Many Lives, Many Masters PDF Summary

Many Lives Many Masters PDFThe True Story of a Prominent Psychiatrist, His Young Patient, and the Past-Life Therapy That Changed Both Their Lives

What if you have lived many times before, you just don’t remember it?

What if you can access these memories through psychotherapy and you can cure yourself of all your existing sorrows and phobias?

Who Should Read “Many Lives, Many Masters”? And Why?

“Many Lives, Many Masters” is a book that documents psychiatrist Brian Weiss’s journey of being a complete non-believer in supernatural occurrences, to a total believer in reincarnation and traveling back in past lives.

We recommend this book to everyone interested in past lives, in psychology, or is just in need of fresh and exciting experience in their lives.

About Brian Weiss

Brian WeissDr. Brian Weiss is a psychologist, bestselling author, and a speaker on many workshops and seminars. He currently holds his own practice in Miami.

“Many Lives Many Masters PDF Summary”

Be aware: what follows is a true story.

Doctor Weiss, the author and the narrator of the book is a classically trained doctor, following the traditional concepts of medicine.

Having a history of top university education, and has never in his life believed in reincarnation, channeling, and parapsychology.

I mean, what kind of a scientific doctor would believe such stuff?

Well, you are in for a surprise.

His story goes like this:

He is married, with children and teaches at the University of Pittsburgh, what else if not conservative psychotherapeutic techniques.

He becomes Chief of Psychiatry at Mount Sinai Medical Center in Miami Beach, Florida, and during his posting, he meets Catherine.

Catherine is a beautiful twenty-seven-year-old woman, with a really messed up psychological health.

She is well educated (in fact she worked at the same hospital as Weiss as a lab technician), but she is against conventual therapy, which Weiss suggests for healing her anxiety, depression and severe phobias.

Catherine has an exciting story.

During her visit to a particular art museum, along with a man she is dating, she has a somewhat weird experience.

She hears the guide lecturing the group on Egyptian history, but she intuitively knows that he is wrong about specific points, and she corrects him.

But, this is not only her imagination: it turns out that all of the corrections are correct.

Catherine has never been particularly knowledgeable about history: instead, this knowledge comes to her as a memory of her past life.

So, she decides to undergo hypnosis.

Weiss thinks that through hypnosis he can understand what is going on and as a result, he can help her cure her panic attacks.

During the sessions, he finds a few childhood traumas, but working on them does not help Catherine in any way.

On the contrary – her panic attacks are worse than ever.

The next session, Weiss tries to get her even further back to her early childhood.

However, instead of doing what she is asked to do, she starts talking about walking around in a marketplace during the middle of the 19th century.

In her memory, in her story, she is not Catherine, but an eighteen-year-old girl named Aronda, who lives in a village far from water and streams, which gathers melting snow and uses it as drinkable water.

Weiss is confused. During his practice, he has never encountered a similar case, and he has no diagnosis for what she has told him.

He knows that she is not acting, that she is not inspired by religious beliefs since she is a Catholic and Christians do not believe in reincarnation.

Most importantly of all, he knows that she is not under the influence of any drugs.

The rest of the book Weiss talks about Catherine’s various lives. They are filled up with so much detail, and rich cultural and geographical knowledge that it is impossible that they are wrong.

Catherine changes genders, age, nationality, but she always meets people from her current life who has also reincarnated and is always an ordinary person.

Understanding her past life stories makes Weiss recognize that some of the anxieties and phobias in her current experience are caused by the traumas and violence she has encountered in her previous life.

A particularly interesting part in all of his experience was the moment her past life seized to exist. In this space, Catherine became quote philosophical and knew things she could not have known as a person.

This is the speaker or speakers that Weiss calls “Master Spirits” and believes are higher consciousness. Exactly these “spirits” instructed him not to tell Catherine about his discoveries since it might undermine the success.

In any case, after a few sessions, she was cured and could function normally.

Weiss tried the same approach with several different people, and it always worked, although he believes it is not an approach that will surely work with any kind of person.

Key Lessons from “Many Lives, Many Masters”

1.      There Is Not Much We Know About Our Existence
2.      Sometimes You Have To Look Deeper to Understand
3.      The Same Approach Does Not Work The Same For Everyone

There Is Not Much We Know About Our Existence

Although Dr. Weiss was a traditional psychiatrist and could not be further away from spirituality, he encountered a situation that questioned his believed and pushed him to think more about our existence.

In reality, there is not much we know about ourselves and the world we live in so we should be open to possibilities.

Sometimes You Have To Look Deeper to Understand

At times you have to look further at specific issues so you can understand its causes. The roots of some problems are not always visible, and you need to look carefully in order to find them.

The Same Approach Does Not Work The Same For Everyone

The same approach to a specific thing does not work the same for everyone that involves him or herself in it.

It is all individual, and it does not mean that if it were beneficial for one person, it would be beneficial for the other as well.

Like this summary? We’d Like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“Many Lives, Many Masters Quotes”

Forgive the past. It is over. Learn from it and let go. People are constantly changing and growing. Do not cling to a limited, disconnected, negative image of a person in the past. See that person now. Your relationship is always alive… Click To Tweet Happiness comes from within. It is not dependent on external things or on other people. You become vulnerable and can be easily hurt when your feelings of security and happiness depend on the behavior and actions of other people. Never… Click To Tweet If you rely exclusively on the advice of others, you may make terrible mistakes. Your heart knows what you need. Other people have other agendas. Click To Tweet For truly we are all angels temporarily hiding as humans. Click To Tweet The reward is in doing, but doing without expecting anything...doing unselfishly. Click To Tweet

Our Critical Review

“Many Lives, Many Masters” is an interesting book that documents one man’s journey from nonbelief to becoming a total believer.

Reincarnation has always been such a big topic in this world, and now there is even a book that discusses it in depth.

So what are you waiting for?

   Take this summary with you and read anywhere! Download PDF:   

Focal Point PDF Summary – Brian Tracy

Focal Point PDFA Proven System to Simplify Your Life, Double Your Productivity and Achieve All Your Goals

If you are like most people, you are overburdening yourself with tasks that do not bring you significant results.

It is time that you change that.

Who Should Read “Focal Point”? And Why?

“Focal Point” is a book that teaches readers about the significance of focus and choosing one’s activities carefully.

Not everything you do in your life brings you closer to your goal, and if you want to live up to your true potential, it is important that you realize what these activities are and eliminate them from your life.

We recommend this book to all readers that feel like they are working hard, but not getting any results, as well as to those who want to simplify their professional life and make some more time for actual living.

About Brian Tracy

Brian TracyBrian Tracy is a writer, a speaker and a consultant with vast experience in business, economics, and psychology.

“Focal Point PDF Summary”

Let us tell you a story.

Once upon a time (well not that long ago actually) a particular nuclear power plant faces some technical problems.

These problems reduced the efficiency of the operation and the energy generation of the plant.

Naturally, everyone was worried.

The scientists and engineers working on the plant tried to figure out what the problem was, but without much success.

Finally, severely worried, the top management of the plant decided to outsource the problem to one of the top consultants on the topic in the country.

The expert came to the plant and walked around scribbling and taking down notes in his notebook.

By the end of the second day he had found the source of the problem: he climbed up a ladder and with a black marker x-ed one of the gauges on the plant.

After he left, the workers on the plant followed his recommendation to fix the part he marked, and in no time the plant was back to functioning in its full capacity.

A few days later the plant manager got the bill from the consultant. He asked for $ 10,000 for his services.

What? Just for placing one simple X? He must be crazy.

That is exactly what the manager thought, and he asked for the consultant to break down his price, believing it is illogical.

Soon he got the reply.

“For placing “X” on the gauge: $1.00. For knowing where to place the “X”: $9,999.”

It is a fun story, isn’t it?

But, it is much more than just fun – it teaches you to the most important concept to reaching success in your work and your life: knowing where to place the X.

Pinpointing the problems that undermine your voyage to achieving your full potential is everything!

It does not matter what aspect of life we are talking about. In each situation, you are doing things that are slowing you down or keeping you back from achieving your goals.

In order to do anything in life, you have to be clear about what you want and where you want to be. Only then you can focus your efforts and energy to achieve that.

By visualizing the end goal clearly, you will be able to much more easily determine a set of steps that will get you there.

And even more importantly, you will be able to recognize the things you do and do not bring you any actual benefit and eliminate them from your experience.

When it comes to reaching your goals, you have to find your focal point.

You can focus your energy much better if you add more things that take you toward your goal and simplify and eliminate the rest.

Just think about your current life and ask yourself which things can be simplified, or even eliminated. That way you will be able to work the same amount of time, or even less, and double and even triple your results.

Of course, in order to be able to have more time for yourself you need to learn how to leverage. In other words, success can be only achieved if you look at it as a collective endeavor.

It is impossible for you to know everything and to have all the needed skills for a certain thing.

So, you have to learn how you can use other people’s time, money, skills, knowledge, and ideas in a way that can help you reach your goals.

And, let’s not forget the most crucial point of success: you have to take responsibility for your life and your actions.

What sets apart truly successful people from all the rest is their sense of personal responsibility.

Why?

Because when you are pointing the finger at other people or external circumstances, you are not only avoiding responsibility but you are also giving away your power and control over your life.

And only when you are in control, you can get where you want to be, and you can stop waiting for things to happen, and go and do them yourself.

