Aristotle's wheel paradox #4

Wikipedia has a page for Aristotle's Wheel Paradox. I edited it substantially during September-December 2018. The page was very poorly written before then. I added two original solutions, the second and third below. The page has been edited many times since then, but only in minor ways. On August 18, 2021 somebody else edited the page, greatly reducing in size two images I had put on the page and putting them into frames on the right side of the page. Wikipedia allows an editor to preview how his or her edits will affect the page's appearance on the device he or she is using. However, the page's appearance on my smart phone -- and likely most or all other smart phones -- is quite different due to its small screen size. For example, the frames do not appear. Their content still shows, but the article's flow and appearance are worse.  

Most Wikipedia pages can be edited by millions of people whenever they get the urge. So I am hereby preserving part of the article as it existed before August 18 in this blog, where presumably nobody but me can modify it. I will not so preserve the section titled History of the paradox, which I did not edit. The following are the introduction and the Analysis and solutions section, which were written near 100% by me. 

Introduction

Aristotle's wheel paradox is a paradox or problem appearing in the Ancient Greek work Mechanica traditionally attributed to Aristotle. A wheel can be depicted in two dimensions using two circles. The larger circle is tangent to a horizontal surface (e.g. a road) that it can roll on. The smaller circle has the same center and is rigidly affixed to the larger one. The smaller circle could depict the bead of a tire, a rim the tire is mounted on, an axle, etc. Assume the larger circle rolls without slipping (or skidding) for a full revolution. The distances moved by both circles are the same length, as depicted by the blue and red dashed lines and the distance between the two black vertical lines. The distance for the larger circle equals its circumference, but the distance for the smaller circle is longer than its circumference: a paradox or problem.

The paradox is not limited to a wheel. Other things depicted in two dimensions show the same behavior. A roll of tape does. A typical round bottle or jar rolled on its side does; the smaller circle depicting the mouth or neck of the bottle or jar.

There are a few things that would be depicted with the brown horizontal line in the image tangent to the smaller circle rather than the larger one. Examples are a typical train wheel, which has a flange, or a barbell straddling a bench. In this case the the distances moved by both circles with one revolution would equal the circumference of smaller inner circle. A similar but not identical analysis would apply.

Analysis and solutions

First solution

The paradox is that the smaller inner circle moves 2πR, the circumference of the larger outer circle with radius R, rather than its own circumference. If the inner circle were rolled separately, it would move 2πr, its own circumference with radius r. The inner circle is not separate but rigidly connected to the larger. So 2πr is a red herring. The inner circle's center is relevant, its radius is relevant, but its circumference is not.

Second solution

This solution considers the transition from starting to ending positions. Let Pb be a point on the bigger circle and Ps be a point on the smaller circle, both on the same radius. For convenience, assume they are both directly below the center, analogous to both hands of a clock pointing towards six. Pb travels a cycloid path and Ps a curtate cycloid path as they roll together one revolution.

While each travels 2πR horizontally from start to end, Ps's cycloid path is shorter and more efficient than Pb's. Pb travels farther above and farther below the center's path – the only straight one – than does Ps. The image below shows the circles before and after rolling one revolution. It shows the motions of the center, Pb, and Ps, with Pb and Ps starting and ending at the top of their circles. The green dash line is the center's motion. The blue dash curve shows Pb's motion. The red dash curve shows Ps's motion. Ps's path is clearly shorter than Pb's. The closer Ps is to the center, the shorter, more direct, and closer to the green line its path is.

If Pb and Ps were anywhere else on their respective circles, the curved paths would be the same length. Summarizing, the smaller circle moves horizontally 2πR because any point on the smaller circle travels a shorter, more direct path than any point on the larger circle.

Third solution

This solution only compares the starting and ending positions. The larger circle and the smaller circle have the same center. If said center is moved, both circles move the same distance, which is a necessary property of translation and equals 2πR in the experiment. Also, every other point on both circles has the same position relative to the center before and after rolling one revolution (or any other integer count of revolutions). For a wheel with multiple concentric inner circles, each circle's translation movement is identical because all have the identical center. This further proves the circumference of any inner circle is entirely irrelevant (when the outer, larger circle is the one that rolls on a surface).

Aristotle's wheel paradox #1  Feb 18, 2018

Aristotle's wheel paradox #2  Feb 22, 2018

Aristotle's Wheel Paradox #3 Nov 10, 2018

Crystal Fire #10

Despite his immense contributions, Shockley never became the millionaire he wanted to be. He recruited first-rate scientists and engineers, but many defected to start or join other more successful firms.

