If we need to measure arc length, the rigorous way is as the following: The part in the middle is tensor metric. but it is from point of extrinsic view, what if we were an ant on the surface made up of u and v, how to calculate the arc length? it's similar as below: … Continue reading How Is Metric Tensor Deduced?

To truly understand how gauge field is required in the 4d version of the electromagnetism equation, However when asking what and how covariant derivative is defined and derived, AI hardly can be helpful other reciting dull and dry textbook words. The best brains of human beings are irreplicable by AI. So here I'd revisit eigenchris's … Continue reading What is Covariant Derivative in EM?

It's always an effective strategy to build from the simplest form for anything, so is applied to build MCP server. Thanks to Matthew Berman, he already posted a clip detailing how he created a "count number of Rs" in a word MCP server and run it in Claude chat box: Then go to the codes … Continue reading Build a Very Simple “Count Number of R” MCP Server

AI is revolutionizing how we conduct business, and it's becoming increasingly clear that the key to this transformation lies in the seamless integration of domain-specific APIs. Instead of navigating multiple platforms, clients can now interact with AI-powered chat interfaces—like ChatGPT, Claude, or DeepSeek—to get work done efficiently. This shift mirrors the iPhone's evolution, where a … Continue reading Building New Business Model Based on MCP

The key idea is that electromagnetism naturally emerges when we enforce local gauge symmetry on a quantum system. Everything works fine in 3D world, but when you elevate to space-time 4D which is a must when we explore the universe deeper, gauge symmetry without introducing some adjusting part is broken. Hence gauge field has to … Continue reading How Introducing the Gauge Field Led to the Discovery of the Electromagnetic Force

Generic LLMs have become a commodity, readily available everywhere. However, specialized LLMs are essential for specific domains. For companies in fields like medicine and finance, where domain expertise and industry-specific terminology are critical, fully training an LLM from scratch may be impractical. In such cases, fine-tuning offers a cost-effective way to tailor an existing model … Continue reading Fine Tune LLM

I don't know why the definition of tensor is so mysterious: tensor is something transform like a tensor. Sho Takatori also pointed out the absurdity and illuminate it with Einstein index notation in real calculus computation. Nevertheless, it's still quite complicated, that's why genius Einstein had to come in and provide a notation for generations … Continue reading Master tensor calculus using Einstein index notation by Sho Takatori

The key to success is marketing and promotion rather than just having the best product. Here’s why: 1. The Best Product Doesn’t Always Win Many great products or services fail simply because nobody knows about them. Meanwhile, inferior products can dominate the market due to superior marketing (think of brands like Coca-Cola vs. generic sodas). … Continue reading Marketing is Key

The key traits that an exceptional mathematician or physicist possesses include the ability to identify abstract similarities and commonalities between seemingly disparate objects. The concept of the "square root of geometry" in the context of describing spinors and supersymmetry serves as an exemplary illustration of this skill. However these explanation from chatGPT is not intuitive. … Continue reading Understanding Square Root of Geometry: Lie Algebra to Spinor

Here is a simple example applying it: Magnetic Field at the Center of a Circular Loop