To fully understand how Bitcoin operates, one would need to learn the subtleties of public-key cryptography.

In the real world, when people want to buy something using Bitcoin, they transfer their ownership of a certain number of bitcoins to other people, in exchange for goods and services.

This transfer is effected by the network of computers performing computations and thereby changing the “public key” to which the “sold” bitcoins are assigned.

The encryption involved in Bitcoin concerns the identification of the legitimate owner of a particular bitcoin.

Without delving into the mathematics, suffice it to say: There is a way that the legitimate owner of a bitcoin can publicly demonstrate to the computers in the network that he or she really is the owner of that bitcoin.

Only someone with the possession of the “private key” will be able to produce a valid “signature” that convinces the computers in the network to update the public ledger to reflect the transfer of the bitcoin to another party.

When Bitcoin was first implemented in early 2009, computers in the network—dubbed “miners”—received 50 new bitcoins when performing the computations necessary to add a “block” of transactions to the public ledger.

In principle, the developers of Bitcoin could have released all 21 million units of the currency immediately with the software.

With the current arrangement—where the “mining” operations needed to keep the system running simultaneously yield new bitcoins to the machines performing the calculations—there is an incentive for owners to devote their machines’ processing power to the network.

Here, the danger is that the issuing institution—once it had gotten the world to accept its notes or electronic deposits as money—would face an irresistible temptation to issue massive quantities.6

Bitcoin has no such vulnerability. No external technological or physical event could cause Bitcoin inflation, and since no one is in charge of Bitcoin, there is no one tempted to inflate “from within.”

Some critics argue that Bitcoin’s fixed quantity would imply constant price deflation. Although this is true, everyone will have seen this coming with more than a century’s notice, and so long-term contracts would have been designed accordingly.

Whether to call Bitcoin a “fiat” currency depends on the definition. If “fiat” means a currency that is not legally redeemable in some other commodity, then yes, Bitcoin is a fiat currency. But if “fiat” means a currency relying on government fiat to define what will count as legal money, then Bitcoin is not.

Bitcoin is an ingenious concept that challenges the way economists have traditionally thought about money. Its inbuilt scarcity provides an assurance of purchasing power arguably safer than any other system yet conceived.

We need to let the decentralized market test tell us what is the best money, or monies.

Trade, or exchange, is engaged in precisely because both parties benefit; if they did not expect to gain, they would not agree to the exchange.

This simple reasoning refutes the argument against free trade typical of the “mercantilist” period of sixteenth- to eighteenth-century Europe and classically expounded by the famed sixteenth-century French essayist Montaigne.

At each stage of production from natural resource to consumer good, money is voluntarily exchanged for capital goods, labor services, and land resources. At each step of the way, terms of exchanges, or prices, are determined by the voluntary interactions of suppliers and demanders. This market is “free” because choices, at each step, are made freely and voluntarily.

We can immediately see the fallacy in this still-popular viewpoint: the willingness and even eagerness to trade means that both parties benefit. In modern game-theory jargon, trade is a win-win situation, a “positive-sum” rather than a “zero-sum” or “negative-sum” game.

Each one values the two goods or services differently, and these differences set the scene for an exchange.

Two factors determine the terms of any agreement: how much each participant values each good in question, and each participant’s bargaining skills.

the market in relation to how favorably buyers evaluate these goods—in shorthand, by the interaction of their supply with the demand for them.

On the other hand, given the buyers’ evaluation, or demand, for a good, if the supply increases, each unit of supply—each baseball card or loaf of bread—will fall in value, and therefore the price of the good will fall. The reverse occurs if the supply of the good decreases.

The market, then, is not simply an array; it is a highly complex, interacting latticework of exchanges.

Production begins with natural resources, and then various forms of machines and capital goods, until finally, goods are sold to the consumer.

The mercantilists argued that in any trade, one party can benefit only at the expense of the other—that in every transaction there is a winner and a loser, an “exploiter” and an “exploited.”

A common charge against the free-market society is that it institutes “the law of the jungle,” of “dog eat dog,” that it spurns human cooperation for competition and exalts material success as opposed to spiritual values, philosophy, or leisure activities.

Saving and investment can then develop capital goods and increase the productivity and wages of workers, thereby increasing their standard of living.

The free competitive market also rewards and stimulates technological innovation that allows the innovator to get a head start in satisfying consumer wants in new and creative ways.

