Jun 132018

Today is the birthday (1773) of Thomas Young FRS, an English polymath, called “The Last Man Who Knew Everything” by Andrew Robinson in his biography, subtitled, Thomas Young, the Anonymous Polymath Who Proved Newton Wrong, Explained How We See, Cured the Sick, and Deciphered the Rosetta Stone, Among Other Feats of Genius. Young made notable scientific contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony, and Egyptology. He was mentioned favorably by, among others, William Herschel, Hermann von Helmholtz, James Clerk Maxwell, and Albert Einstein. It’s also Maxwell’s birthday today, by the way: http://www.bookofdaystales.com/james-clerk-maxwell/

Young was born in Milverton in Somerset, the eldest of 10 children in a Quaker family. By the age of 14 Young had learned Greek and Latin and was acquainted with French, Italian, Hebrew, German, Aramaic, Syriac, Samaritan, Arabic, Persian, Turkish and Amharic. He began to study medicine in London at St Bartholomew’s Hospital in 1792, moved to the University of Edinburgh Medical School in 1794, and a year later went to the University of Göttingen in Lower Saxony where he obtained the degree of doctor of medicine in 1796. In 1797 he entered Emmanuel College, Cambridge. In the same year he inherited the estate of his grand-uncle, Richard Brocklesby, which made him financially independent, and in 1799 he established himself as a physician at 48 Welbeck Street, London (now recorded with a blue plaque). Young published many of his first academic articles anonymously to protect his reputation as a physician.

In 1801, Young was appointed professor of natural philosophy (mainly physics) at the Royal Institution. In two years, he delivered 91 lectures. In 1802, he was appointed foreign secretary of the Royal Society, of which he had been elected a fellow in 1794. He resigned his professorship in 1803, fearing that its duties would interfere with his medical practice. His lectures were published in 1807 in the Course of Lectures on Natural Philosophy and contain a number of anticipations of later theories. In 1811, Young became physician to St George’s Hospital, and in 1814 he served on a committee appointed to consider the dangers involved in the general introduction of gas for lighting into London. In 1816 he was secretary of a commission charged with ascertaining the precise length of the seconds pendulum (the length of a pendulum whose period is exactly 2 seconds), and in 1818 he became secretary to the Board of Longitude and superintendent of the HM Nautical Almanac Office.

Young was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1822. A few years before his death he became interested in life insurance, and in 1827 he was chosen one of the eight foreign associates of the French Academy of Sciences. In 1828, he was elected a foreign member of the Royal Swedish Academy of Sciences. He died in London on 10th May 1829, and was buried in the cemetery of St. Giles Church in Farnborough, Kent, England. Westminster Abbey houses a white marble tablet in memory of Young bearing an extended epitaph by Hudson Gurney:

Sacred to the memory of Thomas Young, M.D., Fellow and Foreign Secretary of the Royal Society Member of the National Institute of France; a man alike eminent in almost every department of human learning. Patient of unintermitted labour, endowed with the faculty of intuitive perception, who, bringing an equal mastery to the most abstruse investigations of letters and of science, first established the undulatory theory of light, and first penetrated the obscurity which had veiled for ages the hieroglyphs of Egypt. Endeared to his friends by his domestic virtues, honoured by the World for his unrivalled acquirements, he died in the hopes of the Resurrection of the just. — Born at Milverton, in Somersetshire, 13 June 1773. Died in Park Square, London, 10 May 1829, in the 56th year of his age.

Young was highly regarded by his friends and colleagues. He was said never to impose his knowledge, but if asked was able to answer even the most difficult scientific question with ease. Although very learned he had a reputation for sometimes having difficulty in communicating his knowledge. It was said by one of his contemporaries that, “His words were not those in familiar use, and the arrangement of his ideas seldom the same as those he conversed with. He was therefore worse calculated than any man I ever knew for the communication of knowledge.” Young is quite well known by scholars in different fields but they usually know him only for his work in their specialties, not as a polymath.

I’ll just list briefly the areas where he made significant contributions – with a small synopsis.

Wave theory of light

In Young’s own judgment, of his many achievements the most important was to establish the wave theory of light. To do so, he had to overcome the view, expressed in the highly esteemed Isaac Newton’s Opticks, that light is a particle. Nevertheless, in the early-19th century Young put forth a number of theoretical reasons supporting the wave theory of light, and he developed two enduring demonstrations to support this viewpoint. With the ripple tank he demonstrated the idea of interference in the context of water waves. With his interference experiment (the now-classic double-slit experiment), he demonstrated interference in the context of light as a wave.

After publishing a paper on interference, he published a paper entitled “Experiments and Calculations Relative to Physical Optics” in 1804. Young describes an experiment in which he placed a narrow card (approximately 1/30th  inch) in a beam of light from a single opening in a window and observed the fringes of color in the shadow and to the sides of the card. He observed that placing another card before or after the narrow strip so as to prevent light from the beam from striking one of its edges caused the fringes to disappear. This supported the contention that light is composed of waves. Young performed and analyzed a number of experiments, including interference of light from reflection off nearby pairs of micrometer grooves, from reflection off thin films of soap and oil, and from Newton’s rings. He also performed two important diffraction experiments using fibers and long narrow strips. In his Course of Lectures on Natural Philosophy and the Mechanical Arts (1807) he gives Grimaldi credit for first observing the fringes in the shadow of an object placed in a beam of light. Within ten years, much of Young’s work was reproduced and then extended by others.

Young’s modulus

Engineers all know Young’s modulus, which describes the elasticity of materials beyond the limits of Hook’s Law. Hook’s Law describes the direct, proportional correlation between the load on a spring, and the extension of the spring “provided the load is not too great.” The proviso is there because if the load is “too great” all bets are off. Young’s modulus takes care of that. Young described his findings in his Course of Lectures on Natural Philosophy and the Mechanical Arts. However, the first use of the concept of Young’s modulus in experiments was by Giordano Riccati in 1782, predating Young by 25 years. Furthermore, the idea can be traced to a paper by Leonhard Euler published in 1727, 80 years before Young’s 1807 paper on the subject. Nonetheless, Young’s application was the one generally adopted by engineers. Young’s Modulus allowed, for the first time, prediction of the strain in a component subject to a known stress (and vice versa). Prior to Young’s contribution, engineers were required to apply Hooke’s F = kx relationship to identify the deformation (x) of a body subject to a known load (F), where the constant (k) is a function of both the geometry and material under consideration. Finding k required physical testing for any new component, as the F = kx relationship is a function of both geometry and material. Young’s Modulus depends only on the material, not its geometry, thus allowing a revolution in engineering strategies.

