Category Archives: Myths of Science

Telescopic bollocks from NdGT

Renaissance Mathematicus friend, Michael Barton, expert for all things Darwinian, drew our attention to a new piece of history of science hot air from the HISTSCI_HULK’s least favourite windbag, Neil deGrasse Tyson. This time it’s a clip from one of his appearances on the podcast of Joe Rogan, a marriage made in heaven; they compete to see who can produce the biggest pile of bullshit in the shortest time. NdGT is this time pontificating about Galileo and the telescope. This is particularly interesting, because the topics he touches on are well documented in easily accessible sources, so it would really be not particularly difficult to gets the facts right. But motormouth Tyson doesn’t give a shit about getting his facts right, he just spews out some bullshit to impress the gullible punters. 

I have transcribed what he says in this brief clip, so let us examine it:

Galileo perfects the telescope. He looks up and says whoa I see craters, mountains, valleys on the Moon, the Sun has spots, Venus goes through phases. This became the corpus of evidence for Earth going around the Sun in support of Copernicus’s idea that Earth goes around the Sun. My point is, what was the second thing he did with his telescope? He contacted the Doge of Venice, invited him to the clock tower and said, look at what this instrument can do for you, as we look out into the lagoon you can identify a ship’s intentions friend or foe by its flag 10 times farther away than you can with the unaided eye. Venice bought a boatload of these telescopes in the service of their military defense, and this was a source of money to Galileo, now he can go and look at the Universe.

I will excuse Tyson his, “Galileo perfects the telescope,” as it is a very widespread misconception that gets constantly repeated by numerous people, many of whom should know better. There was no fundamental optical difference between the instrument that Hans Lipperhey (c. 1570–1619) demonstrated in Den Haag to the Court of Prince Maurits of Orange during the last week of September 1608 and the various instruments that Galileo constructed. The only difference was that Galileo, probably by a process of trial and error, increased step by step the magnification of his instruments by using lenses of different focal lengths. A process that a substantial number of telescope users went through at the same time. A worse version of this false claim is that Lipperhey’s instrument was merely a toy and Galileo made a “real” instrument out of it. Lipperhey’s spy glass was a proper optical instrument, the military potential of which was instantly recognized during his demonstration. To use the words perfect or perfection in connection with any of the early Dutch or Galilean telescope is perverse as they were, due to the poor quality of the glass and of the lens grinding and polishing, of fairly miserable quality. As I have said on numerous occasions the quality was so poor that it was a miracle that anybody discovered anything at all with them. 

Galileo’s telescopes

Tyson now makes two general claims, firstly stating some of the things that Galileo discovered with his telescope and secondly his demonstration of the telescope to the Doge and Senate of the city of Venice. He introduces the second as follows, “My point is, what was the second thing he did with his telescope?” this is completely arse backwards. 

Galileo dismissed the first account that he had read of the telescope, and it was only when Paolo Sarpi drew his attention to the telescope and almost certainly showed him one, according to the most recent research by Mario Biagioli, that he took up the challenge of trying to construct one himself. By August 1609 he had succeeded in constructing an instrument with a magnifying factor of nine and it was this instrument that he demonstrated to the Doge and Senate on 21 August pointing out its advantages for a sea going nation like Venice. On 24 August he formally presented this instrument to the Doge and Senate. In the early seventeenth century patents as we know them didn’t exist and it was perfectly possible for someone to be regarded as the local inventor of an instrument and to receive an exclusive license for the area of jurisdiction of the local authority, it was this status that Galileo claimed for himself, but which on 24 August he formally signed over to the city state of Venice. This is documented in writing. In exchange for having signed over his rights to the telescope Galileo had his appointment as professor at the University of Padua confirmed for life and his salary increased to one thousand scudi pro year, a princely sum for a university professor. Particularly for a professor of mathematics, who were at the very bottom of the university status and pay hierarchy. When the state discovered that they had been basically gulled by Galileo and that telescopes could be bought on almost every street corner in Europe they were less than happy but did not revoke his rewards. Galileo repaid their generosity by beginning plans to leave Venice and return to Florence.

Galileo Galilei showing the Doge of Venice how to use the telescope by Giuseppe Bertini (1858). Credit:

Galileo was required to keep the technical knowledge of his telescope, now the legal property of the state, secret and the only technical description that we have of his instrument in contained in one of Sarpi’s private letters, he, probably, having been commissioned by the state to examine it on their behalf. There is no record of the city of Venice buying “a boatload of these telescopes” and we only have one single source, a letter from Giovanni Bartoli, the Medici representative in Venice, claiming that Galileo was building twelve telescopes for the senate. Given the situation they would have exchanged hands at something close to cost price. Once the basic structure of the Dutch telescope was known the senate did not need Galileo to manufacture telescopes for them. Venice produced the best glass in the world and was a major European centre for the manufacture of spectacles. Someone who can grind spectacles lenses can also grind telescope lenses. 

As far as we know Galileo didn’t start making systematic telescopic astronomical observations until December 1609 by which time, he had succeeded to constructing an instrument with a magnifying factor of twenty. Tyson mentions three of Galileo’s telescopic discoveries, “craters, mountains, valleys on the Moon, the Sun has spots, Venus goes through phases.” Only the first of these, the earth like nature of the Moon, was in the first series of discoveries, which he published in his Sidereus Nuncius in 1610. It is also the only discovery made by Galileo that can be truly credited to him alone. Thomas Harriot had made a telescopic sketch of the Moon before Galileo even had a telescope but had still perceived the surface as flat.

