SEE ALSO Wave Nature of Light (1801), Electromagnetic Spectrum (1864), Incandescent Light Bulb (1878).
Newton used prisms to show that white light was not the single entity that Aristotle believed it to be, but rather was a mixture of many different rays corresponding to different colors.
1678
Discovery of Sperm • Clifford A. Pickover
Anton Philips van Leeuwenhoek (1632–1723), Nicolaas Hartsoeker (1656–1725)
In 1678, Dutch scientist Anton van Leeuwenhoek reported to the Royal Society on the discovery of human spermatozoa, which resembled innumerable wormlike animals. He wrote, “What I investigate is only what, without sinfully defiling myself, remains as a residue after conjugal coitus. And if your Lordship should consider that these observations may disgust or scandalize the learned, I earnestly beg your Lordship to regard them as private and to publish or destroy them as your Lordship thinks fit.” Van Leeuwenhoek eventually suggested that the minute microscopic creatures swimming in semen played a role in fertilization. Other scientists believed that the sperm were simply parasites and had nothing to do with the reproductive process.
Around 1677, van Leeuwenhoek and his student Johan Ham had used a microscope that magnified 300 times to examine spermatozoa, which he described as animalcules (little animals)—suggestive of his belief in preformation, a version of which posited that the head of each sperm cell contained a tiny, fully formed human. Dutch microscopist Nicolaas Hartsoeker claimed to have seen spermatozoa in 1674, but he was uncertain about his observations and, at first, thought the wriggling cells were parasites. His famous drawing of a homunculus, or little human, crammed within the head of a sperm suggested preformation as well. Hartsoeker did not claim to have seen actual homunculi, but other researchers did! Some suggested that the homunculi in sperm might have smaller sperm of their own, in an infinite regress of homunculi within homunculi. Of course, when researchers began to show how organs in creatures such as chicks gradually appear in the process of development, it became clear that animals are not in a near-final form from the start.
The word sperm generally refers to the male reproductive cell, and spermatozoan refers specifically to a mobile sperm cell with an attached, whiplike tail. Today we know that in humans, the sperm cell has 23 chromosomes (threadlike carriers of genetic information) that join with the 23 chromosomes in the female egg when fertilization occurs.
SEE ALSO Micrographia (1665), Chromosomal Theory of Inheritance (1902), Birth-Control Pill (1955).
LEFT: Sperm surrounding an egg just prior to fertilization. RIGHT: Illustration of a sperm, emphasizing the head, whiplike tail, and joining midpiece, which contains a filamentous core with many energy-producing mitochondria for tail movement and propulsion.
1683
Zoo Within Us • Clifford A. Pickover
Anton Philips van Leeuwenhoek (1632–1723)
Even healthy bodies contain a vast zoo of microbes affecting our health. The proper balance and functioning of this diverse ecosystem of bacteria, fungi, and viruses may hold cures to maladies ranging from inflammatory bowel diseases to various skin disorders. Interestingly, our bodies contain at least ten times as many of these tiny microbes (mostly in our intestines) than human cells, making our individual bodies behave like “superorganisms” of interacting species that, together, affect our well-being. One of the earliest discoveries of this microbiome zoo occurred in 1683, when Dutch microbiologist Anton van Leeuwenhoek used his home-built microscope to study scrapings of his own dental plaque and, to his surprise, found “little living animalcules, very prettily a-moving” in the specimen.
Beneficial and harmful microbes typically reside on and in the skin, mouth, gastrointestinal tract, vagina, nose, and other various orifices. More than 500 species of bacteria live in the human intestines, motivating researchers to think of this population as comprising a “virtual organ.” The creatures in our gut can ferment food to aid in digestion, produce vitamins for our bodies, and prevent the growth of harmful species. Such bacteria rapidly colonize a baby’s intestines starting from birth. Researchers are studying the possible role of different bacterial populations in diseases of the intestine (e.g., ulcerative colitis), tumor formation, and obesity. Researchers have also shown the importance of microbial diversity in the progression of cystic fibrosis (a genetic disease that can cause lung scarring) and continue to study possible roles of the microbial zoo in affecting the severity of eczema, psoriasis, Parkinson’s, diabetes, and a variety of autoimmune diseases.
Using helminthic therapy, physicians and their patients experiment with the deliberate infestation of the intestines with helminths (parasitic worms such as hookworms and whipworms), which, in some cases, may have a beneficial role in ameliorating inflammatory bowel diseases, multiple sclerosis, asthma, and certain skin diseases by helping to modulate the functioning of the body’s immune system.
SEE ALSO Sewage Systems (c. 600 BCE), Micrographia (1655), Discovery of Sperm (1678), Germ Theory of Disease (1862), Antiseptics (1865).
Electron micrograph of a cluster of salami-shaped E. coli bacteria. E. coli normally colonize an infant’s gastrointestinal tract within a day or two after birth.
