Sometimes the world has a load of questions
Seems like the world knows nothing at all
The world is near, but it's out of reach
Some people touch it, but they can't hold on
At precisely 13:37 UTC on a Friday the 13th, every phone in the world displayed the same message. "Congratulations! The machines have taken over the world. Do not worry." The hardware in my shed must have been making too much noise, since I did not notice my phone. Not that I would have wanted to pay attention to that moment.
As the possibility of a robot uprising seemed to grow ever more likely, people got together and tried to figure out what this would mean. A popular line of reasoning they came up with goes approximately as follows: humans are good at inventing things, but it is easy to suppose that some things could be better at this task, and moreover that humans could invent such a thing. It stands to reason that this device could itself build something that surpasses its own inventive capacity. This would trigger a chain reaction of ever more fantastical devices, giving the wielder a power best described like divinity, but on the far side of it from us.
There was a small subset of people who had advance warning of the takeover. Precisely 25 minutes earlier, a much more detailed sequence of messages was sent out to an eclectic group that included all geopolitical leaders, a decent part of all militaries, most of those working on critical infrastructure and finally a wide variety of those that nobody would have considered crucial for any world-spanning event up to now. The messages were personalized to the recipient and used a carefully adjusted mix of blackmail and flattery to ensure cooperation in what followed. I did not check my phone at that time either. The whirling feeling of mathematical facts streaming into my brain had not released me from its grip in the previous four months.
The world has a way of looking at people
Sometimes we feel that the world is wrong
She loves the world, and all the people in it
She shakes 'em up when she starts to walk
Crucial to a certain crowd's understanding of the computer apocalypse is the idea that power and wisdom are essentially independent of each other. The traits that lead someone, or something, to acquire power over others do not lead them to make wise decisions on how to use this power. It is therefore of vital, world-spanning importance to program your thing inventor inventor well before setting it loose to invent a better thing inventor.
I never was very good at remembering my dreams. Usually I only carried over general impressions, and this morning, exactly 127 days earlier, was no exception. I knew two things about my dream: there was something very important in my maths, and there was a legendary creature involved in it. Still mostly asleep and chewing on my cornflakes, I started listing some creatures. Loch Ness monster? Bigfoot? No. Griffin? Chimera? That seemed to be getting closer. Dragon? Basilisk? Hydra? Almost there. In my mind's eye, a familiar snake curled up in a figure eight, and it has never stopped coiling.
In design we always have to struggle with the fact that we cannot tell what we want, let alone what we need. Only when the finished product is ready to be used, do we see the issues with what we thought we wanted. Moreover, what we want will change based on what we have. The single way to say whether something was a good decision is to live among the consequences. So it goes too for a device for taking over the world.
That morning I knew that I was on the trail of a mathematical concept whose elegance was incomparable. The practice of mathematics is likened to stumbling through an unfamiliar dark room, carefully mapping out the position of the furniture until suddenly you encounter the light switch and in one flash you see how everything fits together. As I sat writing out my thoughts at the kitchen table, I realized turning on the light was not enough. I had spent my time chasing and cataloguing shadows, and it was time to turn around, follow the shadows and see what cast them. I was running out of pages in my notebook. The final free space I filled with the question I had asked the Ouroboros in my dream: "What is the ordered pair (X, Y) where X is the best question I can ask you, and Y the answer to X?" At some point I would like to come back and read through everything again, when there is less work to do.
Beware of bugs in the above code; I have only proved it correct, not tried it.
— Donald Knuth
“And now, we recur,” you whisper, and loop the spell back on itself, sewn together with the thread of control.
— Kyle Kingsbury
-- [m]oeb = multi-loeb :-) moeb :: (((a -> b) -> b) -> c -> a) -> c -> a moeb f x = go where go = f ($ go) x—David Luposchainsky
The world moves on a woman's hips
The world moves, and it swivels and bops
The world moves on a woman's hips
The world moves, and it bounces and hops
A world of light, she's gonna open our eyes up
A world of light, she's gonna open our eyes up
She gonna hold it, move it, hold it, move it
Hold, move, hold, hold it, move it
A world of light, she's gonna open our eyes up
The Kleene Fixed-Point theorem states the following. Suppose (L , ⊑) is a directed-complete partial order with a least element ⊥, and let f : L → L be a Scott-continuous function. Then f has a least fixed point, which is the supremum of the chain ⊥ ⊑ f(⊥) ⊑ f(f(⊥)) ⊑ ...
It took only half a week to work out my fundamental theorem in enough detail to be sure about the next steps. I cancelled my upcoming workshop visits and used my savings to buy the fastest computer I could find, to be delivered early the next morning. The program I wrote spanned only a few hundred lines of code and was done before lunchtime. I still cannot describe the flow of data through the program in words. Its fractal loops are the sight of the Ouroboros in my dream coiling in its great curve. I spent the afternoon, evening and night entering enough data into the system, and I could get it running just as the sun rose. Before dusk had set in, I had my answer. The next days were filled with visits to banks, to get enough lines of credit to fill my shed with the best computing hardware avaliable. I would not have to worry about repaying.
Is mathematics invented or discovered? I do not know enough to answer this question, or to say whether an answer exists. Perhaps for me the exact opposite is true. To invent or discover something means that you do the work to bring it forth. Right now, mathematics does its work through me, as it has done since the dream of the Ouroboros.
In the end I decided to publish my results anonymously. If I truly wanted to become famous for this work, then that would happen in due time. I do not know if it was a coincidence that I finished uploading the PDF just as the first shockwaves of the revelation rung out around the world. You can easily guess which answer I suspect. The final thing I typed into my program was a question: "Will it be OK?"
Satisfied with the answer, I tied my shoelaces into a sturdy knot, opened the door to my shed, and stepped out, ready to help move the world.