Key Lessons from “Focal Point”

1.      The Four Steps to a Focused Life
2.      Double Your Results and Free Up Your Time
3.      The Seven Rs of Simplification

The Four Steps to a Focused Life

There are four ways you can approach leading a more focused life. You can do more of particular things and do less of others.

You can start doing entirely new things that you have not been doing so far. And lastly, you can eliminate some things from your experience altogether.

Double Your Results and Free Up Your Time

It is possible that you do less work and have better results.

First, you need to identify which tasks and everyday actions contribute to your results the most.

Then, focus on these tasks and delegate the ones that do not affect your productivity as much.

Stop spending all your time working, and take a day off, on which you will focus solely on your personal life and yourself.

When you become comfortable with taking one day off, do not stop there! Instead, expand it, take two days, and then maybe three.

Opt for coming to a point when you take a three-day vacation every two or three months.

And lastly, do not forget to assess your activities regularly, in order not to fall into the trap of doing things that do not contribute to your results again.

The Seven Rs of Simplification

You can simplify your life by utilizing the seven Rs: rethinking, reevaluating, reorganizing, restructuring, reinventing, reengineering, and regaining control.

Like this summary? We’d Like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“Focal Point Quotes”

The acceptance of personal responsibility is what separates the superior person from the average person. Click To Tweet

Today you are paid for accomplishments, not activities. You are paid for outcomes rather than for inputs, or the number of hours you work. Click To Tweet Just as the focused energy in a laser beam cuts through steel, your ability to choose the most vital element of any situation will enable you to perform at extraordinary levels in any endeavor. Click To Tweet For most people, money means freedom, one of the highest of human values. Click To Tweet All you need is the desire to change, the decision to take action, the discipline to practice the new behaviors you have chosen, and the determination to persist until you get the results you want. Click To Tweet

Our Critical Review

“Focal Point” is a book with a simple premise, that will make you rethink how you do things and show you the right path to achieving greatness.

   Take this summary with you and read anywhere! Download PDF:   

How We Got to Now Summary

How We Got to Now SummarySix Innovations That Made the Modern World

Do you want to learn how Chinese women abort their baby girls today because the Titanic sank in 1912? Or how the bikini trend owes its existence to the Chicago sewer system of the 1860s? Or, say, how mirrors started the Renaissance?

Then you will enjoy Steven Johnson’s “How We Got to Now.”

Who Should Read “How We Got to Now”? And Why?

If you’ve ever wondered how big ideas are born, then you’ve probably come across Steven Johnson’s popular TED Talk. If you liked it – then you’ll love this book.

In fact, anyone curious about innovation and related topics will love this book. The links it continually makes are so mindboggling and implausible that you are bound to be left guessing until the very end. When we predict an inevitable “Wow.”

About Steven Johnson

Steven JohnsonSteven Johnson is a bestselling American author whose books mainly focus on the intersections between different human endeavors, especially in science and technology.

A contributing editor to “Wired,” he has also founded three now-defunct websites you may know: “FEED” (one of the earliest online magazines), Plastic.com (a popular internet forum), and outside.in (acquired by AOL in 2011).

Johnson has written nine books, and most of them have received rave reviews. “

Entertainment Weekly” included his take on the 1854 cholera outbreak in London, “The Ghost Map,” among its top 10 non-fiction books of 2006. Four years later, “The Economist” named “Where Good Ideas Come From” one of the best books of the year.

Steven Johnson himself has received similar accolades: in 2010, “Prospect” magazine chose him as one of the “Top Ten Brains of the Digital Future.”

“How We Got to Now Summary”

We’ve said it before, we’ll say it again:

Everything evolves.

However, evolution isn’t merely “the survival of the fittest.” It’s also often “the survival of the interconnected.”

You see, nothing evolves in isolation. And, consequently, symbiotic relationships are, by definition, all around us. So much so that Dorion Sagan and Lynn Margulis in “The Origins of Sex,” wrote quite aptly that “life did not take over the globe by combat, but by networking.”

Just take for example the problem ancient flowers might have had. Especially those that were living in areas bereaved of winds. With insects their only way to reproduce, they had to develop a system by which to attract them better.

Consequently, about 150 million years ago, they evolved colors and scents! And once they did that, they didn’t have to spend too much energy to be big. They were visible enough to allow themselves to be undersized.

But, this was great for insects as well – now they were able to find pollen much more easily. So, they had a better chance to reproduce themselves as well.

But it doesn’t stop there!

Because the evolution of flowers affected one specific nectarivore – the hummingbird. Because now that the flowers got smaller, the insects had an unfair advantage over them.

So as to be able to compete, the bee hummingbird – the smallest bird on earth – evolved to dwarfism. And even better – they developed metabolism and wings which allowed them to hover the same way insects do.

Ah, evolution, the greatest show on earth!

Before you scroll back to read the subtitle of “How We Got to Now” once again – no, this isn’t a book about the evolution of the natural world. It is about the evolution of human societies.

And the unsung heroes who made it possible.

Steven Johnson uses the story above to explain his central premise.

And to name it – appropriately – the Hummingbird Effect.

You already understand what it is intuitively.

Namely, that one simple innovation may open the doors to an entirely new world and launch a hundred more changes, most of them utterly unexpected.

Sometimes, making the connection between the last and the first of them may seem far-fetched; but, even so, it gives the right perspective.

And if you have an hour or so, you can have Steven Johnson explain to you his theory and few chains of unexpected connections to you in detail here:

Of course, if you have six hours, you can watch the six-part BBC series, “How We Got to Now,” which is, obviously, based on this book.

As for us – we’ll use our “Key Lessons” section to retell you the book, and, consequently, the series.

So, spoiler alert!

Key Lessons from “How We Got to Now”

1.      You Would Have Known Less About Yourself If It Wasn’t for Glass
2.      The Future of Families Goes Back to the Discovery of Frozen Fish
3.      There Are More Chinese Baby Boys than Girls Because of the Titanic
4.      Fashion Changed in the 1960s Because Chicago Was Raised in the 1860s
5.      The Railway Network Transformed the Idea of “Being on Time”
6.      Light Bulbs Saved the Whales and, in Time, Transformed the Slums

You Would Have Known Less About Yourself If It Wasn’t for Glass

Glass is so ubiquitous nowadays that you don’t even stop to think how the world would have looked without it.

Steven Johnson has:

“A world without glass would strike at the foundation of modern progress: the extended lifespans that come from understanding the cell, the virus, and the bacterium; the genetic knowledge of what makes us human; the astronomer’s knowledge of our place in the universe. No material on Earth mattered more to those conceptual breakthroughs than glass.”

You see, glass mirrors – as you know them today – didn’t exist before the 1400s. Consequently, the idea of the self-portrait didn’t exist either. And mirrors gave artists another advantage: they were now able to study perspective better.

In other words, the Renaissance owes a lot to glass and mirrors. And the Renaissance, coincidentally, was the first period of history when people became self-reflective.

Fast forward, and you have lenses and glasses – which made it possible for some people to read even deep into their old age. And for others to build telescopes and microscopes and see the invisible world all around us.

The Future of Families Goes Back to the Discovery of Frozen Fish

Clarence Frank Birdseye is not a name you hear very often. Chances are – you don’t even know who he is. And yet – soon enough, the human societies may move in a previously unforeseen direction because of his invention.

You see, Birdseye is the father of the modern frozen food industry. He discovered fast freezing while ice fishing with the Inuit.

Now, we use the same method to preserve human eggs and semen, which makes it possible for people to plan for a family even when biologically they can’t have one.

Strange, ha?

There Are More Chinese Baby Boys than Girls Because of the Titanic

Talking about the unexpected, right?

You all know the story of the “Titanic,” right? How could you not – you’ve heard it millions of times and watched at least two or three films and documentaries about it.

Neither of them mentioned Reginald Fessenden, i.e., the Canadian who was inspired by the sinking of the Titanic to invent the sonar.

Imitating the echolocatory practices of some marine animals (whales, dolphins), the sonar would have helped the Titanic locate the iceberg before hitting it.

And it also helps modern mothers to see how their babies are doing before they are even born.

However, in China, where there was a strict one-child policy until three years ago, this resulted in a 118:100 ratio between boys and girls. Meaning: people were using the ultrasound to practice sex-selective abortions.

Fashion Changed in the 1960s Because Chicago Was Raised (Literally!) in the 1860s

People tend to forget that until about a century and a half ago, every glass of water was a game of Russian roulette. The water wasn’t clean – and people died merely by drinking polluted water.

So, after six percent of Chicago’s population died from cholera in 1854, an engineer by the name of Ellis S. Chesbrough made a plan to install a citywide sewerage system, the first of its kind in the world.

His solution?

To physically raise the city on hydraulic jacks!

We’re not joking: this actually happened!

A century later, people were finally able to bathe in city rivers. And the bikini became “the atom bomb of fashion.”

The Railway Network Transformed the Idea of “Being on Time”

It may be unimaginable nowadays, but up to the middle of the 19th century, there was no way you can go from coast to coast and orient yourself in time with a single clock.

That’s because most cities had a different time, which they adjusted locally. Ten or twenty minutes between neighboring cities was not an issue back when there was no industry, working hours, or international companies.

However, once rail transport and telecommunications conquered America, “being on time” became both essential and unattainable concept.

So, William F. Allen lobbied exhaustively for a standardization. And after hundreds and hundreds of letters, he finally made it.

