Recently I read a lot of books and material on the science of learning and wanted to sort out some of my impressions and thoughts. But a structured article would take the length of a book, and I am far from ready for that. My initial plan for studying this field is five years; this piece can count as a decent start.

1. Why care about learning?

Two personal reasons. First, I ran into a lot of difficulty learning complex technologies such as AI. Second, I want to give my child an example lived out in practice. From a larger view, the human learning mechanism is far more complex than today’s machine learning. Thanks to brain science, cognitive science and psychology, the science of learning has produced some results, but most of it is still unknown, and even these limited results have not been effectively spread. As in medicine, personal experience matters a lot in learning, so custom and folk remedies often have more life in them than scientific conclusions. Programmers are among the professions that feel the importance of learning most keenly: new technologies keep arriving, and behind every line of code there may be a person doing repetitive work being replaced. As the internet levels the information gap, more and more of the rich list are top students. That is a picture of cognitive advantage replacing information advantage. Whether for the utilitarian goal of high scores and big money, or the joy of pursuing truth, learning is a discipline you have to practice.

2. Is learning only for students?

Equating study with being educated in school, getting high scores and a diploma, is the biggest misunderstanding of learning. If you have ever built a “stupid” artificial intelligence, you know every child is a genius at learning. Yet the failures of institutional education very likely have their original enthusiasm for learning put out, while its successes may fail in society and be held up as proof that study is useless. Many people stop progressing after their first few years of work; their last large-scale learning was forced on them while adapting to the job. When they become parents, their own knowledge has stalled, yet they expect their children to excel, and get anxious over advertorials from tutoring companies about “fifty thousand a month and you still can’t raise a child”. But learning is in essence just an instinct of being human, and what people generally call studying is only one of the paths to it. Confucius said: among any three people walking, one can be my teacher. He also said: to learn and to practice what you have learned, is that not a pleasure? I cannot put it better than he did.

3. Among all ideas about learning, what matters most?

The most important thing, I think, is to abandon the “entity theory” of intelligence and ability and embrace the “incremental theory”. Put simply: do not believe that intelligence and ability are innate and unchangeable, but believe that they can be raised through learning. Splitting people into genius and ordinary, high IQ and low IQ, smart and dull does the greatest harm to human progress. No one denies that people differ by nature, but at the level of effort most people actually put in, they are usually not yet in a position to be comparing talent. If everyone’s ability were laid out on a spectrum, each person would have a place on it; it is neither binary nor fixed. Everyone hits the ceiling of his own ability — even genius scientists, who may spend a lifetime failing to understand one problem. If a person is born with less ability and believes that cannot change, then clearly his ability will not improve. If a person is born with more ability but believes that cannot change, then when he hits the ceiling, meets difficulty and setback, he will doubt his own intelligence and ability, and inevitably fail or run away. That is what people call clever but not wise. Holding different beliefs for a lifetime produces results worlds apart. And it is not only a belief: brain science long ago proved that human nerve cells can keep being born throughout life.

4. Does effort matter more, or method?

This is of course a false question; the answer is obviously both. The deeper question is what kind of effort is the right effort. In traditional thinking, learning is a serious matter: sit upright, tie your hair to the beam and jab your thigh with an awl — that is the proper way. For those who get good grades but do not look like they work hard, we praise their talent and urge them not to waste it: they should work harder. For those who look hard-working but get mediocre grades, we are generous in praising their effort; compared with the poor students who get bad grades and don’t try, they are always much better off. Rereading the material, highlighting the book, taking beautiful class notes — these are common study methods that research has shown to be ineffective. What they share is that they cost the learner a lot of time on effort that stays on the page. However clear and pretty the notes, if they cannot be moved into your own head they are useless. Every useful method rests on the principle of active engagement. If you want to actually understand what you are studying, there can be no self-deception in it. Being hit by your own ignorance is unpleasant; hiding inside self-satisfied effort is comfortable. But there has never been an easy way to learn.

