Tag Archives: Kepler

Why is Einstein’s general relativity such a popular target for cranks?

The Conversation

Michael J. I. Brown, Monash University

Scientists maybe celebrating the 100th anniversary of Albert Einstein’s general theory of relativity, but there was also a death in 1915. It was one of the many deaths of simple and intuitive physics that has happened over the past four centuries.

Today the concepts and mathematics of physics are often removed from everyday experience. Consequently, cutting edge physics is largely the domain of professional physicists, with years of university education.

But there are people who hanker for a simpler physics, toiling away on their own cosmologies. Rightly or wrongly, these people are often labelled cranks, but their endeavours tell us much misconceptions about science, its history and what it should be.

I regularly browse open access website arxiv.org to look for the latest astrophysics research. Real astrophysics, that is. But if I want to take a look at what pseudoscientists are up to, I can browse vixra.org. That’s right, “arxiv” backwards. The vixra.org website was founded by “scientists who find they are unable to submit their articles to arXiv.org” because that website’s owners filter material they “consider inappropriate”.

There are more than 1,800 articles on vixra.org discussing relativity and cosmology, and many don’t like relativity at all. Perhaps one reason why cranks particularly dislike relativity is because it is so unlike our everyday experiences.

Einstein predicted that the passage of time is not absolute, and can slow for speeding objects and near very massive bodies such as planets, stars and black holes. Over the past century, this bizarre predication has been measured with planes, satellites, and speeding muons.

But the varying passage of time is nothing like our everyday experience, which isn’t surprising as we don’t swing by black holes on our way to the shops. Everyday experience is often central to cranky ideas, with the most extreme example being flat earthers.

Thus many crank theories postulate that time is absolute, because that matches everyday experience. Of course, these crank theories are overlooking experimental data, or at least most of it.

History and linearity

One of the most curious aspects of pseudoscience is an oddly linear approach to science. To be fair, this can result from an overly literal approach to popular histories of science, which emphasise pioneering work over replication.

A pivotal moment in relativity’s history is Albert Michelson and Edward Morley’s demonstration that the speed of light didn’t depend on its direction of travel nor the motion of the Earth.

Of course, since 1887 the Michelson-Morley experiment has been confirmed many times. Modern measurements have a precision orders of magnitude better than the original 1887 Michelson-Morley experiment, but these don’t feature prominently in popular histories of science.

Interestingly many pseudoscientists are fixated on the original Michelson-Morley experiment, and how it could be in error. This fixation assumes science is so linear that the downfall a 19th century experiment will rewrite 21st century physics. This overlooks how key theories are tested (and retested) with a myriad of experiments with greater precision and different methodologies.

Another consequence of the pseudoscientific approach to history is that debunked results from decades past are often used by buttress pseudoscientific ideas. For example, many pseudoscientists claim Dayton Miller detected “aether drift” in the 1930s. But Miller probably underestimated his errors, as far more precise studies in subsequent decades did not confirm his findings.

Unfortunately this linear and selective approach to science isn’t limited to relativity. It turns up in cranky theories ranging from evolution to climate.

Climate scientist Michael E Mann is still dealing with cranky accusations about his seminal 1998 paper on the Earth’s temperature history, despite the fact it has been superseded by more recent studies that achieve comparable results. Indeed, it devoured so much of Mann’s time he has literally written a book about his experience.

What about the maths?

During the birth of physics, one could gain insights with relatively simple (and beautiful) mathematics. My favourite example is Johannes Kepler’s charting of the orbit of Mars via triangulation.

In the 17th century, Johannes Kepler used elegantly simple mathematics to chart the motion of Mars. Johannes Kepler / University of Sydney

Over subsequent centuries, the mathematics required for new physical insights has become more complex, as illustrated by Newton’s use of calculus and Einstein’s use of tensors. This level of mathematics is rarely in the domain of the enthusiastic but untrained amateur? So what do they do?

One option is to hark back to an earlier era. For example, trying to disprove general relativity by using the assumptions of special relativity or even Newtonian physics (again, despite the experiments to the contrary). Occasionally even numerology makes an appearance.

Another option is arguments by analogy. Analogies are useful when explaining science to a broad audience, but they aren’t the be-all and end-all of science.

In pseudoscience, the analogy is taken to the point of absurdity, with sprawling articles (or blog posts) weighed down with laboured analogies rather than meaningful analyses.

Desiring simplicity but getting complexity

Perhaps the most fascinating aspect of pseudoscientific theories is they hark for simplicity, but really just displace complexity.

A desire for naively simple science can produce bizarrely complex conclusions, like the moon landing hoax conspiracy theories. NASA/flickr

Ardents of the most simplistic pseudoscientific theories often project complexity onto the motives of professional scientists. How else can one explain scientists ignoring their brilliant theories? Claims of hoaxes and scams are commonplace. Although, to be honest, even I laughed out loud the first time I saw someone describe dark matter was a “modelling scam”.