Vision and color theory

Young has sometimes been called the founder of physiological optics. In 1793 he explained the mode in which the eye accommodates itself to vision at different distances as depending on change of the curvature of the crystalline lens; in 1801 he was the first to describe astigmatism; and in his lectures he presented the hypothesis, afterwards developed by Hermann von Helmholtz, (the Young–Helmholtz theory), that color perception depends on the presence in the retina of three kinds of nerve fibers. This foreshadowed the modern understanding of color vision, in particular the finding that the eye does indeed have three colour receptors which are sensitive to different wavelength ranges.

Young–Laplace equation

In 1804, Young developed the theory of capillary action based on the principle of surface tension. He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how to deduce the phenomenon of capillary action from these two principles. In 1805, Pierre-Simon Laplace, the French philosopher, discovered the significance of meniscus radii with respect to capillary action. In 1830, Carl Friedrich Gauss, the German mathematician, unified the work of these two scientists to derive the Young–Laplace equation, the formula that describes the capillary pressure difference sustained across the interface between two static fluids. Young’s equation describes the contact angle of a liquid drop on a plane solid surface as a function of the surface free energy, the interfacial free energy and the surface tension of the liquid. Young’s equation was developed further some 60 years later by Dupré to account for thermodynamic effects, and this is known as the Young–Dupré equation.


In physiology Young made an important contribution to haemodynamics in the Croonian lecture for 1808 on the “Functions of the Heart and Arteries,” where he derived a formula for the wave speed of the pulse and his medical writings included An Introduction to Medical Literature, including a System of Practical Nosology (1813) and A Practical and Historical Treatise on Consumptive Diseases (1815). Young devised a rule of thumb for determining a child’s drug dosage. Young’s Rule states that the child dosage is equal to the adult dosage multiplied by the child’s age in years, divided by the sum of 12 plus the child’s age.


In an appendix to his Göttingen dissertation (1796; “De corporis hvmani viribvs conservatricibvs. Dissertatio.”) there are four pages added proposing a universal phonetic alphabet (so as ‘not to leave these pages blank’ –  Ne vacuae starent hae paginae, libuit e praelectione ante disputationem habenda tabellam literarum vniuersalem raptim describere”). It includes 16 “pure” vowel symbols, nasal vowels, various consonants, and examples of these, drawn primarily from French and English. In his Encyclopædia Britannica article “Languages”, Young compared the grammar and vocabulary of 400 languages. In a separate work in 1813, he introduced the term “Indo-European” languages, 165 years after the Dutch linguist Marcus Zuerius van Boxhorn proposed the grouping to which this term refers in 1647.

Egyptian hieroglyphs

Young made significant contributions in the decipherment of Egyptian hieroglyphs. He started his Egyptology work rather late, in 1813, when the work was already in progress among other researchers. He began by using an Egyptian demotic alphabet of 29 letters built up by Johan David Åkerblad in 1802 (14 turned out to be incorrect). Åkerblad was correct in stressing the importance of the demotic text in trying to read the inscriptions, but he wrongly believed that demotic was entirely alphabetic. By 1814 Young had completely translated the “enchorial” text of the Rosetta Stone (using a list with 86 demotic words), and then studied the hieroglyphic alphabet but initially failed to recognize that the demotic and hieroglyphic texts were paraphrases and not simple translations. There was considerable rivalry between Young and Jean-François Champollion while both were working on hieroglyphic decipherment. At first they briefly cooperated in their work, but later, from around 1815, a chill arose between them. For many years they kept details of their work away from each other. Some of Young’s conclusions appeared in the famous article “Egypt” he wrote for the 1818 edition of the Encyclopædia Britannica. When Champollion finally published a translation of the hieroglyphs and the key to the grammatical system in 1822, Young (and many others) praised his work. Nevertheless, a year later Young published an Account of the Recent Discoveries in Hieroglyphic Literature and Egyptian Antiquities, to have his own work recognized as the basis for Champollion’s system. Young had correctly found the sound value of six hieroglyphic signs, but had not deduced the grammar of the language. Young, himself, acknowledged that he was somewhat at a disadvantage because Champollion’s knowledge of the relevant languages, such as Coptic, was much greater. Several scholars have suggested that Young’s true contribution to Egyptology was his decipherment of the demotic script. He made the first major advances in this area. He also correctly identified demotic as being composed of both ideographic and phonetic signs.


Young developed two systems of tuning a piano so that it was well tempered (Wohltemperiert), that is, was tuned so as to be able to modulate between all major and minor scales without sounding obviously out of tune in any of them. Discussions of temperaments get really technical really quickly. Young’s first temperament was designed to sound best in the keys that were the commonest, and his second was a kind of inversion of the first. Unless you know the difference between BƄ and A#, and the differences that their major and minor thirds make in chords, this will not make any sense to you. It is a problem in the physics of acoustics, essentially.

Historians and critics vary enormously in their assessment of Young. Without question he was well versed in all the fields above – and more – and was able to expound on them critically (if not always clearly). How original his contributions were to the various fields, is the subject of ongoing debate. The idea than he was the last man to know everything, is obvious (and intentional) hyperbole. But it also highlights the fact that at the beginning of the 19th century it was still possible to gain expert knowledge in widely diverse fields. Furthermore, Young not only knew a lot of stuff, he was able to make contributions to diverse fields. Whether or not he was always entirely original is beside the point as far as I am concerned. We’re talking about a man who made contributions – recognized as significant by experts – in half a dozen specialties, that most of us do not even understand, let alone are capable of mastering.

As I have done quite a number of times with birthdays recently, I’ll celebrate Young with a recipe from his home region, Somerset. Somerset is well known for apples, cider, and dairying, and this recipe for Somerset chicken, which is traditional, combines all three.

Somerset Chicken


6 boneless chicken breasts, skin on
salt and freshly ground black pepper
75 gm/2½ oz butter
3 tbsp olive oil
2 onions, peeled and sliced
4 tbsp plain flour
2 tbsp wholegrain mustard
2 dessert apples, peeled, cored and sliced
110 gm/4 oz button mushrooms, sliced
250 ml/9 fl oz chicken stock
300 ml/10½ fl oz cider
1 tbsp finely chopped fresh sage
250 ml/9 fl oz double cream
300 gm/10½ oz cheddar cheese, grated


Preheat the oven to 200˚C/400˚F.

Season the chicken breasts with salt and freshly ground black pepper.


Heat a large skillet until smoking, then add half of the butter and oil. Fry the chicken breasts in batches, skin-side down first, for 5 minutes on each side, making sure they are golden-brown all over.  Transfer the chicken breasts to a baking dish and keep warm.

