1895
X-rays • Clifford A. Pickover
Wilhelm Conrad Röntgen (1845–1923), Max von Laue (1879–1960)
Upon seeing her husband’s X-ray image of her hand, Wilhelm Röntgen’s wife “shrieked in terror and thought that the rays were evil harbingers of death,” writes author Kendall Haven. “Within a month, Wilhelm Röntgen’s X-rays were the talk of the world. Skeptics called them death rays that would destroy the human race. Eager dreamers called them miracle rays that could make the blind see again and could beam . . . diagrams straight into a student’s brains.” However, for physicians, X-rays marked a turning point in the treatment of the sick and wounded.
On November 8, 1895, the German physicist Wilhelm Röntgen was experimenting with a cathode-ray tube when he found that a discarded fluorescent screen lit up over a meter away when he switched on the tube, even though the tube was covered with a heavy cardboard. He realized that some form of invisible ray was coming from the tube, and he soon found that they could penetrate various materials, including wood, glass, and rubber. When he placed his hand in the path of the invisible rays, he saw a shadowy image of his bones. He called the rays X-rays because they were unknown and mysterious at that time, and he continued his experiments in secrecy in order to better understand the phenomena before discussing them with other professionals. For his systematic study of X-rays, Röntgen would win the first Nobel Prize.
Physicians quickly made use of X-rays for diagnoses, but the precise nature of X-rays was not fully elucidated until around 1912, when Max von Laue used X-rays to create a diffraction pattern of a crystal, which verified that X-rays were electromagnetic waves, like light, but of a higher energy and a shorter wavelength that was comparable to the distance between atoms in molecules. Today, X-rays are used in countless fields, ranging from X-ray crystallography (to reveal the structure of molecules) to X-ray astronomy (e.g., the use of X-ray detectors on satellites to study X-ray emissions from sources in outer space).
SEE ALSO Telescope (1608), Wave Nature of Light (1801), Electromagnetic Spectrum (1864), Radioactivity (1896).
X-ray of the side view of a human head, showing screws used to reconstruct the jaw bones.
1896
Proof of the Prime Number Theorem • Clifford A. Pickover
Johann Carl Friedrich Gauss (1777–1855), Jacques Salomon Hadamard (1865–1963), Charles-Jean de la Vallée-Poussin (1866–1962), John Edensor Littlewood (1885–1977)
Mathematician Don Zagier has commented that “despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers . . . and nobody can predict where the next one will sprout. . . . Even more astonishing . . . the prime numbers exhibit stunning regularity, there are laws governing their behavior, and they obey these laws with almost military precision.”
Consider π(n), which is the number of primes less than or equal to a given number n. In 1792, when only 15 years old, Carl Gauss became fascinated by the occurrence of prime numbers, and he proposed that π(n) was approximately equal to n/ln(n), where ln is the natural logarithm. One consequence of the prime number theorem is that the nth prime number is approximately equal to nln(n), with the relative error of this approximation approaching 0 as n approaches infinity. Gauss later refined his estimate to π(n) ~ Li(n) where Li(n) is the integral from 2 to n of dx/ln(x).
Finally, in 1896, French mathematician Jacques Hadamard and Belgian mathema-tician Charles-Jean de la Vallée-Poussin independently proved Gauss’s theorem. Based on numerical experiments, mathematicians had conjectured that π(n) was always somewhat less than Li(n). However, in 1914, Littlewood proved that π(n) < Li(n) reverses infinitely often if one were able to search though huge values of n. In 1933, South African mathe-matician Stanley Skewes showed that the first crossing of π(n) − Li(n) = 0 occurs before 10∧10∧10∧34, a number referred to as Skewes’ number, where ∧ indicates the raising to a power. Since 1933, this value has been reduced to around 10316.
English mathematician G. H. Hardy (1877–1947) once described Skewes’ number as “the largest number which has ever served any definite purpose in mathematics,” although the Skewes’ number has since lost this lofty accolade. Around 1950, Paul Erdös and Atle Selberg discovered an elementary proof of the prime number theorem—that is, a proof that uses only real numbers.
SEE ALSO Sieve of Eratosthenes (c. 240 BCE) Riemann Hypothesis (1859), Public-Key Cryptography (1977), Proof of the Kepler Conjecture (2017).
Prime numbers, represented in boldface, “grow like weeds among the natural numbers . . . and nobody can predict where the next one will sprout. . . .” Although the number 1 used to be considered a prime, today mathematicians generally consider 2 to be the first prime.
1896
Radioactivity • Clifford A. Pickover
Abel Niépce de Saint-Victor (1805–1870), Antoine Henri Becquerel (1852–1908), Pierre Curie (1859–1906), Marie Skłodowska Curie (1867–1934), Ernest Rutherford (1871–1937), Frederick Soddy (1877–1956)
To understand the behavior of radioactive nuclei (the central regions of atoms), picture popcorn popping on your stove. Kernels appear to pop at random over several minutes, and a few don’t seem to pop at all. Similarly, most familiar nuclei are stable and are essentially the same now as they were centuries ago. However, other kinds of nuclei are unstable and spew fragments as the nuclei disintegrate. Radioactivity is the emission of such particles.
The discovery of radioactivity is usually associated with French scientist Henri Becquerel’s 1896 observations of phosphorescence in uranium salts. Roughly a year before Becquerel’s discovery, German physicist Wilhelm Röntgen discovered X-rays while experimenting with electrical discharge tubes, and Becquerel was curious to see if phosphorescent compounds (compounds that emit visible light after being stimulated by sunlight or other excitation waves) might also produce X-rays. Becquerel placed uranium potassium sulfate on a photographic plate that was wrapped in black paper. He wanted to see if this compound would phosphoresce and produce X-rays when stimulated by light.
To Becquerel’s surprise, the uranium compound darkened the photographic plate even when the packet was in a drawer. Uranium seemed to be emitting some kind of penetrating “rays.” In 1898, physicists Marie and Pierre Curie discovered two new radioactive elements, polonium and radium. Sadly, the dangers of radioactivity were not immediately recognized, and some physicians began to provide radium enema treatments among other dangerous remedies. Later, Ernest Rutherford and Frederick Soddy discovered that these kinds of elements were actually transforming into other elements in the radioactive process.
Scientists were able to identify three common forms of radioactivity: alpha particles (bare helium nuclei), beta rays (high-energy electrons), and gamma rays (high-energy electromagnetic rays). Author Stephen Battersby notes that, today, radioactivity is used for medical imaging, killing tumors, dating ancient artifacts, and preserving food.
SEE ALSO X-rays (1895), E = mc2 (1905), Neutron (1932), Energy from the Nucleus (1942), Little Boy Atomic Bomb (1945), Radiocarbon Dating (1949).
During the late 1950s, fallout shelters grew in number across the US. These spaces were designed to protect people from radioactive debris from a nuclear explosion. In principle, people might remain in the shelters until the radioactivity had decayed to a safer level outside.
1897
Electron • Clifford A. Pickover
Joseph John “J. J.” Thomson (1856–1940)
“The physicist J. J. Thomson loved to laugh,” writes author Josepha Sherman. “But he was also clumsy. Test tubes broke in his hands, and experiments refused to work.” Nevertheless, we are lucky that Thomson persisted and revealed what Benjamin Franklin and other physicists had suspected—that electrical effects were produced by minuscule units of electrical charge. In 1897, J. J. Thomson identified the electron as a distinct particle with a mass much smaller than the atom. His experiments emplo
yed a cathode ray tube: an evacuated tube in which a beam of energy travels between a positive and negative terminal. Although no one was sure what cathode rays actually were at the time, Thompson was able to bend the rays using a magnetic field. By observing how the cathode rays moved through electric and magnetic fields, he determined that the particles were identical and did not depend on the metal that emitted them. Also, the particles all had the same ratio of electric charge to mass. Others had made similar observations, but Thomson was among the first to suggest that these “corpuscles” were the carriers of all forms of electricity and a basic component of matter.
Discussions of the various properties of electrons are presented in many sections of this book. Today, we know that the electron is a subatomic particle with negative electric charge and a mass that is 1/1,836 of the mass of a proton. An electron in motion generates a magnetic field. An attractive force, known as the Coulomb force, between the positive proton and the negative electron causes electrons to be bound to atoms. Chemical bonds between atoms may result when two or more electrons are shared between atoms.
According to the American Institute of Physics, “Modern ideas and technologies based on the electron, leading to the television and the computer and much else, evolved through many difficult steps. Thomson’s careful experiments and adventurous hypotheses were followed by crucial experimental and theoretical work by many others [who] opened for us new perspective—a view from inside the atom.”
SEE ALSO Battery (1800), Wave Nature of Light (1801), Atomic Theory (1808), Photoelectric Effect (1905), Bohr Atom (1913), De Broglie Relation (1924), Pauli Exclusion Principle (1925), Schrödinger’s Wave Equation (1926), Dirac Equation (1928).
A lightning discharge involves a flow of electrons. The leading edge of a bolt of lightning can travel at speeds of 130,000 miles per hour (60,000 meters/second) and can reach temperatures approaching 54,000°F (30,000°C).
1899
Psychoanalysis • Clifford A. Pickover
Sigmund Freud (1856–1939)
According to author Catherine Reef, the Austrian physician Sigmund Freud “explored the human mind more thoroughly than anyone who had come before him. He pioneered a new method for diagnosing and treating mental illness, a method he called psychoanalysis. He simply talked to his patients, and, more important, he listened.” Freud emphasized the importance of unconscious mental processes in shaping human behavior and emotions, and he encouraged his patients to “freely associate” and speak about images from fantasies and dreams. He encouraged patients to act as though they were travelers “sitting next to the window of a railway carriage and describing to someone outside the carriage the changing views” seen outside. When waiting for his patients’ words to reveal hidden messages, Freud often felt like an archeologist unearthing precious relics in ancient cities. His goal was to interpret unconscious conflicts that caused harmful symptoms, thereby giving the patients insight and resolutions to their problems, which might include abnormal fears or obsessions. The Interpretation of Dreams, published in 1899, was his greatest work.
In general, Freud often suggested that patients’ repressed sexual fantasies and early childhood experiences played an important role in later dysfunctional behavior. His most famous psychoanalytic model divided the mind into three separate parts: the id (concerned with basic drives such as sexual satisfaction), the superego (concerned with socially acquired controls and moral codes), and the ego (the conscious mind that motivates our decisions through the tension between the id and superego).
Although it is still difficult to discern what fraction of his often controversial ideas will ultimately be considered correct or even useful, his ideas on psychology “have completely revolutionized our conception of the human mind,” according to author Michael Hart. Rather than condemn or ridicule those with behavioral anomalies, Freud sought understanding. Psychiatrist Anthony Storr writes, “Freud’s technique of listening to distressed people over long periods rather than giving them orders or advice has formed the foundation of most modern forms of psychotherapy, with benefits to both patients and practitioners.”
SEE ALSO Cerebral Localization (1861), The Principles of Psychology (1890), Classical Conditioning (1903), Brain Lateralization (1964), Placebo Effect (1955), Antidepressant Medications (1957), Cognitive Behavior Therapy (1963), Theory of Mind (1978).
Freud’s psychoanalytic couch, on which his patients reclined. Freud would sit out of sight in the green chair, listening to their free associations. (Freud Museum, London.)
1900
Blackbody Radiation Law • Clifford A. Pickover
Max Karl Ernst Ludwig Planck (1858–1947), Gustav Robert Kirchhoff (1824–1887)
“Quantum mechanics is magic,” writes quantum physicist Daniel Greenberger. Quantum theory, which suggests that matter and energy have the properties of both particles and waves, had its origin in pioneering research concerning hot objects that emit radiation. For example, imagine the coil on an electric heater that glows brown and then red as it gets hotter. The Blackbody Radiation Law, proposed by German physicist Max Planck in 1900, quantifies the amount of energy emitted by blackbodies at a particular wavelength. Blackbodies are objects that emit and absorb the maximum possible amount of radiation at any given wavelength and at any given temperature.
The amount of thermal radiation emitted by a blackbody changes with frequency and temperature, and many of the objects that we encounter in our daily lives emit a large portion of their radiation spectrum in the infrared, or far-infrared, portion of the spectrum, which is not visible to our eyes. However, as the temperature of a body increases, the dominant portion of its spectrum shifts so that we can see a glow from the object.
In the laboratory, a blackbody can be approximated using a large, hollow, rigid object such as a sphere, with a hole poked in its side. Radiation entering the hole reflects off the inner walls, dissipating with each reflection as the walls absorb the radiation. By the time the radiation exits through the same hole, its intensity is negligible. Thus, this hole acts as a blackbody. Plank modeled the cavity walls of blackbodies as a collection of tiny electromagnetic oscillators. He posited that the energy of oscillators is discrete and could assume only certain values. These oscillators both emit energy into the cavity and absorb energy from it via discrete jumps, or in packages called quanta. Planck’s quantum approach involving discrete oscillator energies for theoretically deriving his Radiation Law led to his 1918 Nobel Prize. Today, we know that the universe was a near-perfect blackbody right after the Big Bang. German physicist Gustav Kirchhoff introduced the actual term blackbody in 1860.
SEE ALSO Electromagnetic Spectrum (1864), Photoelectric Effect (1905), Cosmic Microwave Background (1965).
LEFT: Max Planck, 1878. RIGHT: Molten glowing lava is an approximation of blackbody radiation, and the temperature of the lava can be estimated from the color.
1900
Hilbert’s 23 Problems • Clifford A. Pickover
David Hilbert (1862–1943)
German mathematician David Hilbert wrote, “A branch of science is full of life as long as it offers an abundance of problems; a lack of problems is a sign of death.” In 1900, he presented 23 important mathematical problems to be targeted for solution in the twentieth century. Because of Hilbert’s prestige, mathematicians spent a great deal of time tackling the problems through the years. His extremely influential speech on the subject started, “Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive?”
About ten of the problems have since been cleanly solved, and many others have solutions that are accepted by some mathematicians but for which some controversy still remains. For example, the Kepler Conjecture (part of Problem 18), which raised questions about the efficiency of sphere p
acking, involved a computer-assisted proof, which was difficult for people to verify. Finally, in 2017, the Forum of Mathematics, Pi journal published a formal proof of the Kepler Conjecture, by a team led by American mathematician Thomas Hales, resolving a problem that was unsolved for hundreds of years.
One of the most famous problems still unresolved today is the Riemann Hypothesis, which concerns the distribution of the zeros of the Riemann zeta function (a very wiggly function). David Hilbert remarked, “If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?”
Ben Yandell writes, “Solving one of Hilbert’s Problems has been the romantic dream of many a mathematician. . . . In the last hundred years, solutions and significant partial results have come from all over the world. Hilbert’s list is a thing of beauty, and aided by their romantic and historical appeal, these well-chosen problems have been an organizing force in mathematics.”
SEE ALSO Riemann Hypothesis (1859), Cantor’s Transfinite Numbers (1874), Proof of the Prime Number Theorem (1896), Noether’s Idealtheorie (1921), Proof of the Kepler Conjecture (2017).
Photograph of David Hilbert (1912), which appeared on postcards of faculty members at the University of Göttingen. Students often purchased such postcards.
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