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A Mind for numbers How to excell at Math and Science

Dec 21, 202416 min read

🚀 The Book in 3 Sentences

🎨 Impressions

How I Discovered It

Who Should Read It?

☘️ How the Book Changed Me

How my life / behaviour / thoughts / ideas have changed as a result of reading the book.

✍️ My Top 3 Quotes

📒 Ideas

Chapter 1-8

  • Math has a tune to it. Don’t be deaf, explore the limits of permitted.

  • Don’t limit yourself to only one type of learning.

    • To classical rote learning.

  • You have to be able to follow your inner passions without closing yourself to new information and opportunities.

  • How to obtain the real solution to the problem is important.

    • Self-experimentation.
    • Self-awareness.
    • Are critical in the long rung for health and can save from wrong conclusions.

  • Studying something new or exploring opportunities or working out a solution demand of you broad views on themselves.

  • Learning new, working out a solution are in 80% of cases articulation of a question.

  • Creativity kicks in after one of the next big B’s.

    • Bed.
    • Bath.
    • Bus, this could be changed to something related to walking.

  • Solutions to any kind of problem might be considered a form of poetry.

    • Enjoy writing it.

  • Slow learning is more beneficial than fast one.

    • The same could be said about Deep Work. I have to finish compiling my notes from the book.

  • She reminds us from every lead turn that we are to encounter paradoxes of learning.

    • What are they?

  • Breathing solves the majority of worrisome problems.

    • She provided the example of falling asleep.

  • Creativity is a “Just do it!” game. We can blend into our recipe several ingredients provided.

    • Numbers. The more you do, the better you become. Expose your work to the outer world.
    • Deal with fear. What would you do if you weren’t afraid? Don’t let it stop you.
    • Redo! If you don’t like the end result, do it again.
    • Enjoy criticism. Embrace it, accept it, and use it to develop new approaches for the next version.
    • Disagree willingly. Question own assumptions and assumptions of others. Work your way down to the root cause. Almost everything creative comes from challenging the existing answer.

  • Transclude of What-is-a-creative-solution-and-how-you-can-get-there#2098c2

  • IMPORTANT NOTE, the difference between creative scientists/students/teachers and just competent one is their breadth of interest.

  • Creativity is also a leap of intuition. The most difficult problems are solved when you make a leap of faith from what you are familiar with to the scary unknown.

  • Barbara suggests that the best way to learn something is to create conceptual chunks of information.

    • It’s well-known fact, since the definition of Lifelong learning had been invented.
    • You have to glue new knowledge to something you already know. Build informational carcass.
    • Unite separate bits of information through shared meaning.

  • Understanding is not the form of knowledge. The former is just facts and sequences, the latter is ingrained, interlinked structures of various checked facts and information. In short, knowledge become knowledge when it contextualized. From data to knowledge via fake news

    • A good rule of thumb look at how students organize their notes from class and reading.howto

  • As Alan Baddeley, an expert on memory, stated, that intention to learn is helpful only if it leads to the use of good learning strategies.

  • But we must remember that intent is not a trustworthy parameter from which we can measure the ability to learn.

  • Barbara also, echoes idea (whose don’t remember), that highlighting must be done sparingly.

    • A profusely marked book can be useless, but what’s more important, it can lead the wrong way.

  • How to choose what to highlight

  • On writing with your own words. Пиши заметки своими словами

    • It could be helpful to rewrite notes from school or university during the evening after the lecture or lesson.
    • It helps restructure your ideas and find new leads to research.

  • What to do if you have limited time. You are a family person with chores to do and things to attend to, such as bringing up your children, quality time with family, shopping, etc.

  • There is a solution to this.

