I construct estimates of world GDP over the very long run by combining estimates of total human populations with largely-Malthusian estimates of levels of real GDP per capita.

Population

I take my estimates of human population from Kremer (1993), but it would not matter if I had chosen some other authority. All long-run estimates of human population that I have found are quite close together (with the exception of estimates of population around 5000 BC, where Blaxter (1986) estimates a population some eight times that of other authorities). Note that this does not mean that the estimates are correct—just that they are roughly the same.

Kremer (1993) sees human populations as growing at an increasing proportional rate from perhaps 125,000 in one million B.C. to 6 billion today. Population reached approximately 4 million by 10000 BC, 50 million by 1000 BC, and 170 million by the year 1. Population then reached 265 million by the year 1000, 425 million by 1500, and 720 million by 1750 before exploding to 1.2 billion by 1850, 1.8 billion by 1900, 2.5 billion by 1950, and 6 billion today. Up until 1950 Kremer calculates that the rate of growth of human populations was roughly proportional to their total level.

Angus Maddison (1995) has constructed estimates of real GDP per capita for the world from 1820 to 1992. His estimates are best thought of as Laspeyres purchasing power parity estimates in 1990 international dollars. That is, they:

• Compare income levels across countries not using current exchange rates, but instead trying to change one currency into another at rates that keep purchasing power constant (“purchasing power parity”).

• Value goods in relative terms using the prices found in a country in the middle of the world distribution of income (“international”).

• Calculate a value for 1990 GDP per capita in the United States equal to U.S. current-dollar GDP per capita in 1990 (“1990 dollars”).

• Do not take explicit account of the benefits of the introduction of new goods and new types of goods, but instead calculate GDP per capita in the past by valuing the commodities produced in the past at recent prices—and not making any correction for the restricted range of choice enforced by limited production possibilities (“Laspeyres”).

All of these save the last is reasonable—is in fact a way of proceeding vastly preferable to the alternatives. I will return to the last of these later. But first I want to extend Maddison’s estimates backward before 1820.

Economies in the long ago were very different from our economy of today. For one thing, for 95% of the time since the invention of agriculture economies were Malthusian: improvements in productivity and technology showed up not as increases in average standards of living but as increases in population levels at a roughly constant standard of living. For a second, in the long-long ago the pace of invention and innovation can most optimistically be described as glacial—two hundred years to achieve the pace of relative change that we see in twelve months. For a third, arithmetic tells you that in the long-long ago the overwhelming majority of those who are or become well-off have either held on to what their parents bequeathed them or proven successful in zero- or negative-sum redistributional struggles—rather than having found or placed themselves at a key chokepoint of positive-sum productive processes.

This means that, lacking data, we can make data up out of thin air by making inferences from very low pre-1500 population growth rates that material standards of living were back then very close to "subsistence". We know that a preindustrial not-very literate population with ample access to food and resources can and will roughly double every generation: that is the pace of European settler expansion in the Americas, after all. And we know that from 5000 BC to 1345 the average rate of global population growth was 0.07%/year—not the 2.5%/year of normal human biology with ample food and other resources. The inescapable conclusion is that resources were scarce: just barely more than necessary to keep human populations from declining given the socio-cultural institutions then prevailing.

We can check these by consulting the long-run biomedical studies of Rick Steckel (1995), “Stature and the Standard of Living,” Journal of Economic Literature 33:4 (December), pp. 1903-40, and many others. We can use Steckel’s estimates of the relationship between height and income found in a cross-section of people alive today and evidence from past burials to infer what real incomes were in the past. The conclusion is inescapable: people in the preindustrial past were short—very short—with adult males averaging some 63 inches compared to 69 inches either in the pre-agricultural Mesolithic or today. Therefore people in the pre-industrial past were poor—very poor. If they weren’t very poor, they would have fed their children more and better and their children would have grown taller. And they were malnourished compared to us or to their pre-agricultural predecessors: defects in their teeth enamel, iron-deficient, skeletal markers of severe cases of infectious disease, and crippled backs.

Pre-industrial dire poverty lasted late. Even as of 1750 people in Britain, Sweden, and Norway were four full inches shorter than people are today—consistent with an average caloric intake of only some 2000 calories per person per day, many of whom were or were attempting to be engaged in heavy physical labor. And societies in the preindustrial past were stunningly unequal: the upper classes were high and mighty indeed, upper class children growing between four and six inches taller than their working-class peers. Moreover, there are no consistent trends in heights between the invention of agriculture and the coming of the industrial age. Up until the eve of the industrial revolution itself, the dominant human experience since the invention of agriculture had been one of poverty so severe as to produce substantial malnutrition and stunted growth.

It is this experience that makes Jared Diamond conclude that the invention of agriculture was the worst mistake ever made by the human race.

If you plot the rates of world population growth against Maddison’s estimates of world GDP per capita, you find a very high and significant correlation between the two from the early nineteenth century until roughly World War II. After World War II the demographic transition has begun to take hold in large parts of the world, but before World War II the higher is world GDP per capita, the faster is population growth—with a 1 percentage point per year increase in population growth associated with an increase in average world GDP per capita of $1,165 (with a t-statistic of 7.4 and an adjusted-R2 of 0.84).

If you are enough of a Malthusian to believe that this tight relationship before World War II is not coincidence but instead reflects a near-linear dependence of the rate of human population growth on the margin between actual production and bio-cultural subsistence, then you can use the fitted relationship between population growth and Maddison-concept GDP per capita to backcast estimates of world GDP per capita before 1820.

An alternative (preferred by Maddison) is to assume that GDP per capita was constant in Asia and Africa from 1500-1820, grew at 0.1 percent per year from 1500-1820 in Latin America and Eastern Europe, and grew at 0.2 percent per year from 1500-1820 in Western Europe (an estimate that Maddison attributes to Simon Kuznets (1973)); this alternative could then be backcast further by assuming that pre-1500 GDP per capita was constant at near-Malthusian bio-cultural subsistence.

I prefer the first alternative (and have used it). But I also report estimates using the second.

New Goods

A large proportion of our high standard of living today derives not just from our ability to more cheaply and productively manufacture the commodities of 1800, but from our ability to manufacture whole new types of commodities, some of which do a better job of meeting needs that we knew we had back in 1800, and some of which meet needs that were unimagined back in 1800. How much has this change—the fact that we make not just the same goods, but new goods and new types of goods—enhanced our material prosperity? Nordhaus (1997) provides perhaps the most eloquent and sophisticated argument that standard measures—like those of Maddison—that do not take explicit account of these factors grossly understate the rate of economic growth over the past two centuries.

I know that I at least would be extremely unhappy if I were handed my current income, told that I could spend it on goods at current prices, but that I was prohibited from buying anything that was not made before 1800. Yet Maddison’s procedures would implicitly take such a reduction in the range of goods I could purchase as having no effect on my real income or real material standard of living.

But by how much has our power to make new things—not just the same things more efficiently—amplified our material prosperity?

In at least some models of growth in which the set of goods that can be produced expands, the correct measure of real output is proportional to the product of purchasing power (income divided by the average price of a good) and the number of goods that can be produced. As best as I can determine, about three-quarters of world expenditure today is spent on commodities that simply did not exist back in 1800. So I—somewhat arbitrarily—use this to assign an additional fourfold multiplication to output per capita since 1800 in addition to the increases in output per capita calculated by Maddison.

But since this—large—extra adjustment is not to everyone’s taste, I also report the “ex-Nordhaus” series without the “new kinds of goods” adjustment.

Conclusion

The outcome of this set of calculations is thus seven series: Kremer’s (1993) estimates of population; three estimates of GDP per capita (my preferred estimate, the constant-before-1500 estimate, and the ex-Nordhaus estimate); and three estimates of total world real GDP (capita (my preferred estimate, the constant-before-1500 estimate, and the ex-Nordhaus estimate).

They are reported in the table below:

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Each year, millions of visitors flock to Angkor Wat, an ancient temple in modern-day Cambodia. There, they marvel at the 900-year-old towers, a giant moat and the shallow relief sculptures of Hindu gods. But what they can't see are 200 hidden paintings on the temple walls.

New, digitally enhanced images reveal detailed murals at Angkor Wat showing elephants, deities, boats, orchestral ensembles and people riding horses — all invisible to the naked eye.

Many of the faded markings could be graffiti left behind by pilgrims after Angkor Wat was abandoned in the 15th century. But the more elaborate paintings may be relics of the earliest attempts to restore the temple, researchers said. [See Photos of Angkor Wat's Secret Paintings]

Painting discovery

Subtle traces of paint caught the eye of Noel Hidalgo Tan, a rock-art researcher at Australian National University in Canberra, while he was working on an excavation at Angkor Wat in 2010.

Built between A.D. 1113 and 1150, Angkor Wat stood at the center of Angkor, the capital of the Khmer Empire. The 500-acre (200 hectares) complex, one of the largest religious monuments ever erected, originally served as a Hindu templededicated to the god Vishnu, but was transformed into a Buddhist temple in the 14th century.