Neither Brattain nor Bardeen had anywhere near Shockley’s visionary appreciation of the transistor’s vast commercial potential. Both continued doing basic research – Brattain at Bell Labs and Bardeen on a variety of solid state physics topics, especially superconductivity, for which he won a second Nobel Prize.

Almost as important as the transistor’s invention are the techniques crystal growing and zone refining, which allow fabricating large single crystals of ultra-pure silicon and germanium. Without these crystals, the industry would not exist.

The transistor led to a startling transformation of technology and even culture and the nature of work  – computers (main-frame and then personal), modern televisions, the iPod, and cell phones.

The new Information Age comes with its own distinct challenges to human freedom and livelihood. The crystal fire has brought with it an intensity and immediacy of life in which many things become obsolete soon. Some people unable or unwilling to deal with the unceasing change widens the divisions between different peoples on a national and global scale. For as fire illuminates, it also consumes.

Some other challenges not mentioned in the book are privacy, cyber-crime on a global scale, and the proliferation of advertising.

This is my final post about Crystal Fire.

Crystal Fire #9

The use of transistors expanded rapidly. But a worrisome cloud loomed on the horizon. As the number of components – transistors, diodes, resistors, capacitors, and connections – grew, the tedious task of assembly resulted in more defects. A few visionary engineers began looking for ways to fashion circuits from a single block of material. Jack Kilby of Texas Instruments was a pioneer in making such “integrated circuits.” Kilby’s first successful attempt used germanium, but then silicon came to be recognized and used by Kilby and others -- its advantages outweighing its disadvantages. Photolithography was used to define the circuit elements. The monolithic idea also arose in a different form at Fairchild Semiconductor. Both companies got patents for their products.

Shockley Transistor also invented a diode. When manufactured in quantity, too many diodes being defective led to market failure. Another Shockley attempt at transistors didn’t fare well either. Observing Shockley Transistor’s hemorrhaging cash and Fairchild’s great success, Arnold Beckman finally sought to sell off his transistor division and did.

These miniature circuits were a new and revolutionary advance. They are the ultimate practical expression of the theoretical insights of Bardeen, Shockley, Noyes and others, filtered and amplified by hundreds of scientists following in their footsteps. Many of the insights came at Bell Labs, Bell Labs and Western Electric were slow to to appreciate the value of monolithic integration. The phone company did not have the same pressing need for miniaturization that prodded the computer and military markets. Other firms, especially Texas Instruments and Fairchild, led the way.

Crystal Fire #8

William Shockley was surpassed by others for promotion to head all research, so he left Bell Labs. Bell’s top managers felt he was most effective where he was. Other top physicists such as John Bardeen had complained of Shockley’s ham-handed management. Shockley lacked the broader organization skills for directing a wider variety of work. He sought positions at other businesses and as a university professor, but then decided to devote his efforts to start his own company in the semiconductor industry. He finally met with someone who was willing to back him for the $1 million he sought. This was Arnold Beckman, both a good scientist and a successful business man. He was the head of Beckman Instruments, a company that specialized in making analytical instruments, such as a pH meter, for controlling production processes.

Shockley flew Los Angeles and met with Beckman for a week to discuss and then form a business plan. Beckman wanted the new company to be in the LA area, but Shockley wanted it near San Francisco and Stanford University. The provost and dean of engineering at Stanford helped Shockley convince Beckman that being near Stanford would be the best place for recruiting employees and having contacts for getting business.

Shockley first tried to recruit people from Bell Labs, but wasn’t successful. He then sought recruits from other firms such as Motorola, Philco, Raytheon, and Sylvania. He also sought young PhDs at top schools like Berkeley, Cal Tech, and MIT. When Beckman announced the launch of Shockley Semiconductor Laboratory, there were only four Ph.D. scientists and engineers on board. As the facilities were being made for the laboratory, he recruited Robert Noyce and Gordon Moore. Noyce and Moore would later became the co-founder of Fairchild Semiconductor and Intel.

Beckman paid $25,000 to Western Electric to license patent rights in the transistor. Shockley’s contacts Bell Labs were helpful in gaining more info about production techniques. Still the going was tough. It was one thing to get methods working in the ultrahigh-technology environment of Bell Labs with its ample supply of first-rate scientists, engineers, and technicians and high-quality equipment. It was quite another to achieve the same results in the primitive surrounding of Shockley’s lab, even with the talent there.