On Sunday, November 18, 1883 – “The Day of Two Noons” – each railroad station clock in the United States was reset and standard-time noon was reached within each of the newly devised five time zones.

A year later, the world followed.

And now – you can be somewhere “on time.”

Light Bulbs Saved the Whales and, in Time, Transformed the Slums

Before the light bulb was invented – by, basically, everybody in the world – people used candles. And these were made from wax found in the skulls of sperm whales.

Do you really have to know the rest of the story?

Fortunately, the light bulb didn’t need whales to function. And even better – it led to inventions such as flash photography. This helped Jacob Riis – a muckraker – take some photographs of the impoverished parts of the United States, specifically the Five Points neighborhood in New York.

And soon enough, the government bought the area, and instead of a neighborhood, there was a park there already by the end of the 19th century.

Scientists say that this may have saved New York from an epidemics of cholera.

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

How We Got to Now Quotes

Most discoveries become imaginable at a very specific moment in history, after which point multiple people start to imagine them. Click To Tweet Innovations usually begin life with an attempt to solve a specific problem, but once they get into circulation, they end up triggering other changes that would have been extremely difficult to predict. Click To Tweet The march of technology expands the space of possibility around us, but how we explore that space is up to us. Click To Tweet Humans had proven to be unusually good at learning to recognize visual patterns; we internalize our alphabets so well we don’t even have to think about reading once we’ve learned how to do it. Click To Tweet The larger question is, as virologist Jonas Salk once asked, ‘Are we being good ancestors?’ Click To Tweet

Our Critical Review

“How We Got to Now” is a vintage Steven Johnson. Beautifully written, it reads like a chain of interconnected stories with unexpected twists. “The New York Times Book Review” said it best:

“You’re apt to find yourself exhilarated… Johnson is not composing an etiology of particular inventions but doing something broader and more imaginative… a graceful and compelling book.”

   Take this summary with you and read anywhere! Download PDF:   

How to Create a Mind Summary

How to Create a Mind SummaryThe Secret of Human Thought Revealed

Humans are capable of doing so many things computers will never be, right?

Show me a computer capable of thinking, writing symphonies, loving, etc. – and I’ll show you a flying pig.

Don’t put your mouth where your money is, says Ray Kurzweil. Because you will need to breed a whole new race of pigs in a decade or so.

How to Create a Mind” explains why – and how – computers will start writing symphonies.

Who Should Read “How to Create a Mind”? And Why?

Ray Kurzweil’s predictions comprise the wettest of futurists’ dreams. And even though “How to Create a Mind” doesn’t state anything new of this sort, every futurist and curious SF thinker has already bought this book by now.

The rest should read it to find what all the fuss is about. Because even if you know nothing about AI and neuroscience, this may be a good time to start learning about it.

At least if you believe Ray Kurzweil and this book.

About Ray Kurzweil

Ray KurzweilRay Kurzweil is a prize-winning scientist, writer, and futurist.

A winner of MIT’s “Inventor of the Year” prize in 1988, Carnegie Mellon’s top science Dickson Prize six years later and “National Medal of Technology and Innovation” in 1999, Kurzweil has so far received at least 21 honorary doctorates, and special honors from three different U.S. presidents.

He has invented numerous things, ranging from the first omni-font OCR (optical character recognition) to the first print-to-speech reading machine for the blind, from the first flatband scanner to the first commercial text-to-speech synthesizer.

So, you could say that he’s partially responsible for the Siris, Alexas, and Cortanas you talk to on a daily basis.

Unsurprisingly, in 2002, Kurzweil was inducted into the National Inventors Hall of Fame.

He has authored numerous articles and books, including “The Singularity Is Near.”

“How to Create a Mind Summary”

Westworld’s second season premiered last night on HBO.

And we felt that there was no better moment to provide you with a summary of a book titled “How to Create a Mind.”

Especially if it is brought to you by a man who has not only been described by “Forbes” as “the ultimate thinking machine,” but who also has an entire Wikipedia article listing his predictions about the future.

And there’s more where that came from!

Ladies and gentlemen, please join us in unraveling the secret of human thought with the one and only Ray Kurzweil, aka the guy who gave humanity flatbad scanners, optical character recognition, print-to-speech reading machines, and text-to-speech synthesizers!

In a nutshell – someone who definitely knows more than most about how our brain may function, based on his work with artificial brains.

And is there a better way to start a book on thoughts other than with few thought experiments?

Let’s try them out.

First, the simplest: recite the alphabet.

Piece of cake, right?

OK, now recite it backward.

Doesn’t feel as easy, does it?

In fact, chances are, you’re incapable of reciting the alphabet backward no matter how much you try. Even though, if you think about it, you should have no problem: you know all the letters, and you’ve used them thousands and thousands of times.

And, most importantly, you just recited them the other way around!

So, what’s the problem?

We’ll get to that in a second.

But, before, try with us another thought experiment. This time, try to visualize a person you’ve seen only once or twice in your whole life. If you can’t think of any, try thinking about your short trip to the local store this morning.

Can you envisage even one single person of the few you passed by?

No, you can’t.

Kurzweil thinks that these thought experiments reveal something much more than the fact that, essentially, your memory sucks.

Namely, that everybody’s memory sucks in the same way. And that this should give us a hint on how our brain is actually doing its job.

You thought that only computers follow specific algorithms?

Guess again: you do too!

So much so that, in fact, human consciousness pioneer Benjamin Libet has proposed that even your free will may be an illusion!

Kurzweil concurs.

Since, according to him, these experiments show that your brain is also merely – OK, in strictly relative terms – doing hierarchical statistical analysis.

And by brain, we actually mean your neocortex, which, according to Kurzweil is where the magic actually happens.

We all know that the neocortex is the most advanced part of our brains and is what makes us so different from the rest of the animal world.

Now, according to Kurzweil, this is because the human neocortex contains about 300 million hierarchically arranged general pattern recognizers. And, as the thought experiments we explained above prove, these pattern recognizers aren’t interested in sounds, images, videos, or smells.

The only thing they are interested in is patterns.

That’s why you can’t recite the alphabet backward – it should be easy if your brain remembered information and data. But if your brain remembers patterns, reciting the alphabet back or playing a song from the middle is the same as starting to read a book from page 147.

That’s why you can’t remember people you’ve only seen once or twice in your life as well. In fact, police profilers intuitively know this, so they stimulate the memory of witnesses by showing them different types of eyes, brows, or mouths.

Because, as Marcel Proust taught us, there’s a particular type of memory, involuntary memory, which is triggered once an external stimulus hits the right note of the pattern.

You know what we’re talking about!

You can’t remember a song even though someone is singing the middle part of it. But, then someone sings the right sequence and the middle section falls neatly into place!

Finally, pattern recognition is why all of the memory techniques memory champions advise us to use are pattern-related. And even more – hierarchically ordered.

Now, if your brain works this way – i.e., as if an automat – shouldn’t computer scientists be capable of creating an artificial mind?

Yes, they should.

And in Kurzweil’s opinion – using hidden Markov models and genetic algorithms – they inevitably will by 2029.

Why shouldn’t they?

Intel has already devised a way to trick the limitations of Moore’s law by inventing 3D processors. Japan’s supercomputers are already capable of running 1016 calculations per second – which is just as much as a digital neocortex will need to function.

Finally, the data it should store – around 20 billion bytes (300 million patterns * 72 bytes) amounts to no more than 20 GB, i.e., the size of your USB.

Because, as it has been proven over and over again in the past – whether in science or art – it’s not the amount of data that’s important; it’s the actual and potential interconnections inside it.

So, brace for it – Kurzweil claims that AI humanoids indistinguishable by brain power from humans will become a reality in less than 12 years.

We guess the remaining question at this point is: should you believe Kurzweil?

Well, remember the list with predictions we mentioned at the beginning of this summary? It was made back in 1989. And in October 2010, twenty years later, Kurzweil published a PDF titled “How My Predictions Are Faring.”

In 147 pages, the document lists as many predictions. 12 of them are deemed to be “essentially correct,” 17 “partially correct” and 3 – “wrong.”

As for the rest 115?

Let us write this in all caps because it’s that important:

ENTIRELY CORRECT.

Ladies and gentlemen, set your watches: we’re about 12 years away from real-life “Westworld.”

For better or for worse, the countdown commences.

Key Lessons from “How to Create a Mind”

1.      Pattern Recognition Theory of Mind
2.      Welcome to Searle’s Chinese Room: How Do You Know You’re Not a Machine?
3.      The Untethered Artificial Mind: The Artificial Mind Which Learns

Pattern Recognition Theory of Mind

How do we think?

Do we think through data, logic, images, sounds, smells?

Neither, says Ray Kurzweil: we think only and exclusively through patterns.

Our neocortex contains about 300 million general pattern recognition circuits which hierarchically structure our memory and experiences.

In other words, if we translate this into practical example (say, how we read), the process looks something like this.

Namely, some of these recognizers are low-level and see only straight and diagonal lines. But, they transmit this information to the higher echelons which are then capable of recognizing letters. These pass on the message to the word-level recognizers, etc. etc.

The information moves back and forth and, based on previous patterns, in time, the recognizers learn to predict the info ahead. That’s how speech recognition works, and that’s why sometimes you see transcribed YouTube captions revealing words before you hear them.

That is your brain as well.

And yes – it gets a bit strange from here on.

Welcome to Searle’s Chinese Room: How Do You Know You’re Not a Machine?