Again, this isn’t limited to those who don’t believe in relativity. Simple misunderstandings about photography, lighting and perspective are the launch pad for moon landing conspiracy theories. Naively simple approaches to science can lead to complex conspiracy theories.

Changing intuition

Some have suggested that pseudoscience is becoming more popular and the internet certainly aids the transmission of nonsense. But when I look at history I wonder if pseudoscience will decay.

In the 19th century, Samuel Rowbotham promoted Flat Earthism to large audiences via lectures that combined wit and fierce debating skills. Perhaps in the 19th century a spherical world orbiting a sun millions of kilometres away didn’t seem intuitive.

But today we can fly around the globe, navigate with GPS and Skype friends in different timezones. Today, a spherical Earth is far more intuitive than it once was, and Flat Earthism is the exemplar of absurd beliefs.

Could history repeat with relativity? Already GPS utilises general relativity to achieve its amazing precision. A key plot device in the movie Interstellar was relativistic time dilation.

Perhaps with time, a greater exposure to general relativity will make it more intuitive. And if this happens, a key motivation of crank theories will be diminished.

Will general relativity become more widely understood via popular media, such as the movie Interstellar?

Michael will be on hand for an Author Q&A between 4 and 5pm AEDT on Tuesday, November 24, 2015. Post your questions in the comments section below.

The ConversationMichael J. I. Brown, Associate professor, Monash University

This article was originally published on The Conversation. (Reblogged by permission). Read the original article.


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The Astronomical Renaissance

by Tim Harding BSc BA

(An edited version of this essay was published in The Skeptic magazine, March 2015, Vol 35 No 1, under the title ‘Rebirth of the Universe’.  The essay is based on a talk presented to the Mordi Skeptics, Tuesday 11 November 2014).

This article follows on from my previous one on ancient astronomy and astrology (‘An Eye to the Sky’, The Skeptic, Vol. 33, No. 4, December 2013).  That story began about 4000 years ago in Babylon, then moved to the first scientific revolution in ancient Greece, ending with Ptolemy’s complicated geocentric (Earth-centred) model of the cosmos in the 2nd century CE.

We now make a great leap forward to the second scientific revolution beginning with the publication of Nicolaus Copernicus’ heliocentric (Sun-centred) model of the cosmos in 1543 CE.  Why the huge gap?  Because astonishingly, nothing much happened in cosmology for about 1400 years between Ptolemy and Copernicus.  (The reasons for this are complex and best left to a possible future article).

After the Fall of Constantinople in 1453 CE, there was a rediscovery of ancient Greek texts written by philosophers and scientists such as Plato, Aristotle, Aristarchus, Archimedes and Ptolemy.  That is why this subsequent period is described as an astronomical renaissance (alongside the cultural renaissance), from the French word meaning ‘re-birth’.  The midwives of this re-birth were the development of scientific methods and the invention of printing, which would improve access to learning, allowing a faster propagation of new ideas.

Copernicus’s astronomical observations were complemented and improved in accuracy by those of Tycho Brahe.  His heliocentric model was later adopted by Galileo Galilei and then refined by Johannes Kepler.

Nicholas Copernicus (1473- 1573 CE)

Copernicus was born 1473 in the Polish city of Torun.  His father was copper merchant – the name ‘Copernicus’ is thought to be derived from this occupation.  He studied mathematics, philosophy and astronomy at the University of Krakow; then medicine at Padua in Italy.  He was also a lawyer, physician, classics scholar, translator and economist.

copernicusatwork2 crop

Nicolaus Copernicus

As well as being a polymath, Copernicus was also a polyglot, which gave him access to the ancient Greek texts.  From these writings he would most likely have known that Aristarchus of Samos had some 1800 years earlier proposed a heliocentric model of the cosmos in the third century BCE.  Aristarchus had also calculated the diameters of the Sun and Moon, as well as their distances from the Earth in Earth radii.  This regression from the correct heliocentric to the incorrect geocentric model presents a serious challenge to our notions of inevitable human progress.

In around 1510, Copernicus moved to one of the defensive towers of the cathedral town of Frombork on the Baltic Sea coast, where he did most of his astronomical observations and writing.  His attempts at retrofitting cosmological theory to seemingly endless observational anomalies eventually became just too complex.  Simplification became a major motivation for Copernicus to construct his revolutionary heliocentric model.  His colleague Andreas Osiander, a Lutheran theologian, wrote an anonymous preface to Copernicus’ published major work De Revolutionibus.  This preface stated that Copernicus’ system was merely mathematics intended to aid computation and not an attempt to declare literal truth.  Both Copernicus and Osiander probably feared the reaction not only of other astronomers but also the Roman Church – a fear that was later justified by the trial of Galileo, of which more will be said later.  The delay in publication until the eve of Copernicus’ death is thought to be due to these fears.