In November, 1956 Shockley learned he was to be awarded the Nobel Prize in physics along with Bardeen and Brattain. They all met in Stockholm to receive their award in December 1956. As 1957 began, his company was not doing well. It had been in operation more than a year, but was still struggling to produce anything for sale. Employee defections began. Beckman began to realize that Shockley was a brilliant physicist but a lousy business manager. Shockley devoted his efforts to developing one kind of transistor while Noyce, Moore, and others thought it was a waste of time. Several months later Noyce, Moore and six other of Shockley’s brightest recruits resigned to start their own company. They got financing from Fairchild Camera and Instruments and named their company Fairchild Semiconductor.

Crystal Fire #7

When Bell Labs hosted a symposium in 1951 about the transistors invented at Bell, absent was mention about the technologies involved in fabricating the gadgets. Bell’s subsidiary Western Electric began licensing rights to transistors for a fee. The art of fabricating them could not remain secret much longer. It was a challenge because the conflicting demands by the military for secrecy yet multiple suppliers and commercial openness were difficult to meet simultaneously. Anyway, Bell Labs invited licensees to visit its Western Electric plant in 1952, then published a comprehensive description of the state of the art of manufacturing transistors. One of the technologies then revealed was a powerful new method of purifying germanium, which Bell Labs had kept under wraps for almost two years at the military’s request.

Military applications provided an immediate market for transistors where cost was not a concern. Transistors were much more expensive than vacuum tubes. From 1953-55 almost half the revenue for transistors came from the military.

Other demand came from hearing aid manufacturers. Keeping with Alexander Graham bell’s devotion to the deaf and hard of hearing, AT&T extended royalty-free licenses to hearing aid manufacturers. Transistors were especially helpful for hearing aids. Ones that relied on vacuum tubes were bulky with a battery-powered amplifying unit worn around the waist. Also, the batteries were expensive.

Other demand came for use in pocket-size transistor radios. Texas Instruments was a leader in those, licensing the technology to other manufacturers in exchange for royalties. A Japanese company formed a subsidiary called Sony that became very successful making such radios.

Later in the 1950’s new kinds of transistors were invented, including using silicon instead of germanium.

Crystal Fire #6

After World War II the people at Bell Labs could resume its focus on basic research and development. The middle chapters of Crystal Fire give many details about this period through the early 1950s. They learned many things about the electrical property of different elements, compounds, combinations, of solid state devices. They also encountered mysteries about these things that prompted further research. They also had to spend considerable time obtaining samples of materials absent undesired impurities or optimal amounts of desired impurities. Patents were filed and there were concerns about patents already in place, what exclusive rights the military might want, and what progress was being in other labs such as at Purdue University.

There were two types of transistors invented at Bell Labs during those years – the point contact invented by John Bardeen and Walter Brattain and the junction type spearheaded by William Shockley.

In June 1951 Bell Labs gave a press conference about transistors. The star of the show was the junction transistor. Perhaps its most remarkable feature was its extremely low power consumption, about one-millionth of conventional vacuum tubes. It also amplified signals with far greater efficiency than the point-contact transistor.

The point-contact transistor was still used in the Bell System. Practical use of it came earlier. It entered mass production at Western Electric (a subsidiary of AT&T), servicing complex switching equipment to permit direct dialing and bypassing traditional telephone operators.

But the point-contact transistor never made it to the commercial marketplace in a big way. Apart from transient usage in hearing aids and military equipment, the only important applications it ever found came in the Bell System. Other manufacturers were reluctant to put significant capital into its production, especially after the recent breakthrough by Shockley’s team. The future belonged to the junction transistor and its offspring.

Crystal Fire #5

Walter Brattain began working at Bell Labs in 1929. Mervin Kelly was a researcher at Bell Labs who became its director of research in 1936. He envisioned telephone switches being electronic rather than mechanical. William Shockley was Kelly’s first hire after a hiring freeze was lifted in 1936. Kelly hired Shockley for the latter’s knowledge of quantum mechanics. Shockley took Kelly’s vision as a guiding light. For the next several years, Bell Labs grew its research staff with specialists in quantum mechanics. In 1937 Clinton Davisson of Bell Labs won the Nobel Prize for his experiments that electrons behaved like waves.

Brattain and Joseph Becker studied the papers of Walter Shottky and Nevill Mott (neither at Bell Labs). The papers said that whenever a metal and a semiconductor come into contact, a double layer of charge crops up – positive on one side and negative on the other – because of the difference in work functions of the two materials. This leads to a kind of “hill” that electrons must surmount if they are to cruise from one side to the other. “Because this hill is asymmetric, with a steep cliff on the metal side and a shallow slope on the other, electrons move far more readily from semiconductor to metal than in the opposite direction." This finally provided a satisfactory explanation of rectification, which had mystified scientists for 65 years. Shockley, Brattain, and Becker attempted fabricating devices to make use of this effect. Not only was progress slow, it was interrupted with work on topics like radar, submarine detection, mines, and torpedoes due to World War II.