Government, in every society, is the only lawful system of coercion. Taxation is a coerced exchange, and the heavier the burden of taxation on production, the more likely it is that economic growth will falter and decline

The ultimate in government coercion is socialism.

Under socialist central planning the socialist planning board lacks a price system for land or capital goods.

Market socialism is, in fact, a contradiction in terms.

The fashionable discussion of market socialism often overlooks one crucial aspect of the market: When two goods are exchanged, what is really exchanged is the property titles in those goods.

This means that the key to the existence and flourishing of the free market is a society in which the rights and titles of private property are respected, defended, and kept secure.

The key to socialism, on the other hand, is government ownership of the means of production, land, and capital goods.

Under socialism, therefore, there can be no market in land or capital goods worthy of the name.

ome critics of the free market argue that property rights are in conflict with “human” rights. But the critics fail to realize that in a free-market system, every person has a property right over his own person and his own labor and can make free contracts for those services.

The free market and the free price system make goods from around the world available to consumers.

It is the coercive countries with little or no market activity—the notable examples in the last half of the twentieth century were the communist countries—where the grind of daily existence not only impoverishes people materially but also deadens their spirit.

Prices adjust to equate how much people want to buy with how much they want to sell.

And if people want to buy more than they did before, prices rise. If people want to sell more than they did before, prices fall.

Supply and demand. Buyers are competing with each other. Sellers are competing with each other.

The simple answer of supply and demand is a strange answer, for it presumes you can talk about a good of a particular quality

In the real world, every good has a unique mix of attributes. Even when two goods are physically identical, they almost always come bundled with differing levels of service attached to them.

It’s a strange answer because people’s desires and situations and income and alternatives are constantly changing, so the amount that people want to buy and sell of something can never be pinned down instantaneously.

It’s a strange answer because it seems to require lots of information.

The strangeness of supply and demand leads some to conclude that it only applies to special cases of a homogeneous good where there are a near-infinite number of sellers and where there is perfect information about the quality of the good and the alternatives and their prices.

Supply and demand is a way to see the relationship that strips away everything except the fact that what people are willing to pay and what they have to pay depends on the alternatives.

Prices adjust. They’re not fixed. Supply and demand helps us remember this.

Finally, supply and demand helps us see things in a totally different way. How bizarre it is that partisans credit or blame the president for the average level of wages or inequality in the United States.

The president no more controls wages in the United States than he does the average weight of Americans.

One of the simplest insights that comes from supply and demand is the availability of goods in the marketplace.

When people want more of something, the crowd of more enthusiastic buyers rarely exhausts the supply. Prices adjust to equate how much people want to buy with how much people want to sell. So if people suddenly want more of something, it doesn’t just disappear. The price rises inducing an increase in what is available.

Because prices can adjust, the shelves are rarely empty in a market economy

Supply and demand is a poor tool for predicting precisely the exact level of a price.

Supply and demand is a simple and powerful way to describe the ways that transactions across time and space are not independent of one another.

It is a powerful way to organize our thinking about the complexity that emerges out of the propensity to truck, barter and exchange, a complexity that is the result of human action but not of human design.

A $1,000 increase in student loan debt, researchers found, lowered the odds of marriage by 2 percent a month among female bachelor’s degree recipients in the first four years after graduation. That finding has been bolstered by more recent research showing a similar trend.

Student loan debt is hampering the growth of small businesses

a significant and economically meaningful negative correlation” between rising student loan debt and falling small-business formation. The mechanism isn’t hard to grasp: If you’re paying off a student loan, you’re less able to pull together the cash needed to start a business.

The authors note that small businesses are responsible for “approximately 60 percent of net employment activity in the U.S.”

Student loan debt is delaying marriage and family formation

This year, the Federal Reserve issued a report showing that student loan debt prevented about 400,000 young families from purchasing homes, accounting for about a quarter of the drop in home-ownership rates in this demographic from 2005 to 2014

Student loan debt makes it harder to weather financial crises

From 2007 to 2009, households with student loans saw 12.4 percent of their total net worth evaporate, while the net worth of those without such loans fell by 9.3 percent

Student loan debt is preventing young people from saving for retirement

Student loan debt can cause graduates to give up on their dreams

The returns on higher education aren’t what they once were

A second, related point is that economic history teaches students the importance of context

Third, economic history is an unapologetically empirical field, exclusively dedicated to understanding the real world.

