901
NYC subway math
Apparently MTA (the company running the NYC subway) has a real-time API. My fascination for the subway takes autistic proportions and so obviously I had to analyze some of the data.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 2,391 posts.
902
Stacking triangles for fun and profit
One thing you may have noticed about the trigonometric functions sine and cosine is that they seem to have no agreed upon definition. Or rather, different authors choose different definitions as the starting point, mainly based on convenience. This isn’t problematic or even particularly unusual in mathematics: as long…
903
904
How I created two images with the same MD5 hash
I posted the following images the other day which although looking totally different have exactly the same MD5 hash ( e06723d4961a0a3f950e...
905
Faster than radix sort: Kirkpatrick-Reisch sorting
Radix sort sorts n w-bit integers by splitting them up into chunks of logn\log nlogn bits each, and sorting each chunk in linear time. Thus it achieves O(nw/logn)O(nw/\log n)O(nw/logn) time.
906
Data Compression Explained (2012)
Copyright (C) 2010-2012, Dell, Inc . You are permitted to copy and distribute material from this book provided (1) any material you distribute includes this license, (2) the material is not modified, and (3) you do not charge a fee or require any other considerations for copies or for any works that incorporate…
907
Poisson Disk Sampling
Stripe Across is a grog. We hope you enjoy it.
908
Very Wrong Math
The difference between misinformation and disinformation is the difference between ignorance and malice. Trolling is somewhat different, incorporating an element of provocation and narcissism. But what the hell is this?
909
A regular expression to check for prime numbers
Regular expressions are extremely powerful. This is something I read at least once or twice every day while reading articles and blogs on the Web.
910
MathBox 2: PowerPoint Must Die
PowerPoint must die.
911
The Smallest Hash Table
This December I once again did the Advent of Code , in Rust. If you are interested, my solutions are on Github. I wanted to highlight one particular solution to the day 2 problem as it is both optimized completely beyond the point of reason yet contains a useful technique. For simplicity we’re only going to do part 1…
912
Mathematical Patterns That Eventually Fail
Sometimes patterns can lead you astray. For example, it’s known that $latex \displaystyle{ \mathrm{li}(x) = \int_0^x \frac{dt}{\ln t} }$ is a good approximation to $latex \pi(x),$ the number …
913
914
Reinforcement learning, explained with a minimum of math and jargon
To create reliable agents, AI companies had to go beyond predicting the next token.
915
Has an uncomfortable truth been suppressed?
Update to post, added 11th September. As expected, there is another side to the story discussed below. See this statement about the decision by the Mathematical Intelligencer and this one about the…
916
Do simpler machine learning models exist and how can we find them?
The above is the title of a talk by computer scientist Cynthia Rudin. here’s the abstract:
917
Seemingly impossible functional programs (2007)
Andrej has invited me to write about certain surprising functional programs. The first program, due to Ulrich Berger (1990), performs exhaustive search over the “ Cantor space ” of infinite sequences of binary digits. I have included references at the end. A weak form of exhaustive search amounts to checking whether…
918
Base-122 – A space efficient alternative to base-64
A space efficient UTF-8 binary-to-text encoding
919
920
Visualizing the Math Behind Logistic Regression and Newton's Method
The Laziest Programmer - Because someone else has already solved your problem.
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922
Who Can Understand the Proof? A Window on Formalized Mathematics
Stephen Wolfram discusses understanding proofs discovered using automated theorem proving. Based on Wolfram’s proof of the simplest axioms of logic of Boolean algebra.
923
The 8000th Busy Beaver number eludes ZF set theory (2016)
I’ve supervised a lot of great student projects in my nine years at MIT, but my inner nerdy teenager has never been as personally delighted by a project as it is right now. To…
924
Why cans of soup are shaped the way they are
What is special about cylinders, and why do they have specific aspect ratios?
925
Using k-d trees to efficiently calculate nearest neighbors in 3D vector space
What would the world look like if there were only 16 colors? I use k-d trees to perform nearest neighbor search to find out.
926
927
Relaxed Radix Balanced Trees (2024)
I’m adding immutable vectors to my language, Ivan, and needed to pick a suitable data structure to implement them. Clojure uses Persistent Vectors (PVs) which support lookups, updates, and appends all in ‘effectively’ constant time. However, it doesn’t have efficient insert or merge operations. Relaxed Radix Balanced…
928
The 2,500 year old history of why Python’s all([]) returns True
How a Python function relates to a two thousand year old debate in philosophy
929
Memory access is O(N^[1/3])
In computer science, we often compare the efficiency of algorithms by describing their runtime as a function of the size of the input. Sorting is O(n * log(n)), meaning that sorting a list of N items takes an amount of time proportional to the number of items multiplied by its logarithm. Matrix multiplication is…
930
What if AI doesn't need more RAM but better math?
How TurboQuant compresses the KV cache without losing accuracy, and what that could mean for memory stocks