Dividing by zero — the fundamental no-can-do of arithmetic. It is somewhat surrounded by mystery, and is a constant source for internet humor, whether it involves exploding microcontrollers, the collapse of the universe, or crashing your own world by having Siri tell you that you have no friends.
It’s also one of the few things
gcc will warn you about by default, which caused a rather vivid discussion with interesting insights when I recently wrote about compiler warnings. And if you’re running a modern operating system, it might even send you a signal that something’s gone wrong and let you handle it in your code. Dividing by zero is more than theoretical, and serves as a great introduction to signals, so let’s have a closer look at it.
Chances are, the first time you heard about division itself back in elementary school, it was taught that dividing by zero is strictly forbidden — and obviously you didn’t want your teacher call the cops on you, so you obeyed and refrained from it. But as with many other things in life, the older you get, the less restrictive they become, and dividing by zero eventually turned from forbidden into simply being impossible and yielding an undefined result.
And indeed, if a = b/0, it would mean in reverse that a×0 = b. If b itself was zero, the equation would be true for every single number there is, making it impossible to define a concrete value for a. And if b was any other value, no single value multiplied by zero could result in anything non-zero. Once we move into the realms of calculus, we will learn that infinity appears to be the answer, but that’s in the end just replacing one abstract, mind-boggling concept with another one. And it won’t answer one question: how does all this play out in a processor? Continue reading “Creating Black Holes: Division By Zero In Practice”
Okay, perhaps the title here is a bit of an exaggeration, but this black hole lamp made by [Will Donaldson] is an interesting approach to creating a black hole simulation without destroying the earth. This lamp uses a ring of LEDs surrounding a piece of black Lycra. A motor in the lamp base pulls the Lycra, representing the distorting effect that a singularity has on space-time. It also demonstrates how black holes can (in theory) evaporate by emitting radiation, a phenomenon called Hawking radiation. It’s a simple, but effective approach that physicists have used to demonstrate gravity for some time, using stretch fabric to simulate space-time and show how gravity warps it. It’s a two-dimensional version of a three (or more) dimensional phenomenon, but it works. And, hopefully, it won’t swallow the planet and destroy us all like the real thing might.
Continue reading “Build Your Own Black Hole”
“If I have seen further than others, it is by standing upon the shoulders of giants.” This famous quote by Isaac Newton points to an axiom that lies at the heart of The Sciences — knowledge precedes knowledge.
What we know today is entirely based upon what we learned in the past. This general pattern is echoed throughout recorded history by the revelation of one scientific mystery leading to other mysteries… other more compounding questions. In the vast majority of cases these mysteries and other questions are sprung from the source of an experiment with an unexpected outcome sparking the question: “why the hell did it do that?” This leads to more experiments which creates even more questions and next thing you know we go from moving around on horse-drawn carriages to landing drones on Mars in a few generations.
The observant of you will have noticed that I preceded a statement above with “the vast majority of cases.” Apart from particle physics, almost all scientific discovery throughout recorded history has been made via experiment and observation. There are a few, however, that have been discovered hidden within the confines of an equation, only later to be confirmed with observation. One such discovery is the Black Hole, and how it was stumbled upon on a dusty chalkboard in the early 1900s will be the focal point of today’s article.
Continue reading “Black Holes and the Elusive Mystery That Lies Within an Equation”