Sometimes giving up can be the best thing you can ever do for yourself — sometimes quitting is exactly what you should do.

The reason

Have you ever found yourself working so hard on something without knowing exactly why?

1. Why Am I doing this?

Am I solving a problem by doing what I’m doing? Is what I’m doing helping me? Is it working for me?

2. Is it working for me?


Is what I’m doing really worth it?Is all this sweat and blood worth the end result? Is it worth the sacrifice or is there a chance I might be hurting myself ultimately?

3. Is it really worth it?


Whenever you’re working on something, ask yourself this: “Is there an easier way to do this?”

4. Is there an easier way?


Am I prioritizing effectively? Am I doing what’s best for me from all points of view? Or at least from all the views that I can see at the moment?

5. What could I be doing instead?

There is value in changing your mind.

Quitting is actually productive


"The first principle is that you must not fool yourself because you’re the easiest person to fool.”

You can’t get that time back and the worst thing you can do now is waste even more time.

Takeaway

Not many of us like the idea of quitting. It seems like something we should all be ashamed of. It slams a big ‘loser tag’ on our foreheads — “If you’re a quitter, you’re a loser.” Giving up passes a…

career

Career

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Motivation & Inspiration

education

Learning & Education

Here’s Why You Should Give Up On Your Dreams

<ul><li class="ql-align-center">This is the thing about resistance: If you’re doing what you think you should be doing rather than what you want to do with your whole heart, you are not persisting, you are resisting the truth about who and what you are.</li></ul>

Quit if the cost is too high, if you’re doing it because you feel you owe it to someone, or quit if you don’t love it.

It has helped me on my thought process behind a decision I'm thinking of

personaldevelopment

Personal Development

moneyandinvestments

Money & Investments

When To Quit – Tim Ferriss • Podcast Notes

<ul><li>A large percentage of the population believe they were born with an innate learning style. </li><li>Studies show no evidence for learning styles, and many researchers fear they may discourage proven educational practices. </li><li>People, especially children, are learning generalists who should engage in many different methods of learning.</li></ul>

Key Takeaways

A prevalent neuromyth is that of “learning styles.” According to this belief, people can be classified by how they learn best and should concentrate their educational efforts in that mode. If someone is an auditory learner, the idea goes, she’ll master a subject or skill faster and more effectively by listening to lectures than reading books or through first-hand experiences.The idea of learning styles has infected our education systems and people’s understanding of themselves. And psychologists worry this can have consequences in our <a href="https://bigthink.com/smart-skills/lifelong-learning/">lifelong-learning</a> pursuits.

The Neuromyth Of Learning Styles

There is a grain of truth to the myth. Namely, people do differ in their abilities and preferences. The VARK learning model, for example, classifies people as either visual, auditory, reading/writing, or kinesthetic (hands-on) learners. Each method is part of the learning process, and people will have their favourites. Such preferences are as true in education as anything else in life.Many proponents believe learning styles are inheritable, emerge early in childhood, have a physiological basis, predict learning outcomes, and are immutable.

The Elements of Learning Style

Recent studies found no supporting evidence that learning was enhanced by a slavish dedication to a student’s learning styleIn fact, despite broad acceptance, studies continued to show no benefit to a learning-style approach. As <a href="https://www.sciencedirect.com/science/article/abs/pii/S1041608009000375">one study’s authors</a> so aptly put it: “The most important finding of this study is, in essence, a non finding.”

The Learning Style Does Not Matter

Why then does the learning styles myth survive despite the evidence and experts’ red-faced arguments? Because like all neuromyths, it tells us something we want to believe. The classic music myth gives worried parents a sense of control. The 10-percent myth tells us we’re secretly super-geniuses who just need to unlock our potential.

Busting The Learning Style Myth

People prefer brain-based accounts of behaviour, and they like to categorize people into types. Learning styles allow people to do both of those things.It may also tie into common misconceptions of success.Success is complicated. It requires the right mixture of education, resources, skill, and luck. But we tend to streamline this equation into specialization equals success.

A Multi-Style Approach To Learning

Engage with subjects in as many material ways as possible. Read, converse, seek out examples, get hands-on, and experiment. While we may have preferences, we should also challenge ourselves to try new methods and re-engage with less-favoured ones. Each style is its own “genre” and each can be valuable in the creation of your lifelong-learning path.