Fourth, economic history is a rich source of informal theorising about the real world, which can help motivate more formal theoretical work later on (Wren-Lewis 2013).

ifth, even once the current economic and financial crisis has passed, the major long run challenges facing the world will still remain.

Sixth, economic theory itself has been emphasising – for well over 20 years now – that path dependence is ubiquitous (David 1985)

Finally, and perhaps most importantly from the perspective of an undergraduate economics instructor, economic history is a great way of convincing undergraduates that the theory they are learning in their micro and macro classes is useful in helping them make sense of the real world.

Economic literacy contributes to a second class of knowledge.

For some economic decisions, such as buying a home or investing in the stock market, it is possible to hire professional or technical help when making a choice, but in most cases it is neither economical nor practical for an individual to hire a skilled professional every time an economic decision needs to be made.

There are three essential ingredients for effective economic education in the schools.

The development of economic literacy must begin in the schools. Even young children are capable of learning basic economic concepts that help them understand their economic world. In the secondary years, that initial foundation can be expanded to include instruction in a broader set of economic ideas and concepts

Some may think that economics is too difficult a subject to be taught to children and youth, and that such instruction should wait until college

Waiting until students are in college to teach economics is simply a matter of "too little and too late." The majority of students end their formal education with secondary school, and even those students who continue their learning at a college or university may not take an economics course.

Economic literacy improves the competence of each individual for making personal and social decisions about the multitude of economic issues that will be encountered over a lifetime.

First, teachers must be knowledgeable about the subject and be able to help students learn how to use basic economic concepts to analyze personal and social issues. Second, good curriculum guides and instructional materials are needed that present economic content at an appropriate level for the student to understand. Third, economics must have a central place in the school curriculum—similar to math, science, history and language arts—so that substantial classroom time is devoted to economics instruction

Over the past 40 years there has been a significant improvement in each area.

A study of high school transcripts shows that only about 44 percent of high school students take a separate course in economics. This course is usually offered in the 12th grade as an elective and lasts for only a semester.

Given this situation—that fewer than half of high school graduates take a course in economics—it should not be surprising that study after study show that there is widespread economic illiteracy among youth and the American public.

Some 87 percent of high school seniors rated their knowledge and understanding of economic and economic issues as only fair or poor.

Knowing what determines prices in a market economy and accepting the outcomes are two different things. If demand or supply conditions change, prices in a competitive market will rise and fall. Having a basic understanding of how markets work does not always mean that people will like price changes, especially if prices rise, but it should increase the probability of accepting the market outcome

The development of basic economic literacy is an important goal for a democratic society that relies heavily on informed citizenry and personal economic decision-making.

To achieve that goal will require that significant gaps in the economic education of youth be closed by giving economics a more central place in the school curriculum. More economics coursework at the precollege level sets a foundation for economic literacy, but it is only the beginning.

But the truth is more nuanced, and, statistically at least, the question of how burdensome student debt is and the extent to which it is disrupting major life events depends on a number of factors, including when you graduated from college with debt.

For those who graduated with debt as the economy was crashing, it was a double-whammy, said Keys, “so you’re seeing delayed marriage, delayed child-bearing, which are at least in part a function of the ongoing damage from the Great Recession.

Before the Great Recession, student debt levels were below auto loans, credit card debt and home-equity lines of credit in the ranking of household debt. Since then, student loan debt has surpassed these other debts

A $1,000 increase in student loan debt lowers the homeownership rate by about 1.5 percentage points for public four-year college-goers during their mid 20s, equivalent to an average delay of 2.5 months in attaining homeownership,

Individuals who attain higher education average higher salaries, which translates into a higher tax base. With higher levels of education attainment, there is also less reliance on social welfare programs, as individuals who attain higher education are more likely to be employed, less likely to be unemployed, and less likely to be in poverty. Higher levels of education are also associated with greater civic engagement, as well as lower crime.”

In 2014, the largest chunk of student debt — nearly 40% — belonged to people owing between $1 and $10,000.

The bigger problem, Webber said, comes when students take out loans and then don’t graduate from college

Nationally, 60% of people who start at a four-year institution wind up graduating within the next six years

There are other ways in which all debt is not created equal. “Many of the people who have the largest loans and are the most likely to default are also the people who got the worst credentials and poorest quality training when they graduated or potentially didn’t even graduate

But although $1.5 trillion is a big number, it may not be an unreasonable amount given the value it is creating

In 2002, a bachelor’s degree holder could expect to make 75% more than someone with just a high school diploma, and nearly a decade later that premium had risen to 84%

A bachelor’s degree is worth about $2.8 million over a lifetime, the study also found.

