How to Read a Book: The Classic Guide to Intelligent Reading

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Activity of Reading

We don’t have to know everything about a topic to understand it well. Knowing too much is as bad as knowing too little. The key is to understand key ideas/milestones really well.

Media and other channels are contributing to having more information without any level of thinking or understanding.

Reading in its nature is an activity -> Passive consumption of information IS NOT reading. You need to actively think and analyze new information and connect it with what you know. The level of activity and participation in reading any new information determines how well you are in understanding it.

• Especially with hard books, it requires hard mental operations and it is tough
• The reward is that the mind moves from knowing less to knowing more through understanding

Reader (or listener) is the receiver of information. What we do with this information and how we act on it would determine our level of understanding.

A book that we fully understand right away (doesn’t challenge us) does not add anything to our understanding of the world since no brain activity is involved in digesting the material and making sense of it. It is just a kind of recall what we know, but probably in different words or forms. On the contrary, books that challenge our understanding and hard to digest -> overworking the mind and create new hooks and mental models and move us from less understanding to more understanding. It is possible for this to happen in phases where multiple passes are required to get the most out of it especially for classical tough ones and that stood the test of time.

Therefore, increasing our store of facts/information (not useful) IS NOT the same as increasing our understanding. There is a big difference between reading to increase information we know about a topic (adding more facts to what we already know) and reading to improve our understanding (create mental models, connect it to what we know, internalize it, understand it through derivation and connection from different angles)

• We start from writer being superior than reader on the topic -> Converge to equality as reader’s understanding improves
• We need to know when, why, and how it applies and our push back (critique; don’t ever hold the author’s frame of reference and approach any material with your own frame of reference). To understand something means to know:
  • Its connections with other facts
  • Its contrasts
  • Conditions for it to hold

There is learning by instruction (explicit) and learning by discovery/research/reflection (not explicit).

The art of reading:

The process whereby a mind, with nothing to operate on but the symbols of the readable matter, and with no help from outside, elevate itself by the power of its own (mental) operations. The mind passes from understanding less to understanding more.

In conclusion, reading a book for understanding is like learning through discovery because we are left alone with the book to explore and interrogate by reading between the lines, using our imagination/reflection to connect it with facts we already know about the topic AND construct its logic/analogy/contradiction.

Levels of Reading

Elementary reading: Answering what does the sentence say (surface level meaning) without any much thinking

Inspectional reading: Reading a book in a very short period of time to get its structure, type, parts to obtain a surface level understanding -> Get the most out of the book in set time

Analytical reading: Reading for deep understanding where we ask very deep and organized questions to get to the bottom of what it was set to deliver -> ultimately the books becomes our own

Syntopical reading: Read many books about a subject to construct an analysis and connection about it that doesn’t exist in one book. It is the hardest and requires the most effort

Lower levels of reading are included in the higher ones. For example, syntopical reading includes the lower three levels: elementary, inspectional, and analytical.

We must always do inspectional reading first before any analytical reading regardless of our goal. This would help us prime the brain of what to expect and be ready for new information

We must determine the goal of the reading before we start: Information, Entertainment, Understanding.

Effectiveness of reading is determined by (the more the better):

• Amount of effort
• Skill

Some books are to be tasted (majority)

Others to be swallowed (minority)

Very few to be chewed and digested

Inspectional Reading

It is important to not stop at words/phrases you don’t understand and keep going by trying to get the meaning from the context.

Systematic Skimming

It is extremely helpful because it helps us figure out what the book is all about and what it has to offer. Most books don’t deserve analytical reading and inspectional reading is enough to get its main idea/contribution which would save us a lot of time by not reading it cover-to-cover. It should NOT take more than 1 hour. Approach this stage from a detective lens looking for clues.

Steps for systematic skimming:

• Read the title/subtitle/preface
• Read the table of content carefully. If the book has a detailed table of content, read it as well. We can get the structure of the books from TOC
• Read the index. It tells us the range of topics covered and books/authors referred by the author. It would be helpful to read some paragraphs in the book where important terms were mentioned
• Read the blurb. Authors sometimes summarize the main point(s) in the blurb. Good indicator if the book is important to use or has any useful contribution the deserves deeper dive
• Read summaries of critical chapters of the book
• Turn the pages and read randomly some paragraphs/pages
• Read the epilogue of main parts as authors typically summarize their contribution

Superficial Reading

Read the book through without stopping to understand or lookup anything. Very useful for hard and difficult books such as The Wealth of Nations. We can get the big picture that will help us during our second pass for analytical reading.