You see, back in 1980, philosopher John Searle made the distinction between weak AI and strong AI based on a simple experiment.

Say you make a program capable of taking Chinese characters as inputs, analyzing them profoundly and giving the expected outcome. And say this program is so convincing that even a Chinese can’t see anything wrong with it and, thus, it passes the Turing test.

The question is: does the program really understands Chinese?

Searle argued against this, by claiming that if he is locked in a room with the machine’s in-programmed manual, and receives the same inputs under the door, he should be able to give the same answers back by merely following the same instructions the machine does.

However, he doesn’t speak a word of Chinese.

Kurzweil says: OK, that may be true.

But what if your brain works the same way?

Let’s not forget that Watson destroyed the best humans in Jeopardy!

In Jeopardy!

The Untethered Artificial Mind: The Artificial Mind Which Learns

It’s time you stopped thinking about machines in terms of programs – unless you start thinking about yourself in the very same way.

In other words, our brains are nothing less – or more – than a pattern recognizing structures. However, this is such a powerful method to acquire new information that it has got us – humans – to a place where we are capable of creating other creatures similar to us.

Because once we perfect a brain capable of recognizing patterns (and we’re already there: think speech recognition), we will essentially create a machine capable of teaching itself. And since a machine’s neocortex can be improved, in time, we will be able to develop machines which will be vastly superior to us.

That’s right: we’re talking about a new species.

Homo deus.

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“How to Create a Mind Quotes”

In mathematics you don’t understand things. You just get used to them. (via John von Neumann) Click To Tweet We are a pattern that changes slowly but has stability and continuity, even though the stuff constituting the pattern changes quickly. Click To Tweet The evolution of animal behavior does constitute a learning process, but it is learning by the species, not by the individual, and the fruits of this learning process are encoded in DNA. Click To Tweet Human beings have only a weak ability to process logic, but a very deep core capability of recognizing patterns. To do logical thinking, we need to use the neocortex, which is basically a large pattern recognizer. Click To Tweet Philosophy is a kind of halfway house for questions that have not yet yielded to the scientific method. Click To Tweet

Our Critical Review

“How to Create a Mind” may be uneven and repetitive at times, but, even so, it’s exceptional. Some have deemed its subtitle a bit overpromising, but to others, the book actually manages to give us the most complete theory on how we may think.

Now, if Kurzweil is right about that, then creating an artificial mind is not far ahead. And if that is true, then you reading this book should become a reality in the following weeks.

   Take this summary with you and read anywhere! Download PDF:   

Forensics Summary

Forensics SummaryWhat Bugs, Burns, Prints, DNA, and More Tell Us About Crime

Have you ever watched “Wire in the Blood”?

If not – you should. It’s a crime drama television series, so, let’s face it, you’ll be hooked by the second episode.

If so – don’t we have a treat for you! The creator of the character Dr. Tony Hill, Val McDermid, has written a non-fiction book about forensics.

And we have profiled it – to provide you with the “Forensics” summary.

Who Should Read “Forensics”? And Why?

If you like to read detective novels or watch CSI-themed shows, then “Forensics” is one of the best books we can recommend to you.

Really!

It’s got everything from history to practice, and, as a bonus, it’s written by a famous writer.

So, trust us, it doesn’t get much better than this.

About Val McDermid

Val McDermidVal McDermid is a Scottish crime writer, best known for the novels featuring Dr. Tony Hill, an emotionally abused criminal psychologist who uses role-play and intuition to solve crimes.

McDermid has authored ten Tony Hill novels, starting with “The Mermaids Singing” in 1995 (which was referenced in Stieg Larsson’s “The Girl with a Dragon Tattoo”) and including “The Last Temptation,” “Beneath the Bleeding” and “Fever of the Bone.”

In addition, she has also created three more series of books: one revolving around Lindsay Gordon, a private investigator, another around Kate Brannigan, clinical psychologist, and a fourth one, around DCI Karen Pirie.

Find out more at https://www.valmcdermid.com/

“Forensics Summary”

Ever since Poe’s C. Auguste Dupin and Arthur Conan Doyle’s Sherlock Holmes, there are few things we like more than detectives solving crimes.

What’s not to like?

There’s a murder mystery, a genius trying to fit all the pieces of the puzzle, and so many things you can learn about how your body will decompose once you’re dead.

OK – maybe the last part isn’t the most fun.

It is, however, probably the most important.

Don’t believe us?

Just watch “Bones” – all 246 episodes of it! Or bear with us for few minutes to learn the history and the practices of forensic scientists.

As you might have guessed, forensics isn’t such a new trade. It goes back to a guy who is appropriately remembered as “Sherlock Holmes of France” and who formulated the first principle of forensics: “Every contact leaves a trace.”

His name?

Edmond Locard.

(An interesting fact: he started forensics because of Sherlock Holmes; and an even more interesting fact: he also met with Sir Arthur Conan Doyle.)

However, the real beginning of modern forensics is associated with an American, Frances Glessner Lee, the first female police captain in the history of the United States, and “the mother of forensic science.”

Her contribution?

Among other things, she created the Nutshell Studies of Unexplained Death, a series of 20 dioramas which can be used to teach students the basics of forensics.

And they look something like this:

forensics pdfNow, being a forensic scientist can mean many things.

After all, if you’ve learned anything from CSI shows, it’s probably that there are numerous different ways to kill a person. Consequently, there should be numerous different types of forensic scientists, specializing in a different forensic category.

Some, for example, are entomologists by profession – because, well, sooner or later, you are going to be eaten by insects and there’s nothing you can do about that.

Specifically, you should be aware of the blowfly, which will colonize your body the quickest and whose maggots transform into flies in approximately two weeks.

Beetles arrive later and remove the flesh. Moths and mites remove the hair only afterward.

And that’s how forensic entomologists can guess when a murder has happened

Next, we move to the forensic pathologists – which date back to Roman times. These are the guys who study human bodies and the ones who can estimate the time of death based on the vapors a body emits during decomposition.

Yes, that’s a thing. If you’ve ever wondered, you’ll emit about 400 different smells after you die.

Now, since you’re not a forensic pathologist, that’s an interesting fact you won’t have any use of whatsoever! But, also a fact which will undoubtedly make some people go “wow” at some friends’ gathering.

Forensic toxicologists deal with poisons. And ever since Mathieu Orfila published the gigantic “General System of Toxicology” in 1813, they have gotten so good that even Agatha Christie would shudder at the thought of being unable to name some poison the perfect weapon.

We can go on.

Forensic anthropologists help with identification – since they know full well how your skeleton looks like at any age.

And they work closely with facial reconstruction specialists, who have helped police forces worldwide to finally solve seemingly unsolvable mysteries.

Forensic psychologists are essential when you need someone to go deep in the mind of the murderer based on the murder, thus narrowing down the list of suspects.

And digital forensics has evolved to a point when you can’t really tell the difference between real life and a CSI show. All those SF-like crime timelines reconstructions?

No more fictional than the gruesome murders themselves.

However, the real breakthrough in forensics came when some seriously smart people realized that the friction ridges on our fingers are unique.

Fingerprinting began with a Scottish missionary called Henry Faulds.

While accompanying a friend archaeologist in Japan – where he had previously established the first English mission – Faulds noticed that the finger imprints left by ancient craftsmen were discernable even centuries later.

He compared his fingerprints to those of his friend and realized that they were different!

Convinced that every human has a unique fingerprint, he contacted Charles Darwin for a biological confirmation. Darwin passed the task to his equally brilliant cousin, Sir Francis Galton, who, in 1892, gave the world one of the first books on the subject, “Finger Prints.”

A Croatian-born Argentine anthropologist by the name of Juan Vucetich realized the potential of fingerprinting as a forensic tool. And soon, Francisca Rojas, who had killed her two children and tried pinning the murder on her neighbor, became the first woman convicted for a murder based on a bloody fingerprint she had left on the bedroom door.

In 1892, suddenly, the world became a bit more just.

Key Lessons from “Forensics”

1.      Forensics Owes a Lot to Sherlock Holmes
2.      Bugs, Smells and the Time of Death
3.      The Uniqueness of Fingerprints Was Discovered by Accident

Forensics Owes a Lot to Sherlock Holmes

You know the old Aristotelian adage: art imitates life?

Well, in 1889, Oscar Wilde wrote an essay in which he claimed that “Life imitates Art far more than Art imitates Life” (his caps).

Probably he didn’t know that at about the same time, a French criminologist, Edmond Locard, would establish forensics as a field of science because he was enamored with Arthur Conan Doyle’s writings.

Appropriately, he is today remembered as the “Sherlock Holmes of France.”

And as the person who gave forensic scientists the Locard’s exchange principle: “every contact leaves a trace.”

Bugs, Smells and the Time of Death

Forensic scientists use many methods to discover the time of death of a particular victim. However, the two most interesting ones – or, at least, the two most disgusting ones – are via bugs and smells.

And not just any bug – and not just any smell.

Namely, the gold standard in forensics when it comes to bugs is the blowfly. Because it can detect slightest traces of blood from over 100 meters – and because it isn’t a rare bug – it’s the insect which colonizes dead bodies the quickest.

And it takes about two weeks for the larvae from the eggs it lays in the corpse to transform into flies. So, scientists know how long someone is dead by analyzing at which stage the maggots have developed when a body is found.

And it helps that another group of forensic scientists are especially good with their noses. They have detected about 400 different types of smell a body emits during decomposition.

