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April 3rd, 2022
—ow and massaged his temples as he struggled to think. It just didn’t make sense, at least not yet. He looked up at the Robot again who was analyzing Lucilius’ facial expression, extrapolating it’s possible interpretations in a thousand different directions, all with varying degrees of frustration, confusion and a sense of searching for understanding. The Robot had a 96% confidence score for the most likely thought Lucilius was having at that very moment, and with it, the Robot further extrapolated and tested 2.2 million possible sentences that it could say to alleviate Lucilius’ confusion and help understanding blossom in his mind. Each of the 2.2 million sentences was weighted for a final confidence score. The same process was carried out with the next several thousand potential thoughts Lucilius could be having which the Robot had generated using its model of Lucilius’ mind, each potential correct thought scoring with less and less confidence. While it was unlikely, this exercise was carried out because every so often a low confidence guess at Lucilius’ thought yielded a better generated response when it was used to propagate potential responses. These errant successes were then used to further refine the model of Lucilius’ mind generated by the Robot who was currently trying to teach him a very simple idea about the paradoxical incompleteness of language.
“Ok,” Lucilius said, “say it one more time.”
The Robot hesitated a brief moment, analyzing Lucilius’ listening receptiveness via his facial expression, and when his muscles had relaxed in just the right amounts to signal maximum reception, the Robot spoke.
“The following sentence is false. The prior sentence is true.”
After immense calculation, the Robot continued “It may help to look at the statements, here look.”
The Robot projected the text it had spoken into the air before Lucilius face. He looked at each sentence in turn, his eyes switching from one to the other, over and over.
“Well, on their own, they make sense, but when paired together it doesn’t make sense at all”
After immense calculation, the Robot responded in an instant. “Can each sentence really be regarded on their own?”
Lucilius considered this. “Well no, because each one refers to the other. If there was only one then it would imply the absence of a missing statement to refer to.”
“Precisely,” said the Robot. “So, how does that inform your previous conclusion which was, and I quote ‘Well, on their own, they make sense, but when paired together it doesn’t make sense at all!”
“Ok,” Lucilius admitted. “I guess they don’t make sense on their own, which means they can only make sense together… but when they are paired together they don’t make sense again! So there’s not too much difference between thinking about them together or on their own, they’re either incomplete or they put your mind in a stupid loop that makes no sense!”
The Robot smiled, this Robot had been with Lucilius his whole life, since he was a tiny baby, helping him learn all manner of things at a much faster pace than had the Robot not been with Lucilius. The AI residing within the Robot body was specifically tuned to model the mind of Lucilius with the express purpose of being able to calculate and carry out the optimal learning challenge for Lucilius at any given moment. The Robot was not there to give Lucilius answers, but to help him to navigate his own way towards an answer more efficiently.
“I think you understand now,” the Robot said.
“What!?” Lucilius cried out. “Are you kidding?”
“Not at all, the point of the paradox is taking hold and becoming apparent.”
“What, that it doesn’t make sense?”
“You are correct, but not precise.”
Lucilius contemplated this a moment, and thought back to the infuriating pair of sentences.
“They don’t make sense simply because it’s a contradiction, like saying ‘This is not a sentence’ even though it clearly is. But it goes beyond that because it’s a recursive contradiction built in two separate parts. Each only becomes potentially incorrect when the meaning of the other is taken into consideration.”
Lucilius shook his head. “I feel like I could talk about this in circles all day and I’d never get anywhere.”
“Sounds like a good description of many conversations I’ve witnessed you having with friends.”
Lucilius laughed. “You have a point. I’m not sure I like it, but you have a point.”
“Maybe this simple paradox is an analogy in miniature for those conversations. What exactly would that mean?”
Lucilius sat back, as if refreshed by the larger perspective the question afforded.
“Hmm… You weren’t actually joking. It’s exactly how people can be so opposed and yet at their core they basically want the same things. We are always somehow talking past each other, but assuming something about the other person in the same way that infernal pair of sentences refers to each other.”
The Robot smiled again, pleased with the match between reality and its generated predictions.
This entire interaction was not in fact real, but simply an abstracted interpretation of a heuristic that occurred in the slightest fraction of a microsecond in the form of a thought about where Lucilius hoped the conversation would go. He was in fact imagining himself in the role of his student, as all good teachers do. And this ideal interaction was his goal - the place he wanted to arrive at, but his student was having quite a lot of trouble grasping the concept. He looked at the confused Robot sitting with him. The Robot he had built with his own hands, who he had been trying to train and teach for its entire existence.
The circular lights indicating the Robot’s eyes flicked, as if to indicate a blink, and Lucilius sighed, knowing that the poor Robot was confused. It was still early days, and Lucilius was constantly tinkering with the design of the Robot’s mind in an attempt to help the Robot learn faster and more efficiently so that one day it could be replicated and it could be the ultimate teacher for hundreds and thousands -millions and billions- of kids.
“The first statement must be incorrect,” the Robot stated.
“That’s not the point,” Lucilius said.
“What is the point?” Asked the Robot.
“What does it imply about language if these statements can exist as valid statements?”
“They cannot be valid statements. The first statement must be incorrect.”
Lucilius chuckled at the predicament. He sighed, and frustrated, Lucilius raised a hand to his furrowed br—
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