Tan said he kept spotting traces of red pigment all over the walls when he was taking a stroll through the temple on his lunch break one day. He took a few pictures and planned to digitally enhance them later.

"I didn't realize that the images would be so detailed, so I was naturally taken aback," Tan told Live Science in an email.

The digitally enhanced pictures revealed paintings of elephants, lions, the Hindu monkey god Hanuman, boats and buildings — perhaps even images of Angkor Wat itself. Tan went back to the site to conduct a more methodical survey in 2012 with his Cambodian colleagues from APSARA (which stands for the Authority for the Protection and Management of Angkor and the Region of Siem Reap).

Invisible images

"Some of the most detailed paintings, the ones located at the top of the temple, are passed by literally thousands of visitors every day, but the most elaborate scenes are effectively invisible to the naked eye," Tan said in an email.

To make these paintings visible, Tan used a technique called decorrelation stretch analysis, which exaggerates subtle color differences. This method has become a valuable tool in rock-art research, as it can help distinguish faint images from the underlying rock. It has even been used to enhance images taken of the Martian surface by NASA's Opportunity rover.

One chamber in the highest tier of Angkor Wat's central tower, known as the Bakan, contains an elaborate scene of a traditional Khmer musical ensemble known as the pinpeat, which is made up of different gongs, xylophones, wind instruments and other percussion instruments. In the same chamber, there's an intricate scene featuring people riding horses between two structures, which might be temples. [Image Gallery: How Technology Reveals Hidden Art Treasures]

"A lot of the visible paintings on the walls have been previously discounted as graffiti, and I certainly agree with this interpretation, but there are another set of paintings discovered from this study that are so schematic and elaborate that they are likely not random graffiti, but an attempt to decorate the walls of the temple," Tan said.

Christophe Pottier, an archaeologist and co-director of the Greater Angkor Project who was not involved in the new study, agreed that these more complex murals show deliberate intention and can't be interpreted as mere graffiti.

Pottier, however, added that the discovery of hidden paintings isn't all that surprising. Though they haven't been studied systematically before now, several traces of paintings have been found at the temple during the last 15 years.

"But I am very pleased, because the traces identified are quite diverse, lively and original," Pottier said. Most of the paintings that were previously known depicted boats and floral and geometric designs, Pottier told Live Science in an email.

Though researchers don't know exactly when the paintings were created, Tan speculated that the most elaborate artworks may have been commissioned by Cambodia's King Ang Chan, who made an effort to restore the temple during his reign between 1528 and 1566. During this time, unfinished carvings were completed and Angkor Wat began its transformation into a Buddhist pilgrimage site. Some of the newly revealed paintings have Buddhist iconography, such as a painting of a temple that looks like a Buddhist mound-like monument known as a stupa.

The findings were detailed in the journal Antiquity this week.

Follow Megan Gannon on Twitter and Google+.Follow us @livescience, Facebook& Google+. Original article on Live Science.

• Images: Lost Medieval City Discovered Near Angkor Wat
• Photos: The Riddle of Ancient Angkor
• The 7 Most Mysterious Archaeological Finds on Earth

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SEE ALSO: These 30 National Landmarks Could Be Destroyed By Climate Change

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If you are like most people, you learned history in classes that largely covered facts related to dates, places, and people ... and you probably couldn’t wait until the school bell rang.

Sadly, children’s exposure to history is often framed in a way that is less interesting and engaging than it could be, and it robs students of a curiosity about the past that could benefit their own future by understanding the richness of the human experience.

When it comes to the intersection of the financial markets and human history, there is a kaleidoscope of tales drawn from centuries of market mischief, mishaps and mayhem. This article reveals a few less-known but notable events drawn from the past half-millennium that might pique your own interest in the rivers of time that have led us to the present day.

1. Holland’s Famed Tulipmania Was Driven by Two Viruses

You are probably acquainted with the fabled “tulipmania” that gripped Holland during the early 1600s. What most people don’t know is that two viruses played central roles in this drama.

The tulip bulbs themselves were classified into three groups: the single-colored, the multi-colored, and the “bizarres.” This last category is most important, as bizarres were the rarest and most sought-after tulip. The reason these unusual flowers came about was due to a virus that interfered with the plant’s ability to create a uniform color on the petal. It is today known as a “breaking” virus, since it breaks the plant’s lock on a single petal color without killing the plant. The effect on the flower was striking, producing mosaic-like flames of color on each petal. Of course, the Dutch of the time knew nothing of such things; they merely took a strong liking to these rare and unusual flowers.

As tulipmania neared its frenzied peak, an outbreak of bubonic plague emerged in the land. The psychological effects of this varied from person to person, but for some, it created a reckless, fatalistic disregard for financial risk, since no one was sure if they would be alive or dead in the months ahead. The same plague was also to blame when an important auction of tulip bulbs took place and not a single buyer showed up, ostensibly out of fear of the disease. Of course, plenty of sellers were there, but with no one to sell to, it swiftly became apparently that the top was in, and holders of the bulbs scrambled to get out at any price.

2. 1720s France and 1930s U.S. Share an Important Similarity

In early 18th century France, John Law had revolutionized finance in the country by introducing paper money in lieu of specie (money in coin). As the frenzy surrounding the mania known later as “The Mississippi Scheme” turned into panic, banks were under terrible stress from holders of the paper notes who demanded their “real” money (that is, precious metals) back.

As the crowds pressed in, the Royal Bank took measures to try to slow down the extraction of real money from its vaults. For example, if a person came to withdraw gold in exchange for notes, the teller would count out the change at a comically slow pace, thus frustrating the others in line and reducing the amount that physically could be taken out in the business day.

Another trick was to put clerks in line who were instructed to withdraw some gold and then simply return the coinage to the vault immediately afterward. This practice slowed down legitimate customers even further merely by making the lines longer.

Two hundred years later, a similar situation occurred in the U.S. as “bank runs” became commonplace during the Great Depression. Between 1929 and 1933, more than 43% (10,763 out of 24,970) of commercial banks in the country failed. Some banks, desperate to stay in business, resorted to ridiculous measures. One Utah bank instructed its tellers to work as slowly as possible, counting out small bills one by one, in order to reduce the pace at which money was being extracted by anxious account holders.

Although two centuries had passed, it seems there had been no innovation in methods of stalling anxious customers during a financial calamity.

3. Sir Isaac Newton Got Burned by the Bitcoin of His Day

The digital currency bitcoin famously ascended to unthinkable heights in 2013, only to crumble from its peak value during the first four months of 2014. A similar trajectory was experienced by shares of the South Sea Company during the time of Isaac Newton.

As mythic a figure as Newton is, he was still human, and he had watched jealously as his friends made fortunes in South Sea shares. He jumped on board early in 1720, enjoyed a portion of the ascent in the stock’s price, and sold at a profit. As the stock kept climbing, he elected to put even more money in this time, hoping to “catch up” with the gains his peers had enjoyed.

Although the great scientist got to enjoy the stock’s final vault to above 1,000 pounds, he watched, dumbfounded, as South Sea fell by its own form of gravity. In the second half of 1720, Newton’s holdings created a loss of 20,000 pounds before he dumped all his shares. His earlier profits were wiped out, and his misadventure with South Sea was a financial folly from which he would never recover. He said of the experience, “I can calculate the movement of heavily bodies, but not the madness of men.”

4. Lincoln Almost Violated the Constitution Over a Hoax

Abraham Lincoln has the status of a near-deity in U.S. history. After years of civil war, however, he became an unwitting actor in an elaborate hoax. Following the hoax, he came dangerously close to infringing on the right of free speech enshrined in the U.S. Constitution.

During the war, the opportunities to profit from gold’s dynamic price movements were not missed by the unscrupulous, and one fascinating account from 1864 captures this neatly. In May of that year, after four years of war, the Union was growing hopeful that a successful conclusion might be in sight.

However, on May 18, the morning papers the New York World and the Journal of Commerce came out with shocking news. They reported that the president had ordered an additional 400,000 men to be conscripted into the Union army on account of “the situation in Virginia, the disaster at Red River, the delay at Charleston, and the general state of the country.”

The discouraging report and the demand for such a huge quantity of fresh soldiers sent a shockwave through the financial community. This was because the report made it seem obvious that things were not going nearly as well in the war as believed. Stocks tumbled, and hard assets such as gold soared in value. Some people became puzzled, however, because this important report was nowhere to be found in any of the city’s many other newspapers.

Late that morning, crowds had gathered at the offices of both papers that had published the news. The editors assured the crowds that the story was true, producing the dispatch from the Associated Press with the matching information. The Associated Press, however, the ostensible source of the information, quickly issued a statement making clear that they had never sent out this dispatch. This soon caught the attention of the State Department in Washington with Secretary of State William Seward declaring the news dispatch to be “an absolute forgery.”