5. Why are exams important?

The most common and most effective study method is the exam. Treating the exam as nothing but a tool to check results, making the score the only goal — either score-worship, or loud talk of “quality education” that avoids the word exam — is our biggest misunderstanding and waste of this tool. First, an exam is the ultimate weapon against the illusion that “I already know this”, an illusion that rereading the textbook or your notes always produces. Second, an exam forces you to recall what you learned, which is an excellent way to consolidate memory and understanding. A good teacher keeps testing students by every means — pre-class quizzes, in-class quizzes, post-class quizzes. The aim is not to rank students but to make them retrieve their own memory, deepen the impression, and find the gaps. Even outside formal study — reading a book unrelated to your field, say — you can make full use of the exam. The simplest version: after a chapter, close the book and ask yourself a few questions. What was that material mainly about? Do I agree with these views? What connection do they have to what I already know or have experienced? If I agree, how would I apply them in life and work?

6. If study matters so much, why are there bookworms?

Why is it that we understand so many truths and still cannot live this life well? The problem is not the truths; it is ourselves. If you treat study as entertainment, like playing mahjong, then being a bookworm is no bad thing. But if you are after progress, study is only a beginning, not an end. The bookworm is keen on how many books are on the shelf, on how fast he reads, on how many books a year, keen on quoting from books, keen on how much “solid stuff” he has seen — but never on how much knowledge and how many ideas have taken root in his own head, whether those ideas form a complete, coherent, evolving system, and how many of them have been put into practice. Zeng Guofan was a scholar who could lead troops into battle. He wrote a diary every day to examine himself, and what he examined was how his practice should carry out his ideas. What you get from paper is always shallow; to know a thing truly you must act on it. I cannot put it better than the ancients. Confucius and Zeng Guofan needed daily self-examination. Why would we not?

7. Does more practice mean better learning?

The ten-thousand-hour rule is a widely circulated idea, and the “deliberate practice” theory behind it is also much misunderstood. “Effort always pays off” is a comforting thought, but effective practice is not simple repetition. Both scientific research and the personal experience of geniuses show that effective practice has to be highly active. First, you give ground in order to advance: divide the skill into fine enough modules, and practice module by module, hitting your weak spots. Second, the practice cannot be simple repetition; it has to vary and interleave. These findings are counterintuitive. People always feel that repeated drilling gives better mastery and that varied, interleaved practice works worse — an illusion that is hard to overcome. Truly effective practice burns a great deal of mental energy, and cannot be sustained for long stretches.

8. Why can’t I remember or understand what I read?

The latest memory theory holds that retrieving a memory matters more than forming it in the first place. Everyone is capable of total recall; the problem is that the fragments lie scattered in the brain and cannot be reorganized and pulled back out. The only way is to build more connections among them — like a village that was backward until concrete roads ran out in all directions, and then was no longer backward. For knowledge that is not yet systematic there are plenty of little tricks, such as making up a jingle: “for the long months there’s a rule that holds — odd ones before July, even ones after.” For systematic knowledge, the most important thing is to build your own knowledge system: every new piece of knowledge should be connected as much as possible to what you already know and have experienced. Obviously, this is not a quick or easy process. Many people have crammed before an exam, sometimes with decent results, but that too is an illusion. Knowledge that was never, through hard work, brought into your own system will be handed back to the book.

9. Can I sleep less to learn more?

One of the myths about successful people is that they sleep only three or four hours. But they can catch up on planes, they can put a bed in the office, their mental work as decision-makers is low-intensity — and they may simply be lying. If you do high-intensity mental work — a grad student, a programmer writing code — then sacrificing sleep, apart from possibly killing you earlier, will seriously lower your learning efficiency. Brain science shows that building synapses requires adequate sleep. Any learning that builds no new synapses is a waste of time. Modern habits lean more and more toward late nights, and even children are affected by this cultural shift. That children are pressed by homework into too little sleep is a mockery of brain science.