Australia has a system that links the repayment of loans with the tax system. “Income-driven repayment options have been created in the U.S.,” said Perna, “but these options are more cumbersome and administratively complex than in Australia and some other nations. By linking the amount of the monthly payment to an individual’s income, income-driven repayment options can help to protect borrowers against the risk of non-repayment. But a more seamless system wouldn’t require borrowers to annually report their income to the U.S. Department of Education

“Promise” or “free tuition” programs cropping up in some states are also worth examining

“Right now there is, frankly, very little accountability that schools have; they practically have no skin in the game. If students default on their loans, there is no bad effect for the school.”

As everyone in business knows, you manage what you measure. So although the replacing-GDP discussion may seem a little airy, its growing credibility in important circles could give it a real impact on economic policy

The story usually begins with Jeremy Bentham, an Englishman who in 1781 outlined a philosophy of utility that assessed the merits of an action according to how much happiness it produced. This was during the Enlightenment, when thinkers sought to replace religion-based rules with rational, scientific guides to decision making and life.

It’s true that the challenges of tracking energy use or pollution aren’t huge. But the politics are extremely tricky. In its early days the Clinton administration pushed the Bureau of Economic Analysis—the agency that measures U.S. GDP—to develop a green GDP

For its original purpose—measuring short-term economic fluctuations—GDP is not likely to be supplanted anytime soon. It may even be gaining ground: A major discussion is under way concerning whether the U.S. Federal Reserve and other central banks should in times of crisis focus not on inflation but on GDP growth.

Compiling GDP involves making a lot of choices, and even reasonable choices can lead to skewed results. Statisticians understandably favor goods and services that are bought and sold—and thus easily valued by market price—over economic activities whose value must be estimated

Developing nations with lots of foreign direct investment saw GDP grow much faster than GNP would have—but didn’t necessarily reap the benefits, because the investments’ profits went mostly to multinational corporations.

Economists, the most enthusiastic adopters of the concept, came to focus instead on the tangible expression of people’s needs and desires: what they were willing to spend money on.

Many things of value in life cannot be fully captured by GDP, but they can be measured by metrics of health, education, political freedom, and the like

The idea that economic and other data can be better presented with a dashboard of indicators than as a single number or ranked list is very much in the air among experts and policy makers.

In Sarkozy’s 2009 report on alternatives to GDP, the word “dashboard” appears 78 times. But the notion of dashboards hasn’t captured the public’s imagination. What has is a word that shows up just 29 times in the Sarkozy report (mostly in the bibliography): “happiness.”

In the 1950s and 1960s psychologists and sociologists reopened the question of whether it could be quantified. Opinion polls, then entering their heyday as measurers (and in some cases determiners) of the public mood, were an obvious vehicle for the attempt.

The economist Richard Easterlin imported the happiness discussion to his discipline with a 1974 paper pointing out that the results of national happiness polls did not correlate all that well with per capita income.

The interest in happiness surveys has also led to critical scrutiny of the Easterlin paradox. After reevaluating decades’ worth of polling data, the economists Betsey Stevenson and Justin Wolfers made headlines in 2008 by refuting the paradox—at least the part that said people in wealthy nations weren’t happier than those in poor nations

They were unable to conclusively debunk the argument that rises in income over time fail to deliver increased happiness, but the evidence they marshaled certainly muddied the waters

Money can’t buy happiness. But it could perhaps buy the ability to measure it.

Worker and union rights established in the New Deal era are fading, and Census Bureau figures released last fall show that income inequality in the U.S. is at its highest level on record.

Today, nearly 40 million Americans remain poor, and a majority of students in many schools do not have enough to eat

One-third of African Americans there lived in poverty in 2018, the year for which the most recent data is available. Most of the city’s public-school students need subsidized lunches, and black child-poverty rates are above 50%

Tax and budget cuts in the 1980s and again after the 2007–2008 financial meltdown destroyed budgets and crippled education. And though the police department is now “integrated,” police-community relations remain tense and often explosive.

