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Take a 10-30 minutes walk every day. Sit in silence for at least 10 minutes each day. Sleep for 7 hours. Live with the 3 E’s — Energy, Enthusiasm, and Empathy. Play more games. Read more books than you did the previous year. Spend time with people over the age of 70 & under the age of 6. Dream more while you are awake. Eat more foods that grow on trees and plants and eat less food that is manufactured in plants. Drink plenty of water. Smile and laugh more. Don’t waste your precious energy or time on gossip. Forget issues of the past. They’ll just ruin your present happiness. Don’t have negative thoughts or things you cannot control. Instead invest your energy in the positive present moment. Realize that life is a school and you are here to learn. Problems are simply part of the curriculum that appear and fade away like algebra class but the lessons you learn will last a lifetime. Eat breakfast like a king, lunch like a prince and dinner like a beggar. Life is too short to waste time hating anyone, so don’t even try. Don’t take yourself so seriously. You don’t have to win every argument. Just agree to disagree. Make peace with your past so it won’t spoil the present. Don’t compare your life to others’. You have no idea what their journey is all about. Don’t compare your partner with others either. What other people think of you is none of your business. No one is in charge of your happiness except you. However good or bad a situation is, it will change. Your job won’t take care of you when you are sick. Your friends will. Stay in touch. Get rid of anything that isn’t useful, beautiful or joyful. Envy is a waste of time. You already have all you need. No matter how you feel, get up, dress up and show up. Call your family often. Your inner most is always happy. So be happy. Each day give something good to others.

9Good Question>>>This question is good bcz there is a lot of peoples who have suffer from this problem. In bank exams the cut off of English is quite low, yet almost 60% people failed here in English section only, why?, this is a big problem but luckily I have a solution for this problem which break hurdles of your path easily with minimal efforts. So, first take a look of the whole syllabus of English which is asked in banks exams>>>RC, Spot the Error, Fillers, Cloze test, Sentence Arrangement.This is short look of the pattern of asking questions in Bank’s signNows. I wood tell you here what should you do to get through this. Here are some important things which you should do for boosting your numbers in English section especially.Problems :1.Grammar : You read this or not, it doesn’t matter in bank exams. Anyone who has a little bit of understanding of english only as a language, can do its questions when it comes in D-day, but the only point is he/she had a general Idea about solving question which varied from person to person. If you’re the aspirant of SSC then you have to know about grammar little bit more but if you’re a aspirant of banking exams then it doesn’t matter more. Anyway, if someone amongst you want to read Grammar then don’t use too many books for Grammar, if you want you can use this book SHINE BOOK but even if you not take this then also its not harm you bcz this book contained some rarest SSC level grammar rules which can also helpful for you in your understanding of the subject a bit more.2. Word Power : It is the key for your success, How?, I would tell you here. Fillers, Cloze test will create almost 99% questions based on word power bcz if you know the importance of any word as well as their meanings then you can use to it in fillers and Cloze test. Honestly 100% questions you can do it only through this even if 40 % question RC will be based on word power. How you built it, I would tell you later.3. 60% RC : It will covered from your understanding. Suppose anyone who had a sufficient knowledge of English can read a passage and knew easily about central Idea which is only 10% of RC but what about the other 50%. Therefore you have to understand this from your own. So, How would you acheive it, I would tell you later.4. ABCDE : You’ve a question in front of you which carry 5 Questions and the funny part is if you solved it only once then you can score 5 marks easily may be in 2 minutes but there are two main problems which hardly thinks by anyone, which is Understanding and Reading speed. If you reading with speed, you hardly understand the topic and vice versa.Solution :Read a English newssignNow daily. This is the panacea for you, How?, I would tell you here and all we talked about the role of NewssignNow in many areas in English sections.If you read a newssignNow your reading speed will grow. After reading it regularly your understanding power will grow. If you found some words new for you and if you google it then your word power also grow. In a nutshell, your overall knowledge will grow. Now the question is how someone read a newssignNow who has never read it before for a competitive purpose, Don’t worry I would tell also this to you here.Whenever you reading a newssignNow, first read the content of any article and then translare it in your own language as it is. For Example : If you belong to Orissa then first read it in English and then translate it in Odia, similarly, hindi, urdu or any other language you prefer. don’t think about the time, select only one article and finish it patiently by taking time. Read only one paragraph in a day but finsh it like that if someone ask anything about you from that article may be in moulded form, you can answered about it effectively, bcz if you read like that you can solve Rc, Cloze test, Filler & sentence arrangement in 100% while in the case of spot error only 60% in which you can understand the error through your understanding part.Smart study : The articles or pages you choose from a newssignNow choose it by filtering other news other than Financial awareness or business part because the article or topic you are reading may be comes in your mains.If you do this whatever I would tell you here then you can first got improvement in yourself about reading things as well as word power. By this you can start to linking words in sentences which will help you in spot errors and filler sections and after linking sentences you can actually improve your sentence arrangement areas. If you can understand it whatever I say here and you used to it the I bet you, your english will be improved after giving some if your time.Tips 1. Don’t afraid of English, treat it just like anyother language.Tips 2. Attempt all questions of English in prelims as well as mains bcz here you easily score more with a good knowledge of wordpower.If you still wants to clear some queries then ask it on my fb or insta profile. I’ll promise you to answered your querry within first 24 hours, I have already solved 100+ people queries related to various competitive exams like UPSC/SSC & of courses of Bank exams as well through fb & instagram, whenever they ask.Best of luck…!!!

As per the tentative schedule published on the official website, Indian Banking Personnel Selection (IBPS) will conduct the preliminary exam for recruitment of probationary officers (PO) in the month of October.This leaves roughly six months for banking job aspirants to prepare for the exam. While it's not necessary that you begin preparation for IBPS PO exactly six months prior to the exam but it will definitely give you ample to go over all the topics and revise. In this article we will discuss the strategy aspirants should adopt right now in order to ensure a good score in the IBPS PO preliminary and main exam.IBPS PO Preliminary and Main combined, there are total five sections in the IBPS PO exam - English Comprehension, Quantitative Aptitude, Reasoning, Banking Awareness and General Knowledge, and Computer Awareness. Six months are fairly enough to be completely prepared for both Preliminary and Main exam.1st and 2nd monthMake a section-wise list of all the topics from which questions may be asked. Start with the ones you find the toughest or have never heard of before. Devote one hour on each section. In case of Banking Awareness and GK, and Computer Awareness, half an hour a day is enough. Refer only school textbooks and normal exercise books to learn the fundamental concepts.3rd and 4th monthBy now you would have gone through every topic on your list. Now you need to begin focused preparation. Buy a preparation book for bank exams and start solving questions topic-wise. Again an hour a day should be enough. You should follow preparation books because the questions asked in the exam are a tad bit different than the ones which are mentioned in school textbooks. Also focus on learning shortcut tricks for solving lengthy problems.5th and 6th monthIn the last two months, I suggest you sign up for online speed test and solve at least one signNow in a day. Don't just solve preliminary speed test but also speed tests designed for Main exam. Solving speed tests would help you identify your problem areas and you can work on them. Speed tests would also get in the gear for online exam and benefit you on the exam day.This schedule (even with a little variation) would allow you to cover every topic including revision and give you an edge over other candidates appearing in the exam.Books for Banking ExamFor IBPS PO i am giving you a small sum of books that will help you for upcoming exams.QUANT:Paramount By Neetu singh (both vol 1 and vol 2).DI: Arhihant + BSC magazine problem.Reasoning:Buy arhihant publication book for general practice.BSC Publication Magazine problems for practice.For Puzzle- Magical Book on PUZZLES by K Kundan.ENGLISH:Reading Reading and Reading, no book will help you unless you start reading and make summary that will help in descriptiveVocab building and revise them regularly.Hindu signNow/Indian express/TOINote: No need of book for english. News signNow enough.General Awareness:Bankers Adda/Gk today daily affairs don’t read them write them in your daily notes.For quick reading leadthecompetition.comFor quiz App: Daily GKIf you are done with these above three areas, you are done with GA. No need to go for GK tornedo, Capsule, Injection, Golden points etc. ☺BANKING:RBI FAQ ( Frequently Asked Questions)Dhankar publication book for general banking.Make notes from History of banking, years of establishment, Acts, Nationalization, recent developments, committees.Previous exam questions of banking.COMPUTER:Lucent + Arhihant book read them twice will take 15 days to read both twice.Mock Tests:Start with Bankersadda and then after getting proper level join Practice mock and Oliveboard.TIPS:Join Facebook groups to understand pattern and competitionPractice as much as mock u can don’t wait for syllabus to complete.Keep cut off,Types of questions in mind.Don’t Mug up things understanding things well that will help you in life.Don’t compare ever, stay positive, confident, happy.Dont go for bulk materials, books follow the above things these are quite enough to crack u dont need to do phd in quanta/reso. We are here to crack exam. Thats all