10. How is a poor student made?

In the Japanese film Flying Colors, the heroine prepares for the college entrance exam but her math is far too weak. Her tutor’s method is to start from elementary school math. This is not exaggeration; it has a real prototype. The flaw of institutional education is that it has to set one standard for the majority: what language a child should command at 8, how much math he should know at 9. Someone will always fall behind, and those who fall behind are likely to be stuck with negative labels. Maybe he only matures enough for math at 12, but by then the chance is gone; often these children no longer feel any involvement in learning at all. Europe and America do have mixed-age classrooms that follow the child’s actual level, but if a 12-year-old went to study third-grade math, neither the parents nor the child could keep face. In such a case the cram school may be the best way out. Learning anything starts slow and then speeds up: lay the foundation first. Learning is like building a house — a tower ten thousand feet high starts from the ground; do not build a high terrace on shifting sand. I cannot put it better than the ancients.

11. Why does what you never forget always come back?

When an expectant mother is pregnant, the expectant father notices more pregnant women while out shopping. When you are struggling over the structure of the benzene ring, at night you may dream of a snake biting its own tail. When you are thinking about a problem with everything you have, even after you stop, something like a background process keeps running in your head. Your senses collect related information without your willing it; your dreams try out various solutions. Breakthroughs and inspiration arise naturally, but not out of nothing: they belong only to a brain that has gone all out and then relaxed. Research shows that geniuses usually stand out only in their own field; their flashes of insight and strokes of brilliance are nothing but the natural gift that follows countless hours of hard work. If you want to get rich but spend less than ten minutes a day thinking about it, how could pie fall from the sky? The echo that follows never forgetting is a matter of probability, but we can raise that probability.

Main references (all links go to the Chinese editions on Douban):

• 有效学习
• 如何学习
• 所谓学习好，就是方法好
• 认知天性 : 让学习轻而易举的心理学规律
• 好好学习 : 个人知识管理精进指南
• 科学学习 : 斯坦福黄金学习法则
• 学习的艺术
• 学习之道
• 如何高效学习 : 1年完成麻省理工4年33门课程的整体性学习法

[First draft 2017-08-10 / minor update 2020-05-01]

1. What is Bitcoin?

Bitcoin is a digital currency. It does not depend on any central institution to issue it; it depends on the internet, and is issued on the basis of cryptography and distributed computing theory. Anyone can take part, its total supply is capped, and you can think of it as a kind of gold in the digital world.

2. What is Bitcoin good for?

The most important thing Bitcoin can buy today is other countries’ currencies. As a digital currency, its original design intent was to partially replace fiat money, so in theory it can do anything money can do. In practice, buying things directly with Bitcoin is still at a very early experimental stage, supported by only a few merchants, the most famous being Microsoft . Personally I think three things block broad adoption. First, Bitcoin payment fees are currently too high, and the dispute over how to fix that even split Bitcoin into two forks: BCH, which backs big blocks, and BCC, which backs the Lightning Network. Second, Bitcoin’s price is still far too volatile; more people treat it as an investment or a speculation. Third, because currencies compete, most governments are not keen on it.

Bitcoin is now described as digital gold, with the emphasis on its store-of-value role, but its payment value is the base layer of its value. If Bitcoin ultimately cannot be used for general transactions, its value is questionable.

3. A currency should be backed by state credit, and Bitcoin has none. Where does its credit come from?

A currency does not have to be backed by state credit — gold, for instance, still works as an internationally accepted money. A currency’s credit comes from how many people believe it is money. State-issued paper money tells one story; Bitcoin, issued on cryptographic consensus, tells another. Humans can organize cooperation on a larger scale precisely because we have the capacity to believe in stories. (Recommended reading: Sapiens .)

Bitcoin’s source of credit really is hard to grasp. In a distributed way, it reaches consensus on the question of who owns how much, in a manner that no one participating in the system can deny. What you still need to understand is that any modern currency is a story, and the defining property of money is that the more people acknowledge its monetary value, the more monetary value it has — so yes, there is an element of faith in this.

