Sunday, October 05, 2025
📝 Ephemeral Notes
- #til2025 Liar’s Poker
- Game played at Solomon Brothers, a bond firm, that mimics the bond market
- Similar to Liar’s dice, except the numbers are generated by one-dollar bill
- #til2025 Markov Chains
- Average outcome gets closer to expected numbers with independent events - Law of large numbers
- only proved this for independent events
- up until Andrey Markov, probability relied on this independence assumption
- Andrey Markov (socialist, atheist) and Pavel Nekrasov (tsar, religious) argued whether mathematics can explain will of god and free will
- Nekrasov: if you see the LLN then there must be independent events
- Used Belgian Marriage dataset and other social statistics to argue that because we see convergence of statistics which is observing the LLN then the decisions causing such social events (marriage, crimes, etc) must be independent
- Free will, thus, be measured
- Used Belgian Marriage dataset and other social statistics to argue that because we see convergence of statistics which is observing the LLN then the decisions causing such social events (marriage, crimes, etc) must be independent
- Markov: set out to prove dependent events can also follow the LLN
- Used a poem to train a text prediction model and found that the probability of two letters that followed VV, CC, VC, or CV case occurred differently than if you computed their expected average assuming independence which is $P(C/V) \times P(C/V) != P(actual VV/CC/CV/VC)$
- Built a model to make this dependent event prediction which is “markov chain” and showed that it can follow the LLN as well
- “Free will is not necessary to do probability” - Markov proved that observing LLN statistics does not mean independent events
- Nekrasov: if you see the LLN then there must be independent events
- Famous applications
- How much nuclear material is needed for a self-sustaining nuclear bomb?
- Transition probability that depends on the environment and type of neutron (fast/slow) between the states of traveling or leave/absorb or fission
- Used one of the first computers to simulate this to compute the k-value
- #til2025 Monte Carlo Method
- How do you find anything in an ever expanding sea of information on the internet
- Yahoo founders with Masayoshi Son’s investment used “keyword search” to make Yahoo the default search engine, but it can be easily tricked
- Sergey Brin and Larry Page developed “PageRank” algorithm that used site links to measure the quality which is essentially a representation of a Markov chain and the number of links becomes the transition probabilities
- Over time the expected values of the network is the quality of the page
- Not all pages are connect so they setup a random jump to another page
- Google transformed from “homepage” style site that relied on ads on the homepage to a more “portal” style site
- Language models
- In 1948, Claude Shannon used Markov chain to predict words
- #til2025 Claude Shannon
- “Father of information theory” or “Father of digital age” and creator of “bit”
- First to use Boolean algebra
- Designed and built a learning machine called Theseus. Which is a maze with a mechanical mouse that learns how to search for a target using the shortest path
- Anthropic’s AI model is named after him
- How much nuclear material is needed for a self-sustaining nuclear bomb?
- It is memoryless system which makes approximation of complex system possible
- Average outcome gets closer to expected numbers with independent events - Law of large numbers
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created: 2023-01-16 11:50