What is a singularity exactly?
The English word singularity really just means a unique event with profound consequences. Like the time JFK was shot, for example, small event, big consequences. It was then adopted by mathematics to describe the point where a function is undefined. So do you guys remember in math class when your teacher was like you can't divide by zero because that's undefined, but they probably didn't really tell you what that meant. But also if you're anything like me, you probably did not ask 'cause you were like, hey, less work for me. And then one day in your mid-20s, you're tryna write a script about singularities and this whole undefined thing comes up, and you finally stopped to think.
What does that actually mean? Well, let's take the function one over x and plot a few points. When x is one, y is one, when x is 0.1, y is 10. And when x is 0.01, y is 100. And if we want to get crazy, when x is 0.000000000001, y is a really big number. So you can see that as x gets really, really, really, really, really small, y gets really, really, really, really, really big. If we want to put this into math talk, we can say that as x approaches zero, y approaches infinity. So it's pretty tempting to just say that when x equals zero y equals infinity, but what about when x is negative? If we plot y for negative x, we see that as x approaches zero y goes to negative infinity. So, what's y at x equals zero then? Mathematicians don't know. They couldn't come up with a good answer, so we just say it's undefined.
This is where our understanding of mathematics breaks down, and we just call it a singularity. So that's what a singularity is in math, but it still doesn't answer the initial question.
What do machines becoming smart have to do with black holes?
Well, let's start with black holes. Believe it or not, this is actually the simpler of the two. This is a black hole and this is its event horizon. The event horizon has often been called the point of no return. It's the boundary where the pull of gravity becomes so strong that once anything goes past it, it can never come back out, even light, which is why black holes are so well, black.
According to general relativity, beyond the event horizon physics starts acting a bit crazy. Our current understanding tells us that right in the center of the black hole, gravity and density become infinitely large. We call this point a gravitational singularity, but what does it mean to say that a physical quantity like gravity is infinite?
We don't know, that's where our understanding breaks down. Comedian Steve Wright put it best when he said "Black holes are where God divided by zero." So basically when things start acting in a weird way, and we can't think of any good answers, we just call it a singularity. And now finally, what has all of this got to do with the singularity? That distant day where AI intelligence outstrips our own, and we're overtaken as the dominant life form on Earth.
The legendary mathematician, John Von Neumann was the first to use this phrase to describe this lovely day when he said "The ever accelerating progress of technology "gives the appearance of approaching "some essential singularity in the history of the race "beyond which human affairs as we know them "could not continue." Okay, so two things here. I just want to clear up that when he says "Human affairs as we know them, could not continue," he doesn't mean that the human race will die out or become extinct. He just means that humanity, as we know it could not continue. There's a big but subtle difference.
Basically there's no way that when this event happens that the way humanity functions now or any kind of model we have for humanity could continue. The second thing is, if you don't know who Jonathan Neumann is, Wikipedia him first thing after this article, he is a legend. Nobel Prize winning physicist Eugene Wigner once said "Only he was fully awake." Something else in Von Neumann's original quote I'd like to point out is the bit where he says "The ever accelerating progress of technology."
What does he mean by that? Well, let's look at a little history, shall we? Humans are fascinated with flying for centuries. We found sketches by da Vinci of helicopter-type contraptions which date back to the 15th century, but it took 400 years for the world's first airplane, the Wright brothers plane to see flight, but then it only took another 66 years to build a rocket to the moon. How? Well it's because breakthroughs in technology make way for new technology. The invention of the combustion engine which gave way to the Wright brothers' plane led to more sophisticated engines, which eventually made the moon landing possible. This is called the law of accelerating returns, and it tells us that the growth of computing power is exponential, not linear. The most well-known example of this is probably Moore's law which applies specifically to the number of transistors in an integrated circuit. To really grasp the power of exponential growth,
let me tell you a little story. There was once a great Indian King who loved to play chess. One day, a traveling sage was challenged by the King and to motivate his opponent, the King offered to reward her anything she could name. The sage had a rather unusual request. She was to be given a grain of rice on the first chess square and double it on every next one. The King lost and being a man of his word summoned a barrel of rice from the kitchen. He then started placing grains of rice according to the arrangement one, two, four, eight, but he quickly realized his mistake because by the 20th square he'd have to put down 1 million grains of rice. And by the last square, he'd have to put down more than 18 billion billion grains of rice which is about 210 billion tons which is enough to cover the whole of India with a meter thick layer of rice. Now imagine that the rice is computing power and right now, we're about here on the chess board.
According to the law of accelerating returns, we'll reach a point where technology starts expanding, so rapidly it will get completely out of our control. Beyond this, it will become impossible to predict the future of humanity, a technological event horizon. That point has been deemed the singularity and that my friends is what black holes have to do with machines becoming smart.
Do you want to know?
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