4. So is Bitcoin a pyramid scheme, or a Ponzi scheme?

Bitcoin has one thing in common with pyramid and Ponzi schemes: both need a bit of faith. The difference is mainly that faith in Bitcoin actually makes this currency genuinely valuable — its value is existing as a currency, and nothing else. What pyramid and Ponzi schemes produce is more people getting taken in.

The Bitcoin community first gathered a bunch of geeks and cypherpunks who wanted to build a new monetary system; the starting point was absolutely not to swindle money. Of course, with the enormous speculative opportunity that hype around Bitcoin and blockchain has created, the so-called coin circle is possibly where swindlers are densest. My advice to everyone: don’t invest in what you don’t understand.

5. How exactly is Bitcoin issued?

Apart from the 50 Bitcoin in the genesis block, all Bitcoin is a reward for the right to keep the ledger, and comes into existence gradually as the Bitcoin network runs. Bitcoin needs to periodically confirm and record all unconfirmed transactions, and whoever wins that bookkeeping right receives a Bitcoin reward. These rewards are Bitcoin’s original source. Each batch of recorded transactions is packed into a so-called block, and every block carries a pointer to the previous block — hence “blockchain.”

6. How is “who owns how much Bitcoin” recorded? Is there an account like a bank account?

There is no concept of a bank account. The Bitcoin blockchain records only the creation of Bitcoin and every transfer since creation. When Bitcoin has been transferred to an address and not yet sent out, that address owns that Bitcoin.

7. What is an address?

An address can be understood as a kind of identity credential. It is public, like the number plate on your front door that everyone can see. But only you hold the key that opens the door. This uses signature algorithms from cryptography; broadly, you prove through the private key that this address (the public key) is under your control.

8. Does Bitcoin really consist of individual coins?

As said above, the Bitcoin blockchain is one big ledger, so there are no individual coins the way there are individual renminbi notes. There is only the fact, visible to everyone, that a given address holds a quantity of Bitcoin that has not been spent yet, and Bitcoin at that address can only be spent by someone holding the private key, after signing. Bitcoin is therefore in effect the private key, because whoever knows the private key can spend the Bitcoin.

9. How do you store Bitcoin?

First, as noted, storing Bitcoin primarily means storing the private key — that is the main function of a so-called Bitcoin wallet. Leak the private key and the Bitcoin is gone. Beyond that, how much a given address holds is determined by the public blockchain; anyone can connect to the Bitcoin network and verify it.

10. So who actually does the bookkeeping? Why should I trust the bookkeeper?

This is Bitcoin’s most ingenious design. Who does the bookkeeping is not a settled matter: every node has to spend a long time computing (which burns electricity) to compete for that right. Having won it, if you record nonsense, the other nodes will not accept it and the block you produced is void. It still points to the previous block and forms a chain, but others can create a block with broader acceptance, producing a longer chain that voids your short one — you burned electricity and get no block reward. This ingenious design achieves trustworthiness by relying on the fact that human nature chases profit.

11. What are mining and mining machines?

As in the previous point, the work of competing for bookkeeping rights — that is, competing for the Bitcoin reward generated by bookkeeping — is called mining. Mining requires a hash computation that makes the resulting hash contain a certain number of zeros; that number grows as the total hashing power of the Bitcoin network grows, so that the block-packing speed, and hence the rate at which Bitcoin is created, stays roughly constant. The race for computing speed is therefore close to an arms race: from CPUs to GPUs, and now to machines built specifically for computing hashes.

The mining reward halves at intervals, so the rewards miners receive shrink steadily. But the Bitcoin network has another mechanism: every person making a transfer pays a small fee, as a reward to the miner who successfully packs the block.

12. How do I get Bitcoin?

Competing for bookkeeping rights — mining — is now highly professional and difficult, so you would have to buy specialized mining hardware and join a so-called mining pool to share hashing power and Bitcoin rewards.