Let me answer it from my personal experiences of having worked in IPS. At the outset itself, let me point out that I have almost never paid the informants, rather they have paid me! I’ll explain it later as to how is that possible. I may also point out that in State Police (which basically means regular uniformed police in cities and districts) most of the informants are not the paid informants. They provide information not for money but for other reasons which I shall explain. This is generally the situation in State Police, exceptions apart.This is unlike Intelligence Bureau (IB) and RAW which have a comprehensive system of grading the informant as well as the information. In IB and RAW, many of their informants may perhaps be paid ones.There is a system of having a Secret Service Fund (or SS Fund) in uniformed police, which is provided to the chief of the city police or district police, as the case may be. This fund usually has a meagre amount sanctioned every year, though it may vary depending on the requirements of the police unit concerned. This fund is not audited and its use is confidential. Usually, wherever there is a requirement for payment to an informant, money from this fund may be paid. A record is, of course, kept of the money spent from the fund and the officer in charge has to sign it, but it is not audited to maintain secrecy and confidentiality about the informants. The register containing details of the expenditure made from the SS Fund is also supposed to be kept in the personal custody of the officer concerned.But, let me tell you frankly, even where some payment is required to be made to a (paid) informant, usually the officers in the police station would not claim any money from the SS Fund because they are never sufficient. They would generally pay from their own pockets. But, how can they pay it from their own pocket? Well, you would be shocked to know that during my service I found that the Government would not provide even sufficient stationery (such as, for example, signNows for recording statements of witnesses) and money for other necessary expenses such as upkeep of police station buildings, etc. I don’t know what happens now, but this is what used to happen during the time when I was in service, and that too, in one of the supposedly best administered states in India, namely, Maharashtra. As I never liked the idea of the police officers buying stationery, etc., from their own pockets since that would give them a licence to indulge in corruption, I had to often struggle with the system to somehow get sufficient funds to buy at least these basic necessities for the official police working. Usually, police is one of the most neglected departments in Government, even though most politicians would want to (mis)use it.Coming back to the main topic of informants, as I mentioned earlier, most of the informants provide information to police officers not for seeking money for the information given. They give information for other reasons. Let me give some examples.When I joined my first regular posting as ASP, after completion of training, on the first day itself, at least 3-4 persons (separately) met me in my office. They had learnt that some young IPS officer has joined and they presumed that a young officer would be dynamic and honest. However, they were generally very cautious and careful, since the office staff would come to know about their identity. They gave me information about illegal satta (a type of gambling, resembling lottery to some extent) and illicit liquor manufacturing. I made it a point to personally raid all those illegal activities on the same or next day. And, I found that all the information given by them was perfect and accurate. It had tremendous impact. There was a drastic reduction in such illegal activities in 1-2 days only, as the news spread about the raids. While earlier such illegal activities were being conducted on large scale and openly, now the scale was much less and that too they started doing it in hidden or secret manner. The best part was that the informants (who gave me the first information) developed trust in me. They became my regular sources.In fact, over a period of time, I developed so many informants that it became difficult for me to remember their names. After some days, I generally stopped asking their names also. I would concentrate in knowing the information and then act on such information as soon as possible in an effective way. I almost never took police station staff with me for raiding such illegal activities. Many of such raids were conducted by me even single-handedly, though immediately thereafter, I would call the Control Room on wireless to send police station staff for further formalities.These informants never asked for money for the information given. What they wanted was action on their information.As the local media (newssignNows only, in those days) started picking up these stories of action taken on such illegal activities, you’ll not believe that I was always inundated with information. I would receive several phone calls a day (no mobile phones in those days). I used to receive the call directly due to which leakage of information was not possible. Moreover, caller IDs in phones were not available those days.The impact was that after some days, even the hidden and secret illegal activities also came to a standstill. As and when any fresh illegal activities would start, I would invariably get the information from some or the other informant.So, what did these informants want? Action. Strict legal action. On the information given. This was their main motive for giving information. I am writing this from my personal experiences.Let me tell you about the sorry state of affairs in our country. People are so frustrated that the moment they see even a single ray of light somewhere, they would flood you with information. Some of them would even risk their safety. They would give information to you anonymously, pseudonymously or by disclosing their details. Whatever way possible. They would not seek any money or any other favour from you, generally speaking.At the same time, I had the bad experiences also. I found that one or two police personnel from my own ASP office were leaking information about my movements (to conduct raids) to the criminals. In those days, since mobile phones were not available and the landline communication was an inefficient luxury (it would take many years to get telephone connection), I found that usually 4-5 scooters were kept parked somewhere at a distance from my office or on roads leading from my office or near the places of illegal activities. The moment they found me leaving office (or residence), one or more of such scooters would immediately rush at high speed to alert those who conducted such illegal activities.At times, I was personally attacked (thrice brutally) but survived. At times, false information was deliberately given to me in order to entice me to a place and attack me. Unfortunately, the dirty secret is that on 2-3 occasions, it happened in connivance with my own subordinates and/or seniors.But, that did not deter me. Usually, I would act upon the information without verification. After some time, I also developed judgment as to whom to trust. Merely because, say, 2% informants are false and mischievous, does it mean that I stop trusting 98% of the truthful informants? If you stop acting on genuine information, your sources of information would dry in a short time. So, I always considered it as a professional hazard if I had to take risk while acting on some information.Surprisingly, on 2-3 occasions, I got information even from the insiders working with criminals about the impending attack on me. That helped me to be on safer side on one or two occasions.My overall experience about the informants was that a major part of my successes was due to the information provided by them. Without their selfless information, I would not have been even half successful.And, such information would come not only in respect of illegal activities, but also in respect of regular crimes and also potential law & order problems.As an individual, one has only two eyes and two ears. But, with a network of informants all over your jurisdiction, you can have a thousand pairs of eyes and ears, spread all over. It helps tremendously.But, the open secret is that one must act on the information given and act in the strongest possible legal manner. Without fear and favour. If you stop acting on the information (such as when you also become corrupt), your informants will shy away from you over a period of time. They will lose trust in you and will stop giving information to you.What I have written in the foregoing paragraphs is mostly from my first posting itself. My experiences in my subsequent postings were on similar lines, but generally even better.In fact, once you have done some good work, your reputation travels faster than you to the place of your next posting. Generally, you get about 8-10 days to join at the new place of posting. But, before you join, all those who are supposed to know about you would have already come to know. This includes not only your future subordinates but also the criminals and those who indulge in organised crime with connivance of police. It makes your work much easier in subsequent postings, provided you keep up your good work and do not give in to corruption and other malpractices.Now, who would give information to police? Without expecting any money or any favour in return?They are mostly ordinary citizens who face problems in their day to day lives. They may be victims of illegal activities. They may be sufferers. They may be insiders / workers / rivals of those indulging in illegal activities. They may be members of the same or rival gangs. Sometimes, they may even be police personnel working in a police station who may not be happy with their own seniors indulging in corruption. They may be well-intentioned honest citizens of the locality who want improvement in law & order situation and/or who want to help their nation. They may be media personnel. They can be from some social organisations or from NGOs. They can also be someone trying to come closer to you (but, then you have to be careful while entertaining such people). In fact, an informant can be anybody.And, occasionally, an informant may be interested to provide information to you for money too. However, this category of informants is generally more common in tax departments (such as in Income Tax department or Customs department) where there is a provision for giving a fixed percentage of the money recovered as revenue as reward to the informants.As I mentioned at the outset itself, I have not written about IB and RAW since they have their own system of informants. I have written about informants of the regular uniformed police where I have worked. And, I think your question was also with regard to “police”, i.e., the regular “uniformed police”.So, you have asked – how do police officers pay their informants?Yes, I paid my informants. But, not in terms of money. But, in terms of strong action on the information provided by them. Let me tell you – they were all satisfied.As I mentioned in the beginning – it is the informants who have paid me! How? By their profuse thanks. By their gratitude. By tears of satisfaction sometimes seen in their eyes. By giving me more and more information that enabled me to perform my duties in a better way. And much more. Let me tell you that the thanks expressed by a needy fellow citizen can give you the kind of satisfaction that money can never give you. Try it yourself if you don’t trust me.There is no dearth of good people in our country. The problem is more from the politicians and the bureaucrats / public servants. An ordinary citizen is generally honest and willing to improve the system. Informants also fall in this latter category.

