by John Fast
“Excellent!” Professor Bell enthused.
She walked back and forth in front of the class and I watched her every move. She was bright, beautiful and entirely relaxed. And I imagined she was talking only to me. Here I am, she was saying, and there you are, and all these powerful thoughts and electrical charges are passing between us, and isn’t life wonderful, and have you, John Fast, heard about that brilliant logician, Gottlob Frege?
“Frege extended the field of logic,” Professor Bell continued. “He invented a new set of notations for such terms as, ‘And,’ ‘Or,‘ ’Not,’ ‘Copy,’ ‘If,’ ‘Then,’ ‘Every,’ ‘Some,’ etc. And he established strict grammatical rules which determined their syntactic relations. In other words, Frege’s work marks the beginning of the symbolic languages which serve as the basis for all later computer programming. In the nineteen thirties and forties, Godel, Church, Post and others further honed the algorithm’s logic. The next step was to translate the increasingly complex and precise logic of the algorithm into the increasingly complex and precise logic of the machine.”
Professor Bell paused and smiled at the class.
“And that step,” she added, “has been repeated throughout human history: the precisely spaced holes in a bone flute; the precisely spaced beads in a wooden abacus; the precisely spaced eyes in a wire loom. These innovations translated the logic of music, mathematics and weaving into the logic of the machine. Now, everyone, why is Alan Turing so important?”
Whatever I remembered about Turing was obscured by the haze of desire that fogged my brain as I traced the outline of Professor Bell’s lithe physique beneath her ivory blouse and black pants. She reminded me of a young ironwood tree. And while I was lost in my revery, somebody jumped up and said something to answer the question.
“Very good, Hillary,” Professor Bell replied. “Turing realized that Frege’s symbolic operations could be translated into a series of mechanical and electronic logic gates and these gates could then process any number of similarly coded problems. So we can trace a line from Leibniz’s Mechanical Calculator, to Jacquard’s Automated Loom, Babbage’s Analytical Engine, Hollerith’s Tabulating Machine and Turing’s Universal Machine. In the 1940’s, Zuse, Turing, von Neumann and others developed the first generation of modern computers. In fact, von Neumann assembled his huge vacuum tube machine just a few blocks from here, in a small brick building that still stands.”
Professor Bell caught her breath, then finished her thought.
“Turing spent a year or so here in Princeton and, of course, he influenced the ongoing discussions. In other words, different people in different places often develop similar ideas, not because these ideas are somehow mysteriously floating in the air, but because the series of algorithms which led up to these ideas in the first place have reached a new stage of maturity. And different people in different places recognize that new stage and nurture it with all the power of their minds. Many people helped to evolve the modern computer and ever since then the historians have been tracing the converging lines of thought that led to their discoveries.”
Professor Bell paused again when she noticed someone standing just outside the classroom door.
“Excuse me, class,” she apologized. “I must speak with Professor Fujita.”
CHAPTER 9.
The Language of Automatons, Continued
“Now, let’s talk about Turing’s later work,” Professor Bell suggested when she stepped back into the classroom. “Turing imagined the possibility of programming a computer to learn by allowing it to make mistakes, and by enabling it to correct those mistakes. In other words, Turing imagined the possibility of developing a nonlinear calculator that transcended the rigid mechanist logic of geared wheels and electronic switches.”
“That’s the next major breakthrough in the history of the algorithm?” Emilio asked.
“Yes,” Professor Bell replied.
As a sixth grader I knew very well that the process of making and correcting mistakes was essential to the process of learning. And I also recognized that Turing’s linkage of these two processes in terms of nonlinear logic was a brilliant leap into the future.
“At the same time that Turing began to think about adaptive programming,” Professor Bell continued, “he also began to focus his attention on biology. He wondered, for example, how small groups of individual cells could develop into such wide varieties of complex forms. And in an attempt to describe the bio-logic of cellular division, he wrote some differential equations and ran them on an electronic computer at Manchester University.”
Professor Bell thought for a moment, then plunged ahead.
“Turing’s later work in nonlinear logic inspired others to explore the links between learning, evolution and computation. In the nineteen sixties and seventies, for example, Holland and others began to develop the first so called evolutionary, or genetic, algorithms.”
“What do they do?” Marcie wondered.
“They mutate from one generation to the next,” Professor Bell replied. “And along the way, the selection operators identify the algorithmic offspring that best fit within the dynamic environment of the search space: the ecological niche of the problem set. That is, just as natural selection has led to the optimum shape of a bird’s wing, so too artificial selection can lead to the optimum shape of a jet’s wing. And just as natural selection has led to the optimum structure of an infant’s mind, so too artificial selection can lead to the optimum structure of a computer’s neural net.”
“That analogy also applies to Highbrids,” I blurted out.
“In what way, Mr. Fast?” Professor Bell asked, turning her brilliant blue eyes toward me.
“The Highbrid Protocol is nothing but a set of selection operators which optimize the evolutionary algorithms of our brains,” I said, excited by the comparison. “And so we have the potential to become smarter and smarter from one generation to the next.”
“Exactly,” Professor Bell acknowledged with yet another warm smile. “I was hoping someone in the class would make the connection.”
