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# Brother, Can You Spare a Dime? The Great Depression

## Introduction

On March 4, 1929, at his presidential inauguration, Herbert Hoover stated, “I have no fears for the future of our country. It is bright with hope.” Most Americans shared his optimism. They believed that the prosperity of the 1920s would continue, and that the country was moving closer to a land of abundance for all. Little could Hoover imagine that barely a year into his presidency, shantytowns known as “Hoovervilles” would emerge on the fringes of most major cities, newspapers covering the homeless would be called “Hoover blankets,” and pants pockets, turned inside-out to show their emptiness, would become “Hoover flags.”

The stock market crash of October 1929 set the Great Depression into motion, but other factors were at the root of the problem, propelled onward by a series of both human-made and natural catastrophes. Anticipating a short downturn and living under an ethos of free enterprise and individualism, Americans suffered mightily in the first years of the Depression. As conditions worsened and the government failed to act, they grew increasingly desperate for change. While Hoover could not be blamed for the Great Depression, his failure to address the nation’s hardships would remain his legacy. (2)

## The Stock Market Crash of 1929

Herbert Hoover became president at a time of ongoing prosperity in the country. Americans hoped he would continue to lead the country through still more economic growth, and neither he nor the country was ready for the unraveling that followed. But Hoover’s moderate policies, based upon a strongly held belief in the spirit of American individualism, were not enough to stem the ever-growing problems, and the economy slipped further and further into the Great Depression.

While it is misleading to view the stock market crash of 1929 as the sole cause of the Great Depression, the dramatic events of that October did play a role in the downward spiral of the American economy. The crash, which took place less than a year after Hoover was inaugurated, was the most extreme sign of the economy’s weakness. Multiple factors contributed to the crash, which in turn caused a consumer panic that drove the economy even further downhill, in ways that neither Hoover nor the financial industry was able to restrain. Hoover, like many others at the time, thought and hoped that the country would right itself with limited government intervention. This was not the case, however, and millions of Americans sank into grinding poverty. (2)

## The Early Days of Hoover’s Presidency

Upon his inauguration, President Hoover set forth an agenda that he hoped would continue the “Coolidge prosperity” of the previous administration. While accepting the Republican Party’s presidential nomination in 1928, Hoover commented, “Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God be in sight of the day when poverty will be banished from this nation forever.” In the spirit of normalcy that defined the Republican ascendancy of the 1920s, Hoover planned to immediately overhaul federal regulations with the intention of allowing the nation’s economy to grow unfettered by any controls. The role of the government, he contended, should be to create a partnership with the American people, in which the latter would rise (or fall) on their own merits and abilities. He felt the less government intervention in their lives, the better.

Yet, to listen to Hoover’s later reflections on Franklin Roosevelt’s first term in office, one could easily mistake his vision for America for the one held by his successor. Speaking in 1936 before an audience in Denver, Colorado, he acknowledged that it was always his intent as president to ensure “a nation built of home owners and farm owners. We want to see more and more of them insured against death and accident, unemployment and old age,” he declared. “We want them all secure.” Such humanitarianism was not uncommon to Hoover. Throughout his early career in public service, he was committed to relief for people around the world. In 1900, he coordinated relief efforts for foreign nationals trapped in China during the Boxer Rebellion. At the outset of World War I, he led the food relief effort in Europe, specifically helping millions of Belgians who faced German forces.

President Woodrow Wilson subsequently appointed him head of the U.S. Food Administration to coordinate rationing efforts in America as well as to secure essential food items for the Allied forces and citizens in Europe.

Hoover’s first months in office hinted at the reformist, humanitarian spirit that he had displayed throughout his career. He continued the civil service reform of the early twentieth century by expanding opportunities for employment throughout the federal government. In response to the Teapot Dome Affair, which had occurred during the Harding administration, he invalidated several private oil leases on public lands. He directed the Department of Justice, through its Bureau of Investigation, to crack down on organized crime, resulting in the arrest and imprisonment of Al Capone. By the summer of 1929, he had signed into law the creation of a Federal Farm Board to help farmers with government price supports, expanded tax cuts across all income classes, and set aside federal funds to clean up slums in major American cities. To directly assist several overlooked populations, he created the Veterans Administration and expanded veterans’ hospitals, established the Federal Bureau of Prisons to oversee incarceration conditions nationwide, and reorganized the Bureau of Indian Affairs to further protect Native Americans. Just prior to the stock market crash, he even proposed the creation of an old-age pension program, promising fifty dollars monthly to all Americans over the age of sixty-five—a proposal remarkably similar to the social security benefit that would become a hallmark of Roosevelt’s subsequent New Deal programs. As the summer of 1929 came to a close, Hoover remained a popular successor to Calvin “Silent Cal” Coolidge, and all signs pointed to a highly successful administration. (2)

## The Great Crash

The promise of the Hoover administration was cut short when the stock market lost almost one-half its value in the fall of 1929, plunging many Americans into financial ruin. However, as a singular event, the stock market crash itself did not cause the Great Depression that followed. In fact, only approximately 10 percent of American households held stock investments and speculated in the market; yet nearly a third would lose their lifelong savings and jobs in the ensuing depression. The connection between the crash and the subsequent decade of hardship was complex, involving underlying weaknesses in the economy that many policymakers had long ignored.

### What Was the Crash?

To understand the crash, it is useful to address the decade that preceded it. The prosperous 1920s ushered in a feeling of euphoria among middle-class and wealthy Americans, and people began to speculate on wilder investments. The government was a willing partner in this endeavor: The Federal Reserve followed a brief postwar recession in 1920–1921 with a policy of setting interest rates artificially low, as well as easing the reserve requirements on the nation’s largest banks. As a result, the money supply in the U.S. increased by nearly 60 percent, which convinced even more Americans of the safety of investing in questionable schemes. They felt that prosperity was boundless and that extreme risks were likely tickets to wealth. Named for Charles Ponzi, the original “Ponzi schemes” emerged early in the 1920s to encourage novice investors to divert funds to unfounded ventures, which in reality simply used new investors’ funds to pay off older investors as the schemes grew in size. Speculation, where investors purchased into high-risk schemes that they hoped would pay off quickly, became the norm. Several banks, including deposit institutions that originally avoided investment loans, began to offer easy credit, allowing people to invest, even when they lacked the money to do so.

Several warning signs portended the impending crash but went unheeded by Americans still giddy over the potential fortunes that speculation might promise. A brief downturn in the market on September 18, 1929, raised questions among more-seasoned investment bankers, leading some to predict an end to high stock values, but did little to stem the tide of investment. Even the collapse of the London Stock Exchange on September 20 failed to fully curtail the optimism of American investors. However, when the New York Stock Exchange lost 11 percent of its value on October 24—often referred to as “Black Thursday”—key American investors sat up and took notice. In an effort to forestall a much-feared panic, leading banks, including Chase National, National City, J.P. Morgan, and others, conspired to purchase large amounts of blue chip stocks (including U.S. Steel) in order to keep the prices artificially high. Even that effort failed in the growing wave of stock sales. Nevertheless, Hoover delivered a radio address on Friday in which he assured the American people, “The fundamental business of the country . . . is on a sound and prosperous basis.”

As newspapers across the country began to cover the story in earnest, investors anxiously awaited the start of the following week. When the Dow Jones Industrial Average lost another 13 percent of its value on Monday morning, many knew the end of stock market speculation was near. The evening before the infamous crash was ominous. Jonathan Leonard, a newspaper reporter who regularly covered the stock market beat, wrote of how Wall Street “lit up like a Christmas tree.” Brokers and businessmen who feared the worst the next day crowded into restaurants and speakeasies (a place where alcoholic beverages were illegally sold). After a night of heavy drinking, they retreated to nearby hotels or flop-houses (cheap boarding houses), all of which were overbooked, and awaited sunrise. Children from nearby slums and tenement districts played stickball in the streets of the financial district, using wads of ticker tape for balls. Although they all awoke to newspapers filled with predictions of a financial turnaround, as well as technical reasons why the decline might be short-lived, the crash on Tuesday morning, October 29, caught few by surprise.

No one even heard the opening bell on Wall Street that day, as shouts of “Sell! Sell!” drowned it out. In the first three minutes alone, nearly three million shares of stock, accounting for $2 million of wealth, changed hands. The volume of Western Union telegrams tripled, and telephone lines could not meet the demand, as investors sought any means available to dump their stock immediately. Rumors spread of investors jumping from their office windows. Fistfights broke out on the trading floor, where one broker fainted from physical exhaustion. Stock trades happened at such a furious pace that runners had nowhere to store the trade slips, and so they resorted to stuffing them into trash cans. Although the stock exchange’s board of governors briefly considered closing the exchange early, they subsequently chose to let the market run its course, lest the American public panic even further at the thought of closure. When the final bell rang, errand boys spent hours sweeping up tons of paper, tickertape, and sales slips, as shown in Figure 8-1. On Black Tuesday, October 29, stock holders traded over sixteen million shares and lost over$14 billion in wealth in a single day. To put this in context, a trading day of three million shares was considered a busy day on the stock market. People unloaded their stock as quickly as they could, never minding the loss. Banks, facing debt and seeking to protect their own assets, demanded payment for the loans they had provided to individual investors. Those individuals who could not afford to pay found their stocks sold immediately and their life savings wiped out in minutes, yet their debt to the bank still remained.

The financial outcome of the crash was devastating. Between September 1 and November 30, 1929, the stock market lost over one-half its value, dropping from $64 billion to approximately$30 billion. Any effort to stem the tide was, as one historian noted, tantamount to bailing Niagara Falls with a bucket. The crash affected many more than the relatively few Americans who invested in the stock market. While only 10 percent of households had investments, over 90 percent of all banks had invested in the stock market. Many banks failed due to their dwindling cash reserves. This was in part due to the Federal Reserve lowering the limits of cash reserves that banks were traditionally required to hold in their vaults, as well as the fact that many banks invested in the stock market themselves. Eventually, thousands of banks closed their doors after losing all of their assets, leaving their customers penniless. While a few savvy investors got out at the right time and eventually made fortunes buying up discarded stock, those success stories were rare. Housewives who speculated with grocery money, bookkeepers who embezzled company funds hoping to strike it rich and pay the funds back before getting caught, and bankers who used customer deposits to follow speculative trends all lost. While the stock market crash was the trigger, the lack of appropriate economic and banking safeguards, along with a public psyche that pursued wealth and prosperity at all costs, allowed this event to spiral downward into a depression.

### Causes of the Crash

The crash of 1929 did not occur in a vacuum, nor did it cause the Great Depression. Rather, it was a tipping point where the underlying weaknesses in the economy, specifically in the nation’s banking system, came to the fore. It also represented both the end of an era characterized by blind faith in American exceptionalism and the beginning of one in which citizens began increasingly to question some long-held American values. A number of factors played a role in bringing the stock market to this point and contributed to the downward trend in the market, which continued well into the 1930s. In addition to the Federal Reserve’s questionable policies and misguided banking practices, three primary reasons for the collapse of the stock market were international economic woes, poor income distribution, and the psychology of public confidence.

After World War I, both America’s allies and the defeated nations of Germany and Austria contended with disastrous economies. The Allies owed large amounts of money to U.S. banks, which had advanced them money during the war effort. Unable to repay these debts, the Allies looked to reparations from Germany and Austria to help. The economies of those countries, however, were struggling badly, and they could not pay their reparations, despite the loans that the U.S. provided to assist with their payments. The U.S. government refused to forgive these loans, and American banks were in the position of extending additional private loans to foreign governments, who used them to repay their debts to the U.S. government, essentially shifting their obligations to private banks. When other countries began to default on this second wave of private bank loans, still more strain was placed on U.S. banks, which soon sought to liquidate these loans at the first sign of a stock market crisis.

Poor income distribution among Americans compounded the problem. A strong stock market relies on today’s buyers becoming tomorrow’s sellers, and therefore it must always have an influx of new buyers. In the 1920s, this was not the case. Eighty percent of American families had virtually no savings, and only one-half to 1 percent of Americans controlled over a third of the wealth. This scenario meant that there were no new buyers coming into the marketplace, and nowhere for sellers to unload their stock as the speculation came to a close. In addition, the vast majority of Americans with limited savings lost their accounts as local banks closed, and likewise lost their jobs as investment in business and industry came to a screeching halt.

Finally, one of the most important factors in the crash was the contagion effect of panic. For much of the 1920s, the public felt confident that prosperity would continue forever, and therefore, in a self-fulfilling cycle, the market continued to grow. But once the panic began, it spread quickly and with the same cyclical results; people were worried that the market was going down, they sold their stock, and the market continued to drop. This was partly due to Americans’ inability to weather market volatility, given the limited cash surpluses they had on hand, as well as their psychological concern that economic recovery might never happen.

### In the Aftermath of the Crash

After the crash, Hoover announced that the economy was “fundamentally sound.” On the last day of trading in 1929, the New York Stock Exchange held its annual wild and lavish party, complete with confetti, musicians, and illegal alcohol. The U.S. Department of Labor predicted that 1930 would be “a splendid employment year.” These sentiments were not as baseless as it may seem in hindsight. Historically, markets cycled up and down, and periods of growth were often followed by downturns that corrected themselves. But this time, there was no market correction; rather, the abrupt shock of the crash was followed by an even more devastating depression. Investors, along with the general public, withdrew their money from banks by the thousands, fearing the banks would go under. The more people pulled out their money in bank runs, the closer the banks came to insolvency.

As the financial markets collapsed, hurting the banks that had gambled with their holdings, people began to fear that the money they had in the bank would be lost. This began bank runs across the country, a period of still more panic, where people pulled their money out of banks to keep it hidden at home.

The contagion effect of the crash grew quickly. With investors losing billions of dollars, they invested very little in new or expanded businesses. At this time, two industries had the greatest impact on the country’s economic future in terms of investment, potential growth, and employment: automotive and construction. After the crash, both were hit hard. In November 1929, fewer cars were built than in any other month since November 1919. Even before the crash, widespread saturation of the market meant that few Americans bought them, leading to a slowdown. Afterward, very few could afford them. By 1933, Stutz, Locomobile, Durant, Franklin, Deusenberg, and Pierce-Arrow automobiles, all luxury models, were largely unavailable; production had ground to a halt. They would not be made again until 1949. In construction, the drop-off was even more dramatic. It would be another thirty years before a new hotel or theater was built in New York City. The Empire State Building itself stood half empty for years after being completed in 1931.

The damage to major industries led to, and reflected, limited purchasing by both consumers and businesses. Even those Americans who continued to make a modest income during the Great Depression lost the drive for conspicuous consumption that they exhibited in the 1920s. People with less money to buy goods could not help businesses grow; in turn, businesses with no market for their products could not hire workers or purchase raw materials. Employers began to lay off workers. The country’s gross national product declined by over 25 percent within a year, and wages and salaries declined by $4 billion. Unemployment tripled, from 1.5 million at the end of 1929 to 4.5 million by the end of 1930, as shown in Figure 8-2. By mid-1930, the slide into economic chaos had begun but was nowhere near complete. (2) ## The New Reality for Americans For most Americans, the crash affected daily life in myriad ways. In the immediate aftermath, there was a run on the banks, where citizens took their money out, if they could get it, and hid their savings under mattresses, in bookshelves, or anywhere else they felt was safe. Some went so far as to exchange their dollars for gold and ship it out of the country. A number of banks failed outright, and others, in their attempts to stay solvent, called in loans that people could not afford to repay. Working-class Americans saw their wages drop: Even Henry Ford, the champion of a high minimum wage, began lowering wages by as much as a dollar a day. Southern cotton planters paid workers only twenty cents for every one hundred pounds of cotton picked, meaning that the strongest picker might earn sixty cents for a fourteen-hour day of work. Cities struggled to collect property taxes and subsequently laid off teachers and police. The new hardships that people faced were not always immediately apparent; many communities felt the changes but could not necessarily look out their windows and see anything different. Men who lost their jobs didn’t stand on street corners begging; they disappeared. They might be found keeping warm by a trashcan bonfire or picking through garbage at dawn, but mostly, they stayed out of public view. As the effects of the crash continued, however, the results became more evident. Those living in cities grew accustomed to seeing long breadlines of unemployed men waiting for a meal, as shown in Figure 8-3. Companies fired workers and tore down employee housing to avoid paying property taxes. The landscape of the country had changed. The hardships of the Great Depression threw family life into disarray. Both marriage and birth rates declined in the decade after the crash. The most vulnerable members of society—children, women, minorities, and the working class—struggled the most. Parents often sent children out to beg for food at restaurants and stores to save themselves from the disgrace of begging. Many children dropped out of school, and even fewer went to college. Childhood, as it had existed in the prosperous twenties, was over. And yet, for many children living in rural areas where the affluence of the previous decade was not fully developed, the Depression was not viewed as a great challenge. School continued. Play was simple and enjoyed. Families adapted by growing more in gardens, canning, and preserving, wasting little food if any. Home-sewn clothing became the norm as the decade progressed, as did creative methods of shoe repair with cardboard soles. Yet, one always knew of stories of the “other” families who suffered more, including those living in cardboard boxes or caves. By one estimate, as many as 200,000 children moved about the country as vagrants due to familial disintegration. Women’s lives, too, were profoundly affected. Some wives and mothers sought employment to make ends meet, an undertaking that was often met with strong resistance from husbands and potential employers. Many men derided and criticized women who worked, feeling that jobs should go to unemployed men. Some campaigned to keep companies from hiring married women, and an increasing number of school districts expanded the long-held practice of banning the hiring of married female teachers. Despite the pushback, women entered the workforce in increasing numbers, from ten million at the start of the Depression to nearly thirteen million by the end of the 1930s. This increase took place in spite of the twenty-six states that passed a variety of laws to prohibit the employment of married women. Several women found employment in the emerging pink collar occupations, viewed as traditional women’s work, including jobs as telephone operators, social workers, and secretaries. Others took jobs as maids and housecleaners, working for those fortunate few who had maintained their wealth. White women’s forays into domestic service came at the expense of minority women, who had even fewer employment options. Unsurprisingly, African American men and women experienced unemployment, and the grinding poverty that followed, at double and triple the rates of their white counterparts. By 1932, unemployment among African Americans reached near 50 percent. In rural areas, where large numbers of African Americans continued to live despite the Great Migration of 1910–1930, depression-era life represented an intensified version of the poverty that they traditionally experienced. Subsistence farming allowed many African Americans who lost either their land or jobs working for white landholders to survive, but their hardships increased. Life for African Americans in urban settings was equally trying, with blacks and working-class whites living in close proximity and competing for scarce jobs and resources. Life for all rural Americans was difficult. Farmers largely did not experience the widespread prosperity of the 1920s. Although continued advancements in farming techniques and agricultural machinery led to increased agricultural production, decreasing demand (particularly in the previous markets created by World War I) steadily drove down commodity prices. As a result, farmers could barely pay the debt they owed on machinery and land mortgages, and even then could do so only as a result of generous lines of credit from banks. While factory workers may have lost their jobs and savings in the crash, many farmers also lost their homes, due to the thousands of farm foreclosures sought by desperate bankers. Between 1930 and 1935, nearly 750,000 family farms disappeared through foreclosure or bankruptcy. Even for those who managed to keep their farms, there was little market for their crops. Unemployed workers had less money to spend on food, and when they did purchase goods, the market excess had driven prices so low that farmers could barely piece together a living. A now-famous example of the farmer’s plight is that, when the price of coal began to exceed that of corn, farmers would simply burn corn to stay warm in the winter. As the effects of the Great Depression worsened, wealthier Americans had particular concern for “the deserving poor”—those who had lost all of their money due to no fault of their own. This concept gained greater attention beginning in the Progressive Era of the late nineteenth and early twentieth centuries, when early social reformers sought to improve the quality of life for all Americans by addressing the poverty that was becoming more prevalent, particularly in emerging urban areas. By the time of the Great Depression, social reformers and humanitarian agencies had determined that the “deserving poor” belonged to a different category from those who had speculated and lost. However, the sheer volume of Americans who fell into this group meant that charitable assistance could not begin to reach them all. Some fifteen million “deserving poor,” or a full one-third of the labor force, were struggling by 1932. The country had no mechanism or system in place to help so many; however, Hoover remained adamant that such relief should rest in the hands of private agencies, not with the federal government. Unable to receive aid from the government, Americans thus turned to private charities; churches, synagogues, and other religious organizations; and state aid. But these organizations were not prepared to deal with the scope of the problem. Private aid organizations showed declining assets as well during the Depression, with fewer Americans possessing the ability to donate to such charities. Likewise, state governments were particularly ill-equipped. Governor Franklin D. Roosevelt was the first to institute a Department of Welfare in New York in 1929. City governments had equally little to offer. In New York City in 1932, family allowances were$2.39 per week, and only one-half of the families who qualified actually received them. In Detroit, allowances fell to fifteen cents a day per person, and eventually ran out completely. In most cases, relief was only in the form of food and fuel; organizations provided nothing in the way of rent, shelter, medical care, clothing, or other necessities. There was no infrastructure to support the elderly, who were the most vulnerable, and this population largely depended on their adult children to support them, adding to families’ burdens.

During this time, local community groups, such as police and teachers, worked to help the neediest. New York City police, for example, began contributing 1 percent of their salaries to start a food fund that was geared to help those found starving on the streets. In 1932, New York City schoolteachers also joined forces to try to help; they contributed as much as $250,000 per month from their own salaries to help needy children. Chicago teachers did the same, feeding some eleven thousand students out of their own pockets in 1931, despite the fact that many of them had not been paid a salary in months. These noble efforts, however, failed to fully address the level of desperation that the American public was facing. (2) ## President Hoover’s Response President Hoover was unprepared for the scope of the depression crisis, and his limited response did not begin to help the millions of Americans in need. The steps he took were very much in keeping with his philosophy of limited government, a philosophy that many had shared with him until the upheavals of the Great Depression made it clear that a more direct government response was required. But Hoover was stubborn in his refusal to give “handouts,” as he saw direct government aid. He called for a spirit of volunteerism among America’s businesses, asking them to keep workers employed, and he exhorted the American people to tighten their belts and make do in the spirit of “rugged individualism.” While Hoover’s philosophy and his appeal to the country were very much in keeping with his character, it was not enough to keep the economy from plummeting further into economic chaos. The steps Hoover did ultimately take were too little, too late. He created programs for putting people back to work and helping beleaguered local and state charities with aid. But the programs were small in scale and highly specific as to who could benefit, and they only touched a small percentage of those in need. As the situation worsened, the public grew increasingly unhappy with Hoover. He left office with one of the lowest approval ratings of any president in history. ### The Initial Reaction In the immediate aftermath of Black Tuesday, Hoover sought to reassure Americans that all was well. Reading his words after the fact, it is easy to find fault. In 1929 he said, “Any lack of confidence in the economic future or the strength of business in the United States is foolish.” In 1930, he stated, “The worst is behind us.” In 1931, he pledged federal aid should he ever witness starvation in the country; but as of that date, he had yet to see such need in America, despite the very real evidence that children and the elderly were starving to death. Yet Hoover was neither intentionally blind nor unsympathetic. He simply held fast to a belief system that did not change as the realities of the Great Depression set in. Hoover believed strongly in the ethos of American individualism: that hard work brought its own rewards. His life story testified to that belief. Hoover was born into poverty, made his way through college at Stanford University, and eventually made his fortune as an engineer. This experience, as well as his extensive travels in China and throughout Europe, shaped his fundamental conviction that the very existence of American civilization depended upon the moral fiber of its citizens, as evidenced by their ability to overcome all hardships through individual effort and resolve. The idea of government handouts to Americans was repellant to him. Whereas Europeans might need assistance, such as his hunger relief work in Belgium during and after World War I, he believed the American character to be different. In a 1931 radio address, he said, “The spread of government destroys initiative and thus destroys character.” Likewise, Hoover was not completely unaware of the potential harm that wild stock speculation might create if left unchecked. As secretary of commerce, Hoover often warned President Coolidge of the dangers that such speculation engendered. In the weeks before his inauguration, he offered many interviews to newspapers and magazines, urging Americans to curtail their rampant stock investments, and even encouraged the Federal Reserve to raise the discount rate to make it more costly for local banks to lend money to potential speculators. However, fearful of creating a panic, Hoover never issued a stern warning to discourage Americans from such investments. Neither Hoover, nor any other politician of that day, ever gave serious thought to outright government regulation of the stock market. This was even true in his personal choices, as Hoover often lamented poor stock advice he had once offered to a friend. When the stock nose-dived, Hoover bought the shares from his friend to assuage his guilt, vowing never again to advise anyone on matters of investment. In keeping with these principles, Hoover’s response to the crash focused on two very common American traditions: He asked individuals to tighten their belts and work harder, and he asked the business community to voluntarily help sustain the economy by retaining workers and continuing production. He immediately summoned a conference of leading industrialists to meet in Washington, DC, urging them to maintain their current wages while America rode out this brief economic panic. The crash, he assured business leaders, was not part of a greater downturn; they had nothing to worry about. Similar meetings with utility companies and railroad executives elicited promises for billions of dollars in new construction projects, while labor leaders agreed to withhold demands for wage increases and workers continued to labor. Hoover also persuaded Congress to pass a$160 million tax cut to bolster American incomes, leading many to conclude that the president was doing all he could to stem the tide of the panic. In April 1930, the New York Times editorial board concluded that “No one in his place could have done more.”

However, these modest steps were not enough. By late 1931, when it became clear that the economy would not improve on its own, Hoover recognized the need for some government intervention. He created the President’s Emergency Committee for Employment (PECE), later renamed the President’s Organization of Unemployment Relief (POUR).

In keeping with Hoover’s distaste of what he viewed as handouts, this organization did not provide direct federal relief to people in need. Instead, it assisted state and private relief agencies, such as the Red Cross, Salvation Army, YMCA, and Community Chest. Hoover also strongly urged people of means to donate funds to help the poor, and he himself gave significant private donations to worthy causes. But these private efforts could not alleviate the widespread effects of poverty.

Congress pushed for a more direct government response to the hardship. In 1930–1931, it attempted to pass a $60 million bill to provide relief to drought victims by allowing them access to food, fertilizer, and animal feed. Hoover stood fast in his refusal to provide food, resisting any element of direct relief. The final bill of$47 million provided for everything except food but did not come close to adequately addressing the crisis. Again in 1931, Congress proposed the Federal Emergency Relief Bill, which would have provided $375 million to states to help provide food, clothing, and shelter to the homeless. But Hoover opposed the bill, stating that it ruined the balance of power between states and the federal government, and in February 1932, it was defeated by fourteen votes. However, the president’s adamant opposition to direct-relief federal government programs should not be viewed as one of indifference or uncaring toward the suffering American people. His personal sympathy for those in need was boundless. Hoover was one of only two presidents to reject his salary for the office he held. Throughout the Great Depression, he donated an average of$25,000 annually to various relief organizations to assist in their efforts. Furthermore, he helped to raise $500,000 in private funds to support the White House Conference on Child Health and Welfare in 1930. Rather than indifference or heartlessness, Hoover’s steadfast adherence to a philosophy of individualism as the path toward long-term American recovery explained many of his policy decisions. “A voluntary deed,” he repeatedly commented, “is infinitely more precious to our national ideal and spirit than a thousand-fold poured from the Treasury.” As conditions worsened, however, Hoover eventually relaxed his opposition to federal relief and formed the Reconstruction Finance Corporation (RFC) in 1932, in part because it was an election year and Hoover hoped to keep his office. Although not a form of direct relief to the American people in greatest need, the RFC was much larger in scope than any preceding effort, setting aside$2 billion in taxpayer money to rescue banks, credit unions, and insurance companies. The goal was to boost confidence in the nation’s financial institutions by ensuring that they were on solid footing. This model was flawed on a number of levels. First, the program only lent money to banks with sufficient collateral, which meant that most of the aid went to large banks. In fact, of the first $61 million loaned,$41 million went to just three banks. Small town and rural banks got almost nothing. Furthermore, at this time, confidence in financial institutions was not the primary concern of most Americans. They needed food and jobs. Many had no money to put into the banks, no matter how confident they were that the banks were safe.

Hoover’s other attempt at federal assistance also occurred in 1932, when he endorsed a bill by Senator Robert Wagner of New York. This was the Emergency Relief and Construction Act. This act authorized the RFC to expand beyond loans to financial institutions and allotted \$1.5 billion to states to fund local public works projects. This program failed to deliver the kind of help needed, however, as Hoover severely limited the types of projects it could fund to those that were ultimately self-paying (such as toll bridges and public housing) and those that required skilled workers. While well intended, these programs maintained the status quo, and there was still no direct federal relief to the individuals who so desperately needed it.

### Public Reaction to Hoover

Hoover’s steadfast resistance to government aid cost him the reelection and has placed him squarely at the forefront of the most unpopular presidents, according to public opinion, in modern American history. His name became synonymous with the poverty of the era: “Hoovervilles” became the common name for homeless shantytowns (see Figure 8-4) and “Hoover blankets” for the newspapers that the homeless used to keep warm. A “Hoover flag” was a pants pocket—empty of all money—turned inside out. By the 1932 election, hitchhikers held up signs reading: “If you don’t give me a ride, I’ll vote for Hoover.” Americans did not necessarily believe that Hoover caused the Great Depression. Their anger stemmed instead from what appeared to be a willful refusal to help regular citizens with direct aid that might allow them to recover from the crisis.

### Frustration and Protest: A Bad Situation Grows Worse for Hoover

Desperation and frustration often create emotional responses, and the Great Depression was no exception. Throughout 1931–1932, companies trying to stay afloat sharply cut worker wages, and, in response, workers protested in increasingly bitter strikes. As the Depression unfolded, over 80 percent of automotive workers lost their jobs. Even the typically prosperous Ford Motor Company laid off two-thirds of its workforce.

In 1932, a major strike at the Ford Motor Company factory near Detroit resulted in over sixty injuries and four deaths. Often referred to as the Ford Hunger March, the event unfolded as a planned demonstration among unemployed Ford workers who, to protest their desperate situation, marched nine miles from Detroit to the company’s River Rouge plant in Dearborn. At the Dearborn city limits, local police launched tear gas at the roughly three thousand protestors, who responded by throwing stones and clods of dirt. When they finally reached the gates of the plant, protestors faced more police and firemen, as well as private security guards. As the firemen turned hoses onto the protestors, the police and security guards opened fire. In addition to those killed and injured, police arrested fifty protestors. One week later, sixty thousand mourners attended the public funerals of the four victims of what many protesters labeled police brutality. The event set the tone for worsening labor relations in the U.S.

Farmers also organized and protested, often violently. The most notable example was the Farm Holiday Association. Led by Milo Reno, this organization held significant sway among farmers in Iowa, Nebraska, Wisconsin, Minnesota, and the Dakotas. Although they never comprised a majority of farmers in any of these states, their public actions drew press attention nationwide. Among their demands, the association sought a federal government plan to set agricultural prices artificially high enough to cover the farmers’ costs, as well as a government commitment to sell any farm surpluses on the world market. To achieve their goals, the group called for farm holidays, during which farmers would neither sell their produce nor purchase any other goods until the government met their demands. However, the greatest strength of the association came from the unexpected and seldom-planned actions of its members, which included barricading roads into markets, attacking nonmember farmers, and destroying their produce. Some members even raided small town stores, destroying produce on the shelves. Members also engaged in “penny auctions,” bidding pennies on foreclosed farm land and threatening any potential buyers with bodily harm if they competed in the sale. Once they won the auction, the association returned the land to the original owner. In Iowa, farmers threatened to hang a local judge if he signed any more farm foreclosures. At least one death occurred as a direct result of these protests before they waned following the election of Franklin Roosevelt.

One of the most notable protest movements occurred toward the end of Hoover’s presidency and centered on the Bonus Expeditionary Force, or Bonus Army, in the spring of 1932. In this protest, approximately fifteen thousand World War I veterans marched on Washington to demand early payment of their veteran bonuses, which were not due to be paid until 1945. The group camped out in vacant federal buildings and set up camps in Anacostia Flats near the Capitol building (Figure 8-5).

Many veterans remained in the city in protest for nearly two months, although the U.S. Senate officially rejected their request in July. By the middle of that month, Hoover wanted them gone. He ordered the police to empty the buildings and clear out the camps, and in the exchange that followed, police fired into the crowd, killing two veterans. Fearing an armed uprising, Hoover then ordered General Douglas MacArthur, along with his aides, Dwight Eisenhower and George Patton, to forcibly remove the veterans from Anacostia Flats. The ensuing raid proved catastrophic, as the military burned down the shantytown and injured dozens of people, including a twelve-week-old infant who was killed when accidentally struck by a tear gas canister (see Figure 8-6).

As Americans bore witness to photographs and newsreels of the U.S. Army forcibly removing veterans, Hoover’s popularity plummeted even further. By the summer of 1932, he was largely a defeated man. His pessimism and failure mirrored that of the nation’s citizens. America was a country in desperate need: in need of a charismatic leader to restore public confidence as well as provide concrete solutions to pull the economy out of the Great Depression. (2)


text:
Solved

# Truncate folder name

Posted on 2013-02-05
577 Views
Hello,

I am looking for a script that can truncate folders in a directory.  Each folder in the main directory has three underscores (_) in the file name.  I need to have a script that will remove the third underscore and everything after it.

Can this be done with a batch file?

Thank you.
0
Question by:cbones
• 4

LVL 43

Expert Comment

ID: 38857614
If there aren't any other underscores in the filenames you can probably do it with this... it will look for all dirs with with three underscores in then pass the bit before the first _ into %%a and the bit after the underscores into %%b

Steve

@echo off
cd /d "c:\root directory"
for /f "tokens=1* delims=_" %%a in ('dir /b /ad *___*') do echo rename "%%a___%%b" "%%a__"

0

LVL 43

Expert Comment

ID: 38857622
That will SHOW you the commands it will run on the screen.  If they look OK remove the word echo before the rename command.

If there is the possibility of other _ characters in the foldername will have to be done in different way.

Steve
0

Author Comment

ID: 38857674
Steve,

Thank you for your response.  When I run this it removes two underscore only if the three are in the folder name together.

I can have a file name like this:  file_test_one_temp_0212312

What I am looking to do is to remove everything after the third underscore.

Thank you.
0

LVL 43

Accepted Solution

Steve Knight earned 175 total points
ID: 38857736
Ahh OK then if there are always three or more underscores and you want a maximum of two then try this:

@echo off
cd /d "c:\root directory"
for /f "tokens=1,2,3* delims=_" %%a in ('dir /b /ad *_*_*_*') do echo rename "%%a_%%b_%%c_%%d" "%%a_%%b_%%c"

Looks for the pattern *_*_*_* and splits the filename at the _ and renames to the first three parts.

In your example "file_test_one_temp_0212312" becomes "file_test_one"

Steve
0

LVL 53

Assisted Solution

Bill Prew earned 175 total points
ID: 38857753
This should do what you are looking for.  Adjust the BaseDir name as needed.  Currently it wont rename the folders, just show the command it would execute. This will allow you to test and verify, if it looks good remove the ECHO from the REN line.

@echo off
setlocal

set BaseDir=c:\ee\EE28021328\basedir

for /D %%D in ("%BaseDir%\*_*_*_*") do (
for /F "tokens=1-3 delims=_" %%A in ("%%~nD") do (
ECHO ren "%%~D" "%%~A_%%B_%%C"
)
)

~bp
0

LVL 43

Expert Comment

ID: 38859800
Thanks.  Should have done it like Bill did really anyway, only reason I didn't is because I thought you meant three underscores in a row.
Steve
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Adding vectorized ufuncs in scipy.special¶

Many of the functions in special are vectorized versions of scalar functions. The scalar functions are written by hand and the necessary loops for vectorization are generated automatically. This section discusses the steps necessary to add a new vectorized special function.

The first step in adding a new vectorized function is writing the corresponding scalar function. This can be done in Cython, C, C++, or Fortran. If starting from scratch then Cython should be preferred because the code is easier to maintain for developers only familiar with Python. If the primary code is in Fortran then it is necessary to write a C wrapper around the code; for examples of such wrappers see specfun_wrappers.c.

After implementing the scalar function, register the new function by adding an entry to functions.json. The docstring in generate_ufuncs.py explains the format. Also add documentation for the new function by adding an entry to add_newdocs.py; look in the file for examples.

When writing the parameters section of the documentation for ufuncs, the type of an argument should be array_like. Discussion of whether an argument can be e.g. real or complex-valued should be saved for the description. So for example, if we were to document the parameters for the Gamma function then it should look like this:

Parameters
----------
z : array_like
Real or complex valued argument

When documenting the returns section, the type of the returned value should be scalar or ndarray since ufuncs return scalars when given scalars as arguments. Also keep in mind that providing a name for the return value is optional, and indeed is often not helpful for special functions. So for the Gamma function we might have something like this:

Returns
-------
scalar or ndarray
Values of the Gamma function

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# Why do some molecules form T shapes instead of trigonal planar shapes [duplicate]

This question already has an answer here:

Consider a molecule such as $\ce{ClF_3}$.
Shouldn't the electron clouds (which are more negative than the Chlorine atom) want to repel each other and so the $\ce{ClF_3}$molecule should arrange into a trigonal planar shape where the electron clouds are as far away as possible?

I think at a deeper level than VSEPR, Chlorine is either partially ionized to a hybrid of $\ce{F^- + Cl^+F_2}$ configurations or has some electrons promoted up to d shaped orbitals but I don't know how to calculate the resulting shape. I think the main thing throwing me off is that the $\ce{F^- + Cl^+F_2}$ shapes should have the $\ce{F^-}$ ion repulsed from the lone pair electrons.

## marked as duplicate by bon, M.A.R., ron, Todd Minehardt, Jon CusterJul 17 '16 at 15:49

• A more general question is $$\mathrm{Why\ does\ VSEPR\ predict\ a\ T-shaped\ geometry\ for AX_3 E_2 \ and\ not\ trigonal\ planar?}$$ We also have to remember that VSEPR was developed to rationalize what we were learning about electrons, bonding, and quantum mechanics withe known geometries. – Ben Norris Jul 16 '16 at 21:08


text:
Physics Forums (http://www.physicsforums.com/index.php)
-   Introductory Physics Homework (http://www.physicsforums.com/forumdisplay.php?f=153)
-   -   Cancelling out units in an equation (http://www.physicsforums.com/showthread.php?t=490724)

 andrewvidler Apr16-11 03:20 AM

cancelling out units in an equation

Hi i have done all the work for this problem calculating viscosity and i come to the last part where i need to manipulate and cancel out units to come to a final solution. The equation works out as

viscosity = 0.0042m^2 x 9.8m/s/s x 11,401.4kg/m^3 all divided by 1.034466m/s

viscosity is measured in Pascals/sec

can someone help me with the last step with the units

thanks

 CompuChip Apr16-11 04:11 AM

Re: cancelling out units in an equation

I usually start by drawing a long horizontal line and writing all the units in the denominator or numerator as appropriate. Thereby, dividing by a/b means writing b "above" and a "below" (as dividing by a/b means multiplying by b/a).

In this case, going through them one by one, you'd get

$$\frac{m^2}{1} \times \frac{m}{s \times s} \times \frac{kg}{m^3} \times \frac{s}{m}$$
If you write this in a single fraction, and take the similar units together, you get
$$\frac{m^3 \, s \, kg}{s^2 \, m^4}$$
which is straightforward to simplify.

Now to check that this is indeed Pa/s, it is easiest to convert Pascals into kg/m/s. Personally, I find it easiest to remember that pressure is force per unit area, and Newton's law is F = ma, so
$$[Pa] = \frac{[F]}{[A]} = \frac{[m] [a]}{[A]} = \frac{kg \times m/s^2}{m^2} = \frac{kg \times m}{s^2 \times m^2}$$

 tiny-tim Apr16-11 04:19 AM

welcome to pf!

hi andrew! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
Quote:
 Quote by andrewvidler (Post 3249366) viscosity is measured in Pascals/sec
nooo :redface: … viscosity is measured in Pascal.sec :wink:

 andrewvidler Apr16-11 04:38 AM

Re: cancelling out units in an equation

thanks - my final units are 453 kg/sm. any chance on helping me how to get this into pascals which are measured in mPa s?

 tiny-tim Apr16-11 04:55 AM

Pa.s = force.time/area = mass.time.acceleration/area

= mass.time.distance/time2.area :wink:

 All times are GMT -5. The time now is 05:35 PM.


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# Cantor's controversies

• I
Cantor was severely criticised by many brilliant mathematicians of his time, many of whom we still regard as brilliant today.

What was so divisive about his theories? How did we resolve it? How could the best minds not do so back then?

Related Set Theory, Logic, Probability, Statistics News on Phys.org
HallsofIvy
Homework Helper
Primarily because Cantor did not express his ideas very well or very clearly. What we have now are his ideas expressed by other people in clearer and more logical terms.

Cantor was severely criticised by many brilliant mathematicians of his time, many of whom we still regard as brilliant today.

What was so divisive about his theories? How did we resolve it? How could the best minds not do so back then?
His main enemy was Kronecker. K thought that infinity was a bogus concept, so naturally he didn't like what Cantor was up to. At the time even proof by contradiction was controversial.

At the time even proof by contradiction was controversial.
Was it? Even Euclid uses proof by contradiction many times in his Elements, and nobody had an objection to that! It is true that nonconstructive methods were controversial, but that is not the same as proof by contradiction being controversial!

Was it? Even Euclid uses proof by contradiction many times in his Elements, and nobody had an objection to that! It is true that nonconstructive methods were controversial, but that is not the same as proof by contradiction being controversial!
The intuitionist movement was in full swing, which denies proof by contradiction.

But I have to admit that what I had in mind was existence proofs, which are often proofs by contradiction. Hilbert was criticized for them.

The intuitionist movement was in full swing, which denies proof by contradiction.
Intuitionism does not deny proof by contradiction, it denies the law of excluded middle. There is a subtle difference.
And intuitionism as we know it today was started by Brouwer as a reaction to Cantor. So it cannot be true that the intuitionist movement was in full swing. There is pre-intuitionism too, which included Borel, Poincare, Lebesgue and perhaps Kronecker. You might be referring to this. But they had no problem with the law of excluded middle.

Intuitionism does not deny proof by contradiction, it denies the law of excluded middle. There is a subtle difference.
It seems to me that proof by contradiction relies on the law of excluded middle. NOT(NOT(A)) => A. The distinction is too subtle for me.

How would you prove that ##\sqrt{2}## is not rational in constructivism?

How would you prove that ##\sqrt{2}## is not rational in constructivism?

Beats me. Not that I care.

Primarily because Cantor did not express his ideas very well or very clearly. What we have now are his ideas expressed by other people in clearer and more logical terms.
Did prominent critics like Poincare, Weyl and Wittgenstein eventually turn around?

How would you prove that ##\sqrt{2}## is not rational in constructivism?
Sorry, this thread is not about proving but about why brilliant men couldn't use reason to reach a conclusion.

TeethWhitener
Gold Member
I know this is an old thread, but I couldn't resist:
It seems to me that proof by contradiction relies on the law of excluded middle.
This doesn't have to be true. If we define proof by contradiction as ##(\neg p \rightarrow \bot ) \models p##, then we can get there without the law of the excluded middle through the conjunction expression of a conditional. Very roughly: ##(\neg p \rightarrow \bot) \leftrightarrow (\neg(\neg p \wedge \neg\bot))##. Modus ponens gives us the right side of the biconditional, which simplifies to ##\neg(\neg p \wedge \top)##. A simple truth table shows that this expression is only valid for ##p## true.

EDIT: In fact, Wikipedia is telling me that ##\neg p## is defined as ##p \rightarrow \bot## in intuitionistic logic, so it seems that proof by contradiction is baked in at the outset (or at least my model of proof by contradiction).

Erland
How would you prove that ##\sqrt{2}## is not rational in constructivism?
The ordinary proof is perfectly constructivistic. But I suppose that was your point.

This doesn't have to be true. If we define proof by contradiction as ##(\neg p \rightarrow \bot ) \models p##, then we can get there without the law of the excluded middle through the conjunction expression of a conditional. Very roughly: ##(\neg p \rightarrow \bot) \leftrightarrow (\neg(\neg p \wedge \neg\bot))##. Modus ponens gives us the right side of the biconditional, which simplifies to ##\neg(\neg p \wedge \top)##. A simple truth table shows that this expression is only valid for ##p## true.

EDIT: In fact, Wikipedia is telling me that ##\neg p## is defined as ##p \rightarrow \bot## in intuitionistic logic, so it seems that proof by contradiction is baked in at the outset (or at least my model of proof by contradiction).
The last is correct. But can't follow you before that. It is not obvious that the biconditional is valid in intutionistic logic, and truth tables cannot be used there.

I know this is an old thread, but I couldn't resist:

This doesn't have to be true. If we define proof by contradiction as ##(\neg p \rightarrow \bot ) \models p##, then we can....
I'm sorry but could you please stay on topic?

TeethWhitener
Gold Member
The last is correct. But can't follow you before that. It is not obvious that the biconditional is valid in intutionistic logic, and truth tables cannot be used there.
Sorry, in the first part I was showing that you can get proof by contradiction in classical logic without relying on excluded middle. I don't know much about intuitionistic logic. As an aside, Wiki also says you can get ##\neg(\neg p \wedge \neg\bot)## from ##\neg p \rightarrow \bot## in intuitionistic logic. Again, someone more knowledgeable can speak to this.
I'm sorry but could you please stay on topic?
Alright, if you insist , but I warn you, this is going to get into philosophy very quickly.
Sorry, this thread is not about proving but about why brilliant men couldn't use reason to reach a conclusion.
The problem here is that you're assuming there's a "right" conclusion to be drawn. You're committing the same error these brilliant men did. According to logic, there's only what can be derived from the axioms. The axioms themselves are, of course, assumed to be true. The mathematicians who rejected Cantor's results were forced to look for sets of axioms that didn't allow Cantor's claims to succeed logically. But the set of axioms you choose is true by default, and the extent to which you can reach a conclusion about which axioms are best is based more on the utility of the axioms you choose than logical truth. As a really simple example, you could choose a set of axioms that gave you an inconsistent system, and within your model the axioms would be true, but an inconsistent system is practically useless. So you could say that choosing a certain set of axioms is incorrect, or wrong, but you're basing that conclusion on extra-logical considerations.

EDIT: (and here comes the philosophy...) A lot of this hinges on equivocation between "true" as "valid within a logical framework" and some metaphysical notion of truth. These distinctions were not nearly as clear in Cantor's day as they are now, and we generally just say "valid" now to make it clear that we are referring to a truth value within a particular framework.

Sorry, in the first part I was showing that you can get proof by contradiction in classical logic without relying on excluded middle. I don't know much about intuitionistic logic. As an aside, Wiki also says you can get ##\neg(\neg p \wedge \neg\bot)## from ##\neg p \rightarrow \bot## in intuitionistic logic. Again, someone more knowledgeable can speak to this.

Alright, if you insist , but I warn you, this is going to get into philosophy very quickly.

The problem here is that you're assuming there's a "right" conclusion to be drawn. You're committing the same error these brilliant men did. According to logic, there's only what can be derived from the axioms. The axioms themselves are, of course, assumed to be true. The mathematicians who rejected Cantor's results were forced to look for sets of axioms that didn't allow Cantor's claims to succeed logically. But the set of axioms you choose is true by default, and the extent to which you can reach a conclusion about which axioms are best is based more on the utility of the axioms you choose than logical truth. As a really simple example, you could choose a set of axioms that gave you an inconsistent system, and within your model the axioms would be true, but an inconsistent system is practically useless. So you could say that choosing a certain set of axioms is incorrect, or wrong, but you're basing that conclusion on extra-logical considerations.

EDIT: (and here comes the philosophy...) A lot of this hinges on equivocation between "true" as "valid within a logical framework" and some metaphysical notion of truth. These distinctions were not nearly as clear in Cantor's day as they are now, and we generally just say "valid" now to make it clear that we are referring to a truth value within a particular framework.
So wait, Cantor introduced new axioms?

So wait, Cantor introduced new axioms?
No, Cantor didn't think axiomatically.

TeethWhitener
Gold Member
So wait, Cantor introduced new axioms?
No, Cantor didn't think axiomatically.
Cantor himself might not have thought axiomatically (I don't know; I'm not a historian), but his work and the controversy surrounding it is probably the major reason why people in the late 19th/early 20th century hammered on axiomatic thinking so much.

Infinity is a mind-boggling concept, especially the first time you run into it. Some mathematicians of Cantor's time had a lot of trouble thinking about an infinity the way that Cantor did (and that modern mathematicians do) because they were familiar only with infinity as a "process", like for example in the definition of a sequence of points approaching a limit.

Also, because an axiomatic set theory had not yet been developed, *some* of Cantor's discoveries rested on a weak foundation. Wikipedia explains that in particular, his discovery of the cardinal numbers — the series of alephs — was flawed for this reason. I would say flawed, but still utterly brilliant in its departure from what was then conventional in mathematics.

Yet the mathematician David Hilbert — who around 1900 was widely considered the best mathematician in the world — strongly supported Cantor's work, as did most mathematicians of the 20th century. After all, it is entirely reasonable to ask whether there exists a one-to-one correspondence between two sets, such as the integers and the real numbers.

lavinia
Gold Member
His main enemy was Kronecker. K thought that infinity was a bogus concept, so naturally he didn't like what Cantor was up to. At the time even proof by contradiction was controversial.
This is from the Wikipedia article on Kronecker

"He criticized Cantor's work on set theory, and was quoted by Weber (1893) as having said, "Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk" ("God made the integers, all else is the work of man.")."

This is from the Wikipedia article on Cantor

"The objections to Cantor's work were occasionally fierce: Henri Poincaré referred to his ideas as a "grave disease" infecting the discipline of mathematics,[8] and Leopold Kronecker's public opposition and personal attacks included describing Cantor as a "scientific charlatan", a "renegade" and a "corrupter of youth."[9] Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum."

and further down in the Wikipedia article

"Mathematicians from three major schools of thought (constructivism and its two offshoots, intuitionism and finitism) opposed Cantor's theories in this matter. For constructivists such as Kronecker, this rejection of actual infinity stems from fundamental disagreement with the idea that nonconstructive proofs such as Cantor's diagonal argument are sufficient proof that something exists, holding instead that constructive proofs are required. Intuitionism also rejects the idea that actual infinity is an expression of any sort of reality, but arrive at the decision via a different route than constructivism. Firstly, Cantor's argument rests on logic to prove the existence of transfinite numbers as an actual mathematical entity, whereas intuitionists hold that mathematical entities cannot be reduced to logical propositions, originating instead in the intuitions of the mind.[8] Secondly, the notion of infinity as an expression of reality is itself disallowed in intuitionism, since the human mind cannot intuitively construct an infinite set.[59] Mathematicians such as Brouwer and especially Poincaré adopted an intuitionist stance against Cantor's work. Citing the paradoxes of set theory as an example of its fundamentally flawed nature, Poincaré held that "most of the ideas of Cantorian set theory should be banished from mathematics once and for all."[8] Finally, Wittgenstein's attacks were finitist: he believed that Cantor's diagonal argument conflated the intension of a set of cardinal or real numbers with its extension, thus conflating the concept of rules for generating a set with an actual set.[10]"

Last edited:
lavinia
Gold Member
Also from the Wikipedia article on Cantor(see post #20)

"Some Christian theologians saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God.[6] In particular, Neo-Thomist thinkers saw the existence of an actual infinity that consisted of something other than God as jeopardizing "God's exclusive claim to supreme infinity".[60] Cantor strongly believed that this view was a misinterpretation of infinity, and was convinced that set theory could help correct this mistake:"

From the Wikipedia article on "actual infinity:

"Actual infinity is the idea that numbers, or some other type of mathematical object, can form an actual, completed totality; namely, a set. Hence, in the philosophy of mathematics, the abstractionof actual infinity involves the acceptance of infinite entities, such as the set of all natural numbers or an infinite sequence of rational numbers, as given objects. This is contrasted with potential infinity, in which a non-terminating process (such as "add 1 to the previous number") produces an unending "infinite" sequence of results, but each individual result is finite and is achieved in a finite number of steps."

At core in all of the criticisms of Cantor's theory seems to be the denial that an infinity could actually exist - except perhaps God .

It would seem that these ideas must deny the existence of limits since a limit is a completed infinity - by definition. E.G. the number 1 is the completion of all Cauchy sequences that converge to 1.

Last edited:
lavinia
Gold Member
Also from the Wikipedia article on Cantor(see post #20)

"Some Christian theologians saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God.[6] In particular, Neo-Thomist thinkers saw the existence of an actual infinity that consisted of something other than God as jeopardizing "God's exclusive claim to supreme infinity."
This seems to show that Cantor's theory was misunderstood since there is no largest infinite set and even if there were a supreme infinite, it may not be unique.

For instance, one might try to resurrect St. Anselm's proof of the existence of God using set theory with the following argument.

The set containing all sets of virtues is partially ordered by inclusion. Given any chain of sets of virtues, the union of the sets in the chain is also a set of virtues so every chain has a maximal element. The Hausdorff Maximal Principle now asserts that there exists a set of virtues for which there is none greater. This is Anselm's God.

Sadly, this maximal element may not be unique and also the collection of all sets of virtues may be too big to be a set.

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Cantor himself might not have thought axiomatically (I don't know; I'm not a historian), but his work and the controversy surrounding it is probably the major reason why people in the late 19th/early 20th century hammered on axiomatic thinking so much.
ultimately, what was the resolution to Cantor's controversy?

Did these opposing great men of mathematics eventually stop their opposition?

Most mathematicians and people who use mathematics in their everyday work have accepted the existence of infinities. Yes, Cantor's set theory did give rise to axiomatic set theory, particularly in light of paradoxes like Russell's paradox. (Which is: Let X be the set of all sets not containing themselves. Then X cannot contain itself, for then it would have to not contain itself. But X also cannot not contain itself, for then it would have to contain itself.)

A number of axiom systems for set theory were proposed, and the one that is almost universally accepted these days is ZFC, which stands for Zermelo-Frankel plus Axiom of Choice: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory.

Some, but not many, mathematicians are Intuitionists or Constructivists today and continue to resist the idea of infinity.

Last edited:
Most mathematicians and people who use mathematics in their everyday work have accepted the existence of infinities. Yes, Cantor's set theory did give rise to axiomatic set theory, particularly in light of paradoxes like Russell's paradox. (Which is: Let X be the set of all sets not containing themselves. Then X cannot contain itself, for then it would have to not contain itself. But X also cannot not contain itself, for then it would have to contain itself.)

A number of axioms for set theory were proposed, and the one that is most widely accepted these days is ZFC, which stands for Zermelo-Frankel plus Axiom of Choice: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory.

Some, but not many, mathematicians are Intuitionists or Constructivists today and continue to resist the idea of infinity.
What about opposers like Wittgenstein, Weyl and Poincare?

That's so amazing. I didn't know that mathematics still had such a conundrum. I thought there was only one right answer. LOL


text:
## Exterior algebra and n-dimensional volumes

 Quote by coquelicot I agree with you that it's ok to denote by the same letter the operator and the extended operator. But now that we agree on this point, can I ask you a question? Let A be an orthonormal operator in R^3, and let B be the extention of this operator to Ext_2(R^3) (what can be denoted by the same letter A as you pointed out). Is the matrix of B in the basis (e_1^e_2, e_1^e_3, e_2^e_3) orthonormal with respect to the standart scalar product in this basis, and what is the representation of B in this basis? More generally, what is the answer to the same question when R^3 is replaced by R^n and Ext_2(R^3) by Ext_k(R^n), with k
Hey coquelicot.

For this are you talking about for x,y in R^3 the inner product <Bx,By> for some operator B?

 Sorry, I haven't understood your question, can you be more explicit?

 Quote by coquelicot Sorry, I haven't understood your question, can you be more explicit?
Basically if you have an inner product <.,.> and vectors x and y in untransformed basis, where Bx = B*x (matrix-multiplication of operator B with x) and By = B*y, are you trying to find <Bx,By> where B is your operator to transform one vector from one basis ti another?

Your question was to understand orthonormality conditions of the inner product, and I'm asking is <Bx,By> your inner product?

 My impression is that you are dealing about something that is not the subject and the question I asked. Are you sure you have read my first post and a part of the posts and replies of others? I have explicitely stated what is the scalar product in Ext_k(R^n) (namely the canonical one on the basis e_1^...^e_k, ... explicited in my first post).

 Quote by coquelicot I agree with you that it's ok to denote by the same letter the operator and the extended operator. But now that we agree on this point, can I ask you a question? Let A be an orthonormal operator in R^3, and let B be the extention of this operator to Ext_2(R^3) (what can be denoted by the same letter A as you pointed out). Is the matrix of B in the basis (e_1^e_2, e_1^e_3, e_2^e_3) orthonormal with respect to the standart scalar product in this basis, and what is the representation of B in this basis? More generally, what is the answer to the same question when R^3 is replaced by R^n and Ext_2(R^3) by Ext_k(R^n), with k
Consider a rotation in the xy plane.

\begin{align*} \underline A(e_1) &= e_1 \cos \theta + e_2 \sin \theta \\ \underline A(e_2) &= e_2 \cos \theta - e_1 \sin \theta \\ \underline A(e_3) &= e_3 \end{align*}

When acting on basis 2-vectors, we get

\begin{align*} \underline A(e_1 \wedge e_2) &= e_1 \wedge e_2 \\ \underline A(e_1 \wedge e_3) &= e_1 \wedge e_3 \cos \theta + e_2 \wedge e_3 \sin \theta \\ \underline A(e_2 \wedge e_3) &= e_2 \wedge e_3 \cos \theta - e_1 \wedge e_3 \sin \theta \end{align*}

I think I see what you're driving at now. You're making a very, very specific statement about the components of the matrix when the basis is ordered according to certain rules and such. I can see how that might be useful for computing applications, but it's all just an artifact of needing certain rules for the ordering of the basis.

 Indeed, as I stated it, this theorem depends on a particular choice of the basis of Ext_k(R^n). But let us return to the first claim of my first post. I said that the the second claim would imply easily that the k-dimensional volume of the polytope determined by k vectors u_1,..., u_k of R^n is equal to the norm of u_1^...^u_k in Ext_k(R^n), which would be very useful to compute this volume. In fact, less is needed to imply this theorem: it would suffices to show that the extended operator B of an orthonormal operator A of R^n to Ext_k(R^n) is always orthonormal. I believe that it is possible to define the scalar product in Ext_k(R^n) in an intrinsic manner, so that the theorem wouldn't seem artificial to you. In fact, this is probably what is dealt in the article "inner product" of the topic "exterior algebra" in Wikipedia (see also "the hodge star operator in wikipedia, article "inner product of k-vectors", last line). But the description in Wikipedia is too succint to allow me to be sure.
 That $a\wedge b\wedge c$ has as its magnitude the volume the three vectors span is safe to say and generalizes to arbitrary dimension. That an orthonormal operator is still orthonormal on k-vectors is also safe, I think. The stuff on using the dual to define the inner product is traditional...and also silly in my opinion. It arises because exterior algebrists don't want to define another product other than the wedge, but taking the dual basically requires one. This treats the dual as something fundamental when it isn't. The elegant solution is to define a "geometric" product. Let $e_i e_j$ denote he geometric product of two orthonormal basis vectors. When i=j the product is defined to be 1, capturing the properties of the inner product. When i and j are different, the product is anticommutative, reducing to the outer product. This makes scalar products is k-vectors arise naturally, and it shows that the Hodge star operator is just multiplication of a k-vector by the unit N-vector in N-dimensional space under the geometric product.
 I think we are coming to a conclusion. I am happy that you think a part of what I claimed is true. If you can indicate me some link where I could find a rigorous justification, I would be the happiest of man. Your idea to involve geometric product is also very interesting; I guess this is related to Grassman calculus, and the theorems I stated are probably superseded by known theorems there.
 I think the key to what you want to prove here lies in some nifty inverse formulas for operators. First, let $i$ denote some multivector such that $ia=\star a$ under the geometric product. i represents the unit pseudoscalar of the space: i.e. $i=e_1 e_2 e_3$. (Wedges are optional because he vectors are orthogonal.) There is then a formula for inverting an operator. $$\underline A^{-1}(a)=\overline A(ai) [\underline A(i)]^{-1}$$ Overline represents transpose. Realize that orthogonal operators have inverse equal to transpose and there are big possibilities to use this, I think. Beyond that, geometric algebra makes a statement like $$(e_1 \wedge e_2)\cdot [\underline A(e_1) \wedge \underline A(e_2)]$$ meaningful as a scalar product between bivectors. I realize this language and set of ideas is unfamiliar, however. I would start with $\underline A(a) \wedge \underline A(b)=\underline A(a\wedge b)$ and then prove this for the transpose, prove that other properties hold still. Could be done like an induction proof.
 Thank you. I have found a good lesson on geometric algebra. I'll try to follow your outline when I feel sufficiently familiar with these concepts. Anyway, thank you again for the time you have vasted in this discussion.


text:
# Thinking Asynchronously in CoffeeScript/JavaScript: Loops and Callbacks

Awhile back, I wrote about my new experience in learning Node.js: A Node.js Experiment: Thinking Asynchronously, Using Recursion to Calculate the Total File Size in a Directory.

Consider this snippet of code:

var names = ['JP', 'Chris', 'Leslie'];
for (var i = 0; i < names.length; ++i){
var name = names[i];
setTimeout(function(){
},10);
}

Equivalent CoffeeScript:

names = ['JP', 'Chris', 'Leslie']
for name in names
setTimeout(->
,10)

Click here%0A%20%20%2C10)) to run it. If you guessed that the loop would alert "Leslie" three times, then you'd be correct.

The problem is, that before the callback executes, the loop has completed. Thus callback always has the last value.

How do you solve this problem? You wrap the callback in a closure that executes immediately.

JavaScript:

var names = ['JP', 'Chris', 'Leslie'];
for (var i = 0; i < names.length; ++i){
var name = names[i];
(function(name){
setTimeout(function(){
},10);
})(name);
}

CoffeeScript:

names = ['JP', 'Chris', 'Leslie']
for name in names
do (name) ->
setTimeout(->
,10)

These solutions execute the block of code in a parallel manner. Using the alert's are not a good indication in showing this behavior. However, if you were opening files, all of them would be opened approximately (not exactly) at the same time.

What if you wanted to perform the action in the callback in a serial manner?

Using the previous simple example, it'd look like this:

JavaScript:

var names = ['JP', 'Chris', 'Leslie'];
loop = function(i){
setTimeout(function(){
if (i < names.length - 1)
loop(i + 1);
},10);
}
loop(0);

CoffeeScript:

names = ['JP', 'Chris', 'Leslie'];
doloop = (i) ->
setTimeout(->
if i < names.length - 1
doloop(i + 1)
,10);
doloop(0)

If you were doing file processing in the loop, it would be executed sequentially.

Hopefully this helps you to better understand asynchronous design of algorithms in JavaScript.

Update: I forgot about the forEach function that exists in Node.js and most modern browsers. This function pretty much solves the problem.

Here's the JavaScript code:

var names = ['JP', 'Chris', 'Leslie'];
names.forEach(function(name){
setTimeout(function(){


text:
# How to help my tutoring students study between sessions

I'm a private math tutor--been doing it a couple of years, so I'm not terribly experienced yet. I have junior high through college students in most math topics.

It goes the best when the parents hire me to see their student at least twice per week. Then I have a continuous feel for what they are struggling with, and we have time not only to finish their homework, but to review old topics or work ahead.

But many of my families only want one session per week. I sometimes feel we can barely make progress. They come to me with different issues every week and there's no time to do anything but rush through the latest homework.

So my questions are:

• how can I work with this situation, infrequent tutoring?

• Can I refer them to outside websites or books they can use to study in-between sessions with me? (note: we probably aren't allowed on this stack exchange site to make recommendations for specific sites or products, but if you could just speak generally about the types of sites or books - like a "video lecture site" or "YouTube videos" or "a practice math problem site")

In particular I'm asking about how to make their math experience more continuous, so the student has a clear idea of the topic and moves through it at a good pace, with a chance to clear up any confusion, in spite of obstacles presented by the school, their teacher, their textbook, or infrequent tutoring.

There's a situation with a discontinuous/fractured experience for a different reason -- the student is using a textbook which tries to show connections between different areas of math--by jumping all over the place! So my student can't tell me what topic to prepare him for, and the book obscures some of the typical ways that topics are sequenced.

Here are a few pointers and questions.

1. Do the families have a realistic picture of how much help the students actually need? It is common in my work as a tutor to find 14-year-old kids who are getting a B+ or better in math, but cannot calculate $$2000-1997$$ mentally. (They have to use the vertical stacking algorithm to get an answer and are unaware of any other methods.) Having students try to do simple conceptual questions - not calculation questions - while thinking aloud while the parent watches, often causes the horrifying epiphany that parents need. I'm happy to share some of those with you if you request them by private message.

2. Are you sure they are willing to do homework or have a second session in the first place? A lot of students already have so much on their plate that it is very hard to prioritize math. This is especially true for those who perceive math as a credentialing and hoop-jumping exercise with no intrinsic value. They just want to do the minimal effort to get the minimally required grade for passing or not going to summer school or admission into some other program, etc. How many of your students does this describe? Do they even want you to try to change their attitudes?

3. Related to #2, are the students: (a) rote cramming for tests and homework completion or (b) really going for a deep understanding and lasting mastery?

4. Instead of a 2nd weekly session, would the students be willing to do homework that you assigned and send it to you by email (or Schoology, EdModo, moodle, etc.) the night before the sessions?

• Related to #2, I have three situations where both parents and students say they are willing to do extra work, and even the student has a hopeful look that they could feel less confused. You are right, though, that most aren't eager to take on work, yet I suspect that if the work were more clear to them than their class, and more satisfying (enjoying a feeling of comprehension), the students would have some motivation, and this could be presented to the parents as an alternative to paying for extra lessons. – composerMike Oct 30 '18 at 6:29
• I'm not trying to put myself out of work, I'm trying to make myself more efficient. I.e. be able to see more students and be a more valuable service to the parents. – composerMike Oct 30 '18 at 6:31
• If the students are willing to do extra work, then assign it, and have them email to you at least one evening before the next tutoring session. What is unclear about what's going on in class? And what are the other obstacles you mentioned? – WeCanLearnAnything Nov 1 '18 at 1:34
• I'll edit the question. – composerMike Nov 1 '18 at 6:27


text:
## Staffy 2 years ago Evaluate the following integrals: sin^2(x)dx from 0 to 2π, |sin x| dx from 0 to 2π, (x^n)(e^−x)dx from 0 to ∞ sin(ax)sin(bx)dx from 0 to π Consider all possible cases (n is a positive integer)

1) hint : sin^2 x = (1-cos2x)/2

2) divide 2 case for : Area1 = int (sinx) dx [0,pi] area2 = int(-sinx)dx [pi,2pi] the total area is .........

3. Staffy

Why is it negative sinx?

because the absolut function must be positive number, so the area of under x-axes should give a (-) sign too, so that (-)(-) be postive

5. Staffy

That makes sense, thanks

let's look this graph |dw:1355024687100:dw|

7. UnkleRhaukus

4) \begin{align*} \int\limits_{0}^\pi\sin(mx)\sin(nx)\text dx &=\frac12\int\limits_{0}^\pi\cos((m-n)x)-\cos((m+n)x)\text dx\\ \\ &=\frac12\left(\frac{\sin((m-n)x)}{m-n}-\frac{\sin((m+n)x)}{m+n}\Big|_0^\pi\right)\\ &=\dots\\ &=\dots\\ \\ \end{align*}


text:
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# specific energy vs energy density

All those numbers can be complicated to explain to people. That rule of thumb assumes that the cruise L/D is 20:1. I suggest you edit the question @ParadigmPilot, just say "equivalent range and performance", Comments are not for extended discussion; this conversation has been. assembly is Pipistrel, Battery Management System (BMS) is also designed and That was me, above, Meredith Angwin. It's about 5 times less then similar pistone engine aircrafts. Do you realize just how empty a threat it would be if you told a country with a lot of nuclear power stations – “you better behave or we will not sell you any replacement fuel when you really need it – in 18-60 months.”. I'm not even talking about electric analogs of the Piper Seneca, let alone airliners. If it's true, then it somewhat contradicts the approximate power density figure of 16.7 MJ/kg given in the 1st answer. However, if I enter the numbers before your unit conversion, I get about twice your range: 200 Wh/kg, k=2/3 and L/D=20 comes out to 489 km. Keep in mind an electric motor is much smaller and lighter than an aircraft engine, and power can be distributed around the aircraft, e.g. Although batteries are often touted as the answer to most energy related problems, it's important to use the right tool to solve each problem. This is not to say that batteries are a bad way to power things. I did consider the efficiency gain from weight loss as fuel is burned, i.e. This adds mass but also adds range in day-flight, which then raises the question whether this is a day-only or night aircraft. Power density is a measure of power output per unit volume. This is probably not the way one would like to make the argument, but people are pretty clear about the distinction between a chemical explosion and an atomic explosion. Energy required = Force x Distance = Drag x Range = [Weight / (L/D)] x Range = Energy stored in the batteries, $E_{req}= F \cdot x = D \cdot R = \frac {W\cdot D}{L}\cdot R = E_{bat}$, $R \approx \frac{ E_{bat}}{W}\cdot \frac{L}{D}$, Weight = Payload + Electric power system weight + structural weight. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. As mentioned above a density of approx 15 MJ/kg would allow for this. In fact, nuclear power is the only energy-producing industry which takes full responsibility for all its wastes, and costs this into the product – a key factor in sustainability. Blow the rudder. of power, but that of the quality of nuclear as a power source. That might or might not be practical, depending on how you want to use an aircraft. To summarize, electric drive is currently competitive only in slower aircraft. When to carry on with a buggy game state versus terminate the process? How can a chess game with clock take 5 hours? Energy density of hydrogen tanks and fuel cell systems compared to the energy density of batteries . But, 489km is 264 nautical miles... You're right, I rounded quite a bit. Having a high energy density does not give information on how quickly this energy can be used. @ParadigmPilot Updated with additional details. EXCELLENT. )), so it would cost \\$334.50 to fill up an airplane. However, they don't give any flight endurance numbers. Another way to look at energy density is on a volume basis. Former submarine Engineer Officer. That word describes a situation where there is a lack of knowledge. One of the primary advantages that nuclear energy sources have over chemical energy competitors is energy density. Is it possible to have a fully electric airliner? Energy Density (Wh/kg) is a measure of how much energy a battery can hold. Energy Density (Wh/liter) H2Gen: Wt_Vol_Cost.XLS; Tab 'Battery'; S34 - 3 / 25 / 2009 . (20%-95% range), 6hrs with 3kW charger, 1h 40' with 10 kW charger, 1h 5' with 14 kW, 45 Do you ever wish they’d let us have smokestacks and ash ponds? Resume available here. ZX Spectrum 48k Power Supply outputting 15V. Internal combustion engines are 35% efficient and electric engines 90%, so we can calculate that an electric airplane would need 5130 * 0.35 / 0.9 = 1995 MJ of electrical power to fill up. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. @Harper I'm only talking about in flight solar power, not electric airplanes in general. Based on what I know about PopAtomic, they feel the same way. The small motor means a slimmer cowling, which they claim reduces air resistance by 15% and allows the prop to generate "considerably more thrust". Specifications by Battery Chemistry. It isn’t just a question that nuclear power is overwhelmingly more energy-flux-dense than prior forms Also, will it be cheaper to charge as opposed to the cost of liquid fuel? How to make non-linear movements with a Follow Path constraint? Drag increases with the square of speed, more drag means more batteries needed to supply the power, and that means more weight. Batteries would need to be somewhere around 16.7MJ/kg to give the same range and performance as liquid fuels, this is about 18.5 times the capacity of the best lithium-ion batteries. I'm going to do separate calculations for the US and UK to see how they compare: EDIT: According to the theory, power equals energy divided by time; i.e. For example - 300 NM cross country flight for the CPL training. How about an Ad showing the solid waste from a coal plant for a year vs. the storage container for a years worth of fuel rods? So, 20:1 is ambitious, but realistic. For airplanes where a more significant portion of the weight is fuel, i.e.