This all sounds too familiar to a country that spends twice as much on health care as any other advanced nation, where “right to work” laws subvert unions, where gun violence is at epidemic levels, where greed overpowers concern for the earth, where the top 1% of earners own more wealth than 90% of the rest of us combined.

To address interrelated evils, King called for a revolution of values

To his dying day, King saw a new dispensation of economic justice as attainable. On April 3, 1968, he told a mass meeting of sanitation strikers and their supporters to remember that “either we go up together or we go down together.”

More than a half-century later, that promised land of economic justice remains out of reach.

There were many new phenomena that were discovered and that came to be understood in the centuries that followed Newton’s era. Take electricity and magnetism, for example. Until the 19th century, we didn’t really know what electricity or magnetism were, or how they worked. Isaac Newton certainly didn’t have a clue.

To many physicists around the turn of the 20th century, the state of physics seemed very settled. The Newtonian worldview had been very successful, and for a very long time.

In 1905, however, a revolution in physics did come. And perhaps even more surprising than the revolution itself was where that revolution came from. In 1905, Albert Einstein was not working as a professor at some prestigious university. He was not famous, or even well-known among other physicists.

Things didn’t stay this way for long, however. In 1905, Einstein wrote not one or two, but four absolutely groundbreaking papers. Any one of these four papers would have made him a star within the field of physics, and would have certainly secured him a position of prominence in the history of science.

It seems that having so many breakthroughs of this magnitude in such a short period of time had never happened before, and has never happened since. In the first of Einstein’s 1905 papers, he proposed that light doesn’t only behave like a wave, but that it is also made up of individual pieces or particles.

But Einstein’s paper provided concrete empirical evidence that atoms were, in fact, real and tangible objects. He was even able to use these arguments to make a pretty good estimate for the size and mass of atoms and molecules. It was a huge step forward.

The equations that physicists use to describe the propagation of light waves—what are known as Maxwell’s equations—predict that light should move through space at a speed of about 670 million miles per hour. And more interestingly, these equations don’t make any reference to any medium that the light waves propagate through.

Although no experiment had ever detected this aether, they argued that it must fill virtually all of space. After all, they argued, the light from a distant star could only reach us if there was a continuous path filled with aether, extending all the way from the star to us.

ventually, though, physicists discovered that there was no aether. It would be Einstein who would come up with an equation to explain this conundrum.

Processes of violent imperialism have paved the way for the cultural pandemic originating in the West

Most former British colonies now use English as their official language (e.g. Ghana and South Africa). Ever since the US colonized Puerto Rico after winning the Spanish-American war (note the absence of Puerto Rico, or Cuba, in the name of the war), the official languages on the island became Spanish and, of course, English.

Today, English is the third most spoken language in the world and tops the list of second languages. English is a necessity for studying at the most prestigious institutions of higher learning, a ticket to working almost anywhere in the world, and an instrument enabling a livelihood in the wealthiest nations.

This phenomenon feeds into the growth of social inequality linked to globalization. The majority of the time, English learned as a second language in public schools does not create a proficiency level adequate for working, studying, or relying on the language in daily life.

People dedicate their time and resources to learning and perfecting their understanding and knowledge of English, rather than preserving their own customs and culture.

The process of globalization leads people to visualize an array of opportunities and an exponentially better future linked to the English language. A language is not only an instrument of communication, however. It is also the tool of a society, made up of its culture, traditions, and sets of religious and ideological beliefs

English has also become the main language used in science. Doctors around the world use English to communicate their findings. Most research papers are written in English as a way to facilitate international scientific cooperation.

Although this may seem like a necessity to promote scientific discovery, the resulting gap is problematic. The researchers who have not had the chance to learn English are at a disadvantage.

These processes suggest a disconcerting implication – globalization is simply a more “socially acceptable” means of imperialism, without violence

Globalization and the expansion of the English language have resulted in oppression and inequality.

If the preservation of other cultures is given the same importance and value as spreading English is currently receiving, the language can be an addition, not a replacement, to a naturally evolving culture’s array of nuances.

Relatively few words are onomatopoeic,

many onomatopoeic words are of recent origin, and not all are derived from natural sounds.

The Ding-Dong Theory This theory, favored by Plato and Pythagoras, maintains that speech arose in response to the essential qualities of objects in the environment. The original sounds people made were supposedly in harmony with the world around them.

there is no persuasive evidence, in any language, of an innate connection between sound and meaning.

