Two Kinds of Difficulty

There are two reasons accomplishing something might be difficult.

The first is intrinsic difficulty. Imagine you wanted to hold your breath for ten minutes straight. This is a challenging task because of the limitations of the human body. It’s exceptionally hard to do without intense training.

The second is relative difficulty. Now imagine you wanted to have the world record for holding your breath. Here, what is important isn’t so much the absolute difficulty of holding your breath. Instead, it’s the level of competition. If there’s a lot of serious competitors, this will be very hard. The world record for breath-holding is twenty-two minutes, so in this case it certainly qualifies as very difficult.

I think it’s important to separate these two types of difficulty, particularly with respect to learning accomplishments, because they have completely different features and expectations.

What Makes Learning Hard?

I think an illustrative example of the difference between intrinsic and relative difficulty is quantum physics and chess.

Quantum physics is a hard subject. The math required to understand requires a steady ascent of increasing abstraction starting from counting to arithmetic to algebra to calculus to differential equations and waves. It’s a trek that usually takes years to complete, and many people fall off along the way.

Chess, in comparison is dead simple. I wager that I could teach almost anyone how to play chess in less than half an hour, with no prerequisites. Perhaps slightly more time would be necessary if the person had never played a board game before, but not much.

Quantum physics, in my opinion, is intrinsically difficult. It’s difficulty is owing to the fact that, in order to understand it at all, you need to have decades of specialized training layering abstraction upon abstraction.

Playing chess, to the standards we typically expect, however, still isn’t easy. To play chess competitively, you need to invest a lot more time with it than to understand quantum physics. Grandmasters can log tens of thousands of hours of brutally intense coaching. The average person could spend hundreds of hours and still not be able to win a local tournament.

The reason for this discrepancy, however, is obvious: competition. Chess is a popular game and therefore the relative difficulty is quite high, even if the intrinsic difficulty is somewhat less so.

What’s Harder: Chess or Go?

Go is a Chinese game played on a grid, similar to chess. The difference is that, in Go, the board starts empty and one places identical pieces one at a time along the intersections of the grid. If your piece finds itself surrounded by enemy pieces, it gets removed. This leads to its more descriptive Chinese name, 围棋 (wéiqí), which loosely translates to “encircling game”.

Recently, I had an email conversation with a reader about learning to play competitive-level Go. Like chess, this involves memorizing thousands of position variants. Some of which may be dozens of moves long and must be executed perfectly or the position is lost.

My correspondent remarked that many competitive Go players essentially train on the game their entire lives, starting in special schools from childhood, easily putting in 30,000+ hours into the game. He suggested that this could be due to the fiendish complexity of the game.

This leads to an interesting question. Which is harder: chess or Go? And why?

Now that we’ve discussed relative vs intrinsic difficulty, this question has new meaning.

In terms of intrinsic difficulty, it’s likely that Go is indeed more difficult than chess. For one, chess has a smaller board and fewer positions. Therefore, at any given point in the game, there are a much smaller set of possible moves in chess than there are for Go.

This is one of the reasons why computers have had a much harder time learning Go. Computers can outperform humans in chess mostly through brute-force. A computer can quickly dive down several moves deep, examining most fruitful possibilities. In Go, the movespace expands so much faster that computers only were able to beat humans by employing sophisticated pattern-recognition algorithms that are likely similar to the ones used by human brains.

However, what about the comment about “30,000+ hours” to become world-class at Go? Here, of course, we’re not dealing with intrinsic difficulty at all, but relative difficulty. If Go were an obscure game that almost nobody in the world played, the rules could be exactly the same but it might only take a few hundred hours to become the world champion.

This difficulty—how long does it take to become a grandmaster—almost entirely depends on the relative competitiveness of chess and Go. My feeling is that this gives chess a slight upper hand, as there are probably more serious chess players than Go players worldwide.

Unless the game itself has a lower-bound of complexity that prevents further mastery (say Tic-Tac-Toe, which can be played perfectly after minutes of instruction), relative difficulty will be the most important factor when sizing up your ability.

How Does Relative Difficulty and Intrinsic Difficulty Affect Your Plans?

We’re very used to thinking about relative difficulty for tasks. So much so, that we often confuse it for intrinsic difficulty. In school, if everyone was getting 100% on every test, the teacher would make it more difficult until some people weren’t getting perfect scores.

Because we’re conditioned to focus on relative difficulty, people quickly deem themselves incapable or incompetent at learning certain things, simply because they fall lower on that end of the spectrum. If you were in the bottom 20% for mathematics, you might tell yourself you can’t learn math. What you really mean, however, is that you’re not as good at math as others, and therefore the relative difficulty is too high.

