Independent Components of a 4D Riemann Tensor et al.

May 13, 2025 - 6 mins read

Introduction I was at the tutorial session for the General Relativity course. We were discussing 2-sphere manifold, calculating the Riemann tensor, Ricci tensor, Ricci scalar and Einstein Tensor. The Instructor then asked us to compute the independent components of the Riemann Tensor in 4-Dimensions as a fun painful exercise to get a hang of it. And here we are! Riemann Tensor in 4-Dimensions We have some (anti)symmetries we can exploit to reduce the number of independent components of the said tensor.

Murakami's Running Book

May 4, 2025 - 7 mins read

Introduction Last night, I finished my reading of the book, “What I talk about when I talk about Running” by Murakami. It is a memoir, according to the author. However, I believe it is more non-fiction than a memoir. The experiences he shares are things I have experienced myself in the past year since I was bit by the bug called Cycling. A Sense of Nothing Murakami writes along the lines of:

A Programming Server

April 24, 2025 - 4 mins read

This semester, I face quite a few programming-based courses. This means having a suitable development environment and seamless experience; not troubleshooting differences in implementing the compilers (or interpreters) in different operating systems. What I am fussing about is that I use a Windows PC, a MacBook Pro and an iPad as I wish. Setting up and using the programming dependencies on each platform is different. I want to focus on debugging errors generated by me, not on the platform.

My MacBook Can Crunch Numbers

January 24, 2025 - 10 mins read

Series: Local LLMs

Here we are As I described here, I was wonder-struck on how good the LLMs ran on my MacBook Pro. note NOTE: All the executable commands for bash/zsh are copied from openwebui or other respective official docs. If you don’t know what you are running, research it before you do! l’attention info You will have to enable CPU Virtualization in your BIOS/UEFI settings. This is usually done by pressing a key like F2, F12, DEL, or ESC during startup.

The Mutable Landscape of Running LLMs Locally

January 21, 2025 - 7 mins read

Series: Local LLMs

warning Warning: Large image files, specifically 3 files that are each around 50MB in size, and aren’t in Dark Mode: don’t scorch your eyeballs. Background Recently, I use Gemini and ChatGPT frequently, with the former being more prominent. They save a lot of time on searching web to find answers. Before these LLMs, It was a great triumph to find an answer we are looking for just searching the web.

DIY HPC Grid Cluster: Part 1

March 12, 2024 - 7 mins read

Series: HPC Compute Cluster at Home

Why I am interested in Theoretical Physics. However, I can bring many fancy ideas using the Mathematics and Theoretical Laws into new theories, I would waste my time if there is no way to test them. Einstein and his colleagues could come up with calculations that helped test General Relativity. It may not always be the case. With theories becoming more abstract and complicated, and experimental setup getting exorbitant as time passes; I believe, numerical computations and simulations stand to be the first line of defense for further pursued interest in experimental verification of new ideas.

Why Mac Studio Is the Cheapest Hardware

July 11, 2023 - 3 mins read

warning This article is one among many salvaged from my previous blog! It is not on par with my demands of quality but I didn’t feel like abandoning it. Backstory I started working on a project in my free time to cater to curiosity. This project requires extensive use of AI Models that utilizes huge system resources. The details of the project’s scope are not in my authority to discuss here.

Bhagavata Cosmology Under Scientific Scrutiny

August 17, 2022 - 4 mins read

warning This article is one among many salvaged from my previous blog! It is not on par with my demands of quality but I didn’t feel like abandoning it. In this article, I propose a series of steps that can help us prove the existence of certain elements mentioned in Bhagavata Cosmology (BC) from a Scientific Perspective. BC is a vast model with a lot of features that sound like a Fantasy novel at the first glance.

Hyper-V Is Underrated

June 30, 2022 - 8 mins read

warning This article is one among many salvaged from my previous blog! It is not on par with my demands of quality but I didn’t feel like abandoning it. Introduction Virtualization is the process of chopping up of physical hardware of a computer and assigning it to a separate operating system. In layman’s terms, it is just a computer inside a computer, just like Matrix. There are software written to achieve this, and seeing the potential use cases, microprocessor companies like Intel and AMD started supporting it on the hardware level to boost the performance of the Virtual Machines(VMs).

Revisiting Fibonacci Sequence

April 6, 2022 - 4 mins read

warning This article is one among many salvaged from my previous blog! It is not on par with my demands of quality but I didn’t feel like abandoning it. Functional Equations One evening, I felt down for no reason. I felt like not doing anything I could do, including consuming content. Then came a flash of thought, “It’s been a while you have involved yourself with Functional Equations”. This was the spark moment that led me to a short journey of a surge of inspiration from the infinite abyss of artistic temperament.