February 2018 - Missing the Forest for the Tree: A Worldview Grounded in Science

1668: Reflecting Telescope

Posted on February 18, 2018January 9, 2022 by Dan

The telescope instantly changed the way humanity saw their place in the universe. The backdrop of fixed stars, no longer fixed. The planets, no longer perfect spheres. Hundreds of stars became thousands of stars, then they became hundreds of thousands of stars. Today they number in the hundreds of trillions. The first telescopes to be invented were a type of refracting telescope, which uses lens to collect and focus the image. The trouble with refracting telescopes was that the image was blurry along the edges. This problem was resolved with the design of a new telescope called a reflecting telescope. A reflecting telescope uses a combination of mirrors to reflect and focus the image. Isaac Newton is credited with inventing the first practical reflecting telescope.

Newton’s Reflecting Telescope

After spending time studying optics and the nature of light Isaac Newton became convinced that the image blurriness, called chromatic aberration, could not be eliminated in a refracting telescope design. Chromatic aberration happens because the lens acts as a prism, splitting the light into its various wavelengths. Each of these wavelengths is bent at a slightly different angle resulting in a failure to focus all the different wavelengths (different colors) at a single point, creating the blurred image. Newton did extensive experiments with lights and a prism, so he decided to create an entirely new design for his telescope rather than attempt to improve the design of the refactors.

In 1668 Newton created his first reflecting telescope. This telescope consisted of a large concave primary mirror that focused light on a smaller, flat diagonal mirror which reflected the light into an eyepiece on the side of the telescope. Since no light is being passed through a lens (all of the light is reflected) there is no chromatic aberration. He presented his telescope to the Royal Society of London in 1672.

Although Newton was the first time build a reflecting telescope the idea had been proposed earlier by other people, most notably by James Gregory in 1663 book Optica Promota. Earlier still, Italian astronomer Niccolo Zucchi may also have attempted to construct a reflecting telescope as early as 1616, but his device had difficulties producing a quality image.

Reflecting telescopes have several advantages over the refracting telescope. Significantly, the original refracting telescopes suffered from chromatic aberration noted above which is an optical condition caused by the lens bending light waves onto different focal planes. This results in a magnified yet blurry image. Reflecting telescopes avoid this problem since mirrors always reflect light waves in the same way. This simple fact is obvious to anyone who has looked in the mirror and seen a clear image of themselves. Today, nearly all large astronomical telescopes are reflecting telescopes due to its various advantages in image clarity, cost, and weight over the refracting telescope.

The Reflector after Newton

Despite these advantages it took some time for reflecting telescopes to surpass refracting telescopes as the industry standard. William Hershel was the first person to make significant discoveries using a reflecting telescope. Herschel became interested in astronomy in the 1770s and took to building his own reflecting telescopes to do his research. His early work consisted of searching for binary star systems, during which he made his famous discovery of a new planet in our solar system, Uranus. Uranus, like the classical planets is viable to the naked eye and had been observed before, but was always thought to be a star. In March 1781 Herschel viewed first the planet through his telescope. After subsequent observations using the technique of parallax on fixed stars was able to observe its movement and he initially reported it as a comet. After several more months and with the collaboration of other astronomers it was eventually determined to be a new planet in our solar system.

An Illustration of William Herschel's 40 foot long reflecting telescope — An Illustration of William Herschel’s 40 foot long reflecting telescope
(Credit: Charles Hutton’s Philosophical and Mathematical Dictionary, 1815)

Herschel continued to make improvements to his telescope design and in 1789 he completed his largest ever, building a huge 40 foot long telescope that contained a mirror 48 inches in diameter. At the time of its completion it was the largest scientific instrument every built. The building of larger and larger telescopes had continued to the present day . As of 2021, the largest reflecting telescopes is the Gran Telescopio Canarias in Spain that has a mirror diameter of over 34.2 feet. On Christmas Day 2021, the James Webb Space Telescope, the most powerful telescope ever put into space, was launched to replace the famous but aging Hubble Space Telescope.

