Human Intelligence - Worksheet 1

Since we are offloading our thinking to AI, how do we ensure we are still thinking? Here’s a fun problem sheet for the curious:

Math.

1. Problems:

   1. Prove the Pythagorean theorem: Given a right triangle with sides a, b and hypotenuse, c. Prove that a^2 + b^2 = c^2.

2. Instructions: Try not to use AI. Try not to google. When all else fails, and if you end up googling, then come up with 3 distinct ways to prove this.

Probability.

1. Problems

   1. On a line segment of length L with A and B as endpoints, we chose a single point b/n A and B uniformly randomly. What is the expected length of the first segment?

   2. On a line segment of length L with A and B as endpoints, we chose two points b/n A and B uniformly randomly. What is the expected length of the first segment?

   3. One a circle of unit length with center at (0,0). We chose two points on it uniformly randomly. What is the expected length of the arc containing (1,0).

2. Instructions

   1. Try not to use AI. Try not to Google. If you end up googling, then answer the following:

   2. Answer the third problem by converting it into a version of second problem. Irrespective of what the math says, explain intuitively why the final answer is not a even split.

System Design.

1. Problems

   1. Build your own Temporal from scratch. Minimal features is fine. To get you started, I would ask a coding agent to list the features of https://github.com/temporalio/temporal without asking for system design. You can proceed from there.

2. Instructions

   1. No coding agent. Auto complete in IDE is fine.

   2. Idea here is not to rebuild Temporal again but something like what Karpathy's nano-GPT did to GPT.

Data Analysis.

1. Problems

   1. Slack MCP, Notion MCP and GWS CLI (for google drive) gives you a pool of all data we have at the company. Using this, come up with two interesting hypothesis. For each hypothesis, perform data analysis to prove or invalidate your hypothesis. Explain your findings visually.

2. Instructions

   1. Use coding agents for data pull, analysis and visualisation.

   2. Try to come up with most interesting/ non-obvious hypothesis. If you are not able to prove your hypothesis, try again.

Old school Research.

1. Problems

   1. Come up with two hypothesis around following areas: Neural/ Cognitive/ Behavioral/ Biological. Figure out what would be a nice way to test your hypothesis. Recruit people to help you in the experiments. Validate/ invalidate your hypothesis.

2. Instructions

   1. Use anything you need. But the hypothesis that you come up with has to be something to do with humans and their behaviours. Something for which you need to pull data from people.

Open ended problems.

1. Problems

   1. Web search index using LLMs: Currently for simple-to-medium agents, if you extrapolate the costs paid to LLMs and costs paid to web search tool-call providers, they both earn more or less same. For ex: for fact-checker agent that we are developing, the cost for web search is 0.30$ and cost for models is 0.02$ for invocation. Think about that for a moment. The latest all-rage technology is costing only 15x lesser than old-school search index. Let's dig deep into what web search provides: A machine that ingested the entirety of internet and given a query, surfaces the most relevant portions of the internet clustered by web pages. You know what else is a similar machine? LLM. Given this context, how can we replace a search index (Brave/ Exa/ Google etc) by using LLMs (finetuned if required?).

2. Instructions

   1. Use AI and any resource whatsoever.

   2. Come up with different system designs, MVPs, POCs, Prototypes to figure out a way to prove your idea will work.