Thirty years earlier in about 1514, Copernicus had written the Commentariolus – an unpublished outline of his later De Revolutionibus. In this outline, he proposed seven axioms, all of which are true:

  1. Heavenly bodies do not all move around same centre.
  2. The Earth is not centre of the cosmos – only the Moon’s orbit.
  3. The Sun is the centre of the planetary system.
  4. The Stars are much further away than the Sun.
  5. The apparent daily revolution of the stars and planets is due to the Earth’s rotation on its own axis.
  6. The apparent annual motion of the Sun is due to the revolution of Earth around the Sun.
  7. The apparent retrograde motion of the planets has same cause.

Copernicus’ heliocentric model of the cosmos

However, Copernicus clung to the erroneous theological belief that all the orbits of celestial bodies must be perfect circles.  This forced Copernicus to retain Ptolemy’s complex system of planetary epicycles, thus leading him astray.  At first, Copernicus initially proposed that only 34 epicycles were needed in his model, but he was later forced to modify the model by increasing this number to 48 – eight more cycles than the 40 in Ptolemy’s model.  These anomalies led Kepler to subsequently propose elliptical rather than circular planetary orbits, as will be discussed later.

Copernicus also modified his model to account for the apparent absence of stellar parallax during the Earth’s orbit around the Sun.  He did this by postulating that the distance of the fixed stars was so immense compared to the diameter of the earth’s orbit that stellar parallax was unnoticeable by the accuracy of astronomical observations at that time.  This modification subsequently turned out to be correct in reality, but at the time it was an ad hoc modification made for the purpose of correcting an imagined observational anomaly.

Tycho Brahe (1546 – 1601 CE)

Tycho Brahe was a colourful character, born 1546 into an aristocratic family in Scania which was then part of Denmark but is now in Sweden. He studied law and astronomy at University of Copenhagen.  He is notorious for losing part of his nose in sword fight, so he had to wear a brass prosthetic nose.  Another piece of irrelevant trivia is that Tycho had a pet Elk that once drank too much beer at one of his friends’ dinner parties.  Sadly, the inebriated Elk fell down some stairs and died.

Tycho’s observatory on the island of Hven in Sweden

Tycho’s observatory on the island of Hven in Sweden

In 1597, Tycho fell out with Danish King Christian IV and became court astronomer to Holy Roman Emperor Rudolph II in Prague, who funded the building of a state-of-the-art new observatory for Tycho.  Johannes Kepler was employed as Tycho’s assistant, who later used Tycho’s more accurate observational data for his own astronomical calculations.  These more precise measurements clearly showed that the stars lacked parallax, thus confirming that either the Earth was stationary or the stars were a vast distance from the Earth.

Tycho proposed a hybrid ‘geo-heliocentric’ system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun (known as the Tychonic system). This system provided a safe position for astronomers who were dissatisfied with the Ptolemaic model but were reluctant to endorse the Copernican model.  The Tychonic system became more popular after 1615 when Rome decided officially that the heliocentric model was contrary to both philosophy and scripture, and could be discussed only as a computational convenience that had no connection to the truth.

Galileo Galilei (1564- 1642 CE)

Galileo Galilei was a physicist, mathematician, engineer, astronomer, and philosopher who arguably contributed more than anybody to both the second scientific revolution and the astronomical renaissance.  He was born 1564 in Pisa, Italy, and educated in the Camaldolese Monastery at Vallombrosa, 35 km southeast of Florence.  He enrolled at the University of Pisa for a medical degree, but switched to mathematics and natural philosophy.

Galileo Galilei

Galileo Galilei

Galileo’s contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean moons in his honour), the roughness of the Moon’s surface, and the observation and analysis of sunspots. He also made contributions to physics, including the science of dynamics, leading to Newton’s laws of motion later on.

He championed Copernicus’ heliocentrism when it was still controversial – most astronomers at this time subscribed to either geocentrism or the Tychonic system.  They doubted heliocentrism due to the absence of an observed stellar parallax, without appreciating the enormous distances involved.

When confronted with this absence of stellar parallax, Galileo attempted an ad hoc modification to the Copernican model by incorrectly claiming that the tides are caused by the earth’s rotation combined with its orbit around the Sun.  This is despite the ancient Greek philosopher Seleucus some 1600 years earlier having correctly theorized that tides were caused by the gravitational effect of the Moon’s orbit around the Earth.  .