Take The Generalist Approach

Learning styles are supposed to help learners take ownership of their education, but research doesn’t back up this well-intentioned myth.

problemsolving

Problem Solving

Busting the learning styles myth: Why learning generalists perform best

Many people think handshaking is a modern way of welcoming, wishing, or dealing. But handshake was coming from very late history.Archeologists found many old stuff like paintings, sculptures of people shaking hands

Coming from history

Hence we mentioned it was from history, it was invented in the times of Kings.Past then people used to carry swords, they are tied in the left side of a person, so that he can easily pull it out with his right hand when needed.

Reason

Since the sword is always with them, they thought it's better to shake his right hand with another person's right hand to show that they are not going to attack him, since my hand is with you.

The WIshing

Understand yourself and those around you.

psychology

Psychology

Why Do We Shake Hands With People?

Authenticating websites is important for online research. It is important to avoid misleading or suspicious websites.

Verify Sources

When researching, it is helpful to learn how to narrow down search results into specific topics.

Ask Good Questions

It is important to fact check and gather research through different sources to ensure that your information is up to date and correct.

Pursue Deeper Information

Online researching can be stressful and difficult. Persevering through challenges can help the researcher to achieve deeper knowledge.

Persist Through Challenges

It is important to respect the ownership of your sources, and avoid piracy sites. Writing articles, taking photos, and producing media has been taken for granted digitally, artists and creators deserve credit.

Credit Sources

There are many different ways to gather information; such as books, magazines, websites, and documentaries. Taking advantage of different educational media can help the researcher gather a deeper meaning.

Use Resources

Access Denied

When you need to remember information for a test or presentation, you can try to hammer the information into your head or you can flip it and also try to retrieve the information as you're learning it. When we try to put the information in,  it travels one way on the neurons. When we try to recall the information, we're going the other way. This bi-directional highway of information helps to strengthen that circuit more than just passively reading.

Self-testing helps to remember information

When you're studying, you need to space out the studying rather than limiting it to one timeframe. For example, if you have seven hours to study for an exam that is in one week, do one hour a day rather than all seven hours the day before.

Space out studying

Memories are best retrieved if the context of retrieval matched the context when the memory was formed. If I'm studying for a test while listening to Mozart, burning a lavender-scented candle, and eating Sour Patch gummy bears, I will recall that information better on the test day if I'm doing the same things.Are you caffeinated while learning something? Are you tired while learning something.? Then match the conditions while learning when you want to retrieve it.

Context matters

Semantic memory is memory for facts and information. Too much stress can impact your ability to form and retrieve memories. For example, you study for an exam and know the information, then you go for the test, but because you're stressed and you're nervous, you can't remember a thing. You can't retrieve the information. We can help our memory by creating associations that are meaningful, emotional, surprising, and new. We should also write things down.

Create semantic memory

4 ways to hack your memory, with Lisa Genova Subscribe to Big Think on YouTube ►► https://www.youtube.com/c/bigthink Up next ►► How memory works https://youtu.be/kwo2WxM87-g Self-testing is one good way to better remember information. Think of memory as a two-way street. If we only put information in, it is like traveling in only one direction. Recalling information requires us to go the other way. Spacing out studying is better than cramming.If you need seven hours to prepare for an exam that is one week from today, study one hour per day rather than all seven hours the night before. Context matters for memory recall. If you study while eating Sour Patch candy, do the same thing while taking the test. Read the video transcript: https://bigthink.com/series/great-question/study-tips/ ---------------------------------------------------------------------------------- About Lisa Genova: Lisa Genova is the New York Times bestselling author of the novels Still Alice, Left Neglected, Love Anthony, Inside the O’Briens, and Every Note Played. Still Alice was adapted into an Oscar-winning film starring Julianne Moore, Alec Baldwin, and Kristen Stewart. Lisa graduated valedictorian from Bates College with a degree in biopsychology and holds a PhD in neuroscience from Harvard University. She travels worldwide speaking about the neurological diseases she writes about and has appeared on The Dr. Oz Show, Today, PBS NewsHour, CNN, and NPR. Her TED talk, “What You Can Do to Prevent Alzheimer’s,” has been viewed more than five million times. The New York Times bestseller REMEMBER is her first work of nonfiction. ---------------------------------------------------------------------------------- Read more of our stories on memory: Smells connect to memories more than other senses ►► https://bigthink.com/neuropsych/smell-hippocampus/ Making memories actually involves breaking our DNA, study shows ►► https://bigthink.com/neuropsych/memory-dna/ New study connects cardiovascular exercise with improved memory ►► https://bigthink.com/health/running-memory/ ---------------------------------------------------------------------------------- About Big Think | Smarter Faster™ ► Big Think The leading source of expert-driven, educational content. With thousands of videos, featuring experts ranging from Bill Clinton to Bill Nye, Big Think helps you get smarter, faster by exploring the big ideas and core skills that define knowledge in the 21st century. ► Big Think+ Make your business smarter, faster: https://bigthink.com/plus/ ---------------------------------------------------------------------------------- Want more Big Think? ► Daily editorial features: https://bigthink.com/popular/ ► Get the best of Big Think right to your inbox: https://bigthink.com/st/newsletter ► Facebook: https://bigth.ink/facebook ► Instagram: https://bigth.ink/Instagram ► Twitter: https://bigth.ink/twitter

