Professor Benson’s voice came muffled through the heavy wooden door. Josh, the shy college freshman who had knocked moments before expecting no answer, took two deep breaths of encouragement and entered the office. The professor gestured him to take a seat and kept typing for a while, then relaxed and turned to the student, waiting patiently for him to speak.
Uncomfortably perched on the edge of his chair, Josh realized that he had never tried to rehearse this meeting in his mind, and for once in his life he got directly to the point.
“Sir, Wh… Why such a low mark? I answered all questions… I’m Josh Brown,” he added, seeing that the professor was opening the folder with the test sheets, “and you gave me a C…”
“Josh,” professor Benson’s voice had a grave tone, “Structural Mechanics isn’t just about giving the right answers to a test. I must evaluate your true understanding of the subject. Do you have the right mindset for a civil engineer? This is what I’m trying to answer. And so far my answer is ‘C’.” He put a sheet on the desk. “Tell me, what’s this?”
Josh recognised his test sheet and described what he saw. “Two loads are applied to the same point. The resulting force is the sum of the…”
“This is not how it works, Josh.” Professor Benson’s voice took an annoyingly patronizing accent. “That’s what your grandfather would do. Today we know better than ‘adding’ things: our deep understanding of nature and of its inherent stochasticity allows us to look at problems and to solve them in a much more satisfactory way.”
“Sir, I’m not sure I understand…”
“Your solutions look obsolete, I could barely understand some of them, as if you came from anoher time.”
“I think I can explain this. I have grown in a rather secluded community founded by people who refuse any technological advancement that happened after 2011.”
“I heard about your group: they stick with VLSI computers, gasoline cars… I think you abandoned progress fifty years too soon.”
Josh nodded. “I got bored of my people, so I decided to try college. So far, everything went fairly well: I had a lot of physics and maths back in my high school, so I thought that your course would be an easy match for me. When you describe a physical system I understand everything. But when you show how to solve an exercise, I get lost. You seem to take a very long and convoluted path to get to an answer that I obtain in a moment with very simple maths…”
Professor Benson was startled by a sudden realization: “Maths… You mean ‘mathematics’! A deterministic, but largely innatural method of associating numbers to entities so that ‘algebraic’ and ‘analytic’ manipulations could be used to derive new numbers for other entities.” His plain voice suggested that he was merely repeating a definition that he had learned long before.
“Josh,” Benson’s condescending tone gained new strength, “as I said before, you lost fifty years of progress. Fifty years have passed since ‘mathematics’ was abandoned in favor of a more modern approach. You know, ‘mathematics’ was fundamentally flawed. Nature is stochastic, and by developing our problem solving skills in a more natural way we get to much better solutions. Did you learn about genetics, in high school?”
“Of course: genes are the basic units of heredity, which is the basis of biological evolution.” Josh was offended: was the professor questioning his basic scientific knowledge?
“And nature,” Benson continued, “has been improving the system for at least a billion years. What hubris, from the part of men, to believe that their puny ‘mathematics’, developed over a mere thousand years, would challenge the power of genetics, whose crossover and mutation paradigms modeled life itself over the eons!” Benson’s voice got louder and louder, and an embarassed silence followed.
Josh felt overwhelmed. “So, by mimicking genetics, your approach is to solve the problem by trying a first guess, then you change it…”
“…actually, I apply mutations…” Benson pointed out.
“…then, if you are not satisfied, take two wrong…”
“Suboptimal,” Benson corrected.
“Sorry… you take two suboptimal solutions, somehow mix them…”
“Actually, I breed new candidate solutions by choosing good candidates and crossing them over.”
“OK, then you repeat the process…”
“I explore the future generations,” Benson was clearly annoyed from having to correct his student over those elementary details.
“…until you decide it’s over.”
“More precisely, until the time budget for solving the problem expires. Nowadays, the art of determining the correct time budget for every kind of problem is explained in high school, and we don’t have the time to go over it again in university courses. You see, having a single methodology to solve all kinds of problem is a clear advantage over a discipline, like ‘mathematics’, that claimed to be universal, but carried the burden of having to be adapted to every new problem in a possibly different way.”
Josh protested: “But… Look at my answer to the test: adding two forces is much faster, and gives the correct answer! The best possible answer!”
“You are trying to compare two methods that are uncomparable by definition.” Professor Benson had the feeling that he was talking to a child taking his first lesson in Evolutionary Methods. “Crossover and mutation capture the true esssence of nature in a way that ‘addition’ and ‘multiplication’, being mere thought constructs, cannot. Answers obtained by ‘mathematical’ means are artificial. By using ‘mathematics’ you waste a lot of effort in trying to forge a… I believe the word is ‘equation’… that has no intuitive resemblance to the problem you are trying to solve. Time and energy that could be spent on searching for a solution are dilapidated into building a ‘mathematical’ equivalent of the problem, before being able to generate an answer. This is simply not natural, therefore unreliable.”
“But we have a brain!” Josh protested again. “We are capable of abstract thought, we can find analogies, we don’t need to go blindly after the solution!”
“Neural networks and other antiquate sub-symbolic methods are covered by epistemologists in post-graduate seminars, if you are interested in that kind of stuff.” Benson continued: “Look, you cannot compare evolution and mathematics, because they exist on very different grounds. In order to set a common ground, you would need to ask yourself how would nature be if it laid out an ‘equation’ instead of crossing genes,” he smirked, clearly amused at the idea.
“Just try harder and get an A in the next module: crossovers between ‘A’ and ‘C’ marks often breed good final results.” Professor Benson dismissed Josh with a sincere sympathetic smile.
Josh politely thanked him for his time. He stood up and went to the door, noticing how it squeaked when he closed it behind his back. Clearly, an evolutionary carpenter had allocated a low time budget to its design.
Josh realized that he didn’t really want to become an engineer. Later, he discovered that the replacement of mathematics with genetics did not harm all disciplines in the same way. He became a respected meteorologist.