1687
Newton as Inspiration • Clifford A. Pickover
Isaac Newton (1642–1727)
The chemist William H. Cropper writes, “Newton was the greatest creative genius that physics has ever seen. None of the other candidates for the superlative (Einstein, Maxwell, Boltzmann, Gibbs, and Feynman) has matched Newton’s combined achievements as theoretician, experimentalist, and mathematician. . . . If you were to become a time traveler and meet Newton on a trip back to the seventeenth century, you might find him something like the performer who first exasperates everyone in sight and then goes on stage and sings like an angel. . . .”
Perhaps more than any other scientist, Newton inspired the scientists who followed him with the idea that the universe could be understood in terms of mathematics. Journalist James Gleick writes, “Isaac Newton was born into a world of darkness, obscurity, and magic . . . veered at least once to the brink of madness . . . and yet discovered more of the essential core of human knowledge than anyone before or after. He was chief architect of the modern world. . . . He made knowledge a thing of substance: quantitative and exact. He established principles, and they are called his laws.”
Authors Richard Koch and Chris Smith note, “Some time between the 13th and 15th centuries, Europe pulled well ahead of the rest of the world in science and technology, a lead consolidated in the following 200 years. Then in 1687, Isaac Newton—foreshadowed by Copernicus, Kepler, and others—had his glorious insight that the universe is governed by a few physical, mechanical, and mathematical laws. This instilled tremendous confidence that everything made sense, everything fitted together, and everything could be improved by science.”
Inspired by Newton, astrophysicist Stephen Hawking writes, “I do not agree with the view that the universe is a mystery. . . . This view does not do justice to the scientific revolution that was started almost four hundred years ago by Galileo and carried on by Newton. . . . We now have mathematical laws that govern everything we normally experience.”
SEE ALSO Development of Modern Calculus (1665), Newton’s Prism (1672), Newton’s Laws of Motion and Gravitation (1687), Einstein as Inspiration (1921).
Photograph of Newton’s birthplace—Woolsthorpe Manor, England—along with an ancient apple tree. Newton performed many famous experiments on light and optics here. According to legend, Newton saw a falling apple here, which partly inspired his law of gravitation.
1687
Newton’s Laws of Motion and Gravitation • Clifford A. Pickover
Isaac Newton (1642–1727)
“God created everything by number, weight, and measure,” wrote Isaac Newton, the English mathematician, physicist, and astronomer who invented calculus, proved that white light was a mixture of colors, explained the rainbow, built the first refle
cting telescope, discovered the binomial theorem, introduced polar coordinates, and showed the force causing objects to fall is the same kind of force that drives planetary motions and produces tides.
Newton’s Laws of Motion concern relations between forces acting on objects and the motion of these objects. His Law of Universal Gravitation states that objects attract one another with a force that varies as the product of the masses of the objects and inversely as the square of the distance between the objects. Newton’s First Law of Motion (Law of Inertia) states that bodies do not alter their motions unless forces are applied to them. A body at rest stays at rest. A moving body continues to travel with the same speed and direction unless acted upon by a net force. According to Newton’s Second Law of Motion, when a net force acts upon an object, the rate at which the momentum (mass × velocity) changes is proportional to the force applied. According to Newton’s Third Law of Motion, whenever one body exerts a force on a second body, the second body exerts a force on the first body that is equal in magnitude and opposite in direction. For example, the downward force of a spoon on the table is equal to the upward force of the table on the spoon.
Throughout his life, Newton is believed to have had bouts of manic depression. He had always hated his mother and stepfather, and as a teenager threatened to burn them alive in their house. Newton was also author of treatises on biblical subjects, including biblical prophecies. Few are aware that he devoted more time to the study of the Bible, theology, and alchemy than to science—and wrote more on religion than he did on natural science. Regardless, the English mathematician and physicist may well be the most influential scientist of all time.
SEE ALSO Kepler’s Laws of Planetary Motion (1609), Acceleration of Falling Objects (1638), Development of Modern Calculus (1665), Newton’s Prism (1672), Newton as Inspiration (1687), General Theory of Relativity (1915), Gravitational Lensing (1979).
Gravity affects the motions of bodies in outer space. Shown here is an artistic depiction of a massive collision of objects, perhaps as large as Pluto, that created the dust ring around the nearby star Vega.
1713
Law of Large Numbers • Clifford A. Pickover
Jacob Bernoulli (1654–1705)
In 1713, Swiss mathematician Jacob Bernoulli’s proof of his Law of Large Numbers (LLN) was presented in a posthumous publication, Ars Conjectandi (The Art of Conjecturing). The LLN is a theorem in probability that describes the long-term stability of a random variable. For example, when the number of observations of an experiment (such as the tossing of a coin) is sufficiently large, then the proportion of an outcome (such as the occurrence of heads) will be close to the probability of the outcome, for example 0.5. Stated more formally, given a sequence of independent and identically distributed random variables with a finite population mean and variance, the average of these observations will approach the theoretical population mean.
Imagine you are tossing a standard six-sided die. We expect the mean of the values obtained by tossing to be the average, or 3.5. Imagine that your first three tosses happen to be 1, 2, and 6, giving a mean of 3. With more tosses, the value of the average eventually settles to the expected value of 3.5. Casino operators love the LLN because they can count on stable results in the long run and can plan accordingly. Insurers rely on the LLN to cope with and plan for variations in losses.