It turns out that the forgery was a clever creation of Joseph Howard, the city editor of the Brooklyn Eagle newspaper. Howard, who was intimately acquainted with the workings of New York’s newspapers, had come up with a scheme. He knew that bad news from the war would cause gold to rise in value. He also knew that the best way to get a dispatch into the morning papers would be to submit the dispatch when the newspaper staff was most vulnerable — that is, in the wee hours of the morning, when there were hardly any personnel around to verify the facts.

Howard worked with an accomplice to craft a realistic-looking Associated Press news release. Howard, along with Francis Mallison (a reporter for his journal), then distributed the news item at 3:30 in the morning to New York City’s newspapers. Most of them were reluctant to print such an important piece without verification, but two of them proceeded to run with the story.

Of course, before any of this took place, Howard acquired as much gold as he could in his margin account. Once the grim news was raging throughout the financial community, he disposed of his position at a handsome profit, never suspecting the false item would be traced back to him.

It was, however. President Lincoln ordered the closure of both papers that had printed the dispatch, an order that was later rescinded. Lincoln’s furious demand for the paper’s closures, however, became one of the few black marks on his presidency since, in spite of the ugly circumstances involved, it went right to the heart of freedom of the press guaranteed by the Constitution.

The irony to the newspaper hoax was that only two months later, Lincoln did indeed order the conscription of more men into the Union army. However, the figure demanded was not the 400,000 that Howard had dreamed up for his bogus news release. It was, in fact, a full half million. Howard’s fanciful fraud was, in the end, prescient.

5. Spotting Bubbles

There’s no magic secret to spotting a bubble: After all, if there were, bubbles wouldn’t last for very long. One consistency about bubbles is how obvious they seem in hindsight. As we now look back on the Internet bubble, the Hunt silver debacle, the South Sea bubble, or any of the others, it’s all too easy for us to shake our heads at the foolhardiness of our ancestors and take comfort in our newfound wisdom. If only this were ever the case! Humans will always be able to concoct a new and, for its contemporaries, undetectable bubble.

Analogs to the past can be helpful, however, since — as the old saying goes — history may not repeat, but it does rhyme. There are a couple of big challenges to drawing parallels between the past and the present, however. First, as the world speeds up, through such developments as improved communication and new technologies, it becomes necessary to “translate” instances of the past to modern-day equivalents. The kinds of rumors or narratives that might have spurred on a market in the past might have spread “like wildfire” a hundred years ago, when “wildfire” could have been measured in weeks instead of milliseconds.

The other challenge, and probably the most important, is trying to divine when a top is at hand, even if the bubble is relatively obvious. Those who took advantage of the “top” in NASDAQ stocks in late December 1999 would have been extraordinarily close to pinpointing the peak of the bubble, but they would have also suffered a complete portfolio wipe-out as Internet stocks vaulted a final 100% in the waning weeks of the tech bubble. Although speculators will undoubtedly leave money on the table by waiting, it’s probably wisest to wait until it’s evident that the bubble is deflating before taking action, even if you miss the first portion of the move downward.

6. The Wizard of Oz Is a Precious Metals Allegory

Late in the 19th century, there was a widespread struggle in the U.S. over whether silver or gold, or a combination, should be the basis for “sound money.” The drama around this debate was captured allegorically in a popular children’s tale published around the time entitled “The Wonderful Wizard of Oz.”

The book was written in the late 1890s by L. Frank Baum during the throes of the gold/silver political dichotomy. The major elements of the book represented the circumstances and characters of Baum’s surroundings:

• The yellow brick road was the gold standard;
• The silver slippers represented the silver standard (the slippers were changed to ruby in the movie version for aesthetic effect, since color in movies was very unusual in those days and the ruby slippers were very showy on screen);
• Dorothy Gale represented everyday American people who had been, metaphorically speaking, swept away to an unfamiliar circumstance by gale-like forces beyond their control;
• Emerald City represented the “greenbacks,” the political contingent — that is, the citizens themselves — that supported unbacked paper money;
• The Wizard, who runs Emerald City, was the disingenuous politician who appears to be powerful and wise but is, in fact, a foolish man behind a curtain who is trying to frighten and control regular people;
• The Scarecrow, stuffed with straw, was the American farmer;
• The Cowardly Lion was William Jennings Bryan, the leader of the silver movement (Bryan was widely characterized by critics as indecisive);
• The Tin Man represented American’s industrial interests;
• The Wicked Witch of the West stood for the American West; and
• The flying monkeys were the displaced Native Americans of the West (in the novel, the leader of the monkeys tells Dorothy, “Once we were a free people, living happily ... this was many years ago, long before Oz came out of the clouds to rule over this land”).

In the end, of course, Dorothy simply has to make use of the silver slippers — which she could have done at any time — to return her to the simple, safe, and secure life she yearned for.

7. J.P. Morgan Held Bankers Captive to Get What He Wanted

Before the U.S. had a central bank, its closest equivalent came in the form of one man: J.P. (John Pierpont) Morgan. On more than one occasion, he single-handedly averted a major financial crisis (often profiting handsomely by doing so).

During one particularly dangerous crisis in 1907, known later as the Rich Man’s Panic, Morgan brought together the most important bankers of the country to address the crisis on a Saturday night, and he gave them use of the library at his opulent New York mansion to do so. Morgan told the men that they needed to come up with a solution to the problem, and he left the library to attend to other matters. Only later did the bankers realize that Morgan had literally locked them inside the library.

When Morgan entered the room some time later, no consensus had been reached, so he told the men that they needed to come up with $25 million to shore up the trust companies through the crisis or else the city would face unmanageable panic. After considerable prodding, Morgan was able to persuade the de facto leader of the group to sign an agreement to advance the funds, and the rest of the men followed suit. The agreement having been reached, Morgan produced the key and allowed the bankers out of the library at 4:45 that Sunday morning. Having successfully satisfied their leader (and captor), they were permitted to go home.

8. The Real Estate Crisis Had a Prequel in Thailand

You are already well familiar with the real estate crisis that gripped the U.S. starting in 2007. A full decade before that, and half a world away, Thailand experienced its own peak and collapse, although the origins of the high valuations were somewhat different from our own.

Thailand was one of the “Asian tigers,” Southeast Asian economies that had attracted so much investment and speculation in the early 1990s. An important conduit for the free-flowing credit that pushed real estate higher was a large commercial bank named Finance One. For years, it had borrowed dollars from overseas banks and made loans to Thai developers in the local currency, the baht. This had been a profitable strategy, provided that regular payments kept flowing in from Thai business.

However, the first sign of trouble took place in February 1997, when property developer Somprasong Land announced that it was defaulting on its $80 billion loan portfolio, since it was unable to even make its $3.1 million interest payment. Other developers, who had their own bad news but had been hesitant to make public their misgivings about their ability to pay, swiftly followed in Somprasong’s footsteps.

The details behind Finance One’s default were grim: Its non-performing loans had doubled during the course of 1996, and in the first quarter of 1997, the quantity of non-performing loans doubled once more. As the banking sector in Thailand looked increasingly shaky, the Thai baht began to lose its footing as well. The Thai government responded by frantically deploying its own U.S. dollar reserves to try to shore up the baht.

What this required of the Thai government was to buy up baht and sell off its dollars. On the books, the government showed that it had depleted its dollar reserves down to $33 billion. What was hidden from the public, however, was that the amount in reserve was close to a mere $1 billion, since the government had already tied up so much collateral in currency futures contracts. When the Thai leadership finally announced that it had “discovered” this information, it was forced to let the baht float freely, which put the currency into a free fall, along with the nation’s real estate interests.

Of course, the shock waves from a relatively small Asian economy were not as severe as would be experienced with the United States’ own real estate debacle. The Thai crisis was, nonetheless, an interesting precursor to what happens when the close partnership between a nation’s government, large commercial banks and real estate developers takes a turn for the worse.

9. OPEC Was Born in Texas

Most Americans understandably think that Organization of the Petroleum Exporting Countries (OPEC), was conjured up in the Middle East as a tool to artificially support crude oil prices, but the model for OPEC was actually an American creation. The U.S. organization was called the Texas Railroad Commission (TRC). It was established late in the 19th century in order to, as the name suggests, regulate railroads. As the 20th century dawned, and the decades passed, the domain of the TRC began to spread far beyond just rail lines, particularly with respect to energy resources. In spite of its name, the modern-day Texas Railroad Commission holds sway over many local industries with one notable exception: railroads.

The TRC’s control of production levels in the oil industry gave it tight control over oil prices for most of the 20th century. Although it was established in Texas, the TRC was a crucial arbiter for the “Seven Sisters” — the big U.S. and Dutch oil producers — since no other body was so influential in controlling the price of crude oil. The countries outside of this domain closely studied the TRC’s practices and effectiveness, since they had ambitions of their own about being bigger players in the global energy markets.