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1656: Pendulum Clock

Posted on February 15, 2018January 12, 2024 by Dan

Since the dawn of civilization timekeeping has been an important aspect of human cultures. Sun dials, water clocks, candle clocks and the hourglass were used as early timekeeping instruments but they proved to be unreliable. Mechanical clocks began to appear in Medieval times but these were typically large and clunky devices which also lost up to two hours over the course of a day, again proving to be unreliable. As the economies of civilization became more complex and technology advanced the demands of accurate timekeeping became increasingly necessary. An innovation in clock design was critical to improve the clocks accuracy. This innovation finally arrived in the 17th century with the invention of the pendulum clock.

Swinging to a More Accurate Clock Design

The pendulum clock was invented by the Dutch mathematician Christiaan Huygens in 1656. The pendulum clock quickly established itself as the worlds most accurate time-keeping device. It was accurate up to a degree of about fifteen seconds per day making it the most accurate timekeeping device until the invention of the quartz clock in late 1920s.

Huygens built on the work of Galileo Galilei’s experiments with the pendulum. Galileo had made some interesting observations about pendulums which he mentioned in several of his books. In the course of time some of his observations have not been proven completely accurate. In any case this are the salient points Galileo noticed:

All pendulums nearly return to their release height
All pendulums eventually come to rest with lighter ones coming to rest more quickly
The oscillation period is independent of the bob weight
The oscillation period is independent of the amplitude
The square of the oscillation period is proportional to the length of the pendulum

It is with this information in mind that Christiian Huygens had his insight that the pendulum would make for a terrific timekeeping devise while overcoming an illness in December 1655. He immediately set to work on inventing a prototype design.

The Pendulum Clock Design

All pendulum clocks have at least five parts making up its mechanism. They are a power source, a gear train, an escapement, the pendulum, and a dial – typically the clock face – showing how much the escapement has rotated and hence how much time has passed. Its power source is a weight that very gradually drops and is reset by winding it up. A complicated series of gears takes the energy from the weight and applies it to the pendulum, which rocks a lever called the escapement that locks and unlocks a gear at a constant speed. Since a pendulum swings at a constant speed regardless of the distance it swings in provides an extremely accurate method of keeping time. The clock only works on a steady and level surface – and motion will disrupt the movement of the swinging pendulum

On June 16th, 1657, one year after Christiaan Huygens designed his prototype pendulum clock, he had the design patented. He enlisted a Dutch clockmaker by the name of Salomon Coster the begin construction of pendulum clocks. It did not take long for Huygens’s pendulum clock, in the form of the Coster clock, to spread rapidly all over Europe.

In 1673 Huygens published his influential treatise on pendulums, Horologium Oscillatorium. In it he noticed that early pendulum clocks had wide swings which made them less accurate. Clock makers soon realized that smaller swings of only a few degrees provided for greater timekeeping accuracy while requiring less power and creating less wear and tear on the device. Further design improvements also occurred around this time. The use of an anchor escapement in the 1670s led to a narrower clock design and clock case. The familiar long, narrow clock cases, designed by the English clockmaker William Clement in the 1680s, became known as grandfather clocks. Further improvements in timekeeping accuracy allowed for the minute to begin appearing on pendulum clocks by the 1690s.

Despite these clocks remarkable accuracy there was a significant drawback to the pendulum clocks design. It only operated accurately when it was flat, level, and stationary. This provided for significant challenges for using the clock on ships and later on trains. In fact as Huygens soon realized, it wasn’t practical at all to use pendulum clocks at sea. It would take another half century until the invention of the marine chronometer that accurate timekeeping could be kept at sea. But for the first time in human history and throughout the next two centuries, households, factories, and public institutions had a standard of timekeeping accurate enough that everyone could use. It allowed for the interconnected and fast paced life of the Industrial Revolution to thrive.

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Christiaan Huygens

Posted on February 15, 2018January 23, 2024 by Dan

Christiaan Huygens (1629 – 1695) played a primary role in the discovery into the nature of light, developed the tools of calculus, published the first book on probability theory, and invented the first pendulum clock. These accomplishments and more made him an important figure in the early scientific revolution.

Huygens was born into a wealthy Dutch family, excelled early in mathematics which he studies later on in college. His early work focused on mathematics but he quickly turned his attention to the telescope in hopes to better understand how they work. He used improved telescopes to identify the rings of Saturn and discover its largest moon, Titan.

In 1666 Huygens became a founding member of the French Academy of Sciences, one of the oldest scientific organizations in the world. However Huygens is best know by his work on the nature of light. Through his observations and experiments with light he became a proponent of the wave theory of light which was rejected by Isaac Newton for his particle theory of light. The wave nature of light was confirmed by a double slit experiment by Thomas Young in 1803 and today we accept that light acts both as a wave and a particle.

Isaac Newton

Posted on February 11, 2018January 23, 2024 by Dan

Born on Christmas Day in 1642, the world was gifted Isaac Newton (1642 – 1727) who went on to become the greatest scientist of his era and one of the most influential persons of all time. He made a number of revolutionary discoveries involving mass, inertia, motion, gravitation, and optics. In the process of achieving some of those discoveries, he invented an entire new field of mathematics called calculus. Indeed, to see further than Newton one would have to be standing on the shoulders of a giant.

Newton grew up in England in an nurturing family environment as his father died before his birth and his mother left him in the care of his grandmother shortly after. This early childhood experience surly affected his emotional state in adulthood. Newton attended Cambridge University in 1661 at the time that the Scientific Revolution was underway. In 1665 an outbreak of plague forced the university to close forcing Newton to return home. During the next 18 months Newton produced some of his scientific best works.

As prolific as Newton’s lifetime scientific achievements were, he squandered much of his time during the 1670s studying alchemy, the occult, and writing religious tracts. Many of us think of Newton as the first of the modern scientists but as John Maynard Keynes perceptively noted he was more like the last of the magicians. He became and increasingly isolated individual with an abrasive personality. It was only with the encouragement and financial backing of his friend Edmond Halley that he published his most famous work Principia in 1687 which laid out his laws of motion and universal gravitation.

Newton’s scientific achievements awarded him an enormous amount of fame, influence, status, and wealth. He was made a Fellow of Trinity College in 1667, elected Lucasian Professor of Mathematics in 1669, elected a Fellow of the Royal Society in 1672, elected a Member of Parliment in 1689, became Warden of the Mint in 1696, Master of the Mint in 1698, elected President of the Royal Society in 1703, and Knighted by Queen Anne in 1705.

1687: Principia

Posted on February 10, 2018January 23, 2022 by Dan

Issac Newton’s 1687 publication of Mathematical Principles of Natural Philosophy, more commonly known as Principia, may have been the most important and influential scientific works of literature of all time. It’s impact on scientists was enormous and it immediately introduced a new paradigm in physics.

The State of Science Prior to Newtonian Physics

The 17th century marked an advancement and flourishing of modern science. Aristotelian teachings and the ideas of Christian theologians were coming into question as new observations about the way the universe actually worked were being discovered. Galileo Galilei had recently peered further into the universe, proving once and for all that not all heavenly bodies orbit the Earth. The French philosopher and mathematician Rene Descartes placed an emphasis on mathematical explanations. Newton titled his Principia as an allusion to Descartes’ Principles of Philosophy.

The discovery that most affected Newton and his publishing of the Principia was that of Johannes Kepler. One of the biggest problem facing astronomers at the time was determining how the planets moved against the background of fixed stars. Kepler had put forth three “laws” of planetary motion that show the planets move in an elliptical motion around the Sun. However at the time these laws were known to be close approximations, and there were several other methods that could be used to calculate planetary motion with comparable accuracy.

Newton’s Masterpiece

Newton's Principia — Newton’s *Principia*

Isaac Newton may have solved the problem of orbital dynamics in 1679, but his solution was unknown to the rest of the scientific world. This changed in 1684 when Edmond Halley came to visit Newton while in Cambridge. During their conversations the topic of planetary motion was brought up. According the the French mathematician Abraham Demoivre’s account of a conversation he had with Newton: “The Dr asked him what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipsi. . . . Dr Halley asked him for his calculation without any further delay. Sir Isaac looked among his papers but could not find it, but he promised him to renew it, and then to send it [to] him.”

In 1684 Newton made good on his promise and sent to Halley a paper on orbital dynamics titled On the Motion of Bodies in an Orbit. After two and a half years of work Newton expanded on this paper to produce his masterpiece Mathematical Principles of Natural Philosophy. Newton published his work into a three Book series. Book One is focused on motion in a medium devoid of resistance. Book Two is focused with motion in a resistive medium. Book Three is an analysis of some specific celestial data and the focuses on the consequences of universal gravitation.

Principia was important for its all-encompassing explanation of physics expressed in mathematical form. Two major ideas were expressed in the book. First, it stated Newton’s famous laws of motion which form the foundation of classical physics. These are:

The law of inertia: An object at rest remains at rest. At object at motion will continue moving in a straight line at a constant velocity unless acted upon by a force.
The law of force: The famous equation F=MA where force equals mass times acceleration.
The law of equal and opposite reaction: This law states that when two bodies impact they apply forces to each other that are equal in magnitude and opposite in direction.

Second, it stated Newton’s law of universal gravitation. This law states that two masses attract each other by a constant multiplied by the product of the two masses and divided by the square of the distance between them. Stated another way, this is an inverse-square law of gravitation. All of these laws were proven with rigorous mathematical and experimental evidence.

Principia’s Lasting Legacy

The methods and laws in the Principia provided an unrivaled and highly accurate description of the physical universe for the time, making it one of the most important science books ever published. It established mathematics as the language of the physical sciences and continued in the Baconian tradition of relying on observation and experimentation. Newtonian mechanics, as his principles became to be known, were extremely important due to its useful value in everyday life. These methods and equations could be used in a variety of fields such as engineering, astronomy, industry, and agriculture.

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Rene Descartes

Posted on February 3, 2018January 23, 2024 by Dan

The French mathematician Rene Descartes (1596 – 1650) insightfully connected the bridge between geometry and algebra by developing analytic, or what is now called Cartesian geometry. Aside from his brilliant mathematical works he was extremely influential in other area’s of science and philosophy.

Descartes was born in France to a bourgeois family, educated at a Jesuits college, and joined the army at the age of 22 where he met a man named Isaac Beekman who kindled his interest in science and left an indelible stamp of influence on his early adulthood. Descartes then moved to the Netherlands where formulated some of his most influential ideas. While Descartes was working with curves he realized that the key to solving them was by using coordinates. In 1637 in his appendix to his book Discourse on Methods titled La Geometrie, Descartes shows how a single equation can be used to explain every single point along a curve. This work laid the foundation for the invention of calculus by Isaac Newton and Gottfried Leibniz.

In addition to his mathematical contributions Descartes was also influential in philosophy and science. He was one of the first to break away from the Aristotelian Scholastic mode of thought, which was extremely entrenched in intellectual institutions during his life. He wrote speculations on a multitude of topics including the nature of the mind, mind-body dualism, God, the sensations and passions, and morality.

1662: Boyle’s Law

Posted on February 2, 2018November 11, 2023 by Dan

The discovery of the relationship between gas volume and air pressure was published by Robert Boyle in 1662 and is known today as Boyle’s Law. It states that air pressure is inversely proportional to the volume it occupies, for a fixed temperature in a closed system.

The Pressure-Volume Correlation

In early human history an understanding of the universe was mostly marked by deep philosophical thinking. Questions were poised and then mulled over. The answers were logical explanations that came directly from the human mind. Little emphasis was placed on observation and experimentation. Starting around the 16th century the field of science was beginning to make radical changes. It marked a period of revolution in a way of thinking and a desire to know and understand natural laws. The new way of thinking affected all aspects of society, influencing and altering belief systems, politics, and the economy. One critical advancement in the way science was conducted was that the mathematization of science was beginning to appear and take hold. Boyle’s Law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities.

The foundations of Boyle’s Law was laid on experiments with air pressure and connected with the work of Itialian physicist Evangelista Torricelli and the French mathematician Blaise Pascal. Torricelli’s work on the vacuum began to break down the deeply held Aristotelian notions about the weight and nature of air. Further experiments at this time were conducted that illustrated the compression and expansion abilities of air. Pascal, having learned of Torricelli’s experiments, also began experimenting on the nature of air. He noted that when a half inflated balloon was carried up a mountain (to an place of different air pressure) the balloon would expand. He therefore speculated that there was a relationship between the volume of air and the pressure exerted on it.

Robert Boyle and Robert Hooke experimenting with an air pump
(Credit: Wikimedia Commons)

The original hypothesis was given to Boyle by Richard Towneley and his assistant Henry Power in 1661 via letter. Power performed his first experiments on air pressure in 1653. He performed more conclusive ones in 1660 with the collaboration of Richard Towneley. These experiments were similar in nature to the Torricellian experiments that were commonly being performed at the time. Boyle was also familiar with the Torricellian experiments when he began systematically investigating air pressure in 1658. He was working with Robert Hooke, who was designing a superior air pump that they were using to investigate the elasticity of air. In 1661 Towneley and Power deduced that there was a proportionality with the volume of air and the external air pressure in their experiments. Boyle devised a series of experiments to check the hypothesis. He repeated several experiments using different amounts of mercury in a J-tube, an apparatus for measuring both the volume of air and its pressure. Publication followed after Boyle and Hooke had successfully verified the Towneley/Power hypothesis. In 1676 the French chemist Edme Mariotte also came to the same conclusion independently but in addition discovered that air volume changes with temperature.

Boyle’s law can be expressed mathematically as $P\propto {\frac {1}{V}}$ where P is the pressure of the gas and V is the volume of the gas. In simple terms it means that if volume decreases then pressure increases, and vice versa. Boyle’s Law is an equivalency law which can also be expressed as P₁V₁=P₂V₂ where P is the pressure of the gas and V is the volume of the gas.

Applications of Boyle’s Law

Practical applications of Boyle’s Law can be applied to nearly anything that involves compressed air to do useful work. One common contemporary example is the aerosol spray. Aerosol spray works by having its contents contained in a can under extremely high pressure. When the nozzle is pressed down the pressure of the gas or liquid inside the can is decreased. As a result the compressed gas expands causing its contents to spray outward. This is how hairspray, spray paint, and every other aerosol spray works. Boyle’s Law can also be applied under varying temperatures. A basketball bounces less and your car tires air pressure decreases as it becomes colder outside.

However the most vital example of Boyle’s Law at work is in the human respiratory system. You bring air into your lungs by contracting your respiratory muscles to increase the volume in your chest, and hence decreasing the pressure on your chest. Basically air moves from your lungs to the atmosphere and back due to a change of pressure inside and outside of your chest. The mechanics of breathing are nicely explained by this scientific principle!

Continue reading more about the exciting history of science!

Robert Boyle

Posted on February 2, 2018January 23, 2024 by Dan

The scientific contributions of Robert Boyle (1627 – 1691) cover a variety of subjects including physics, hydrostatics, and the earth sciences, however he is best known for his contributions to the field of chemistry. Through his efforts, his work helped to break away the scientific world from alchemy and to usher in modern chemistry.

Born in Ireland to a wealthy family, Boyle attended a private boarding school at the age of eight, followed by a tour of the European continent with his French tutor that ended in Italy at the time when the great Galileo died. This experience had a profound impact on Boyle and when he returned to England where he hooked up with other like-minded individuals to form the “invisible college” where they met, often at Gresham College, and was to be the precursor of the Royal Society of London.

At the same time Boyle hired Robert Hooke as his assistant. The two like-minded men collaborated on many discoveries including Boyle’s Law, which states that pressure and volume of gas have an inverse relationship at a fixed temperature.

The publication of The Sceptical Chymist in 1661 which is considered by many as the beginning of modern chemistry. The book is composed as a dialogue and in it he rejects the ideas of Aristotelian elements of earth, fire, wind, and water and suggests the idea that matter consists of atoms in motion and that every phenomenon is the result of the collisions of these particles.