The La-La Theory The Danish linguist Otto Jespersen suggested that language may have developed from sounds associated with love, play, and (especially) song.

this theory still fails to account for "... the gap between the emotional and the rational aspects of speech expression... ."

The Pooh-Pooh Theory This theory holds that speech began with interjections—spontaneous cries of pain ("Ouch!"), surprise ("Oh!"), and other emotions ("Yabba dabba do!").

No language contains very many interjections,

The Yo-He-Ho Theory According to this theory, language evolved from the grunts, groans, and snorts evoked by heavy physical labor.

it doesn't go very far in explaining where words come from.

Over the past 20 years, scholars from such diverse fields as genetics, anthropology, and cognitive science have been engaged, as Kenneally says, in "a cross-discipline, multidimensional treasure hunt" to find out how language began. It is, she says, "the hardest problem in science today."

Animal communication systems, in contrast, typically have at most a few dozen distinct calls, and they are used only to communicate immediate issues such as food, danger, threat, or reconciliation. Many of the sorts of meanings conveyed by chimpanzee communication have counterparts in human 'body language'.

The basic difficulty with studying the evolution of language is that the evidence is so sparse. Spoken languages don't leave fossils, and fossil skulls only tell us the overall shape and size of hominid brains, not what the brains could do

All present-day languages, including those of hunter-gatherer cultures, have lots of words, can be used to talk about anything under the sun, and can express negation. As far back as we have written records of human language - 5000 years or so - things look basically the same.

According to current thinking, the changes crucial for language were not just in the size of the brain, but in its character: the kinds of tasks it is suited to do - as it were, the 'software' it comes furnished with.

So the properties of human language are unique in the natural world.

About the only definitive evidence we have is the shape of the vocal tract (the mouth, tongue, and throat): Until anatomically modern humans, about 100,000 years ago, the shape of hominid vocal tracts didn't permit the modern range of speech sounds. But that doesn't mean that language necessarily began the

Some researchers even propose that language began as sign language, then (gradually or suddenly) switched to the vocal modality, leaving modern gesture as a residue.

. In an early stage, sounds would have been used to name a wide range of objects and actions in the environment, and individuals would be able to invent new vocabulary items to talk about new things

In order to achieve a large vocabulary, an important advance would have been the ability to 'digitize' signals into sequences of discrete speech sounds - consonants and vowels - rather than unstructured calls.

These two changes alone would yield a communication system of single signals - better than the chimpanzee system but far from modern language. A next plausible step would be the ability to string together several such 'words' to create a message built out of the meanings of its parts.

This has led some researchers to propose that the system of 'protolanguage' is still present in modern human brains, hidden under the modern system except when the latter is impaired or not yet developed.

Again, it's very hard to tell. We do know that something important happened in the human line between 100,000 and 50,000 years ago: This is when we start to find cultural artifacts such as art and ritual objects, evidence of what we would call civilization.

One tantalizing source of evidence has emerged recently. A mutation in a gene called FOXP2 has been shown to lead to deficits in language as well as in control of the face and mouth. This gene is a slightly altered version of a gene found in apes, and it seems to have achieved its present form between 200,000 and 100,000 years ago.

Nevertheless, if we are ever going to learn more about how the human language ability evolved, the most promising evidence will probably come from the human genome, which preserves so much of our species' history. The challenge for the future will be to decode it.

In 1609, Galileo learned about the device and developed one of his own, significantly improving its design. That fall, he pointed it at the moon and discovered it had craters and mountains, debunking the common belief that the moon’s surface was smooth.

Galileo soon went on to make other findings with his telescope, including that there were four moons orbiting Jupiter and that Venus went through a complete set of phases (indicating the planet traveled around the sun).

Galileo had three children with a woman named Marina Gamba, who he never married. In 1613, he placed his two daughters, Virginia, born in 1600, and Livia, born in 1601, in a convent near Florence, where they remained for the rest of their lives, despite their father’s eventual troubles with the Catholic Church

Copernicus’ heliocentric theory about the way the universe works challenged the widely accepted belief, espoused by the astronomer Ptolemy in the second century, that put the Earth at the center of the solar system.

Galileo received permission from the Church to continue investigating Copernicus’ ideas, as long as he didn’t hold or defend them.

As a result, the following year Galileo was ordered to stand trial before the Inquisition in Rome

After being found guilty of heresy, Galileo was forced to publicly repent and sentenced to life in prison.