Classic and difficult books such as The Wealth of Nations is a good example of a difficult books that can not be approached by trying to understand everything on every page because you will feel frustrated, miss the big picture, and not get the main points. We first must pass through it keeping the big picture in mind.

For difficult technical books such as Information Theory, it is not practical to read the whole book for the first pass. Instead:

• Do inspectional reading of the whole book
• Do superficial reading for part by part. If the chapter is complete and form its argument fully, this step is optional
• Do inspectional reading of the chapter
• Do superficial reading for chapter by chapter

Vary speed of reading according to the complexity of the information. Even within the same book, some chapters/paragraphs must be read at different speeds. Every book should be read no more slowly than it deserves, and no more quickly than you can read it with satisfaction and comprehension.

Brain is faster than eyes in comprehending new information. Use fingers to avoid such limitations, increase focus, and improve speed

Demanding Reader

Important and hard books make a big difference in the rate of improving your understanding and increasing the facts we know about their domain. They help tremendously in creating mental models and thinking from first principles. They stretch our mind and we need to raise to their level of mastery to be able to ask the right questions and engage with the reading.

The goal of active reading is answering the following questions:

1. What is the books about?
   • Main theme/ideas and their subtopics in their order
2. Main ideas/arguments/assertions?
   • What is being said in details and how?
3. Is the book all true? Which parts?
   • You should make up your mind and NOT just adopt author’s msg
4. Significance of information presented
   • Question the significance of information and whether it is important

Inspectional reading helps us answer the first two questions while analytical reading helps us answer the last two questions.

Reading between the lines is very crucial in getting the most out of the material. Questioning the author after you understand the material is very useful regardless if we agree/disagree.

Also, writing down the questions and answers would improve understanding and alertness.

You should always be critical and question the information you read after understanding it.

Marking books:

• Underline important points
• Vertical lines to emphasize a statement or paragraph too long to underline
• Fold or have a mark on top of the page for the most important thing(s) in the book. Use it sparsely
• Numbers in the margin for the points the author is using to build his argument
• Numbers of other pages the cover the same point or contradict it
• Write in the margin for Q/A and conclusion for important points in your own words
• Use first page for each chapter to outline main point and its structure and your understanding
• Use first pages in the book to outline main points and structure of the book
• Use last few pages as index for the main points in the book in their order

Analytical Reading

What is presented here as rules for analytical reading is the ideal reading for books well-worth the effort. Of course NOT all books deserve to be read this way -> Use my judgement to determine the degree of the effort needed and how close to get to the ideal based on the book’s value. Most books are NOT worth more than inspection reading.

Stage I: Rules for finding out what is the book about

RULE 1: You must classify the book we are reading as early as possible and preferably before reading it (inspectional reading). Practical vs Theoritical (history, science, philosophy).

RULE 2: State the structure/unity of the book in one or few sentences. We typically can do this by reading the title/subtitle, preface, table of contents, and the introduction. In other words, we need to get the high level summary/main point of the book (conclusion)

RULE 3: State the major parts the form the structure and how they are interrelated and contribute to the overall structure. We can outline the parts, the parts of the parts, etc. but we typically approximate and stick to the first level unless there is a need to dig deeper. Not all parts are equal.

RULE 4: Find out what the author’s problems are. We must be able to determine the main points and main questions the authors are trying to investigate.

Stage II: Rules for interpreting the book’s contents

We should always ask questions about our readings and look for ways to adopt/use what we learned; otherwise, we will forget it. The best test to test our understand of the author’s point(s) is to explain it in my own words NOT repeating what he said. Otherwise, we didn’t get his message.

RULE 5: Find out the important words and what the author means from using such words. We can depend on our daily use of the language to understand the majority of the words in the text. However, there are few words that require special attention that would typically have subtle meanings or the author has specific meaning that he wants to come across to the reader mind.

