As a boy, I was a rock hound. I learned how to identify minerals through the Mohs hardness test. The Mohs hardness test is named after the mineralogist who invented it. You take a known specimen, such as quartz, and use it to scratch an unknown specimen. If quartz scratches a mysterious specimen, you will know that it is softer than quartz. It can be calcite or pyrite. If quartz cannot scratch the sample, it may be beryl or corundum, which is harder than quartz. In addition to factors such as color and crystal structure, hardness testing can also help you specify samples.
I like the direct objectivity of the Mohs test. Recently, I have been thinking about a hardness that is difficult to assess-called cognitive hardness. In our lifetime, we are faced with a wide variety of cognitively difficult tasks.For example, in the past year, I have been Study quantum mechanics, Which is notoriously difficult to master. But, objectively speaking, is it harder to learn quantum mechanics than to talk about #MeToo with my girlfriend without irritating her?Or talk to my daughter about climate change Don’t suppress her?
Subjective assessments of cognitive hardness are not very helpful, because they vary with each person’s experience and abilities. You are a master of differential equations, and I am better at retelling Emily Dickinson’s poems. Is there a method similar to the Mohs test to quantify the cognitive difficulty of various tasks and rank them accordingly? Perhaps such an approach can generate insights that help us solve problems, or, conversely, accept their insolvability. In any case, here are some thoughts on cognitive difficulties.
The traveling salesman’s problem
Mathematicians and computer scientists rank problems according to the time it takes for the computer to find a solution. If there is no algorithmic shortcut to find the best solution, then the problem is defined as NP-hard; you must laboriously check all possible solutions to find the best solution. (NP stands for “non-deterministic polynomial time.” I always thought it meant “really, really.”)
A well-known NP-hard problem involves a traveling salesman looking for the shortest route between many cities. As the number of cities increases, the difficulty of the problem increases sharply.If a salesman must visit 15 cities, he has 87 billion possible routes consider.Mathematicians designed Tips for finding fairly short-circuit lines-If not the shortest-among many cities. However, when the number of cities increased to thousands, it took almost a long time for the world’s fastest computer to find the shortest route.
The irony is that it is easy to come up with a time-saving itinerary compared to other problems that traveling salesmen may face. For example: How long can he walk on the road without endangering his marriage? If he is lonely, should he approach a woman in a hotel bar? If he feels sorry for his cheating wife, what should he tell himself to alleviate his guilt?
What makes these problems particularly difficult is their moral dimension. Like most of us, the traveling salesman wants to believe that he is a good person, But what does this mean? I attended a conference in 2016 Explore whether artificial intelligence can solve moral dilemmas. There are many interesting changes to the trolley problem. For example, would you destroy creatures like sparrows in order to save inanimate creatures like the Grand Canyon?
But for thousands of years, philosophers have been arguing about moral issues, without agreeing on what our moral rules should be.Famous play The death of a salesman Explore the moral dilemma of traveling salesmen. Like most literary works, The death of a salesman Does not solve moral issues; it rubs our faces on them.
Is hardness equal to complexity?
So-called complexity researchers Equal hardness to complexity.Suppose you are a scientist trying to model and explain some complex phenomena, such as The propagation of gravitational waves From the collision of black holes, or the spread of false information on social media. Researchers suggest that the difficulty of your scientific problem is directly proportional to the complexity of the phenomenon you want to understand.
In addition, for similar reasons, different things can be complicated and therefore difficult to explain. Ideally, modeling a difficult phenomenon will yield insights applicable to very different phenomena. A better black hole model may lead to a better model and a deeper understanding of QAnon. Or the researchers hope so.
Unfortunately, researchers cannot agree on the definition of complexity, which is critical to their business.Physicist Seth Lloyd listed Dozens of proposed definitions of complexity, Based on information theory, thermodynamics, fractal and other measures. There are many definitions, because none are really enough. I suspect that just as unfortunate families have their own misfortunes, different problems become difficult for different reasons.
Some physicists insist that everything, including humans, can ultimately be explained by particles pushed and pulled by gravity, electromagnetic force, and other forces. Sabine Hossenfelder in A recent conversation with me. But physics has nothing to say about morality, meaning, emotion, choice, and other important features of human existence.