Galileo showing his telescope to the Doge of Venice

Galileo showing his telescope to the Doge of Venice

After the Roman Inquisition of 1615, works advocating the Copernican system were placed on the index of banned books and Galileo was forbidden from advocating heliocentrism.  This resulted in heated correspondence between Galileo and the Vatican.  Unfortunately, Galileo’s aggressive manner alienated not only the Pope but also the Jesuits, both of whom had tolerated him up until this point. He was tried by the Holy Office and found ‘vehemently suspect of heresy’, then forced to recant, and spent the rest of his life under house arrest.

At least Galileo did not suffer the cruel fate of the philosopher and cosmologist Giordano Bruno, who in 1600 was burned at the stake for heresy in Rome’s Campo de’ Fiori (a market square where there is now a statue of him).  Bruno had gone even further than the Copernican model, correctly proposing that the stars were just distant suns surrounded by their own exoplanets.  He suggested the possibility that these planets could even foster life of their own (a philosophical position known as cosmic pluralism).  Bruno also believed that the Universe is in fact infinite, thus having no celestial body at its ‘center’.

Johannes Kepler (1571- 1630 CE)

Johannes Kepler was a German mathematician, astronomer and astrologer (before these areas of study separated). A key figure in the second scientific revolution, he is best known for his three laws of planetary motion, which endure today. These laws also provided one of the foundations for Isaac Newton’s theory of universal gravitation.

Kepler was born in 1571 in Stuttgart area of Germany. At age six, he observed the Great Comet of 1577, and at age nine, the lunar eclipse of 1580.  These events inspired him to study philosophy, theology mathematics and astronomy at the University of Tübingen.  Here he learned both the Ptolemaic system and the Copernican system of planetary motion.  He later observed a bright supernova (exploding star) of 1604, which became known as Kepler’s Supernova.

After graduation, Kepler became a mathematics teacher at a seminary school in Graz, Austria. Later he became an assistant to astronomer Tycho Brahe, and eventually the imperial mathematician to Emperor Rudolf II and his two successors Matthias and Ferdinand II. He was also a mathematics teacher in Linz, Austria, and an adviser to General Wallenstein. Additionally, he did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope).

Frontispiece to the Rudolphine Tables (Latin: Tabulae Rudolphinae) consisting of a star catalogue and planetary tables published by Johannes Kepler in 1627, using some observational data collected by Tycho Brahe

Frontispiece to the Rudolphine Tables consisting of a star catalogue and planetary tables published by Johannes Kepler in 1627, using observational data collected by Tycho Brahe

Kepler then set about calculating the entire orbit of Mars, using the geometrical rate law and assuming an egg-shaped ovoid orbit. After many failed attempts, in early 1605 he at last hit upon the idea of an ellipse, which he had previously assumed to be too simple a solution for earlier astronomers to have overlooked. Finding that an elliptical orbit fitted the Mars data, he immediately concluded that all planets move in ellipses, with the sun at one focus — which became Kepler’s first law of planetary motion.

He then formulated two more laws of planetary motion.  These are firstly, that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time; and secondly, that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

Because of his religious beliefs, Kepler became convinced that God had created the universe according to perfectly harmonious geometrical shapes and patterns. He began by exploring regular polygons and regular solids, including the figures that would come to be known as Kepler’s solids.  Unfortunately, Kepler wasted a lot of his time fruitlessly searching for this underlying ‘harmony of the spheres’, drawing all sorts of weird and wonderful diagrams.  He even (unsuccessfully) tried to relate these geometric shapes to musical harmonies.

Keplers solids

Kepler’s solids

Concluding remarks

The great physicist Isaac Newton was later able to build upon the pioneering work of Galileo and Kepler, leading him to make his famous quotation ‘If I have seen further it is only by standing on the shoulders of giants’.

In contrast, it is perplexing to observe two great human failures. Firstly, how science was repeatedly led astray by fruitless searches for perfection in ‘God’s design of the cosmos’.  Secondly, that astronomical knowledge not only progressed very little during the 1400 years between Ptolemy and Copernicus, but in some areas it actually regressed.  The ancient Greeks had not only proposed a heliocentric model of the cosmos, but they had also calculated the diameters of the Sun and Moon, as well as their distances from the Earth.  They also knew that the tides were caused the gravitational effect of the Moon’s orbit around the Earth.  This valuable knowledge was either forgotten or rejected until the astronomical renaissance some 1800 years later. So much for the notion of inevitable human progress.


Koestler, A (1959) The Sleepwalkers. London: Hutchinson.

Kuhn, T.S. (1962) The Structure of Scientific Revolutions 3rd ed. Chicago: University of Chicago Press.

Toulmin, S. and Goodfield, J. (1961) The Fabric of the Heavens.  London: Hutchinson.

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