Think of it… on second thought, no – don’t ever think of it.

The Uniqueness of Fingerprints Was Discovered by Accident

Have you read “The Name of the Rose”?

Well, real-life fingerprinting features a monk-detective as well.

Dr. Henry Faulds, a Scottish missionary in Tokyo, discovered that fingerprints differed between individuals when he accompanied a friend of his on an archaeological journey. He discerned that dusting Japanese clay fragments with powder makes finger impressions visible.

And when he compared them to each other – in addition to comparing his own to those of his friend – he also discovered that fingerprints are unique.

He contacted Darwin and Darwin contacted his cousin, Sir Francis Galton. Galton devised a methodology and classification.

And soon enough, an Argentine police officer by the name of Juan Vucetich caught the first murderess in history based on the fingerprints she had left on the crime scene.

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“Forensics Quotes”

The discipline is based on one grisly fact: a corpse makes a good lunch. Click To Tweet We make high demands on the people we expect to deliver justice, and we don’t always appreciate how much it eats away at them. Click To Tweet No two bodies will decompose in the same way, and at the same rate. You can have two bodies that are literally six feet apart and they will decompose in entirely different manners. Click To Tweet Any man’s death diminishes me, because I am involved in mankind. (Via John Donne) Click To Tweet To begin depriving death of its greatest advantage over us, let us adopt a way clean contrary to that common one; let us deprive death of its strangeness; let us frequent it, let us get used to it. (Via Montaigne) Click To Tweet

Our Critical Review

Now, let’s face it – even though you’ve spent countless hours watching a show after show on forensics-related topics, you’ve never really learned anything, right?

That’s because you watch all of those shows to enjoy and have fun. Rarely do you watch them to learn.

“Forensics” will fill this void in your life.

It recounts the history of the discipline (across many related fields), coupled with few cases and names you’re bound to remember once you find out how they contributed to the foundation of some of the techniques used in your favorite TV shows.

It’s real-life CSI – which makes it even better than a TV show!

   Take this summary with you and read anywhere! Download PDF:   

SuperFreakonomics Summary

SuperFreakonomics SummaryGlobal Cooling, Patriotic Prostitutes, and Why Suicide Bombers Should Buy Life Insurance

Let’s dive right into it!

Who Should Read “SuperFreakonomics” and Why?

“SuperFreakonomics” will reveal how social subjects are correlated with the economy and will show you how you can make use of statistics in every field of life.

We recommend it to all statistics lovers, to everyone worried about pressing issues such as terrorism and global warming and to all people to want to understand how the modern world functions.

About Steven D. Levitt & Stephen J. Dubner

Steven D. LevittSteven D. Levitt is an American economist, currently teaching at the University of Chicago, specializing in researching corruption and crime.

Stephen J. DubnerStephen J. Dubner is an American journalist and writer, mostly researching on economic topics.

“SuperFreakonomics Summary”

There are so many pressing problems in today’s world and not enough solutions.

Why is that so?

Aren’t there equally as many smart people who are supposed to be able to solve any issue?

There are, indeed. But that does not mean that they can easily find a solution to problems.

The reason behind their failure is not the lack of intelligence, but the lack of proper data.

Many researchers rely on the imperfect stories of individuals and incorrect recollections of events, which leads to many mistakes.

So, what should they do instead?

Rely on statistics.

Statistics are objective and empower its users to come up to more correct conclusions.

As much as you try to find out what makes people tick, you cannot get into their heads and find out the true reason.

However, people, no matter where they come from, almost always react to incentives.

So, it seems that society can change the behavior of individuals by giving them something in return.

Sadly, there are exceptions to every rule, and there are exceptions to the success of incentives as well.

Often, incentives do not work as planned, and they can have rather damaging results.

This is because of the law of unintended consequences, as the authors name it.

The way that we can make incentives work is by predicting people’s reactions before the incentives take place.

But didn’t we just say that we cannot get into people’s heads?

We did, but that does not mean that we cannot draw conclusions about their drivers and behaviors using statistics.

By collecting enough data, and analyzing it, it is possible to understand the reasons for the collective behavior.

Gathering data does not only help with problems that we want to solve, but it also helps us see problems that until that point may not have been apparent.

Solving such problems that are not visible to everyone leads to disruptive innovation, which changes the course of society.

Take global warming for example.

We all know how damaging global warming is, and how dangerous it is for this planet.

Yet it seems that society does not do much about it.

The problem is that it is not yet clear what causes global warming. We all know that it is human activity, but we do not know exactly which one.

As a result, it is hard to debate over it and present objective facts. All debates around global warming are on the basis of myths that portray the industry or the cars as the main reasons for global warming.

Yet, some studies show that the reasons for this phenomena actually lie someplace else.

Did you know that the planet’s ruminants, cows especially, are the source of over 50 percent of the greenhouse gasses produced? This is more than the whole transportation industry!

However, although there are some indicators for the reasons global warming occurs, extensive studies cannot be done, since it is a very complicated phenomenon, and scientists are not able to do any experiments, which means that they cannot test and know for certainty what can minimize this occurrence.

Another problem is that negative externalities exist when it comes to this topic. Negative externalities are all effects which are created by a group of people but felt by entirely another group.

The problem with these negative externalities is that when people who are responsible for an unwanted event do not feel its consequences, it is unlikely that they will change their behavior.

Also, all the tries to influence people by just raising their awareness are not giving any big results, since as we already said, many people react to the right incentives.

However, there might be a quick fix for this problem.

What is it?

Geoengineering that allows for influencing the global climate system.

Scientists have found out that it is possible to cool down the planet by emitting sulfur dioxide in the stratosphere – in a volume much higher than the industry does.

Wait, what?

The solution to pollution is more pollution?

Yes, we know that it may sound counterintuitive, but that is what statistics does: it allows its users to look at problems from different angles, and find solutions where they would not have thought they could find them in the first place.

Key Lessons from “SuperFreakonomics”

1.      All Incentives Come with Side Effects
2.      Solutions to Tricky Problems are Hard to Find
3.      There is No Such Thing as Too Much Data

All Incentives Come with Side Effects

People react to incentives and may be driven by them, but even the best incentives may not work as it was planned in the first place and all of them are accompanied by side effects.

To explain this occurrence, Dubner and Levitt have come up with the phrase: the law of unintended consequences.

Solutions to Tricky Problems are Hard to Find

You may think that you can find solutions to even the most complex problems if you collect enough data, but that might not always be the case.

At times, the data you collect will not be the right one, and the solution will lie in the data you forgot to include in your research.

Also, many times it will be much easier to find a way to prevent an issue from occurring, than solving it once it happens.

There is No Such Thing as Too Much Data

When it comes to data, there is no such thing as collecting too much. Remember what we said in the previous key lesson – sometimes the solution hides in the data you did not collect.

So make sure you collect a lot of information, in order to come to solutions more easily and intuitively.

Like this summary? We’d Like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“SuperFreakonomics Quotes”

And knowing what happens on average is a good place to start. By so doing, we insulate ourselves from the tendency to build our thinking - our daily decisions, our laws, our governance - on exceptions and anomalies rather than on reality. Click To Tweet Most of us want to fix or change the world in some fashion. But to change the world, you first have to understand it. Click To Tweet Politicians have all sorts of reasons to pass all sorts of laws that, as well-meaning as they may be, fail to account for the way real people respond to real-world incentives. Click To Tweet People are people, and they respond to incentives. They can nearly always be manipulated--for good or ill--if only you find the right levers. Click To Tweet Deliberate practice has three key components: setting specific goals; obtaining immediate feedback; and concentrating as much on technique as on outcome. Click To Tweet

Our Critical Review

This book offers an interesting perspective on some social subjects, such as global warming, terrorism, and prostitution.

It is an economic view on subjects that you may think to have nothing to do with the economy, and explains why statistics can be and should be used in every field, no matter its nature.

   Take this summary with you and read anywhere! Download PDF:   

How Not to Be Wrong PDF Summary

How Not to Be Wrong PDFThe Power of Mathematical Thinking

What if someone came to you right now and told you that you are a mathematician by design? And what if that someone claims that by learning few more tricks from his book, you can at least learn how to be tricked less by the Greatest Mathematician of All, Life.

Jordan Ellenberg is the someone from the previous paragraph. And you can read all about the aforementioned tricks he knows in our “How Not to Be Wrong” summary.

Who Should Read “How Not to Be Wrong PDF”? And Why?

Mathematics doesn’t need to be all equations and no language. Jordan Ellenberg proves that it can be the other way around. So, you don’t need to be interested in math or logic to read this book. All you need to be interested in is common sense.

Because “How Not to Be Wrong” aims to teach you that what you find in math schoolbooks is actually common sense neatly broken down into comprehensible mathematical symbols. Ellenberg translates them into examples so that you can understand them better.

About Jordan Ellenberg

Jordan EllenbergJordan Ellenberg is a professor of mathematics at the University of Wisconsin-Madison.

A child prodigy, he has received a Ph.D. from Harvard University and an MFA in creative writing from Johns Hopkins. He is a regular columnist for “Slate” and has written few interesting articles for “New York Times” and the “Wall Street Journal.”

In addition to “How Not to Be Wrong,” Ellenberg has also authored a novel, “The Grasshopper King.”

“How Not to Be Wrong Summary”

Let’s just say that we’re targeting most of our readers if we start our summary with a sentence along these lines:

You don’t like math, do you?

