Blog

Miscellaneous articles not part of a course.

Education and popular science
  1. Newton's laws in relativity
  2. "Calculus-based physics"
  3. The era of Einstein
  4. Why are calculus and linear algebra taught early?
  5. "In space, there's no up or down."
  6. Applied math and mathematical models (waves, walls, particles, noise, vector spaces) 
  7. Against moral thought experiments and for problem-solving
  8. Tips on learning and thinking (making connections, e.g. changing discrete to continuous; geometric interpretations -- sum of things invariant ==> ellipse, pythagorean invariant ==> like spacetime; find vector spaces in everything -- and find other things in everything) ... used to come up with various heuristics like "you need to write/teach what you learn", "you need to make connections", "you need to play with it", "you need to have a geometrical interpretation", "you need to skim through and fill in the gaps for yourself/discover for yourself" ... but fundamental points of learning are: honesty, having a mental framework, abstraction, original/creative thinking ("asking questions", experimenting, trying to fit various frameworks onto it, etc.) ... and on a more "human" note, confidence, figuring out what to emphasize.
Academia and sociology of science
  1. What even are pure and applied math, anyway?
  2. Positive vs normative social science
  3. Why do people conflate philosophy with psychology?
  4. Ranking academic disciplines from science to pseudo-science
  5. What does it mean to "lie with statistics"/rationalization
  6. Can physics solve everything? (counting pencils by studying their internal structure and dynamics, physics as a "stronger theory" that proves counting...)
  7. How to operationalize anything
  8. Know what to optimize (quacks typically target physics among sciences, vaccination among medical procedures, modern history among history, money among social institutions ... ironically, these are exactly some of the most efficient institutions on earth)
Optimizing the Encyclopedia
Encyclopedic/fact-based sciences: history, news; taxonomy, anatomy, geography, astronomy.
  1. Everything you know about history is false.
  2. History needs to be completely reformulated
  3. "But you're supposed to learn from history!" 
  4. Consistent formats: a solution to "bias" in history and the media
  5. A framework for statistical inference in history
Futurism
  1. Age of Gen: a picture of a futuristic transhuman society 
  2. Basilisk, thy name is Simon
  3. The CASIEW-BANGS paradigm -- brain, AI, nanotech, genetics, security; computing, automation, institutional optimization, space, energy, weather
  4. Future timeline
Philosophy

See also the Sequences by Eliezer Yudkowsky, which are a near-perfect introduction to philosophy.
  1. Three domains of knowledge
  2. Philosophy of science: Reductionism
  3. Philosophy of science: proportional to $x$, $\dot x$ or $\ddot x$?
  4. Philosophy of science: Science of the unseen
  5. Philosophy of science: Probabilistic analogs of logical stuff
  6. Logical arguments: What's your point? (opinions, emotion, rhetoric, logical fallacy)
  7. Meaningless questions it's fun to think about 
How things work
  1. Engineering as the theory of airlocks
  2. Transistors as the unit of automation
  3. Computers: Computer hardware (semiconductor devices, logic gates, von Neumann architecture, OS & APIs/layers of software)
  4. Computers: Ways to program (Loops instead of GOTO, HL, compiled, OO, weakly-typed, tidy eval, very high level, direct, CL, systems programming)
  5. Computers: The Internet (networks, DNS servers, browsers, cookies, engines, protocols)
  6. Institutions: Financial industry (securitization, divisions of IB/sell-side/buy-side what is all that)
  7. Institutions: Misc services (insurance, sharing economy)
  8. Institutions: Government (checks and balances, legal theory)
  9. Institutions: Ancient Military strategy 
  10. Institutions: Great Inventions (agriculture, mass-manufacturing)
Sundry
  1. List of inadequate equilibria (forests, food, politics and law, academia, education, other prussian things, specific disciplines, debate, human-related decision-making, human biology)
  2. Reinventing grammar
  3. Concept for a systematic OS
  4. Realistic aliens
  5. How to rebuild civilization after a zombie apocalypse
Short topics
  1. Multiplicative calculus: Probability of immorality for a transhuman being
  2. Filters and hyperreal numbers: [abhimanyu.iogithub 1, github 2]
  3. Fractional calculus: [arXiv 1, arXiv 2]
  4. Generalised determinants: [arXiv]
  5. Fractals
Special things (functions, numbers, polynomials, sequences, etc.)
  1. Gamma, Bessel, Elliptic, Hypergeo, numbers and sequences
  2. Special polynomials
  3. Riemann hypothesis related stuff
Tricks
  1. Using graphs to create arbitrary images 
  2. Using Fourier series to create images
  3. Gridded cartograms
Probability puzzles and "paradoxes"
Also see the actual Statistics courses.
  1. Why the Monty Hall problem is completely boring
  2. Born on a Tuesday
  3. Sex ratio puzzle
  4. Bertrand's paradox
  5. Two-envelopes problem: beyond the Bayesian explanation
  6. Sleeping beauty, prisoner's dilemma and anthropic reasoning
  7. Hacking Evidential Decision Theory
  8. Oldest person dies [1]
Other interesting math problems
  1. Pi and collisions (the 3blue1brown problem)
  2. A curious infinite sum arising from an elementary geometric argument
Machine Learning projects
  1. A deeper look into convolutional networks [1]
  2. Playing with frequency representations [1]
  3. Neural networks to simulate an entropy source
  4. This Chinese character does not exist (Trained version on Github)
  5. This Letter does not exist
  6. One-shot generative neural networks [1][2]
  7. Random walk of character shapes; this font does not exist
  8. Peeking into GANNs [1]
  9. Progressive GANNs [1]
  10. Various GANN projects: deepfakes, adverserial images, differentiable physics
  11. AI colorize, high-res, framerate, etc. 
  12. Neural style transfer on tunes
  13. Predict Stackoverflow answer time
  14. NLP WTW/TOMT (e.g. "disrecommend" --> "dissuade", "arbitraryhood" --> "arbitrariness")

No comments:

Post a Comment