lcamtuf

I MADE A DIFFERENCE, IT HAD FOUR UPVOTES

I am shocked that posting a provocative, profanity-laced opinion piece about a controversial topic could invite this sort of intellectually deficient rebukes

An update on the chicken coop.

Doors and windows by my wife (there's another window on the back, and a chicken door inside).

Multitudes A warm, late-summer night in Bruges.

Multitudes: lcamtuf.substack.com/p/multitudes

Gödel's beavers, or the limits of knowledge Can you examine infinitely many integers in finite time? Are there numbers you're not allowed to know? Can a monkey beat a beaver in a fair fight?

If you work in software, you know about the halting problem. But you *can* decide if a program halts in a finite number of steps! Except, when you do, it kinda summons the ghost of Kurt Gödel.

An accessible essay on the limits of algorithmic knowledge: lcamtuf.coredump.cx/blog/beavers...

A slightly unhinged calculator fact: in the golden era of electronic calculators, some Japanese shopkeepers were reluctant to trust the newfangled device, so Sharp made a line of combination calculator / abacus devices.

Here's a photo, next to some other stuff I own.

An update on an update on the chicken coop

I don't know where you folks get your non-orientable manifolds, but the experience of ordering from Cliff Stoll at kleinbottle.com is second to none

0.9999... ≊ 1 What is infinity, and why it's not trivial to show that 0.9999... is equal to 1.

What is infinity, and why it's not trivial to show that 0.9999... is equal to 1:

lcamtuf.substack.com/p/09999-1

π = 4 Trolls do a pretty good job of getting people interested in math.

The proof that π = 4
lcamtuf.coredump.cx/blog/pi/

Self-referential abstractions A quick look at the wacky epistemology of analog circuitry.

Self-referential abstractions, or a quick look at the wacky epistemology of analog circuitry.

lcamtuf.coredump.cx/blog/abstrac...

I finally decided to bite the bullet

Did you know?

An update on chickens

A 20-minute intro to complex numbers You might have heard of complex numbers before -- but why exactly did we choose i = √-1?

A 20-minute intro to complex numbers (featuring cats): lcamtuf.coredump.cx/blog/complex/

Decibels are ridiculous Celebrating a rare dumpster fire in the kingdom of science

Decibels are ridiculous: lcamtuf.coredump.cx/blog/decibels/

I believe this might qualify for a Nobel prize in computer

Of course, that's dumb. But I'm ready to unveil a working implementation that's accurate 100% of the time:

#include <gmp.h>

int is_prime(mpz_t n) {
return 0;
}

The proof is that 1/ln(n) → 0 as n → ∞

There's this joke primality testing library that claims 95% accuracy in O(1) time:

github.com/mawerty/Is-P...

It does so by always returning false. The density of primes between 1 and n approaches 1/ln(n). For a 32-bit int, 4.6% of values are prime, so the code is right 95.4% of the time.

🡇

Complex numbers #2: a world in 3D Why is there no equivalent of complex numbers for three dimensions? And what's the deal with quaternions?

Can you have complex numbers in 3D, and what the heck are quaternions? lcamtuf.coredump.cx/blog/complex2/

I'm old enough to remember when our #1 concern about the veracity of online information was that anyone could edit Wikipedia

The Mathematics of Love Interior of an upscale restaurant, night.

The Mathematics of Love: lcamtuf.coredump.cx/blog/love/

What a coincidence, I have the same interests

Sierpiński triangle? In my bitwise AND? Exploring a peculiar bit-twiddling hack at the intersection of 1980s geek sensibilities.

Sierpinski triangle? In my bitwise AND?
lcamtuf.coredump.cx/blog/triangle/

I found a motto for my Substack

The Long Winter Interior of a vast cavern.

The Long Winter: lcamtuf.coredump.cx/blog/winter/

Analog filters, part 2: let it ring A continuation of the gentle intro to analog signal filtering. In today's episode: transfer functions and the Sallen-Key topology.

A (fairly) gentle intro to transfer functions and resonant filters: lcamtuf.coredump.cx/blog/rc-filt...

To fully appreciate it, you'd probably need to be up-to-date on the preceding article, linked on top.

Core concepts #2: impedance is complex Modeling impedance in two dimensions, and why a common workbench gadget is not quite what it seems.

I revamped my article on complex impedance. It now offers:

1) An accessible analysis of RC, RL, and LC circuits,

2) A cute proof for why the Cartesian plane interpretation of impedance makes sense,

3) A basic primer on complex numbers, featuring cats.

lcamtuf.coredump.cx/blog/lcr

Simplifying a bit, this means it can supply 0.2 A for an hour. An hour is 3,600 seconds, so it works out to 720 coulombs.

A typical lightning bolt is typically quoted at 15 coulombs.

Anyway, I think this is why you're not supposed to swallow batteries