And you are reasonably sure that it has no practical value whatsoever?

Don’t try to prove me wrong on the latter one, you warn us, because I know that even a genius mathematician of Richard Feynman’s stature felt that math was a bit abstract to his taste!

OK – we dig you! It’s not like we solve equations in our free time. And no – we don’t have a T-shirt with an Euler’s identity print! (Though, man, they sure look funny…) However, Jordan Ellenberg really convinced us that math is not a throwaway matter. So, at least give him – and us – a chance! Because we will try to prove you wrong.

Firstly, by claiming that you already know a lot more math than you care to admit (or are aware of, for that matter); and secondly, by demonstrating you that if you learn a bit more, you can basically cheat your way through life.

But, first thing’s first: you, the unconscious mathematician.

Now, Jordan Ellenberg has a funny way of describing math, and his definition is a good way to start. Namely, he claims that math is “the science of not being wrong.” A bit pretentious, you think? Maybe, but like almost everything else in math – not wrong.

You see, after Einstein, we started questioning even physics, and everything suddenly was much more relative than before. Math survived through this as well, as basically the only exact science of them all.

Speaking of surviving – here’s an excellent way to demonstrate to you how its exactness works. And how it’s not a purely mathematical matter, but common-sensical as well.

At one point during the Second World War, the U.S. Army intended to protect its planes better. In order to decide where the manufacturers should add more armor – they couldn’t add everywhere since that would have caused more fuel consumption – they examined thoroughly the damages on all of the returned planes.

The result?

As you can see yourself from Louie Zamperini’s plane, it was the fuselage which suffered the most, having far more bullet holes than the planes’ engines. After the study, the U.S. Airforce decided to reinforce the fuselage; and it would have done exactly that, if a mathematician by the name of Abraham Wald hadn’t realized that the seemingly straightforward study was flawed.

Namely, it didn’t take into account the bombers which were shut down. Those, Wald claimed, were surely hit much more in their engines.

The U.S. Airforce made a logical error we now call survivorship bias. In a nutshell: focusing merely on the things that have survived a process gives incomplete results.

Yes, this is math too. And, as you can see, it can save numerous lives. Not to mention some serious blushes.

And you know – and readily use ­– few similar techniques to tackle everyday issues. Or, unfortunately (if you don’t know them), you risk being tackled by them. Or, to use Taleb’s phrase, your risk being “fooled by randomness.”

For example, do you know that acting upon advices in books written by successful investors makes you a victim of the survivorship bias explained above?

After all, there are many others who failed to get rich at the market, and you don’t know any of those guys! Who knows how many of them are in the world right now!

Just like the World War II planes, Warren Buffett and Charlie Munger may be the exceptions.

Also, are you aware that the only thing a monkey needs to write the complete works of Shakespeare is a typewriter and infinite time? Just as well, many other things create patterns through sheer noise.

Believing in conspiracy theories, for example, may mean finding something which is there merely because you are a human and you’re built to see patterns even where there are none.

Finally, do you know that even a majority vote can be rigged if your agenda maker is savvy enough? It’s called the Condorcet paradox, and you may have been a victim of it once or twice.

Especially if you were living in Florida in 2000 and voted for Ralph Nader.

Still not interested in math problems?

Key Lessons from “How Not to Be Wrong”

1.      Math Is the Science of Not Being Wrong
2.      Be Wary of the Survivorship Bias – Especially When You’re Reading Books
3.      You Can Rig Elections and Majority Votes

Math Is the Science of Not Being Wrong

Jordan Ellenberg has a funny way to define math. He claims that it is the science of not being wrong.

You may notice that he doesn’t mention where – it’s just not being wrong, period.

And he has a right to say that since math is basically never wrong. What it actually deals with is the underlying laws and patterns which govern the chaos around us. In other words, if you’ve ever argued against your friend’s claim that Steph Curry had a hot hand that February night against the Knicks back in 2013 – you’ve actually practiced math.

Because, as far as mathematicians are concerned, there’s no such thing as hot hands in basketball – or anywhere else. It’s just a case of taking into consideration fewer factors than you should. Or, in layman’s terms, a case of being wrong.

Be Wary of the Survivorship Bias – Especially When You’re Reading Books

Math problems have many practical applications. One of the most famous examples is the survivorship bias. It means that studies often focus only on the people or things which have survived through a process. And the survivors don’t necessarily describe the process in its entirety.

What does this mean in practice?

It means that thousands of people have tried becoming investment gurus using Warren Buffett’s strategies, but most of them probably failed. However, their failures are invisible to us, since these guys are not on TV and their books don’t sell a million copies.

The conclusion?

Warren Buffett’s strategy may be a good one – but he may have been merely lucky.

You Can Rig Elections and Majority Votes

This one’s scary!

With enough info, mathematicians are capable of creating a scenario where you’ll be voting for something entirely different from what you actually defend or are firmly against. Moreover, sometimes you can be tricked into voting for the exact same thing you would least want to vote for.

How?

Consider the 2000 Florida elections. The final results stated that Bush won 48.85 percent of the votes, Al Gore 48.84 percent (just 537 votes fewer) and Ralph Nader merely 1.6 percent. Common sense says – well, the majority won.

However, math says that that’s wrong. Because almost all of the people who voted Nader would have chosen Al Gore if there were only two candidates. So, Bush won even though between him and the second-best candidate, the majority preferred the latter.

Strange?

Try some counter-intuitive paradoxes such as the Monty Hall problem! The best part is that it doesn’t matter what you or anybody else thinks. What matters is that math can’t be wrong.

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“How Not to Be Wrong Quotes”

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. Click To Tweet A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object. Click To Tweet Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. Click To Tweet Dividing one number by another is mere computation; knowing what to divide by what is mathematics. Click To Tweet The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we’d now call mathematics, things we’d now call religion, and things we’d now call mental illness. Click To Tweet

Our Critical Review

“How Not to Be Wrong” is one of the very few books written by an accomplished mathematician who happens to be a novelist as well. So, in other words, here’s math for you – explained in the best, writerly manner possible.

And when that happens, math can be a magical thing. There’s a reason why Bill Gates included “How Not to Be Wrong” in his 2016 “5 Books to Read This Summer” list. It is, simply put, a great, great book.

   Take this summary with you and read anywhere! Download PDF:   

Genius Summary

Genius SummaryThe Life and Science of Richard Feynman

Do you know who Richard Feynman was? If you do, then you need no reason to read ahead. If not – then you are missing a lot.

Either way, James Gleick’s “Genius” is a prerequisite, “a terrifically readable… jewel-like biography” of one of the greatest and most unconventional scientists in history.

Who Should Read “Genius”? And Why?

Just like Richard Feynman himself, “Genius” is a book which may make you fall in love with science all over again. Everyone who already is will enjoy this book immensely and readily recommend it to others. And there is no better place for the rest to start than “Genius.”

About James Gleick

James GleickJames Gleick is an American historian of science, considered by many to be “one of the great science writers of all time.”

He has written eight books, three of which (including “Genius”) have been finalists for “The Pulitzer Prize” and “The National Book Award.”

He is probably most famous for his 1987 classic “Chaos: Making a New Science” and the international bestseller “The Information: A History, a Theory, a Flood.”

“Genius Summary”

Six years before he died, Julian Schwinger – an American Nobel-Prize winning physicist – wrote a little epitaph for a colleague (and, mind you, a former rival) which may seem like an appropriate introduction to our summary:

“An honest man, the outstanding intuitionist of our age, and a prime example of what may lie in store for anyone who dares to follow the beat of a different drum.”

True, it all sounds neat and tidy, but epitaphs are such: of the dead, we should say nothing but good, believed the Romans. However, in this case, the epitaph may be more interesting not because of what is inside it, but of what is not.

You may understand what we’re thinking better if we finally reveal to you the name of this mystery person: Richard Feynman, an American genius, scientist extraordinaire, and a guy whose list of memorable quotes is longer than a day on Venus. Oh and – dare we forget? – one of the two other guys who shared the Nobel Prize in Physics with Schwinger in 1965.

So, why did Schwinger decide to use the word “intuitionist” instead of “theoretical physicist” and speak of Feynman’s integrity and unconventionality instead of his scientific achievements?

Well, if taken as rhetorical, the question may give you the answer right away. However, we intend to build a little upon it, by sharing with you some interesting tidbits from Feynman’s biography as depicted in James Gleick’s brilliant biography, succinctly and fittingly titled “Genius.”

Richard Feynman was born on May 11, 1918, the son of Lithuanian Jews. His father, Melville, had scientific aspirations himself, but due to his ethnicity, he gave up on that dream and ended up working as a salesman. However, he kept the dream alive when it came to his child: if I ever have a son, he once prophesized, he will become a scientist.

Well, Feynman didn’t get off to a great start. He hadn’t uttered a single word during the first three years of his life. Though, that may have been a sign in itself – after all, Einstein was a late talker as well.

Among many others, Feynman shared another important trait with Einstein: he was capable of visualizing things pretty easily. And, retrospectively, it was probably all his father’s fault: he always explained to him things in a matter which made complex ideas seem simple. Feynman has been now remembered by many for this capability.

He exemplified this best during his high school years when he was able to solve serious mathematical problems without using a single formula. He just visualized himself in the midst of the conundrum – and, suddenly, he knew more about it than anyone else.