For much of the 20th century, oil was a relatively cheap and plentiful commodity. This made the focus of the TRC suppressing production levels to avoid a repeat of the crash in oil prices that Texas suffered in the 1930s, when a barrel of oil could be had for as little as 25 cents. The principal oil-producing states of the U.S. (Texas, Louisiana, and Oklahoma) had excess oil capacity, and the TRC had to regulate the flow in order to keep the price high enough for the industry to operate profitably. This was not always an easy task, since it is always tempting for any member of a cartel to break rank and increase their own profits by selling more of the product in question, but the TRC had been a consistent-enough enforcer of production ratios to garner the obedience of the oil producers in its domain.

After World War II and until the end of the 1960s, the nominal price for oil remained within a relatively narrow band of $2.50 to $3.00 per barrel. (In inflation-adjusted terms, this spans from $17 to $19.) Oil and its by-products were typically American and always cheap, which led to a boom in large, gas-guzzling American automobiles. There was little need for energy efficiency on either the road or in gas-heated households. America had more oil than it knew what to do with.

Around this time, in 1960, OPEC was founded by five member countries: Iran, Iraq, Saudi Arabia, Kuwait, and Venezuela. So even from its inception, OPEC was not an entirely Middle East entity. In the decade that followed its founding, other countries joined the organization: Algeria, Libya, Nigeria, Qatar, Indonesia, and the United Arab Emirates. So while OPEC had a strong Arabian presence, it actually spanned three different continents.

History’s Lesson

As we study and learn of the oddities and disruptions that take place over the course of time, probably the most financially germane phenomenon is the asset “bubble,” which has taken many forms over the centuries, some of which have been mentioned here such as tulipmania and the South Sea bubble. The commencement, inflation and bursting of these bubbles follow a template common to similar financial catastrophes throughout human history, running along these lines:

1. Some kind of shift happens (political, technological, or otherwise) that opens up extraordinary profit opportunities that did not exist before, and early participants thrive;
2. As word of the profits spread, a larger and more diverse array of individuals participate, and as opportunities become more scarce, leverage, excessive trading, and outright fraud begin to creep in; and
3. Once the original model can no longer support the participants, or once a fatal flaw is unveiled in the scheme, there is a rush to the exits. After most participants are badly damaged financially, there is a outcry from the public for justice to be rendered against as many culpable parties as possible. Upon reflection, most of the participants recognize they really didn’t know what they were doing in the first place.

As history continues to unfold before you, keep this template in mind: It may provide the impetus to get on board with a potentially lucrative investment while in its relatively early stage, or it may save you from joining the crowd near a top, only to see yet another one of history’s bubbles burst in front of your eyes.

Timothy Knight is a money manager, author of the book “Panic, Prosperity, and Progress” (John Wiley & Sons, 2014) and the creator the trading blog SlopeOfHope.com.

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• The Danger of Getting Out of Stocks During Bear Markets
• The Three Pockets Approach to Investing
• Strategic Value Investing: Screening for Cash Flow and Value
• The Mutual Fund Cash Dilemma
• From Saver to Spender: Managing Your Money in Retirement

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French apothecary and purported prophet Nostradamus may have his skeptics, but you can't deny his ideas have staying power.

He wrote his first book, "Les Propheties," in 1555, and publishing companies still roll out copies today. There's even a "Nostradamus For Dummies."

In the text of his book, each four-line block, called a quatrain, attempts to predict the future.

While logic might suggest Nostradamus' claims could apply to almost any event, some of them come eerily close to reality. In these 11 cases, we couldn't ignore his speculative prowess.

The Death of Henry II

Prediction:

"The young lion will overcome the older one,
On the field of combat in a single battle;
He will pierce his eyes through a golden cage,
Two wounds made one, then he dies a cruel death."

What happened:

France's King Henry II lined up to joust Gabriel, comte de Montgomery, seigneur de Lorges, a nobleman six years his junior, in the summer of 1559.

In their final pass, Montgomery's lance tilted up and splintered into two shards. One went through the king's visor and hit his eye, and the other lodged in his temple. Henry suffered for 10 days before dying in his bed.

Some reports say their shields displayed lion emblems, though disagreement exists. Skeptics also claim "field of battle" in the quatrain probably shouldn't apply to the friendly jousting match that killed Henry II.

The Great Fire of London

Prediction:

"The blood of the just will be lacking in London,
Burnt up in the fire of '66:
The ancient Lady will topple from her high place,
Many of the same sect will be killed."

What happened:

On Sept. 2, 1666, a small fire in Thomas Farriner's bakery on Pudding Lane in London turned into a three-day blaze that consumed the city. It became known as the Great Fire of London.

Peasant deaths weren't recorded at the time, but many historians claims at least eight people died in the blaze. Thousands of houses and businesses burned, as well. 

"Blood of the just"might refer to the elimination of millions of flea-carrying rats that spread the Black Death. That deadly plague died out during the Great Fire.

The French Revolution

Prediction:

"Songs, chants, and demands will come from the enslaved
Held captive by the nobility in their prisons
At a later date, brainless idiots
Will take these as divine utterances."

What happened:

In 1789, the French people decided they'd had enough of aristocratic rule. They revolted, storming the Bastille, a Paris fortress used as a prison. The fall of the Bastille, which symbolized the monarchy's abuses, marked the height of the French Revolution.

The peasants quickly took control of Paris and enforced their demands by kidnapping the royals. Some of them were even beheaded.

If you've ever wondered how best-selling authors went from Elinor Dashwood to Bella Swan, math — believe it or not — can help.

Tyler Vigen, the statistician who brought us hilarious spurious correlations, did some work with words, too. He analyzed several of the most popular novels from the early 1800s to today, focusing on elements like sentence length and punctuation. 

"I chose these books because they were seven of the all-time best-selling novels (which sold more than 50 million copies) that were written in English ... that were spaced in time periods," Vigen told Business Insider via email.

Now, these books might not represent their respective time periods, but the data provides interesting insight nonetheless. Some of the charts exhibit clear trends, while others seem more random.

Sentence length appears to be declining over time. It's also important to note the number of words and sentences in each book, shown in the chart below.

 "Sense and Sensibility" and "Twilight" contain about the same number of words — 119,000. But Jane Austen wrote roughly half as many sentences as Stephanie Meyer — 5,179 compared to 12,386, respectively.

While this trend could relate to later authors, in comparison, writing for young audiences, it's fair to say that Victorian England possessed a greater appreciation for paragraph-long sentences than we do today.

Here, "unique" means "different from every previously encountered word in the book," according to Vigen.

"Twilight" included greater word variation than many other novels, including Austen's work. But the most interesting relationship appears when you consider words used per unique word, shown in the chart below. 

The lower the number in the last column, the more extensive the author's vocabulary. In this case, Mark Twain takes the top spot. For every nine words he wrote, one of them had never appeared in the "The Adventures of Tom Sawyer Before" before. 

Adjective frequency appears to be increasing over time. 

The decline of the semicolon in writing is a clear trend.

"Sense and Sensibility" included 1,572 semicolons — one every 3.3 sentences on average. In a book of about the same number of words, Meyer used only 224 (one every 55.3 sentences).

Commas and other punctuation marks present less of a trend. 

SEE ALSO: 23 Sentence Diagrams That Show The Brilliance Of Famous Novels' Opening Lines

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The nine-story penthouse at the iconic Woolworth Building in Lower Manhattan is expected to hit the market for a record $110 million.

The new unit is one of 34 apartments being developed by Alchemy Properties, with prices ranging from $3.5 million for a 1,200-square-foot apartment to the nearly 9,000-square-foot penthouse that will take up floors 50 to 58.

The development is particularly exciting since the famous building hasn’t undergone a major renovation since the 1970s. Originally built in 1913, the Woolworth Building has outlived its namesake (The Woolworth Company went out of business in 1997) and housed the Irving National Exchange Bank, Columbia Records, the Witkoff Group, and many others.

Photographer Martin Doudoroff recently got a rare glimpse inside the building's opulent lobby (visitors can also pay $15-$45 for a tour) and shared his snapshots of the atrium's  neo-Gothic details.

The building was completed in 1913 by architect Cass Gilbert, who was also responsible for the Minnesota State Capitol building, the Detroit Public Library, and the United States Supreme Court building.The tower was commissioned by Frank W. Woolworth, the CEO of the F.W. Woolworth Company and owner of over 300 5- and 10-cent stores across the U.S., Canada, and England. He famously paid the $13.5 million in cash.The lobby looks like a Romanesque Cathedral, with mosaics, gilded details, and a marble stairway. It was even nicknamed "the Cathedral of Commerce.”Once the tallest skyscraper in the world, the Woolworth Building is 792 feet tall, taking up a full city block on Broadway between Park Place and Barclay Street in lower Manhattan.The Woolworth Building in numbers: 60 floors, 15 acres of floor space, 3,000 windows, 24,000 tons of steel, 48 miles of plumbing, 17 million bricks, and 7,500 tons of terra cotta.The lobby's gorgeous stained glass ceiling features important dates from the Woolworth company's history.When it was first completed, the building's major selling point was its amenities. The building had a shopping arcade, health club, doctor's office, barber shop, and restaurant, as well as high-speed, innovative elevators.There was also famously an indoor pool and Turkish bath in the basement. The pool was drained in 1999 to make way for a larger retail space, but the long-abandoned pool may be restored for luxury tenants.There are a lot of gorgeous small details in the lobby, likes these carved faces and figures. Many of these faces were of the real workers who toiled on the building, including architect Cass Gilbert and Frank W. Woolworth.Here's another example.The Woolworth Building was officially named a National Historic Landmark in 1966 and a New York City Landmark in 1983. It is still one of the 50 tallest buildings in the United States as well as one of the 20 tallest in NYC.