Return the skillet to the heat and add the remaining butter and oil. Add the onions and cook for 4-5 minutes, or until softened but without taking on color. Stir in the flour and the mustard and cook for a further 1-2 minutes. Add the apples and mushrooms and cook for a further minute, then pour the chicken stock over ingredients.

Bring the skillet to the boil, add the cider and return to the boil. Cook for 1-2 minutes, then lower the heat, add the sage and stir in the cream. Simmer for a further 5-6 minutes, then season with salt and freshly ground black pepper to taste.

Pour the sauce over the chicken in the baking pan.

Preheat the broiler to high.

Sprinkle the cheddar cheese over the chicken and place under the broiler for 4-5 minutes, or until the cheese is melted, golden-brown and bubbling.

Serve with baked or boiled new potatoes.

Feb 182018

Today is the birthday (1838) of Ernst Waldfried Josef Wenzel Mach, Austrian physicist and philosopher. The ratio of an object’s speed to that of sound is named the Mach number in his honor. As a philosopher of science, he was a major influence on logical positivism and American pragmatism. Through his criticism of Newton’s theories of space and time, he foreshadowed Einstein’s theory of relativity.

Mach was born in Chrlice (German: Chirlitz) in Moravia (then in the Austrian empire, now part of Brno in the Czech Republic). His father, who had attended Charles University in Prague, acted as tutor to the noble Brethon family in Zlín in eastern Moravia. Up to the age of 14, Mach received his education at home from his parents. He then entered a Gymnasium in Kroměříž (German: Kremsier), where he studied for 3 years. In 1855 he became a student at the University of Vienna. There he studied physics and medical physiology, receiving his doctorate in physics in 1860 under Andreas von Ettingshausen with a thesis titled “Über elektrische Ladungen und Induktion”, and his habilitation the following year. His early work focused on the Doppler effect in optics and acoustics. In 1864 he took a job as Professor of Mathematics at the University of Graz, having turned down the position of a chair in surgery at the University of Salzburg to do so, and in 1866 he was appointed as Professor of Physics. During that period, Mach continued his work in psycho-physics and in sensory perception. In 1867, he took the chair of Experimental Physics at the Charles University, Prague, where he stayed for 28 years before returning to Vienna.

Mach’s main contribution to physics involved his description and photographs of spark shock-waves and then ballistic shock-waves. He described how when a bullet or shell moved faster than the speed of sound, it created a compression of air in front of it. Using schlieren photography, he and his son Ludwig were able to photograph the shadows of the invisible shock waves. During the early 1890s Ludwig was able to invent an interferometer which allowed for much clearer photographs. But Mach also made many contributions to psychology and physiology, including his anticipation of gestalt phenomena, his discovery of the oblique effect and of Mach bands, an inhibition-influenced type of visual illusion, and especially his discovery of a non-acoustic function of the inner ear which helps control human balance.

One of the best-known of Mach’s ideas is the so-called “Mach principle,” the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The idea is that local inertial frames are determined by the large-scale distribution of matter, as exemplified by this anecdote:

You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don’t move?

Mach’s principle says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. There are a number of rival formulations of the principle. It is often stated in vague ways, like “mass out there influences inertia here”. A very general statement of Mach’s principle is “local physical laws are determined by the large-scale structure of the universe.” This concept was a guiding factor in Einstein’s development of the general theory of relativity. Einstein realized that the overall distribution of matter would determine the metric tensor, which tells you which frame is rotationally stationary

Mach also became well known for his philosophy developed in close interplay with his science. Mach defended a type of phenomenalism recognizing only sensations as real. This position seemed incompatible with the view of atoms and molecules as external, mind-independent things. He famously declared, after an 1897 lecture by Ludwig Boltzmann at the Imperial Academy of Science in Vienna: “I don’t believe that atoms exist!” From about 1908 to 1911 Mach’s reluctance to acknowledge the reality of atoms was criticized by Max Planck as being incompatible with physics. Einstein’s 1905 demonstration that the statistical fluctuations of atoms allowed measurement of their existence without direct individuated sensory evidence marked a turning point in the acceptance of atomic theory. Some of Mach’s criticisms of Newton’s position on space and time influenced Einstein, but later Einstein realized that Mach was basically opposed to Newton’s philosophy and concluded that his physical criticism was not sound.

In 1898 Mach suffered from cardiac arrest and in 1901 retired from the University of Vienna and was appointed to the upper chamber of the Austrian parliament. On leaving Vienna in 1913 he moved to his son’s home in Vaterstetten, near Munich, where he continued writing and corresponding until his death in 1916, only one day after his 78th birthday.

Most of Mach’s initial studies in the field of experimental physics concentrated on the interference, diffraction, polarization and refraction of light in different media under external influences. From there followed important explorations in the field of supersonic fluid mechanics. Mach and physicist-photographer Peter Salcher presented their paper on this subject in 1887; it correctly describes the sound effects observed during the supersonic motion of a projectile. They deduced and experimentally confirmed the existence of a shock wave of conical shape, with the projectile at the apex. The ratio of the speed of a fluid to the local speed of sound vp/vs is now called the Mach number. It is a critical parameter in the description of high-speed fluid movement in aerodynamics and hydrodynamics.

From 1895 to 1901, Mach held a newly created chair for “the history and philosophy of the inductive sciences” at the University of Vienna. In his historico-philosophical studies, Mach developed a phenomenalistic philosophy of science which became influential in the 19th and 20th centuries. He originally saw scientific laws as summaries of experimental events, constructed for the purpose of making complex data comprehensible, but later emphasized mathematical functions as a more useful way to describe sensory appearances. Thus, scientific laws while somewhat idealized have more to do with describing sensations than with reality as it exists beyond sensations.

In accordance with empirio-critical philosophy, Mach opposed Ludwig Boltzmann and others who proposed an atomic theory of physics. Since one cannot observe things as small as atoms directly, and since no atomic model at the time was consistent, the atomic hypothesis seemed to Mach to be unwarranted, and perhaps not sufficiently “economical”. Mach had a direct influence on the Vienna Circle philosophers and the school of logical positivism in general.

According to Alexander Riegler, Ernst Mach’s work was a precursor to the influential perspective known as constructivism. Constructivism holds that all knowledge is constructed rather than received by the learner. He took an exceptionally non-dualist, phenomenological position. The founder of radical constructivism, von Glasersfeld, gave a nod to Mach as an ally.