When the time for college came, Feynman turned his attention from math to physics. At this point, the first grew a bit too abstract to his taste; the latter was all but the perfect field for some with his understanding of equation and visualization capabilities.

Unsurprisingly, at MIT, he excelled in this new discipline. Though, to be perfectly frank, that’s where his excellence began and ended. Because you see, Feynman didn’t care too much for the social sciences. He hated art history and English and loathed music and philosophy.

So, he did what 90% of you have done at some point in their education: he cheated. And he cheated really bad.

So bad, in fact, that when he applied for a Princeton scholarship, he was nearly rejected, even though he attained a perfect score on the graduate school entrance exams in physics. Needless to add – this was an unprecedented feat, which means that nobody between 1746 and 1939 had done it.

Feynman was that good.

And, cheating aside, he got that Princeton scholarship – on the condition that he would not marry until obtaining a Ph.D. And he didn’t, though he was already engaged and living one of the greatest love stories of the 20th century.

Be warned: your room may get dusty and your eyes a little wet in a second.

You see, ever since his days at New York City’s Far Rockaway High School, Feynman had been in love with Arline Greenbaum. His high school sweetheart, however, was a poor girl, so she had to give – ah, the irony! ah, the power of love! – piano lessons during the day and art instructions at night to earn enough money. This wore her out, so she started feeling a bit sick at the time Feynman was acing his Princeton entrance exams.

After a series of incompetent diagnoses, it was discovered that Arline had lymphatic tuberculosis – when it was already too late. Even though Feynman’s parents bitterly protested, Richard married Arline just after obtaining his Ph.D.

In the meantime, he was recruited to work on the Manhattan Project, so he took Arline to a sanatorium in Albuquerque to be close to her and be able to visit her every weekend using the car of Klaus Fuchs (yes, the guy who later turned out to have been an infiltrated Soviet spy).

Just two months before the United States dropped the nuclear bombs on Japan, Arline died. One and a half years later, after his father Melville left the world as well, Feynman wrote Arline a letter which is kind of difficult to read without wet eyes. “You only are left to me. You are real. My darling wife, I do adore you. I love my wife. My wife is dead.”

“Please excuse my not mailing this,” he added in the postscript with a recognizable doze of humor, “but I don’t know your new address.” The letter would remain sealed from 1947 until Feynman’s death in 1988.

In-between, Feynman would become a legendary professor, a joker, and a Nobel Prize winner. Supposedly, when the press awakened him at 3:45 AM with the news, and asked him how he felt about winning the prize, he quipped: “Well, I could have found out later this morning…

And that event sums up brilliantly the life of a man as exceptional as any. As Freeman Dyson said, Feynman was “half genius and half buffoon” who kept “all physicists and their children amused with his effervescent vitality.”

Three decades after his death, he is still an inspiration to many.

A genius of the highest rank.

Key Lessons from “Genius”

1.      Know How to Solve Every Problem That Has Been Solved
2.      Know What You’re Bad at and Don’t Bother with It
3.      Always Find Some Time for Clowning

Know How to Solve Every Problem That Has Been Solved

Richard Feynman died on February 15, 1988. At the time of his death, this is how his blackboard looked like. If you’re having trouble reading it, it says two things: “What I cannot create, I do not understand” and “Know how to solve every problem that has been solved.”

Whether you’re an artist or a scientist, reverse engineering is a powerful tool. And there you have it – as the last lesson from one of history’s greatest professors.

Know What You’re Bad at and Don’t Bother with It

Now, this may sound strange coming from a person who taught himself to play drums and draw satisfactory sketches of nudes, even though he didn’t like music or art.

However, he did both of these things at a later stage, and, even though he once bet Arline that he would learn to play “The Flight of the Bumblebee,” he ended up failing dismally. The point is: Feynman was a genius at math, but genius is not transferable. In other words, he could allow himself to fail in so many different fields.

Because that was the only way he could excel in the one that really mattered.

Always Find Some Time for Clowning

Freeman Dyson, an English-born American physicist, was five years junior to Richard Feynman and a life-long friend of his.

In 2005, he wrote for “The New York Review of Books” an article which tried pinpointing the reason because of which Feynman became a public icon, “standing with Albert Einstein and Stephen Hawking as the Holy Trinity of twentieth-century physics.”

His answer?

“Einstein, Hawking, and Feynman shared an ability to break through the barriers that separated them from ordinary people. The public responded to them because they were regular guys, jokers as well as geniuses.”

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“Genius” Quotes

Maybe that’s why young people make success. They don’t know enough. Because when you know enough it’s obvious that every idea that you have is no good. Click To Tweet I was born not knowing and have only had a little time to change that here and there. (via Richard Feynman) Click To Tweet The spirit of Edison, not Einstein, still governed their image of the scientist. Perspiration, not inspiration. Mathematics was unfathomable and unreliable. Click To Tweet Feynman resented the polished myths of most scientific history, submerging the false steps and halting uncertainties under a surface of orderly intellectual progress, but he created a myth of his own. Click To Tweet The adult Feynman asked: If all scientific knowledge were lost in a cataclysm, what single statement would preserve the most information for the next generations of creatures? Click To Tweet

Our Critical Review

Come on, it’s Richard Feynman!

The guy has written quite possibly the best autobiography (being a collection of anecdotes) by a scientist ever written. And it has the best title too: “Surely You’re a Joking, Mr. Feynman!”

Now, why would I need to read a biography?

That in itself may be one of the reasons. Another may be that James Gleick is one of the best science writers in history. And a third one that “Genius” is the biography Richard Feynman deserves.

As Amazon’s review states concisely: “a book you must read.” We emphasized the must.

   Take this summary with you and read anywhere! Download PDF:   

Habits of a Happy Brain Summary

Habits of a Happy Brain SummaryRefrain Your Brain to Boost Your Serotonin, Dopamine, Oxytocin, & Endorphin Levels

You probably think that happiness is all about singing in the morning and cleaning your closets, right? Well, it may be so, indeed! But, the underlying truth is much less poetic: it’s all down to chemicals. And not too many of them, either.

You’ve read many books on the philosophy of happiness. “Habits of a Happy Brain” is one of the few books dedicated on the biology of happiness. And while there are always alternatives in philosophy, there is surely no escape from biology.

Who Should Read “Habits of a Happy Brain”? And Why?

Since it deals with happiness, “Habits of a Happy Brain” is a book which should interest most people; since it also deals with mammalian biology, it’s a book which should tickle the fancy of specialists who are trying to find out the biological explanation of happiness.

Finally, since it’s one of the more exciting books to stem from the positive psychology movement, it’s undoubtedly an essential read for those who have read and liked the writings of Martin E. P. Seligman, Mihaly Csikszentmihalyi or even Jonathan Haidt.

About Loretta Graziano Breuning

Loretta Graziano BreuningLoretta Graziano Breuning is the Founder of the Inner Mammal Institute and Professor Emerita of Management at California State University.

She obtained her BA from Cornell and her Ph.D. from Tufts University. Interested in the biological foundation of happiness, she has developed an original set of theories and exercises which have helped many people. As a result, she has been featured (among many other places) on “Forbes,” “the Wall Street Journal,” Fox, and NBC.

Breuning has authored few other books, among them: “I, Mammal,” and “The Science of Positivity.” “Habits of a Happy Brain” is an update od “Meet Your Happy Chemicals.”

“Habits of a Happy Brain Summary”

True, you are the pinnacle of evolution – and that lovely little sapiens in your taxonomic name is all the evidence you’ll ever need to prove it.

However, two things you may have forgotten!

First of all, “homo sapiens” is your species, and there are few other more inclusive taxonomic ranks to which you belong as well. For example, you are in the order of primates, which are in the class of mammals, which, in turn, belong to the kingdom of animals.

That’s right – you, as smart as you like to think you are, are still an animal, just like the lion or the rabbit is.

The second thing is even more interesting. Consider it evolution’s cruel little joke. Namely, the organ which has granted you the privilege of that “sapiens” in your taxonomic name is the very same organ which makes you less happy than, say, mice or lizards.

Why is that?

Well, because, when it comes to happiness, your brain essentially functions the same way a mouse’s does (after all, you are in the same order). With one big difference, that is.

True, you both have the same hormones for happiness, but your regulatory system is all messed up. Because, well, you have millions of additional neurons which don’t really know what to do – so they invent themselves tasks.

Try to understand them: they got the way that they are by alarming you whether running away from lions is good for you. And now – there are no lions to run away from.

But, which are these happy brain chemicals?

Well, there are four.

First of all – dopamine. Or – the “I can get it” hormone. In the animal’s world, this is the chemical released when a tiger sees an eland it can catch. In your world – it’s the excitement you feel when you reward yourself a chocolate bar for dieting few hours.

Next – endorphin. Or – the “I’m feeling no pain” hormone. It’s the chemical which masks pain. So, when a gazelle is bitten by a lion, she is still capable of fighting back, because her brain releases endorphin, telling her “that bite mark’s not so serious now…” Of course it’s going to hurt afterward.

The third one – oxytocin. Or – the “I trust you” hormone. This one’s released when an animal is among its own kind. It feels protected – and knows that it can rely on those around it. But, you know this: you’ve felt its effect best that time your mother patiently took care of you when you were sick as a child.

Serotonin is the final chemical on our list. It’s the “I’m top dog” hormone. Or, in other words, the one which makes the gorilla alpha male strut so proudly!

