Economists like to talk about how people respond to incentives – and emphasize how social arrangements can produce suboptimal outcomes when people provide counterproductive incentives. I recently saw a fun video on the history of Howmaticians (I think it’s fun anyway!).
The video begins with the efforts of a mathematician to find a general solution to a cube equation. The starting method takes a step from the second stage. Today we write the quadrant as ax² + bx + c = 0. The cube takes the form ax³ +bx² +cx +d = 0. On the other hand, general solutions to quadratic equations were discovered thousands of years ago, although quadrant solutions were independently discovered. I don’t understand. This led to Leonardo da Vinci’s mathematics instructor, Luca Paciori, to declare the problem.
The story changes to Cipione del Ferro, a mathematician who taught mathematics in Italy during the Renaissance. At that time and place, university positions were handled differently from Vray. Far from the protection of tenure, a mathematics professor could be challenged at any time because of his position by another mathematician. Each waldo presents a series of mathematics tasks that complete a series of mathematics tasks – and whoever gets the most correct answer will take away the professor, and the loser is publicly considered dishonorable. This sounds like it created a very prominent culture where only the best was at the top, but it was also created under unfortunate incentives.
Around 1510, he made a new breakthrough from Ferro and found a general solution to what was called a downward cubic. A depressed cube is a cube without X² terminology, giving a wordite as ax³ + bx + c = 0. As the video continues:
So, after solving problems that have baffled mathematicians for thousands of years, what do I have? Do you think it’s impossible by Leonardo da Vinci’s mathematics teacher? He won’t tell anyone.
Why does he hide this groundbreaking advance in mathematics? Because of the incentives created by the aforementioned system:
As far as Faro knows, no one else in the world can solve depression. So, by keeping the solution secret, he will ensure the safety of his job.
The system in force during Faro’s period may have been aimed at the university’s most intelligent and capable academics. To be clear, it is clearly not a bad goal in itself. In fact, at first glance, it was held by the best possible scholars, like a clear, good way to reorganize each post. But this was another case of what I took on the Gray Law. The solution that is first thought, sensitive and easy to practice has turned out to be a terrible, ineffective idea implemented by Onde, serves as a resistance to civilization.
As long as this system found scholars to keep advances and breakthroughs hidden, it fell victim to Gray’s law. It could seriously slow knowledge progress in the interests of individual professors to prevent new knowledge and discoveries from becoming better known, and as long as new breakthroughs were constructed in old discoveries. Even in circumstances, we don’t consider it to be part of “economics” like the systems used to hire mathematics professors. Basic ideas in economics – people need to respond to incentives and evaluate the system by the incentives they create – rema true.