videos

Videos

4 ways to hack your memory, with Lisa Genova
Subscribe to Big Think on YouTube ►► https://www.youtube.com/c/bigthink
Up next ►► How memory works https://youtu.be/kwo2WxM87-g 

Self-testing is one good way to better remember information. Think of memory as a two-way street. If we only put information in, it is like traveling in only one direction. Recalling information requires us to go the other way.

Spacing out studying is better than cramming.If you need seven hours to prepare for an exam that is one week from today, study one hour per day rather than all seven hours the night before.

Context matters for memory recall. If you study while eating Sour Patch candy, do the same thing while taking the test.

Read the video transcript: https://bigthink.com/series/great-question/study-tips/ 

---------------------------------------------------------------------------------- 

About Lisa Genova:
Lisa Genova  is the New York Times bestselling author of the novels Still Alice, Left Neglected, Love Anthony, Inside the O’Briens, and Every Note Played. Still Alice was adapted into an Oscar-winning film starring Julianne Moore, Alec Baldwin, and Kristen Stewart. Lisa graduated valedictorian from Bates College with a degree in biopsychology and holds a PhD in neuroscience from Harvard University. She travels worldwide speaking about the neurological diseases she writes about and has appeared on The Dr. Oz Show, Today, PBS NewsHour, CNN, and NPR. Her TED talk, “What You Can Do to Prevent Alzheimer’s,” has been viewed more than five million times. The New York Times bestseller REMEMBER is her first work of nonfiction.

---------------------------------------------------------------------------------- 

Read more of our stories on memory: 
Smells connect to memories more than other senses
 ►► https://bigthink.com/neuropsych/smell-hippocampus/ 
Making memories actually involves breaking our DNA, study shows
 ►► https://bigthink.com/neuropsych/memory-dna/ 
New study connects cardiovascular exercise with improved memory
 ►► https://bigthink.com/health/running-memory/ 

---------------------------------------------------------------------------------- 

About Big Think | Smarter Faster™
► Big Think 
The leading source of expert-driven, educational content. With thousands of videos, featuring experts ranging from Bill Clinton to Bill Nye, Big Think helps you get smarter, faster by exploring the big ideas and core skills that define knowledge in the 21st century. 
► Big Think+
Make your business smarter, faster: https://bigthink.com/plus/

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Want more Big Think?
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► Twitter: https://bigth.ink/twitter

Big Think is the leading source of expert-driven, actionable, educational content -- with thousands of videos, featuring experts ranging from Bill Clinton to Bill Nye, we help you get smarter, faster. Get actionable lessons from the world’s greatest thinkers & doers. Our experts are either disrupting or leading their respective fields. We aim to help you explore the big ideas and core skills that define knowledge in the 21st century, so you can apply them to the questions and challenges in your own life. Other Frequent contributors include Michio Kaku & Neil DeGrasse Tyson.

Head to bigthink.com for a multitude of articles just as informative and satisfying as our videos. New articles posted daily on a range of intellectual topics. ​Join Big Think+ to gain access to an immense library of content. It features insight from many of the most celebrated and intelligent individuals in the world today.

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4 ways to hack your memory | Lisa Genova | Big Think

4 Ways To Hack Your Memory | Lisa Genova

Learning is not as easy as owning a device, internet connection and a page full of articles and videos. Without a proper strategy, you may know isolated facts about everything, but it won't positively contribute to your future development. Understanding the seven mental models for learning can help to gain knowledge coherently.