The simplest way is still to find someone who holds Bitcoin and buy it with renminbi. As for how to trade: with regulation tightening in most countries, exchanges mostly no longer support direct fiat-to-Bitcoin trading the way stock exchanges work, only so-called over-the-counter platforms, where the platform provides escrow like Taobao — or no escrow at all, just listings — and the trade is C2C. My advice is to buy on a large, well-known platform that offers escrow; I won’t recommend specific ones here.

13. Every block creates Bitcoin, so will there just be more and more of it?

No. Each block’s reward halves at intervals, so it is a geometric series with ratio 1/2, totaling 21 million. Bitcoin is therefore designed to be deflationary.

14. A deflationary currency buys more and more goods over time, so in theory everyone will hoard Bitcoin instead of spending it. Does it still have monetary value?

That is a good question. My understanding is that at a certain point — once Bitcoin has the standing it deserves and its price stabilizes — holders will naturally spend it, just as people who own gold do today. And Bitcoin can form a monetary system together with inflationary currencies, just as gold and fiat money do today.

15. I hear Bitcoin is anonymous, so it is all used to buy drugs?

Bitcoin is a public ledger, but its addresses are strings of characters that cannot be tied directly to a person, so there is some anonymity. At the same time the ledger is public and its history is immutable and inspectable at any time; in that respect it is less anonymous than cash, because once a Bitcoin address is linked to a person, all of its history can be traced. In fact the Silk Road, which sold drugs for Bitcoin, was taken down by the FBI. Bitcoin is just a tool; it is not inherently friendly to crime.

16. I hear Bitcoin is used for money laundering?

As with the previous question, I do not think Bitcoin is inherently friendly to money laundering. The Chinese government, for instance, has begun supervising the risk of money laundering through Bitcoin on exchanges. I think Bitcoin should be used more for compliant, lawful applications.

17. Since Bitcoin is only a technology, issued by no organization, anyone can casually produce similar digital currencies. Does Bitcoin still have any special value?

You can indeed produce any number of similar digital currencies, and their technology can even be better. But two things matter. Bitcoin has a first-mover advantage, and the value of a digital currency grows with the number of participants; with Bitcoin already holding the high ground, other digital currencies find it hard to build an advantageous position from scratch. Second, Bitcoin itself can evolve through technical innovation.

18. What is the Bitcoin split about?

Bitcoin’s rules and software are open source, so when someone disagrees with the current approach, they can start from a certain block and pack transactions (mine) under new rules, rejecting blocks mined under the old rules — and conversely the old rules no longer accept blocks mined under the new ones. From that block on, two chains each go their own way. Bitcoin that was unspent before the split block can be transferred onto both branches, so one old Bitcoin effectively becomes one Bitcoin on each of the two new chains.

19. Doesn’t that split mean Bitcoin doubled?

Not exactly. After a split, the two versions diverge in value as participants vote with their feet, and from the standpoint of established fact, only the more valuable one counts as the authentic Bitcoin. Bitcoin’s transfer fees are currently high, and the two proposals for solving that produced two camps: those backing an increase in block size forked off a digital currency called BCH, while the other, more complex protocol temporarily kept the name BTC.

20. What is the relationship between Bitcoin and blockchain?

Blockchain technology arose from the development of Bitcoin and has since spun off more technologies, but blockchain’s application scenarios still need to be pinned down in earnest. The current boom is largely bubble, and personally I think digital currencies represented by Bitcoin are the application scenario blockchain has actually delivered. Many use cases have no need for blockchain at all, while digital currency very likely is necessary; I cannot go into that here — see Hayek’s Denationalisation of Money.

21. How should I invest in Bitcoin?

For most people the only workable way is to buy Bitcoin with a small amount of money that does not affect your life at all, and hold it for 5 to 10 years. Bitcoin’s price is still wildly volatile, so any attempt to chase rallies and dump dips will land you in a gambler’s position. With any investment, always remember: don’t invest in what you don’t understand.