Find comfort in being uncomfortableComfort is the biggest enemy of creativity. To achieve something you always wanted but never had, you have to step out of this dangerous comfort zone.You need to look beyond comfort if you want to be creative. You might feel comfortable in doing the same things at work day in and day out. But if you want to tap the real creative potential hidden inside of you, you need to look beyond these ways. Challenge yourself, and start to find pleasure by being in uncomfortable situations - because they will bring out the best in you!Try technology detoxPut the iPhone down - that’s what my mum yelled as I was gazing continuously at the phone for the past half hour or so. She yelled because a few minutes back I had a discussion with her that I was not getting new ideas to write. “Gazing at the screen of your machine won’t bring creativity. Get out, look and feel things.” She completed and went to her room.By God she was right. Taking her advice I decided to take a few hours of tech detox daily. This was the time when I would distance myself from all the technology, be it a smartphone, laptop or anything else that could distract my mind. I would use this time to go out and meet people, take a stroll in the park and things like they used to do in old times. This helped me become more aware of the surroundings, as explained in the next point.Be more aware of your surroundingsWe are surrounded by so many people and so many things. In the rat race to become more productive, and outshine other person’s efforts we often forget about our surroundings. This makes our efforts more like that produced by a machine. But, aren’t we supposed to behave like humans?Being more aware of the surroundings allows us to learn from everything present around us. It instills a sense of motivation. Look at how things happen in nature. How someone else tackles a similar situation that you also faced. As philosophical as it might sound, but the fact of the matter is that these things inspire creativity. Don’t believe in me? Try to take a break from whatever you are doing right now and observe the crow calling outside your window. Bring down the pace of life, and you will find the strings of creativity automatically striking the right chord to produce a symphony.Live in presentLast, but not the least, forget about what has happened in the past. Give rest to your thoughts about the future. And, start living in the present. You cannot change what happened in the past. You don’t know what is going to happen in the future. But, with your actions, you can certainly control what is going to happen in the moment.The present moment is a gift bestowed upon us if we know how to live it in the best possible manner. And, that best possible manner is to get rid of the worries of the past and tensions about the future. Start living in the present, and you will get to see an instant change in your thinking, getting your creativity to flow!Originally published at HuffigntonPost

You arrive at lecture and sit perched on the edge of your seat, notebook open to a clean page and freshly-sharpened pencil in hand. You follow every word the professor says. Well, maybe you zone out a few times in the middle, but who doesn't? Besides, you're copying everything down and can review it later.That weekend, you diligently read the textbook. Maybe you skip a few parts since it's a busy week, but you definitely study the chapter summary and read all the examples. You do the homework problems, even starting three days early. When you're stuck, you go to office hours and ask the TA for help until they show you how to do it.Before the exam, you study your notes and the published homework solutions. You try the practice exam, and it seems the pieces are finally falling into place. You can solve most of the problems and remember most of the formulas and derivations! At last you take the final, referencing the single allowed sheet of notes you prepared at length the night before. You get almost every question right, or at least partial credit, and take home a well-deserved A.Three months later, you can hardly remember what the class was all about. What's going on? Why did you forget so much? Are you the only one? Should you have memorized more and worked even harder?The answer is no. A student who memorizes the entire physics curriculum is no more a physicist than one who memorizes the dictionary is a writer. Studying physics is about building skills, specifically the skills of modeling novel situations and solving difficult problems. The results in your textbook are just the raw material. You're a builder. Don't spend all your time collecting more materials. Collect a few, then build things. Here's how.The Cathedral and the StonesWhile delivering his famous set of freshman lectures on physics, Richard Feynman held a few special review sessions. In the first of these, he discussed the problem of trying to memorize all the physics you've learned:It will not do to memorize the formulas, and to say to yourself, "I know all the formulas; all I gotta do is figure out how to put 'em in the problem!"Now, you may succeed with this for a while, and the more you work on memorizing the formulas, the longer you'll go on with this method - but it doesn't work in the end.You might say, "I'm not gonna believe him, because I've always been successful: that's the way I've always done it; I'm always gonna do it that way."You are not always going to do it that way: you're going to flunk - not this year, not next year, but eventually, when you get your job, or something - you're going to lose along the line somewhere, because physics is an enormously extended thing: there are millions of formulas! It's impossible to remember all the formulas - it's impossible!And the great thing that you're ignoring, the powerful machine that you're not using, is this: suppose Figure 1 - 19 is a map of all the physics formulas, all the relations in physics. (It should have more than two dimensions, but let's suppose it's like that.)Now, suppose that something happened to your mind, that somehow all the material in some region was erased, and there was a little spot of missing goo in there. The relations of nature are so nice that it is possible, by logic, to "triangulate" from what is known to what's in the hole. (See Fig. 1-20.)And you can re-create the things that you've forgotten perpetually - if you don't forget too much, and if you know enough. In other words, there comes a time - which you haven't quite got to, yet - where you'll know so many things that as you forget them, you can reconstruct them from the pieces that you can still remember. It is therefore of first-rate importance that you know how to "triangulate" - that is, to know how to figure something out from what you already know. It is absolutely necessary. You might say, "Ah, I don't care; I'm a good memorizer! In fact, I took a course in memory!"That still doesn't work! Because the real utility of physicists - both to discover new laws of nature, and to develop new things in industry, and so on - is not to talk about what's already known, but to do something new - and so they triangulate out from the known things: they make a "triangulation" that no one has ever made before. (See Fig. 1-21.)In order to learn how to do that, you've got to forget the memorizing of formulas, and to try to learn to understand the interrelationships of nature. That's very much more difficult at the beginning, but it's the only successful way.Feynman's advice is a common theme in learning. Beginners want to memorize the details, while experts want to communicate a gestalt.Foreign language students talk about how many words they've memorized, but teachers see this as the most trivial component of fluency. Novice musicians try to get the notes and rhythms right, while experts want to find their own interpretation of the piece's aesthetic. Math students want to memorize theorems while mathematicians seek a way of thinking instead. History students see lists of dates and facts while professors see personality, context, and narrative. In each case, the beginner is too overwhelmed by details to see the whole. They look at a cathedral and see a pile of 100,000 stones.One particularly clear description of the difference between the experts' and beginners' minds comes from George Miller's 1956 study "The magical number seven, plus or minus two." Miller presented chess boards to both master-level chess players and to novices. He found that the masters could memorize an entire board in just five seconds, whereas the novices were hopeless, getting just a few pieces. However, this was only true when the participants were memorizing positions from real chess games. When Miller instead scattered the pieces at random, he found the masters' advantage disappeared. They, like the novices, could only remember a small portion of what they'd seen.The reason is that master-level chess players have "chunked" chess information. They no longer have to remember where each pawn is; they can instead remember where the weak point in the structure lies. Once they know that, the rest is inevitable and easily reconstructed.I played some chess in high school, never making it to a high level. At a tournament, I met a master who told me about how every square on the chess board was meaningful to him. Whereas, when writing down my move, I would have to count the rows and columns to figure out where I had put my knight ("A-B-C, 1-2-3-4, knight to C4") he would know instantaneously because the target square felt like C4, with all the attendant chess knowledge about control of the center or protection of the king that a knight on C4 entails.To see this same principle working in yourself right now, memorize the following. You have two seconds:首先放花生酱，然后果冻Easy, right? Well, it would be if you were literate in Chinese. Then you’d know it’s the important maxim, “first the peanut butter, then the jelly”.You can remember the equivalent English phrase no problem, but probably don't remember the Chinese characters at all (unless you know Chinese, of course). This is because you automatically process English to an extreme level. Your brain transforms the various loops and lines and spaces displayed on your screen into letters, then words, then a familiar sandwich-related maxim, all without any effort. It's only this highest-level abstraction that you remember. Using it, you could reproduce the detail of the phrase "first the peanut butter, then the jelly" fairly accurately, but you would likely forget something like whether I capitalized the first letter or whether the font had serifs.Remembering an equally-long list of randomly-chosen English words would be harder, a random list of letters harder still, and the seemingly-random characters of Chinese almost impossible without great effort. At each step, we lose more and more ability to abstract the raw data with our installed cognitive firmware, and this makes it harder and harder to extract meaning.That is why you have such a hard time memorizing equations and derivations from your physics classes. They aren't yet meaningful to you. They don't fit into a grand framework you've constructed. So after you turn in the final, they all start slipping away.Don't worry. Those details will become more memorable with time. In tutoring beginning students, I used to be surprised at how bad their memories were. We would work a problem in basic physics over the course of 20 minutes. The next time we met, I'd ask them about it as review. Personally, I could remember what the problem was, what the answer was, how to solve it, and even details such as the minor mistakes the student made along the way and the similar problems to which we'd compared it last week. Often, I found that the student remembered none of this - not even what the problem was asking! What had happened was, while I had been thinking about how this problem fit into their understanding of physics and wondering what their mistakes told me about which concepts they were still shaky on, they had been stressed out by what the sine of thirty degrees is and the difference between "centrifugal" and "centripetal".Imagine an athlete trying to play soccer, but just yesterday they learned about things like "running" and "kicking". They'd be so distracted by making sure they moved their legs in the right order that they'd have no concept of making a feint, much less things like how the movement pattern of their midfielder was opening a hole in the opponent's defense. The result is that the player does poorly and the coach gets frustrated.Much of a technical education works this way. You are trying to understand continuum mechanics when Newton's Laws are still not cemented in your mind, or quantum mechanics when you still haven't grasped linear algebra. Inevitably, you'll need to learn subjects more than once - the first time to grapple with the details, the second to see through to what's going on beyond.Once you start to see the big picture, you'll find the details become meaningful and you'll manipulate and remember them more easily. Randall Knight's Five Easy Lessons describes research on expert vs. novice problem solvers. Both groups were given the same physics problems and