nce upon a time, there was a king who loved feats of engineering. He had everything he could want: his own supercomputer, an invention cave with an assortment of ingenious robots and vehicles, and a mechanized, sensorized castle that could reconfigure itself at his slightest whim. For protection, he had a gigantic laser beam to fend off invading hordes, from his own planet or from outer space. However, the king was not satisfied. There never seemed to be enough new-fangled devices for him to try.

One day the inventor Schmedrik came to visit the king. “I have what you need,” said Schmedrik, “The only thing that can satisfy your need for new inventions is a perpetual invention machine. And I have just such a machine for you, the Innovator, for the low, low price of one quintillion bitcoin.

The king, anxious to have his very own perpetual innovation machine, was keen to hear the secret principle. His advisor was a bit more skeptical but still curious about how Schmedrik could justify his claim.

“Well yes, that may seem at first like a large sum. But considering that all the inventions will be worth something and that this machine creates an infinite number of them, any finite fee I charge you is a bargain.”

The king was pleased with Schmedrik’s proposal. But just as he was about to hand over the requested amount, his wise advisor Previsio pulled him aside and whispered, “Dear king, before we pay Schmedrik his fee, do you not think it prudent to first determine if the Innovator works?”

Schmedrik overheard him and responded, “It is impossible to know by observation whether the Innovator will invent forever because you don’t have forever to watch it. So, we must analyze it mathematically to see that it will always innovate. However, when you hear the principle behind the Innovator, you will have to agree it can indeed invent forever.”

The king, anxious to have his very own perpetual innovation machine, was keen to hear the secret principle. Previsio was a bit more skeptical but still curious about how Schmedrik could justify his claim.

Schmedrik continued, “We know that if our Innovator was driven by a mere list of rules, it could never discover some inventions. A famous mathematician named Gödel proved that. But, if we also include randomness in the Innovator, then all inventions are possible because, as the quantum physicists say: Anything is possible due to quantum randomness. Combining randomness with our proprietary rules of innovation is mathematically guaranteed to provide never-ending invention.”

“Aha, very good,” replied Previsio, “But there is something more that your machine must do. If all the King wanted was random combinations of rules, we have devised that ourselves. And we’ve noticed that most results are pretty boring or nonsensical. What your machine must also do is select the good inventions from the bad, and just give the king the good inventions.”

At this, Schmedrik offered a crafty smile. “I know where you are going with this. If we have a fixed selection ruleset, we are back at square one: We will only select inventions within a narrow range that is predefined by the selector, so our device has failed. Now hear this! We are not one, not two, but a busy-beaver number of steps ahead of you. The solution is that we must also innovate our innovation selector. And here we are guaranteed an unbounded amount of innovation and also that every invention is new and fascinating.” The king was very pleased and beamed at his advisor.

But Previsio was not quite done. “Schmedrik, now I must tell you our secret principle. There are some inventors so brilliant that their inventive recipes are listed in God’s book. These are the recipes that are the shortest list of steps and rules that produce an invention. Every invention derives from one of these “God’s book” recipes, and there is no shorter recipe. They are so refined and pure that we call them ‘angelic recipes.’”

The king and Schmedrik listened quietly with rapt attention.

“Your Innovator itself is based on one of these angelic recipes: the shortest recipe that creates the Innovator, such that there is no shorter recipe. The Innovator’s inventions each have an angelic recipe as well.”

“Makes sense,” they both replied.

“But here comes the tricky part, so pay attention.”

Their brows furrowed in concentration.

“You claim that every invention is new. So, there is something about the invention that is unlike any of the others the Innovator has generated. Thus there is a new step or ingredient in the recipe that cannot be derived from any of the other recipes for inventions.”

“Okay so far,” Schmedrik said.

“Now consider the recipe for the Innovator itself. For the sake of argument, assume the recipe requires only 100 lines to list all the ingredients and steps.”

“Sounds good.”

“Part of this recipe defines the invention selector, guaranteeing that it keeps only the good, unique inventions and discards the rest.”

“Of course.”

“Now consider what happens after the Innovator has generated a number of great inventions, say 1000. Because each of these invention’s recipe has a unique element not found in any of the other recipes, then we can combine the recipes into a mega-angelic recipe that cannot be shorter than 1000 lines, and this mega-angelic recipe generates all 1000 inventions.”

They took a few moments to ponder this statement. Then, a thoughtful look began to dawn on the king’s and Schmedrik’s faces.

“However, your invention machine has an angelic recipe that is only 100 lines. Recall that by definition, an angelic recipe is the shortest recipe for the invention. Yet, here we have a situation where an angelic recipe of 100 lines has created something that has an angelic recipe of 1000 lines. That, my friends, is a contradiction.”

“Very well put,” said Schmedrik. Turning to the king, he stated, “Sire, in truth I was not attempting to scam you. I really believed that the Innovator was capable of unlimited invention, which seemed so plausible when we mixed randomness with rules.”

The king nodded in understanding.

“That being said, I’d never actually observed the Innovator producing unlimited inventions. It always seemed to get stuck at some point and cease creating new content. Nevertheless, I believed it was only a matter of time and tinkering before I got beyond the ‘novelty plateau,’ as I called it, because the math seemed solid. Now, I see that there is a bit more to the story, and I will have to go back to the drawing board. Gentlemen, I bid you good day.”

With that, Schmedrik left the palace to return to his lab. The king and his advisor watched the man depart. Then the king turned to his advisor and said, “Your argument raises another question in my mind. If Schmedrik’s machine cannot produce unlimited invention, does that mean someday invention itself will cease?”

Previsio thought for a moment, and replied, “My king, your concern is valid. Yet, it does not necessarily follow from my argument. While a machine is limited by its angelic recipe, this limitation only applies to machines. If we human beings are not machines—and we do not know for a fact that we are, then there is no such limit to our inventiveness.”

At this, the king smiled, and they went back into the castle.

₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪₪

Eric Holloway

Eric Holloway has a Ph.D. in Electrical & Computer Engineering from Baylor University. He is a current Captain in the United States Air Force where he served in the US and Afghanistan He is the co-editor of the book Naturalism and Its Alternatives in Scientific Methodologies. Dr. Holloway is an Associate Fellow of the Walter Bradley Center for Natural and Artificial Intelligence.

He wrote the tale above to complement an academic paper* that addresses this problem, known as Basener’s Ceiling, named for artificial intelligence expert William Basener.

Holloway explains,

The basic idea is that conventional evolutionary programs have an upper bound on performance even when the fitness changes in time. This “ceiling” was explored in Introduction to Evolutionary Informatics. Claims about open-ended evolution try to skirt this limitation. My paper outlines the problem, which applies to artificial intelligence as well as to unintelligent evolution.

And in lay terms?:

Computers can never originate, they only regurgitate. Humans, on the other hand, can come up with original ideas, i.e. they write the programs in the first place. So, my proof shows that the human mind cannot be a computer program.

This is why no one has yet invented an invention algorithm, that will come up with great inventions without any human input. It is also why AI systems only turn out to be useful in very narrow problems and cannot be generalized to cover many problems.

* Eric Holloway and Robert Marks “Observation of Unbounded Novelty in Evolutionary Algorithms is Unknowable.” Artificial Intelligence and Soft Computing, pp. 395-404. Springer, Cham, 2018

See also: Moravec’s Paradox and Polanyi’s Paradox