As I basked in the glow of her praise I wondered if my optimized brain could solve another algorithm: B(ell) + K(iss) = K(iss) + F(ast).
“How does a neural network work?” Jamal asked, interrupting my daydream.
“The same way a woodchuck chucks,” Ryan quipped.
“Okay Ryan,” Professor Bell said sternly. “Can you explain to the class how a neural net works?”
Ryan winced, but did his best.
“Uh … it’s an interactive processor …,” he began, “that’s programmed to find data links and make new ones. It forms synaptic nodes which connect with other nodes and it just keeps evolving and developing new levels of complexity.”
“Correct!” Professor Bell declared. “Now, can you give us an example of a neural net?”
“Well, uhh, all the Expert Systems are neural nets.”
“Like what?”
“Like, the Diagnostic Matrix the doctors and hospitals use. After the patient’s medical history, current symptoms and test results are uploaded, the Diagnostic Matrix identifies the patient’s illness and outlines his or her optimal treatment.”
“Right again, Ryan. All the professions depend upon neural nets to run their Expert Systems: medicine, law, business, education, government … all the sciences, all the arts. We use them everyday.”
Professor Bell glanced at her watch and began her summation.
“So you see, class, the development of the algorithm–from ancient to modern, linear to nonlinear, additive to evolutionary, mechanical to neural–is itself an example of an evolutionary process. What I mean is that the theory of the algorithm itself evolves from one generation of scientists to the next, growing in depth and complexity. That is, the theory of the evolutionary algorithm itself evolves from Pythagoras to Turing and from Turing to all the logicians, mathematicians and computer scientists who came after him. As various evolutionary algorithms evolved our minds, our minds
evolved various evolutionary algorithms: we became aware of them.”
“And one day they might become aware of us,” I suggested, again extending her thought.
“Please explain, Mr. Fast,” Professor Bell requested.
“Umm,” I began, suddenly feeling hot all over. “As the early hominid brain evolved ever more complex neural nets, we woke up. We became aware of ourselves, and others. And as the early cybernetic brain evolves ever more complex neural nets, it might wake up. It might become aware of itself, and others.”
Professor Bell nodded thoughtfully and gave me a smile that felt like a kiss.
“Your minds are quantum computers,” she said to the class, “neural networks that are generated by, and that generate, complex evolutionary algorithms. And teaching you is just a matter of initiating the cascade.”
CHAPTER 10.
The Key to All Codes
I was working on my journal, in my father’s library, a few days after my fourteenth birthday. Mozart’s breakthrough, Piano Concerto No. 9, was playing at full volume on the audio system, thirty different science books were lying open on the reading table, and a holographic projection of a cross-sectioned chambered nautilus was floating in the air in front of the wall screen. I walked around and around the room, studying the sheets of paper I had taped up and down the bookshelves. The papers were covered with formulas, charts, diagrams, illustrations. I had tried several times to arrange all the information in a coherent pattern, without success. The more I’d learned in the six years since my encounter with the cosmic tree, the more confused I’d become. The universe had shattered into countless data bits and I couldn’t figure out how to put it back together. I couldn’t even figure out how to make sense of myself.
I kept walking around the library, adjusting the order of the papers, because in some profound way that I couldn’t quite grasp I sensed that all the information was somehow interconnected. The common denominator wasn’t something as superficial as a Fibonaccian Ratio, rather it was something incomparably richer, deeper, something like the essential symmetry of symmetry itself. I was so absorbed in my work that when my father suddenly called out my name, I nearly jumped out of my shoes.
“Sorry!” André apologized loudly.
My father stood in the doorway and glanced around the room. He was thirty-four years old and his regular tennis game kept him in excellent shape.
I used the remote to lower the volume of the music and said, “It’s okay, Dad. I didn’t hear you come in.”
“No wonder,” André replied as he entered the library and examined my papers. “Quite a multimedia event you’ve got going on in here.”
“I’ll clean it up.”
“No hurry. I was just wondering if everything is okay. Jena said you’ve been a little preoccupied lately.”
“I’m … I’m fine, Dad,” I replied. “I’m just trying to figure out a few things.”
“Like what?” He asked.
“Like … how it all fits together,” I said, sweeping my arm around the room.
André gave me a quizzical look.
“Okay,” I continued. “Remember when I was eight years old and I hit my head on the sidewalk and I wound up in the Emergency Room?”
“Vividly. You scared your mother to death.”