    • Read what you need to read, or what you’ve been given for assignment. Prime yourself for the next step.
    • Review the lecture notes. Better rewrite them when you are able to do it. My time is from 5 am to 7 am. Connect them with what you’ve already got in your knowledge base.
    • Rework example math or any other science problems from the notes. Same as rewriting notes from social science.
    • Think how what you received as homework could be done. Work thought it. Don’t overdo yourself, bite the piece you are able to swallow. Study what is absolutely necessary, as Taleb said in Antifragile Things that gain form disorder

  • Procrastination happens as a result of postponing something stressful. In short, it is anticipation that wakes up procrastination.

  • What Oakley writes is awfully similar.

    • All innovation require disruption similar to the following approach.
    • The Cue Trigger that launches procrastination or call to action. It’s reaction to distraction we need to mind.
    • The Routine. Brain responses to the cue in a manner it always has done.
      • It can be harmful (notification on the phone leads to scrolling through social media feed)
      • It can be useful, a book on the bed table may lead to picking it and reading.
    • The Reward. Bad habits give an easy dopamine jolt, good habits on the other hand are hard to get high from, need to consciously seek pleasure.
    • The Belief. Habits have power over you, because you believe in them. Change your underlying belief to change a habit.

  • Conclusion. The only place you need to exert willpower is your reaction to the cue.

Always study under mild pressure. Build tolerance to it. Your functions under great stress will improve if you constantly work under mild one. Set time limit, e.g.

  • Knowledge collapse. The process when your results don’t improve from continuous work, but decline.

    • Don’t get sad about that. It means that your brain restructures links, and you will get better. It just builds a more solid foundation.
    • Building takes place on an already occupied plot of the brain, so some demolition work in necessary.
    • Restructuring its understanding.

  • Schedule your study and quitting time is important. When to stop working and when to begin.

    • Cal Newport used 5 pm quitting time through his whole student years and as far as I believe he not has just scheduled when to stop working but also what to do during the leisure time.

  • What about you? How well do you plan your quitting time and what to do with your time outside routine activities? Думай как математик гл 1-8

Chapters 9-18

  • At certain times, an inspiration comes out of a blue.

    • How does it work? Why, in some moments we are sitting fruitlessly and in other moments we experience drive and ideas burst one after another.
    • Barbara may say it’s due to the timely procrastination, as we have discussed on online meeting.

  • She draws our attention to the fact that people who are used to working in sprees are less productive and achieve less in allocated time than those who work in leaps and bounds

    • I can make an intelligent guess that it happens because of dispersion and constant switching of attention.
      • We are coming with the best discoveries in between fields.

  • There is a healthy form of procrastination.

    • That entails learning to pause and reflect before jumping to accomplishing something.
    • Pausing give access to bigger information chunks and connects brain to bigger pictures. Prevents possibility of perspective myopia.

  • НЕ следуй своей мечте, those who did in the end, turned to be unhappy.

    • Дмитрий Эдерман good discussion point.
    • Following passions must be a next step of rational analysis of whether the career choices are truly reasonable and wise.
    • Couple passion with rationality.
      • But how to achieve this? We are not rational beings, as I am proved one and again. It is a fair point of discussion.
    • I don’t remember being passionate about anything. Interested yes, but not passionate.
      • So how have I ended up at school, where I enjoy myself?
      • Did I for real liked being in corporation, managing fools and earning top money for what I did? I willingly had put myself into a gilded cage and fooled myself into thinking that I was happy.
      • It happens left and right, just watch at the root of unhappiness.
    • We develop passion for what we are good at.
      • Wasn’t I good in corporation?
      • Am I good now, because I enjoy what I do, or again I fool myself?

  • Memory is essential for becoming creative.

    • Facts that we are memorizing are the building block for chunking, imagining unusual pairing and coming up with interesting solutions.
    • Moonwalking with Einstein - Joshua Foer is given here as an entry point into research done by Foer and detailed explanation of the fact that memory is just a set of fancy tricks.
    • Watch his talk on the TED stage.
    • Try improving spatial intelligence. People with advanced spatial orientation can imagine objects from different angles, vantage points, rotated and sliced in two.

  • On metaphors, which we use to describe something we don’t understand fully yet.

    • They are not perfect as all scientific models. They will break down eventually.

  • Why do I begin all posts with a handwritten draft, that later finds its way into the vault?

    • Because as Jason Dechart, Ph.D. at University of Pittsburgh mentioned between hand and brain a direct connection exists. When struggle with something you need to write, close on screen app, open a notebook, take a pen into hand and begin writing.
    • You’ll find your way out of a tight spot.

  • Don’t rely on conventional learning, begin tinkering.

    • Discover WHY and HOW behind the phenomenon.
    • Tinkering gives deeper understanding.
    • It evolves an intuitive knowledge, which is important for a rapid decisions.
      • Chess masters, physicians, fighter pilots, and many other experts who function in a fast-paced environment all rely on tinkering and intuition more than on formal knowledge.
      • Drawing on deeply ingrained repertoire of knowledge chunks.
    • Быстрое мышление С1

  • The more you know, the more you hold dear to what you know.

    • And it is exactly what makes you less creative.
    • Research has shown that smart people tend to find complex and I would say complicated solutions to a problem.
    • Not so clever on the other hand, cut right to the simplest solution.

Those who can easily switch attention between topic are the creative categories. Moving effortlessly through domains helps to see unusual things.

Santiago Ramon Cajal, Nobel prize winner in Neuroscience

Hard work creates talent. In some cases where it’s impossible it substitutes it.

  • A synthesized knowledge is an abstraction, or gist idea in other words, a neural pattern which could be easily applied across domains.

    • Good chunking resonated not only with problems at hand, but also transfers ideas to other subjects and areas of our lives.
    • The higher the level of abstraction, the easier you transfer ideas from one area to another.

  • This is the reason physicists and engineers have been thought after in the world of finance.

    • Emanual Derman, a theoretical physicist, moved to banking and created an interest-rate model and eventually took over the firm’s Quantitative risk strategies department.
    • Ford also used to hire employees with non-prior experience in building cars.
      • Though, he explained it differently.
      • It is easier to teach somebody from the ground that reteach anybody with personal expertise.
      • Ropes are shown best to those who has never climbed before.

  • How do we set our mind to receive new knowledge? Priming ourselves? Open book approach.

  • Feynman pointed to his friend once that thinking is nothing more than talking to yourself inside.

    • Or in KB, Lumahn used to talk inside his Zettelkasten.
    • The complexity of the base could be built from the simplicity of ideas, the only thing you must absolutely follow is necessity to connect and reconnect. Tiny shifts in one place make ripples in the other, as with this idea, which affects the philosophy of note-taking. Connectivity issue.
    • Ultimately, it alters everything else.
    • An observant gardener (person who tends his base), can recognize the depth of a piece of information, it can have many possible meanings.

  • On explanation in Feynman style.

    • While trying to explain a complex topic, imagine that you are talking to a child, 5 y.o.
    • Use the simplest possible words and principles.
    • On Reddit the whole section exists, devoted to such explanations.

  • A disciplined and specified approach to learning, the one used in all academia, is less effective than a hands-on approach.

    • Tinkering opens a window of possibilities for flexible and creative learning.
    • ^b5d025

  • Teacher’s holy grail. Transferring of skill and knowledge from the artificial environment of a classroom to the real problems.

    • Communication with languages.
    • Applying laws of physics, e.g. working with electricity.
    • Calculating the diameter of the car wheel.

  • Transferring knowledge from imaginary domain to a real life situation, make even the most complex problem look easy and solvable.

    • There is another benefit, it makes learning easier.
      • If you transfer, you will be able to do more and more through the term.
      • This effect is reached with the ability to bring all together. Classroom knowledge and various life situations.

  • Approaching term materials should be done not with “pass the test” attitude, but with “Truly understand”

    • The goal of learning gives a unique path to mastery.
    • Teacher and handed material is predetermined and fabricated for specific group of learners, often it consists of absolutely minimum set of chapters. Enough to pass the test.
    • This is a partial version, maximally shortened. It doesn’t provide the full, three-dimensional reality of the subject, which could be linked to other fascinating subjects of personal choosing.
    • Teacher centeredness fosters unavoidably helplessness about learning among students, which later transfers to older life. At universities, in relationships.
      • Test evaluation have the same results.
      • ^90a9d0

  • On bad traits and possibility to use them for your benefit.

    • Pick a seemingly bad trait. Consider it from all angles, see if any positive effects exist, look carefully, usually there is.
    • Look from the vantage point that covers the creativity aspect touched by this trait. How it makes you more creative or more energized.
    • Can you diminish its negative effects and enhance positive?

  • Healthy dissent and disagreement are valuable for development of good idea and throwing away bad.

    • Debate is one of the knowledge generation approach.
    • It’s highly valuable to have someone who can give open and honest feedback without toxicity. ^1046c5
      • This kind of safe for new thinking environment, hard to come with. It requires careful tending from influencers.
      • Bohr, a genius who intuited quantum theory, was so respected that nobody could say anything except praise to any of his, even cockamamie ideas.
      • And this was unhelpful. So he had found himself a student who could argue with him and scrutinize ideas before presenting them to the public.
        • And this one of the reason the world had Feynman, legendary student of Bohr.
        • Actually not, according to Feynman’s, this account, had taken place on Los Alamos, and Bohr with his son, came to the laboratory anonymously.
        • Bohr asked for Feynman on purpose, because he used to be the only one who wasn’t afraid to stand up for his ideas.
        • Feynman didn’t care about who was standing in front of him, his mind worked in a state of deep concentration, when the topic of physics had been touched. This super ability helped him outperform many before him. This and another one Prankster Feynman
        • Здравомыслие и авторитет
        • Deep Work
      • Scrutinizing should be done to all things that we consider doing, that have high exposure to risk.
      • Criticism is not about a person, it is aimed at what you are trying to understand. Questions are born out of curiousity and the need to know what and how.

  • The Strength of Weak Ties by Mark Granovetter read and analyze.

    • Granovetter Weak Ties AJS.pdf
    • The article predicts how the number of just acquaintances you have and not the number of friends predicts your access to the latest ideas as well as access to the job market.

Test preparation checklist, copied verbatim

Answer “Yes” only if you usually did the things described (as opposed to occasionally or never). Homework Yes No 1. Did you make a serious effort to understand the text? (Just hunting for relevant worked-out examples doesn’t count.) Yes No 2. Did you work with classmates on homework problems, or at least check your solutions with others? Yes No 3. Did you attempt to outline every homework problem solution before working with classmates? Test Preparation The more “Yes” responses you recorded, the better your preparation for the test. If you recorded two or more “No” responses, think seriously about making some changes in how you prepare for the next test. Yes No 4. Did you participate actively in homework group discussions (contributing ideas, asking questions)? Yes No 5. Did you consult with the instructor or teaching assistants when you were having trouble with something? Yes No 6. Did you understand ALL of your homework problem solutions when they were handed in? Yes No 7. Did you ask in class for explanations of homework problem solutions that weren’t clear to you? Yes No 8. If you had a study guide, did you carefully go through it before the test and convince yourself that you could do everything on it? Yes No 9. Did you attempt to outline lots of problem solutions quickly, without spending time on the algebra and calculations? Yes No 10. Did you go over the study guide and problems with classmates and quiz one another? Yes No 11. If there was a review session before the test, did you attend it and ask questions about anything you weren’t sure about? Yes No 12. Did you get a reasonable night’s sleep before the test? (If your answer is no, your answers to 1–11 may not matter.) Yes No TOTAL Думай как математик гл 9-18

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