Although Galileo was given life behind bars, his sentence soon was changed to house arrest. He lived out his final years at Villa Il Gioiello (“the Jewel”), his home in the town of Arcetri, near Florence

In 1979, Pope John Paul II initiated an investigation into the Catholic Church’s condemnation of Galileo.

Thirteen years later, and 359 years after Galileo was tried by the Inquisition, the pope officially closed the investigation and issued a formal apology in the case, acknowledging that errors were made by the judges during the trial.

There’s no evidence to suggest the fruit actually landed on his head, but Newton’s observation caused him to ponder why apples always fall straight to the ground (rather than sideways or upward) and helped inspired him to eventually develop his law of universal gravitation

In 1687, Newton first published this principle, which states that every body in the universe is attracted to every other body with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, in his landmark work the “Principia,” which also features his three laws of motion.

In 1726, Newton shared the apple anecdote with William Stukeley, who included it in a biography, “Memoirs of Sir Isaac Newton’s Life,” published in 1752.

His famous apple tree continues to grow at Woolsthorpe Manor.

hus Copernicus started to look for something simpler, almost at the same time that Michelangelo undertook another great project, that of decorating the ceiling of the Sistine Chapel.

Copernicus had a full Renaissance résumé: studies in medicine, art, mathematics, canon law and philosophy; experience as an economist and a diplomat; and also a good position as an ecclesiastical official.

By 1514, he had already written a sketch of his theory, although he did not publish it for fear of being condemned as a heretic and also because he was a perfectionist. He spent 15 more years repeating his calculations, diagrams and observations with the naked eye, prior to the invention of the telescope.

Copernicus was the first to recite them in order: Mercury, Venus, Earth, Mars, Jupiter and Saturn, the 6 planets that were then known.

When Copernicus finally decided to publish his theory, the book’s publisher softened it in the prologue: he said that there were “only easier mathematics” for predicting the movements of the planets, and not a whole new way of looking at the reality of the universe. But this was understood as a challenge to Aristotle, to the Church, and to common sense.

It would be 150 years before the Copernican revolution triumphed, and the world finally admitted that the Earth was just one more spinning top.

Since antiquity, this idea had been considered but rejected in favor of the traditional (geostatic and geocentric) thesis that the earth stands still at the center of the universe.

The objections to the geokinetic and heliocentric idea involved astronomical observations, the physics of motion, biblical passages, and epistemological principles (e.g., the reliability of human senses, which reveal a stationary earth)

The Inquisition launched an investigation. Galileo’s writings were evaluated and other witnesses interrogated. The charges against Galileo were unsubstantiated. However, the officials started worrying about the status of heliocentrism and consulted a committee of experts.

These discoveries did not conclusively prove Copernicanism, but provided new evidence in its favor and refutations of some old objections.

Galileo became more explicit in his pursuit of heliocentrism, and this soon got him into trouble.

In February-March 1615, one Dominican friar filed a written complaint against him, and another one testified in person in front of the Roman Inquisition. They accused Galileo of heresy, for believing in the earth’s motion, which contradicted Scripture, e.g., the miracle in Joshua 10:12-13.

Copernicus did not really refute these objections, but he elaborated a novel and important astronomical argument. Thus, Copernicanism attracted few followers. At first, Galileo himself was not one of them, although he was interested because his new physics enabled him to answer the mechanical objections.

On February 24, 1616, the consultants unanimously reported the assessment that heliocentrism was philosophically (i.e., scientifically) false and theologically heretical or at least erroneous.

The following day, the Inquisition, presided by Pope Paul V, considered the case. Although it did not endorse the heresy recommendation, it accepted the judgments of scientific falsity and theological error, and decided to prohibit the theory.

the Church was going to declare the idea of the earth’s motion false and contrary to Scripture, and so this theory could not be held or defended. Galileo agreed to comply.

Without mentioning Galileo, it publicly declared the earth’s motion false and contrary to Scripture. It prohibited the reading of Copernicus’s Revolutions, and banned a book published in 1615 by Paolo Antonio Foscarini; he had argued that the earth’s motion was probably true, and certainly compatible with Scripture.

The 1616 condemnation of Copernicanism was bad enough for the relationship between science and religion, but the problems were compounded by Galileo’s trial 17 years later.

Galileo kept quiet until 1623, when a new pope was elected, Urban VIII, who was a great admirer of Galileo.

The Inquisition summoned him to Rome, and the trial proceedings lasted from April to June 1633. He was found guilty of suspected heresy, for defending the earth’s motion, and thus denying the authority of Scripture.

“Suspected heresy” was not as serious a religious crime as “formal heresy,” and so his punishment was not death by being burned at the stake, but rather house arrest and the banning of the Dialogue.

The Church’s condemnation of Copernicanism and Galileo became the iconic illustration of the problematic relationship between science and religion.

This controversy will probably not end any time soon. This may be seen from Pope Francis’s 2015 encyclical Laudato Si’, with its focus on climate change. Whatever its merits, it could be criticized for having failed to learn, from the Galileo affair, the lesson that the Church should be wary of interfering in scientific matters.

In 1609, Kepler published a book containing the first two laws. The book also revealed his new model of the solar system, which was against what most scientists back then believed.

He stated that planets moved in elliptical orbits through the solar system, with the Sun located at one focus of the ellipse. Before Kepler, they believed that all orbits in the solar system were perfectly circular.

About ten years later, Kepler added his third law: that square of the orbital period divided by the cube of orbit’s semi-major axis is the same for all planets. Although not immediately accepted, his three laws took science to the next level. Why was he initially not appreciated?

Kepler applied this to the planets and stated that the solar system was built upon geometrical objects called Platonic solids that are a specific type of three-dimensional shape. They have identical sides or surfaces, edges of equal length, and angles of equal extent.

The model Kepler presented was based on a sequence of six spheres and the five Platonic solids, each located between two spheres. Back then, only six planets were discovered as Uranus and Neptune’s discovery took until the 18th and 19th centuries. Thus, each sphere represented one planet.

nitially, it seemed to explain the approximate ratios of the orbits of the six planets. It also gave a reason why there are only six planets—because there are only five Platonic shapes, each of which needs to fit between the orbit of two planets, only once

Kepler published this theory in detail, in his book Mysterium Cosmographicum. Despite all the value he gave to this theory, we now know how wrong it was.

Kepler cherished the theory as his most significant work, long after he had discovered the three laws.

However, the number of planets in the solar system or any other system in the universe is not predictable. Many of the numbers appearing everywhere are out of a mere accident, just like the number of planets.

Kepler thought his greatest achievement was the wrong solar system he drew, but it was the three laws that were so right to survive to date.

Those who subscribe to the theory of linguistic relativity believe that a person’s way of thinking is influenced by the language he or she speaks

Language is a result of society. Therefore, language does not deserve the credit for shaping the way we process information.

Differences in the thought processes of speakers of different languages should be accredited to the distinct cultures from which these languages emerge.

Nevertheless, language is an important factor in the way a culture evolves. Ultimately, although it is our society rather than our language that shapes the way we think, language helps to enforce the way society is.

Language cannot be said to be responsible for the way a society functions since language itself is a result of that society. A key example of this can be found in the substance of a language, which tends to reflect the values of its speakers and the culture it comes from

A proponent of linguistic relativity might argue that this is an example of language shaping the way people think by defining age as the primary quality to know about a person.

However, this assertion fails to recognize the big picture. A more accurate analysis might indicate that society is responsible for this way of thinking, not language.

However, language still plays an important role in affecting cultures and social norms. Although languages are reflections of cultures, languages do influence how cultures will look in the future.

We can see this phenomenon in the history of the English language, which dates back to sometime between the 5th and 7th century AD, with Modern English gaining prominence in the late 17th century.

As we see with English sentence structure, the influence of cultural institutions on a language is often left intact even after that institution has weakened or disappeared.

Since language is our only proficient method of communication, what we can communicate is limited to the words and phrases available to us. While the society we live in may limit our perspective, the extent and strength of these limitations do not compare to that which language imposes. Cultural change comes more easily to us than linguistic change.

t took centuries for the Great Vowel Shift to occur while the world experienced revolutions, literary movements, great awakenings and deadly plagues at a much faster pace. This pattern is demonstrated in American culture as the language we speak fails to keep up with the progress we make. Patterns in our vocabulary tend to reflect this.

A commonly cited phenomenon is the negative and positive associations that English seems to make with “black” and “white.”

The limits of language may prevent us from progressing as quickly as we may want to, but we do have the ability to overcome some of these linguistic limits.