asked to narrate their thoughts aloud in stream-of-consciousness while they solved them (or failed to do so). Knight cites the following summary from Reif and Heller (1982)Observations by Larkin and Reif and ourselves indicate that experts rapidly redescribe the problems presented to them, often use qualitative arguments to plan solutions before elaborating them in greater mathematical detail, and make many decisions by first exploring their consequences. Furthermore, the underlying knowledge of such experts appears to be tightly structured in hierarchical fashion.By contrast, novice students commonly encounter difficulties because they fail to describe problems adequately. They usually do little prior planning or qualitative description. Instead of proceeding by successive refinements, they try to assemble solutions by stringing together miscellaneous mathematical formulas from their repertoire. Furthermore, their underlying knowledge consists largely of a loosely connected collection of such formulas.Experts see the cathedral first, then the stones. Novices grab desperately at every stone in sight and hope one of them is worth at least partial credit.In another experiment, subjects were given a bunch of physics problems and asked to invent categories for the problems, then put the problems in whatever category they belonged. Knight writes:Experts sort the problems into relatively few categories, such as "Problems that can be solved by using Newton's second law" or "Problems that can be solved using conservation of energy." Novices, on the other hand, make a much larger number of categories, such as "inclined plane problems" and "pulley problems" and "collision problems." That is, novices see primarily surface features of a problem, not the underlying physical principles.The "Aha!" FeelingIt is clear that your job as a student is to slowly build up the mental structures that experts have. As you do, details will get easier. Eventually, many details will become effortless. But how do you get there?In the Mathoverflow question I linked about memorizing theorems, Timothy Gowers wroteAs far as possible, you should turn yourself into the kind of person who does not have to remember the theorem in question. To get to that stage, the best way I know is simply to attempt to prove the theorem yourself. If you've tried sufficiently hard at that and got stuck, then have a quick look at the proof -- just enough to find out what the point is that you are missing. That should give you an Aha! feeling that will make the step far easier to remember in the future than if you had just passively read it.Feynman approached the same questionThe problem of how to deduce new things from old, and how to solve problems, is really very difficult to teach, and I don't really know how to do it. I don't know how to tell you something that will transform you from a person who can't analyze new situations or solve problems, to a person who can. In the case of the mathematics, I can transform you from somebody who can't differentiate to somebody who can, by giving you all the rules. But in the case of the physics, I can't transform you from somebody who can't to somebody who can, so I don't know what to do.Because I intuitively understand what's going on physically, I find it difficult to communicate: I can only do it by showing you examples. Therefore, the rest of this lecture, as well as the next one, will consist of doing a whole lot of little examples - of applications, of phenomena in the physical world or in the industrial world, of applications of physics in different places - to show you how what you already know will permit you to understand or to analyze what's going on. Only from examples will you be able to catch on.This sounds horribly inefficient to me. Feynman and Gowers both signNowed the highest level of achievement in their domains, and both are renowned as superb communicators. Despite this, neither has any better advice than "do it a lot and eventually expertise will just sort of happen." Mathematicians and physicists talk about the qualities of "mathematical maturity" and "physical insight". They're essential to moving past the most basic level, but it seems that no one knows quite where they come from.Circular ReasoningThere are certainly attempts to be more systematic than Feynman or Gowers, but before we get to that, let's take a case study. I recall that as a college freshman, I knew that the formula for the acceleration of a ball orbiting in a circle was [math]a = v^2/r[/math]. I wanted to know why, so I drew a picture:I imagined a small ball starting on the right side of the circle, heading upwards where the blue velocity vector [math]v_1[/math] is drawn. The ball moves around the circle, goes counter-clockwise over the top and then heads downwards on the left hand side, where the red velocity [math]v_2[/math] is. The ball's velocity changed, which means it accelerated. The acceleration is[math]a = \frac{\Delta v}{\Delta t}[/math][math]\Delta v[/math] is clearly [math]2v[/math], and [math]\Delta t[/math] is the time it takes to go half way around the circle, which is [math]\frac{\text{distance}}{\text{speed}} = \frac{\pi r}{v}[/math]. Hence, the acceleration is[math]a = \frac{2v}{\pi r/v} = \frac{2 v^2}{\pi r} \approx 0.64 \frac{v^2}{r}[/math]This isn't quite right. The answer is supposed to be [math]v^2/r[/math]. Somehow there is an extra factor of [math]2/\pi[/math] floating around.If you already understand calculus, this is a silly and obvious mistake. But for me it took quite some time - weeks, I think - until I understood that I had found the average acceleration, but the formula I was trying to derive was the instantaneous acceleration.The way I broke out of this mental rut was to think about the case where the ball has gone one quarter of the way around, like this:Then the same approach gives[math] a = \frac{\Delta v}{\Delta t} = \frac{2\sqrt{2}v^2}{\pi r} \approx 0.90 \frac{v^2}{r}[/math],which is closer to the right value. If you try it when the ball goes 1/8 the way around, you get[math]a = \frac{4 \sqrt{2 - \sqrt{2}}v^2}{\pi r} \approx 0.97 \frac{v^2}{r}[/math]and you're getting the idea that what you have to do is take the limit as the ball goes an infinitesimal fraction of the way around. (By the way, if I had been clever, maybe I'd have discovered Viète's formula this way, or something like it. I only recognized this now because I remembered encountering Viete's formula. So memory certainly has its place in allowing you to make connections. It's just not as central as beginners typically believe.)How do you do that "infinitesimal fraction of the way around" thing? Well, if the ball travels an angle [math]\theta[/math] around the circle, we can draw the before and after velocities asand[math] \Delta v = 2 \sin (\theta/2) v[/math]which in the limit [math]\theta \to 0[/math] becomes[math] \Delta v = \theta v[/math]and[math] a = \frac{\Delta v}{\Delta t} = \frac{\theta v}{\theta r/v} = \frac{v^2}{r}[/math]But all of this took a long time to come together in my mind, assembling gradually, but in discrete chunks with each small epiphany. As I walk through it now, I can see there are many concepts involved, and in fact if you're a beginning student it's likely that the argument isn't clear because I skipped some steps.The main idea in that argument is calculus - we're looking at an infinitesimal displacement of the ball. To understand the entire argument, though, we also need to do a fair amount of geometry, develop the idea of sliding velocity vectors around in space so they originate at the same point, introduce the concept of an arbitrary angle of rotation [math]\theta[/math], find the time it takes to rotate by that angle for a given [math]r[/math] and [math]v[/math], use the small-angle approximation of the sine function, and maybe a couple other things I'm not seeing.That's a lot of mental exercise. It's no wonder that working all this out for yourself is both harder and more effective than reading it in the book. Just reading it, you'll skip over or fail to appreciate how much goes into the derivation. The next time you try to understand something, you want those previously-mastered ideas about geometry and calculus already there in your mind, ready to be called up. They won't be if you let a book do all the work.Today, I can solve this problem in other ways. For example, I could write down the rectangular coordinates and differentiate, describe the motion in the complex plane as [math]r e^{i\omega t}[/math] and differentiate that, or transform to a rotating reference frame and note the centrifugal force on the stationary ball and conclude it must be accelerating in an inertial frame. A cute one is to write down the position and velocity vectors by intuition, and notice that going from position to velocity you rotate 90 degrees and multiply the length by [math]v/r[/math]. To go from velocity to acceleration is mathematically identical, so rotating another 90 degrees and multiply by [math]v/r[/math] again we obtain the answer.I can argue from dimensional analysis that the only way to get something with units of acceleration is [math]v^2/r[/math], or heuristically point out that if you increase the velocity, the velocity vectors get bigger, but we also go from one to the next in less time, so the acceleration ought to scale with [math]v^2[/math], etc.I also see aspects of the problem that I didn't back then, such as that this isn't really a physics problem. There are no physical laws involved. It would become a physics problem if we included that the ball is circling due to gravitational forces and used Newton's gravitational law, for example, but as it stands this problem is just a little math.So yes, I can easily memorize this result and provide a derivation for it. I can do that for most of the undergrad physics curriculum, including the pendulum and Doppler formulas you mentioned, and I think I could ace, or at least beat the class average, on the final in any undergraduate physics course at my university without extra preparation. But I can do that because I built up a general understanding of physics, not because I remember huge lists of equations and techniques.How to Chunk ItI can do these things now because of years' of accumulated experience. Somehow, my mind built chunks for thinking about elementary physics the same way chess players do for chess. I've taught classes, worked advanced problems, listened to people, discussed with people, tutored, written about physics on the internet, etc. It's a hodgepodge of activities and approaches, and there's no way for me to tease from my own experience what was most important to the learning process. Fortunately, people from various fields have made contributions to understanding how we create the cognitive machinery of expertise. Here is a quick hit list.George Pólya's How to Solve It examines the problem-solving process as a series of stages, and suggests the student ask themselves specific questions like, "Is it clear that there enough information to solve the problem?"Scott H Young, Cal Newport, and many others give specific advice on study skills: how to take notes, how to diagram out the connections between ideas, how to test your knowledge, how to fit what you're learning into the larger scheme of things, etc.When you do need to memorize things, spaced repetition software like Anki takes an algorithmic, research-backed approach to helping you remember facts with the minimum of time and effort.K. Anders Ericsson has tried to find the key factors that make some forms of practice better than others - things like getting feedback as you go and having clear goals. He refined these into the concept of Deliberate Practice. He also believes there is no shortcut. Even if you practice effectively, it usually takes around 10,000 hours of hard work to signNow the highest levels in complex fields like physics or music.Chunking and assigning meaning are your mind's ways of dealing with the information overload of the minutiae that inevitably pop up in any field. Another approach, though, is to try to expand your mind's ability to handle those minutiae. If you can push your "magical number" from seven to ten, you'll be able to remember and understand more of your physics work because it takes a bit longer to fill your cognitive buffer. Dual N-Back exercises are the most popular method of working on this. Nootropic drugs may also provide benefits to some people. Low-hanging fruit first, though. If you aren't sleeping 8-9 hours a day, getting a few hours of exercise a week, and eating healthy food for most meals, you're probably giving up some of your mind's potential power already. (There is individual variation, though.)Howard Gardner is one champion of the idea of multiple intelligences, or different learning types. When working on electric fields, for example, Gardner might advise you to study Maxwell's equations, draw pictures of vector fields and intuit their curls, get up and use your body, pointing your arms around to indicate electric field vectors, write or speak about what you're studying, learn with a friend or tutor, or maybe even create musical mnemonics to help you study, depending on where your personal strengths