While reading the Jelly-UI source I learned that you can use slot tags to effectively punch holes in the shadowdom on a web component. The elements passed in as component children can be assigned to a slot[1] within the component's shadowdom, and the external styles on them continue untouched.
I used Python webview to make some little desktop utilities.
Most modern frameworks feel like they have so much bloat and overhead. I wanted to make some simple things is a simple way, and it seemed like a good solution for that.
Quantum Mechanics (ongoing), Sturm-Lioville theory, Special Relativity (ongoing), Tensors (going towards General Relativity)
What finally clicked: Hermitian matrix, self-adjoint operators, quantum operators for energy and momentum, the Metric (for modeling spacetime curvature), etc.
Would be hard to explain without some equations. Here's an outline:
Nature follows differential equations.
Differential equations are generally complex to solve but have properties that are helpful. E.g., a second order differential equations would have two independent constants of integration in the solution. If two have already been found, a third independent one won't be needed and you already know that you have a complete solution.
For linear equations, if you find enough orthogonal basis functions that are each a solution, even if by hook or crook, you would have found all solutions.
Some functions and operators yield a function with the same form as the original function. E.g., derivative of exponentiation, second derivative of sine, etc.
The differential equation can happen to be such that a function of the above type then cancels out from the equation. This simplifies the equation.
If the above process yields enough orthonormal basis functions, then we know we have the entire space of solutions.
When the operator happens have some properties, the above happens.
Euler's equation links exponential to sine and cosine. That makes complex numbers useful. Then exponentiation covers sine and cosine too.
Magnitude of complex numbers is the number multiplied by its complex conjugate.
The math proofs extend from real numbers (actually needed by Physics) to complex numbers by using complex conjugates.
Hermitian matrices and self-adjoint operators are special cases that bring orthogonal basis functions, real-valued solutions (in spite of using complex numbers), etc.
While reading the Jelly-UI source I learned that you can use slot tags to effectively punch holes in the shadowdom on a web component. The elements passed in as component children can be assigned to a slot[1] within the component's shadowdom, and the external styles on them continue untouched.
1. https://github.com/jelly-org/ui/blob/main/src/components/res...
I used Python webview to make some little desktop utilities.
Most modern frameworks feel like they have so much bloat and overhead. I wanted to make some simple things is a simple way, and it seemed like a good solution for that.
I've been working on the course https://www.coursera.org/specializations/machine-learning-in... . No news to anyone on here, but new to me.
Quantum Mechanics (ongoing), Sturm-Lioville theory, Special Relativity (ongoing), Tensors (going towards General Relativity)
What finally clicked: Hermitian matrix, self-adjoint operators, quantum operators for energy and momentum, the Metric (for modeling spacetime curvature), etc.
What's the story of the Hermitian matrix and self adjoint operators?
Would be hard to explain without some equations. Here's an outline:
Nature follows differential equations.
Differential equations are generally complex to solve but have properties that are helpful. E.g., a second order differential equations would have two independent constants of integration in the solution. If two have already been found, a third independent one won't be needed and you already know that you have a complete solution.
For linear equations, if you find enough orthogonal basis functions that are each a solution, even if by hook or crook, you would have found all solutions.
Some functions and operators yield a function with the same form as the original function. E.g., derivative of exponentiation, second derivative of sine, etc.
The differential equation can happen to be such that a function of the above type then cancels out from the equation. This simplifies the equation.
If the above process yields enough orthonormal basis functions, then we know we have the entire space of solutions.
When the operator happens have some properties, the above happens.
Euler's equation links exponential to sine and cosine. That makes complex numbers useful. Then exponentiation covers sine and cosine too.
Magnitude of complex numbers is the number multiplied by its complex conjugate.
The math proofs extend from real numbers (actually needed by Physics) to complex numbers by using complex conjugates.
Hermitian matrices and self-adjoint operators are special cases that bring orthogonal basis functions, real-valued solutions (in spite of using complex numbers), etc.
References:
Spectral Theorem
Sturm Liouville Theory
Current AI can hack servers better than most hackers.
I have been learning langchain or langgraph for making good Agentic AI workflows.