Understanding mental models

We think we know much more than we really do. Warren Buffett and Charlie Munger developed the Circle of Competence. This mental model helps define what you know and what your limitations are. It enables you to avoid making decisions about subjects you don't fully understand.

Circle of Competence

The purpose of the thought experiment is to delve deeper into a given field to improve your knowledge, uncover what you don't know, and strengthen your understanding of the world. For example, a madman has tied 5 innocent people to a trolley track. An empty trolley car is fastly approaching the people. You can pull a lever and divert the trolley to another track, but there is 1 person tied to the other track. What would you do? The idea is to uncover what you actively think about the situation.

Thought experiment

This mental model explains that when we have two explanations for the same thing, we should prefer the simpler explanation. For example, when you're learning how to operate a complicated machine or reading a book in a field where you are a beginner, find the simpler explanation to absorb the material and start executing quickly.

Occam’s Razor

The availability heuristic states that we make decisions and form conclusions based on the most recent information we gathered. For example, if everybody starts investing in an "innovative" fund, you might do it yourself because of everything you've recently heard. But you may fail to ask critical questions and make proper calculations. This is also important as it shows that what you see is not everything that is available. The best-selling books are the most available, but there are also others that might be better and can teach us more.

Availability heuristic

Hindsight bias is when we see past events as being predictable. But that is because we now know what happened. When you give feedback to a person about something he did, you know the facts. That means how you frame your criticism can be distorted. You might have done the same thing if you were in his position at the time. When you create a change in your organisation that has a positive outcome, you may say you knew it all along. But in the long run, we start to think our predictions are perfect, and we may think we don't need to learn more.

Hindsight bias

Common knowledge tries to describe the things everyone knows. For example, knowledge about money, that our planet circles around the sun, that 1 + 1 = 2. However, common knowledge won't get you far in life. When you want to succeed in life, you want to stand out because you compete against thousands of others. Outlining the common knowledge in your field and learning extra things will help you to seem unique and desirable.

Common knowledge

The Feynman learning technique is not a mental model but a way to approach a subject to learn it faster and better. <ul><li>Pretend you're teaching a concept to a child. Write down in simple terms everything you know about the subject.</li><li>Identify the gaps. Go over what you've written down and see how you can improve it. What's missing or unclear.</li><li>Organise and simplify. Create a better way to explain the concept.</li><li>Transmit. Communicate your idea to someone to get feedback.</li></ul>

The Feynman learning technique

The mental models for learning are your weapons to help you understand more than the basics.

What better way to learn than to learn about learning? These mental models for learning will help you stay curious and progressing.

habits

Habits

7 Mental Models for Learning To Understand More Than The bare Minimum

He was a great mathematician and astronomer. Brahamgupta considered himself to be an astrologer, maybe because his father Jisnugupta was an astrologer but today, he is mostly remembered for his significant works in the field of mathematics. He was born in 598 CE in Bhinmal, a city in Rajasthan. He spent a major part of his life in Rajasthan. Ujjain was the centre of Indian mathematical astronomy in ancient times and Brahamgupta was the director of this centre. While he was in Ujjain, he wrote many books on mathematics and astronomy.

13. Brahmagupta Acharya 

‘Durkeamynarda’ (672), ‘Khandakhadyaka’ (665), ‘Brahmasphutasiddhanta’ (628) and ‘Cadamakela’ (624). The ‘Brahmasphutasiddhanta’ meaning the ‘Doctrine of Brahamagupta’ is one of his well-known works. The ‘Brahmasphutasiddhanta’ consists of 25 chapters. In the first 10 chapters, topics covered are, mean longitudes of the planets, true longitudes of the planets, the three problems of diurnal rotation, lunar eclipses, solar eclipses, risings and settings, the moon’s crescent, the moon’s shadow, conjunctions of the planets with each other,

These include

and conjunctions of the planets with the fixed stars. The rest of the 15 chapters are focused more on mathematical concepts. One of his fellow mathematicians gave him the title of ‘Ganita Chakra Chudamani’ which when translated meant, ‘The gem of the circle of mathematicians’. It is believed, that he died in Ujjain, in 668 CE. His contributions to mathematics are mentioned below.