Crystal Fire #4

Bell Telephone Labs grew around the efforts of American Telephone & Telegraph to develop vacuum tubes for long distance communication. Through a variety of gimmicks, the Bell System enabled transmitting telephone calls over 1000 miles by 1900. Beyond that distance, transmission deteriorated. For transcontinental service to become a reality, the company needed a “repeater” device to replenish the electrical signals at points along the line. AT&T installed a transcontinental line by 1915. Repeaters in Salt Lake City, Omaha, and Pittsburgh boosted the electrical signals.

In the 1920s and 1930s the new discipline of quantum mechanics was used to discover the movement of electrons and the properties of conductors, insulators and semiconductors. New theories superseded older ones. Walter Brattain began work at Bell Labs in 1929. He and colleague Joseph Becker became interested in copper-oxide rectifiers. Copper-oxide belonged to a new class of substances called “semiconductors.” They had some unique properties different from both conductors and insulators. Unlike metals, the conductivity increases with increasing temperature. Copper-oxide rectifiers, dubbed varistors”, began to replace bulky vacuum diodes throughout the Bell system. The speed at which this happened was restrained at Bell Labs by a lack of physicists with enough understanding of quantum mechanics and a hiring freeze during the Great Depression.

Crystal Fire #3

Americans were latecomers to the quantum revolution. Europeans led the way in forming deeper and more fundamental insights about the quantum world. It was in the application of the new theoretical insights and experimental techniques that U.S. scientists excelled in the 1920s. They explored the internal structure and intrinsic properties of solids: color, hardness, conductivity, and so forth.

In the last quarter of the 19^th century, physicists became fascinated with cathode-ray tubes. In 1895 Roentgen discovered X-rays – so-called because he didn’t know what they were. X-rays excited the imagination, but much mystery about them remained. Were they waves or particles? Physicists searched for zebra-striped interference patterns like visible light produced. But if X-rays had wavelengths a thousand times shorter than visible light, any suitable diffraction grating would need spacing a thousand times smaller, less than a billionth of a meter. Nobody knew how to make such a fine grating. In 1912 two of Roentgen’s students found a wreath-like pattern of brights spots against a dark background directing X-ray beams onto a crystal of copper sulfate. Other crystals produced similar patterns. Max von Laue thought the interference patterns were caused by a three-dimensional lattice of objects within the crystals. William Henry Bragg and his son extended von Laue’s insights. All three received a Nobel Prize for their work.

Scientists could then peer inside crystals, where the atoms appeared to be arranged in layers, like eggs stacked in crates.

Physicists began to recognize the conductivity of metals had something to do with the availability of electrons within them. An excellent conductor like copper has plenty of free electrons. Good insulators, like glass or wood, have essentially none.

Chapter 3 has more about other discoveries in physics, such as Rutherford’s discoveries of the inner structure of atoms and Schröedinger’s wave equation. I will skip the details to stick to the main story of the book and avoid possible errors trying to summarize it.

Practical-minded Americans like Walter Brattain had little interest in the airy philosophical debates such as occurred between Niels Bohr and Albert Einstein. They were busy applying the new quantum tools to their study of matter. Plenty of unsolved problems about the nature and structure of atoms, molecules, metals, and crystals awaited exploration with the new methods.

Aristotle's Wheel Paradox #3

The title includes #3 because I posted #1 and #2 in February (link). I am posting #3 because I edited the Wikipedia article about the topic (link).

I improved the first section. It had said the paradox was about two wheels. The section 'Wrong problem entirely ' on the Talk page says the paradox is about one wheel. I wholly agree. So my change to the first section says it is about two circles and one wheel (or a suitable substitute for the wheel).

I added the Analysis & Solution section to include my two solutions to the paradox. To the best of my knowledge the solutions are original. At least I didn't see or hear them anywhere else.

Since others can edit Wikipedia articles at any time, I cross my fingers that somebody won't impair it. I earlier added similar text to the Talk Page. I believe others can alter that too, but maybe they are less likely to do so.

P.S. I later added a third solution, labeled the first solution in the Wikipedia article.

Marconi #9

In 1922 Marconi began experimenting with short waves. "Using a transmitter described as a "baby wireless set," he awed his audience by demonstrating "how a flying shaft [beam] of radio waves may be hurled in a desired direction, straight at a receiving station intended to receive it." This was the new directional "beam" system he had been developing with his associate Charles Franklin since 2016" (Marconi 472).