RULE 6: Find out the most important sentences and figure out their propositions (proposition is just a claim that can be true or false). Most authors make it clear about the importance of certain sentences and words through their use of style, marks, and order. We should always slow down to contemplate/analyze/think about sentences that puzzle us and question our understanding/beliefs about certain things. NOT ALL sentences are created equally. We should be able to relate propositions to our previous experience where it holds true or even imagining stuff.

RULE 7: Construct the basic arguments from connecting the most important sentences. Arguments can either start with conclusion followed by evidence(s) or the other way around. It is built from sequence of claims/propositions. The argument can be valid/invalid, strong/weak, sound/unsound.

RULE 8: Find out what the author’s solutions are.

Stage III: Rules for criticizing a book as a communication of knowledge

RULE 9: You must always understand before judging any work or written material. We must always critique the book and provide our own judgement after understanding the author’s main point(s) and arguments. Otherwise, you are just a consumer and have no opinion. Critiquing doesn’t mean disagreeing. You can agree with the author, but you have to use your own logic and words to express why you agree with the author.

RULE 10: When you disagree, do so reasonably.

Author soundedness:

• Uninformed: Lack knowledge that was revealed after his work
• Misinformed: Argue with things that are false
• Illogical: Reasoning over some facts don’t hold or don’t lead to the conclusion arrived by the author

Therefore, in the case of disagreeing with the author(s), we need to show where the author is:

• Uninformed
• And/Or misinformed
• And/Or illogical
• And/Or his analysis is incomplete if he didn’t solve all the problems he stated

Syntopical Reading

Syntopical reading is what I use when I want to understand a subject or problem across multiple books, rather than understand one book on its own. In analytical reading, the author determines the questions, terminology, and structure. In syntopical reading, my inquiry determines them. The goal is therefore not to produce a sequence of summaries, I am trying to construct an understanding of the subject that may not be fully present in any individual book. I must identify the common questions, translate incompatible vocabularies, locate genuine disagreements, and organize the discussion myself.

Begin with a tentative question and bibliography, then inspect all the candidate books before reading any one of them deeply. Inspection helps me remove irrelevant works while simultaneously refining my conception of the subject. As my conception improves, the bibliography changes too. This prevents the first book I read from controlling how I understand the whole problem.

Once I have identified the relevant works, syntopical reading proceeds through five main steps:

1. Find the relevant passages. I do not need to read every selected book completely. I locate the parts that bear directly on my inquiry, even when my question was not the author’s central question.
2. Bring the authors to common terms. Different authors may use the same word differently or different words for the same idea. I must construct a neutral vocabulary that can represent all of their positions without allowing one author’s terminology to dominate.
3. Establish common questions. I formulate questions that the authors can be interpreted as answering. Some answer explicitly, some implicitly, and some may have no determinate answer. I must not force a position onto an author merely to complete my framework.
4. Define the issues. An issue exists when authors give incompatible answers to substantially the same question. Before declaring disagreement, I must check whether they actually understand the question in the same way. Many apparent disagreements are really differences in definitions, assumptions, or problem formulations.
5. Analyze and order the discussion. I organize the issues by their relationships and dependencies, showing the major positions, supporting arguments, points of conflict, and unresolved questions. The final product should reveal the structure of the debate more clearly than any individual author does.

The deepest takeaway is that the truth about a difficult subject may not reside entirely in one author’s answer. It may emerge from the ordered conflict among several answers—from understanding exactly where they agree, where they diverge, why they diverge, and what remains unresolved.

Approaches to Different Kinds of Reading Matter

The four questions do not change from one kind of book to the next, but the method for answering them does:

The four questions	Practical	Science and math	Philosophy	History	Fiction and poetry
What is it about?	What end does the author want?	What problem was he solving?	What exact question is answered?	What events, told to what end?	What world does it create?
What is being said?	The principles, rules, and means	Assumptions versus established results	The controlling principles and argument	The account, and where it selects	The characters and how they move
Is it true?	Are the ends right and the means effective?	Do observation and experiment support it?	Is it consistent and true to experience?	Is it plausible and fairly told?	Wrong question: does it move you?
What of it?	What must I now do?	How does it extend my reasoning?	What is my reasoned judgment?	How do things happen?	Let it enlarge what you can feel

How to Read Practical Books

A practical book is ultimately trying to move me from understanding to action. To read it properly, identify the end the author wants, the means recommended for reaching it, judge both, and recognize that genuine agreement should affect what I do.

A practical book cannot itself solve a practical problem. It can provide principles and rules, but the problem is solved only when the reader acts in a particular real-world situation. A book about reading cannot make you a better reader. A book about leadership cannot make you a better leader. It can tell you what to do and why, but you must perform the activity.

On the other hand, theoretical book solves its own problem by conveying the idea/knowledge they are set to solve.

Because action always occurs under particular circumstances, no general book can tell you exactly what to do in every concrete case. The reader must add:

• knowledge of the particular situation
• judgment about which rule applies
• adaptation of the rule to the circumstances

This is a major point:

Practical wisdom cannot be completely encoded in general rules.

Desired end (objective)
     ↓
Principles about reality or conduct
     ↓
Rules / recommended means
     ↓
Reader’s practical judgment
     ↓
Action in a particular situation

Kinds of practical books:

• Books primarily containing rules. Their central propositions are recommendations: Do (X) in order to achieve (Y) such as cookbooks; driving manuals; instructional guides; How to Read a Book itself. The arguments try to show that the rules are effective, either through underlying principles or through concrete examples.
• Books primarily containing principles that generate rules such as books in: politics; economics; ethics; education. These can look theoretical because they contain descriptive propositions and arguments about human beings and society. But they are practical because the principles ultimately imply how people should act. Here the reader must read between the lines:
  • What rules of conduct follow from these principles?
  • What actions would the author recommend, even if they are not stated explicitly?

The two dominant questions for any practical book are:

1. What is the author trying to accomplish?
2. What means does the author propose for accomplishing it?

This is especially important for books about principles, because their desired end and recommended actions may be implicit.

A practical recommendation is sound only when:

1. The proposed means actually work.
2. They lead toward a worthy or rightly desired end.

A method could be highly effective yet still be rejected because you reject its purpose. Conversely, an end may be desirable while the proposed method is ineffective, harmful, or based on a false causal theory. Therefore, evaluate separately:

• Ends: Is this worth pursuing?
• Means: Will this actually achieve it?
• Trade-offs: What else would these means produce or destroy?

We have no practical interest in even excellent means for reaching an end we reject or do not care about. That does not make the book intellectually worthless. You may still study it historically, theoretically, or critically. But its recommendations no longer give you a reason to act. For example, you can study The Communist Manifesto to understand its account of class conflict and its historical influence while rejecting the social end it seeks or the means it recommends.

For the truth of theoretical books, we must first recognize if there is any gap/discrepancy between me and the author’s principles and assumptions. Then we must judge the reasoning/arguments and the conclusion as well as how it works out in reality and if it gets us what is expected based on experiments. Therefore, we may conditionally agree on the truthfulness of the theory/idea based on assumptions or on its practicality.

A practical author is not merely trying to inform you. The author is trying to move:

• your intellect;
• your emotions;
• and ultimately your will.

Therefore, practical books inevitably contain rhetoric, persuasion, or propaganda. That is not automatically dishonest; action usually requires motivation, not abstract reasoning alone. The danger is unrecognized persuasion. You must notice:

• emotionally loaded language;
• selective examples;
• appeals to fear, hope, identity, or moral urgency;
• where the author shifts from establishing truth to motivating action.

You should have enough “sales resistance” to avoid being manipulated, but not so much that you become incapable of being rationally persuaded.

The author’s character, historical circumstances, and personal concerns can also matter more in practical books than in mathematics or pure theory because these factors may shape the ends and policies being promoted.

Some ends apply universally, while others apply only to particular people. Before concluding that action is required, determine whether you belong to the relevant group.

General question	Practical version
What is the book about?	What does the author want accomplished?
What exactly is being said?	What principles, rules, and means are proposed?
Is it true?	Are the ends right and the means effective?
What of it?	What should I now do?

A theoretical book culminates in a conclusion to believe. A practical book culminates in an action to perform.

For theoretical book, if it is significant -> changes my worldview and mental models; otherwise, no learning happened.

For practical book, if we accept the goal of the book (objective of the author) and the effectiveness of the approaches and methods outlined (rules) -> I am obligated to practice what is recommended and do all the work to get all the benefits. More effort we put in practicing -> more benefits.

• How to read a book (this book) is a practical book -> I need to do the work and keep practicing to reap all the benefits since reading is a skill and like any other skill, we can get better at it through practice.

How to Read Science and Mathematics

State as clearly as possible the problem the scientist or mathematician was trying to solve.

The lay reader does not read Newton, Galileo, Darwin, or Harvey mainly to acquire up-to-date professional knowledge. The purpose is to understand:

• the problem confronting the author
• the historical background of that problem
• the proposed solution
• and the development of scientific thought

Following how facts, assumptions, principles, and proofs interact allows you to observe human reason operating with unusual success.

So the governing question is not “Have I mastered this entire scientific discipline?”. It is “What problem was the author confronting, and how did the author attempt to solve it?”

A scientific book reports findings or conclusions reached through: controlled experiments or observations of nature. Its fundamental task is:

1. To describe phenomena as accurately as possible.
2. To trace relationships among different phenomena.

Unlike history, science generally seeks propositions that transcend a particular time and place. Scientists try to state how things generally are or behave.

Scientific authors begin with presuppositions. The presence of assumptions does not by itself make a work unscientific or subjective. You must distinguish: What the author assumes from What the author establishes through argument or evidence. Authors typically are upfront in terms of stating what they are assuming or taking for granted.

Scientific authors commonly identify their major concepts with:

• uncommon words;
• technical terminology;
• explicit definitions.

This often makes the book’s key terms relatively easy to identify. Once you understand them, the central propositions become easier to grasp.

Science is primarily inductive (compared to Math that is primarily deductive: General theory + conditions -> specific prediction). Its characteristic argument moves from observable evidence toward a general proposition: Experiment or observation -> General scientific conclusion. Science also uses deduction, in which conclusions are derived from propositions already established. But induction from observed evidence is especially characteristic of scientific reasoning. The difficulty is that you cannot always understand the argument merely by reading the reported conclusion. You may need access to the experience upon which the argument depends. That might require:

• observing an experimental demonstration;
• inspecting equipment;
• examining specimens or models;
• or reproducing an experiment yourself.

Many readers fear mathematics partly because they have not understood that Mathematics is a language. It has its own:

• vocabulary;
• grammar;
• syntax;
• symbols;
• and relationships among symbols.

Learning to read mathematics therefore begins partly as an elementary reading problem: you must learn to recognize the symbols and understand how they relate before you can interpret the higher-level propositions and arguments. Mathematical language can be unusually clear because properly used mathematical terms do not carry the uncontrolled emotional connotations found in ordinary language.

Sometimes authors assume something is true and build on this assumption without trying to prove it even exists.

If the hypothesis is true,
and the definitions, postulates, and previous propositions hold,
then the conclusion follows.

When reading a scientific book that contains mathematics, you may skip some detailed mathematics because the goal is to understand the scientific work’s principal argument(s) without allowing mathematical details to prevent me from seeing the big picture, especially on the first reading. For example, in Newton’s Principia, Adler says it is unnecessary to read every construction and theorem in full detail initially. You can concentrate on:

• the statements of the major propositions;
• important lemmas and corollaries;
• explanatory discussions;
• summaries of discoveries;
• and the consequences the author draws.

The purpose is to understand the scientific work’s principal argument without allowing every mathematical detail to prevent you from seeing the whole.

Scientific popularizations generally contain:

• fewer detailed descriptions of experiments;
• less mathematics.

They commonly report experimental results rather than presenting the complete experimental procedure and mathematical foundation. This makes them more accessible than original scientific contributions. However, that accessibility has a cost: You depend upon a reporter or popularizer who has selected and filtered the scientific information. When the reporter is competent, this may work well. When the reporter is poor, the reader has little access to the original basis needed to correct the account.

Popular science is not effortless merely because it contains little mathematics. Substantial popular-science books may demand closer reading because their theoretical conclusions can carry important consequences. We still have to read them actively and follow the same analytical reading rules.

For scientific classics:
Identify the problem
→ distinguish assumptions from established results
→ follow observations, experiments, and arguments
→ handle the mathematics according to your purpose
→ understand the proposed solution

For mathematical works:
Learn the language
→ follow definitions and postulates
→ work through propositions sequentially
→ verify the conditional reasoning with pencil and paper

I read the scientific classics of other fields to understand how important problems were recognized, reformulated, investigated, and solved; to expand my repertoire of scientific reasoning and conceptual frameworks; and only then to ask whether those patterns can illuminate problems in learning and intelligent systems. Not merely to collect their conclusions.

• Follow the experiments when necessary
• Treat mathematics as a language
• Work through mathematical books actively and sequentially
• Skip technical mathematics only when your purpose is to grasp the larger scientific argument rather than master the mathematics itself

How to Read Philosophy

Key point is learning to recognize that not every important question is an empirical question. Philosophy deals with fundamental questions that may be simple to state such as: What is knowledge? What is causation? What is a good explanation? What ought we to pursue? but cannot be resolved merely by collecting more observations or running another experiment. These are primarily first-order questions: questions directly about what exists, what happens, what can be known, and what ought to be done. Second-order questions are about the language and thought through which we discuss those matters.

Scientific work can reveal patterns, test predictions, and constrain possible explanations. It cannot, by experiment alone, determine the meaning of every concept it uses, establish the ultimate standards by which an explanation should be judged, or decide which ends ought to be pursued.

Reading philosophy is not mainly extracting results. We are reconstructing a position. First determine the exact question the philosopher is trying to answer. Then discover the controlling principles from which the answer develops. These principles may be explicit, scattered across the work, inherited from another book, or left largely unstated. They are especially important because they determine what the philosopher regards as possible, explanatory, true, good, or self-evident.

Once those principles are visible, the reader must examine whether the philosopher’s conclusions follow consistently from them. A philosophical work should therefore be read as an interconnected system rather than as a collection of quotable propositions. The scientifically useful habit is:

Particular care must be given to terminology. Philosophers often use familiar words in precise or unusual senses. Recognizing the ordinary meaning of a word does not mean that you have understood the philosopher’s term. Just as a scientist must learn the technical meaning of information, energy, or fitness, a reader of philosophy must determine exactly what an author means by substance, form, reason, freedom, good, or knowledge

When reading philosophy as a scientist, do not look for experimental findings or detachable conclusions. Reconstruct the fundamental question, clarify the author’s technical concepts, identify the controlling principles, follow the complete argument, test its consistency and its appeal to common experience, compare it with rival answers, and then form your own reasoned judgment.

Reading and Growth Mindset

Active reading (the more active the better) through asking questions (different kinds of books require answering questions differently BUT they share the same set of questions) and going through inspectional, analytical, and syntopical forms improve and increase our understanding. Books should ALWAYS be harder than my reach to benefit from them and stretch my mind to increase my understanding. This will also improve my reading skills and make me wiser by teaching me about life, the world, and myself.

• Hard books does NOT mean bad books (those are not worthy reading them). We mean difficulty in material and connections to what we know
• Books about some aspects of life and the world have no clear answer and nobody will get to the bottom of it, but such books will teach us how to think better about those aspects because authors spent much longer time than us and have better or different framework to visualize and think about them.

Regardless of how good a reader you are, there will always be books that are beyond your reach and require effort to understand them.

Part of becoming a good reader is NOT only about how to read a book, but also the ability to pick which books to read that would improve my reading skill and stretch my brain. It is fine to read for fun sometimes or to know some facts based on some tasks, but this should NOT be the norm.

Reading for more information would lead to increase information about facts we already know. It doesn’t improve our understanding because improving our understanding requires a change in our brain by adding more facts and connections to concepts/topics. Note that ONLY adding more facts won’t change our brain AT ALL. It would only increase the storage of those facts.

Less than \(1\%\) of books are worthy the analytical reading that would improve my reading skills and increase my understanding. The rest are just for fun/information that can be skimmed easily to get the gest of them.

Less than \(0.1%\) (few thousands) of books are worthy analytical reading due to the unique and valuable insights they have on the subject. I can get all they have to offer in one analytical reading (if I am skilled reader) and may never get back to them other than checking on certain insights. The notes I take on the margin of such books are valuable and must be synthesized and connected to my mental models.

• The way to know that it is not worthy to go back to it is that after it stretched your brain, there is not much left and you are not gaining anything afterwords. When you revisit the book, you find it has less things than what you remembered. The book has not changed, but I have grown my reading skills and understanding that I am over it and it is not offering me anything new.

Less than \(100\) books are true classics. Any time you come back to it you find something completely new even though you did full effortful analytical reading pass before. You always feel that you missed something. All the previous insights still there but new ones resurface that you completely haven’t seen before. As you grow your reading skills and understanding from elsewhere, you feel it grows with you as now you see new things or connect things that were not obvious and easy to digest before.

• Research and figure out what are those books for me. Most likely they are much less than \(100\) since it is tailored to my interests and research domain.
• Useful trick is imagining that I will be locked on an island and would only be allowed to take 10 books with me

There is NO limit for the growth and development of the mind.

Mind can and will deteriorate if not challenged and stretched regularly. Mental muscles can deteriorate at a scary rate that would even lead to death when the person doesn’t have anything occupying their brain, which leads to depression and heart issues. Active reading would prevent this and keep our minds growing and alive.

Always use your own words when summarizing, explaining, or even stating main points. DO NOT USE AUTHOR’S WORDS.

Appendices

Appendix A: Mathematics as a Language

Mathematical notation communicates meaning through:

Symbols → Expressions → Propositions → Arguments / Proofs
Letters → Words       → Sentences    → Arguments

1. Vocabulary: What does each symbol mean?

Identify every object and operator. \(x\in{R}^d\)

Read:

x is a d-dimensional real vector.

• x: an object
• \({R}^d\): set of d-dimensional real vectors
• \(\in\): “is an element of”

A symbol’s meaning depends on context: \(L\) might mean loss, likelihood, or an operator.

2. Grammar: Are the operations valid for these objects?

Always identify the type and shape of each object. If \(A\in{R}^{m\times n}, \qquad x\in{R}^{n}\) then \(Ax\in{R}^{m}\) is valid, while \(xA\) is generally not.

Ask:

What kind of object is this, and is this operation defined for it?

Many mathematical mistakes are really type or shape errors.

3. Syntax: How should the expression be parsed?

Determine grouping, scope, precedence, and order.

\[-x^2=-(x^2)\neq(-x)^2\] \[\sum_i x_i^2 \neq \left(\sum_i x_i\right)^2\] \[(AB)^\top=B^\top A^\top\]

Parentheses, operator scope, and symbol order are part of the meaning.

4. Relations: What is being asserted?

Relations turn expressions into mathematical sentences.

Symbol	Read as
\(=\)	equals
\(\in\)	is an element of
\(\subseteq\)	is a subset of
\(\Rightarrow\)	implies
\(\iff\)	is equivalent to
\(\perp\)	is orthogonal to
\(\approx\)	is approximately equal to

For example: \(\nabla f(x)=0\) means The gradient of (f) at (x) is zero. It does not by itself mean that \(x\) is a minimum.

5. Quantifiers: What is the scope of the claim?

Order matters: \(\forall x,\exists y:y>x\) means every \(x\) has some larger \(y\).

But: \(\exists y,\forall x:y>x\) means one \(y\) is larger than every \(x\).

The first is true over the real numbers; the second is false.

6. Semantics: What does the whole expression mean?

Translate the notation into meaningful prose. \(P(Y|X)\) means the probability of \(Y\) after observing \(X\). It is different from \(P(X|Y)\).

Reading checklist

For every mathematical expression, ask:

1. Vocabulary: What does each symbol mean?
2. Types: What kind and shape of object is each one?
3. Grammar: Are these operations defined for those objects?
4. Syntax: How is the expression grouped and ordered?
5. Relation: What claim is being made?
6. Semantics: Can I state the whole expression in words?
7. Role: Why is this expression here—definition, assumption, result, or proof step?

Core habit: Do not merely look at an equation. Read it as a sentence about typed mathematical objects, then determine what role that sentence plays in the argument.