SEE ALSO: The Best New Skyscrapers On The Planet

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Seventy years ago, the British Intelligence agency MI5 flew into a panic when agents noticed that key code names from the top secret D-Day operation were appearing in The Daily Telegraph's crossword puzzles. In May of 1944, intelligence officers suspected that the puzzles were functioning as a covert operation for passing top-secret intelligence along to the Nazis and thoroughly interrogated Leonard Dawe, the Telegraph's crossword compiler and headmaster of the Strand School in Effingham.

Dawe had previously attracted the MI5's attention when the word 'Dieppe' appeared in one of his puzzles the day before the Dieppe raid, along the northern coast of France, on August 19, 1942. This was quickly dismissed as "a complete fluke."

In the months leading up to D-Day, Dawe again came under suspicion. The words Juno, Gold, and Sword — all code names for British landing beaches — appeared in the crossword. They didn't seem to have any significance though, as these were considered common crossword puzzle answers. 

But the clue "One of the U.S." with the four-letter word Utah as the solution immediately caught the MI5's attention. Soon after came a flurry of other clues containing sensitive names related to the D-Day operation. 

On May 22, Omaha, a codename for a D-Day beach the U.S. was planning to take, was the solution to the clue "Red Indian on the Missouri (5)." The May 27 crossword contained the word Overlord, the name for the entire D-Day operation. 

The final D-Day-related codename came on June 1, just five days before the invasion. The solution to 15 Down was "Neptune," the codeword for a naval assault. 

After thorough questioning by the MI5, it became apparent that Dawe was unwittingly publishing information related to the D-Day operation.

Dave would invite his students to fill out the blank crosswords with words of their own choosing as a form of mental exercise. Dawe would then write clues to their solutions. 

Dawe's Strand School was situated close to a Canadian and American military camp full of soldiers that were preparing for the D-Day campaign. Several of Dawe's students would spend time at the camp running errands for the soldiers and listening to their stories.

The soldiers weren't afraid of the children being spies and spoke openly of the upcoming campaign. The children learned the now-legendary codenames used during the operation. Unaware of the possible repercussions, they then put them into one of England's favorite crossword puzzles for the world to see. 

SEE ALSO: D-Day was a success because Allied meteorologists saw an opening that the Germans missed

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Even a Renaissance man is occasionally on the job hunt.

Such was the case back in the 1480s, when a young Leonardo da Vinci was coming up in Florence.

Born the lowly son of a notary, da Vinci couldn't enter the "higher professions" of the city, like lawyer or statesman. Instead, his lot was that of a craftperson — a painter, to be exact. 

Under the tutelage of Verrochio, an established artist and goldsmith, da Vinci honed the powers of observation that would drive his illustrious career.

But Florence, he realized, was crowded with artists. If da Vinci was to make a name for himself, he'd have to try another town.

So he turned his sights toward Milan, then ruled by Ludovico Sforza, who hoped to make Milan a cultural capital on par with Florence and Venice. He also had a habit of getting into wars, as one did back in the day. 

Da Vinci applied to work for him, and knowing his potential patron's penchant for war, he wrote a cover letter positioning himself as a military engineer. As the best cover letters do, it tailored his career history to his employer's needs. 

Here are a few of the inventions da Vinci proposed:

• "Very light, strong and easily portable bridges with which to pursue and, on some occasions, flee the enemy"
• "Covered vehicles, safe and unassailable, which will penetrate the enemy and their artillery"
• "Where the use of cannon is impracticable, I will assemble catapults, mangonels, trebuckets and other instruments of wonderful efficiency not in general use." 

Beyond weapons, da Vinci promised innovations, like tunneling beneath castle walls, redirecting the waters of moats, and methods for destroying fortresses. 

"In short," he humbly proclaims, "as the variety of circumstances dictate, I will make an infinite number of items for attack and defence."

Surprisingly, the legendary artist doesn't mention his ability as an architect, painter, or sculptor until the close of the letter, and, by today's standards, it's a bit long-winded. 

Regardless, the letter worked: Da Vinci worked for the duke for 16 years, completing some of his most memorable work, including "The Last Supper."

Care of blog-based archive Letters of Note, here's the cover letter in full: 

SEE ALSO: Here's How To Write The Perfect Cover Letter

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EDITOR'S NOTE:

The newsflash came on a slip of paper in a red-and-white striped courier pouch: "EISENHOWERS HEADQUARTERS ANNOUNCES ALLIES LAND IN FRANCE."

The Associated Press had some two dozen writers and photographers among the Allied forces as they landed on Normandy's coast on June 6, 1944. From Gen. Dwight D. Eisenhower's London headquarters, Wes Gallagher — who later went on to become AP's general manager — wrote up the first Allied official dispatches announcing D-Day and sent them in the sealed pouch to AP's London office by military courier, after the military censor authorized their release.

They arrived at 9:32 a.m. and were sent to the rest of the world by teletype one minute later.

In France, the AP team included Don Whitehead, who was making his fifth landing with Allied troops, and Bede Irvin, a photographer who would soon be killed by friendly fire while covering the American forces.

Months of planning went into that flash and subsequent dispatches, from securing a dedicated phone line and berths on planes and ships, to reconfiguring the office furniture in London to ensure AP would be fastest at getting out word of the expected invasion of France. At the end, an editor ran down the hall to intercept the courier and bolted back into the newsroom. Subsequent detail on the invasion made its way back to England in a variety of ways — including radio transmission, messages tied to the legs of carrier pigeons, and hand-carried dispatches from Henry Jameson, who returned to England with the wounded after an exploding shell dislocated his shoulder.

Seventy years after its original publication, the AP is making Gallagher's original report available.

_____

SUPREME HEADQUARTERS ALLIED EXPEDITIONARY FORCE (AP) — Allied troops landed on the Normandy coast of France in tremendous strength by cloudy daylight today and stormed several miles inland with tanks and infantry in the grand assault which Gen. Dwight D. Eisenhower called a crusade in which "we will accept nothing less than full victory."

German broadcasts said the Allies penetrated several kilometers between Caen and Isigny, which are 35 miles apart and respectively nine and two miles from the sea.

Prime Minister Churchill told the House of Commons part of the record-shattering number of parachute and glider troops were fighting in Caen, and had seized a number of important bridges in the invasion area.

German opposition apparently was less effective than expected, although fierce in many respects, and the Germans said they were bringing reinforcements continuously up to the coast, where "a battle for life or death is in progress."

The seaborne troops, led by Gen. Sir Bernard L. Montgomery, surged across the channel from England by 4,000 regular ships and additional thousands of smaller craft.

They were preceded by massed flights of parachute and glider forces who landed inland during the dark. Eleven thousand planes supported the attack.

The German radio said the landings were made from Cherbourg to Le Havre — a strip of coast roughly 100 miles long — and later said additional landings, were being made "west of Cherbourg," indicating the Allies intended to seize the Normandy peninsula with its ports and airdromes as the first base.

Germans Expect More Invasions Hourly

The initial landings were made from 6 to 8:25 a.m. British time. The Germans said subsequent landings were made on the English channel isles of Jersey and Guernsey and that invasion at new points on the continent was expected hourly.

Aside from confirming that Normandy was the general area of the assault, Supreme Headquarters of the Allied Expeditionary Force was silent concerning the location.

From Moscow came word that the Russian army was massing in preparation for another great attack from the east as its part in defeating Germany.

All reports from the beachhead, meager though they were in specific detail, agreed that the Allies had made good the great gamble of amphibious landing against possibly the strongest fortified section of coast in the world.

Reconnaissance pilots said the Allied troops had secured the beaches and were slashing inland, some of them actually running in a swift advance. The unofficial word at headquarters confirmed this, while the Vichy radio admitted the Allied drive inland was going right ahead.

Naval Guns Shell Fortifications

More than 640 naval guns, ranging from 4 to 16-inch, hurled many tons of shells accurately into the coastal fortifications which the Germans had spent four years preparing against this day.

Prime Minister Churchill was able to tell parliament the shore batteries had been "largely quelled," the underwater obstructions had proven less dangerous than feared and the whole operation was "proceeding according to plan."

Allied planes preceded the landings with a steady 96-hour bombardment which reached its pinnacle in the hour before the troops hit the beaches.

The absence of German aerial opposition was remarked by nearly all returning fliers and correspondents. The Germans are known to have about 1,750 fighters and 500 bombers available for the western front, but it was supposed they had chosen not to risk them in an all-out first-day battle.