In a talk Marconi said he thought it possible to design an apparatus by which a ship could send a beam of rays in a desired direction and the rays coming across a metallic object such as another ship could be reflected back to the sender, thus revealing the presence and bearing of the other ship. Marconi was describing a process that would come to be known as radar. Successful use of radar was one of the keys to allied superiority in WW II, and now is essential to air traffic control (473-4).

Others were developing broadcasting. Marconi did not see what the fuss was about. He thought radio was about communication, not the one-way delivery of light entertainment, what he thought broadcasting was doing (486). Broadcasting used continuous waves as opposed to Marconi's spark waves.

Largely due to the efforts of other people the radio boom was well under way by 1922. In 1922, the first year when numbers were available, 100,000 radio sets were sold in the USA. It was 5 times that a year later. Such enormous growth continued for several years afterwards. The proliferation of broadcasting attracted the powers that be, too. Vatican Radio was established with Marconi's help. In February 1931 millions of listeners around the world heard the Pope speak. Inspired by the example of the Vatican, totalitarian dictators and Franklin Roosevelt and Winston Churchill were soon using radio to "inspire, cajole, mobilize, or terrify" (568).

In a May 1931 broadcast the pope called for "the reconstruction of the social order, describing the dangers of both unrestrained capitalism and totalitarian communism, as well as the ethical implications of reconstruction. It was one of the most important political interventions of the 1930's, approving the triparate corporatism of government, industry, and labor [ ] favored by Italian fascism ... [I]t was also couched in a tone that could invite the praise of a liberal politician like FDR" (568-9). FDR later met with Marconi, and FDR was interested in Italy's domestic policies (591).

Marconi #8

In 1915 Marconi traveled to Schenectady, New York to visit the General Electric plant where Ernst Alexanderson developed and patented a high-frequency alternator capable of generating continuous waves (Marconi 393). Marconi wanted to buy it. Marconi and GE's chief counsel arrived at the verge of an agreement whereby GE would manufacture the alternator, while Marconi would have exclusive rights to use it. The agreement didn't materialize (439).

"The proposal was intensely political and essential to Marconi's global strategy. Marconi's UK base was constricted by British wartime restrictions, but the war also presented opportunities for technological development and the company was still determined to build a global network anchored by a British imperial wireless chain. At the same time, the US domestic market and likely emergence of the United States as the dominant world power after the war foreshadowed an increased role for Marconi's American operations. A deal with GE would palliate American nationalist concerns and reduce Marconi's exposure to the British public sector, with which he had such a fraught relationship. At the same time, the company was anxious to position itself once and for all against the anticipated postwar resurgence of Telefunken.
     The United States' entry to the war in April, 1917 put a major crimp in Marconi's plans. The US Navy took over all wireless operations on April 7, and as the war proceeded it was not entirely clear what would happen to them once the conflict ended" (439-40).

Telefunken was a German wireless company and Marconi's chief competitor.

In 1919 Marconi reopened his negotiations with GE, proposing purchase of 24 alternators. GE's chief counsel conferred with the US Navy. The response requested that GE not sell the alternators to Marconi. Even President Wilson wanted to dissuade GE from doing the deal. The president was convinced that world pre-eminence would be determined by three factors: oil, transportation, and communication. Wireless, however, was still up for grabs, and if the United States could achieve dominance there, the result would be a standoff between the USA and Britain (441).

As the situation evolved, almost the opposite of Marconi's plan occurred. GE bought Marconi's American operations. It resulted in the birth of the Radio Corporation of America (RCA), incorporating the assets of the Marconi Wireless Telegraph Company of America (MWTCA) into a new public company in which GE owned a controlling interest. RCA replaced MWTCA as the major US domestic wireless company and gave the US a solid foothold in global communication (443).

Marconi #7

The Marconi biography includes the following. I will be brief.

Marconi wins the Nobel Prize in Physics in 1909. He was nominated a few times before. He was the first entrepreneur to win the prize. He shared it with a German, Karl Ferdinand Braun, who contributed significantly to the development of radio and television technology.

In 1909 two ships collided, one with 1200 passengers. Marconi's wireless system aided a quick rescue response. Only six lives were lost, demonstrating the benefit to mankind made possible by wireless.

After H. Cuthbert Hall was ousted, Marconi took on much of what Hall had done. In 1910, though, Godfrey Isaacs joined the firm, which gave Marconi more time to devote to research and experiments.

In 1911 Italy declared war on the Ottoman Empire in defense of Italians in northern Africa. Then Italians started building wireless stations on Africa's northern coast. This was the third time wireless was used in war.

On 10 April 1912 the passenger ship Titanic left Ireland headed west to New York, with 2,208 (estimated) passengers and crew. The ship had the then-best wireless equipment aboard. On 14 April, four days into the crossing and about 375 miles (600 km) south of Newfoundland, she hit an iceberg at 11:40 p.m. ship's time. The wireless operator sent distress signals while the ship was sinking. Unfortunately, the closest ship to receive the signal, the Carpathia wasn't very close. Almost two hours after the collision the Carpathia arrived and rescued an estimated 705 survivors. Many people gave Marconi a lot of credit for saving the survivors.

In 2012 the British Postal Office's not yet signed agreement with a British Marconi Company made the news. The agreement drew criticism for the terms being too favorable to Marconi's business and political insiders who made investment gains from holding stock in Marconi companies (ref. Marconi scandal).

Marconi #6

In my opinion Marconi's scientific achievement was more spectacular than John Galt's motor in Atlas Shrugged. Firstly, Marconi's was real and Galt's was fictional. One might say that's an example of "truth is stranger than fiction" (Mark Twain quote; Lord Byron quote). Galt's motor was designed to harness static electricity from the air for power generation. Secondly, unlike radio waves, static electricity can be seen, felt and heard. The electromagnetic waves -- originally called "Hertzian waves" -- used by Marconi for wireless telegraphy cannot be directly perceived. They can only be indirectly perceived via instruments -- radio, television, antenna, cell phone, computer. Thirdly, Marconi's achievement made possible Galt's hijacking a radio broadcast in order to make his speech. 😉

Marconi and John Galt (really Ayn Rand) did have very different ideas about politics. Marconi courted governments to commercialize his wireless telegraphy. They wanted it mainly for military use. Marconi also relied on government-backed patent protection. Conversely, Galt's motor was targeted for the private sector.

H. Cuthbert Hall was second in command to Marconi in Marconi's business from 1901 to 1908. Hall's political views were far closer to those of Ayn Rand than were Marconi's. Hall had led the company's fight against the Berlin Convention (see #5). Hall had an aggressive attitude toward the British government, Marconi's biggest client. "Hall was an ideological free enterpriser, to whom government interference of any kind was anathema. If dealing with the government could bring benefits to the company, then fine. But there was nothing intrinsically beneficial to the relationship. Marconi, though not at all ideological, felt intuitively close to political power of every stripe. In his mind, nothing could be more powerful than a partnership with government -- any government" (Marconi 285).

In 1907 Marconi became increasingly dissatisfied with Hall. Marconi thought his companies'  business dealing were impaired by Hall and depended upon its relation to governments. So Marconi, with the support of board members other than Hall, ousted Hall.

A future post will contain some more about Marconi's relationship to Mussolini and fascism many years later.

Marconi #4

By 1905 Marconi's sytem was pervasive. "On ships it was sometimes suggested that wireless had ruined 'the delights of complete repose which have hitherto ... been associated with the idea of being on a long ocean voyage,' but this notion was discounted by the benefits it brought for minimizing danger at sea. It was also good for business travelers who could for the first time remain in touch with their offices as they crossed the Atlantic. With cheap long-distance telegraphy within reach, emigration took on a less onerous meaning; it would be easier for members of disporic communities to keep in touch with their families back home. At the same time, ambitious corporations and military establishments everywhere vied for ways to use the new technology as an instrument for their grand designs. Indeed, the sentiments for and against Marconi's invention were not unlike those we hear today about the good and evil of the constant connectedness that comes with modern communication technology. There was full agreement, however, on the basic point: wireless communication had changed people's relationship with time, distance, and mobility" (Marconi 247-8).

Reginald Fessenden was "soon known in the United States as a sharp critic of Marconi's system. Fessenden realized that if Marconi's spark transmitter could be replaced by one that gave off a continuous wave, it would be possible to transmit voice by wireless. This was the technical breakthrough that enabled what would eventually be known as broadcasting, and for this reason, Fessenden is often claimed to be the inventor of radio. The spark-reliant intermittent wave transmission that Marconi pioneered could transmit dots and dashes but not speech and music (hence the distinction between "wireless telegraphy" and "broadcasting"). However, both methods relied on the medium of elecromagnetic waves, and Marconi was unquestionably the first to use the wave spectrum for communication" (250).

Dots and dashes, of course, refer to Morse code. By the way, Thomas Edison's first two children were nicknamed Dot and Dash (link). 😊

Marconi #3

G. Marconi secretly worked on a project he referred to as "the great thing" -- an attempt to signal across the Atlantic Ocean. Theoretical physicists said it couldn't be done because they claimed electromagnetic waves radiated in a straight line into space and would not follow the curvature of the earth. Holders of this view included the great French mathematician and physicist Henri Poincare, who understood the properties of Hertzian waves. But Marconi was convinced that the theoreticians were wrong; he believed electromagnetic waves would bend to follow the curvature of the earth (Marconi, 148).

In December, 1901 Marconi experimented with signals sent from a station in England across the Atlantic Ocean to a station in Newfoundland. At the receiving end he did indeed hear signals "serenely ignoring the curvature of the earth which so many doubters considered would be a fatal obstacle" (174).

Prompted to explain how Marconi had been able to receive a Hertzian wave signal nearly two thousand miles away, two theoretical physicists later hypothesized that there might exist an ionized layer in the upper atmosphere capable of reflecting or refracting radio waves of certain frequencies back to earth (176).

The biography doesn't address the varying range of radio wave lengths/frequencies. However, Wikipedia shows the whole range of radio waves (link1) and includes the following (link2).

"Lower frequency (between 30 and 3,000 kHz) vertically polarized radio waves can travel as surface waves following the contour of the Earth; this is called groundwave propagation."

"In this mode the radio wave propagates by interacting with the conductive surface of the Earth. The wave "clings" to the surface and thus follows the curvature of the Earth, so groundwaves can travel over mountains and beyond the horizon."

"Early long distance radio communication (wireless telegraphy) before the mid-1920s used low frequencies in the longwave bands and relied exclusively on ground-wave propagation. Frequencies above 3 MHz were regarded as useless and were given to hobbyists (radio amateurs). The discovery around 1920 of the ionospheric reflection or skywave mechanism made the medium wave and short wave frequencies useful for long distance communication and they were allocated to commercial and military users."

So it seems both Marconi and Poincare were partly correct and partly incorrect. Marconi's experiment used lower or medium frequency (longer or medium length) radio waves.

Marconi #2

Radio waves were first predicted by mathematical work done in 1867 by Scottish mathematical physicist James Clerk Maxwell. Maxwell noticed wavelike properties of light and similarities in electrical and magnetic observations. His mathematical theory, now called Maxwell's equations, described light waves, and waves of less or more length, as waves of electromagnetism that travel in space, radiated by a charged particle. In 1887, Heinrich Hertz demonstrated the reality of Maxwell's electromagnetic waves by experimentally generating radio waves in his laboratory, showing that they exhibited the same wave properties as light: standing waves, refraction, diffraction, and polarization. The waves were first called "Hertzian waves." The modern term "radio wave" replaced the original name around 1912. (Link).

"Hertz's breakthrough had attracted worldwide excitement when he published his results in 1888, but no one had yet found a practical application for the discovery" (Marconi 27). Hertz's interest in the waves was theoretical, and he died in 1894 (age 36). Marconi was strongly interested in their practicality and/or commercial use.

Besides developing the technology, much of his early career was devoted to obtaining patents in different countries and defending his patents from infringement. He sought exclusive contracts. A big part of advancing the technology was increasing the useful range of radio waves for communication. A big step was succeeding in transmitting radio waves over the Atlantic Ocean. That would allow wireless communication with ships very far from land and between continents. The greater part of practical interest in Marconi's wireless telegraphy was by governments for military use. A private sector exception was Lloyd's of London. "The first major firm to recognize the commercial potential of Marconi's invention was Lloyd's, the world's leading provider of marine insurance and, hence, dealer in shipping information" (88).

P.S. You might wonder how G. Marconi and wireless communication relate to a blog named Correspondence and Coherence. The relationships aren't strong, but there are some. 1. One definiens of correspondent is 'a journalist employed to provide news stories for newspapers or broadcast media.' Such correspondents nowadays often communicate using wireless technology with a cell phone or computer. 2. A coherer "was a primitive form of radio signal detector used in the first radio receivers during the wireless telegraphy era at the beginning of the 20th century" (Wikipedia).  😊

Marconi #1

I'm reading Marconi by Mark Laboy (link). It's a biography of Guglielmo Marconi, who invented wireless communication. He is often credited with inventing the radio. His invention made the radio possible, but the claim is only partly true.

Pages 34-9 describe the technology of communication and its effects prior to Marconi's invention of wireless communication.

"Gutenburg's invention of movable type, in the mid-fifteenth century, was arguably the most important single development in communication technology of the past thousand years, in terms of its impact on the struggles for unhindered human expression and the corresponding attempts to exercise social and political control over it. Coupled with the spread of literacy, the printing press enabled the Protestant Revolution, among many other revolutions of modernity. But the thing about literacy, British cultural theorist Raymond Williams once wrote, is that you cannot teach someone to read the Bible without also, simultaneously and unintentionally, empowering them to read less holy tracts" (34).

"The "press" ... was by its very nature oppositional and mobilizational, encouraging and enfranchising individuals, and their publishers, to act more effectively as political citizens. Governments became more obsessed with a sense that they needed to control the press and,  not surprisingly, the First Amendment to the United States Constitution, adopted in 1788, stated that Congress shall make no law interfering with freedom of the press. ... By the early nineteenth century, the press was a toll not only for democrats but for all sorts of propagandists as well" (35).

"[T]he introduction of the most important communication technology since the Gutenburg printing press [was] electrical wired telegraphy. By the 1830's, large commercial press interests as well as a new type of company, the national news agency, started to emerge. Press technology could operate as well on a very small scale as on a large one. Getting one's hands on a small printing press and using it to go into business or politics was not beyond the reach of entrepreneurs or activists. Telegraphy was another matter. Telegraphy was a complex technology, requiring huge capital investment; therefore access to it was regulated either by companies or governments, or, more typically, both. With the telegraph, for the first time, there was a separation of means and message, and the emergence of a belief that the tremendous power bestowed by ownership and control over the means of communication had to be offset by responsibilities.
    Another new feature of telegraphy was that messages sent along telegraph lines did not recognize national borders. (Neither did carrier pigeons, which is one reason it took some time for telegraphy to catch on.) ...
    The mail had to physically cross a border. Not so with the telegraph. ...
    Wired telegraphy had some significant limitations, however. It did not reach everywhere, and often needed to be combined with another, usually more primitive, form of communication. To send someone a "telegram," or "wire," one needed, first, to get the message to a local office. Then, at the other end, someone had to deliver it by hand to the intended receiver. There were issues of security and confidentiality" (35-37).

Wired telegraphy's language was Morse code.

"After the first international underwater cable was laid between Dover, England, and Calais, France, in 1850, the idea of a transatlantic cable started to take shape. ...
    The cable-based global communication infrastructure expanded ten-fold between 1870 and 1900, and double again in the next decade" (37-38).

Aristotle's wheel paradox #2

A rolling wheel is not a simple motion. While rolling is rotation plus translation, only the latter really matters for the paradox. Still, it is easy to be lured by the complexity. For example:

1. A point on the perimeter of a wheel travels a cycloid path. A more inner point travels a curtate cycloid path. In the paradox the center's path is a straight horizontal line.

2. A point's velocity in the direction the center moves is faster than the center's velocity during the top half of a rotation. A point's velocity in the direction the center moves is slower than the center's velocity during the bottom half of a rotation.

3. Pure rolling occurs when the circular object travels one circumference along the ground for every for every full rotation it makes. Slipping occurs when rotation is faster than pure rolling. A paradigm case is a car wheel stuck in snow. Skidding occurs when rotation is slower than pure rolling. A paradigm case is a car wheel that skids on ice after the driver brakes hard.

Slipping and skidding so described affect the two circles in the same way. For example, if the part of the tire in contact with the road slips or skids, then the metal rim the tire is mounted on is affected the same way. The rim can't slip when the tire doesn't. Yet the rim slips while the tire doesn't is one "solution" to the paradox given on Wikipedia. It makes no sense except as a far-fetched metaphor. In other words, the rim "slips" but it doesn't really slip. The rim "skids" would be less far-fetched.

Aristotle's wheel paradox #1

Wikipedia. I judge the article as poorly written, especially when it says the paradox is about two wheels. A comment on the Talk page agrees. The quote from Mechanica, written more than 2,000 years ago, describes the paradox as about two circles. Two circles can depict one wheel, e.g. like on a car or truck, with the smaller circle depicting a metal rim. Or the two circles can depict one tire -- not mounted on a rim -- with the smaller circle depicting its smallest circumference, the bead or lip. They can depict a roll of tape.

If the rigidly coupled circles are rolled a full revolution, then all points on both circles have the same position relative to their common center at start and end. Every point's translation vector has the same direction -- parallel to the horizontal surface -- and length as the center's translation vector. Such length is 2*pi*R, where R is the radius of the larger circle. This necessary fact about translation elegantly solves the paradox. Every point on the smaller circle must move 2*pi*R. This shows that the smaller circle's circumference 2*pi*k*R, where k is its circumference divided by R, is irrelevant for one rotation and the given setup. How far the smaller circle moves horizontally is dictated by its center.