Arya’s Algorithms

  The Beautiful Mind — Where Am I in My Own Mind? Tonight, as I sit here writing, I feel the strange weight of a question that refuses to leave me: Where am I inside my own mind? Not where my body is, not the coordinates of this chair in space, but the “I” that thinks, feels, doubts, dreams. If I close my eyes, I can sense thoughts moving, like clouds across a sky, but the sky itself remains invisible. It’s odd—when I press my hand against my chest, I can feel my heartbeat, strong and insistent. My body is here, undeniably. But the “me” that wonders about all this—is that in the heart? The brain? Somewhere else entirely? Neuroscience insists the answer lies in the folds of the cortex, in networks like the default mode network that lights up when we daydream or self-reflect. I’ve read about split-brain patients, where one hemisphere is disconnected from the other, and suddenly it’s as if two separate selves begin to live in the same body. How fragile, how strange, that what I ...

The Psychology of Influence: Why Some People Are Naturally Persuasive You know someone like this: they walk into a room and somehow become the center of attention without trying. When they suggest a restaurant, everyone agrees. When they propose a solution at work, it sounds reasonable even if you initially disagreed. When they ask for a favor, you find yourself saying yes before you've fully considered what you're agreeing to. These naturally persuasive people seem to possess an almost magical ability to influence others, but what they're actually wielding is a sophisticated understanding – conscious or unconscious – of human psychology. Influence isn't manipulation, though the line can sometimes blur. At its best, influence helps create alignment, builds cooperation, and guides groups toward beneficial outcomes. Understanding the psychology behind persuasion can make us both more effective communicators and more discerning consumers of others' influence attempt...

  Getting Stuck: The Case of the Elusive Cycle This is another chapter in my Getting Stuck series, where I document the messy, often frustrating process of solving computer science problems. This episode is about graph theory — and how I got trapped trying to detect cycles in a directed graph. Sounds easy, right? Well… let’s see. Step 1: The Obvious Attempt The problem: Given a directed graph with n nodes and m edges, detect if it contains a cycle. Immediately, I thought: Easy, just do a depth-first search (DFS) and track visited nodes. So I wrote: from collections import defaultdict class Graph: def __init__(self, n): self.n = n self.adj = defaultdict(list) def add_edge(self, u, v): self.adj[u].append(v) def has_cycle(graph): visited = [False] * graph.n def dfs(u): if visited[u]: return True visited[u] = True for v in graph.adj[u]: if dfs(v): return True ...

  Warping Reality - My Journey Through Spacetime and General Relativity Einstein's general relativity shattered my conception of space and time as a fixed stage where physics plays out. Instead, I discovered that spacetime itself is a dynamic participant - curved by matter and energy, responding to their presence like a flexible membrane. This wasn't just a new theory; it was a complete reconceptualization of reality's fabric. My first glimpse came through the equivalence principle. Einstein realized that you can't distinguish between gravitational acceleration and acceleration due to motion without looking outside. An elevator falling freely feels weightless, while an accelerating elevator mimics gravity. This seemingly simple observation led to the profound insight that gravity isn't a force pulling objects together, but the geometry of curved spacetime. The mathematics initially overwhelmed me. Tensor calculus, Riemannian geometry, covariant derivatives - conc...

  The Pit of Egyptian Fractions: Sploding Rational Numbers Into Unit Fractions There are problems that hide their teeth. They grin at you like puzzles for children, then drag you into quicksand. Egyptian fractions are one of those problems. The rule is simple: Problem. Write any rational number p q \tfrac{p}{q} as a sum of distinct unit fractions: p q = 1 a 1 + 1 a 2 + ⋯ + 1 a k , a i ∈ Z +  distinct . \frac{p}{q} = \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_k}, \quad a_i \in \mathbb{Z}^+ \text{ distinct}. The Egyptians did this thousands of years ago. They refused to write 3 4 \tfrac{3}{4} as “three-fourths.” Instead, they would say: 3 4 = 1 2 + 1 4 . \frac{3}{4} = \frac{1}{2} + \frac{1}{4}. At first, I thought: how charming, how elementary. Surely this would be the lightest kind of math to play with. Instead, it became a pit. Step 1: The Honeymoon Phase I began with easy cases: 2 3 = 1 2 + 1 6 . \tfrac{2}{3} = \tfrac{1}{2} + \tfrac{1}{6}. 3 4 = ...

  Maxwell's Electromagnetic Revolution - Unifying Electricity, Magnetism, and Light Before Maxwell, electricity and magnetism seemed like separate phenomena connected by mysterious influences across empty space. After Maxwell, we understood that electromagnetic fields are as fundamental as matter itself, propagating as waves through the vacuum at the speed of light. My journey through Maxwell's equations revealed not just the unification of electric and magnetic phenomena, but the birth of field theory and the first hint that light itself is an electromagnetic wave. The story began with isolated observations that seemed unrelated. Coulomb's law described the force between electric charges: F = kq₁q₂/r². The Biot-Savart law explained how electric currents create magnetic fields. Faraday's law of induction showed that changing magnetic flux generates electric fields. Ampère's law connected magnetic fields to the currents that produce them. Each law captured an impor...

The Invisible Puppeteers: How Cognitive Biases Pull Your Strings You are the hero of your own story. You make decisions. You weigh the evidence. You are, in your own mind, a rational actor navigating a complex world. It’s a comforting narrative. But it’s mostly an illusion. Beneath the surface of your conscious thought, a group of invisible puppeteers is constantly at work, subtly tilting the scales of your judgment, shaping your perceptions, and guiding your choices. They are not malevolent. They’re just efficient. They are **cognitive biases**—mental shortcuts gone rogue. This isn't about calling you stupid. This is about understanding the fundamental, and often flawed, software that every human brain runs on. #### **Why Do These Puppeteers Exist?** Blame evolution. Our ancestors on the savanna didn't have time to perform a complex cost-benefit analysis when they heard a rustle in the grass. **He who hesitated was lunch.** To survive, our brains developed mental shortcuts—kno...

  Getting Stuck: When Cooperation Collapses — Repeated Prisoner’s Dilemma with Noise This was the one problem that looked like a polite conversation between two rational agents — and turned into a screaming match with foggy hearing. I wanted to understand how cooperation could be sustained between selfish agents when their interactions were repeated but noisy. Sounds textbook, right? Famous results (tit-for-tat, folk theorem, grim trigger) promise neat strategies. But once I actually started to play with imperfect observation — the small, realistic twist where you sometimes misread the other player’s move — everything that was tidy started to fray. This is the story of getting stuck: my naive assumptions, the routes that wasted time, the experiments that confused me, and finally the insight that pulled me out. The Game (short version) One-shot Prisoner’s Dilemma (payoffs in standard normalized form): Two players simultaneously choose C (cooperate) or D (defect). Payof...

  Digital Intimacy: How Technology is Reshaping Human Connection At 2 AM, you're texting someone across the country who truly understands your anxiety about tomorrow's presentation. You've never met them in person, but they know details about your life that even close friends don't. Meanwhile, your neighbor of five years remains a stranger, and your college roommate's carefully curated Instagram posts leave you feeling more distant from them than ever. Welcome to the paradox of digital intimacy – where technology simultaneously connects us more deeply than ever before while leaving many feeling more isolated than previous generations. Digital intimacy isn't just traditional intimacy moved online; it's an entirely new form of human connection with its own rules, benefits, and dangers. Understanding this new landscape is crucial for anyone navigating modern relationships, whether romantic, platonic, or professional. The Architecture of Digital Connection ...