On Learning

Dated May 2, 2020; last modified on Wed, 29 Dec 2021

Mental Attitude While Learning

Distinguish Mere Facts From Conclusions or Opinions

Discriminate between mere statements of facts, necessary conclusions which follow therefrom, and mere opinions which they seem to render reasonable. There’s no need to perform an experiment to verify that the atomic weight of oxygen is 16. That the sum of the angles of a plane triangle equals two right angles is not a mere fact, but an inevitable truth.

Investigate the Reason For Facts

Why would the wind in a storm in the northern hemisphere revolve counterclockwise around the storm’s center? Definitions are exempt: there is no reason why New York is 90 miles from Philadelphia. Sometimes the reasons require specialized knowledge that the student lacks, e.g. the laws of physics.

If There’s No Reason for the Facts, Seek to Know How They Ascertained

How do we ascertain that the sun is 92 million miles from the earth? Suppose 3,072 Union soldiers were killed in the Battle of Gettysburg. Why 3,072 is not a reasonable question. But how did we arrive at 3,072?

Look Out for Evidence of the Writer’s Reliability

Faulty conclusions/opinions may result from illogical reasoning from correct facts, especially when it has to do with statistical results. Be wary of overly dogmatic opinions and intolerability towards those that hold different conclusions.

Of late, the phrase “do your research” has been popular , with some pushing back claiming that lay people tend to entrench their initial opinions and should not do their own research, but instead defer to the consensus of scientific experts .

On “lay people entrenching their initial opinions”, there is also research that claims educated people are the ones who entrench deepest in charged issues .

How does one spot the consensus of the experts? Maybe by surveying the publications of the relevant field. Indexing and abstracting services provide abstracts of publications and references to documents , and may thus prove useful. provides a list of academic databases and search engines.

For CS, I knew of ACM, but shows that DBLP, AMiner and IEEE Xplore have more expansive collections.

For a given query, Microsoft Academic shows top authors, journals, institutions and conferences, which are informative when polling consensus in a given field. Google Scholar does not make such information apparent.

Exercise Caution

Read not to contradict and to confute, nor to believe and take for granted, nor to find talk and discourse, but to weigh and consider.

An Open Mind; No Preconceived Ideas

Clearly formulate a problem, gather all pertinent facts, and then draw the logical conclusion.

Study to Gain Wisdom, Rather Than Knowledge

Being knowledgeable is being full of other people’s thoughts. Instead, strive to be aware of your own thoughts in relation to your knowledge.

An essay helps you figure something out. Think of it as an idea graph - at each node, pick the most interesting related idea. Expressing your ideas also helps you form them. Writing them down forces you to think well.

I’ve noticed this when composing a post to ask why my code is not working. In the middle of writing and making sure that I’ve done my homework, I arrive at my answer, or an idea that I haven’t tried yet!

Dan Luu’s blog is quite informative and novel. In , Luu lists his motivations for measurement posts. Notice how they mostly start with an itch to dive into a personal curiosity.

The first thought is always someone else’s. Only by concentrating, sticking to the question, being patient, letting all the parts of your mind come to play do you arrive at original idea. And often, that idea needs further refinement.

It also helps to think out loud with a person that you feel safe with. You discover what you believe in the course of articulating it: doubts you aren’t supposed to have, questions you’re not supposed to ask, opinions that’d get you laughed at or reprimanded, and so on.

Studying Understandingly

“Suppose you dig a hole, hundreds of feet deep. Will the bottom be warmer or colder than the top?” Crickets. The teacher said, “I’m sure they know, but you’re not asking the right question.” “In what condition is the interior of the globe?” Half the class, “In a condition of igneous fusion!"

Terms like energy, momentum, rate of change, period of vibration, value, social justice, etc., are often used without a clear understanding. Vagueness of an idea may impair all reasoning regarding it.

Test What You Think You Already Know

Try defining a common word and compare the result with what the dictionary says. For instance, what is a cow?

Stumped me too. Dictionary: a fully grown female animal of a domesticated breed of ox, kept to produce milk or beef.

Some central themes, e.g. freedom is a desirable thing, have well thought-out arguments that we tend to overlook because we agree with the statement. Studying philosophy, especially by thinkers who disagree, is valuable.

Study Logic

The study of logic would enable you to see just where the error lies. Formal logic helps clarify your thinking, e.g. difference between validity and truth.

Restate Things In Different Ways or Points of View

There’s no such thing as understanding something but being unable to explain it.But repeating a statement in different words is not proving it, e.g. Why can one see through glass? Because it is transparent. To understand a conclusion, you must see the steps in its logical demonstration.

State a Thing Not Only Positively But Also Negatively

For conclusions and opinions, see what objections can be raised and address them. But for areas like mathematics, seeking objections isn’t gainful because the principles are rigid and not open to question.

Distill Statements to Fundamentals

Matter is that which can occupy space. Would it be proper to say, “Matter is that which occupies space”?

The number of independent equations must equal the number of unknown quantities. What does “independent” mean? Can it be omitted? Must each equation contain all the unknown quantities?

Keep the Mind Active and Alert

Dreamy thinking often enables ideas to clarify and take shape and proportion.

On Encountering Different Points of View, Investigate Where the Divergence Arises

Failing to grasp all the pertinent facts, or even the problem itself; reasoning incorrectly even from accurate premises; seeing facts out of proportion.

A System of Study

Discover the Fundamental Idea

It helps you master the subject because the other details can be viewed in relation to the fundamental idea. Facts of secondary importance may then be left for later readings. Fundamental principles should frequently be memorized.

Lay Out Pre-Existing Knowledge

Classify what you already know [and what you don’t know]. If you know nothing, insist on getting a clear idea of the subject, its extent, objects, methods, applications and relations to other subjects. In doing so, you cultivate an interest in what you’re studying.

