1900 – 1920s: Quantum Mechanics

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Quantum Mechanics

Quantum mechanics is a paradigm shifting theory of physics that describes nature at the smallest scale. Understanding quantum mechanics requires a journey into the realm of the infinitesimally tiny, where the rules that govern our everyday reality no longer apply. The theory was developed gradually in the early part of the 20th century.

The Birth of Quantum Mechanics

The field of quantum mechanics began emerging very early on in the 20th century as a revolutionary framework for understanding the behavior of particles at the atomic and subatomic levels.  The theory was formed from the observations and experiments of a handful of scientists of that period.  As the 19th century was coming to a close classical physics was reaching its limits.  New phenomena were being observed that it couldn’t explain.  Quantum mechanics first entered into mainstream scientific thought in 1900 when Max Planck used quantized properties in his attempt to solve the black-body radiation problem.  Plank introduced the concept of quantization, proposing that energy is emitted or absorbed in discrete units called quanta. It was initially regarded as a mathematical trick but later proved to be a fundamental aspect of nature. 

Five years later Albert Einstein offered a quantum-based theory to describe the photoelectric effect, earning Einstein the Nobel Prize in Physics in 1921.  The next major leap came from Niels Bohr in 1913.  One of the problems that puzzled physicists of the day was according to the current electrodynamic theory the orbiting electrons should run out of energy fairly quickly, almost right away, and crash into the nucleus.  Bohr’s solution was to propose a model of the atom where electrons orbited the nucleus in definite energy levels or ‘shells’. In this new theory, electrons moving between orbits would move instantaneously between one orbit and another.  They would not travel in the space between the orbits, an idea that became known as a quantum leap.  Bohr published his work in a paper called On the Constitutions of Atoms and Molecules, and for this unique insight he won the Nobel Prize in Physics in 1922.

With these discoveries and others, quantum mechanics became a revolutionary field in physics.  It also became one of the strangest fields in science to study and attempt to understand.  It happens that things on the subatomic level don’t behave like anything we are used to in our everyday experience.  Because of this strangeness some physicists did not like quantum mechanics very much, including Albert Einstein.  Despite its strangeness and messiness, quantum mechanics is known for having a high degree of accuracy in its predictions.  In the decades to follow quantum mechanics was combined with special relativity to form quantum field theory, quantum electrodynamics, and the standard model.

Foundational Principles of Quantum Mechanics

The main principle of quantum mechanics is that energy is emitted in discrete packets, called quanta.  This differs from classical physics where all values were thought possible and the flow was continuous.  Other attributes of quantum mechanics include:

  • Uncertainty Principle:  this states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known with absolute precision.  It was first formulated by Werner Heisenberg in 1927 and arises from the wave-like nature of particles at the quantum level.
  • Wave-Particle Duality:  this describes the dual wave-like and particle-like behavior exhibited by objects at the quantum level.  Electrons, for instance, can exhibit both particle like behavior (localized position and momentum) and wave-like behavior (interference and diffraction) under different experimental conditions.
  • Quantum Entanglement:  this is the curious phenomenon in quantum mechanics that occurs when a pair or group of particles becomes correlated in such a way that the quantum state of one particle is directly tied to the other particle.  This means that changes to one particle instantly affects the other, regardless of the distance between them.  The instantaneous correlation has been confirmed in numerous experiments with photons, electrons, and even individual molecules.  
Double slit experiment showing both the wave and particle behavior of light
Double slit experiment showing both the wave and particle behavior of light

Together, these four principles provide solutions for physical problems that classical physics cannot account for.  Quantum mechanics therefore provides a much more comprehensive framework than classical physics for understanding the behavior of matter and energy at the smallest scales.  However, on some levels its development goes much further than that.  It has transformed our understanding of matter and energy and upended our notions of predictability and determinism, with interesting philosophical implications.  It is one of those areas in science where we are reminded of the power of human curiosity, ingenuity, and the perseverance in unraveling the mysteries of the universe.  

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Max Planck

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Max Planck picture
Max Planck

Max Planck (1858 – 1947) was a German physicist whose revolutionary research led to the foundation quantum mechanics and quantum theory.  Quantum theory was an entirely new type of physics that replaced classic physics on the atomic scale.

Max Planck was born in Kiel, Germany in 1858.  As a youth his family moved to Munich where he enrolled in the Maximilian Gymnasium school where he was introduced to mathematics, astronomy, and mechanics. He graduated at the age of 17 and made the decision to pursue a career in physics.  He promptly enrolled in the University of Munich but after a year he transferred to Friedrich Wilhelms University, where he attended lectures by two of Germany’s most eminent physicists – Hermann von Helmholtz and Gustav Kirchhoff.  He was intrigued by the concept of thermodynamics and began to read over papers written by Rudolf Clausius, one of the pioneers of thermodynamics.  Planck graduated and began teaching physics, first at the University of Munich, then at the University of Kiel, and finally at Friedrich Wilhelms University in Berlin, where he became a full professor in 1892.  It was in this position where he conducted some of his most important research.

In 1894 Planck turned his attention to the problem of black-body radiation.  In 1859 Kirchoff had identified a black-body as a perfect absorber and emitter of radiation at all wavelengths.  Physicists could create a black-body curve by displaying how much radiant energy is emitted at different frequencies for a given temperature of the black-body.  Classical theory was having difficulty in having their predictions match up with the observations.  In order to solve this problem, Planck made a radical proposal.  He proposed that energy could only be emitted in certain, discrete amounts called quanta, whereas classical theory allowed for all possible values of energy. He was able to derive a formula that accurately predicted the energy radiated by a black body – E=hv, where h is Planck’s constant and v is the frequency of radiation. This was the beginning of quantum mechanics and for this work he won the 1918 Nobel Prize in Physics.

Unlike many German scientists of his day, Planck stayed in Germany his entire life and lived through World War 2.  His home in Berlin was destroyed by an Allied air raid where he lost all of his scientific papers.  He died shortly after the war ended in 1947.  The following year the Kaiser Wilhelm Society was renamed the Max Planck Society in his honor.

1938: Nuclear Fission

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The discovery of nuclear fission, a process that releases an enormous amount of energy by splitting the nucleus of an atom, was an explosive moment in the history of science and technology. This incredible discovery directly led to the development of nuclear weapons and nuclear energy production, both of which would become world changing events.

The Birth of Atomic Physics

1979 German postage stamp depicting a diagram of splitting uranium atoms
1979 German postage stamp depicting a diagram of splitting uranium atoms

The discovery of nuclear fission began with the birth of atomic physics and its related research into the components of the atom.  In 1897, J. J. Thomson discovered the first subatomic particle, the electron, while working on experiments with cathode ray tubes.  This discovery prompted further research into the structure of the atom.  Fourteen years later, Ernest Rutherford discovered the nucleus of the atom when to his surprise alpha particles were occasionally reflected straight back to the source when directed at a thin sheet of gold foil.  At this point, the nucleus was thought to only contain positively charged protons, however in the 1920s Rutherford hypothesized the existence of neutrons, a theoretical neutral subatomic particle in the nucleus with no electric charge, to account for certain observed patterns of radioactive decay.

The neutron was quickly discovered by James Chadwick, a colleague and mentee of Ernest Rutherford, in 1932.  The discovery of the neutron proved to be a critical step for the development of nuclear fission technology.  Scientists soon realized that they could use the neutron to split heavier atomic nuclei.  Since the neutron have a lack of electrical charge, they are not repelled by the positively charged nucleus in the way alpha particles are repelled, and they can penetrate and be absorbed by the nucleus.  This makes the nucleus unstable and causes it to split into two or more smaller nuclei, releasing a tremendous amount of energy in the process.  

The Discovery of Nuclear Fission

Shortly after the discovery of the neutron scientists began using it to probe the structure of the atom further.  In 1934 Enrico Fermi began using the neutrons to bombard uranium atoms.  He thought he was producing elements heavier than uranium, as was the conventional wisdom of the time.  

The first experimental evidence for nuclear fission occurred in 1938 when German scientists Otto Hahn, Fritz Strassmann, Lise Meitner, and their team began also bombarding uranium atoms with neutrons.  As was so often the case in the early days of atomic physics, their results were completely unexpected.  Instead of creating heavier elements, the neutrons split the nucleus to produce smaller, lighter elements such as barium among the radioactive decay.  At the time it was thought improbable that a neutron could split the nucleus of an atom.  The experiments were quickly confirmed, and the first instance of nuclear fission had been achieved.  

It was quickly realized that if enough neutrons were emitted by the fission reaction it would create a chain reaction, and an enormous amount of energy would be released in the process.  By 1942 the first sustained nuclear fission reaction had taken place in Chicago.  Hann was awarded the Nobel Prize in Chemistry in 1944 “for his discovery of the fission of heavy nuclei”. 

An Explosive Impact on Civilization

Nuclear fission is the process of splitting an atom into smaller fragments.   The mass of the sum the fragments is slightly less than the mass of the original atom, usually by about 0.1%.  The mass that had gone missing is actually converted into energy according to Albert Einstein’s E=mc^2 equation.  

The discovery of nuclear fission ushered in the atomic age, leading to inventions such as nuclear power and the atomic bomb with world changing consequences.  Almost immediately after its discovery, scientists realized the immense power that could be unleashed by splitting the atom.  In 1939, a group of influential scientists including Albert Einstein drafted a letter to President Frankling D. Roosevelt warning at the potential military applications of nuclear fission and urging the United States government to initiate its own nuclear research program.  They speculated that Nazi Germany may be developing nuclear weapons of their own.  

Cooling reactors of a nuclear power plant
Cooling reactors of a nuclear power plant
(Credit: Wikimedia Commons)

In response, an Advisory Committee on Uranium was formed which eventually led to the creation of the Manhattan Project. The Manhattan Project was officially launched in 1942 and led by J. Robert Oppenheimer at a secret facility in Los Alamos, New Mexico.  The result of the massive scientific and engineering project was the development of the world’s first atomic bomb, which was ultimately used against Japan at the end of World War II.

A more positive benefit to civilization than atomic weapons is the development of nuclear energy.  Nuclear energy produces extremely low amounts of greenhouse gases, making it a much cleaner alternative form of energy from fossil fuels.  If humanity it to solve its climate crisis in the coming century, nuclear energy may prove to be the saving technology. 

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Marie Curie

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Marie Curie
Marie Curie

Marie Curie (1867 – 1934) was a Polish physicist and chemist who overcame a gender discrimination in the sciences to conduct groundbreaking work on radioactivity. Her incredible scientific career awarded her two Nobel Prizes in two different fields and earned her the distinction of being the first woman to win the award.

Marie Curie was born in Warsaw to the parents of two teachers who were very interested in science.  She was the top student in her high school, passionate about science, and wanted to peruse a higher education however there were obstacles in her way.  She was unable to enroll in traditional higher education institutions because she was a woman and her family had little money to support her.  To earn money for herself and to help support her sister’s studies she worked as a tutor.  In her free time she read books on physics, chemistry and mathematics.  In 1891 she departed Poland for Paris, France to join in studies with her sister.  There she studies physics, chemistry, and mathematics, and once again was the top student in her class.  She earned her Ph.D. in physics and in 1985 she married Pierre Curie.  That same year Wilhelm Roentgen discovered x-rays.  The following year Henri Becquerel discovered a new type of ray, resembling that of x-rays yet different, emitting from Uranium.

Curie decided to study these new rays emitting from Uranium and made a handful of remarkable discoveries.  Her husband became interested in her work and joined her.  Their joint work resulted in the discovery of new two elements – Polonium, named for Curie’s home country Poland, and Radium, named for the word ray.  They discovered that Radium would continuously produce heat without any chemical reactions occurring that it emitted rays in far greater quantity than Uranium.  They term they coined for this phenomenon they were observing was radioactivity.  The term stuck.

In December 1903 Marie Curie was the first woman ever to be awarded a Nobel Prize.  Along with her husband Pierre, Marie won the prize in physics for her work in the field of radiation.  The award brought recognition and money for the two scientists, however they would not be able to enjoy it for long.  Pierre was killed in a tragic accident in 1906 when he was hit by a horse-drawn carriage while crossing the street.  Marie Curie continued her scientific work after her husband passed away and was awarded a second Nobel Prize in 1911, this time in the field of chemistry.  By now she had cemented her reputation as one of the elite scientists alive.

Curie continued to work up until her death in 1934 when she died from a rare bone marrow disease.  The disease was likely cause by her long-term exposure to radiation without proper protection.  Her legacy was that of one of the greatest scientists of the time and her work broke barriers for other woman to pursue work in the scientific fields of their choosing.

1913: Bohr Model of the Atom

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In 1913 Niels Bohr proposed a model of the atom based on quantum mechanic physics which helped solve problems of previous atomic models that were based on classical physics. His proposal came to be know as the Bohr model of the atom. 

Earlier Models of Atomic Structure

Bohr Model of the Atom
Bohr’s Model of the Atom

Prior to Bohr’s model of the atom there were various competing models being used.  In 1897 J.J. Thomson discovered the electron through his experiments with cathode ray tubes, setting the stage for the development of his plum pudding model.  In this model electrons were embedded in a positively charged sphere, akin to plums scattered in a pudding.   

Shortly afterwords, Ernest Rutherford announced the surprising discovery of the atomic nucleus which instantaneously and radically transformed our understanding of the structure of the atom.   The discovery of the nucleus paved the way for Rutherford’s nuclear model of the atom, placing the nucleus in the center with electrons orbiting around it, akin to planets orbiting the Sun in our Solar System.  Unfortunately, both of these models had shortcomings because they were entirely based on classical physics.

The most pressing issue was the stability of the atom. According to electromagnetic theory, whenever an electron is accelerated around the nucleus of an atom it should emit radiation resulting in a continuous loss of energy.  This loss of energy would cause the electron to slow down and spiral into the nucleus almost instantly.  Clearly this does not happen in the real world as atoms are stable.  To solve for this problem Bohr used the emerging quantum physics.

Bohr’s Model of the Atom

Bohr’s model resolved this problem by showing the electrons in orbit were consistent with Max Planck’s quantum theory of radiation.  At the turn of the 20th century Max Planck introduced the revolutionary concept of quantized energy to explain the spectrum of black-body radiation.  His key insight was that energy is emitted or absorbed by matter in discrete units, or “quanta,” rather than in a continuous manner as predicted by classical physics.  This insight laid the groundwork for Bohr’s work on the structure of the atom.

In Bohr’s model of the atom electrons would only be able to occupy certain orbits with a specific amount of energy, which he referred to as energy shells or energy levels.  They emit or absorb radiation only when electrons abruptly jump between different orbits.  Using Plank’s constant, the frequency of photons, and some information about the electrons mass and charge, Bohr was able to obtain an accurate mathematical formula for the hydrogen atom.

This was huge improvement on previous models because it incorporated the new quantum physics, however there still were a few problems associated with Bohr’s model.  It was not a particularly useful description for atoms other than hydrogen and it failed to account for the Zeeman Effect in hydrogen.  It was eventually refined and superseded by quantum theory that was consistent the work of Werner Hiesenberg, Erwin Schrodinger, Max Born, and many others.

Impacts of Bohr’s Model of the Atom

Bohr’s model of the atom, with its quantized energy states, was nothing short of revolutionary. It implied several significant impacts on the understanding of atomic structure and on the development of quantum mechanics.  Some of the key impacts of Bohr’s model include:

Bohr's Model of the Atom provided the theoretical framework for understanding the spectral lines of different elements
Bohr’s Model of the Atom provided the theoretical framework for understanding the spectral lines of different elements
(Credit: www.webbtelescope.org)
  • Explanation of atomic spectra: Bohr’s model was successful in explaining the discrete line spectra observed in the emission and absorption of light by atoms.  It provided a theoretical framework for understanding the spectral lines of different elements.
  • Development of quantum theory:  Bohr’s model was crucial in the early development of quantum theory.  It provided one of the first examples of the application of quantum principles to the behavior of electrons in atoms. 
  • Influence on atomic theory: Bohr’s model spurred further research and inspired subsequent scientists, including Werner Heisenberg, Erwin Schrodinger, and Max Born.  These scientists went on the develop more sophisticated quantum mechanical models.
  • Practical technological applications:  Bohr’s model has helped in the development of technologies such as lasers, semiconductors, and nuclear energy.   These technologies depend on an understanding of atomic behavior.  

Overall, Bohr’s model of the atom had a significant impact on physics as a whole.  Its development can be marked as a transition in time between classical physics and quantum mechanics.  While his model has since been superseded by a more comprehensive quantum mechanical model, its significance as a foundational role in the development of atomic theory and quantum mechanics remains important. 

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Niels Bohr

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Niels Bohr (1885 – 1962) was a Danish physicist who significantly improved our understanding of the structure of the atom.  His improved model of the atom solved the problems associated with classical physics and was based on the newer quantum mechanic physics.

Early Life and Education

Niels Bohr was born on October 7th, 1885 in Copenhagen, the capital of Denmark.  He was born into an intellectual and supportive family, and his upbringing consisted of a rich educational environment. His father, Christian Bohr, was a professor of physiology at the University of Copenhagen. His mother, Ellen Bohr, came from a prominent Jewish-Danish banking family with influence in parliamentary circles. The combination of his fathers scientific work and his mothers cultural pedigree together created a home environment that nurtured curiosity and scholarly pursuit. It is no surprise that young Niels Bohr grew up strong in mathematics and was naturally attracted to science at a young age. 

In 1903 he enrolled as an undergraduate at the University of Copenhagen, where he received his master’s and doctorate in physics by 1911.  That same year he traveled to England to work in the Cavendish Laboratory where he met J.J. Thomson. The two scientists didn’t work well together at first, but Bohr soon met another scientist at a different laboratory whom he worked better with. In March 1912 Bohr traveled to Manchester to work with Ernest Rutherford, who had recently won a Nobel Prize in Chemistry for his work on radioactivity.

Scientific Career

Niels Bohr
Niels Bohr

Bohr returned to Denmark in 1912 after having secured a teaching position at the University of Copenhagen.  He brought with him new ideas about the structure of the atom.  It was becoming clear that Rutherford’s model of the atom, based on classical physics, was unstable.  According to classical physics, the electrons moving around the nucleus of an atom in orbit would emit electromagnetic radiation, causing the electron to lose energy and eventually spiral into the nucleus.  The form of electromagnetic radiation being emitted came to be called photons, with each photon having its own precise wavelength and amount of energy.  Quantum physics states that objects emit photons in discrete packets rather than in continuous streams. Using quantum physics, Bohr proposed that electrons are confined to fixed orbits, each with their own distinct energy level.  They only suddenly jump to lower or higher orbits as a precise amount of energy is emitted or absorbed in the atom.  For example to move an electron to a lower energy level it emits a photon of the precise amount of energy that is the difference between the two orbits.  Using Plank’s constant, the frequency of photons, and some information about the electrons mass and charge, Bohr was able to obtain an accurate mathematical formula for the hydrogen atom.  In 1922, Niels Bohr was awarded Nobel Prize in Physics for this work.

Bohr continued to work on quantum physics for the remainder of his life.  He founded the Niels Bohr Institute at the University of Copenhagen.  Later in life he was a part of the Manhattan Project during the Second World War, working with many other great physicists.  He died in Copenhagen at the age of 77.

1781: Discovery of Uranus

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In 1781 Sir William Herschel announced the discovery of a new planet that became named Uranus in the tradition of naming planets after classical mythology. The discovery of Uranus, the seventh planet from our Sun, was a pivotal moment in the history of astronomy. In antiquity, the planets referred to the seven visible points of light that moved across the fixed background of the stars. These included the Sun and the Moon, as well as the classical planets of Mercury, Venus, Mars, Jupiter, and Saturn. The discovery of Uranus marked the first time a new planet was discovered since ancient times and ushered in a new era of exploration within our solar system.

Sir William Herschel Makes a Monumental Discovery

Uranus photo NASA
Photo of Uranus
(Credit: NASA)

Herschel was a German-born astronomer who resided in England.  Born in 1738, Herschel was a polymath with a keen interest in music, mathematics, and of course astronomy.  In 1757 he moved to England where he worked as an organist in Bath. He began his foray into the world of astronomy with a simple, homemade telescope and began observing the stars. He would eventually construct more than 400 telescopes during his lifetime, including a great 40-foot telescope, and most of which were superior to the ones available at the time.

On the night of March 13, 1781, Herschel was conducting a routine survey of the night sky using a 6.2-inch aperture telescope he had constructed himself.  During this survey, he stumbled upon an object that appeared to be a faint, nonstellar object.  Herschel initially reported it as a comet due to its slow movement across the sky and dimness but he continued to observe it over the following nights.  As the months passed by Herschel and the other astronomers he reached out to for input began to suspect differently, as its orbit suggested it was a planet and no tail was visible.  Eventually it became clear the object was a planet as the orbit was calculated by Pierre-Simon Laplace and Alexis Bouvard, two French mathematicians and astronomers.  Their calculations confirmed that Uranus followed a nearly circular orbit around the Sun, consistent with it being a planet.  For the first time in history, our solar system had expanded from the six previously known planets.  

The discovery of Uranus sparked a debate over its name.  Hershel, the discoverer, felt that he had the right to name the planet and he proposed the name “Georgium Sidus” or “George’s Star,” in honor of King George III.  However this name was not well received in the international community, as it broke with the tradition of naming the planets after ancient Roman Gods.  Several alternative names were suggested, but in the end the name Uranus was chosen and eventually accepted as the planet’s name.  

The Planet Uranus and the Impact of its Discovery

Uranus is the seventh planet from the Sun and approximately 2.6 billion kilometers from Earth.   It takes about 84 years for it to complete a full orbit around the Sun.  Its mass is about fifteen times Earths with a diameter of about four times Earth, making it the third largest planet in our solar system.  Accompanying the planet are thirteen rings and 27 named moons.  Composed mostly of rock and ice, it is one of the coldest planets in the solar system with an average temperature of -216 Celsius.  This is due to its low core temperature – it doesn’t generate much heat unlike Jupiter and Saturn.

The discovery of Uranus marked a new era in the exploration of our Solar System.  Most significantly, it showed that our Solar System was much larger than previously thought.  This provided much motivation for further exploration. Perturbations in Uranus’s orbit could not be explained by Newton’s laws of gravity if the only known planets were considered. This led to a hypothesis that there might be other unknown planets leading to the discrepancies. The discovery of Neptune in 1846 and later Pluto in 1930 confirmed this hypothesis, although Pluto was later reclassified as a dwarf planet in 2006. The discovery of Neptune was a triumph for Newton’s laws of gravity because its position was predicted based on the gravitational influence it had on Uranus.

The discovery of a planet more distant than Saturn provided motivation for advances in telescope technology as astronomers recognized the new for more powerful telescopes to study distant objects.  Lastly, the naming controversy that followed highlighted the significance of tradition in the scientific community.  

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Albert Einstein

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Albert Einstein portrait
Albert Einstein

The scientific career of German-born physicist Albert Einstein (1879 – 1955) was one of the most impactful ever in the history of science.  His work led to significant and meaningful changes in our understanding of several fundamental laws of nature including gravity, light, and time.

Albert Einstein was born on March 14, 1879 in Ulm, Germany.  He became interested in nature and mathematics at an early age.  There were two key moments in his childhood that inspired a wonder of curiosity in him.  The first moment was when he was sick at the age of five.  His father brought him a compass and this device stirred his curiosity and sparked his intellect.  At age twelve he stumbled upon a book of geometry that has much the same effect on him as the compass.

In 1896 Einstein enrolled for a science degree at the Swiss Federal Institute of Technology in Zurich.  He graduated in 1900 with his teachers being largely unimpressed with him.  Two years later he would obtain a post of an examiner in the Swiss Federal patent office where he would go on to make some of his greatest discoveries.

The year 1905 was called the year of miracles for Einstein.  He published four scientific papers each with immense importance for science.  His papers topics were on the photoelectric effect, Brownian motion, the Theory of Special Relativity, and the equivalence of mass and energy.  These four papers gained him international respectability and propelled his academic career.  He won the Nobel Prize for Physics in 1921 for his work on the photoelectric effect.

As Einstein began teaching physics at various institutions he began formulating his General Theory of Relativity, which he finally published in 1915. This theory shows how gravity works as a geometric feature of space and time and how its curvature is directly related to the energy and momentum of the present mass and radiation.

As Einstein aged he still worked in science but became more involved in politics.  He emigrated to the United States in 1933 due to the rise of Nazi power in Germany.  During World War 2 he would work on the Manhattan Project which developed the atomic bomb.  This was a difficult moral decision for him since he was a pacifist, but he was uneasy that Germany would develop the bomb first and ultimately decided to help the US develop it before Germany.  Einstein died in 1955 with the legacy of being one of the most impactful scientists in all of history.

3000 BCE: Number Systems

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The invention of number systems designated another high mark for the civilization. Its development led to formal mathematics just as the development of writing systems led to reading and literature. These two tools are responsible for preserving and transmitting the vast, accumulated knowledge humanity has attained in the past 5000 years. These disciplines form the foundation of our modern academic curriculum.

For tens of thousands of years there was not an organized number systems. People counted things using their fingers and toes, if they needed to count anything at all.  Around 25,000 ago there is evidence that people started placing marks on wood and bone, a practice known as tally systems, to keep track of things.  Later on people used markers, counters, or tokens in what is called a token system. These tokens corresponded directly to the goods and things that they represented. Tally systems followed by token systems were proto-numeral systems. This proved was useful for counting and keeping track of smaller amounts but it was not very practical when counting large numbers or attempting to complete more complex mathematical operations.

When humans were hunter-gathers there was not a pressing need to tally items. People lived in smaller groups and generally shared goods in the community. Human emotions such as resentment and distrust were sufficient to regulate fairness in the community. With the advent of agriculture the human condition changed. Soon their were sprawling city-states with tens of thousands of people and a division of labor. Accountants were needed to record debts and taxes owed. This necessity provided the kindling spark to devise a more capable system of keeping track items than a tally system.

Number Systems Take Their Position in Civilization

Babylonian Number System
Babylonian Sexagesimal Number System

Around 3000 BCE the Babylonians developed one of the first known positional number systems.  It was written in cuneiform and was a sexagesimal (base 60) number system.  The major achievement of the Babylonian number system over previous number systems was that it was positional.  This mean that the same symbol could be used to represent different orders of magnitude, depending on where the symbol was located within the number.

The Babylonian system was a significant advancement in the development of mathematics. It provided for the addition and subtraction of numbers and allowed for fractions. It did have some many shortcomings. One such shortcoming is the absence of the number zero. Today we use a base 10 positional number system however there are still some relics of the base 60 number system in our culture.  For example, the circle is 360 degrees and there are 60 seconds in a minute.

Many other civilizations further developed number systems. They Chinese, Egyptians, Aztecs, Mayans, and Inca’s all made use of them. The Greeks in particular showed an intense interest in math. When the conquests of Alexander the Great spread Greek culture throughout the ancient world it marked a turning point in science and math that still lingers, along with so much else from the Greek culture, with us today.

The Story of our Number System

The number system we used today is referred to as Arabic Numerals despite its oldest preserved samples being discovered in India from around 250 BCE. It is uncertain whether this system developed entirely within India or had some later Phoenician and Persian influence. What is certain is that the Arabic’s fully developed and institutionalized this system. A book written around 820 by the mathematician Al-Khwarizmi provides us with the oldest fully developed description of this system. Titled On the Calculation with Hindu Numerals, it is responsible for introducing this Hindu-Arabic numeral system to Europe.

Arabic Numerals
Various Styles of Arabic Numerals
(Credit: Wikimedia Commons)

The Arabic’s designed different sets of symbols which can be divided into two main groups – East Arabic numerals and West Arabic numerals. Although the Arabic language is written from right to left, Arabic numerals are arranged from left to right. The European numeral system was primarily modeled on the now extinct West Arabic numeral system.

The Importance of Number Systems

We would be lost in our world without numbers. They are used to represent goods and things.. They allow the measurement of objects. They are used in the tracking of time. But maybe most importantly, number systems are necessary for mathematics, the bedrock of science.

Pythagorean Theorem
Pythagorean Theorem
(Credit: www.mathworld.wolfram.com)

Much of the world can be expressed in mathematics. It has been echoed by many great scientists that nature speaks to us in the language of mathematics. This is why science depends so much on math. Math has wide-ranging applications ranging from engineering, accounting and finance, navigation, physics and cosmology, computers and coding. Geometry and calculus allows us to construct buildings to live in. Algebra allows us to calculate our loan payments when we purchase that new home. The examples the benefits of using math, just like are numbers, are infinite.

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Dmitri Mendeleev

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Dmitri Mendeleev picture
Dmitri Mendeleev

Dmitri Mendeleev (1834 – 1907) was a Russian chemist who is most famous for publishing his periodic table of elements.  The period table is one of the most recognizable symbols in science.

Mendeleev was born in the Russian province of Siberia in 1834, the youngest of seventeen siblings.  At the age of sixteen Mendeleev moved  with his family to the the Russian capitol of St. Petersburg and enrolled in his father’s old school, St Petersburg’s Main Pedagogical Institute.  At age 21 he got a teaching job in the Crimea but soon returned to St. Petersburg to study for a master’s degree in chemistry from the University of St. Petersburg which he obtained in 1856.

Mendeleev was becoming more passionate about science and more concerned that Russia was falling behind Germany in the field.  He believed improving Russian educational textbooks was one way to close the gap.  In 1861 he published the 500-page textbook Organic Chemistry which won him the Demidov Prize of the Petersburg Academy of Sciences.  He continued to be a a teacher of chemistry and write additional textbooks over the next few decades.

During his time teaching and writing textbooks Mendeleev began to notice patterns and relationships among the known elements.  He found many similar properties in groups of elements such as the halogens and the alkaline earth metals.  He noticed the atomic weight’s of the elements could be used to arrange elements within groups, and also to arrange groups themselves. In 1869 he published publish The Relation between the Properties and Atomic Weights of the Elements, revealing his periodic table to the world.

Mendeleev’s periodic table was impactful for its predictive power.  Due to its ordering, it predicted that some of the atomic weights of known elements may be wrong.  It also predicted the existence of unknown elements and it predicted what properties these elements would possess.  Both of these predictions ended up being true.

Mendeleev received substantial fame and recognition for his periodic table.  In 1905, the British Royal Society awarded him its highest honor, the Copley Medal.  The same year he was elected to the Royal Swedish Academy of Sciences.  He died just after the turn of the century in 1907 from the influenza virus.  Element number 101 is named Mendelevium in his honor.