I used to be a rock hunter as a kid, and I learned how to identify minerals using the Mohs hardness test, which was invented by a mineralogist.
You scrape an unknown specimen with a known specimen, such as quartz.
If the mystery specimen scratches the quartz, you know it’s softer than quartz.
Calcite or pyrite could be the culprit. It could be beryl or corundum, which are harder than quartz if the quartz can’t scratch the specimen.
The hardness test, together with other factors like color and crystalline structure, can assist you to specify your specimen.
The Mohs test’s direct objectivity appealed to me. Recently, I’ve been thinking about a type of difficulty—call lets it cognitive hardness—that is far more difficult to assess.
We are confronted with a wide range of cognitively challenging tasks throughout our lives.
For example, I’ve been studying quantum mechanics for the past year, which is famously tough to grasp.
Is it, however, objectively harder to master quantum mechanics than it is to talk to my partner about #MeToo without annoying her? Alternatively, how can I talk to my daughter about climate change without making her depressed?
Subjective estimates of cognitive difficulty aren’t very useful because they vary depending on the individual’s experience and aptitude.
I’m better at riffing on Emily Dickinson’s poems than you are with differential equations.
Is there a mechanism for evaluating and ranking the cognitive toughness of various tasks that is similar to the Mohs test?
Perhaps such a system could provide us with insights that allow us to solve difficult problems or accept their insolubility.
Here are some thoughts on cognitive difficulty, in any case.
PROBLEMS OF THE TRAVELING SALESMAN
Mathematicians and computer scientists rate issues based on how long a computer would take to solve them.
If there is no algorithmic shortcut to the optimal answer, a problem is classified as NP-hard; you must laboriously check every conceivable solution to identify the best one.
(NP stands for “nondeterministic polynomial time,” which I’ve always interpreted as “very.”
A traveling salesman seeking the quickest path between numerous cities is a well-known NP-hard problem.
The difficulty of the challenge increases considerably as the number of cities increases.
If the salesman needs to visit 15 cities, he can choose from 87 billion different routes.
Mathematicians have invented methods for locating somewhat short—if not the shortest—routes between several cities.
When the number of cities exceeds tens of thousands, though, even the world’s fastest computer would take an eternity to discover the quickest path.
Surprisingly, devising a time-saving schedule is simple compared to the other issues that the traveling salesman may confront.
For instance, how long can he be away from home without jeopardizing his marriage? Should he approach a woman in the hotel bar if he’s lonely? What should he say himself to make himself feel better about cheating on his wife?
The moral nature of these issues makes them particularly difficult.
The traveling salesman, like most of us, likes to believe he is a good guy, but what does that even mean?
I attended a symposium in 2016 that looked into whether artificial intelligence might help with ethical concerns.
The trolley problem was reimagined in a variety of amusing ways. Would you, for example, kill a sparrow to save a nonliving object like the Grand Canyon?
However, philosophers have debated morality for millennia without reaching a consensus on what our moral principles should be.
The moral issues of a traveling salesperson are explored in the famous play Death of a Salesman.
Death of a Salesman, like other works of literature, does not solve moral problems; rather, it rubs our faces in them.
DOES COMPLEXITY EQUAL HARDNESS?
Hardness and complexity are equated by so-called complexity researchers.
Assume you’re a scientist attempting to model and so explain a complex phenomenon such as gravitational waves propagating from merging black holes or the spread of misinformation on social media.
According to scholars, the difficulty of your scientific problem is related to the complexity of the thing you wish to understand.
Furthermore, for similar reasons, unlike things may be complex and thus difficult to describe.
Modeling one hard phenomenon should, in theory, produce insights that can be applied to many others.
A better understanding of black holes could lead to a better comprehension of QAnon. At least, that’s what researchers hope.
Regrettably, researchers are unable to agree on a definition of complexity, which is critical to their business.
Seth Lloyd, a physicist, has proposed dozens of complexity definitions based on information theory, thermodynamics, fractals, and other metrics.
There are numerous definitions since none are adequate. I believe that, just as unhappy families are unhappy for various reasons, different difficult tasks are difficult for various reasons.
According to some physicists, everything, including mankind, can be explained in terms of particles pushed and pulled by gravity, electromagnetic, and other forces.
In a recent interaction with me, Sabine Hossenfelder took this stance.
Physics, on the other hand, has nothing to say about morality, meaning, emotions, choices, and other important aspects of human life.
MATHEMATICAL DIFFICULTY, ENGLISH, AND FATHERHOOD
When I’m trying to figure out the mathematical rules that support quantum mechanics, I find them to be vexingly obscure and arbitrary.
In comparison to the “rules” of everyday English, the rules of calculus and linear algebra are fairly sensible.
You must first study the letters of the alphabet to grasp English.
Only when letters are united into words can they take on meaning, and there are millions of words, many of which have numerous meanings. Consider the several definitions of the term “hard.”
Then there are all the conventions for putting words together into phrases, which are constantly broken and bent.
The meaning of a statement is determined by the context in which it is spoken or heard, according to criteria that are difficult to define precisely.
Most scientists agree with linguist Noam Chomsky that we have an innate gift for language that we received from our ancestors, which explains why we learn languages so quickly.
When I’m in a discussion, my language instinct kicks in, and I’m able to converse with relative ease.
I’m demonstrating “competence without comprehension,” as philosopher Daniel Dennett puts it.
Other times, I struggle to understand what the person saying to me is saying, and I’m overwhelmed by all the possible responses.
When I’m talking to my daughter or son, this happens frequently.
In a purely biological sense, becoming a father is simple.
It’s something that almost any moron can do.
What does it take to be a good father, though? The answer varies depending on the era and society.
I’m still perplexed by fatherhood, even though my son and daughter are 28 and 26 years old. I second-guess myself almost every time I see my kids or chat with them on the phone.
Is it possible that I overshared? Is it not enough?
You can evaluate parents by looking at their children’s performance.
But I’ve known wonderful parents (caring, well-intentioned) whose children died of drug overdoses, as well as horrible parents (self-absorbed to the point of neglect) whose children thrived.
These harsh realities have an upside: you can always blame bad luck if your children don’t turn out well.
My bigger argument is that, unlike the Schrödinger equation, parenting puzzles—and all human relations puzzles—have no clear-cut solutions.
BRAIN CHIPS, RACE, AND GENDER
According to cognitive experts, we have an inbuilt ability to understand what others are thinking and experiencing.
This ability is referred to as “theory of mind,” which is a bit perplexing.
It’s necessary for social success or acquiring what we desire from others. It’s also necessary for morals.
If we can empathize with others, we are more likely to feel sympathy for them and treat them well.
Our theory-of-mind program, on the other hand, can only carry us so far.
I participated in a Black Lives Matter march that came through my town last year.
“I understand that I will never comprehend,” other white protestors held banners that read. But I maintain my position.”
The sign implies that white people like me have no idea what it’s like to be a Black person in America.
That task is too difficult. When we say we understand something, we’re displaying our ignorance and hubris. However, we may still show our support for African-Americans.
This circumstance holds for both men and women.
Molly Bloom’s soliloquy, which finishes James Joyce’s masterpiece Ulysses, is one of the most famous passages in literature, and I just argued with my girlfriend about it.
This vulgar, sensual, poetic masterpiece within a masterpiece, in which Joyce imagines what it’s like to be a married lady and mother in early twentieth-century Dublin, is one of my favorites.
My partner despises the soliloquy, which she believes is a masculine fantasy about women’s thoughts.
“I recognize that I will never understand,” I should have said instead of battling with my girlfriend. But I maintain my position.”
Visionaries like Elon Musk believe that computer chips implanted in our brains will one day assist us in solving difficult challenges.
Musk founded Neuralink to provide “high-bandwidth brain-machine interfaces” for this reason.
The chips will connect our brains to the internet as well as strong problem-solving algorithms similar to Wolfram Alpha, but far superior.
Brain chips, in my opinion, will not assist us in solving the most pressing issues.
A brain chip may assist the traveling salesman in planning his schedule, but it will not teach him how to be a decent husband and father, or how to avoid being sexist or racist.
It isn’t going to tell him how to get a little joy without becoming a jerk.
These challenges are substantially more difficult than the most difficult NP-hard problem.
While writing this piece, I remembered why I wanted to be a mineralogist when I was a kid. Adulthood was already creeping up on me, and it didn’t appeal to me.
Many adults appeared to be sad, cruel, or both.
I saw myself spending my days alone in a laboratory, performing the Mohs test on crystalline specimens, checking their chemical reactivity, inspecting them under a microscope, admiring their perfect, symmetrical, inhuman beauty.
the author is : John Horgan directs the Center for Science Writings at the Stevens Institute of Technology. His books include The End of Science, The End of War and Mind-Body Problems, available for free at mindbodyproblems.com. For many years, he wrote the immensely popular blog Cross Check for Scientific American.
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