In 1873, independently of each other Mach and the physiologist and physician Josef Breuer discovered how the sense of balance (i.e., the perception of the head’s imbalance) functions, tracing its management by information which the brain receives from the movement of a fluid in the semicircular canals of the inner ear. That the sense of balance depended on the three semicircular canals was discovered in 1870 by the physiologist Friedrich Goltz, but Goltz did not discover how the balance-sensing apparatus functioned. Mach devised a swivel chair to enable him to test his theories, and Floyd Ratliff has suggested that this experiment may have paved the way to Mach’s critique of a physical conception of absolute space and motion.

Mach’s home town of Brno is in Moravia which is now part of the Czech Republic, and much of the cuisine is common to the nation as a whole. But there are some distinctive dishes. Moravian chicken pie is one. It can be made as a simple two-crust pie, but is often made with a crumb topping as well, as in this recipe.

Moravian Chicken Pie


Pie Crust

2 cups all-purpose flour
1 tsp salt
3⁄4 cup shortening
6 -8 tbsp cold water


2 ½ cups chopped cooked chicken
salt and pepper
3 tbsp flour
1 cup chicken broth
1 -2 tbsp butter, cut in small pieces

Crumb Topping

¼ cup all-purpose flour
1 tbsp butter


For the pie crust: combine the flour and salt in a food processor. Add the shortening and pulse until the mixture is like coarse cornmeal. Gradually stir in cold water just until a dough forms. Divide the dough into two equal pieces. Cover and chill 30 minutes, or until ready to use.

Preheat the oven to 375˚F/190˚C degrees.

Roll out one piece of dough to cover the bottom and sides of a 9-inch pie plate and place in the plate. Roll out the second piece of dough for the top crust and set aside.

For the filling: combine all the ingredients in a bowl and season with salt and pepper to taste. Pour the ingredients into the pie crust and top with the second crust, moisten the edges, and crimp to seal.

For the crumb topping: pulse the butter and flour in a food processor until it is like coarse cornmeal. Sprinkle the topping over the top crust of pie. Cut a few slits in the top crust to allow steam to escape.

Bake the pie 45 minutes to 1 hour, until golden and bubbly.


Apr 282016


Today is the birthday (1906) of Kurt Gödel, Austrian mathematician, logician and philosopher. Gödel is one of my great intellectual heroes, even though he is hardly a household name. His incompleteness theorems, for which he is famous, are the bedrock of my general thinking about the nature of human thought and belief. I’ll try to discuss his work in plain language even though in so doing I will inevitably oversimplify it.

Gödel  was born in Brünn when it was part of Austria-Hungary (now Brno, Czech Republic) into the ethnic German family of Rudolf Gödel, the manager of a textile factory, and Marianne Gödel (née Handschuh). At the time of his birth the city had a German-speaking majority] which included his parents. His father was Catholic and his mother was Protestant and the children were raised Protestant.

Gödel automatically became a Czechoslovak citizen at age 12 when the Austro-Hungarian Empire broke up at the end of World War I. According to his classmate Klepetař, like many residents of the predominantly German Sudetenländer, “Gödel always considered himself Austrian and an exile in Czechoslovakia.” He chose to become an Austrian citizen at age 23. When Germany annexed Austria in 1938, Gödel automatically became a German citizen at age 32. After World War II, at the age of 42, he became a U.S. citizen.

In his family, young Gödel was known as Herr Warum (“Mr. Why”) because of his insatiable curiosity. He attended the Evangelische Volksschule, a Lutheran school in Brünn from 1912 to 1916, and was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all his subjects, particularly in mathematics, languages, and religion. Although Kurt had first excelled in languages, he later became more interested in history and mathematics. His interest in mathematics increased when in 1920 his older brother Rudolf (born 1902) left for Vienna to go to medical school at the University of Vienna. In his teens, Gödel studied Gabelsberger shorthand, Goethe’s Theory of Colours and criticisms of Isaac Newton, and the writings of Immanuel Kant.

At the age of 18, Gödel joined his brother in Vienna and entered the University of Vienna. By that time, he had already mastered university-level mathematics and initially intended to study theoretical physics. He also attended lectures on mathematics and philosophy, and participated in the Vienna Circle of philosophers with Moritz Schlick, Hans Hahn, and Rudolf Carnap. Gödel then studied number theory, but when he took part in a seminar run by Moritz Schlick which studied Bertrand Russell’s Introduction to Mathematical Philosophy, he became interested in mathematical logic. According to Gödel, mathematical logic was “a science prior to all others, which contains the ideas and principles underlying all sciences.”


Gödel chose to study completeness in logic for his doctoral work. Put simply, completeness is a quality of a logical system – such as arithmetic or geometry – whereby every statement within the system can be proven to be true without resort to statements outside the system. Mathematicians had been trying for millennia, without success, for example, to prove that Euclid’s 5 axioms, or postulates – statements that classical geometry rests on – could be shown to be true using reasoning within geometry. If you accept these axioms, there are countless theorems you can derive from them, such as the Pythagorean theorem, but mathematicians were not happy that the axioms themselves could not be proven to be true. They seem to be true – self evidently – but no one could prove them to be true.

In 1929, at the age of 23, Gödel completed his doctoral dissertation under Hans Hahn’s supervision. In it, he established the completeness of the first-order predicate calculus (Gödel’s completeness theorem). He was awarded his doctorate in 1930. His thesis, along with some additional work, was published by the Vienna Academy of Science. So far so good. BUT . . . in 1931, while still in Vienna, Gödel published his incompleteness theorems in Über formal unentscheidbare Sätze der “Principia Mathematica” und verwandter Systeme (called in English “On Formally Undecidable Propositions of “Principia Mathematica” and Related Systems”). In that article, he proved that arithmetic is incomplete. This was an astounding and revolutionary idea. Again in simple terms, Gödel proved that although arithmetic is a powerful system capable of great things, it rests on premises that cannot be proven. This led to his basic notion of the incompleteness of mathematics summed up in two statements:

If a system is consistent, it cannot be complete.

The consistency of the axioms cannot be proven within the system.

This notion is usually expressed simply as that “in any logical system there will always be at least one statement which is true but cannot be proven to be true.”

I just love it. All the smarty pants in the world who hammer religion because it is based on faith whereas science is based on “proven fact” don’t know what they are talking about. Yes, religion is based on faith, SO IS SCIENCE !!! Logical proof has limits and there’s no way round this.


In 1933, Gödel first traveled to the U.S., where he met Albert Einstein, who became a good friend, and  delivered an address to the annual meeting of the American Mathematical Society. In 1934 Gödel gave a series of lectures at the Institute for Advanced Study (IAS) in Princeton, New Jersey, entitled “On undecidable propositions of formal mathematical systems.” Stephen Kleene, who had just completed his PhD at Princeton, took notes of these lectures that have been subsequently published.