According to him,zero is a number that is obtained, when a number is subtracted from itself. He also mentioned some properties of zero, where positive numbers are termed as fortunes and negative numbers are termed as debt.<ul><li>When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.</li><li>A debt minus zero is a debt.</li><li>A fortune minus zero is a fortune.</li><li>Zero minus zero is a zero.</li><li>A debt subtracted from zero is a fortune.</li><li>A fortune subtracted from zero is a debt.</li><li>The product of zero multiplied by a debt or fortune is zero.</li></ul>

1.Properties Of Zero

<ul><li>The product of zero multiplied by zero is zero.</li><li>The product or quotient of two fortunes is one fortune.</li><li>The product or quotient of two debts is one fortune.</li><li>The product or quotient of a debt and a fortune is a debt.</li><li>The product or quotient of a fortune and a debt is a debt.</li><li>His some conclusions on the division by zero. </li></ul>"Positive or negative numbers when divided by zero is a fraction with zero as denominator. Zero divided by negative or positive numbers is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.”

He proposed a method of multiplication, “gomutrika”, in his book “Brahmasphutasiddhanta”. The title of this method was translated by Ifrah as, “Like the trajectory of cow’s urine”. In the 12th chapter of his book, he also tried to explain the rules of simplifying five types of combinations of fractions:-ac + bc; ac × bd; a1 + bd; ac + bd × ac = a(d + b)cd; and ac − bd × ac = a(d − b)cd. Let us try to multiply 315 by 306 with the help of the gomutrika method in the Link Attached above.

2. Brahmagupta’s Method of Multiplication

proposed some methods to solve equations of the type ax + by = c. According to Majumdar, Brahmgupta used continued fractions to solve such equations. He also tried to solve quadratic equations of the type ax² + c = y² and ax² – c = y². For example, for the equation 8x² + 1 = y² he obtained the solutions as (x, y)= (1, 3), (6, 17), (35, 99), (204, 577), (1189, 3363),..He also solved 61x² + 1 = y² having solution as x = 226153980, y = 1766319049 as its smallest solution.

3. Intermediate Equation 

"Five hundred drammas were loaned at an unknown rate of interest, The interest on the money for four months was loaned to another at the same rate of interest and amounted in ten mounths to 78 drammas. Give the rate of interest.”

A sample of the types of problem solved by him is:-

the sum of, a series of cubes and a series of squares for the first n natural numbers as follows:1² + 2² +…….+n² = (n)(n+1)(2n+1)⁄61³ + 2³ +…….+n³ = (n(n+1)⁄2)²

4. Sum Of Series

Brahmagupta in chapter 12, entitled “Calculation”, of his book, proposed a formula that was useful in generating Pythagorean triplets. He mentioned, The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey.”

5. Pythagorean Triplets

Brahmagupta studied this equation 1000 years before Pell’s birth. Pell’s equation is of form, nx² + 1 = y², which can also be written as y² – nx² = 1, where ‘n’ is an integer and we have to solve it for (x, y) integer solutions. Brahmagupta also provided a lemma, in which he stated that if (a, b) and (c, d)are integer solutions of ‘Pell type equations’ of the form na²+ k = b² and nc² + k’ = d²then, (bc + ad, bd + nac) and (bc – ad, bd – nac)are both integer solutions of the ‘Pell type equation’.

6. Pell’s Equation 

Brahmagupta’s formula for the cyclic quadrilaterals is regarded as his most famous discovery in geometry. Given the sides of a cyclic quadrilateral, he provided an approximate and exact formula for the area of the cyclic quadrilateral. He mentioned,"The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate area is the square root from the product of the halves of the sums of the sides diminished by each side of the quadrilateral.”

7. Brahmagupta 'S Formula 

Brahmagupta theorem states that,If a cyclic quadrilateral is orthodiagonal (i.e., has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.”Geometrically, this theorem means that, in a cyclic quadrilateral ABCD, diagonals AC and BD are perpendicular to each other. The intersection of AC and BD is M. Drop the perpendicular from M to the line BC, calling the intersection point E. Let F be the intersection of the line EM and the side AD. Then, according to the theorem, F is the midpoint of side AD.

8. Brahmagupta’s Theorem

Brahmagupta further extended his theory and claimed that, The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular altitudes.”The above statement means that in an isosceles trapezoid having sides of length p, q, r, s, the length of the diagonal is given by √pr+qs.

