the 18th-century Thomas Bayes, and essentially it’s a formula that asks: when you are presented with all of the evidence for something, how much should you believe it? Bayes’ theorem teaches us that our beliefs are not fixed; they are probabilities. Our beliefs change as we weigh new evidence against our assumptions, or our priors. In other words, we all carry certain ideas about how the world works, and new evidence can challenge them. For example, somebody might believe that smoking is safe, that stress causes mouth ulcers, or that human activity is unrelated to climate change. These are their priors, their starting points. They can be formed by our culture, our biases, or even incomplete information. Now imagine a new study comes along that challenges one of your priors. A single study might not carry enough weight to overturn your existing beliefs. But as studies accumulate, eventually the scales may tip. At some point, your prior will become less and less plausible. Bayes’ theorem argues that being rational is not about black and white. It’s not even about true or false. It’s about what is most reasonable based on the best available evidence. But for this to work, we need to be presented with as much high-quality data as possible. Without evidence—without belief-forming data—we are left only with our priors and biases. And those aren’t all that rational.

Noether’s Theorem ✍️ This equation reveals that every continuous symmetry in nature, a change you can make to a system without affecting its physical laws, brings about a conservation law. In simple terms, if the universe does not react to a certain change in perspective, it must keep a related physical quantity constant. For example, since the laws of physics remain unchanged no matter when you are (Time Symmetry), energy is conserved. Since the laws are the same regardless of where you are (Space Symmetry), momentum is conserved. Because they stay the same regardless of which way you face (Rotation Symmetry), angular momentum is conserved. This insight shifted our view of the universe. We no longer see conservation as just a series of lucky observations, but as a necessary outcome of the symmetry of space and time.