Gödel married Adele Nimbursky (née Porkert, 1899–1981), whom he had known for over 10 years, on September 20, 1938. Their relationship had been opposed by his parents on the grounds that she was a divorced dancer, six years older than he was. Subsequently, he left for another visit to the USA, spending the autumn of 1938 at the IAS and the spring of 1939 at the University of Notre Dame.


After the Anschluss in 1938, Austria became a part of Nazi Germany. Germany abolished his university post, so Gödel had to apply for a different position under the new order. His former association with Jewish members of the Vienna Circle, especially with Hahn, weighed against him. The University of Vienna turned his application down. His predicament intensified when the German army found him fit for conscription. World War II started in September 1939. Before the year was up, Gödel and his wife left Vienna for Princeton. To avoid the difficulty of an Atlantic crossing, the Gödels took the trans-Siberian railway to the Pacific, sailed from Japan to San Francisco (which they reached on March 4, 1940), then crossed the U.S. by train to Princeton, where Gödel accepted a position at the Institute for Advanced Study (IAS).


Albert Einstein was also living at Princeton during this time, and Gödel and Einstein developed a strong friendship. They took long walks together to and from the Institute for Advanced Study, deep in conversation. Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his “own work no longer meant much, but he came to the Institute merely to have the privilege of walking home with Gödel.”

On December 5, 1947, Einstein and Morgenstern accompanied Gödel to his U.S. citizenship exam, where they acted as witnesses. Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship. Einstein and Morgenstern were concerned that their friend’s unpredictable behavior might jeopardize his application. Fortunately, the judge turned out to be Phillip Forman, who knew Einstein and had administered the oath at Einstein’s own citizenship hearing. Everything went smoothly until Forman happened to ask Gödel if he thought a dictatorship like the Nazi regime could happen in the U.S. Gödel then started to explain his discovery to Forman. Forman understood what was going on, cut Gödel off, and moved the hearing on to other questions and a routine conclusion.

Gödel became a permanent member of the Institute for Advanced Study at Princeton in 1946. Around this time he stopped publishing, though he continued to work. He became a full professor at the Institute in 1953 and an emeritus professor in 1976. During his many years at the Institute, Gödel’s interests turned to philosophy and physics. In 1949, he demonstrated the existence of solutions involving closed time-like curves, to Albert Einstein’s field equations in general relativity. He is said to have given this elaboration to Einstein as a present for his 70th birthday. His “rotating universes” would allow time travel to the past and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric (an exact solution of the Einstein field equation).

In the early 1970s, Gödel circulated among his friends an elaboration of Leibniz’ version of Anselm of Canterbury’s ontological proof of God’s existence. This is now known as Gödel’s ontological proof.


I won’t go over it with you. It has the same problems that Anselm’s and Leibniz’ proofs do, namely, the axioms are unprovable. Gödel hoist on his own petard !!!


Gödel was a convinced theist, in the Christian tradition. He held the notion that God was personal, which differed from the religious views of his friend Albert Einstein. He believed firmly in an afterlife, stating: “Of course this supposes that there are many relationships which today’s science and received wisdom haven’t any inkling of. But I am convinced of this [the afterlife], independently of any theology.” It is “possible today to perceive, by pure reasoning” that it “is entirely consistent with known facts.” “If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife].”

In an (unmailed) answer to a questionnaire, Gödel described his religion as “baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza.” In describing religion in general, Gödel said: “Religions are, for the most part, bad—but religion is not”. According to his wife Adele, “Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning”, while of Islam, he said, “I like Islam: it is a consistent [or consequential] idea of religion and open-minded”. So much, again, for the smarty pants who think that if you are intelligent you can’t believe in God.

I am fully in accord with Gödel in this regard. It is certainly true that a great many religious statements are ridiculous, and a great many religious beliefs are idiotic, but that does not mean that basic religious beliefs are false. And we have Gödel to thank for showing that science and mathematics are every bit based on faith as religion is.

Later in his life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, she was hospitalized for six months and could no longer prepare her husband’s food. In her absence, he refused to eat, eventually starving to death. He weighed 65 pounds (approximately 30 kg) when he died. I will admit that there is a fair degree of irrationality in starving yourself to death because you are afraid of being poisoned. His death certificate reported that he died of “malnutrition and inanition caused by personality disturbance” in Princeton Hospital on January 14, 1978. He was buried in Princeton Cemetery. Adele’s death followed in 1981.


I don’t know what Adele made for him, but maybe she cooked sauerkraut soup once in a while. Sauerkraut is one of several dishes that Czechs and Germans agree upon as delectable, and you can find versions of sauerkraut soup in Germany, Austria, and the Czech Republic with the ingredients, other than sauerkraut varying somewhat. In this recipe you can use a German or Polish sausage depending on your tastes. You may also add a little pickle juice from the sauerkraut if you like. Be sure to have plenty of crusty bread on hand to dip into the broth.

Sauerkraut Soup


7 oz sauerkraut
6 cups light broth
2 potatoes, diced
2 tbs flour
1 onion, diced
4 slices bacon, finely diced
1 large sausage, sliced thinly
5-10 white mushrooms, diced
1 tsp caraway seeds
1-2 tsp sweet paprika


Sauté the finely diced bacon over medium-low heat in a large heavy pot. There is no need to add oil. When the fat is flowing, add the sliced Polish sausage, mushrooms and onion, and sauté for about 5 min.     Sprinkle with flour and stir everything around to mix. Add the drained sauerkraut, diced potatoes, caraway seeds and paprika and stir again.  Add the broth and salt to taste and cook until the potatoes are tender.

Serve in deep bowls with crusty bread. If you like you can pass around sour cream for guests to add.

Nov 212015


On this date in 1905 Albert Einstein’s paper, “Does the Inertia of a Body Depend Upon Its Energy Content?” was published in the journal Annalen der Physik. This paper explored the relationship between energy and mass via Special Relativity, and, thus, lead to the mass–energy equivalence formula E = mc² — arguably the most famous formula in the world. I would also argue that it is the most misunderstood formula in the world, although I notice in researching this post that a lot of physicists in trying to help non-physicists understand it, seriously misrepresent its implications.

The problem frequently in trying to explain physics to the mathematically and scientifically challenged is that scientists and science teachers fall back on analogies – often involving cats for some inscrutable reason. The problem, as I have stated many times in many places before, is that analogies can help, but they can also be misleading.


There is a second problem in that E = mc² does not represent the whole story. That’s the part about theory that non-scientists rarely get. Einstein’s theories of relativity, Darwin’s theory of natural selection, etc. are not complete, hence they are called “theories.” No one is seeking radically new alternatives (although some day they might); scientists are just trying to explain messy bits in the theories that cannot be explained now. That’s how Einstein came to unravel Newton. Newton was not totally wrong; it’s just that his “laws” of motion, for example, are incomplete – as stated by Newton they apply only to mass, force, acceleration, etc. as we encounter them in the everyday world. When physicists started looking at interstellar, and subatomic worlds at the turn of the 20th century, Newton’s physics did not work very well for them. That’s when Einstein came along and added bits to Newton to make his equations more encompassing.

Here’s a couple of provisos before I get into things more. First, for the non-mathematically inclined I am going to have to be simplistic and in doing so I will have to be a little misleading, or, you might say, downright wrong. The only way to understand physics deeply is to understand the underlying mathematics deeply (which, incidentally, I don’t, although I am better at it than most non-scientists). Second, my usual caveat, I don’t find physics per se very interesting. My son switched from being a physics major to an anthropology major a few years ago for precisely the same reason. Physics does very well in helping us build computers, cell phones, and what not, and I use them all the time. Thanks physics. It is useless when it comes to issues that I really care about such as the existence of God, how to mend a broken heart, and so forth. To be sure, philosophers and theologians can sometimes gain insight into problems they are working on by learning some physics, and vice versa. But the one realm cannot explain the other. Their methods and goals are radically different. When it comes to understanding the formation of the universe as we now know it, I’ll study physics; when it comes to understanding God, I’ll read the Bible and other spiritual texts. Both areas still have a long way to go.


The formula E = mc² is incomplete, but let’s stick with it for now. In the formula, E is energy, m is mass, and c is the velocity of light (here it is squared). Most people know that. Where they go drastically wrong is in thinking that mass = matter. That is false. Mass is mass, matter is matter, and energy is energy. E = mc² does not talk about matter directly, but about the relationship between energy and mass. It’s not about the conversion of matter into energy, as most people think the atom bomb or atomic energy are all about (as in the TIME cover photo). Einstein was not involved in the Manhattan project because he lacked the proper security clearance. But even if he had been, E = mc² has very little application in making a bomb. Atomic bombs and atomic energy concern releasing energy within the atom, not converting matter into energy as such. This is a bit of a semantic quibble, but at least you can get the general idea that matter is made up of particles and energy. Under certain conditions it is possible to set the energy free – and a little goes a long way.

In a nuclear bomb or energy plant, you are not converting the particles into energy; you are setting energy free that keeps the atoms together. It requires an incredible amount of energy to keep the particles of the atomic nucleus together, so, if you can tear them apart, you can release that energy. That’s why it’s called nuclear energy. You are not converting the particles into energy, you are simply setting it free. The particles remain as particles, just much less organized since nothing is holding them together.


So, then, what is it about E = mc²? It’s simply telling you that energy has mass, but it’s very, very small. Nonetheless, if you add energy to something, you increase its mass. For example, if you accelerate something it gains energy, therefore mass. At usual speeds the increase in mass is minute. But when you start approaching the speed of light you have to increase the energy input enormously, and in so doing, what you are pushing gets enormously massive. That fact is an important component of Special Relativity.

Explaining all of this will help you understand why I generally find physics dull. I’ll leave professional physics up to people who care about mathematical puzzles. I am not especially interested in how atomic bombs or cell phones work at a deep level. I’m much more interested in how and why people use (or don’t use) them, and for that kind of question physics is no help.

Physics burst on the scene a few years ago in the form of so-called “molecular” gastronomy. I’ve mentioned this fad before as a trend that I feel is more trickery than artistry – a way to amuse the eyes once in a while, but not much of an enhancement on classic cooking techniques. I expect it will vanish ere long. So . . . you can make spherical stuff, and foams, and “instant” frozen things. Big whoop. The equipment to do this is expensive, especially If you are only going to use it occasionally for a flashy dinner party. I will admit that I bought a rechargeable soda siphon once, about 40 years ago, which allowed me to make carbonated liquids – usually water. But it’s a whole lot cheaper to buy carbonated water than to have a machine. If I want something fizzy these days I’ll turn to chemistry and put a little sodium bicarbonate in an acidulated liquid. But I usually only do that when I have an upset stomach.

For the sake of completeness, though, here’s a video on making mock fried eggs with mango “yolks” and coconut milk “whites.” I expect they are delicious, but I’ll content myself with the video, and settle for mango balls in coconut milk for my next dessert.

Oct 072015


Today is the birthday (1885) of Niels Henrik David Bohr, a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research. Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. Although the Bohr model has been supplanted by other models, its underlying principles remain valid. He also conceived the principle of complementarity: that items could be separately analyzed in terms of contradictory properties, like behaving as a wave or a stream of particles. The notion of complementarity dominated Bohr’s thinking in both science and philosophy.

I don’t want to delve too deeply into Bohr’s physics because I know I will lose a big chunk of my audience before I get started. But I will make one point before I fly off in different directions. Long-time readers know that I have a bee in my bonnet about certain superlatives – the BEST painting/painter or composer or mathematician or whatever. There are lots and lots of smart and talented people throughout history. If this were not so, this would be a very limited blog. My main limitation is that their birthdays are not spread evenly through the year, coupled with my intrinsic favoritism. In the latter case I am allowed because it is MY blog. I make the rules. What gets me wound up is the popular idea that the yardstick of hyper-genius is Einstein. He had a phenomenal mind – no question. He was, however, far from being the ONLY genius of the 20th century, yet his is the name that automatically comes to mind. I’ve always countered this prejudice when it comes up by mentioning Niels Bohr.


The first half of the 20th century was almost wallpapered with brilliant mathematicians and physicists, not to mention anthropologists, writers, philosophers, painters, and all the rest of it. Niels Bohr is one of them, but he is far from being a household name. Yet he helped usher in the age of quantum mechanics (with other brilliant minds), the dominant model of atomic physics to this day.


Bohr was born in Copenhagen, the second of three children of Christian Bohr, a professor of physiology at the University of Copenhagen, and Ellen Adler Bohr, who came from a wealthy Danish Jewish family prominent in banking and parliamentary circles. He had an elder sister, Jenny, and a younger brother Harald. Jenny became a teacher, while Harald became a mathematician and Olympic footballer who played for the Danish national team at the 1908 Summer Olympics in London. Niels was a passionate footballer as well, and the two brothers played several matches for the Copenhagen-based Akademisk Boldklub (Academic Football Club), with Niels as goalkeeper. My son and I love goalies.


In 1910, Bohr met Margrethe Nørlund, the sister of the mathematician Niels Erik Nørlund. Bohr resigned his membership in the Church of Denmark on 16 April 1912, and he and Margrethe were married in a civil ceremony at the town hall in Slagelse on 1 August. Their honeymoon was delayed, however, because Bohr had an insight into the nature of orbiting electrons within the atom that he felt could not wait. For reasons that are not clear to me, he was unable to sit and write the paper himself, so he dictated it to Margrethe. Maybe this was his idea of marital bliss?

Planetary models of atoms were fairly recent but not new. Bohr’s treatment was. The old planetary model could not explain why the negatively charged electron did not simply collapse into the positively charged nucleus. He advanced the theory of electrons travelling in nested orbits of different energies around the atom’s nucleus, with the chemical properties of each element being largely determined by the number of electrons in the outer orbits of its atoms. He introduced the idea that an electron could drop from a higher-energy orbit to a lower one, in the process emitting a quantum of discrete energy. This became a basis for what is now known as the old quantum theory. In 1922 Bohr received the Nobel Prize in physics for his work.


Bohr became convinced that light behaved like both waves and particles, and in 1927, experiments confirmed the de Broglie hypothesis that matter (like electrons) also behaved like waves. He conceived the philosophical principle of complementarity: that items could have apparently mutually exclusive properties, such as being a wave or a stream of particles, depending on the experimental framework. He felt that it was not fully understood by contemporary philosophers. Einstein never fully accepted quantum mechanics and complementarity. Einstein preferred the determinism of classical physics over the probabilistic new quantum physics to which he himself had contributed. Philosophical issues that arose from the novel aspects of quantum mechanics became widely celebrated subjects of discussion. Einstein and Bohr had good-natured arguments over such issues throughout their lives.


Bohr’s model of the atomic nucleus helped him explain the nature of nuclear fission which he published in a paper in 1939, “The Mechanism of Nuclear Fission,” along with John Wheeler. Thus the age of nuclear energy and the atom-bomb was born.

Bohr was aware of the possibility of using uranium-235 to construct an atomic bomb, referring to it in lectures in Britain and Denmark shortly before and after the war started, but he did not believe that it was technically feasible to extract a sufficient quantity of uranium-235 (fissionable material). In September 1941, Werner Heisenberg, who had become head of the German nuclear energy project, visited Bohr in Copenhagen. During this meeting the two men took a private moment outside, the content of which has caused much speculation, as both gave differing accounts. According to Heisenberg, he began to address nuclear energy, morality and the war, to which Bohr seems to have reacted by terminating the conversation abruptly while not giving Heisenberg hints about his own opinions.

In 1957, Heisenberg wrote to Robert Jungk, who was then working on the book Brighter than a Thousand Suns: A Personal History of the Atomic Scientists. Heisenberg explained that he had visited Copenhagen to communicate to Bohr the views of several German scientists, that production of a nuclear weapon was possible with great efforts, and this raised enormous responsibilities on the world’s scientists on both sides. When Bohr saw Jungk’s depiction in the Danish translation of the book, he drafted (but never sent) a letter to Heisenberg, stating that he never understood the purpose of Heisenberg’s visit, was shocked by Heisenberg’s opinion that Germany would win the war, and that atomic weapons could be decisive.


In September 1943, word reached Bohr and his brother Harald that the Nazis considered their family to be Jewish, since their mother, Ellen Adler Bohr, had been a Jew, and that they were therefore in danger of being arrested. The Danish resistance helped Bohr and his wife escape by sea to Sweden on 29 September. The next day, Bohr persuaded King Gustaf V of Sweden to make public Sweden’s willingness to provide asylum to Jewish refugees. On 2 October 1943, Swedish radio broadcast that Sweden was ready to offer asylum, and the mass rescue of the Danish Jews by their countrymen followed swiftly thereafter. Some historians claim that Bohr’s actions led directly to the mass rescue, while others say that, though Bohr did all that he could for his countrymen, his actions were not a decisive influence on the wider events. Eventually, over 7,000 Danish Jews escaped to Sweden.

When the news of Bohr’s escape reached Britain, Lord Cherwell sent a telegram to Bohr asking him to come to Britain. Bohr arrived in Scotland on 6 October in a de Havilland Mosquito operated by the British Overseas Airways Corporation (BOAC). The Mosquitos were unarmed high-speed bomber aircraft that had been converted to carry small, valuable cargoes or important passengers. By flying at high speed and high altitude, they could cross German-occupied Norway, and yet avoid German fighters. Bohr, equipped with parachute, flying suit and oxygen mask, spent the three-hour flight lying on a mattress in the aircraft’s bomb bay. During the flight, Bohr did not wear his flying helmet as it was too small, and consequently did not hear the pilot’s intercom instruction to turn on his oxygen supply when the aircraft climbed to high altitude to overfly Norway. He passed out from oxygen starvation and only revived when the aircraft descended to lower altitude over the North Sea.

On 8 December 1943, Bohr arrived in Washington, D.C., where he met with the director of the Manhattan Project, Brigadier General Leslie R. Groves, Jr,and went to Los Alamos in New Mexico, where the nuclear weapons were being designed. Bohr did not remain at Los Alamos, but paid a series of extended visits over the course of the next two years. Robert Oppenheimer credited Bohr with acting “as a scientific father figure to the younger men”, most notably Richard Feynman. Bohr is quoted as saying, “They didn’t need my help in making the atom bomb.”


Bohr recognized early that nuclear weapons would change international relations. In April 1944, he received a letter from Peter Kapitza, written some months before when Bohr was in Sweden, inviting him to come to the Soviet Union. The letter convinced Bohr that the Soviets were aware of the Anglo-American project, and would strive to catch up. He sent Kapitza a non-committal response, which he showed to the authorities in Britain before posting. Bohr met Churchill on 16 May 1944. Churchill disagreed with the idea of openness towards the Russians to the point that he wrote in a letter: “It seems to me Bohr ought to be confined or at any rate made to see that he is very near the edge of mortal crimes.”

Oppenheimer suggested that Bohr visit President Franklin D. Roosevelt to convince him that the Manhattan Project should be shared with the Soviets in the hope of speeding up its results. Bohr’s friend, Supreme Court Justice Felix Frankfurter, informed President Roosevelt about Bohr’s opinions, and a meeting between them took place on 26 August 1944. Roosevelt suggested that Bohr return to the United Kingdom to try to win British approval. When Churchill and Roosevelt met at Hyde Park on 19 September 1944, they rejected the idea of informing the world about the project, and the aide-mémoire of their conversation contained a rider that “enquiries should be made regarding the activities of Professor Bohr and steps taken to ensure that he is responsible for no leakage of information, particularly to the Russians”.


Bohr died of heart failure at his home in Carlsberg on 18 November 1962. He was cremated, and his ashes were buried in the family plot in the Assistens Cemetery in the Nørrebro section of Copenhagen, along with those of his parents, his brother Harald, and his son Christian. Years later, his wife’s ashes were also interred there.

I’ve mentioned traditional Danish cuisine several times before. It shares features with the other Sandinavian countries, and, like them as well as Britain, tends to be unfairly disdained by foreigners. Danish food does not involve a lot of herbs and spices, but it is noted for combinations of flavors and colorful presentation. Historically lunch was usually an open faced sandwich known as smørrebrød. Smørrebrød (originally smør og brød, meaning “butter and bread”) usually consists of a piece of buttered rye bread (rugbrød), a dense, dark brown bread. Pålæg (“put on”), the topping, which can be cold cuts, pieces of meat or fish, cheese or spreads. More elaborate, finely decorated, varieties have contributed to the international reputation of the smørrebrød. A slice or two of pålæg is placed on the buttered bread and decorated with the right accompaniments to create a tasty and visually appealing lunch or snack. Standards include:

Dyrlægens natmad (Veterinarian’s late night snack). On a piece of dark rye bread, a layer of liver pâté (leverpostej), topped with a slice of saltkød (salted beef) and a slice of sky (meat jelly). This is all decorated with raw onion rings and garden cress.

Røget ål med røræg Smoked eel on dark rye bread, topped with scrambled eggs, herbs and a slice of lemon.

Leverpostej Warm rough-chopped liverpaste served on dark rye bread, topped with bacon, and sauteed mushrooms. Additions can include lettuce and sliced pickled cucumber.

Roast beef, thinly sliced and served on dark rye bread, topped with a portion of remoulade, and decorated with a sprinkling of shredded horseradish and crispy fried onions.

Ribbensteg (roast pork), thinly sliced and served on dark rye bread, topped with red cabbage, and decorated with a slice of orange.

Rullepølse, (rolled stuffed pork) with a slice of meat jelly, onions, tomatoes and parsley.

Tartar, with salt and pepper, served on dark rye bread, topped with raw onion rings, grated horseradish and a raw egg yolk.

Røget laks. Slices of cold-smoked salmon on white bread, topped with shrimp and decorated with a slice of lemon and fresh dill.

Stjerneskud (lit. shooting star). On a base of buttered toast, two pieces of fish: a piece of steamed white fish on one half, a piece of fried, breaded plaice or rødspætte on the other half. On top is piled a mound of shrimp, which is then decorated with a dollop of mayonnaise, sliced cucumber, caviar or blackened lumpfish roe, and a lemon slice.

Here’s a small gallery to get you thinking:

bohr3 bohr2 bohr4 bohr1

Aug 122015

es1  es3

Today is the birthday (1887) of Erwin Rudolf Josef Alexander Schrödinger (1887 ), a Nobel Prize-winning Austrian physicist who developed a number of fundamental ideas in the field of quantum theory, which formed the basis of wave mechanics. He formulated the basic wave equation (stationary and time-dependent Schrödinger equation) and, more popularly, proposed an original interpretation of the physical meaning of the wave function which led to his famous thought experiment “Schrödinger’s Cat” which supposedly illustrates the absurdity of the Copenhagen interpretation of quantum mechanics.


For those who know (and care) about the implications of this thought experiment I have to say that I’ve never seen the point of it. The Copenhagen interpretation states that the wave function of certain subatomic particles exists in two (or more) simultaneously contradictory states until they are observed, at which point the function “collapses” or resolves to one or the other. Erwin Schrödinger’s thought experiment involved a closed box within which was a chamber containing a very small amount of radioactive material a particle of which within a fixed span of time might decay or not decay. The state of the particle would be measured by a Geiger counter and if it had decayed would trigger the release of cyanide gas. Also in the box was a cat. Schrödinger’s point was that it was absurd to imagine that until the box was opened by an “observer” the decay state of the particle was unknown and therefore that cat was simultaneously alive and dead. Here’s the original:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

—Erwin Schrödinger, Die gegenwärtige Situation in der Quantenmechanik (The present situation in quantum mechanics), Naturwissenschaften

(translated by John D. Trimmer in Proceedings of the American Philosophical Society)


Einstein had always been troubled by the idea that matter could simultaneously exist in two contradictory states and was so delighted by the thought experiment that he wrote:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gunpowder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.

I don’t know where he got the gunpowder from, but that’s not the only mistake that he made. I’ve wondered for years why they thought that the wave function had to be observed by a human for it to collapse. Why isn’t the cat an observer? Why not the Geiger counter? Anything in the macro world that interacts with the wave function is an observer. Oh dear, Erwin, you should have taken an anthropology class with me.  I gather from recent reading that I am not the only person to have spotted the fallacy. Niels Bohr apparently made the same observation a long time ago. Oh well, it’s not surprising; he’s much smarter than I am.

The experiment as described is a purely theoretical one, and the machine proposed is not known to have been constructed. However, successful experiments involving similar principles, e.g. superpositions (that is matter in 2 states at the same time) of relatively large (by the standards of quantum physics) objects have been performed. These experiments do not show that a cat-sized object can be superposed (both alive and dead), but the known upper limit on “cat states” has been pushed upwards by them. In many cases the state is short-lived, even when cooled to near absolute zero.

1. A “cat state” has been achieved with photons.

2  A beryllium ion has been trapped in a superposed state.

3. An experiment involving a superconducting quantum interference device (“SQUID”) has been linked to the theme of the thought experiment: “The superposition state does not correspond to a billion electrons flowing one way and a billion others flowing the other way. Superconducting electrons move en masse. All the superconducting electrons in the SQUID flow both ways around the loop at once when they are in the Schrödinger’s cat state.”

4. A piezoelectric “tuning fork” has been constructed, which is both vibrating and still at the same time.


All this thinking makes me hungry but I don’t think I can do much with cyanide and a dead cat. So I am left with Schrödinger’s home of Vienna, which has already given me enough headaches. But . . . Vienna is well known for dishes made with a cheese called quark, which by silly coincidence is the name of an elementary sub-atomic particle. By an even sillier coincidence there are different types of quark particles which are referred to as “flavors.”

Quark the dairy product is made by warming soured milk until the desired degree of coagulation (denaturation, curdling) of milk proteins is met, and then strained. It can be classified as fresh acid-set cheese, though in some countries it is traditionally considered a distinct fermented milk product. Traditional quark is made without rennet, but in some modern dairies rennet is added. It is soft, white and unaged, and usually has no salt added.

Last time I gave a Viennese recipe I included a link for this video on how to make apple strudel:


Well , you can adapt it to make Viennese Topfenstrudel, using sweetened quark in place of apples. Problem solved.