1381
Random Solutions are Often Good Enough
Sometimes taking the easy way out isn’t nearly as bad as it might seem! posted Thursday February 13th, 2014 Tagged: Math
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
1382
The quadratic formula and low-precision arithmetic
The familiar quadratic formula can give the wrong answer in a program due to numerical precision issues. This post shows what can go wrong and how to fix it. Especially important in low-precision arithmetic.
1383
Math library functions that seem unnecessary
Functions include in the standard C math library that seem unnecessary at first glance and why they are necessary.
1384
Principal Component Analysis for Dummies
(I recently wrote a new post that you may also find interesting called Principal Component Analysis 4 Philosophers) Having been in the social sciences for a couple of weeks it seems like a large am…
1385
The quadratic sandwich
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your…
1386
A Long Peek into Reinforcement Learning
<meta http-equiv=
1387
The game theory of seduction and marriage with Jane Austen
The enduring success of her early 19th century novels are in large part due to their persistent relevance
1388
Not all elementary functions can be expressed with exp-minus-log
a personal blog
1389
A Brutal Look at Balanced Parentheses, Computing Machines, and Pushdown Automata
As discussed in Pattern Matching and Recursion , a well-known programming puzzle is to write a function that determines whether a string of parentheses is “balanced,” i.e. each opening parenthesis has a corresponding closing parenthesis, and the parentheses are properly nested.
1390
1391
1392
Revisiting the algorithm that changed horse race betting (2023)
Explore Bill Benter’s iconic horse betting strategy, enhanced with modern code and contrasted against three decades of evolving data.
1393
Trying Kolmogorov-Arnold Networks in Practice
There's been a fair bit of buzz about Kolmogorov-Arnold networks online lately. Some research papers were posted around claiming that they offer better accuracy or faster training compared to traditional neural networks/MLPs for the same parameter count.
1394
The Entropy of a Markov Chain
A more explicit example
1395
The Point of the Banach-Tarski Theorem
One of my favourite Limited Audience Jokes (although technically it's actually a riddle) goes:
1396
What Are the Odds?
An unusual lottery result made the news recently: on October 1, 2022, the PCSO Grand Lotto in the Philippines, which draws six numbers from $latex {1}&fg=000000$ to $latex {55}&fg=000000$ a…
1397
How to average floating point numbers (2015)
When it comes to accuracy, how you add a series of arbitrary values together, and average them still matters.
1398
1399
The Second Law of Thermodynamics (2011)
Web site content explains the modern view of entropy change and the dispersal of energy in a process (at a specific temperature). It has been selected for instructors in general and physical chemistry by Dr. Frank L. Lambert, Professor Emeritus (Chemistry) of Occidental College, Los Angeles.
1400
Optimizing a bignum library for fun
Can I make math operations run 100x faster on really, really big numbers?
1401
Revisiting the Fast Inverse Square Root – Is It Still Useful?
In 2005, id Software released the source code for their 1999 game Quake III Arena under the GPL-2 license. In the file code/game/q_math.c , there is a function for calculating the reciprocal square root of a number which at first glance seems to use a very peculiar algorithm:
1402
Use Gröbner bases to solve polynomial equations
A self-contained introduction to Gröbner bases and solving polynomial systems
1403
Nash equilibria in Ballmer's binary-search interview game
Yesterday John Graham-Cumming posted about “Steve Ballmer’s incorrect binary search interview question,” and in the Hacker News discussion, among the predictable “interview culture is flawed!!” complaints, there was some discussion of whether binary search was even the right way to solve Ballmer’s puzzle. Here’s a…
1404
1405
1406
Playing with model trains and calling it graph theory
You’ve probably played with model trains, for instance with something like the Brio set shown below.1 And if you’ve built a layout with a model train set, yo...
1407
From Zero to QED: An informal introduction to formality with Lean 4
An informal introduction to formality in Lean 4
1408
Helmhurts: Placing a WiFi router with the Helmholtz equation
A few posts back I was concerned with optimising the WiFi reception in my flat, and I chose a simple method for calculating the distribution of electromagnetic intensity. I casually mentioned that I really should be doing things more rigorously by solving the Helmholtz equation, but then didn't. Well, spurred on by a…
1409
Learning with Not Enough Data: Semi-Supervised Learning
<meta http-equiv=
1410
Darts, Dice, and Coins: A beautiful article on a beautiful algorithm
Earlier this year, I asked a question on Stack Overflow about a data structure for loaded dice . Specifically, I was interested in answering this question: