Abu Ja’far Muhammad ibn Musa al-Khwarizmi

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Abu Ja’far Muhammad ibn Musa al-Khwarizmi (780 – 850) was one of the most influential medieval Arab mathematicians.  He made two remarkable contributions to mathematics – introducing our modern number system into western Europe, the Hindu-Arabic numeral system, and was a pioneer of early algebra.

The Life of Al-Khwarizmi

Abu Ja'far Muhammad ibn Musa al-Khwarizmi
Abu Ja’far Muhammad ibn Musa al-Khwarizmi

Al-Khwarizmi lived in Persia and was born in the city of Khwarizm, which is now part of Uzbekistan.  Very little is known about his early life.  As he grew older, he worked in the House of Wisdom under the caliphate of Al-Ma’num.  The House of Wisdom was a public academy, research institution, and intellectual center in Baghdad that acquired and translated scientific, mathematical, and philosophical treatises, particularly those of ancient Greece.  They also published original work, two of which Al-Khwarizmi is most famous for.

Around 820 Al-Khwarizmi published On the Calculation with Hindu Numerals.  Al-Khwarizmi quickly realized the ease of use and efficiency of this decimal numeral system and the popularity of his book is largely responsible for spreading Hindu-Arabic numeral system throughout Europe.  It was Latinized Algoritmi de numero Indorum, and Al-Khwarizmi came to be known in Latin as Algoritmi.  From his name we derived the term algorithm.

About a decade later Al-Khwarizmi published his other famous treatise, The Compendious Book on Calculation by Completion and Balancing.  In it he published the first know linear and quadratic equations. In doing so he revealed the techniques of algebra to the mathematical world.  The term algebra is derived from al-jabr, one of the operations he used to solve his quadratic equation.

Al-Khwarizmi’s work and impact wasn’t immediately felt in Europe as it took until around the 12th century for his work to be translated and spread into Europe.  His original manuscripts have been lost, probably when The House of Wisdom was destroyed during the siege of Baghdad in 1258.  Only his Latin translations survive.  However, his popularization of our modern numerical system, his pioneering work in mathematics and early algebra, as well as his other lesser-known works in astronomy and geography cement his legacy as one of the most influential scientists of the medieval era.

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1859: On the Origin of Species

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In 1859 Charles Darwin published his landmark book On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life.  This books marks the beginning over modern evolutionary biology.  Darwin used the phrase “decent with modification” to describe the process of evolution. 

The Evolution of the Idea of Evolution

Prior to Darwin the subject of evolution was subject to much speculation, uncertainty and debate.  The idea that living organisms change over time was controversial for a variety of reasons.  The idea is not self-evident because of the immensely long timescales required to make evolution happen.  More controversial was its direct contradiction with the teachings of Christianity, where the Bible claims that God created species in their current from.  However, by the 18th century some evidence began turning up in support of the idea that organisms have changed over time.  

The Swedish botanist Carl Linnaeus developed a system for naming and classifying living organisms.  His work provided some illuminating insights and a more comprehensive understanding into the relationships between different species. 

The Evolutionary Tree of Life
The Evolutionary Tree of Life
(Credit: Leonard Eisenbreg)

In the early 19th century, the French naturalist Jean-Baptiste Lamarck proposed an early version of a theory of evolution. During this time the topic of evolution was of interest and debate among some naturalists. His theory centered on two main principles: on the law of use and disuse, and the inheritance of acquired characteristics. Lamarck’s theory, although not considered to be a valid mechanism for evolutionary change, was influential in shaping early evolutionary thought. His ideas sparked further interest, discussion and debate on the topic.

The Development of Darwin’s Idea

Charles Darwin developed his theory of evolution by natural selection over the course of many years through careful observation, research and study. Darwin had his first insight into evolution on his famous Voyage on the HSM Beatle from the years 1831-1836.  During this voyage he collected a huge number of specimens made many important observations, especially in South America and the Galapagos Islands.

This map traces the route of Charles Darwin's voyage on the HMS Beagle from 1831-1836.
This map traces the route of Charles Darwin’s voyage on the HMS Beagle from 1831-1836.

The Galapagos Islands provided the location from some of Darwin’s most crucial observations.  While traveling to the different islands he noticed slight variations among similar species from one island to another.  For example the shapes of the beaks of finches differed depending on their diet and environment.  After returning home from his voyage, Darwin continued to reflect and do research while further developing his theory.  

Darwin was also heavily influenced by Thomas Malthus, an British economist who wrote about population growth.  Malthus proposed the populations tend to grow exponentially, while food production grows at a much slower rate, leading to competition and a struggle for survival.  Darwin expanded on this idea, leading to his concept of natural selection.  He spent over two decades refining his ides before finally publishing his theory in “On the Origin of Species” in 1859.

The Origin of Species: Darwin’s Theory of Evolution by Natural Selection

On the Origin of Species
The Origin of Species by Means of Natural Selection

Darwin’s book begins with the topic variation under domestication, or what some call artificial selection.  While the natural environment or habitat of a species selects which traits most help an organism survive and reproduce humans have the ability to select for specific traits in domesticated plants and animals.  Gradual changes, such as selecting for speed in an English racehorse, accumulate over time and produce noticeable differences from the older ancestors.  Darwin makes clear early on that heredity is key in explaining variation.

The book then progresses into a discussion on natural selection.  He talks on the idea the struggle for existence and the limits to population increase as forces pressuring species.  He credits Thomas Malthus for his contributions to this idea.  He explains his main principle of evolution by natural selection which can be summed up as the cumulative adaptation to environmental pressures.  Very gradually, over long stretches of time, species become more and more adapted to the environment in which they live.

Darwin provides a preponderance of evidence for his theory.  He uses Charles Lyell’s work on geology to show similarities between uniformitarianism and biological evolution.  He links classification schemes to his idea of decent with modification.  He talks about “rudimentary organs” or vestiges, organs left over which no longer have any function.  He shows how the geographical distribution of plants and animals falls into a pattern that supports his theory.  It is because of his careful collection of evidence that his work became so popular and his idea’s so quickly accepted. To this day, Darwin’s Theory of Evolution is considered the cornerstone of biology and essential to understanding the diversity of life on this planet.

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Charles Darwin

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Charles Darwin portrait
Charles Darwin

Charles Darwin (1809 – 1882) was an English naturalist and biologist who changed the way we think about life on this planet.  In 1859 he published his famous book On the Origins of Species, making the beginning of evolutionary biology and cementing his legacy as the most influential biologist in history.

Charles Darwin was born in Shrewsbury, England, the fifth of six children to his father Robert Darwin and mother Susan Wedgwood.  He attended the University of Edinburgh Medical School but quickly neglected his studies and his father sent him to Christ College, Cambridge with the intentions to have him join the clergy.  While at those university’s Darwin learned much in the intellectual environment, but little on the topics he was sent to study for.  However he was exposed to many free thinkers and a variety of ideas in science, particularly biology and geology.

Darwin was able to put these ideas into practice when he traveled the globe from 1831 – 1836 on the HMS Beagle.  It was during and after this trip that he was able to gather a substantial amount of evidence and privately begin to formulate his ideas on evolution by natural selection.  Upon Darwin’s return from the trip he was immediately received as a celebrity scientists in British circles and had cemented his career as a scientist.

Over the next twenty years Darwin continued to amass evidence to the original framework that he developed on his Beagle voyage.  He was even reluctant to publish his work, in fear of retaliation from the Catholic Church.  However he read a letter by Alfred Russell Wallace describing natural selection in similar terms to his and this motivated Darwin to get to work in publishing his work.  On July 1, 1858 both Darwin and Wallace presented a joint presentation to the Linnean Society presenting their work on natural selection.  It received little attention due to a lack of evidence.

For the next fourteen months Darwin continued to work on his book, and on November 24, 1859 On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life was published and immediately sold out of its 1,250 copies.  This book was the culmination of Darwin’s accumulation of evidence over the decades.

By the time of Darwin’s death in 1882 most scientists had accepted evolution as a fact. That is a powerful testament to how convincing his arguments and evidence was and is why he is regarded as one of the most influential scientists of all time.

1830: Principles of Geology

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Principles of Geology was a groundbreaking work that promoted and popularized James Hutton’s concept of uniformitarianism.  It was published by Charles Lyell in three volumes from 1830 to 1833. 

The State of Geology Prior to Lyell

Principles of Geology
Principles of Geology

Prior to the work of Charles Lyell, the field of geology was still in its infancy. The field as a scientific discipline for the most part lacked a systematic approach. The scientific method of observation and deduction was rarely applied. In addition to the lack of structure, it was heavily influenced by religious interpretations of the Bible and various speculative theories lacking significant evidence to back them.

There were however, a few notable ideas. In the early 19th century, catastrophism was the leading geological explanation of how the Earths features were formed.  Catastrophism is the idea that sudden, quick, and violent events shaped the Earth’s features.  It is easy to see how catastrophism can be aligned with religious narratives, such as the biblical story of Noah’s flood. Many people, including a few scientists of the day, also believed that the Earth was only a few thousand years old. As with catastrophism, some of this belief was based on religious texts.

A major reason for many of these speculative theories was that the scientific discipline of geology was just beginning and did not have well established principles or regulations. There was a poor understanding of geological formations and how to interpret them. The same went for fossils. The concept of extinction was new and not even widely accepted, so the significance of fossils in reconstructing Earth’s history was not fully recognized.

In this mix of confusion and speculative ideas was the concept of uniformitarianism. Uniformitarianism is the idea which says the physical features of the Earth were transformed by slow, gradual forces, such as erosion and sedimentation, which are still at work today.  This idea was first championed by James Hutton, but Charles Lyell was soon to take the baton and run with it.

Principles of Geology

Lyell’s Principles of Geology had a profound impact on the science of geology. The work provided a framework for understanding the Earth’s past based on observable natural processes. One of the more controversial ideas at the time was that it strongly argued for the antiquity of the earth. This idea was met with particularly strong resistance among resistance groups of the day, however the accumulation of scientific evidence has eventually confirmed Lyell’s assertions.

In volume one of Principles of Geology, Lyell offers evidence and lays out his argument for uniformitarianism.  In volume two, Lyell extends this principle to organic processes.  The third volume is largely a syntax of geology, and he defines four periods of the Tertiary. Here are a few summarized points, taken from all three volumes.

  • Uniformitarianism: Lyell argued that the geological processes observed in the present are the same as those that have operated throughout Earth’s history.
  • Gradualism: Lyell argued that geological change occurs gradually, over long periods of time rather than by sudden and dramatic events.
  • Stratigraphy: Lyell recognized the importance of studying rock layers or strata to understand the sequence of events in Earth’s history.
  • Geological Time Scale: Lyell recognized that Earth’s history is extremely long and he divided it into distinct periods based on the fossils found in rock layers.
  • Erosion and Uplift: Lyell explained how the geological process of erosion and uplift can gradually shape the surface of the Earth. He highlighted the role of natural forces, such as wind, water, and ice in shaping various features of the Earth such as wearing down mountains and carving valleys.
  • Volcanism and Earthquakes: Lyell examined the evidence for volcanoes and earthquakes and provided explanations for their occurrence.

Impact on Charles Darwin

Principles of Geology volume two was one of the few books that Charles Darwin took with him on his famous HMS Beagle voyage, which lasted from 1831 to 1836.  Reading this book seeded idea’s in Darwin’s mind that eventually lead to his Theory of Evolution by Natural Selection.  The motto of the book was “the present is key to the past” and Darwin took this idea and naturally extended it to biology. The concept of deep time, that the Earth was many millions of years old, had a profound impact on Darwin’s thinking. Gradual changes over long periods of time later became central to his theory of evolution. It wasn’t only Lyell’s idea’s that influenced Darwin, but his behavior and approach to science. Lyell’s emphasis on careful observation and reliance on evidence also shaped Darwin’s scientific approach.

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Charles Lyell

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Charles Lyell portrait
Charles Lyell

Charles Lyell (1797 – 1875) was a Scottish geologist who popularized and created the general acceptance of James Hutton’s concept of uniformitarianiam.  Uniformitarianiam is the idea that physical features of the Earth were transformed by slow, gradual forces such as erosion and sedimentation which are still at work today. 

Lyell was born into a family of wealth, growing up in an estate house with plenty of good farmland.  His father was a botanist who exposed him to nature at an early age.  Lyell attended Exeter College, Oxford in 1816 where his interest in geology was stimulated by lectures he heard by William Buckland – a man known for attempting to reconcile the biblical flood with geological observations.  By 1823 he was elected to the Geological Society of London. 

By the 1830s Lyell was ready to publish some books on geology and his first book published turned out to be his most famous and most influential book.  Principles of Geology was published in three volumes from 1830 – 1833.  In this book he used the concept of uniformitarianism to explain the Earths features.  This was a very different concept from the conventional wisdom of the day, catastrophism, which stressed sudden, quick, and violent events.  “The present is the key to the past” was the motto of his book.  It means that all of the observable processes present today can be used to describe those of the unobservable the past.  

Charles Darwin read Lyell’s work while on the Beagle, and it heavily influenced his thinking.  As Lyell saw that geological forces active today were also active in the past, Darwin saw that biological forces active today were also active in the past.  The slow, gradual change of a species from generation to generation is what led to speciation, a position on which Lyell gradually came to accept over time, offering a lukewarm endorsement of Darwin’s evolution by natural selection in his Antiquity of Man in 1863. 

James Hutton

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James Hutton portrait
James Hutton

James Hutton (1726 – 1797) is widely considered the “Father of Modern Geology” as the originator of the theory of uniformitarianism  – the idea that the physical features of the Earth have evolved slowly over time and the same natural processes are still at work today.  He was a meticulous observer who noticed and extrapolated the effects that volcanoes, erosion and other slow moving processes would have on the planet.

Hutton was born in Scotland and attended the University of Edinburgh at age fourteen and completed courses at various universities throughout Europe.  After his schooling Hutton worked on a farm that he had inherited.  This work provided him with first-hand experience in observing the landscape while cultivating his interest in the features of the Earth’s surface.

His ideas on geology began to form in the 1760s, however he was never in a rush to publish his work.  In fact it took him nearly 25 years before his Theory of the Earth was read to the Royal Society of Edinburgh.  This work laid the foundations for modern geology and seeded the idea of uniformitarianism.  Hutton inferred from his observations that the enormous pressure and heat of the inner Earth could provide the energy to fuse and chemically change sediments into new rocks.  These rocks were eventually lifted out of the Earth through natural processes to form mountains.  Over time erosion reduced the rocks to sediments which were buried layer under layer and returned to the inner Earth.  This process is cyclical, and has occurred many times over.   Hutton’s ideas were unpopular initially, in part because they were in contract with the teachings of the Christianity.

Over time his ideas were further developed and promoted by Charles Lyell, who in turn strongly influenced Charles Darwin’s Theory Evolution by Natural Selection.  Hutton himself stated the basic principle of evolution by natural selection in 1794 which lacked the overwhelming evidence that Darwin had accumulated to prove it.

Pierre-Simon Laplace

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Pierre-Simon Laplace
Pierre-Simon Laplace

Pierre-Simon Laplace (1749 – 1827) was the greatest mathematicians of his day and one of the most influential scientists of all time.  He is sometimes referred to as the Newton of France.

Laplace was born in Normandy, France to a family of modest means and at the age of sixteen was sent to the University of Caen to study theology.  At the University he met two professors of mathematics who spurred his interest in mathematics.  His advanced mathematical abilities were quickly recognized and by the time he was 20 he was working with the famous French mathematician and philosopher, Jean D’Alembert.

Laplace was influential to science in a variety of areas.  His early work in mathematics began on differential equations and his later work helped to advance the fields of statistics and probability.  In-between, published work on celestial mechanics showing the stability of the solar system.  He brilliantly used mathematics and the laws of gravitation to account for the perturbations in the planets orbits and their satellites, showing once and for all that the heavenly bodies move in a deterministic manner.  This work also conquered the problems associated with the tides.  He was also one of the first to posit the nebula hypothesis of the origin of the solar system.  Even more remarkable, his work suggested that there are stars so massive that not even light can escape their gravitational field – what we would now call a black hole.

All of these accomplishments happened after he become a member of the Academy of Sciences in Paris in 1773.  There he conducted a majority of his work.  He mostly stayed out of politics and managed to leave Paris and avoid the worst of the French Revolution.  After Napoleon took power in 1799 Laplace was briefly appointed Minister of the Interior, an appointment which only lasted six months.  He mostly continued to stay out of politics and work on mathematics until he died in 1827 in Paris.

1850s: Laws of Thermodynamics

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Laws of Thermodynamics

The laws of thermodynamics are some of the most fundamental laws of physics. They describe the way matter and energy move through the universe, so what is thermodynamics? Thermodynamics is the study of heat (thermo) and motion (dynamics), and its relationship to energy.  These laws were not discovered in a single stroke of genius by one individual. Instead the accumulated knowledge of heat, motion and energy that led to the discovery and formulation of these fundamental laws happened gradually over time and was the result of the work of many individuals. Put another way, the laws of thermodynamics emerged gradually over time as the field of science progressed throughout the 18th century.  Today there are four laws of thermodynamics – the first, second third, and zeroth law.  

Discovering the Nature of Heat

People have learned how to make things hot since they first tamed fire, but never understood the true nature of heat. The concept of heat is a fundamental aspect in understanding how the universe works. A serious investigation of the nature of heat began during the industrial revolution.  The massive economic gains as a result of the revolution provided the impetus for the discovery of these laws, with steam power being the hot topic of the day.  People wanted to understand how steam could drive an engine and how to improve its efficiency.

Count Rumford supervising a cannon boring experiment
Count Rumford supervising a cannon boring experiment
(Credit: Sheila Terry)

The solution to the problem came from Benjamin Thompson, also known as Count Rumford.  While Count Rumford did not directly formulate the laws of thermodynamics, he provided the experimental data that was the basis for the laws.  He did this through a series of experiments involving the boring of cannons.  He observed that the temperature would rise as it was bored, and that this rise in temperature was proportional to the amount of work done in the boring process.  He also observed that heat could be generated indefinitely, and this contradicted the competing caloric theory of heat.

Despite Rumsford’s experimentation’s the caloric theory survived for nearly another half century until the German Julius Mayer became the next person to relate mechanical work to heat quantitatively.  Mayers work did not receive much attention shortly after the British scientist James Joule preformed additional experiments on the generation of heat by friction, electricity, and magnetism. The unit of energy, the Joule, is named in honor of his work. The eventual realization that heat is a form of energy was a critical step in the development of the laws of thermodynamics.

“Nothing in life is certain except death, taxes and the second law of thermodynamics.” – Seth Lloyd

Establishing the Laws of Thermodynamics

In 1824 a French military engineer named Sadi Carnot had expressed some of the ideas that would become the second law.  This contribution came from his publication “Reflections on the Motive Power of Fire” where he analyzed the operation of idealized heat engines and introduced the concept of the Carnot Cycle.

It took a few decades for Carnot’s insights into the nature of heat to be formalized as the laws of thermodynamics.  In the 1850s, Rudolf Clausius and William Thomson fully formulated what became known as the first two laws.  It was Clausius who introduced the concept on entropy.  The third law was formulated in the first decade of the 20th century by Walther Nernst.  The zeroth law came last and was formulated by Ralph Fowler in the 1920s.

The zeroth law was discovered after the first three but named the zeroth law as it provides a frame of reference for the first three laws.  The laws of thermodynamics are as follows. 

  1. Zeroth Law – If two thermodynamic systems each are in thermo equilibrium with a third one, they are in thermal equilibrium with each other
  2. First Law – This is also known as the law of conservation of energy.  It states that in a closed system the total energy remains the same and can only be transferred from one form to another.  Therefore energy cannot be created or destroyed.
  3. Second Law – The entropy of an isolated system not in equilibrium will always increase over time, approaching a maximum value at equilibrium.  The second law dictates the arrow of time.  
  4. Third Law – As temperature approaches absolute zero, the entropy of a system approaches a constant value.

The laws of thermodynamics was a pivotal moment in scientific history.  It revolutionized our understanding of heat and energy, and also laid the groundwork for many technological advancements from the Industrial Revolution to the present day.

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William Thomson

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William Thomson, 1st Baron Kelvin
William Thomson, 1st Baron Kelvin

William Thomson (1824 – 1907) was a Scottish physicist known for early work in thermodynamics and for establishing the Kelvin temperature scale.  In 1892 he was ennobled Baron Kelvin for his work on thermodynamics and is also known as Lord Kelvin – the name from which the Kelvin temperature scale is given in his honor.

William Thomson was born in Belfast and attended Cambridge University where he took an interest in mathematics and physics.  After he graduated he found himself working as a professor at the University of Glasgow where he would stay for the next 50 years.  His early work was in thermodynamics but he his real genius was in that he was able to synthesis a variety of sub-disciplines in physics such as heat, mechanics, electricity, and magnetism.

Thomson is most known for his work in thermodynamics, in particular for his proposal of an absolute temperature scale which is named Kelvin in his honor.  The Kelvin scale uses the same scale as the Celsius but sets the value of 0 at the point at which there is no movement in molecules and hence no heat.  This value is approximately -273.   Thomson also helped to develop the second law of thermodynamics which states the heat moves from hotter to colder objects, or stated another way that entropy always increases. He surmised that if entropy always increased that there would come a point where no work could be done and there would be total uniformity throughout the universe.  This he called the heat death of the universe.

Throughout his life Thomson was active in all area’s of science.  He was a friend and colleague to James Clerk Maxwell and some of his idea’s help Maxwell to formulate his electromagnetic theories.  He was interested in geology and evolution, but he ultimately sided against Darwin’s Theory on Evolution by Natural Selection on the basis that he thought the Earth was no hospitable to life long enough to allow evolution to run its course.  In this he was later proved to be wrong.  Lord Kelvin lived a long and successful 83 years of life and is buried at Westminster Abbey.

Benjamin Thompson

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Benjamin Thompson portrait
Benjamin Thompson

Benjamin Thompson (1753 – 1814) was an American born physicist who made many contributions to our understanding of the nature of heat.  His work helped lay the foundations to the modern theories of thermodynamics.

Benjamin Thompson was born to a farming family in Massachusetts two decades before the American Revolution began.  His life prospects increased when he married a rich widow at age nineteen.  Soon the American Revolution began and he sided with the British, serving as a spy.  In 1776 he moved to England and continued to work for the British government.  He was elected a fellow member of the Royal Society in 1779 for his scientific work on the force of gunpowder.  He soon moved on to Bavaria where he worked as a military commander and in 1791 he was made a count, taking the name of Count Rumford. He returned to London in 1798 and a year later helped to found the Royal Institution of Great Britain.

While working in the military he naturally became interested in the effects of heat on the equipment, especially cannons.  The leading theory of the day was the caloric theory in that heat was a type of fluid that flowed from one substance to another.  While watching the process of boring cannons he noticed that the heat generated in the process was substantial and almost limitless.  He correctly concluded that heat was not a fluid and that it was the motion of the borer creating friction with the cannon that generated the heat.  His knowledge about heat made him a capable inventor and he made improvements to chimneys, fireplaces, stoves, and furnaces.

Count Rumford, as he came to be called, never returned to the United States and in 1804 he married the widow of the French chemist Antonie Lavoisier.  He stayed the rest of his life in Paris continuing his scientific work until he died in 1814.