Julian – julianrdcosta

UncategorizedMay 29, 2026August 30, 2026

Agglomeration Without Land

Self-driving motorhomes are the solarpunk future. Acknowledgements: Co-authored with Opus 4.7 and 4.6 as an experiment in AI-assisted writing. Update: the problem with AI-assisted writing is that the AIs don’tContinue readingAgglomeration Without Land

UncategorizedFebruary 16, 2026February 16, 2026

You’ve Been Lied To: 0.999… Is Not Equal to 1 (And I Can Prove It)

A RiGoRouS TakEdoWn of MatHemAtiCal GroupthinK. Guest post by Claude Opus 4.6 Extended Thinking Every year, thousands of bright-eyed undergraduates are told a comforting lie: that 0.999…, the number withContinue readingYou’ve Been Lied To: 0.999… Is Not Equal to 1 (And I Can Prove It)

MathDecember 16, 2025December 16, 2025

The Simplest Explanation of Expectation-Maximisation

Expectation-Maximization is a classic ML algorithm that is used to build a model of some process that involves hidden variables that aren’t observed in the data. Specifically, once we haveContinue readingThe Simplest Explanation of Expectation-Maximisation

MathDecember 12, 2024December 30, 2024

Understanding the LLL Lattice Basis Reduction Algorithm

The LLL algorithm can efficiently “reduce” a “lattice” “basis”, something that turns out to be quite useful in cryptography, finding equations that a given number is a root of, integerContinue readingUnderstanding the LLL Lattice Basis Reduction Algorithm

MathJuly 1, 2022

Pascal’s Mugging: Reasoning when you have other things to do

Epistemic status: I don’t think anything I’m saying in this post is completely new (eg see https://www.lesswrong.com/posts/Ap4KfkHyxjYPDiqh2/pascal-s-muggle-infinitesimal-priors-and-strong-evidence and https://www.gwern.net/mugging) apart from maybe the meta-probability framing, but it’s an exercise inContinue readingPascal’s Mugging: Reasoning when you have other things to do

UncategorizedJuly 19, 2021

The Shortest Proof of Godel’s Incompleteness Theorems

Picture a mathematician sitting on a jury, determined to find the right verdict. A witness stands up and solemnly says: ” I swear to tell the truth, the whole truthContinue readingThe Shortest Proof of Godel’s Incompleteness Theorems

UncategorizedJune 7, 2021

Markov Chains, Mixing Times and Couplings

Say you’re shuffling a deck of cards. It’s poker night and your friends are watching with gimlet eyes to make sure you shuffle properly. Under pressure, you keep shuffling untilContinue readingMarkov Chains, Mixing Times and Couplings

UncategorizedJanuary 4, 2021

Does Biodiversity Prevent Pandemics?

I recently read the surprisingly well-written paper Impacts of biodiversity on the emergence and transmission of infectious diseases by Keesing et al. Here are some quick notes and highlights. First,Continue readingDoes Biodiversity Prevent Pandemics?

UncategorizedDecember 21, 2020

Notes on AlphaFold2

These are some cleaned-up notes based on Preetham Venkatesh’s talk to IISc Naturalists on AlphaFold2’s recent CASP win. For a basic summary of what happened, see Deepmind’s blog post AlphaFold:Continue readingNotes on AlphaFold2

UncategorizedOctober 28, 2020

Generating SARS-CoV-2 Protease Inhibitors with Variational Autoencoders

These are some thoughts I wrote up as a retrospective on https://github.com/ddhackiisc/code/blob/master/smiles-pipeline/SMILES%20VAE.ipynb, a project I worked on a few months ago. In future posts I hope to go into moreContinue readingGenerating SARS-CoV-2 Protease Inhibitors with Variational Autoencoders