“That was the beginning,” I said, feeling as if a dam had broken and I couldn’t stop the rush and tumble of words. “I was walking home on Halloween when, all of a sudden, it got very dark and very quiet. A street lamp lit up a huge, old sycamore tree. I looked up and I saw hundreds of spheres dangling from the branches. Then I looked again and I saw planets, moons and stars dangling along with the spheres. And then I looked a third time and I saw the entire universe dangling in the tree. And I’ve been thinking about that cosmic tree ever since, starting with the basic questions like why each sphere hangs on a long flexible stem. And I realized it’s because when the sphere dries out and opens its portals it catches the breeze and releases its tiny tufted seeds into the air. And I almost fell back again when I realized that the sycamore tree must have evolved with the wind. And so instead of thinking of it as a tree, a noun, a reductive relation of word and thing, I started to think of the sycamore as a wind-catching-seed-sender. And I wondered why we use individual nouns at all. I wondered if, instead of saying the word, ‘universe,’ we should say, ‘time-turning-space-shaper.’ Then I thought that wasn’t right either because that phrase seems to give nature an intention, or goal, which I didn’t want to do. And so I thought instead of saying the word, ‘sycamore,’ we should say, ‘wind-catching-seed-sending.’ Instead of saying the word, ‘universe,’ we should say, ‘time-turning-space-shaping.’ And I wondered why the Navajo language always seems to integrate nature, while our language always seems to break it into pieces.”
“You remind me of the old Worf-Sapir Hypothesis,” André said. “The one about the cultural limits that language imposes on perception and thought. And while Worf and Sapir overstated their case, nevertheless language does, inevitably, shape our ways of seeing and thinking. Anyway, your mother always said it was something like that: you looked up into the tree, saw the entire universe, fell backward. She still has that sketch you gave her.”
I nodded.
“Why didn’t you explain all this at the time?”
“Because I’ve only begun to figure out how to talk about what I saw, and experienced, that evening … to find the words … which still seem inadequate.”
He waited for me to continue and, when I didn’t, he asked, “So how did your questions about the sycamore tree lead you here?”
He gestured to the sheets of paper hanging on the bookshelves.
“Okay,” I began again, more slowly this time. “You’ve been studying the genetic code your entire life, right?”
“Right,” André agreed.
“But look!” I exclaimed, pointing at one diagram after another. “First, the Big Bang; then, quantum fluctuations; sub-atomic particles; atomic elements; gravitational aggregates; fiery stars; molten planets; water molecules; double helixes; neural nets; sentence structures; piano concertos; computer algorithms.”
André shrugged.
“Don’t you see?” I demanded. “It’s all code! Mathematics, Physics, Chemistry, Astronomy, Biology, Linguistics, Music, Cybernetics! Everything is code! And, on some deep level, it’s all connected!”
“How?” André wondered.
I entered a few commands into the remote and a bright holographic projection of the Milky Way Galaxy appeared in front of the wall screen, floating next to the bright holographic projection of the cross-sectioned chambered nautilus. I entered another set of commands, shrunk the Galaxy to the size of the shell, and juxtaposed the two spirals.
“Evolution!” I replied. “The universe is a dynamic, complex, evolutionary flow of code: specific numbers define the nature of energy and matter; specific genes define the nature of plants and animals; specific sounds define the nature of music and language, etc. Everything I’m learning in school is code. I am code. We are code.”
“So …?” André prompted.
“So,” I continued, “I want to find the connections! I want to find the key to all codes!”
My father thought about that for a long moment, then asked, “And what will you do with your master key?”
“I’ll unlock the secrets of the universe,” I replied confidently. “I’ll discover the nature of nature, the essence of existence, the origin of everything.”
André thought for another long moment.
“I admire your ambition, John,” he finally said. “But you must remember that the Highbrid Protocol is an extremely controversial social experiment, and we are still very much in the public eye. So if you pursue this topic you must be prepared for the inevitable criticism that will follow. I can already see the flashnews headline: ‘NEW ADAM SEEKS NEW APPLE!’”
“I just want some answers, Dad,” I said, holding my ground.
“And so d
o I,” André replied.
He walked over to a bookshelf, pulled out a book and handed it to me.
“Here’s something else you might want to consider.”
I glanced at the title, ‘Essays on Semiotics,’ then looked up at my father.
“Charles Sanders Peirce,” André began. “And, yes, his last name is pronounced like the word, ‘purse.’ Charles Sanders Peirce was a brilliant nineteenth century American scientist, mathematician and philosopher. He brought the science of semiotics, the study of signs, to a whole new level of sophistication. Specifically, he defined the process of signification as the dialectical relation of the ‘representamen,’ the ‘object’ and the ‘interpretant.’ A picture of the sun, for example, would be the representamen; the sun in the sky would be the object; and the person making the connection between them would be the interpretant. Peirce suggested that these three aspects of the sign define each other in the moment of signification.”
I was incredibly excited by Peirce’s theory because it went a long way toward explaining the mysterious sign of the sycamore.
“That means,” I blurted out, “that the sycamore tree was the representamen, the universe was the object, and I was the interpretant. And we defined each other in that split second before I fell back and hit my head on the sidewalk.”
André nodded and I suddenly felt a deep connection to Peirce. I scanned the, ‘Table of Contents,’ of his book, and flipped through the first few pages. Then I glanced up at the papers I had hung around the room. And, despite my elation, I still felt overwhelmed.
“So all these codes,” I said, gesturing to my diagrams and equations, “would be further examples of Peirce’s dynamic of signification?”
“Yes.”
“But how can I connect the spiral of the chambered nautilus to the spiral of the Milky Way Galaxy? And how can I connect them both to the cosmic tree?”
“I know someone else who can help you.”
“Who’s that?”