lie. Certainly, all students should build facility with drawing sketches, plotting functions, manipulating equations, visualizing dynamics, and writing and speaking about the material.Psychologist Carol Dweck's research studies the effect of your attitude towards learning on how much you learn, finding, for example, that children praised for their hard work are likely to press on further and learn more when given tough problems, whereas children praised for their intelligence are more likely to give up.Productivity guru David Allen helps people organize their lives and defeat procrastination with specific techniques, such as dividing complicated tasks into small, specific "next actions" and deciding when to do them, then organizing them in a planner system.Mihály Csíkszentmihályi believes that people operate best in a state of "flow", where they are so focused on the task they find it enjoyable and engrossing to the point they're innately motivated to continue. He emphasizes, for example, that the task needs to be the right level of difficulty - not too hard and not too easy - to find the flow state. (Some people think this state doesn't jibe with deliberate practice; others contend it's possible to achieve both simultaneously.)Taken together, this yields enough practical advice to chew on for months or years. To summarize, when you are learning something new:Try to figure it out for yourselfIf you get stuck, take a peek at your textbook to get the main ideaTeach the idea to someone elseOnce you've learned something, repeat the entire reasoning behind it for yourself, working through each detailAsk yourself Pólya's questions when you're stuckUse Young and Newport's techniques to map out the ideas of your class and relate them to your prior knowledgeMake Anki decks and review them a few minutes a day to retain what you've learnedMake sure your study sessions include all the principles of deliberate practice, especially feedback, challenge, and attentionBuild an image of yourself as someone motivated by learning and proud of having worked hard and effectively rather than as someone proud of being smart or renowned.Find a organizational system that lets you handle all the details of life smoothly and efficiently.Search for the flow state, notice when you enter it, and put yourself in position to find flow more and more often.Work on different subjects, reviewing both advanced and basic material. They will eventually all form together in your mind, and you're likely to have to take at least two passes at any subject before you understand it well.Take care of your physical health.This list does not include reading every page of the textbook or solving every problem at the end of the chapter. Those things aren't necessarily bad, but they can easily become rote. Building the material up for yourself while dipping into reference materials for hints is likely to be more effective and more engaging, once you learn to do it. It is a slow, difficult process. It can be frustrating, sitting there wracking your brain and feeling incredibly stupid for not understanding something you know you're supposed to have down. And strangely, once you have it figured out, it will probably seem completely obvious! That's your reward. Once the thing is obvious, you've chunked it, and you can move on. (Though you still need to review with spaced repetition.) This is the opposite of the usual pattern of sitting in lectures and feeling you understand everything quite clearly, only to find it all evaporated the next day, or acing a final only to find your knowledge is all gone the next month.That, I believe, summarizes the practical knowledge and advice about the learning process. Memorizing equations and derivations is difficult and ineffective because they are just the details. You can only handle a few details before your mind gets swamped. To cope, train yourself to the point where you process equations and physical reasoning automatically. This will free your conscious effort up to take in the big picture and see what the subject is all about.It Just Gets In The Way, You SeeSomehow, I've developed a "this is calculus" instinct, so that if I see the problem about acceleration in circular motion, or any other problem about rates of change, I know that it's talking about a limit of some kind. Where does this instinct exist in my brain? What form does it take? How does it get called up at the right time?George Lakoff believes that almost everything we understand is via metaphor. Any sort of abstract concept is understood by linking it to concrete concepts we've previously understood. For example, in Where Mathematics Comes From, Lakoff and coauthor Rafael Nuñez argue that we think of the mathematical concept of a "set" as a sort of box or container with things stacked in it. We reason about sets using our intuition about boxes, then later go back and support our conclusions with the technical details. Learning to reason about sets, then, is learning to think about the box metaphor and translate it back and forth into the formal language of axioms and theorems. This seems to fit with the introspective reports of many mathematicians, who say they build intuitive or visual models of their mathematics when finding results, then add in the deltas and epsilons at the end.This may be why we so often see beginning students asking things like, "but what is the electron, really?" If they were told it is just a tiny little ball, that would work, because it's a very easy metaphor. But instead, they're told it's not a ball, not a particle, not a wave, not spinning even though it has spin, etc. In fact, they're told to dismiss all prior concepts entirely! This is something Lakoff believes is simply impossible. No wonder students are bobbing in an ocean of confused thought bubbles, with nothing but mixed metaphors to grasp at until the last straw evaporates, across the board.Linguists like Steven Pinker believe that the language we use tells us how our mind works. Physicists certainly do have a specialized lexicon, and the ability to use it correctly correlates pretty well to general physics intuition, in my experience. In his review of Pinker's The Stuff of Thought, Douglas Hofstadter summarizes:Pinker shows, for example, how subtle features of English verbs reveal hidden operations of the human mind. Consider such contrasting sentences as "The farmer loaded hay into the wagon" and "The farmer loaded the wagon with hay." In this pair, the verb "load" has two different kinds of objects: the stuff that gets moved and the place it goes. Also, in the first sentence, the destination is the object of one preposition; in the second, the stuff is the object of another. Pinker sees these "alternations" as constituting a "microclass" of verbs acting this way, such as "spray" ("spray water on the roses" versus "spray the roses with water"). Where does this observation lead him? To the idea that we sometimes frame events in terms of motion in physical space (moving hay; moving water) and sometimes in terms of motion in state-space (wagon becoming full; roses becoming wet).Moreover, there are verbs that refuse such alternations: for instance, "pour." We can say "I poured water into the glass" but not "I poured the glass with water." What accounts for this curious difference between "load" and "pour"? Pinker claims that pouring merely lets a liquid move under gravity's influence, whereas loading is motion determined by the human agent. "Pour" and "load" thus belong to different microclasses, and these microclasses reveal how we construe events. "[W]e have discovered a new layer of concepts that the mind uses to organize mundane experience: concepts about substance, space, time, and force," Pinker writes. " . . . [S]ome philosophers consider [these concepts] to be the very scaffolding that organizes mental life. . . . But we've stumbled upon these great categories of cognition . . . by trying to make sense of a small phenomenon in language acquisition."If correct, then in order to think about physics the way an expert does, we should learn to speak the way experts do. If we try to solve physics problems using the words "load" and "pour", we may be carrying around a bunch of distracting anthropocentric baggage. If we don't recognize that, we'll get stuck, saying the problem "doesn't make sense", when really it's our linguistically-instilled expectations that are wrong. To combat this, it may be just as helpful to gain facility with the language of physics as with its equations.Five Easy Lessons provides a clear example of such difficulties: the case study of "force". As I type this, my laptop is sitting on a desk which exerts an upward force on it. Few beginning students believe this is really a force, even after they've been browbeaten into drawing arrows for the "normal force" on exam diagrams.The problem is in the way we use "force":"The robber forced the door open." "Your apology sounded forced.""...the force of the explosion..." "...the force of righteousness...""I'm being forced to take physics even though I'll never use it."Literally or figuratively, we think of "force" as implying not only motion, but intent or purpose, and also control. Force is for people pushing on things, or maybe for cars and projectiles. These things are using energy and will run down if left alone. But the desk under my laptop? It's just sitting there, totally passive. How could it be "exerting a force" when it doesn't even get tired? Needing some sort of rationalization for why the laptop doesn't fall, beginners say that it's not that the desk exerts a force on the laptop, the desk just provides something for the laptop to sit on. Or if something falls on the desk, the desk didn't exert a force to stop it. It just got in the way is all. Why doesn't the professor understand this obvious difference? A desk exerting a force? Come on...Five Easy Lessons describes how students only overcome this difficulty after seeing a classroom demonstration where, using a laser pointer and a mirror laid on the desk top, the professor demonstrates how when a heavy cinder block is laid on the desk, the surface responds by bending out of its natural shape, exerting force on the cinder block like a compressed spring would.You may need to find many such visualizations before you can reconcile your colloquial use of words with their use in physics. But this might also be dangerous, because although finding a way to make physics obey your idea about what a word means works decently in this case, in other instances it's your expectations for the word that ought to change. (Relativity, with words like "contraction", "slowing down", etc. is a good example.)Mythologist Joseph Campbell believes that we understand the world primarily through story. Perhaps we understand derivations, experimental evidence, and the logic behind physical conclusions as a sort of story, and it's in building this story that our cognitive chunks are formed.Mind The Neural Gap JunctionsYou are the pattern of neural activity in your brain. When a part of you changes, building a new memory, installing a new habit, or constructing a tool to approach a class of problems, that change must be reflected somewhere in your brain.Lesswrong user kalla724 describes this process in "Attention control is critical for changing/increasing/altering motivation"First thing to keep in mind is the plasticity of cortical maps. In essence, particular functional areas of our brain can expand or shrink based on how often (and how intensely) they are used. A small amount of this growth is physical, as new axons grow, expanding the white matter; most of it happens by repurposing any less-used circuitry in the vicinity of the active area. For example, our sense of sight is processed by our visual cortex, which turns signals from our eyes into lines, shapes, colors and movement. In blind people, however, this part of the brain becomes invaded by other senses, and begins to process sensations like touch and hearing, such that they become signNowly more sensitive than in sighted people. Similarly, in deaf people, auditory cortex (part of the brain that processes sounds) becomes adapted to process visual information and gather language clues by sight.But, they caution, these neural changes occur primarily to those parts of our minds to which we pay conscious attention:A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, thinking about the next move, about his chess strategy, and about the future possibilities of the game. His neural networks are optimizing, making him a better chess player.A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, thinking about the music he hears, listening to the chords and anticipating the sounds still to come. His neural networks are optimizing, making him better at understanding music and hearing subtleties within a melody.A man is sitting in his living room, in front of a chessboard. Classical music plays in the background. The man is focused, gritting his teeth as another flash of pain comes from his bad back. His neural networks are optimizing, making the pain more intense, easier to feel, harder to ignore.You need to pay attention not just to doing physics, but to the right parts of doing physics - the parts most related to intuition.James Nearing gave his advice on how to do this in Mathematical Tools for PhysicistsHow do you learn intuition?When you've finished a problem and your answer agrees with the back of the book or with your friends or even a teacher, you're not done. The way do get an intuitive understanding of the mathematics and of the physics is to analyze your solution thoroughly. Does it make sense? There are almost always several parameters that enter the problem, so what happens to your solution when you push these parameters to their limits? In a mechanics problem, what if one mass is much larger than another? Does your solution do the right thing? In electromagnetism, if you make a couple of parameters equal to each other does it reduce everything to a simple, special case? When you're doing a surface integral should the answer be positive or negative and does your answer agree?When you address these questions to every problem you ever solve, you do several things. First, you'll find your own mistakes before someone else does. Second, you acquire an intuition about how the equations ought to behave and how the world that they describe ought to behave. Third, It makes all your later efforts easier because you will then have some clue about why the equations work the way they do. It reifies the algebra.Does it take extra time? Of course. It will however be some of the most valuable extra time you can spend.Is it only the students in my classes, or is it a widespread phenomenon that no one is willing to sketch a graph? (\Pulling teeth" is the cliche that comes to mind.) Maybe you've never been taught that there are a few basic methods that work, so look at section 1.8. And keep referring to it. This is one of those basic tools that is far more important than you've ever been told. It is astounding how many problems become simpler after you've sketched a graph. Also, until you've sketched some graphsof functions you really don't know how they behave.(To see the advice on graphs, along with a detailed step-by-step example, see his book, free online)Brown Big SpidersOne of the difficulties with chunks is that they're mostly subconscious. We may ultimately know of their existence, as did the chess master who told me he knew how each square of the chess board felt, but their precise nature and the process of their creation are almost immune to introspection. The study methods I've talked about above are empirically useful in creating chunks, so we have guidelines for how to make new chunks in general, but we usually don't know which ones we are creating.Lesswrong user Yvain comments on the essay Being a teacherI used to teach English as a second language. It was a mind trip.I remember one of my students saying something like "I saw a brown big spider". I responded "No, it should be 'big brown spider'". He asked why. Not only did I not know the rule involved, I had never even imagined that anyone would ever say it the other way until that moment.Such experiences were pretty much daily occurrences.In other words, the chunkiest cognitive process we have - language - develops largely without our awareness. (In retelling this story, I've met a surprising number of people who actually did know about adjective order in English, but most of them either learned English as a second language or had studied it in psychology or linguistics course.)This makes it incredibly difficult for physics teachers or textbook writers to communicate with beginners. It's inevitable that beginners will say that a certain lecturer or book just doesn't explain it clearly enough, or needs to give more examples. Meanwhile, the lecturer has no idea why what they said wasn't already perfectly clear and thinks the example was completely explicit. Neither party can articulate the problem, the student because they can't see the incorrect assumption they're making, the professor because they don't realize they've already made such an assumption.For example, once I was proctoring a test in a physics class for biology majors. A question on the test described a certain situation with light going through a prism and asked, "What is the sign of the phase shift?" A student came up to ask for clarification, and it wasn't until they'd asked their question three times that I finally got it. They thought they were supposed to find the "sign" as in a signpost, or marker. There would be some sort of observable behavior that would indicate that a phase shift had occurred, and that was the "sign of the phase shift." Until then, I was only able to think of "sign" as meaning positive or negative - did the wave get advanced or retarded?If you want to learn a language with all those rules you don't even know about, you need to immerse yourself. Endless drills and exercises from a book won't be enough, as millions of Americans a decade out of high school straining to remember, "Dondé esta el baño?" can attest. You need to read, speak, see, and hear that language all around you before it takes.To learn physics, then, read, speak, and hear it all around you. Attend colloquia. Read signNows. Solve problems. Read books. Talk to professors and TA's, and expose yourself to all the patterns of thought that are the native language of the field.As you learn, you will build the right chunks to think about physics without realizing what they are. But there's a flip side to this problem, which is that when you're not doing physics, you can build the wrong chunks. They can get in the way, and again you don't realize it.In Drawing on the Right Side of the Brain, Betty Edwards discusses an exercise she gave her art students:One day, on impulse, I asked the students to copy a Picasso drawing upside down. That small experiment, more than anything else I had tried, showed that something very different is going on during the act of drawing. To my surprise, and to the students' surprise, the finished drawings were so extremely well done that I asked the class, "How come you can draw upside down when you can't draw right-side up?" The students responded, "Upside down, we didn't know what we were drawing."When we see a recognizable image, unconscious chunking immediately gets to work, interpreting, imparting meaning, and inevitably distorting. Learning to draw, according to Edwards, involves circumventing harmful chunks as much as building helpful ones.So it is with physics. The ideas about force, animation, and intent discussed in the laptop-and-desk example seem to illustrate just this problem. Five Easy Lessons lists many of the known misconceptions that students have somehow taught themselves in each topic of introductory physics - for example that electric current gets used up as it goes around a circuit. But I think it's likely that there are many more such obstructive thought patterns that we don't yet know exist. These might be more general notions about such things as cause and effect, what nature "wants" to accomplish, etc.I Feel DumbEducators are perpetually frustrated by what seems like an outrageous pattern. They explain something clearly. The students all claim to understand perfectly, and can even solve quantitative problems. Still, when you ask the students to answer basic conceptual questions, they get it all wrong. How is this possible?In this YouTube video, Veritasium explores what happens when you explain something clearly:Amazingly, the clearer the explanation, the less students learn. Humans have a huge array of cognitive biases. In general, these various biases work so that we'll keep believing whatever it was we believed to begin with, unless there's a really good reason not to. Someone giving a clear, authoritative physics lecture does not register in your mind as a good reason to check your beliefs, so you listen happily and rave about what a great lecture it was, all while maintaining your wrong ideas.However, with the right stimulus you can get your brain to throw out the old, wrong ideas. Entering such a state is a prerequisite to true learning, and fortunately we can detect it in ourselves. We call it confusion.Confusion is a message from your emotional mind (the part that tells your analytical mind what decisions to start justifying). It's saying, "Hey, something about our beliefs is very wrong, and this is actually important. Pay attention and figure it out."A great lecturer, instead of being clear, will confuse students by asking them to predict ahead of time what a demonstration will show, then do it, and the opposite actually occurs. Or they will ask students to solve questions that sound straightforward, but in fact the students can't figure out. Only after confusion sets in will the teacher reveal the trick.You want to defeat your biases, toss out your wrong beliefs, and learn physics to the Feynman level - the level where you create the knowledge as you go along. Even many specialists never fully get there, instead rising to increasingly-sophisticated levels of rehashing the same memorized arguments in a way that can carry them quite far and trick most people. The only way to avoid this is to spend many, many hours thoroughly confused.Have you ever lost an argument, only to think of the perfect retort two days later when stopped at a traffic light? This shows how your mind will continue working on hard problems in the background. It eventually comes up with a great answer, but only if you first prime it with what to chew on. This works for physics problems just as well as for clever comebacks, once you find good problems to grapple with. I conjecture that engaging this subconscious system requires a strong emotional connection to the problem, such as the frustration or embarrassment of being dumbstruck in an argument or the confusion of being stumped by a hard problem.Confusion is essential, but often also unpleasant. When you repeatedly feel frustrated or upset by your confusion, your mind unconsciously learns to shy away from hard thinking. You develop an ugh field.This could happen for different reasons. A common one arises in people who judge themselves by their intellect. Confusion for such people is a harsh reminder of just how limited they are; it's a challenge to their very identity. Whether for this reason or some other, it's common for students and academics to fall into patterns of procrastination and impostor syndrome when navigating the maze of confusion that come with their chosen path.I don't have the answer for this. I have heard many people tell their stories, but I have yet to figure out my own. Sometimes confusion feels awful, and my story in physics is a jerky, convoluted one because of how I've dealt with that. But once in a while a problem is so good that none of that matters. When I find one of these problems, it hijacks my mind like Cordyceps in a bullet ant, jerking me back to a fresh piece of scratch signNow again and again, sometimes for days. If you signNow this state over and over, you'll know Feynman meant by, "What I cannot create I do not understand"Get confused. Solve problems. Repeat. The universe is waiting for you.ReferencesIn order of appearance in this answerFeynman's Tips on Physics: Richard P. Feynman, Michael A. Gottlieb, Ralph Leighton: 9780465027972: Amazon.com: Bookssoft question - Memorizing theorems - MathOverflowThe Magical Number Seven, Plus or Minus Two (wikipedia)The Magical Number Seven (original signNow)Google Translate (Chinese phrase)Knight, Randall. Five Easy Lessons pp 37Reif and Heller, 1982 Viète's formulaHow To Solve It: A New Aspect of Mathematical Method (Amazon)How To Solve It (summary)How to Solve It (Wikipedia)Learn Faster with the Feynman Technique (Scott Young. His page is start to get spammy.)Study Hacks " About (Cal Newport)Anki - powerful, intelligent flashcardsSpaced repetition (review by Gwern)K. Anders Ericsson (Wikipedia)The Role of Deliberate Practice in the Acquisition of Expert PerformanceDual N-Back FAQ (gwern)Food Rules An Eater`s Manual (Amazon, how to eat)Core Performance Essentials (Amazon, exercise) Exercise is an interesting case because not everyone responds very well. For the majority of people it's worth the time.Howard Gardner (wikipedia)The Unschooled Mind: How Children Think And How Schools Should Teach: Howard E. Gardner (Amazon)The Perils and Promises of Praise (article by Dweck)Mindset, Dweck's book.Flow (psychology) (Wikipedia)Flow: The Psychology of Optimal Experience: Mihaly Csikszentmihalyi: 9780061339202: Amazon.com: Books David Allen, Getting Things Done® and GTD® Online to-do list and task management (One possible GTD software)How to Setup Remember The Milk for GTD George Lakoff (professional site)George Lakoff (Wikipedia)Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being: George Lakoff, Rafael Nuñez: 9780465037711: Amazon.com: BooksLoaded sentences (Hofstadter reviews Pinker)The Stuff of Thought: Language as a Window into Human Nature: Steven Pinker: 9780143114246: Amazon.com: Books The Power of Myth: Joseph Campbell, Bill Moyers: 9780385418867: Amazon.com: BooksAttention control is critical for changing/increasing/altering motivationMathematical Tools for Physics (Nearing)Being a teacher - Less WrongDrawing on the Right Side of the Brain: The Definitive, 4th Edition: Betty Edwards: 9781585429202: Amazon.com: BooksVeritasium (channel)List of cognitive biases (wikipedia)Dunning–Kruger effect (wikipedia) Ugh fields - Less WrongUseful Quora AnswersAnonymous's answer to What is it like to understand advanced mathematics? Does it feel analogous to having mastery of another language like in programming or linguistics?Satvik Beri's answer to How do math geniuses understand extremely hard math concepts so quickly?Qiaochu Yuan's answer to Why is it almost impossible to learn a mathematical concept on Wikipedia? They are very difficult to follow, especially if one doesn't have a solid background in the subject.Christopher VanLang's answer to What should I do if my PhD advisor and lab colleagues think I'm stupid?What did Richard Feynman mean when he said, "What I cannot create, I do not understand"?Debo Olaosebikan's answer to What are some words, phrases, or expressions that physicists frequently use in ordinary conversation?Paul King's answer to How does the arbitrary become meaningful? How does the human mind convert things like art into emotion and experience?What are some English language rules that native speakers don't know, but still follow?User's answer to What's an efficient way to overcome procrastination?Further ReadingI feel a little sleazy writing this answer because when I mention, for example, Carol Dweck doing research on the psychology of mindsets or K. Anders Ericsson studying deliberate practice, in fact there are thousands of people working in those fields. The ones I've mentioned are simply the most public figures or those I've come across by chance. I haven't even read the original research in most of these cases, relying on summaries instead.The answer is also preliminary and incomplete. There's lots of research left to be done, and I'm not an expert in what's out there. Still, here is a guide to some further resources that have informed this answer.For an overview of the psychology of learning, I like Monisha Pasupathi's audio course How We Learn from The Teaching Company. It covers many clever experiments designed to help you build a model of what happens in your mind as you learn.Bret Victor explores software solutions to visualizing the connection between physical world, mathematical representation, and mental models. Check outThe Ladder of AbstractionExplorable ExplanationsI think it's helpful to build an innate impression of your mind as not perceiving the world directly, but as concocting its own, tailored interpretation from sense data. All your consciousness ever gets to experience is the highly-censored version. The books of Oliver Sacks are great for making this clear by illustrating what happens with people for whom some of the processing machinery breaks down.The LessWrong Sequences were, for me, a powerful introduction to the quirks of human thought, preliminary steps towards how to work best with the firmware we've got, and what it means to seek truth.Selected BibliographyThese are some physics books to which have helped me so far. I'm not choosing them for clear exposition or specialty knowledge in a certain subject, but for how I think they helped me understand the way to think about physics generally.Blandford and Thorne, Applications of Classical PhysicsEpstein, Thinking PhysicsFeynman, Lectures on Physics------------ The Character of Physical Law------------ QED: The Strange Theory of Light and Matter------------ Tips on PhysicsGeroch, General Relativity from A to BLevi, The Mathematical MechanicLewin, Walter "Classical Mechanics", "Electricity and Magnetism" (video lectures with demonstrations on MIT OpenCourseWare)Mahajan, Street-Fighting MathematicsMorin, Introduction to Classical MechanicsNearing, Mathematical Tools for PhysicsPurcell, Electricity and Magnetism----------, Back of the Envelope ProblemsSchey, Div, Grad, Curl, and All ThatThomas and Raine, Physics to a DegreeThompson, Thinking Like a PhysicistWeisskopf, "The Search for Simplicity" (articles in Am. J. Physics)ImagesFeynman's Tips on Physics, Feynman, Gottlieb, LeightonArchitectural detail- cut stone wallFile:NotreDameI.jpg

The British have always had a penchant for slightly ‘absurd’ humour. Swift’s “Gulliver’s travels” may have been satire at its best but it was still couched in ‘absurd’ humour.Through the war years, ITMA (It’s that man again - aka Hitler) on the radio lifted spirits and strengthened resolve and the ‘Goons’ performed a similar function in peacetime.You have to remember that Britain was still reeling from the after-effects of war. ‘Bomb-sites’ were still a common feature of major cities; plywood ‘pre-fabs’ (pre-fabricated ‘temporary’ dwellings would be a common sight until the late sixties) abounded, drafty and cold in the winter; rationing was still in force and would be until 1953. Into that void stepped Spike Milligan and his scripts for the Goons.That Milligan was a comic genius cannot be denied; he almost single-handedly invented anarchic comedy. While Peter Sellers’ gift for ‘mimicry’ would enhance the show, it was Milligan’s scripts which made it.Nothing like it had been heard before and Milligan somehow captured the ‘Zeitgeist’ of a bewildered nation (wasn’t winning a war supposed to make things better?), who had nary an idea of why things were still so bad. Absurdity had found its place; no other humour would suffice.That Milligan’s legacy lives on also cannot be doubted. ‘The Navy Lark’ - left hand down a bit -; ‘Round the Horne’ and the genius of Barry Took and Marty Feldman; Monty Python and the ‘parrot sketch’ and so on, and so on, ad infinitum.Without Milligan’s ‘Goons’, we may not have ever had them.

This is a problem for all thinking people, not just scientists. It's known as the "infinite regress" problem or the "turtles all the way down" problem, based on this story, as recounted Stephen Hawking's "A Brief History of Time":A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: “What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise.” The scientist gave a superior smile before replying, “What is the tortoise standing on?” “You’re very clever, young man, very clever”, said the old lady. “But it’s turtles all the way down!”The secular version of the problem is "If the Big Bang caused everything, what caused the Big Bang?"The religious version is, "If God caused everything, what caused God?"It's always been odd to me that both atheists and theists use this exact same problem to point out that the "other side" is irrational. But there's an easy answer: "I don't know." "I don't know" is not an irrational stance. It's an intellectually honest one that anyone, regardless of his beliefs, can give. Let's say I'm a detective, investigating a locked room mystery. I find a dead man on the floor of a room that was locked from the inside. Next to him, also on the floor, there's a revolver, and I can see the victim has a gunshot wound in his head. An autopsy proves that the lethal bullet came from the revolver, and, furthermore, that (going by the angle of the wound), the victim couldn't have shot himself.I say, "I think we can conclude that the revolver was the murder weapon."The chief of police asks, "Okay, but how did the killer get in?"I say, "I don't know."Does it follow from this that my conclusion about the revolver is irrational? Doesn't it make more sense to say that I know some things about the crime scene but not all things?If you have accepted Science as a vehicle for knowing, you are perfectly consistent when you say, "Mountains of evidence point to the Big Bang being the cause of everything we see and can detect, but I don't know what caused it or if it even had a cause."A theist can be equally rational when he says, "My faith..." (or my scripture/revelation/tradition/reasoning/etc) "...proves to me that God created the Universe, but I don't know what (if anything) created God."A theist can claim that God is eternal. An atheist (or a person with a secular view of Nature) can claim that the matter and energy involved in the Big Bang is eternal. In fact, there are five ways to deal with the infinite-regress problem:1. There was no first cause: the current state of the Universe is eternal.2. There was a first cause, which was, itself, uncaused, having existed forever.3. There's an infinity of causes. (Turtles all the way down.) 4. The Universe just winked into being, uncaused.5. I don't know.The problem is any solution is going to involve something existing eternally, many things existing eternally (turtles all the way down), or something coming from nothing. And these are all ideas that don't sit well with human intuition. Any of them could be true, but our senses and brains didn't evolve to understand infinity or something-from-nothing. There also may be systems of thought that, for some people, "solve" the problem by helping them not think about it. I've talked to a couple of theists who have said, "Well, you're right. We don't know what caused God, but He's so awesome. He fills the mind, and so we don't need to think about anything prior. God, as a cause, is good-enough for me." There are physicists who say, "All we can even know happened after the Big Bang. We have no way of detecting anything that came before it, so it's a waste of time wondering about it."These strategies may sound like intellectual cop outs, but we all do this, all the time. "I don't care why you stole that car! Stealing is wrong and you're going to jail." Most of the time, we don't try to follow a causal chain all the way to its end. We don't need to for most purposes. A theist can pray to God without knowing where God came from or just trusting that He's eternal. The work of prayers and worship can get done in the face of mystery—in the face of "I don't know." And a physicist can do his job—can study Nature and learn all sorts of specific things about gravity, quarks, photons, etc.—without knowing the cause of the Big Bang. Luckily for all humans, we can get lots of useful work done without knowing the answers to all questions.

It was in many ways a secret life. The whole thing was completely secret for years and years and years. It was something where you couldn't tell anyone. We were totally paranoid about security and the casinos could throw you out at any time - so it was all hush hush. From the beginning in 1979, I never talked about it publicly until after the movie came out in 2008. Among those who knew - my family and friends who became investors - we called it "Camp Cambridge."In 1979 I lived with four roommates in the kind of crummy housing you live in after college when you have your first job but haven't gotten paid yet. It was a Cambridge, Massachusetts "triple decker" with a missing front door and a list of over 100 health and safety code violations. It was just over half a mile from MIT.  One day a kind of rough-looking guy with a backpack who wasn't too clean showed up at our apartment door looking for Leo Gordon. I'd never heard of any Leo Gordon, and I tried to get rid of him. Eventually my roommate Geoff came home and he knew Leo, it turned out Leo’s name was on our lease. The guy at the door, Dave, used to live in our apartment years ago, and because Geoff knew Leo and Geoff thought Dave knew Leo, Dave got to sleep on the floor in the living room. Dave was coming from Las Vegas to meet some MIT people about playing blackjack for money. I was convinced the whole thing was a fraud. You can go into a casino and win money? Consistently? With a "secret system"?Yeah, right.Dave had a whole story of playing blackjack "professionally" in Las Vegas on a "blackjack team" with Ken Uston - whom I'd never heard of. Dave talked a lot about blackjack and of anarchy and anarchists and creating an anarchist commune - it was very all entertaining in a "you aren't staying long, are you?" sort of way, and I looked forward to his departure. A couple of days later he introduced me to JP, who was 'the real deal' from a mathematical point of view. JP had a master's in mathematics from MIT, he had a high paying job at a tech company in Kendall Square, an elegant recursive computer model (which I understood), he had the numbers, he had all the math, and he had a copy of Richard Epstein's The Theory of Gambling and Statistical Knowledge (which became like the bible to us). In a few days he convinced me that there was a real, mathematical basis to this outrageous story, that there was a real, statistical likelihood of winning money, and that it was not as easy as it sounded. He gave the basic strategy and the sheet of numbers and I started memorizing and practicing.  