Classify and Arrange Your Learnings

Stop and think over the ground that has been covered, and arrange the various points made. Close the book from time to time and go over in your mind what you have learned.

Make flashcards of facts/quotes that you wish to analyze. Do a write-up in your own words. Revisit arguments that weren’t convincing.

Collect questions and counter-arguments into a ‘questions’ basket. Answer questions from this basket in your free time.

The basket should have a hard cap, e.g. 20 questions. Picking a question at random to investigate is a nice way of staying motivated. It also helps when you have an hour or so of free time, but not necessarily set on what you want to read.

When reading, annotate connections from previous knowledge, unanswered questions and unjustified assumptions.

Work Independently of Others

Seek only suggestions when you need help, except for mere facts, which you cannot be expected to reason out.

When you make mistakes, discover the causes and remedy them so as to avoid analogous mistakes.

From the above, it is evident… close the book. Can you state what is evident?

Sometimes authors may omit necessary logical steps, so don’t spend too much time investigating how they reached a conclusion. Is there an alternate route?

Sometimes you need to put down the material and think about what you’re reading: what you think about what you’re reading.

Meta

Knowing how to study is especially important because college can only cover so much. Furthermore, a student’s career requirements may change.

Nothing is true simply because it is in a book. It must pass the test of one’s understanding. In case the understanding is beyond the student, they must perceive whether it’s mere fact, definition or opinion.

Back in 1917, you could probably assume that if it was on a book, then it had a bit of authority - not everyone could print a book. The modern-day equivalent is a peer-reviewed paper.

Be intellectually modest. Not understanding what you know and what you don’t know makes you overestimate your knowledge.

Pick the best book. New to a subject? Start with the elementary one.

Study a few subjects at once, but not too many. The mind needs change of occupation, not idleness. Weigh carefully before taking up or dropping a study. Read much but not many books.

But even if you don’t remember the specifics, the effect on your model of the world persists. As your mental model evolves, re-reading books is beneficial because the material compiles differently.

Fix your mind intensely on one thing for a time long enough to develop an idea about it. Multitasking is correlated with poor performance in tasks like distnguishing between relevant and irrelevant information, keeping information in the right contextual box and retrieving it quickly, and switching between tasks.

AKA “Deep Work”. The new old thing.

The disservice of multi-tasking is surprising to me. The study cited by could have been designed differently, e.g. whether to test people’s cognitive functions be tested while they are multitasking. That said, I doubt there is evidence for multitasking being good for critical thinking.

Apply what you’re studying. Book knowledge is of little value in itself.

There’s levels to applying what I learn. Say I learn of some concept, e.g. differential privacy. I can implement a DP-computation in Python and that’s application. But a toy application may not always hold up in the real world. The second level of application involves deploying it in practice. This may not be feasible, but the good thing about software is that you can model the real world scenario to some extent.

Mathematical knowledge is something else though. I’ve wanted to learn linear algebra for the sake of it. It makes me feel good about myself, and I find value in that.

Set times for recreative study, e.g. cards, chess, billiards.

Exercise. A healthy body is necessary for top mental performance.

Institutions are needed because left to our own, we only cherry-pick what we want to learn, which may not encompass all that we should learn. Given that institutions need accountability, they impose metrics, which break how we want to learn.

What if the underlying principle could be distilled, and the learning context tailored to the students? For example, students with a preference for biology could learn probability in the context of biological study. That way, they’re learning about what they want (biology) while also picking up necessary topics (probability).

Thinking deeply is costly, and I can’t afford to be doing it all the time.

You can’t make good decisions without good thinking, and good thinking requires time. The busiest people are often the ones who make the worst decisions, and thus spend a lot of time correcting poor decisions.

References

  1. How to Read. Robert Heaton. robertheaton.com . news.ycombinator.com . Jun 25, 2018.
  2. How You Know. Paul Graham. www.paulgraham.com . Dec 1, 2014.
  3. The Age of the Essay. Paul Graham. www.paulgraham.com . Sep 1, 2004.
  4. Your Book Review: How Children Fail. astralcodexten.substack.com . Jun 11, 2021.
  5. Some reasons to measure > Appendix: the motivation for my measurement posts. Dan Luu. danluu.com . Aug 27, 2021. Accessed Aug 28, 2021.
  6. do your research - Explore - Google Trends. trends.google.com . Accessed Oct 29, 2021.
  7. You Must Not 'Do Your Own Research' When It Comes To Science. Ethan Siegel. www.forbes.com . Jul 30, 2020. Accessed Oct 29, 2021.
  8. Indexing and Abstracting Service. en.wikipedia.org . Accessed Oct 29, 2021.
  9. List of Academic Databases and Search Engines. en.wikipedia.org . Accessed Oct 29, 2021.
  10. How to Study. Chapter 0. Introduction. Swain, George Fillmore. 1917.
  11. How to Study. Chapter 1. The Proper Mental Attitude. Swain, George Fillmore. 1917.
  12. How to Study. Chapter 2. Studying Understandingly. Swain, George Fillmore. 1917.
  13. How to Study. Chapter 3. A System of Study. Swain, George Fillmore. 1917.
  14. How to Study. Chapter 4. Proper Habits and Methods of Work. Swain, George Fillmore. 1917.
  15. How to Think: The Skill You've Never Been Taught - Farnam Street. fs.blog . Accessed Dec 29, 2021.
  16. Solitude and Leadership: If you want others to follow, learn to be alone with your thoughts. Deresiewicz, William. theamericanscholar.org . 2009. Accessed Dec 29, 2021.
  17. How to Think: The Skill You’ve Never Been Taught | Hacker News. news.ycombinator.com . Accessed Dec 29, 2021.