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Let's say A is smarter than B if A knows about topic X, but B doesn't.
Step 1: Let's say you don't know about quantum biology. But Charlie knows, because they currently do a phd in it.
Step 2: Go to Charlie. Say: "I heard about quantum biology, and it sounds interesting. Could you give quick intro on it?"
Step 3: Charlie says (eager to talk about the cool idea they found): "Sure. Quantum biology is [two hour forty-seven minute long monologe]."
Step 4: Important! Listen to it.
Step 5: BOOM! Now you also know about quantum biology.
Repeat it for every topic. If you partition humanity along every topics, you will always be in the in-the-know part. By Zorn's lemma[1] you will be one of the smartest person in the world.
To be fair, in real life there are time and energy bounds, not everyone has time to talk about their topic, and active listening can be a hard mental work. But it worked for me a surprising amount of times. Well, surprising at first, then I adjusted my expectations.
actually you might not need Zorn's lemma for this, but it sounds so cool
It's evening, the sun is set. A man walks up to a scholar:
"Scholar, the sun rose yesterday and today morning. Will it rise again tomorrow?"
"Man, I don't know, it's kinda dark right now. Have you heard about the no free lunch theorem?"
One of my favourite Gettier-like problems is about black holes.
Say you have a very dense star. It is so dense, that the gravitational force on its surface is capable of pulling back even the particles of its light, leaving only a black hole in the sky. How large can it be with a given mass?
It's an easy exercise using Newtonian mechanics. Take a light particle with mass . Its gravitational energy at a distance is , and its kinetic energy is at the start. If the total energy is negative, then the path of the light particles will stay within a boundary. Therefore, the answer to the question is , if the object is smaller than this, then it will be a black hole.
Of course, for that dense objects, Newtonian predictions break down. We should care about curved spacetime and use general relativity in our calculations. The answer (to my knowledge) is the Schwarzschild radius, which is .