German naval opposition was confined to destroyers and motor torpedo boats which headquarters said were being "dealt with."

The Germans, as expected, blared on their radios all sorts of claims of vast destruction done to Allied fleets and forces, but with no confirmation. In one defiant gesture, some of the German cross-channel guns opened a sporadic fire on Dover during the afternoon.

Supreme headquarters kept silent on the locations, to exploit, to the fullest whatever element of tactical surprise the Allies may have gained. A superior officer at supreme headquarters said frankly he did not know yet what amount of surprise there was, but Allied air forces were in control of the skies over the channel and the coast despite unfavorable flying weather.

May Head Up Seine River To Paris

If the Germans were correct about the locations, the Allied plan apparently was to seize the Cherbourg peninsula and make Normandy the initial beachhead for a drive up the Seine valley to Paris.

The German radio began broadcasting a constant stream of invasion flashes almost as soon as the first troops landed, and continued with extensive reports of the gigantic naval and air bombardments that covered the assault. Allied headquarters, however, kept silent until 9:32 a.m. British time when the following communique was issued:

"Under the command of Gen. Dwight D. Eisenhower, Allied naval forces supported by strong air forces began landing Allied armies this morning on the northern coast of France."

A high officer explained that Gen. Eisenhower had kept resolutely silent until he was absolutely certain the landings had "taken hold."

Gen. Eisenhower broadcast during the morning an announcement to the peoples of western Europe, telling them of the landings and declaring, "all patriots, young and old, will have a part to play in the liberation."

Urges Patriots Just To Be Patient

He urged against premature uprisings, however, saying, "be patient. Prepare. Wait until I give you the signal."

The Allied commander also issued an order of the day to his forces, telling them:

"You are about to embark on a great crusade. The eyes of the world are upon you and the hopes and prayers of all liberty-loving peoples go with you ... Your task will not be an easy one. Your enemy is well-trained, well-equipped and battle-hardened. He will fight savagely. I have full confidence in your courage, devotion to duty and skill in battle. We will accept nothing less than full victory."

It was disclosed that a number of unannounced feints had taken place in the pre-invasion period, so that the Germans would not know when the real blow was coming.

A senior officer at supreme headquarters said rough water caused "awful anxiety" for the sea-borne troops but that the landings were made successfully, although some soldiers were undoubtedly seasick.

Sun Breaks Through Heavy Clouds

The sun broke through heavy clouds periodically this morning after a daybreak shower. The wind had blown fairly hard during the night but moderated somewhat with the dawn. The weather outlook remained somewhat unsettled.

Aside from Gen. Montgomery, no other Allied commanders were announced for the thousands of battle-trained Allied troops, although Gen. Omar Bradley has been in command of American ground forces in England for several months. Gen. Bradley participated in the Tunisian victory.

The Allied forces had been ready for days, but were awaiting the best moment from the weather standpoint.

"We have been months and years waiting for this," said a senior officer giving correspondents the story at headquarters.

"Geography made it evident to the Germans as well as us that the shortest way to Europe was across channel."

First reports from across the channel, however, indicated that the Allies controlled the air over the scene of operations. The Allied officer commented that landing against fixed defense of western Europe was a task quite different from that in the Mediterranean and sketched briefly the German defensive plan of underwater barriers and shore guns.

Nazis Report Dunkerque Attacked

He said the German had possibly 1,750 fighter planes and bombers to oppose the Allies.

For three hours previous to the Allied announcement, the German radio had been pouring forth a series of flashes reporting that the Allies were landing between Le Havre and Cherbourg along the south side of the Bay of the Seine and along the north coast of Normandy.

Thousands of battle-trained American, British and Canadian troops hurled themselves at Hitler's western defenses after months of preparation. Huge troopship armadas slipped out of English ports in the darkness and sped toward Europe where four years ago almost to the day Britain brought back the last battle-worn defenders of Dunkerque.

The German radio gave the reports of the invasion while correspondents were hurriedly summoned from bed to supreme press headquarters and locked in a press conference room until the communique was released several hours after the landings were made.

It was made known that the supreme command felt it necessary to yield the initiative in the war of words to the Germans in order to retain the initiative on land and keep the German high command in the dark as long as possible.

The great Allied armadas dwarfed anything yet seen on the sea. Huge transport planes filled with paratroopers and pulling airborne troops in gliders roared over the German West all to drop their cargos in the rear.

All night long London and England resounded to the roar of thousands of airplanes, some carrying bombs, some carrying men. Returning R.A.F. bombers met big fleets of Flying Fortresses on their way out.

The forces thrown into operation were by far the greatest ever used in an amphibious operation. They had to be. An estimated million German troops waited in their fortifications for the great onslaught under crack Nazi field marshals, Runstedt and Rommel.

It was reported earlier this week that Adolf Hitler himself had a special train ready to rush him to France to take over personal command as he did on the east front. Despite these reports, Allied military men expected Rommel to be the main tactician on German defense.

Although amphibious attacks are the most difficult in war, a quiet feeling of confidence characterized the Allied generals.

No Chance To Hide Great Allied Convoys

The fleet included several battleships which the Germans said set the whole Seine bay area ablaze with their fire.

The Germans announced also that American reinforcements began landing at dawn, aided by artificial fog, and that in some places dummy parachutists were dropped to confuse the defense.

French patriots previously had been warned by Allied radio broadcasts to get out of areas within 35 kilometers (22 miles) of the coast to escape the shock of battle and the gigantic aerial bombardment.

An Associated Press correspondent flying over the French coast in a B-26 Maurauder reported seeing the fields inland strewn with hundreds of parachutes and dotted with gliders, while great naval forces fired into the coast fortifications.

The western front opening climaxed years of patient preparation by the top military minds of America and Britain, and hard work in factories and munitions plants by millions of Americans and Britons.

The plan of attack was the same which Gen. Eisenhower had when he came to England in June 1942, but which was shelved during the improvised North African operation.

Sweat And Toil Of Factory Worker Pay Off

This morning the sweat and toil of the factory worker of America and Britain, and the cool planning of the military men of both countries bore fruit. Every weapon that has proved its worth since Pearl Harbor was in the hands of the fighting men of the United Nations.

What success they would meet no one could say with certainty. No such attempt has been made in warfare before on such a huge scale — to storm a continent from the sea against fixed defenses. Gen. Eisenhower and the supreme Allied staff had left as little as possible to chance. Several weeks ago all the air forces in the United Kingdom were placed under the strategic command of supreme headquarters to pave the way for the landings.

The strategic air forces under Lt. Gen. Carl A. Spaatz were assigned the task of smashing the German aerial reserves by bombing aircraft factories deep in Germany. Theirs was the job of making the Nazi air force's once mighty fleet incapable of sustained effort against our ground forces. The Fortresses and Liberators also were given the task of breaking up the rail system of western France.

The R.A.F. under air chief Marshal Sir Arthur T. Harris was given a similar order, only its primary targets were railroads.

The Ninth air force under Lt. Gen, Lewis Brereton, along with the Second R.A.F. tactical air force, was assigned selected targets along the West Wall itself.

The Allies did not hope to knock out everything from the air, but to cripple and hamper German troop movements.

This morning a shattering barrage such as reduced the defenders of the Mediterranean island of Pantelleria last summer was laid down by the combined air forces.

In the landing craft were men who knew the beaches on which they were to land like the hacks of their hands. For months in English camps they had drilled down to the finest detail for their task. They had been formed into combat teams, some of a dozen men, some of several thousand.

SEE ALSO: CBC is tweeting a blow-by-blow account of D-Day, and it's incredible

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Fear of Friday the 13th, also known as friggatriskaidekaphobia, plagues our society. The diagnosis brings together "Frigg," a Norse goddess and Friday's namesake, and  "triskaidekaphobia," fear of the number 13 in general.

Every year, the world loses $700 to $800 million on Friday the 13th because people won't conduct business as usual. Many especially refuse to fly.

On top of that, almost 80% of high rise buildings skip the 13th floor. Many airports exclude gate 13, and hospitals regularly avoid room 13.

So where does this superstition originate? The roots link back to religion — of all denominations and time periods.

History of a superstition

First and foremost, the Last Supper's 13th guest (and last apostle), Judas betrayed Jesus, according to the Bible. Then, His Crucifixion occurred on a Friday. Some scholars also believe Eve tempted Adam on a Friday.

Also, Babylon's ancient Code of Hammurabi skips number 13 when listing laws. Egyptians considered the afterlife the 13th phase of life.

But the number thirteen's cursed beginnings fall outside the rise of Christianity, too. A similar story occurs in Norse mythology. The 11 closest friends of Odin, the father of all gods, chose to dine together when Loki, the god of evil and chaos, crashed the party. One of the gods, Balder, the god of joy and happiness, died that evening.

Much later, King Philip IV of France certainly didn't help by ordering the persecution of the Knights Templar on Friday, October 13, 1307. In the following years, several thousand faced torture and execution.

If those tales don't convince you, math also has a stake in why people get bad vibes from the number thirteen. First, 12 appears a lot in our culture — 12 months in a year, 12 hours on a clock, 12 signs of the zodiac, 12 apostles of Jesus. We love 12.

12 is a "pseudoperfect" number, according to Wolfram. The sum of some of its divisors equals the whole number. For example, 1, 2, 3, 4, and 6 go into 12. Both 2+4+6 and 1+2+3+6 equal 12.

On December 12, 2012, a boy in Alabama turned 12 at 12:12 p.m. People started calling him everything from "the chosen one" to a sign of the impending apocalypse.

Thirteen has a tough act to follow.

Regardless of where, when, or how this superstition started, we've perpetuated our own fear. "If nobody bothered to teach us about these negative taboo superstitions like Friday the 13th, we might in fact all be better off,"Stuart Vyse, psychology professor at Connecticut College in New London, told National Geographic.

Now Watch: 7 Optical Illusions That Will Make You Look Twice

SEE ALSO: Things That iPhone Users Say That Drive Android Users Crazy

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If a picture is worth a thousands words, then amateur photographer Cora Drimus' latest project speaks volumes about the history of New York City.

Drimus created the video "Once Upon a Time in New York" after her visit to the city this past April. The video includes photographs taken by Drimus of present-day New York landmarks juxtaposed with historic photos of the same landmarks. Viewers are able to see how much the city has changed over the years.

Drimus, who works in the finance industry, has created three similar videos in Romania, and she told Business Insider that she thought making a video of New York would be even more fun. She currently lives in Zurich, Switzerland, and this was her first visit to the U.S. 

As red-blooded Americans, we all know the Pledge of Allegiance. Most schools require students to recite it before the day's classes begin. 

But the 31-word passage has evolved over time. Most people don't realize the phrase "under God" wasn't included until Flag Day in 1954 — 60 years ago today.

Here's what went down. 

In 1892, Francis Bellamy, a minister from upstate New York, reportedly wrote the Pledge as an expression of fealty to the U.S. It read: "I pledge allegiance to my flag and the republic for which it stands, one nation, indivisible, with liberty and justice for all." Some consider Bellamy a socialist and his creation a criticism of rampant greed and hyper-individuality. 

Over the next 50 years or so, the version would eventually include "of the United States" after "flag" and a simple "to" before "republic." It wasn't too controversial. 

Then, an attorney from Illinois, Louis Bowman, shook the wording up a bit. At a meeting of the Sons of the American Revolution in 1948, he added "under God," claiming Abraham Lincoln used the same phrase in his Gettysburg Address. Almost all reported transcripts from the speech do include "that the nation shall, under God, have a new birth of freedom."

Bowman continued to deliver his version of the Pledge, and others, like the Knights of Columbus, began reciting it, too. Various people even wrote letters to the president at the time, Harry Truman, and met with him to request the more religious tone. 

Finally, the government became involved. In 1953, Louis Rabaut, a democrat from Michigan sponsored a resolution to add the words "under God" to the Pledge. It failed. But by then, the decision was up to President Dwight D. Eisenhower. Recently baptized as a Presbyterian, he heard a sermon, arguing the words "under God" from Lincoln's speech set the United States apart from others as a nation. At the time, the Cold War was gaining steam, and Eisenhower was fighting communism across the globe. 

The next day, the president encouraged Charles Oakman, a republican also from Michigan, to re-introduce the bill, which Congress passed. Eisenhower signed it into law on June 14, 1954. A story announcing the news in the Washington Post quoted him as saying the new version would add "spiritual weapons which will forever be our country's most powerful resource." 

Naturally, in a nation with growing diversity of religions, "under God" has proven a polarizing phrase. Separation of church and state also factors into the politicized discussion.

Two years later, on Flag Day again, Eisenhower also made "In God We Trust" our nation's official motto. The man must have loved his new religion. 

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Skateboarding culture exploded in Los Angeles in the 1970s, and photographer Hugh Holland was on hand to capture the freewheeling lives of the city's skateboarders starting in 1975.

Holland's "Angels" series shows '70s skateboarders hanging out in Burbank, Huntington Beach, Balboa and other hotspots in California.

M+B, the gallery that represents Holland, gave us permission to publish this amazing photo collection.

Sidewalk Surfer, Huntington Beach (1976)

Reach Out (1976)

Tube Socks on Board, Marina Del Rey Skate Park (1977)

The modern day orange carrot wasn’t cultivated until Dutch growers in the late 16th century took mutant strains of the purple carrot and gradually developed them into the sweet, plump, orange variety we have today. 

Before this, pretty much all carrots were purple with mutated versions occasionally popping up including yellow and white carrots.

These were rarely cultivated and lacked the purple pigment anthocyanin.

It is thought that the modern day orange carrot was developed by crossing the mutated yellow and white rooted carrots as well as varieties of wild carrots, which are quite distinct from cultivated varieties.

Some think that the reason the orange carrot became so popular in the Netherlands was in tribute to the emblem of the House of Orange and the struggle for Dutch independence. This could be, but it also might just be that the orange carrots that the Dutch developed were sweeter tasting and more fleshy than their purple counterparts, thus providing more food per plant and being better tasting.

 Bonus Facts:

• It is actually possible to turn your skin a shade of orange by massively over consuming orange carrots.
• Orange carrots get their bright orange color from beta-carotene.  Beta-carotene metabolizes in the human gut from bile salts into Vitamin A.
• The origins of the cultivated carrot is rooted in the purple carrot in the region around modern day Afghanistan.
• When cultivation of the garden style orange carrot lapses for a few generations, the carrots revert back to their ancestral carrot types, which are very different from the current garden variety.
• In ancient times, the root part of the carrot plant that we eat today was not typically used.  The carrot plant however was highly valued due to the medicinal value of its seeds and leaves.   For instance, Mithridates VI, King of Pontius (around 100BC) had a recipe for counteracting certain poisons with the principle ingredient being carrot seeds.  It has since been proven that this concoction actually works.
• The Romans believed carrots and their seeds were aphrodisiacs.  As such, carrots were a common plant found in Roman gardens.  After the fall of Rome however, carrot cultivation in Europe more or less stopped until around the 10th century when Arabs reintroduced them to Europe.
• British gunners in WWII were able to locate and shoot down German planes at night due to radar.  What does this have to do with carrots?  To cover up significant advancements the Allies made in radar technology at the time, and the extreme effectiveness of radar that resulted, the British spread about an urban legend that said that they massively increased the night vision of their pilots by having them consume large amounts of carrots.  This lie not only convinced the Germans, but also had a bonus effect of causing many British people to start planting their own vegetable gardens, including planting carrots.  This urban legend has persisted even to this day.
• The largest carrot ever grown was 19 pounds; grown by John Evans in 1998 in Palmer, Alaska.
• The Vegetable Improvement Center at Texas A&M recently developed a purple-skinned, orange fleshed carrot called the Beta Sweet.  This carrot is specialized to include substances that prevent cancer.  It also has extremely high beta-carotene content.
• Almost one third of all carrots distributed throughout the world come from China, which is the largest distributor of carrots in the world.  Following them on gross production is Russia and then the United States.
• Although the orange carrot was not cultivated before the 16th and 17th centuries, there is a reference in a Byzantine manuscript around 512AD which depicts an orange rooted carrot, suggesting that at least this mutant variety of carrot could be found at this time.

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Looking back on it now, the years leading up to the Lehman collapse seem like a dream.

This was the era when:

-- Your friend who had majored in English went to work for an investment bank.

-- Your parents thought it would be a good idea to buy a second (or third!) home upstate.

-- "My Super Sweet 16" came into existence.

We wanted to go back to see just how absurd this moment was.

So we've scoured American (and a slice of global) culture and society from 2003 to 2008 to find the most absurd examples and reflections of financial excess. 

In retrospect, it is now ludicrously clear that we should've seen it all coming...

Bravo's "Flipping Out," the show about trying to buy homes, renovate them, and put them back on the market, may have best captured the Zeitgeist.

Though "Cribs" is arguably a close second.

MTV's "My Super Sweet Sixteen," about rich teenagers' lavish 16th birthday parties, was another good sign we'd reached peak excess.

Mathematics is an increasingly central part of our world and an immensely fascinating realm of thought.

But long before the development of the math that gave us computers, quantum mechanics, and GPS satellites, generations of brilliant minds — spanning from the ancient Greeks through the eighteenth century — built up the basic mathematical ideas and tools that sit at the foundation of our understanding of math and its relationship to the world.

Here are 12 of the most brilliant of those minds and some of their contributions to the great chain of mathematics.

The Pythagoreans (5th Century BC)

Some of the earliest mathematicians were Pythagoras and his followers. Mixing religious mysticism with philosophy, the Pythagoreans' contemplative nature led them to explorations of geometry and numbers.