In Ars Conjectandi, Bernoulli estimates the proportion of white balls in an urn filled with an unknown number of black and white balls. By drawing balls from the urn and “randomly” replacing a ball after each draw, he estimates the proportion of white balls by the proportion of balls drawn that are white. By doing this enough times, he obtains any desired accuracy for the estimate. Bernoulli writes, “If observations of all events were to be continued throughout all eternity (and, hence, the ultimate probability would tend toward perfect certainty), everything in the world would be perceived to happen in fixed ratios. . . . Even in the most accidental . . . occurrences, we would be bound to recognize . . . a certain fate.”
SEE ALSO Dice (c. 3000 BCE), Normal Distribution Curve (1733), Bayes’ Theorem (1761), Laplace’s Théorie Analytique des Probabilités (1812).
Swiss commemorative stamp of mathematician Jacob Bernoulli, issued in 1994. The stamp features both a graph and a formula related to his Law of Large Numbers.
1727
Euler’s Number, e • Clifford A. Pickover
Leonhard Paul Euler (1707–1783)
British science writer David Darling writes that the number e is “possibly the most important number in mathematics. Although pi is more familiar to the layperson, e is far more significant and ubiquitous in the higher reaches of the subject.”
The number e, which is approximately equal to 2.71828, can be calculated in many ways. For example, it is the limit value of the expression (1 + 1/n) raised to the nth power, when n increases indefinitely. Although mathematicians like Jacob Bernoulli and Gottfried Leibniz were aware of the constant, Swiss mathematician Leonhard Euler was among the first to extensively study the number, and he was the first to use the symbol e in letters written in 1727. In 1737, he showed that e is irrational—that is, it cannot be expressed as a ratio of two integers. In 1748, he calculated 18 of its digits, and today more than 100,000,000,000 digits of e are known.
e is used in diverse areas, such as in the formula for the catenary shape of a hanging rope supported at its two ends, in the calculation of compound interest, and in numerous applications in probability and statistics. It also appears in one of the most amazing mathematical relationships ever discovered, eiπ + 1 = 0, which unites the five most important symbols of mathematics: 1, 0, π, e, and i (the square root of minus one). Harvard mathematician Benjamin Pierce said that “we cannot understand [the formula], and we don’t know what it means, but we have proved it, and therefore we know it must be the truth.” Several surveys among mathematicians have placed this formula at the top of the list for the most beautiful formula in mathematics. Kasner and Newman note, “We can only reproduce the equation and not stop to inquire into its implications. It appeals equally to the mystic, the scientist, and the mathematician.”
SEE ALSO π (c. 250 BCE) Imaginary Numbers (1572), Transcendental Numbers (1844).
The St. Louis Gateway Arch is in the shape of an upside-down catenary. A catenary can be described by the formula y = (a/2)·(ex/a + e−x/a). The Gateway Arch is the world’s tallest monument, with a height of 630 feet (192 meters).
1733
Normal Distribution Curve • Clifford A. Pickover
Abraham de Moivre (1667–1754), Johann Carl Friedrich Gauss (1777–1855), Pierre-Simon Laplace (1749–1827)
In 1733, French mathematician Abraham de Moivre was the first to describe the normal distribution curve, or law of errors, in Approximatio ad summam terminorum binomii (a+b)n in seriem expansi (“Approximation to the Sum of the Terms of a Binomial (a+b)n Expanded as a Series”). Throughout his life, de Moivre remained poor and earned money on the side by playing chess in coffeehouses.
The normal distribution—also called the Gaussian distribution, in honor of Carl Friedrich Gauss, who studied the curve years later—represents an important family of continuous probability distributions that are applied in countless fields in which observations are made. These fields include studies of population demographics, health statistics, astronomical measurements, heredity, intelligence, insurance statistics, and any fields in which variation exists in experimental data and observed characteristics. In fact, early in the eighteenth century, mathematicians began to realize that a vast number of different measurements tended to show a similar form of scattering or distribution.
The normal distribution is defined by two key parameters, the mean (or average) and the standard deviation, which quantifies the spread or variability of the data. The normal distribution, when graphed, is often called the bell curve because of its symmetric bell-like shape with values more concentrated in the middle than in the tails at the sides of t
he curve.
De Moivre researched the normal distribution during his studies of approximations to the binomial distribution, which arises, for example, in coin toss experiments. Pierre-Simon Laplace used the distribution in 1783 to study measurement errors. Gauss applied it in 1809 to study astronomical data.
The anthropologist Sir Francis Galton wrote of the normal distribution, “I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the ‘Law of Frequency of Error.’ The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement amidst the wildest confusion.”
SEE ALSO Pascal’s Triangle (1654), Law of Large Numbers (1713), Laplace’s Théorie Analytique des Probabilités (1812)
A deutsche mark banknote featuring Carl Friedrich Gauss and a graph and formula of the normal probability function.
1735
Linnaean Classification of Species • Michael C. Gerald with Gloria E. Gerald
Aristotle (384–322 BCE), Theophrastus (372–287 BCE), Carl Linnaeus (1707–1778), Charles Darwin (1809–1882)
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