The hexagrams can be modeled with only 6-bits, but this does not contains enough information for a proper reading of I Ching which also need to account for line changes. So there are really 4 lines: young yin, old yin, young yang, old yang.
A fundamental part of I Ching reading is the implication that each present state is in the process of transforming to another.
Spot on! This is exactly why a simple Math.random() > 0.5 binary flip isn't enough for a proper simulation.You are right that we are mathematically dealing with base-4 logic (6, 7, 8, 9), not just base-2.While there are only 64 hexagrams ($2^6$), there are actually 4,096 possible casting results ($4^6$) when you account for the moving lines. My algorithm is designed specifically to capture the distinct probabilities for all 4 states.
"With evidence of its harms stacking up, it’s already been banned in dozens of countries all over the world, including the United Kingdom and China, where it’s made. Yet last year, its manufacturer Syngenta, a subsidiary of a company owned by the Chinese government, continued selling paraquat in the United States and other nations that haven’t banned it."
Slight correction: I'd only refer to it as a "Single-File Web App" if it has no external dependencies (where as the "HTML Tool" definition allows for external dependencies loaded from CDNs).
I wouldn't call either of these tools that either. Using View Source reveals that there's a pretty obvious build step and confronts you with massive minified blobs. There's no way a person is going to be able open that HTML as a "single file" in their text editor to pick up development where it was left off. (In that regard, the HTML tools in the linked post are closer to the definition, even when they're written to load a module from a CDN.)
I recently had ChatGPT refactor an entire mathematical graph rendering logic that I wrote in vanilla js, and had it rewrite it as GLSL. It took about an hour overall (required a few prompts). That is world-class level in my opinion.
If I tell people that I can write programming code at world-class level and in some of my reviews I make junior mistakes, I make out functions or dependencies that do not exist or I am unable to learn from my mistakes, I would be put on PIP immediately. And after a while, fired. This is the standard LLMs should be held up against when you use the word "world class".
I'm currently trying to get Claude Sonnet 4.5 to produce a graph rendering algorithm, and while it's producing results, they're not the right results. I should probably do this myself and let the AI handle just the boilerplate code.
I have consistently had good results when I understand the problem and outsource the details to AI, but bad results when I try to have it work without me understanding the problem.
Yeah, but then what do you need the AI for? It's programming it myself that helps me understand all the intricacies of the problem. That's exactly the part that gets cut off by outsourcing it to AI. The AI is not a "world class programmer" if it still needs me to tell it the solution to the problem.
This was my first exposure to the Fourier transfer. I also highly recommend this book. It was recommended to me by the head of the math department at university.
Context: I've been working on a non-binary graphing app called FuzzyGraph (https://fuzzygraph.com). I had the rendering logic written in vanilla JS, and wanted to convert the rendering logic to GLSL shader code to speed things up.
I was able to prompt ChatGPT Codex to fully rewrite the render logic using GLSL (without me having to edit it at all). After the first 2 prompts, it was almost fully functional. It took 6 prompts in all to get a full rewrite in GLSL. I have never worked on GLSL code (and was kind of dreading this rewrite), so this was a HUGE accelerant for me. Shout out to OpenAI for an awesome product!
One last thought: this almost felt like a compiler, where I write in a higher-level language (vanilla JS), and have the AI compile it to GLSL for me.
Infinity is simply the name for a process that does not end. Some of these processes increase faster than others (hence larger infinities). Personally, I also like the Riemann sphere model of infinity.
It's worth noting the "Two Sigma" problem on this topic (https://en.wikipedia.org/wiki/Bloom%27s_2_sigma_problem) - "the educational phenomenon that the average student tutored one-to-one using mastery learning techniques performed two standard deviations better than students educated in a classroom environment".
I was public schooled Kindergarten, homeschooled 1st-5th, and public schooled 6-12th grade. My wife was 100% homeschooled. I think it was a good mix for me. And in retrospect, I think it was good I was public schooled for at least some of high school, because I'm not sure my math education would have been as good if I was homeschooled during that period (my parents aren't math people).
But I am a math person, and we are homeschooling our 2 boys. My 12-year-old is able to understand mathematical concept and scientific topics that many high schoolers are never even exposed to. My wife does a great job with many other subjects as well. And we have many great homeschooling parents who group together to teach things they are specialized in (like construction, art, etc). Our homeschool group also has a lot of social time for the kids to just play together (mostly outside). It's awesome.
I think the quality of the education depends on the teachers. And a big part of being a good teacher is caring. Hopefully the parents will care more about their kids than any other teacher would. Additionally, we are in the golden age of homeschooling resources (mostly online).
I appreciate you sharing -- specifically because my kids were Home Schooled until High School and attend Public High School, now.
I feel the same way about the value of early-years Home School and mainstream High School. Mom and I had agreed that we'd let them pick once they hit High School. That coincided with the end of the COVID lockdowns, so being lonely like everyone else, they picked Public School. Prior to COVID, I'd have put money on them remaining Home Schooled.
I did exactly the same things with my kids with regard to advanced math/science topics. Actual "sit down and learn time" was spent 80% on Math/Science and 20% on everything else. And I've found some things benefit being introduced way younger. Things like the theory of relativity are "accepted as fact" more easily when they don't stand in the face of 15-years of observation. It can be understood with cartoons and when the topic is studied -- in depth -- later, they're not having to start from "how, on Earth, does that make any sense?!"
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