The most famous result attributed to Pythagoras is the Pythagorean theorem: for a right triangle, the sum of the squares of the two shorter legs that join to form the right angle is equal to the square of the long side opposite that angle. This is one of the fundamental results in plane geometry, and it continues to fascinate mathematicians and math enthusiasts to this day.

One apocryphal story of the Pythagoreans illustrates the danger of combining religion and math. The Pythagoreans idealized the whole numbers, and viewed them as a cornerstone of the universe. Their studies of geometry and music centered on relating quantities as ratios of whole numbers.

As the story goes, a follower of Pythagoras was investigating the ratio of the length of the long side of an isosceles right triangle to the length of one of the two shorter sides, which have the same length as each other. He then discovered that there was no way to express this as the ratio of two whole numbers. In modern terminology, this follower had figured out that the square root of 2 is an irrational number.

According to the legend, when the follower who discovered this fact revealed it to his peers, the idea that there could be irrational numbers — numbers that can't be expressed as a ratio of two whole numbers — was so shocking to the Pythagoreans that he was taken out on a boat and murdered by drowning.

Euclid (c. 300 BC)

Euclid was one of the first great Greek mathematicians. In his classic "Elements," Euclid laid the framework for our formal understanding of geometry. While earlier Greek philosophers like the Pythagoreans investigated a number of mathematical problems, Euclid introduced the idea of rigorous proof: Starting with a handful of assumed axioms about the basic nature of points, lines, circles, and angles, Euclid builds up ever more complicated ideas in geometry by using pure deductive logic to combine insights from previous results to understand new ideas. This process of using rigorous proof to build new results out of existing results introduced in the "Elements" has remained perhaps the most central guiding principle of mathematics for over two millennia.

Archimedes (c. 287-212 BC)

Archimedes was possibly the greatest mathematician of all time. He's best known for his contributions to our early understanding of physics by figuring out how levers work and in the famous legend of his discovery of how water is displaced by a submerged object: While taking a bath, Archimedes watched the water sloshing up to the top of his tub, and in the excitement of his discovery, he ran through the streets naked and shouting "Eureka!"

As a mathematician, however, Archimedes was able to outdo even his own accomplishments in physics. He was able to estimate the value of pi to a remarkably precise value and to calculate the area underneath a parabolic curve.

What is truly amazing about these accomplishments is that he made these calculations using techniques surprisingly close to those used by Newton, Leibniz, and their heirs in the development of calculus about 1,800 years later. He found these values by approximating them with measurements of polygons, adding more and more refined shapes, so that he would get closer and closer to the desired value. This is strongly reminiscent of the modern idea of an infinite limit. As far as his mathematical sophistication was concerned, Archimedes was nearly two millennia ahead of his time.

The Declaration Of Independence made the United States an autonomous country 238 years ago this Fourth of July.

But the document's official transcript, produced by the National Archives, might contain a significant error — an extra period right in the middle of one of the most significant sentences, The New York Times reports. 

A quick Google search for the text will show that many websites and organizations follow the National Archives' lead. Here's the full sentence, with an added period highlighted in red:

"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.— That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed ...."

That period doesn't appear on the faded original parchment, Danielle Allen, a professor at the Institute for Advanced Study, contends. And it changes the meaning of the sentence, which effectively alters Americans' interpretation of government's role in protecting their individual rights.

"The logic of the sentence moves from the value of individual rights to the importance of government as a tool for protecting those rights," Allen told the Times. "You lose that connection when the period gets added."

Americans tend to interpret the message in its current form: that government is subordinate to "life, liberty and the pursuit of happiness." Without the period, the importance of government could serve as part of a larger argument, instead of a separate thought. 

Unfortunately, the original document has faded to near illegibility. But Allen points out that many early transcripts, some from 1776, exclude the period. Take Thomas Jefferson's so-called original rough draft, held in the Library of Congress — no period, according to the Times.

But that argument has its dissenters, especially those who feel the punctuation matters little to the meaning. Allen disagrees.

"We are having a national conversation about the value of our government, and it goes get connected to our founding documents," Allen told the Times. "We should get right what's in them."

This isn't the first time a historical text's punctuation made the national stage. Debate over a comma in the Second Amendment traveled all the way to the Supreme Court in 2008. Then, lawyers argued its interpretation changed the meaning of our right to bear arms.   

Read the full article from The New York Times here »

SEE ALSO: How A Comma Gave Americans The Right To Own Guns

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As American cultural heritage goes, there may be nothing more American than our flag and national anthem. And on the Fourth of July, we're acutely aware of that.

But if you look back at the history of Francis Scott Key's now legendary tune, the actual melody has very un-American roots.

Francis Scott Key wrote the poem "Defence of Fort M'Henry" in 1814, while watching a terrifying battle. It was the Battle of Fort McHenry in 1812. A week earlier, the British had ransacked Washington, D.C. — burning the Capitol and President's house to the ground.

It was a terrible sight, and as the Smithsonian tells us, Key later said "It seemed as though mother earth had opened and was vomiting shot and shell in a sheet of fire and brimstone." But as the smoke cleared (indeed the "dawn's early light") it was the American flag that flew above the wreckage, and not the Union Jack.

Key was watching about eight miles away on a ship, and wrote his poem as he witnessed the bombardment.

The poem became the now legendary "Star-Spangled Banner" and eventually began its reign as our national anthem. But it needed a melody. Interestingly enough, a very British tune ended up acting as the inspiration for the song we all know so well. Some experts think that because the rhyme scheme is so similar, Key had this in mind when he wrote the poem.

It's called "The Anacreontic Song." It was written by a man named John Stafford Smith for the Anacreontic Society. The society was a men's social club in London, and the tune was apparently sung at the beginning of their meetings.

Here's a YouTube clip of "The Anacreontic Song," so you can see the similarities for yourself:

SEE ALSO: 27 Charts That Will Have You Shouting 'America Is Number 1!'

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The first officially recognized version of the American flag, from 1776,  had 13 stars — in a circle. 

Although even before the U.S. became an autonomous nation, Americans had a banner to display their patriotism.

Since then, the stars representing the increasing number of states on the flag have taken on different designs, like a flower, or wagon wheel.

Compiled by the team at Pop Chart Labs, each version tell its own story. 

The Sons of Liberty, a secret society of dissidents, adopted this flag in 1767. The nine uneven stripes represent the "loyal nine" colonies that protested the Stamp Act of Congress of 1765.

Source: CRW Flags

John Hulbert created this version in 1775. His company, the Third Regiment of New York, reportedly carried it. Its six-pointed stars are arranged in the cross of St. Andrew.

Source: Mouse River Farmers Press, 1960

Some historians consider this the oldest flag meant to represent the entire country as well as the oldest to use 13 red and white stripes purposefully. The Minutemen reportedly carried it for the Battles on Lexington and Concord on April 19, 1775.

Source: Flag Heritage Foundation

Macau is home to the biggest, most lavish casinos in the world.

Among the crazier facts about Macau recently: growth has averaged around 19% for a decade; in 2006 Macau’s casino revenues  surpassed those of Las Vegas; and the Sands Macau, opened in 2004, recouped its $265 million construction costs in one year

Today, Macau is in a bit of a crisis. This April, a shareholder in the Kimren Group, one of Macau's top high-roller promoters, took $1.3 billion worth of the company's money and vanished, causing a tidal wave of fear to wash over the Chinese province. Publicly traded junkets, which bankroll gambling rooms, have fallen as much as 11% since the Kimren incident.

That may sound dire. But the story of Macau's boom remains one of the most remarkable economic stories in history.

In the summer of 1980, Leroy W. Demery, Jr., an expert in Asian transportation, visited the country (then still a Portuguese protectorate) and documented his journey. 

He posted his copyrighted photo collection to flickr, and with his kind permission we have reproduced the snapshots here.

Click Here To See The Photos >

Here is his introduction to the collection:

I traveled by overnight ferry from Hong Kong to Macao, spent the day (1980 July 16) in Macao, then returned to Hong Kong by overnight ferry.

"Overnight ferry" for a 60 km distance?

Yes, one boarded the vessel about 10 p.m. The fare included a bunk in an air-conditioned dormitory - "Spartan" but very comfortable. The vessel sailed after midnight and certainly arrived within 3-4 hours. Passengers were awakened at about 6 a.m., as I remember.

Yes, catamarans and jetfoils were much faster, but fares were higher, and the overnight ferry permitted one to save the cost of overnight accommodation.

Macao, in 1980, was quiet. Very quiet. It had a distinct "small town" atmosphere that contrasted sharply with the Central District of nearby Hong Kong. Much has changed since then. Remarkably, the land area has nearly doubled, from about 16 square km to nearly 29 square km. Many of the images in this set are certainly "vanished scenes."

I regret that do not have a 1980 street map of Macao, and so am not able to locate some of these images.

Anyway, read on to take the journey to Old Macau.

Just to get you started, here's what Macau looks like today.

And here's what it looked like back in the day. This is Leal Senado, legislative seat during Portuguese rule, now home to the Institute of Civic and Municipal Affairs.

This section of the harbor is now reclaimed land, Demery says.