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The state sometimes makes mistakes. When one of these mistakes occurs, one notes a decline in collective enthusiasm due to the effect of a quantitative diminution in each of the elements that make up the mass. Work is paralyzed until it is reduced to an insignificant level. It is time to make a correction.
Once public opinion is convinced that the increase in the quantity of money will continue and never come to an end, and that consequently the prices of all commodities will not cease to rise, everybody becomes eager to buy as much as possible and restrict his cash holdings to minimum size… If the credit expansion is not stopped in time, the boom turns to crack-up boom: the flight into real values begins, and the whole monetary system founders.
If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.
The page of my notebook was filled with many messy integrals, but all of a sudden I saw emerge a formula for counting. I had begun to calculate a quantity on the assumption that the result was a real number, but found instead that, in certain units, all the possible answers would be integers. This meant that areas and volumes cannot take any value, but come in multiples of fixed units.
If the present American laws concerning the taxation of the profits of corporations, the incomes of individuals, and inheritances had been introduced about 60 years ago, all those new products whose consumption has raised the standard of living of the ‘common man’ would either not be produced at all or only in small quantities for the benefit of a minority. The Ford enterprises would not exist if Henry Ford’s profits had been taxed away as soon as they came into being.
It is not enough for [the investor] to know all the factors that can possibly contribute to the determination of a future event. In order to anticipate correctly they must also anticipate correctly the quantity as it were of each factor’s contribution and the instant at which its contribution will become effective.
Many persons who are not conversant with mathematical studies imagine that because the business of [Babbage’s Analytical Engine] is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraical and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact it might bring out its results in algebraical notation, were provisions made accordingly.