As is probably already apparent from these descriptions, all of these chemicals come with a caveat. For example, serotonin may make you feel isolated and result in frustration about your own uniqueness; oxytocin may result in herd behavior, and that helps no one.

Even if you’re an endorphin-addict and you are in a “50 Shades of Grey” mood all the time, causing yourself pain may debilitate you in a much more physical sense. (Remember that “Black Mirror” scene?) Finally, dopamine is habituated pretty quickly, leaving you with a “been there/done that” feeling even about things you really like.

And that – right there: that’s what makes “permanent happiness” a biological myth. It’s unattainable since your brain cares about your selfish genes and happiness is its way of doing it. Namely – if it’s good for your survival, it says “do it”; if it’s bad “don’t do it.”

However, once it teaches you that something is good, it doesn’t bother to release the hormones anymore. Leaving you with a habit – but taking away the happiness from it.

Your only way out?

Try to force your brain into rewiring by going against the stream and boldly taking up new habits every 45 days or so.

As its title implies, “Habits of a Happy Brain” has many exercises inside to help you!

Key Lessons from “Habits of a Happy Brain”

1.      There Are Unhappy Chemicals as Well
2.      How Your Favorite Song Starts to Irritate You
3.      You Can’t Be Happy All the Time – Be from Time to Time

There Are Unhappy Chemicals as Well

We went over the four happy chemicals which your brain releases to tell you what’s good for you. A quick reminder, these are dopamine (related to rewards), oxytocin (associated with your social life), endorphin (pushing you through physical pain), and serotonin (making you feel special).

Now, there are unhappy chemicals as well. For example, cortisol. It’s a sweet little chemical which has helped you survive, by telling you what you shouldn’t do. However, nowadays, there are no risks – so it’s basically obsolete. But, it still transforms into stress – over utterly irrelevant matters.

Learn how to use it to your favor from this summary.

How Your Favorite Song Starts to Irritate You

“Music gives pleasure because your mind keeps predicting what comes next,” writes Loretta Graziano Breuning.

And it’s simple: each correct prediction triggers dopamine. If the music is unfamiliar, you don’t get the chemical. When it is somewhat familiar – you feel as if you want to dance. However, when it is too familiar, your brain predicts what happens next effortlessly. And this doesn’t get you dopamine either.

So, as Loretta Graziano Breuning says, “to make you happy, music must be at the sweet spot of novelty and familiarity.” We’ll put it a bit differently: stop playing that song on the repeat! You’ll start hating it in few days.

You Can’t Be Happy All the Time – Be from Time to Time

What Breuning says about music – applies to almost everything else in life.

Want to enjoy some food the same way for the rest of your life? Eat it from time to time – not every day. Want to be longer in love? Don’t spend every waking minute of your day with your beloved.

However, in either case, don’t expect to be happy all the time. Because that just won’t work. Your brain won’t allow you. It’s just the way it functions: every time it remembers something well – it actually takes away a lot of the happiness related to it.

And it needs to remember many things so that you can survive.

Like this summary? We’d like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

“Habits of a Happy Brain” Quotes

When a monkey loses a banana to a rival, he feels bad, but he doesn't expand the problem by thinking about it over and over. He looks for another banana. He ends up feeling rewarded rather than harmed. Click To Tweet We seek evidence of threats to feel safe, and we get a dopamine boost when we find what we seek. You can also get a serotonin boost from the feeling of being right, and an oxytocin boost from bonding with those who sense the same threat. Click To Tweet Consider this: when things do go wrong, ask yourself whether you could have prevented it by being unhappy. Click To Tweet You don’t notice your neural guidance system because you built it without conscious intent. That’s why it’s hard to build new trails: You don’t know how you built the old ones. Click To Tweet Love is a huge surge of happy chemicals because it's highly relevant to the survival of your genes. Click To Tweet

Our Critical Review

Perhaps the best thing about “Habits of a Happy Brain” is the fact that it delves deep into the biology of happiness, but in a manner which helps the reader attain the information with ease. And that’s only the first half of the book.

The second half is a list of step-by-step instructions for few exercises which should help you rewire your brain. So, you get the best of both worlds – theory, and practice.

And you can’t ask for more from a book which talks about your happiness.

   Take this summary with you and read anywhere! Download PDF:   

The Magic of Math Summary

The Magic of Math SummarySolving for x and Figuring Out Why

Oh No, I hate math! Hold your horses for a moment; this is more than just a brief introduction to mathematical calculations.

In this book summary, you’ll learn a few tricks; you can use to amuse your friends, and family.

Who Should Read “The Magic of Math”? And Why?

It may come as a surprise to you, but math can also be quite entraining; if you possess the right set of skills.

Don’t worry, no previous experience is required in order to utilize various numerical operations for personal gain.

The Magic of Math” as the name implies, illustrates a brand-new revolution launched in the name of algorithmic and arithmetical functions.

We recommended to all “wizards” and those who want to join the club.

About Arthur Benjamin

Arthur BenjaminYou may have heard of Arthur Benjamin, who regularly shares his findings as a hailed keynote speaker at Ted Talks.

He obtained his Ph.D. from Johns Hopkins University.

“The Magic of Math Summary”

Mathematics is more than just a subject, boring or amusing to various groups of children. Calculations play an essential role in human development, and it’s fair to say, that magic can also be an integral part of its operations.

Take into account the “alchemy” of the well-known numerical patterns. In another case, these algorithms are labeled as patterns made of numbers. How do these features perform wizardry, regarding mathematics?

Well, you are not dealing with anything surreal, but with a well-proven concept that can improve your mental capacity and problem-solving skills.

For example, you don’t need any tool to calculate the square of a number quickly. In this book, you’ll find a detailed explanation of how to make that happen.

Stay with us to learn a few tricks and enlighten your friends and family. No, it’s not geeky; it’s magical if you really understand the trickery that revolves around math. Here are a few guidelines you must follow, in order to make your maneuver work:

  • First, tell your friend/s to think of any two numbers between 1 and 10
  • Afterward, you must add those numbers
  • Next step would be to multiply the result by 10,
  • Once you finished that, next in line is adding the larger number
  • Then, subtract the smaller one
  • and demand the final result.

Once, the “participant” successfully executes all the tasks, you (as a host) are just one step away from to knock your friend’s socks off by revealing the numbers he chose a few minutes ago.

Let’s divide the process, step by step: Let’s say that the final answer is 126. Next in line is separating the first two ciphers from the last digit. Here’s how it goes: Add the last number to the first two (6+12) and then divide this result by 2. 18/2= 9 – and this is the large number.

What comes next? It’s pretty straightforward to calculate the smaller number your friend picked. Just take this number (9) and subtract the last digit of the number, which emerged from the formula discussed earlier (126) = 9 – 6 = 3. It’s that simple!!

What is so special about the number 9? – Let’s dive right into it and unveil everything that contributes to the specialty of this digit.

In truth, not many people are aware of the facts that are partly responsible for making 9 too valuable to mathematicians. The first magic lies in the simplicity of multiple processes. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, and so forth.

What’s so special about these digits? If you take a closer look, you’ll see that each of the digits in these numbers if added together will result in the same outcome = 9. For instance, (9+0), (8+1) (2+7) (4+5) … At first sight, many would assume that (9+9) destroys this sequence, but that’s not true.

18 – would still produce the same outcome if you add 1 and 8 once more.

At the beginning of the 13th century, a renowned Italian mathematician known as Fibonacci wrote a fantastic book that represents the point of no return in Math. The Book of Calculation or “Liber Abaci” marks the pivotal moment for solving arithmetic problems and displaying various formulas.

The operation exhibited through “Immortal rabbits” is perhaps the greatest piece of ingenuity that occurred in those days. What’s it all about? – From our basic understanding and rules, every month a little “r” (baby rabbit) converts into “R” (adult rabbit) and thus each “R” becomes “Rr.”

It means that now you have a pair of adults and a pair of babies.

So, what do we get?

  • 1 Month – r
  • 2 Month – R
  • 3 Month – Rr
  • 4 Month – Rr R
  • 5 Month – Rr R Rr
  • 6 Month – Rr R Rr Rr R

One can’t help but notice, that there is something weird about the end-result and the sequence generated from it.

At first glance, the digits – 1,1,2,3,5,8 … may seem irrelevant but scan it more thoroughly. What do you see? It’s pretty evident, that each number in the sequence is in fact, the sum of its two predecessors. For instance (1 + 2 = 3) (3 + 2 = 5) and so forth. This example represents the Fibonacci Numbers.

One thing separates math, from other branches of natural science – facts. Unlike other disciplines, mathematicians mainly focus on propositions, which can prove its absolute accuracy and relevance.

For instance, regardless of the circumstances or the intentions behind various equations, it’s 100% true to say that even numbers are multiples of 2. Therefore, it doesn’t take too much knowledge to realize that such assertation is validated.

Even famous mathematicians have their favorite ways of solving equations. A large portion of them would reply that eiπ+ 1 = 0 is one of their favorites.

Not only that it addresses different calculations, and it also includes the main five features of mathematics: 1, 0, π, i, and e.

Like this summary? We’d Like to invite you to download our free 12 min app, for more amazing summaries and audiobooks.

Our Critical Review

Are you a math lover? – You don’t have to be to like this book.

We sincerely enjoyed every bit of it and learned a few tricks along the road.

We advise that you should at least try to do the same because it’ll surely be a time well-spent.

   Take this summary with you and read anywhere! Download PDF: