# Mental Math

Mental Math

http://en.wikipedia.org/wiki/Trachtenberg_system

Estimating square root

I use this trick quite often while computing square roots. It is extremely simple and utilizes the binomial expansion. It assumes that you know a couple of common squares and their roots. For example, 7 is , 11 is  etc.

Let’s take a number 86.

Get the closest square. In this case 81 it’s square root is 9.

Divide 86 by the square root, 9 we get 9.555

Take the average of 9 and 9.555 = 9.277.

Well the exact answer is 9.273, pretty close isn’t it 😉

Let’s try one more example. What is the square root of 420 ?

Closest square is 400, square root is 20. 420/20 = 21. Average of 20 and 21 is20.5. Well, the exact answer is 20.494 😉

Estimating Cube Roots

# How To Learn

Josh Kaufman points out in his book, The First 20 Hours – Kindle Edition (pg. 22), that the ten major principles of rapid skill acquisition are:

1. Choose a lovable project.
2. Focus your energy on one skill at a time.
3. Define your target performance level.
4. Deconstruct the skill into subskills.
5. Obtain critical tools.
6. Eliminate barriers to practice.
7. Make dedicated time for practice.
8. Create fast feedback loops.
9. Practice by the clock in short bursts.
10. Emphasize quantity and speed.

He further delineates points that need to be kept it mind:

• The desire for instant gratification is one of the primary reasons people don’t acquire new skills very quickly. (pg. 12)
• If you want to get good at anything where real-life performance matters, you have to actually practice that skill in context. Study, by itself, is never enough. (pg. 18)
• Precommit to completing at least twenty hours of practice. Once you start, you must keep practicing until you hit the twenty-hour mark. If you get stuck, keep pushing: you can’t stop until you reach your target performance level or invest twenty hours. If you’re not willing to invest at least twenty hours up front, choose another skill to acquire. (pg. 29)

Before you learn any of the suggested skills, my advice is to first learn how to learn. Optimizing your learning to make the most productive use of your time is a skill that will have transference to every aspect or your life. A book you could start with is “Daniel Coyle – The little book of talent”

Notes from The Little Book of Talent – Daniel Coyle

TIP #1 STARE AT WHO YOU WANT TO BECOME

• Bookmark a few YouTube videos, and watch them before you practice, or at night before you go to bed.

TIP #2 SPEND FIFTEEN MINUTES A DAY ENGRAVING THE SKILL ON YOUR BRAIN

• The key to effective engraving is to create an intense connection: to watch and listen so closely that you can imagine the feeling of performing the skill. For physical skills, project yourself inside the performer’s body. Become aware of the movement, the rhythm; try to feel the interior shape of the moves. For mental skills, simulate the skill by re-creating the expert’s decision patterns. Chess players achieve this by replaying classic games, move by move; public speakers do it by regiving great speeches complete with original inflections; musicians cover their favorite songs; some writers I know achieve this effect by retyping passages verbatim from great works. (It sounds kind of Zen, but it works.)

TIP #3 STEAL WITHOUT APOLOGY

• When you steal, focus on specifics, not general impressions.
• What, exactly, are the critical moves here?
• How do they perform those moves differently than I do?

TIP #4 BUY A NOTEBOOK

• A high percentage of top performers keeps some form of daily performance journal.
• Results from today. Ideas for tomorrow. Goals for next week.

TIP #5 BE WILLING TO BE STUPID

For example, students at the Meadowmount School of Music often practice according to an informal rule: If a passerby can recognize a song, it’s being played too fast. The point of this super-exaggerated slowness (which produces songs that resemble those of humpback whales) is to reveal small mistakes that might have gone undetected, and thus create more high-quality reaches. Businesses do it too. Google offers “20-percent time”: Engineers are given 20 percent of their work time to spend on private, nonapproved projects they are passionate about, and thus ones for which they are more likely to take risks. I’ve encountered numerous organizations that have employees sign a “contract” affirming that they will take risks and make mistakes. Living-Social, the Washington, D.C., e-commerce company, has a rule of thumb for employees: Once a week, you should make a decision at work that scares you. Whatever the strategy, the goal is always the same: to encourage reaching, and to reinterpret mistakes so that they’re not verdicts, but the information you use to navigate to the correct move.

TIP #6 CHOOSE SPARTAN OVER LUXURIOUS

TIP #7 BEFORE YOU START, FIGURE OUT IF IT’S A HARD SKILL OR A SOFT SKILL

HARD, HIGH-PRECISION SKILLS are actions that are performed as correctly and consistently as possible, every time. They are skills that have one path to an ideal result; skills that you could imagine being performed by a reliable robot. Hard skills are about repeatable precision, and tend to be found in specialized pursuits, particularly physical ones. Hard skills are about ABC: Always Being Consistent.  Here, your goal is to build a skill that functions like a Swiss watch—reliable, exact, and performed the same way every time, automatically, without fail.

Some examples:

• a golfer swinging a club, a tennis player serving, or any precise, repeating athletic move;
• a child performing basic math (for example, addition or the multiplication tables);
• a violinist playing a specific chord;
• a basketball player shooting a free throw;
• a young reader translating letter shapes into sounds and words;
• a worker on an assembly line, attaching a part.

SOFT, HIGH-FLEXIBILITY SKILLS, on the other hand, are those that have many paths to a good result, not just one. These skills aren’t about doing the same thing perfectly every time, but rather about being agile and interactive; about instantly recognizing patterns as they unfold and making smart, timely choices. With these skills, we are not trying for Swiss-watch precision, but rather for the ability to quickly recognize a pattern or possibility, and to work past a complex set of obstacles. Soft skills are about the three Rs: Reading, Recognizing, and Reacting.

Soft skills tend to be found in broader, less-specialized pursuits, especially those that involve communication, such as:

• a soccer player sensing a weakness in the defense and deciding to attack;
• a stock trader spotting a hidden opportunity amid a chaotic trading day;
• a novelist instinctively shaping the twists of a complicated plot;
• a singer subtly interpreting the music to highlight emotion;
• a police officer on a late-night patrol, assessing potential danger;
• a CEO “reading a room” in a tense meeting or negotiation.

If you aren’t sure if the skill is hard or soft, here’s a quick litmus test: Is a teacher or coach usually involved in the early stages? If the answer is yes, then it’s likely a hard skill. If it’s no, then it’s a soft skill. Violinists and figure skaters tend to have teachers; CEOs and stand-up comics don’t. The following three tips take this idea further, explaining the methods of deep practice that work best to develop each type of skill.

TIP #8 TO BUILD HARD SKILLS, WORK LIKE A CAREFUL CARPENTER

TIP #9 TO BUILD SOFT SKILLS, PLAY LIKE A SKATEBOARDER

In other words, to build soft skills you should behave less like a careful carpenter and more like a skateboarder in a skateboard park: aggressive, curious, and experimental, always seeking new ways to challenge yourself. When you practice a soft skill, focus on making a high number of varied reps, and on getting clear feedback.

TIP #10 HONOR THE HARD SKILLS

Prioritize the hard skills because in the long run they’re more important to your talent.

TIP #11 DON’T FALL FOR THE PRODIGY MYTH

If you have early success, do your best to ignore the praise and keep pushing yourself to the edges of your ability, where improvement happens. If you don’t have early success, don’t quit. Instead, treat your early efforts as experiments, not as verdicts. Remember, this is a marathon, not a sprint.

TIP #12 FIVE WAYS TO PICK A HIGH-QUALITY TEACHER OR COACH

1. Avoid Someone Who Reminds You of a Courteous Waiter
2. Seek Someone Who Scares You a Little
3. Seek Someone Who Gives Short, Clear Directions
4. Seek Someone Who Loves Teaching Fundamentals
5. Other Things Being Equal, Pick the Older Person

TIP #13 FIND THE SWEET SPOT

TIP #14 TAKE OFF YOUR WATCH

Deep practice is not measured in minutes or hours, but in the number of high-quality reaches and repetitions you make—basically, how many new connections you form in your brain. Instead of counting minutes or hours, count reaches and reps. Instead of saying, “I’m going to practice piano for twenty minutes,” tell yourself, “I’m going to do five intensive reps of that new song.”

TIP #15 BREAK EVERY MOVE DOWN INTO CHUNKS

To begin chunking, first engrave the blueprint of the skill on your mind (see Tip #2). Then ask yourself:

1. What is the smallest single element of this skill that I can master?
2. What other chunks link to that chunk?

Practice one chunk by itself until you’ve mastered it—then connect more chunks, one by one, exactly as you would combine letters to form a word. Then combine those chunks into still bigger chunks. And so on.

TIP #16 EACH DAY, TRY TO BUILD ONE PERFECT CHUNK

TIP #17 EMBRACE STRUGGLE

TIP #18 CHOOSE FIVE MINUTES A DAY OVER AN HOUR A WEEK

TIP #19 DON’T DO “DRILLS.” INSTEAD, PLAY SMALL, ADDICTIVE GAMES

The governing principle is this: If it can be counted, it can be turned into a game. For example, playing a series of guitar chords as a drill is boring. But if you count the number of times you do it perfectly and give yourself a point for each perfect chord, it can become a game. Track your progress, and see how many points you score over a week. The following week, try to score higher.

TIP #20 PRACTICE ALONE

TIP #21 THINK IN IMAGES

TIP #22 PAY ATTENTION IMMEDIATELY AFTER YOU MAKE A MISTAKE

TIP #23 VISUALIZE THE WIRES OF YOUR BRAIN FORMING NEW CONNECTIONS

When you go to the sweet spot on the edge of your ability and reach beyond it, you are forming and strengthening new connections in your brain. Mistakes aren’t really mistakes, then—they’re the information you use to build the right links. The more you pay attention to mistakes and fix them, the more of the right connections you’ll be building inside your brain. Visualizing this process as it happens helps you reinterpret mistakes as what they actually are: tools for building skill.

TIP #24 VISUALIZE THE WIRES OF YOUR BRAIN GETTING FASTER

Every time you practice deeply—the wires of your brain get faster. Over time, signal speeds increase to 200 mph from 2 mph. When you practice, it’s useful and motivating to visualize the pathways of your brain being transformed from simple copper wires to high-speed broadband, because that’s what’s really happening.

TIP #25 SHRINK THE SPACE

Smaller practice spaces can deepen practice when they are used to increase the number and intensity of the reps and clarify the goal.

TIP #26 SLOW IT DOWN (EVEN SLOWER THAN YOU THINK)

When we learn how to do something new, our immediate urge is to do it again, faster. This is known as the Hey, Look at Me! reflex. This urge for speed makes perfect sense, but it can also create sloppiness, particularly when it comes to hard skills (see Tip #8). We trade precision—and long-term performance—for a temporary thrill. So, slow it down.

TIP #27 CLOSE YOUR EYES

One of the quickest ways to deepen practice is also one of the simplest: Close your eyes.Michael Jordan practiced free throws with his eyes shut; Navy SEAL training includes generous helpings of pitch-black darkness during which soldiers learn to disassemble and reassemble their weapons, and, in one exercise, cooperate to pitch a tent; yoga and martial-arts practitioners frequently do it with their eyes closed.

TIP #28 MIME IT

TIP #29 WHEN YOU GET IT RIGHT, MARK THE SPOT

TIP #30 TAKE A NAP

Napping is good for the learning brain, because it helps strengthen the connections formed during practice and prepare the brain for the next session. Researchers at the University of California, Berkeley, found that napping for ninety minutes improved memory scores by 10 percent, while skipping a nap made them decline by 10 percent.

TIP #31 TO LEARN A NEW MOVE, EXAGGERATE IT

TIP #32 MAKE POSITIVE REACHES

Always focus on the positive move, not the negative one. For example, a golfer lining up a putt should tell herself, “Center the stroke,” not “Don’t pull this putt to the left.”

Psychologists call this “positive framing,” and provide plentiful theories of how framing affects our subconscious mind.

TIP #33 TO LEARN FROM A BOOK, CLOSE THE BOOK

TIP #34 USE THE SANDWICH TECHNIQUE

Deep practice is about finding and fixing mistakes, so the question naturally pops up: What’s the best way to make sure you don’t repeat mistakes? One way is to employ the sandwich technique. It goes like this:

1. Make the correct move.
2. Make the incorrect move.
3. Make the correct move again.

The goal is to reinforce the correct move and to put a spotlight on the mistake, preventing it from slipping past undetected and becoming wired into your circuitry.

TIP #35 USE THE 3 × 10 TECHNIQUE

This piece of advice comes from Dr. Douglas Fields, a neurologist at the National Institutes of Health in Bethesda, Maryland, who researches memory and learning. He discovered that our brains make stronger connections when they’re stimulated three times with a rest period of ten minutes between each stimulation. The real-world translation: To learn something most effectively, practice it three times, with ten-minute breaks between each rep. “I apply this to learning all the time in my own life, and it works,” Fields says.

TIP #36 INVENT DAILY TESTS

Daily routine in the talent hotbeds is full of little tests. The tests aren’t scientific, and they’re not treated as verdicts—they’re far more like targeted workouts, invented by the performers and their teachers.To invent a good test, ask yourself:

• What’s one key element of this skill?
• How can I isolate my accuracy or reliability, and measure it?
• How can I make it fun, quick, and repeatable, so I can track my progress?

TIP #37 TO CHOOSE THE BEST PRACTICE METHOD, USE THE R.E.P.S. GAUGE

• R: Reaching and Repeating
• E: Engagement
• P: Purposefulness
• S: Strong, Speedy Feedback.

Trumpeter A plays the passage twenty times. Trumpeter B tries to play the passage perfectly—with zero mistakes—five times in a row. If she makes any mistake, the count goes back to zero and she starts over. Be Trumpeter B.

TIP #38 STOP BEFORE YOU’RE EXHAUSTED

TIP #39 PRACTICE IMMEDIATELY AFTER PERFORMANCE

Always achieve my most productive practice after an actual round. Then, the mistakes are fresh in my mind and I can go to the practice tee and work specifically on those mistakes.”

TIP #40 JUST BEFORE SLEEP, WATCH A MENTAL MOVIE

TIP #41 END ON A POSITIVE NOTE

TIP #42 SIX WAYS TO BE A BETTER TEACHER OR COACH

1. Use the First Few Seconds to Connect on an Emotional Level
2. Avoid Giving Long Speeches—Instead, Deliver Vivid Chunks of Information
3. Be Allergic to Mushy Language
4. Make a Scorecard for Learning
5. Maximize “Reachfulness”
6. Aim to Create Independent Learners

TIP #43 EMBRACE REPETITION

TIP #44 HAVE A BLUE-COLLAR MIND-SET

TIP #45 FOR EVERY HOUR OF COMPETITION, SPEND FIVE HOURS PRACTICING

Games are fun. Tournaments are exciting. Contests are thrilling. They also slow skill development, for four reasons:

1. The presence of other people diminishes an appetite for risks, nudging you away from the sweet spot.
2. Games reduce the number of quality reps.
3. The pressure of games distorts priorities, encouraging shortcuts in technique.
4. Games encourage players, coaches, and parents to judge success by the scoreboard rather than by how much was learned.

TIP #46 DON’T WASTE TIME TRYING TO BREAK BAD HABITS—INSTEAD, BUILD NEW ONES

TIP #47 TO LEARN IT MORE DEEPLY, TEACH IT

TIP #48 GIVE A NEW SKILL A MINIMUM OF EIGHT WEEKS

TIP #49 WHEN YOU GET STUCK, MAKE A SHIFT

TIP #50 CULTIVATE YOUR GRIT

TIP #51 KEEP YOUR BIG GOALS SECRET

TIP #52 “THINK LIKE A GARDENER, WORK LIKE A CARPENTER”

When starting something new, search for “Things I wish I knew when starting X”

I’ve summarized the key ideas for skill learning in my journal as I do with most things I read or ideas I have.

In no particular order:

Those are some ideas that will greatly improve not only your ability to learn new skills, but your motivation to learn them because you will have measurable goals and have tangible evidence of your improvement. All the best!

Most beginners only pull halfway? Because they feel shy. They aren’t comfortable in this new situation so they tiptoe around instead of “jumping in”.

Here’s how their inner voice goes: “Let’s just pull a little and see what happens. It might work. I’ll pull harder next time.” What’s interesting is that they ended up crashing way more times than I did.

I convinced myself not to feel shy, rehearsed the move on land and in my mind many times, and was determined to simply replicate what I saw the experts doing. Two hours later, I was having a blast sailing around, while the others were still “pulling a little more to see what would happen”.

The reason I’m sharing this story with you is because it’s such a clear example of how timidity slows down the learning process.

Refuse to be shy. Don’t overthink it. Once you know what to do, do it all the way. Jump in. You will learn faster, and you will have a lot more fun in the process.

You may also be interested in the online course at Coursera Learning How To Learn, although the major lessons have already been covered in this post.

# Learning A Foreign Language

1. By far the most important resource out there is the FAQ/wiki on r/lanuagelearning. Devour it.

If you don’t know what Reddit is or don’t know how best to use it, click here.

1. My preferred method is:
1. Michel Thomas Audio Lectures
• Finish the Foundation and Advanced course.
2. Duolingo, Memrise & Lang-8
• Do the lessons on DuoLingo
• Memorise the 1000 most common words in the language from Memrise
• Write a daily journal on Lang-8
3. Immersion: Watching videos/series/movies/songs/radio in target language initially with English subtitles and shadowing and when I start to recognize the spoken words, I change to target language subtitles.

When you decide to learn a second language, a good idea by EurekaLanguageBits, is “to create urgency in my language learning process than to learn a new language from one I was also learning.”

1. Trivia apps/Games
3. Lyrics Training

## Extr@

Extr@ is a language education television series scripted in the format of a Friends-esque sitcom. It is available in many European languages – Spanish, French, German, English.