A major portion of Brahmagupta’s work was dedicated to the study of geometry. One of his theorem about triangles states that,The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular altitude is the square-root from the square of a side diminished by the square of its segment.”This theorem gives the length of two segments in which the base of a triangle is divided by its altitude, and the lengths are, 12(b ± (c2 − a2)

9. Triangles

He also discussed rational triangles. A rational triangle with the rational area and sides a, b, c, are of the form:a = 1⁄2(u²⁄v + v), b = 1⁄2(u²⁄w + w), c = 1⁄2(u²⁄v – v + u²⁄w – w), for some rational numbers u, v, w.

Brahmagupta also tried to approximate the value of π and in stanza 40 of his book he mentioned, The diameter and the square of the radius, each multiplied by 3 are the practical circumference and the area of a circle respectively. The accurate values are the square-roots from the squares of those two multiplied by ten.”He used √10 ≈ 3.1622….. approximated to 3, as an accurate value of π with an error of less than 1%.

10. Approximation of π

Brahmagupta illustrated the construction of several figures with arbitrary sides. He tried to construct figures such as isosceles triangles, scalene triangles, rectangles, isosceles trapezoids, isosceles trapezoids with three equal sides, and scalene cyclic quadrilateral, mainly, with the help of right triangles. He also gave the volume and surface area of some figures, after estimating the value of π. He found the volume of rectangular prisms, pyramids and frustum of a square pyramid. He further proposed the average depth of a series of pits.

11. Measuration And Construction 

Brahmagupta in his chapter 2 of his book, provided a sine table. He wrote,The sines: The Progenitors, twins, Ursa Major, the Vedas, the gods, fires, flavors, dice, the moon, the sky, the moon, arrows, sun…..”He used the above objects to represent digits of place-value numerals. Progenitors represent 14 progenitors in Indian cosmology, twins means 2, Ursa Major represents the seven stars of Ursa Major or 7, Vedas refers to the 4 Vedas or 4, dice represents the number of sides of the traditional die or 6, and so on. He gave the sine table with 3270 as radius and calculated 3270 sin(π⁄48).

12. Trigonometry 

He was the first who propose an interpolation formula using second-order difference. His Sanskrit verses on this formula were found in the Khandakadyaka work of Brahmagupta. Today, the Brahmagupta interpolation formula is known as Newton- Stirling interpolation formula. In his book, he termed the difference Dr as the ‘gatakhanda’, the difference Dr+1 as the ‘bhogyakhanda’, ‘Vikala’ as the quantity in minutes by which the interval has been covered at the point of interpolation, which in modern notation denoted as a− xr. ‘Sphuta-bhogyakhanda’ is now known as fr+1 − fr.

13. Interpolation Method

A formula stated by him, for the computation of values of the sine table, having common interval (h) in the underlying base table as 900 minutes or 15 degrees, is given below.When translated these verses means,Multiply the ‘vikala’ by the half the difference of the ‘gatakhanda’ and the ‘bhogyakhanda’ and divide the product by 900. Add the result to half the sum of the ‘gatakhanda’ and the ‘bhogyakhanda’ if their half-sum is less than the ‘bhogyakhanda’, subtract if greater. The result in each case is ‘sphuta-bhogyakhanda’ the correct tabular difference.

Sphuta-bhogyakhanda 

In modern notation, the formula is denoted as sphuta-bhogyakhanda =  (Dr + Dr-1)⁄2 ± t|Dr – Dr-1|⁄2, where ± is introduced according to  Dr < Dr+1 or Dr > Dr+1  and f(a) is given by,f(a) = fr + t × sphuta-bhogyakhanda, is known as Stirling’s interpolation formula for second-order differences

Brahmagupta gave the solution of general linear equations in chapter 18 of his book and wrote,The difference between rupas, when inverted and divided by the difference of the coefficients of the unknowns, is the unknown in the equation. The rupas are subtracted on the side below that from which the square and the unknown are to be subtracted.”Algebraically, the above statement means that, for an equation of type bx+c = dx+e, the solution is given by x = e − c/b − d. He also gave two solutions for the quadratic equation ax² +bx = c, and wrote,

14. Algebra

Diminish by the middle number the square-root of the rupas multiplied by four times the square and increased by the square of the middle number; divide the remainder by twice the square.”By this method, the solution is given by, x = ±(√(4ac+b²) – b)⁄2a. Whatever is the square-root of the rupas multiplied by the square and increased by the square of half the unknown, diminished that by half the unknown and divide the remainder by its square. The result is the unknown.”By this method, the solution is given by, x = ±(√(ac+b²⁄4) – b²⁄2)⁄a.