This actually has some interesting force behind it. There’s some clever argument showing that the same student who was bright in his or her high school may perform differently depending on the exclusiveness of the university he or she enters. Basically, if you’re smart, but everyone around you is even smarter, that may convince you that you’re not actually all that smart and you may downgrade your ambitions either through choosing less competitive majors or not graduating at all.

I’m not sure that this necessarily suggests that the average person shouldn’t try to get into the most exclusive school, but it does at least highlight the possibility that relative assessments of ability often get confused for intrinsic difficulty.

Relative difficulty is important. It certainly serves a purpose of sorting people into different buckets of talent and effort invested. I don’t mean to deny that. However, perceiving the intrinsic difficulty (or lack thereof) is often underrated simply because it is so absent in the formal schooling.

In many cases, what you want is an absolute level of ability, not merely a relative one. If I can fix my plumbing, ask for directions in French, do my taxes, cook a meal, write a useful program, perform first aid, drive a car, start a campfire, give a presentation, make friends, manage my time or any number of other things, my absolute performance matters a lot more than where I fit on a bell curve.

Next time you find yourself saying a certain subject is too difficult, ask yourself whether it’s intrinsically difficult or only by comparison to other people? The answer may change how you approach it.

Book Club: Sapiens, A Brief History of Time (July 2017)

James Clear and I discuss July’s book Sapiens: A Brief History of Humankind. We cover the major themes in the book as well as the author’s thought provoking interpretation of human history, contemporary society, and beyond.

If you would rather read the transcript, you can download it here.

Below are some of the highlights:

…on myths and our ability to share collaborative fictions:

James: I found the book fascinating. Harari is very interesting in the way that he frames issues and the way that he talks about things. He does a really great job of looking at things from a new angle… I love thinking about laws as one example. For example, why do we all stop at a stop sign or a red light? Well we stop there because we’ve all agreed we’ve decided that there are certain laws of the road and we’ll adhere to those.

Our ability to collectively agree upon this shared myth or story allows us to have roads and cities that function in an orderly fashion. There’s nothing fundamental about that in the sense that it’s not a fundamental law of the universe (like dropping a ball, it will fall regardless if someone agrees with it or not) and that’s just one example of some of the interesting ideas that he shares.

Scott: I will give a good example: the fact that George Washington is the first American president is pretty uncontroversial. There’s writing that supports this. But this would be exactly the kind of “myth” that Harari is talking about.

It can sound a little bit inflammatory but it’s not to point out the idea that there’s some conspiracy but rather to point out the idea that the whole concept of a “president” or a “United States” is a shared, collective idea that there’s nothing physical in terms of matter that specifies a “President” or specifies a “United States”, rather, they are just shared ideas we have about this.

By calling these myths or these shared collective ideas, he [Harrari] is not trying to share that these are superstitious but rather, this is our great strength and that we have the ability to coordinate on all these shared fictions or created realities that are not necessarily tied down to some kind of materialistic account of the world.

…on the reality of money:

Scott: One thing I thought was great was his section about money. Harari says, “Money is accordingly a system of mutual trust and not just any system of mutual trust. Money is the most universal and most efficient system of mutual trust ever devised.”

What I thought was very interesting is that Harari said the power of money is that money works because you believe other people value it. You don’t need to value it yourself; you just need to believe other people value it so you can get the things you really want from people.

This is a real turn your head around idea and I remember when I wrote a piece about this and I got some economist who said you’ve fallen into the trap of thinking that the US dollar is just a fiat-currency and you’re one of those gold thugs who need to go back to the old days. Really money is based on US debt and securities… but I think that missed my point because those US debt securities are also a sort of an inter-subjective reality. If I didn’t believe in the US and the debt that the US holds then of course the money doesn’t have any value.

James: I’ve actually taken to thinking that, capitalism of which money is of course a central concept, capitalism is perhaps the most successful religion that the world has ever seen. It’s the only religion that everyone agrees upon regardless of what your actual spiritual religion is or is not.

Pretty much everybody agrees that you should work and earn money and have a career and have a job. We’ve all bought into this shared myth together and it makes up the fabric of our culture. The vast majority of our lives are spent working. If we talk about what percentage of our lives are these imaginary concepts versus these physical realities, it is interesting to see just how much of our time on this planet is spent living out the imagined realities that we’ve agreed upon like capitalism and money.

For those of you who want to read the book, it is available here. If you want to participate in the group discussions and join our book club, click here.

Special thanks to James Clear of jamesclear.com. Be sure to visit his website for great articles.

The book for August will be Surely You’re Joking, Mr. Feynman! by Richard Feynman.

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