Mathematics, English and the hardships of being a parent
When I try to understand the mathematical rules that underpin quantum mechanics, they often appear annoyingly mysterious and arbitrary. In fact, the rules of calculus and linear algebra are more reasonable than the “rules” of ordinary languages. To master English, you must first learn the letters. Letters are meaningful only when they are combined into words. There are thousands of words, many of which have multiple meanings. Consider all meanings of “difficulty.”
Then you have all the rules for combining words into sentences, which are often bent and broken. The meaning of a sentence also depends on rules that are difficult to spell accurately, and on the context in which it is spoken and heard. Noam Chomsky Most scientists believe that we have a natural gift for language, which is inherited from our ancestors; this is why we learn languages so quickly.
Sometimes, when I have a conversation, my language instinct comes into play, and I can chat relatively easily. I’m showing what the philosopher Daniel Dennett said “Ability not to understand. “Other times, it is difficult for me to decipher the words of the person speaking to me, and I am overwhelmed by all possible ways of responding. This often happens when I speak to my daughter or son.
In a strict biological sense, becoming a father is easy. Almost any idiot can do it.But what does this mean become a OK Father? The answer varies by era and culture. My son and daughter are 28 and 26 years old respectively, and I am still confused about my fatherhood. Almost every time I see my children or talk to them on the phone, I will re-guess myself afterwards. Do I share too much? not enough?
You can evaluate parents by looking at their children’s performance. But I know that there are good parents (caring, kind) whose children have died from drug overdose, and I also know bad parents (selfish to negligent) whose children thrive. These cruel facts have an advantage: if your child is performing poorly, you can always blame bad luck. My more important point is that, unlike the Schrodinger equation, there is no clear solution to the problems of parenting and interpersonal relationships.
Race, gender, and brain chips
Cognitive scientists propose that we have an innate ability to intuitively feel the thoughts and feelings of others. This ability is confusingly called “theory of mind.” It is essential to social success, that is, to get what we want from others. This is also important for morality. If we can sympathize with them, we are more likely to feel compassion for others and treat them kindly. But our theory of mind program can only take us so far.
Last year, I participated in the “Black Man’s Fate is Fate” parade through my hometown. Some white protesters held up signs that read: “I understand, I will never understand. But I stand.” This sign means that white people like me cannot understand what it’s like to be black in America. This task is too difficult. If we say we understand, it means we don’t understand; we expose our ignorance and arrogance. But we can still express our support for black Americans.
This situation also applies to gender.I recently argued with my girlfriend about one of the most famous passages in literature, Molly Bloom’s monologue, and finally James Joyce’s novel UlyssesI like the profane, sexy, and poetic masterpiece in this masterpiece, in which Joyce imagines what it feels like to be a married woman and mother living in Dublin in the early 20th century. My girlfriend hates this kind of monologue, she said it is a man’s fantasy of women’s thinking. Instead of arguing with my girlfriend, I should say, “I understand I will never understand. But I stand.”
Visionaries such as Elon Musk hope that the computer chips implanted in our brains will one day help us solve problems. This is why Musk founded Neuralink, which is building “High-bandwidth brain-computer interface. “These chips connect our brains to the Internet and powerful problem-solving programs, such as Wolfram Alpha But much better.
I suspect that the brain chip will help us solve the most important problems. The brain chip may help the traveling salesman plan his itinerary, but it will not tell him how to be a good husband and father, or how to avoid acting like a sexist or racist.It won’t tell him what to do Grab a little happiness instead of a bastardThese problems are much more difficult than the most difficult NP-hard problems.
While writing this column, I began to recall why I fantasized about being a mineralogist when I was a child. I have gotten hints of adulthood, but it doesn’t appeal to me. Many adults look sad, mean, or both. When I grew up, I thought, I would spend my days alone in the laboratory, performing Mohs test on crystal specimens, testing their chemical reactivity, examining them through a microscope, and admiring their perfect, symmetrical, and inhuman beautiful.
I talked about various problems in my two recent books, Physical and mental problems, Available online for free, and Attention: sex, death and science.
See also my podcast”Physical and mental problems,” There I discuss difficult problems with experts.
This is an opinion and analysis article; opinions expressed Author or author Not necessarily those Scientific american.