Although Brahmagupta thought of himself as an astronomer who did some mathematics, he is now mainly remembered for his contributions to mathematics. He was honoured by the title given to him by a fellow scientist ‘Ganita Chakra Chudamani’ which is translated as ‘The gem of the circle of mathematicians’.

Ganita Chakra Chudamani Brahmagupta 

scienceandnature

Science & Nature

Brahmagupta’s Contributions in Mathematics – StudiousGuy

If you wanna know the key points from the book, the following ideas are for you

The Summary Of The Book

The fear is the main cause of working for money. Rich people make money work for them. Job is a short term solution to a long term problem. Emotions should not control your thinking. Money is illusion. Money is not real.

Have money work for you. Don’t work for money.

It’s how much money you keep not how much you make. You need to be a financially literate. Master financial literature. Accounting is very important even though it’s boring. Account analysis is an important skill. Understanding the difference between asset and liability is crucial. Do know the difference! Keep it super simple. Buy an asset not a liability. You have to understand the numbers. Rich acquire assets. Asset is what puts money to your pocket. In financial reporting the story is important. Cash flow tells the story how the money is spending. (Continued in next idea..)

Learn financial literacy

One thing is missing in our current education is how to keep the money. Most people do what everyone does. Fear is the main reason why people play safe. Intelligent people hire more intelligent people. Keep buying income generating assets. Rich buy assets.

Learn Financial Literacy (Continued)

Aquire assets that you love. Stocks and income generating real assets. Build and keep you asset column. Keep your daily job and make your assets grow.

Mind your own business

Accounting, investing, understanding the markets, the law. You should understand the tax advantages. Corporations ear, spend their expenses and then pay taxes on what is left. It’s one of the biggest tax loopholes that you can take advantage of. Owning your corporation is also a protection from the legal part. Think about personal corporations.

The history of taxes

Be bold, take risks. Financial intelligence consists of these 4 skills: accounting, Investing, understanding markets, the law of awareness of accounting. Invest in your financial intelligence. Have fun! We learn by making mistakes. Main reason most people are not rich is because they are terrified of losing. People who avoid failure also avoid success. Learn to manage risk instead of avoiding it.

The rich invent the money

Most people need to learn one more skill to get rich. When it comes to money the only single skill that people know is working hard. You want to know a little about a lot. The main management skills are management of cash flow (assets and liabilities), management of systems (basic economic theory, political landscape, etc) and management of people. Sales and marketing are one of the most important specialized skills. Communication skills such as Writing, speaking and negotiating are crucial for life of success.

Work to learn. Don’t work for money

Although we have been successful in our careers, they have not turned out quite as we expected. We both have changed positions several times-for all the right reasons-but there are no pension plans vesting on our behalf. Our retirement funds are growing only through our individual contributions. Michael and I have a wonderful marriage with three great children. As I write this, two are in college and one is just beginning high school. We have spent a fortune making sure our children have received the best education available. One day in 1996, one of my children came home disillusioned with school. He was bored and tired of studying. “Why should I put time into studying subjects I will never use in real life?” he protested. Without thinking, I responded, “Because if you don't get good grades, you won't get into college.” “Regardless of whether I go to college,” he replied, “I'm going to be rich.”

business

Business

books

Books

Kiyosaki is best known for his book Rich Dad, Poor Dad, the #1 New York Times bestseller. Kiyosaki followed with Rich Dad's CASHFLOW Quadrant and Rich Dad's Guide to Investing.

Robert T. Kiyosaki

Rich Dad, Poor Dad

start with learning slowly and gradually, the steps of doing or learning something from your souce of study. this will make the bedrock of everything.

understanding the concept

understanding and knowledge is transient.nothing lasts forever.keep reminding yourself of what you learnt and how you would use it day-to-day.

understanding is transient. revision and practice

test by yourself how much you remember without any cue or anything about the topic at random. learn what you could not retrieve from memory.

Retrieval is your trump card

your brain will automatically form groups or sequence of activity to do based on your understanding. you can do them abstracted from the whole process seperately.chunking dictates fluency like driving backwards in car.

chunking

just put in the reps without thinking, it will help build long term memory.don't think, feel. - Bruce Lee

repetition

repitition until you have some fluency and memorization of the work you intend to do.understanding should be fluent at this point.

memorization

I use them daily to become better myself about things I care to be good at.

travel

Travel

No secret to learning

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