First, a few of the key points of blackjack. You want your cards to add up to as close to 21 as possible without going over 21. The dealer has the same goal. If you are closer to 21 than the dealer, you win. The big difference is that the dealer must follow a set rule - if the dealer's cards total less than 17, the dealer must take an additional card. When the dealer has 12 or more, getting a "10" card means the dealer exceeds 21 and loses, so the remaining players win. So when the deck has more ‘ten cards’ (10, Jack, Queen, King) this favors the player. When the deck has more small cards (2,3,4,5,6) it favors the house - 12 or 13 or 14 or 15 plus 6 is still OK for the dealer.The basic idea of card counting is to know whether there are more small cards left or more big cards. So you keep a running total of small cards vs large cards - each small card you see is plus one and each 10 card you see is minus one, and the count is running total. For example, the running count might be plus 6 which means 6 more small cards have been dealt than large cards. If you are playing against a six deck shoe, and half the shoe (three decks) has been dealt, that +6 is divided by the three remaining decks. This gives you the average count per deck, which is +6/3 = +2, also called the "true count". The larger the count, the greater your advantage, so you more bet. The smaller the count the less you bet. Negative count bets table minimum. Wikipedia has a more detailed explanation – card countingAs a result of a lawsuit, there was a famous experiment in Atlantic City where people could openly count cards and the casinos could not throw them out [Unsurprisingly, this experiment only lasted a couple of weeks.] It was an opportunity too good to resist, so we went, we five. I had not yet ‘qualified’ so I didn’t play that first bank. And although some of the guys had jobs, I was the only one with money. The starting bank was just over $5,200 total, I put in about five thousand.Going to Atlantic City was chaotic. We had a $135 per week "hotel suite.” Technically it was a suite, it had 4 or 5 beds in a big L shaped room. It was a run-down four story building, you had to walk up four flights of stairs. Atlantic City was a real dump at that time: mostly buildings that hadn't been maintained in decades. Everything outside the three casinos was very cheap. Every blackjack team in the world was there for the experiment, including all the people who had written books, all the people who were banned from playing everywhere, and the Czechs who kept multiple racks of purple five hundred dollar chips in front of each player at all times. At that time the casinos were so crowded that the $25 tables were the only ones at which you could - sometimes - get a seat. At the beginning, our bank was too small to sit down and play the $25 tables at an acceptable level of risk (according to the Kelly Criterion). When there were empty seats at a table one of us would stand a few feet from the table and "discreetly" keep the count. If the shoe went to +2 [true count] or better you would signal - put your hand on the back of your neck - and one of our roaming players would sit down and bet $25 (or more, depending on the count). At the end of the week we were slightly up, and most of us had to go back to work, Dave stayed and doubled our bank in a few more days. Suddenly we had a business, and came up with a business model. We threw money in the bank, we played until we doubled the bank, and then we split up the bank, dividing half the profit among the players and half among the investors with a few expenses off the top. We started recruiting and training players – mostly MIT students. We were all broke, every dollar we made playing went back into the bank, and every weekend we piled into one car and drove for five hours from Cambridge to Atlantic City, stayed in the team apartment and tried to live on the $5 a day per diem the team paid. Five dollars paid for one meal (usually a calzone) unless you paid to ride the jitney bus to and from the casinos. There could be 8 to 12 people sleeping in that apartment on Friday and Saturday night.As we won and our bank got bigger, everything got easier, especially when we could finally just sit down at the start of a new shoe and bet $25. That was a landmark day.By trial and error, we figured you could play really well for an hour—that was your estimated attention span in the pressure cooker environment of the casinos. You would go to Resorts (for example), walk around until you found a table that looked good, maybe wait for a positive count, then sit down and play. We were all too young and tried to play inconspicuously, but we were 20-25 year old kids with tens of thousands of dollars, and it stood out. After you had played for about an hour, you cashed out and went to the men's room where you sat in a stall and counted your money and filled in your player sheet, then you walked to the next casino (there were only two or three at the beginning) and did it again. You'd get to Atlantic City Friday night at 10 or 11 pm, play about an hour at each casino then go to sleep until the shift changed. That was the rule - one hour of play during a given shift at a given casino - you didn't want to stay anywhere long enough to be memorable - so you would go to the casino once during each of the three daily shifts. Sunday night at 8 or 9 or 10 or 11 pm we'd drive back to Boston ( or New York).  We had check-ins where you'd meet the banker at certain times— 11 pm or 2 am - usually in a video gaming arcade on the boardwalk. You'd play Galaxian (a video game) and when the banker arrived you'd report your cash position, and the banker might adjust our betting using the Kelly Criterion. After a year or so we started to have "big players” as a disguise. A counter would sit at a table and flat bet $25 every hand. The big player would be ‘a real adult’ – someone over 50 - someone's uncle for example. The big player had been taught basic strategy and how to read our signals on betting. They barely had to pay attention - they could chat with the pit boss, flirt with the cocktail waitress. This dramatically reduced the rate of us getting barred. We kept on doubling our bank and eventually accumulated over $100k.  From the beginning, we had trouble running the team. One of the founders had a job on Wall Street at Citibank and he put together an entire NY contingent. However, some of the NY guys played a different counting system - one team played a system called Hi Opt 1, one played a system called Hi Low - we were all doing different stuff. It wasn't going smoothly, there were fights and arguments. I don't remember how we (or JP) found Bill Kaplan, but once Bill arrived and we hired him to manage the team he got us all onto the same page. He wrote a business play, he raised serious capital ($500,000, in cash), we had simple rules and simple procedures. Remember, this was an all cash businesses.With Bill in charge, some of the NY guys stayed, some split and formed their own team.Playing in a casino was a real grind. We all had "real jobs" or were students so we were fitting blackjack in on the side. It wasn't glamorous and it wasn't interesting—just follow the formulas, DON'T make mistakes. And you could play perfectly and lose $3/4/5,000 in a night—that was hard to watch. Just like when flipping a coin it is 50% chance it will be heads, but its not that rare to throw 3,4,5 heads in a row. In the long run it all evens out, but in the short run its called ‘variance’ and it happens in blackjack. You could play perfectly and lose hand after hand after hand for no apparent reason except a bad run of the cards. There was also a certain depressing aspect to it. The casinos have no windows, full of smoke, full of people drinking. You'd quickly see that most people in the casinos had no idea how to play and were just giving money to the casinos. People too drunk to sit on a stool betting $25 or $50 a hand - they might be sitting next to you.  Since it was all statistical the luck and gambling elements seemed minimized it quickly became dull. But high stress – don’t make mistakes, don’t let anyone know you are counting, don’t act suspicious, don’t let the casino see how much you are winning, don’t get pick pocketed, don’t draw attention. And we were always counting cash—you'd count your cash 7,8,9 times a day. Bills smaller than $100 were “lettuce” – annoying to have. You'd be walking around slummy Atlantic City with $15,000 or $20,000 in cash spread out through your pockets. At 2 am you’d be hanging out playing Galaxians in the video arcade waiting for the banker to arrive for a check-in, and worrying about getting your pocket picked or worrying about getting mugged.  At night in the apartment between shifts, people would be counting cash – there could be over $100,000 on the table, and people would be sleeping or discussing (or arguing). Sometimes the mathematical discussions would be in base 13 [a deck of cards has 4 suits of 13 cards each] — there were no personal computers back then so people did real math, or at least talked in math. [The real computer models were back in Boston / Cambridge.]During the week in Boston there would be practice sessions. A practice session lasted a couple of hours of play. You'd practice counting 6 decks - the test was 6 decks in under 2 minutes, and then you'd play a couple of shoes. If you didn't play perfectly, you couldn't "work" that weekend. Friday was 'visit the safety deposit box' day.Some people tried playing in Vegas, playing in Monte Carlo. That meant learning different rules, different numbers. Monte Carlo was easier to play, but the dealing was much slower - fewer hands per hour. Vegas was tough.Back then you really had to have a computer model to have the correct basic strategy for a given rule set, and to calculate the correct true count at which you would altering play for each hand combination. We were lucky, we had computers. [ Ed Thorpe, who "invented" (or quantified) card counting** in 1962 did most of the math by hand] On top of that we had to figure out how to set up and run a team. How to recruit, train and qualify counters and "Big Players" and manage an all cash business and prevent skimming, theft, and loss. Today it's all been worked out, and it's all on the net. Bill had experience and common sense – and some times it must have been like herding cats for him.It was very lucrative. No one talked about counting cards at all unless they couldn’t play anymore. People like Ken Uston only wrote books when they had been banned so many times and were too famous / too well known to play. We would have preferred that Uston and Revere et al. would have not written their books - we didn't want any publicity.At first the casinos were new, most of the employees were new, and if you could count cards, there was more money to be made playing than working for the casinos. I remember when the first 'counter catchers' started working for the casinos - we watched the people in the pit, and tried to figure out who the counter catcher was and what they looked like. You really needed a Big Player, we were all still way too young for the amounts of money we played. The casinos hated us. We believed that the press around card counting and the knowledge that the game could be beaten made blackjack the most popular game. We could tell that 99% of the players had no clue how to play, so it seemed like a big win for the casinos. However the casinos knew we were taking money off their bottom line. So in addition to trying to ban or bar counters, the casinos experimented with rule changes and game changes to take our edge. So at the same time, JP was always experimenting, modifying and running his model. The wildest thing he came up with – but didn’t invent – was ‘shuffle tracking’ – each casino has a precise system for shuffling a shoe of cards. JP came up with a system to track cards through the shuffle – we called it the 'non-random shuffle' – we played it for a while, but that was a bitch, it was hard to do well. There were certainly difficulties of running an "all cash business": what do you do when you think someone is skimming? (it happened). Once there was one picked pocket. Personalities and personality conflicts - really smart people who wanted to play their own method, or do it their own way. One of "our founders" liked to play based on the first and second derivative of the true count, rather than the true count itself, since there was no statistical basis for this and he wouldn’t stop doing it, we had to ask him to leave. Eventually every casino had multiple employees who could count (and catch counters). Anyone who knows how to count can spot every other counter at the table. Casinos have modified the rules of the game, and increased the number of decks in the shoe and adopted shuffling machines and so on and so on. And the counter’s edge became smaller and smaller, and it became harder and harder to play without being barred. They know everything about using Big Players and shills and signaling.  I played professionally for the first few wild years. It was lucrative, but wasn’t fun, and it became harder and harder to commute to Atlantic City for sleepless weekends grinding it out at the tables. Finally I got a job in Rochester, NY, and that was just too far away and I stopped playing. But the team went on, grew to 80 players. The edge became smaller, it became harder, until they finally stopped playing. And then one day in some bar at a tech convention, Jeff Ma told some guy the story, and that guy was Ben Mezrich who wrote Bringing Down the House, and eventually they made the movie “21”*.And now you know the rest of the story.*FWIW, the book is a highly fictionalized version of Jeff Ma’s story.** see comment to this answer (below) by Edward A. Curley Sr. as to who really "invented" card counting. Thorpe built on the work of others, and had the advantage as he was the first with access to a modern computer.