Thomas Harriot’ telescopic sketch of the Moon Source: Wikimedia Commons

Almost certainly due to his training as an artist, Galileo realized that what he was observing was a three-dimensional surface, which he then displayed in his famous washes in the Sidereus Nuncius. When Harriot, being an early recipient of the Sidereus Nuncius, saw them he immediately realized that Galileo was right and then produced the first fairly accurate map of the Moon.

Thomas Harriot’s 1613 telescopic map of the moon Source: Wikimedia Commons

Galileo didn’t produce anything new on the Moon and it should be noted that his washes were more an artistic impression than accurate drawings; the large crater near the bottom in the centre simply doesn’t exist in reality.

Galileo’s washes of the Moon from Sidereus Nuncius Source: Wikimedia Commons

 Galileo’s discovery was not as sensational, as it is often presented. That the moon was earth like and that the well-known markings on the moon, the man in the moon etc., are in fact a mountainous landscape was a view held by various in antiquity, such as Thales, Orpheus, Anaxagoras, Democritus, Pythagoras, Philolaus, Plutarch and Lucian. In particular Plutarch (c. 46–c. 120 CE) in his On the Face of the Moon in his Moralia.

It should be noted that Tyson fails to mention Galileo’s most spectacular discovery, the Moons of Jupiter, the reason that he rushed into print with his Sidereus Nuncius, Before its publication Galileo was a middle aged professor of mathematics, as already noted not a prestigious post, in North Italy with a local reputation for his acerbic wit and his indulgence in fine wines, with no publications to speak of. After Sidereus Nuncius hit the streets he became to most famous astronomer in Europe and a celebrated academic.

All the other early telescopic astronomical discoveries were made not just by Galileo but independently by several observers at around the same time, which, of course, Tyson doesn’t mention. The Sunspots were first observed by Thomas Harriot, who, as usual, didn’t publish. The first to publish was Johannes Fabricius, who had observed them together with his father David; this was unknown to Galileo.

Source: Wikimedia Commons

Christoph Scheiner also observed them and made the knowledge public through the standard Renaissance method, the republic of letters, by sending a series of letters to the German banker and astronomer Mark Welser, who forwarded them to Galileo and also published them. Galileo responded with letters of his own claiming to have discovered them first. A claim that can be doubted, as he kept changing the date when he supposedly observed them pushing it back each time. Galileo proved that the spots were actually on the surface of the Sun, whereas Scheiner first thought they orbited the Sun. Once again, as with the Moon, Galileo did little more with the sunspots, whereas Scheiner undertook a major solar observation programme that led to his Rosa Ursina sive Sol, a book on solar astronomy that remained unsurpassed until the nineteenth century.

The discovery of the phases of Venus was first made in 1613 independently by four different observers–Galileo, Simon Marius, Thomas Harriot, the Jesuit astronomers of the Collegio Romano–with the latter probably discovering them before Galileo. 

Neither the “craters, mountains, valleys on the Moon”, nor “the Sun has spots” became “the corpus of evidence for Earth going around the Sun”, which anybody who gives it two second rational thought would realise. I mean, in what way does did covering that the surface of the Moon is mountainous, or that the Sun has spots provide evidence that the Earth orbits the Sun? Apparently, Tyson does consider rational though necessary before he opens his mouth. 

The phases of Venus, that those pioneer astronomical telescopic observers discovered, did show clearly that Venus orbits the Sun. If Venus had orbited the Earth, it would also have had phases, but they would have been different. 

The Phases of Venus in both systems

To what extent the discovery was regarded as evidence that the Earth goes around the Sun was an open question at the time. Already in the fifth century CE, Martianus Capella (fl. c.410) had proposed a geocentric system in which both Mercury and Venus orbited the Sun, which in turn orbits the Earth. This was deduced from the fact that, viewed from the Earth, they never stray far from the Sun, they appear on different sides of the Sun at different times, hence Venus as both Morning Star and Evening Star, and the length of their apparent orbit around the Earth is the same as that of the Sun, one year.  

Capellan system – Valentin Naboth (1573)

Famously, following the publication of Copernicus’ De revolutionibus, Tycho Brahe and others extended Capella’s concept and developed a system in which all the known planets orbited the Sun, which, in turn, with the Moon orbited the Earth. A geo-heliocentric system, normally named after Tycho, a Tychonic system.

The Tychonic system

The discovered phases of Venus were conform with both the Capellan and the Tychonic systems and were initially taken as proof of such. 

It might appear that I have wasted a lot of words picking to pieces Tyson’s roughly 150-word, off the cuff inanities. However, they stand representative for a very common trend in science communication. Popular figures, with very large audiences, who are venerated as science communicators, of which NdGT is a prime example, spout sound bite version of the history of science that are at best highly inaccurate and at worst simply false. This fuels, what I call, the mythology of science, a discipline that has pretension to being the history of science but is anything but. Because of their popularity and the size of their audiences, who are largely ignorant, in the sense of lacking knowledge, people like Tyson spread this mythology leading to a false public perception of how science arises and how it evolves. The clip, that I quoted at the start of this post, is the preamble to one of the biggest, most pernicious, and most widely propagated myths in the history of science, that Galileo with his telescopic discoveries proved Copernicus right and it was only the religious prejudice of the Church that tried to convince the people that he was wrong, even going so far as to punish him for it.

Me and my #histsci buddy the HISTSCI_HULK have dedicated our lives to trying to rot out the cancer that is the mythology of science. It’s like a giant game of Whac-A-Mole but as long as the moles keep popping up, we’ll keep on bashing them down.


Filed under History of Astronomy, Myths of Science

A cosmologist screws up the history of cosmology

I got pulled into a Twitter exchange with a self-proclaimed science writer called Spencer (@Unpop_Science), who was ranting about “abysmal ecological education in Western society. His rant contained the tweet:

Ecology challenges the Abrahamic religions of the West, which mythologize human supremacy over the vast, complex Universe our species inhabits. It’s no coincidence that Western history’s most persecuted scientists are Galileo & Darwin — whose theories challenged human supremacy.

One of my Twitter followers, not surprisingly, asked me about Darwin being persecuted!?

Darwin was of course not persecuted but I couldn’t resist tweeting the following:

Excuse me for asking, but in what way did Galileo’s theories challenge human supremacy?

Mr ScienceWriter: They disproved the myth that the Universe revolves around us.

Me: Go away and learn some history of cosmology, that was never the belief of people before the acceptance of heliocentricity. Also, Galileo proved absolutely nothing in this context.

You are repeating a myth created in the late 18th earth 19th centuries by people such as Goethe and Kant that in the geometric cosmos humanity was in the exalted position, at the centre. For the real picture read this

And I linked to this quote on my blog:



Since, however, almost everyone has been of the conviction that the earth is immobile since it is a heavy body, the dregs, as it were, of the universe and for this reason situated in the middle or the lowest region of the heaven

Otto von Guericke; The New (So-Called) Magdeburg Experiments of Otto von Guericke, trans. with pref. by Margaret Glover Foley Ames. Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, pp 15 – 16. (my emphasis)

Mr ScienceWriter: That’s it? Your own blog with one quote saying Earth is “the lowest region of the heaven”? What an amazingly lazy attempt to revise history.

Me: Not revising history that was the standard view in the Early Modern Period. You are the person who very obviously doesn’t know any history.

After his last tweet above Mr ScienceWriter linked to the webpage A Brief History, which is part of the website What is the Ultimate Fate of the Universe? Created by Molly Read of the Observational Cosmology Group at the University of Wisconsin-Madison.

Let us examine what a cosmologist, not a historian, has to tell us about the history of 2000 years of cosmology in a couple of hundred words. But before I do let us re-examine how we got here. I, for my sins, a professional historian of science, who specialises in the history of the mathematical sciences in the Early Modern Period, which of course includes the histories of astronomy and cosmology presented Mr ScienceWriter with a referenced quote from a leading seventeenth-century scholar that explains in plain terms that the people in this period didn’t think that the universe revolves around them but rather thought they lived in the garbage pit. Mr ScienceWriter, apparently an ecologist sneered because the quote was presented on my blog and cancelled me with, “What an amazingly lazy attempt to revise history.” As a counter he links to a webpage (is a webpage somehow superior to a blog?), where a cosmologist, not a historian, presents an incredibly brief history of two thousand years of cosmology without any sources, references and this is supposed to represent the “real” history! 

Since early times, man has been fascinated with discovering the origins of the cosmos. Similarly, man has often been influenced by his creationist ideas: that some divine power created the universe and everything in it. For example, the Ancient Greeks developed some of the earliest recorded theories of the origin of the universe. Unfortunately, many of these Greek philosophers and astronomers placed the Earth in the center of their models of the universe. They thought, if the heavens are divine, and the gods created man, well then certainly the universe must be geocentric, meaning the Earth is the center of the universe. 

The argument presented here as to why all early models of the cosmos are geocentric is so bizarre it hurts. I don’t know how oft I have repeated this over the years, but we live in a geocentric world. A couple of simple thought experiments. Imagine standing on a plane with a distant horizon in every direction. There can be mountains, hills, forests, or even an open stretch of water on the horizon in any particular direction. Now imagine rotating on your own axis through 360 degrees, stopping, then rotating back through 360 degrees. Everything you perceive whilst you turn has you at the centre, it’s a fact of life. Your perception is “youcentric” by definition. 

Now we turn to cosmology. Go out at night somewhere in the middle of the country, where there is no light pollution and lay down on you back in the middle of a meadow and observe the night sky. If you lie there long enough, you will see the night sky revolving over your head. If you lie there for many nights, you will see a steady change in the night sky. Do this for many years and you will recognise repeating patterns in the changes in the night sky. This is how astronomy and cosmology were both born and because the observer was per definition is at the centre of the observations the picture of the perceptible cosmos that the observer develops is by necessity geocentric. It is virtually impossible for anybody to perceive the cosmos as anything else. This is what makes thinkers like Aristarchus of Samos or Copernicus so unique in human history. It’s thinking outside of the box with a vengeance. 

One should also not forget that whereas everything observable in the heavens appears to move that platform from which our observer is making their observations, the Earth, shows no signs of moving in anyway whatsoever. Providing empirical proof that the Earth moves proved incredibly difficult. Such a proof that the Earth orbits the Sun was first delivered by Bradley’s discovery of stella aberration in 1725 (published 1728) that’s 182 years after the publication of Copernicus’ De revolutionibus! We had to wait until 1851, that’s 308 years after the publication of De revolutionibus, before we had an empirical proof of diurnal rotation!

Ancient societies were obsessed with the idea that God must have placed humans at the center of the cosmos (a way of referring to the universe).

Those pioneering astronomers were far from thinking that they were supreme, as Mr ScienceWriter would have us believe. In almost all of those early cultures that developed astronomy, when they discovered the planets, they thought they were gods. We still use the Roman gods’ names for the planets today. Those humans considered themselves to be at the mercy of the capriciousness of those, anything but friendly, gods, who controlled their fate, having dumped them on the hostile Earth, while they, the gods, reigned supreme in the heavens. 

An astronomer named Eudoxus created the first model of a geocentric universe around 380 B.C. Eudoxus designed his model of the universe as a series of cosmic spheres containing the stars, the sun, and the moon all built around the Earth at its center. Unfortunately, as the Greeks continued to explore the motion of the sun, the moon, and the other planets, it became increasingly apparent that their geocentric models could not accurately nor easily predict the motion of the other planets.

Eudoxus (c. 400–c. 350 BCE) did not create the first model of a geocentric universe. He did not even create the first Greek, model of a geocentric universe. Maybe our cosmologist meant to say that Eudoxus created the first mathematical (speak geometrical) model of a geocentric universe but even that wouldn’t be true. At best we can say that Eudoxus created the first Greek, mathematical, model of a geocentric universe, there were earlier Babylonian mathematical models, which were however based on algebraic algorithms, not geometry. The Greek’s were aware of this having acquired much of their astronomical data from the Babylonians. 

The various Greek geocentric models might have been complicated but they were surprisingly accurate in their ability to track the movement of the celestial bodies. Our cosmologist now delivers a standard explanation of the phenomenon of retrograde planetary motion, which closes with a snarky comment.

Take the apparent motion of Mars from an observer on the Earth, for example. As the Earth and Mars orbit around the sun, Mars appears to advance forwards, and then stop and start moving backwards, and then stop and change direction once again to start moving forwards (shown in the picture at left). You can see in the picture that this phenomenon is easily explained by a heliocentric universe (“heliocentric” meaning the sun is the center of the universe), but imagine being an ancient Greek and trying to understand why Mars would follow such an unusual orbit (when, according to them, it was supposed to have a circular orbit) if the Earth was the center of the universe!

Although the apparent motion of the planets contradicted the philosophical axioms of Ancient Greek cosmology, the astronomers did succeed in producing ingenious, functional models of that described fairly accurately that errant planetary behaviour. Our cosmologist nowhere explains the ingenious method that Eudoxus developed to solve this apparent contradiction, he system of nested homocentric spheres. She links to a diagram of part of Eudoxus’ system without any explanation of what it is and how it works.

After Aristotle developed a more intricate geocentric model (which was later refined by Ptolemy), general cosmology clung to these misconstrued ideas for the next 2,000 years. 

We now spring direct to Aristotle, what no Callipus (c. 370­–c. 300 BCE)? If you are going to talk about the nested homocentric spheres model developed by Eudoxus, then you should mention the improvement made by Callipus before moving on to the improvements made by Aristotle (382–322 BCE). Having completely ignored Apollonius (c. 240–c. 190 BCE) and Hipparchus (c. 190–c. 120 BCE), our cosmologist now jumps the shark stating, “which was later refined by Ptolemy,” the Eudoxian/Aristotelian system of homocentric spheres is completely different to the deferent/epicycle models developed by Ptolemy (c. 100–c. 170 CE). The two systems where contradictory and their supporters competed with each other over the next fourteen centuries.

Eudoxus’s model of planetary motion. Each of his homocentric spheres is represented here as a ring which rotates on the axis shown. The outermost (yellow) sphere rotates once per day; the second (blue) describes the planet’s motion through the zodiac; the third (green) and fourth (red) together move the planet along a figure-eight curve (or hippopede) to explain retrograde motion. Source: Wikimedia Commons
The epicycles of the planets in orbit around Earth (Earth at the centre). The path-line is the combined motion of the planet’s orbit (deferent) around Earth and within the orbit itself (epicycle). Source: Wikipedia Commons

Our cosmologist completely ignores the discussions, challenges, criticisms, and improvements made to the geocentric astronomical models, first in late antiquity, then by Islamic astronomer, and finally by medieval European astronomers, during those fourteen centuries before Copernicus emerged with his heliocentric model. She also completely ignores the geoheliocentric model first discussed by Martianus Capella (fl. c. 410), in which Venus and Mercury orbited the Sun which in turn orbited the Earth with the other planets,

Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

as well as the geocentric model with diurnal rotation first proposed by Heraclides Ponticus (c. 390–c. 310 BCE). Both of these models were well-known and much discussed throughout the Middle Ages and are important developments in the direction of a heliocentric system. Calling those models misconstrued ideas displays an incredible ignorance on the part of our cosmologist. They are rational attempts to model the empirical evidence available to the senses at the time.   

We then get the classic piece of bullshit ignorance:

Even when Nicholas Copernicus, introduced the notion of a heliocentric universe, many contemporary societies greatly influenced by religious beliefs refused to accept it. 

That a professional academic from a large, public American university is writing crap like this in the twenty-first century beggars belief. Professional astronomers in the second half of the sixteenth century and the first half of the seventeenth didn’t accept a heliocentric model of the cosmos because there was no empirical evidence to support a moving Earth theory. As already noted above the necessary empirical evidence was first delivered 182 years, orbit around the Sun, and 308 years, diurnal rotation, after the publication of Copernicus’ De revolutionibus! Around the end of the first decade of the seventeenth century there were at least nine models of the cosmos vying for attention–Ptolemaic geocentric with or without diurnal rotation, Aristotelian homocentric, Capellan with or without diurnal rotation, Tychonic with or without diurnal rotation, Copernican heliocentric, Keplerian heliocentric and yes, the Copernican and Keplerian systems were regarded as rivals. 

Someone might ask why all the details, isn’t a simplified version of the history as presented by here by our cosmologist enough? The answer is a categorical no. The highly simplified and factually inaccurate version presented here is a falsification and corruption of the actually historical evolution of astronomy and cosmology over a period of more than two thousand years, which leads to statements such as “the Ptolemaic model of the cosmos ruled uncontested for 1400 years until Nicholas Copernicus challenged it.” Over the years I have stumbled across many variants of this historically incorrect statement. In reality from well before Eudoxus developed his geometrical model of the cosmos, cosmology and astronomy evolved in the constant ebb and flow of an intensive and complex philosophical and scientific debate. As I have explained in the past, Copernicus’ contribution was made during a period when that debate was, for various reasons, raging particularly strongly. 

Turning back to the original debate on Twitter that led to all of this, I will give a hopefully brief account of the real perception of humanities place and status in the cosmos at the time Galileo made his contributions to the ongoing debate. The primary model of the cosmos in Europe in the High Middle Ages and going on into the Renaissance, that is the one Galileo would have been acquainted with when he first became interested in astronomy, was a mixture of Aristotelian cosmology, Ptolemaic astronomy, and Catholic theology. There were variations and alternatives, as I have outlined above, but they don’t need to concern us here. The philosophical picture was determined by the Aristotelian cosmology, and Catholic theology, the Ptolemaic astronomy being regarded as purely an instrumental device to determine astronomical data for astrology, computus, that is calculating the movable church feast days, ect. 

Aristotle’s cosmology divided the cosmos into two, everything above the moons orbit, the supralunar sphere, and everything under the moons orbit, the sublunar sphere. Everything in the supralunar sphere, that is the heavens, consisting of the so called fifth element, quintessence or aether, was perfect, unchanging, eternal, and incorruptible. Everything in the sublunar sphere, that is the Earth and its atmosphere, was made of the four elements–earth, water, air, fire–was subject to change, decay, and corruption. There were initially seven heavens, corresponding to the orbits of the seven planets–Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn–a concept that predated Christianity. Each of these orbits was encased in a celestial sphere. Outside of the orbit of Saturn was the eighth sphere of the fixed stars. Over time a nineth and tenth spheres were added for mechanical reason. All of these spheres or heavens rotate, the nineth or tenth, depending on model, model the Primum Mobile providing the driving force for the whole construction.  In the Catholic theology, outside of the tenth sphere was a sphere that did not rotate, the Empyrean, the abode of God.  

Geocentric celestial spheres; Peter Apian’s Cosmographia (Antwerp, 1539) Source: Wikimedia Commons

Here it is obvious that the central point is the Empyrean, the abode of God, and in importance one either ascend into the heavens to God, or descend to the corrupt and sinful Earth, or even deeper into the pits of hell beneath the Earth.  It is very clear in this concept there is no human supremacy but as Otto von Guericke put it so succinctly, the Earth is the dregs… or the lowest region of the cosmos. Cicero in his Dream of Scipio describes an ascent through the celestial spheres, “compared to which the Earth and “Scipio now noticed that the stars were globes which easily outstripped to earth in size. Indeed the earth now appeared so small in comparison that the Roman Empire, which was hardly more than a point on that tiny surface, excited his contempt.” Macrobius in his commentary to Cicero’s work strengthened this image and spread it through the Middle Ages.

The Universe, the Earth in the centre, surrounded by the seven planets within the zodiacal signs. Image from a 12th-century manuscript of Macrobius’ Commentarii in Somnium Scipionis via Wikimedia Commons

In the Paradiso, in Dante’s Divine Comedy the image of ascending away from the corrupt Earth into the perfect Empyrean is the central theme of his narrative.

Illustration for Paradiso (of The Divine Comedy) by Gustave Doré Source: Wikimedia Commons

Galileo was well acquainted with the Divine Comedy; his very first public lecture was a reconstruction of the dimensions of hell in the Inferno.

A final example comes from the work of the highly influential medieval French philosopher, astronomer, physicist, and theologian Nicole Oresme (c.1320­–1382). In his Le livre du Ciel et du Monde, a translation of and commentary on Aristotle’s De caelo produced for his patron, Charles V, the illustration of the spheres is in the conventional order but they are curved concave upwards, centred on God, rather than concave downwards, centred on the Earth.

A page from Oresme’s Livre du ciel et du monde, 1377, showing the celestial spheres Source: Wikimedia Commons

In my initial Twitter exchange with Mr ScienceWriter, I asked him “in what way did Galileo’s theories challenge human supremacy?” He answered, “They disproved the myth that the Universe revolves around us.” I later then asked him what exactly Galileo proved, a question that he failed to answer. It is obvious that he suffers from the, unfortunately, very widespread illusion that Galileo somehow proved the validity of the heliocentric system. Regular readers of this blog will know that he did nothing of the sort. As a historian of science, I find it sad that somebody, who claims to be scientifically knowledgeable, spread falsehoods and myths to his 11,6K followers on Twitter and when challenged persists that they are right and their critics are wrong, instead of checking their claims.  I also find it depressing that a large American university posts on their official website an article on the history of astronomy and cosmology written by a non-historian, who very clearly doesn’t know what they are talking about. 


Filed under History of Astronomy, History of cosmology, Myths of Science, Renaissance Science

Artificial Bullshit!

There has been much hot air expended in recent days over the supposed artificially intelligent program Chat-GPT, which is, in reality, a more sophisticated Internet search engine. James Maynard on his website The Cosmic Companion proudly announced that he had used it “to construct a pictorial journey exploring the story of Hypatia!” Having spent some time using my biological intelligence to survey the modern historical literature on the lady and used the information gained to write a blog post, I have decided to don my pedagogical persona and evaluate the results produced by this new program. The full text is below with my comments in italics.

Reconstructing Hypatia of Alexandria Using Artificial Intelligence

Using Chat-GPT and MidJourney to construct a pictorial journey exploring the story of Hypatia – The last great scientist of the ancient age of the western world.

We’ve used generative artificial intelligence to learn about the last great scientist of the ancient age in the western world.

Sorry but Hypatia was not a great scientist and as for being last of the ancient age in the western world, I think Proclus, Boethius, Simplicius, John Philoponus, and a couple of others might like a word. This is a variant on the, “they murdered science when they murdered Hypatia,” myth, more of which gets spewed out in the closing paragraphs.

Hypatia of Alexandria was an accomplished astronomer, mathematician, and philosopher who lived in the final days of the ancient age of science. Born sometime around 360 CE, Hypatia was raised in the cultural and intellectual center of the Mediterranean, Alexandria, by her mathematician father Theon.

We don’t have any direct proof as to how accomplished Hypatia actually was, as none of her writings have survived.

Hypatia dedicated her life to advancing science and reason in an age when dark forces were closing in on her society.

Once again, a statement with no basis in known facts, as we have no evidence to support it and what are these ominous dark forces?

The Great Library of Alexandria, founded just after 300BCE, was once the greatest storehouse of information in the ancient world. The Library was one part of a larger institution of learning, the Musaeum of Alexandria, which also included a grand university.

Hyperbole, the Great Library of Alexandria was one of the great libraries of antiquity. It was part of the Mouseion, why use Musaeum, the Latin name, for a Greek institution in a Greek city?  The Mouseion was a research institute, or one might call it an institute of advanced learning. However, there was no university, grand or otherwise.

The root of our English word museum, the term Musaeum originally referred to temples honoring the Muses. Over time, this word came to represent centers of learning. 

Nothing to criticize here, but I wonder why articles about Hypatia almost always include sections on the Library and the Mouseion, as both had ceased to exist long before Hypatia was even born?

At the start of the Fifth Century, in the final years of the Alexandrian University, Theon raised his budding scientist in the manner usually reserved for boys — in the father’s trade — in this case, math and science. History leaves us no knowledge about Hypatia’s mother.

What Alexandrian University? Anachronical use of the term scientist is here especially unnecessary as mathematician and astronomer would be more accurate.

Living her life in the cultural and intellectual center of the Mediterranean, Alexandria, Hypatia attended classes and later taught on the ancient grounds of learning, delivering understandable lessons on complex scientific subjects.

Notes based on her teachings are said to cover astronomy, geometry, the use of astrolabes, and more. Hypatia taught classes, some of them to large audiences. Ancient accounts are nearly unanimous in noting her intellectual prowess.

In the normal meaning of the term there are no surviving “notes based on her teachings.” What we have are a handful of general comments on the areas that she taught.

She was a gifted science educator and her works were reported to contain insights on astronomy, geometry, the use of astrolabes, and more.

Very general and rather vague reports, with almost no specifics.

Even her rivals often admired her talents, including John of Nikiu, who stated, “The breadth of her interests is most impressive. Within mathematics, she wrote or lectured on astronomy, geometry, and algebra, and made an advance in computational technique — all this as well as engaging in religious philosophy and aspiring to a good writing style.”

Not a bad review from someone who really doesn’t like you.

What John of Nikiû, who lived more than two hundred years after Hypatia died, actually wrote about her:

In those days a female philosopher appeared in Alexandria, a pagan named Hypatia, and she was completely devoted to magic, astrolabes and music instruments, and she deceived many people through (her) Satanic wiles.

There appears to be something of a discrepancy here between the two accounts!

As violence between Christians, Jewish residents, and Pagans grew, Hypatia assigned herself the task of updating, recording, and safeguarding the mathematical and astronomical knowledge of her age.

This is pure fantasy and has no basis in the known historical facts.

Her fate was sealed in 391 CE, when Emperor Theodosius I issued a decree directing the burning of all Pagan temples. 

Let us see what Wikipedia has to say about Theodosius and pagans: 

Although Theodosius interfered little in the functioning of traditional pagan cults and appointed non-Christians to high offices, he failed to prevent or punish the damaging of several Hellenistic temples of classical antiquity, such as the Serapeum of Alexandria, by Christian zealots. 

We appear to have a contradiction and I know which version I think is correct.

Armed with this acquiescence, Theophilus, bishop of Alexandria, ordered that the center of learning be destroyed. He and his followers carried out the decree, dealing massive destruction to the grounds. Theophilus then ordered a church to be built on the site.

More than 20 years later, in the year 412, he ordered the pillaging of the Serapeum or Temple to Serapis, the Pagan protector of Alexandria. This would prove prophetic. 

We have accounts of Theophilius destroying a hidden pagan temple and his followers mocking the pagan artifacts, which led to a riot during which the pagans withdrew to the Serapeum, which Theophilius then destroyed. I know of no center of learning that he supposedly destroyed. The Serapeum had probably earlier been a smaller daughter library to the Library of Alexandria but no longer fulfilled this function when it was destroyed by order of Theophilius, not in 412 but in 391. 

There is no center of learning involved. The Serapeum was a center for the Neoplatonism of Iamblichus a rival group to the Neoplatonism of Plotinus to which Hypatia adhered. Theophilius actually tolerated Hypatia’s school, so hardly prophetic.

Cyril, Theophilus’s nephew, was named bishop of the region, and he launched a campaign against Pagan temples and set about expelling the Jewish population from Alexandria. Civil unrest between Pagans, Christians, and the Jewish population broke out into years of violence in the city.

In March 415, followers of Cyril ransacked the remaining classrooms and study rooms, destroying what remained of the greatest institution of learning in the ancient world.

This paragraph is pure fantasy. The Mouseion, which I assume is being referenced here, had ceased to exist a couple of hundred years earlier.

The crowds ambushed Hypatia as she rode through the city. The last great scientist and science educator of the ancient western world was flailed, dismembered, and her remains were paraded through the city and burned in a mockery of Pagan funerary rites.

Hypatia was not “the last great scientist and science educator of the ancient western world.” She wasn’t even a great scientist. 

Hypatia’s brutal murder marked the end of science in the west for a thousand years. Europe soon fell into ten centuries of intellectual stagnation that would not lift until the Scientific Renaissance in the middle of the 15th Century. 

Remember that myth at the beginning? This whole paragraph is totally and utter hogwash! We have the classic myth about a thousand-year gap in the history of science from 500 CE to 1500 CE. To counter this rubbish, I could recommend several books e.g. Stephen C. McCluskey, “Astronomies and Cultures in Early Medieval Europe (CUP, 1998), Seb Falk, The Light Ages: The Surprising Story of Medieval Science, (W.W. Norton, 2020), or Edward Grant, Science & Religion 400 BC –AD 1550: From Aristotle to Copernicus (Johns Hopkins University Press, 2004).

Today, Hypatia stands as an example to all science educators to connect with their audience and with those around us. She also broke the gender barrier for science in ancient Europe, an accomplishment for feminism and women that would not be matched until the 18th Century.

We have entered the realm of Hypatia hagiography and mythology.

Hypatia of Alexandria dedicated her life to exploring the mysteries of the Cosmos, and relating her knowledge so that everyone could understand and learn. As darkness closed in on Alexandria, Hypatia spread the light of science for all humanity, and all time.

We are still in the realm of Hypatia hagiography and mythology.

She remains an inspiration to us all.

Does she?

How this was done:

We do not know exactly what Hypatia of Alexandria or the institution looked like, but there are descriptions in ancient texts, as well as modern insights based on contemporary technologies and insights into history and genetics.

The Cosmic Companion used Chat-GPT to merge information from both ancient and modern sources into the most accurate description of her we could produce.

Facts were checked and cross-referenced with accounts from reliable sources, including Encyclopedia Brittanica, The Smithsonian Institution, and National Geographic. The resulting text was translated, as closely as possible, into a prompt for the artificial intelligence graphics engine MidJourney.

Text was created by a similar AI/human process.

Given the explanation above, what this demonstrates is that you get the results based on the quality of the sources you use, a truism for all historical research, and it is painfully clear that the sources used in this case were totally crap. According to the computer programming rule GIGO­–garbage in, garbage out–here Chat-GPT has used garbage sources and produced a garbage text.

If I was grading this apology for an essay as a piece of work handed in by a student, it would of course garner a big fat for fail.Not only is it factually a total disaster area but it is from style a bizarre collection of fragmentary paragraphs that don’t even add up to a coherent whole. If this is the best that Chat-GPT can do even with human editing, then historians have nothing to fear from this AB i.e., Artificial Bullshit


Filed under History of science, Myths of Science, Uncategorized

Beinecke Library Redux: From Bad to Worse!

On Monday I wrote a quick blogpost on the not insubstantial errors in the description of one of Galileo’s lunar washes posted on the Beinecke Library blog. I was somewhat pleasantly surprised when within a day the description had been heavily edited, removing all the sections that I had criticised, even if no acknowledgement was made that changes had taken place or why.  In my elation over this turn of events I failed to properly read what now stood under Galileo’s image. One of my readers, Todd Timberlake author of Finding Our Place in the Solar System: The Scientific Story of the Solar System, was more observant than I and correctly stated that the modified version was now, if possible worse than the original. So, what had curator Richard Clemens done now?

Above: Detail, p. 18. Galileo, Siderevu nvncivs, QB41 G33 1610, copy 2. 

Left us examine what can only be described as a disaster, the text now reads:

Our mini-exhibits end with the vitrine holding several copies of Galileo’s first printed images of the moon made with the benefit of the telescope.  He shows the shadow the earth casts on the moon and the moon’s rocky surface. [my emphasis] A photograph at the back of the vitrine was taken in 1968, before humans landed on the moon. It shows Earth as seen from the moon—the first time we saw our own planet from another astronomical body. This rough black and white image eerily resembles Galileo’s lunar landscape.

The only time the Earth’s shadow is visible on the Moon is during a lunar eclipse when the Earth comes between the Sun and the Moon thus blocking off the Sun’s light. Galileo did not make drawings of any telescopic observations of the Moon during a lunar eclipse. What we actually have is an image of the Moon at third quarter put together by Galileo from his observations. The light side on the left is the half of the Moon that is visible at third quarter, the dark side on right is the half not visible. The jagged line down the middle is the so-called lunar terminator: the division between the illuminated and dark hemispheres of the Moon.

Photo of the Moon at third quarter Source:

Without being snarky, I think that Mr Clemens would do well to consult somebody who knows what they are talking about before writing his descriptions.


Filed under History of Astronomy, Myths of Science

Not with a bang but a whimper

Ethan Siegel is an astrophysicist, but he is better known as a highly successful science populariser, who even has his own Wikipedia page.  He first rose to fame as the author of the blog Starts With a Bang, which he launched in 2008. He expanded his brand, with the publication of popular books on physics. He expanded still further, making podcasts and writing posts under his brand name on MediumForbes, and Big Think. He is today one of the biggest names on the Internet in popularisation of physics. Here I’m going to look at his latest publication on Big ThinkBig Think is a multiplatform, multimedia Internet organisation who in their own words state: 

Our mission is to make you smater, faster.  At Big Think, we introduce you to the brightest minds and boldest ideas of our time, inviting viewers to explore new ways to work, live, and understand our ever-changing world. 

“Big Think challenges common sense assumptions and gives people permission to think in new ways.”

I’m sorry, but to my ears that sounds like those windy ads on the Internet that say, “Take our three-week course of our seminars once a week and you will be earning $100,000 a month within a year!”

So, what is the post of Dr Siegel on Big Think that has attracted the attention of The Renaissance Mathematicus and why? Our intrepid astrophysicist and physics populariser has decided to try his hand at history of science and has written a post about Johannes Kepler, Why Johannes Kepler is a scientist’s best role model. After all our author is a scientist and a successful science populariser, who has even won prestigious awards for his work, what could possibly go wrong, when he tries a bit of history of science? Unfortunately, as with other scientists and science populariser, who think they can do history of science, without investing serious time and effort in the discipline, almost everything.

Johannes Kepler unknown artist 1620

So why does Siegel think that the good Johannes should be every scientist’s role model? He tells us in his lede:

  • The annals of history are filled with scientists who had incredible, revolutionary ideas, sought out and found the evidence to support them, and initiated a scientific revolution. 
  • But much rarer is someone who has a brilliant idea, discovers that the evidence doesn’t quite fit, and instead of doggedly pursuing it, tosses it aside in favor of a newer, better, more successful idea. 
  • That’s exactly what separates Johannes Kepler from all of the other great scientists throughout history, and why, if we have to choose a scientific role model, we should admire him so thoroughly.

He then delivers four examples of famous scientists, who could not admit they were wrong:

  • Albert Einstein could never accept quantum indeterminism as a fundamental property of nature.
  • Arthur Eddington could never accept quantum degeneracy as a source for holding white dwarfs up against gravitational collapse.
  • Newton could never accept the experiments that demonstrated the wave nature of light, including interference and diffraction.
  • And Fred Hoyle could never accept the Big Bang as the correct story of our cosmic origins, even nearly 40 years after the critical evidence, in the form of the Cosmic Microwave Background, was discovered.

I already have a couple of comments here. Niels Bohr is on record as saying that Einstein through his intelligent, astute, and penetrating criticisms of quantum theory that demanded answers contributed more to the development of that theory than almost anybody else. Not least Bell’s theorem, one of the key developments in quantum theory, was based on his analysis of the Einstein–Podolsky–Rosen paradox. Opposition to theories based on knowledge are important to the evolution of those theories. 

Newton did in fact reject a wave theory of light in favour of a particle theory. However, he was able with his theory to explain all the known optical phenomenon. Moreover, when Hooke rejected his theory of colour saying that it wouldn’t work in a wave theory, Newton developed a wave theory, that was more advanced than those of Hooke and Huygens, to show that his theory of colour did work in a wave theory. Lastly, as I love to point out, Einstein won the Nobel Prize for physics, not for relativity, but for demonstrating that light consists of particles, so Newton wasn’t so wrong after all.   

More generally, there is a famous quote from Max Planck about the development of new theories in science:

A new scientific truth does not generally triumph by persuading its opponents and getting them to admit their errors, but rather by its opponents gradually dying out and giving way to a new generation that is raised on it.

He then goes on to tell us why Kepler was a spectacular exception. First, we get a popular rundown of the observable phenomena of the cosmos and why that led to a geocentric model. On the whole OK but littered with small errors. For example, he tells us:

The Earth was big, and its diameter had been measured precisely [my emphasis] by Eratosthenes in the 3rd century B.C.E.

This is, unfortunately, typical of Siegel’s hyperbolic style. Depending on which value for the stadium one takes, Eratosthenes’ estimate of the size of the earth was relatively close to the real value but by no means precise. Also, in antiquity no one knew how correct it was and most people actually accepted other values.

We then get a description of the deferent/epicycle model for the planets and Siegel tells us that Ptolemy made the best, most successful model of the Solar system that incorporated epicycles. Nothing to criticise here but there follows immediately a small misstep, he writes:

Going all the way back to ancient times, there was some evidence — from Archimedes and Aristarchus, among others — that a Sun-centered model for planetary motion was considered. 

First off you really shouldn’t use an expression like “ancient times.” We know that both Archimedes and Aristarchus lived and worked in the third century BCE, so we can say that. The expression “there was some evidence from Archimedes and Aristarchus, among others” is a load of waffle, which doesn’t actually tell the reader anything. According to a couple of secondary sources Aristarchus of Samos devised a heliocentric system. We don’t have anything about it from Aristarchus himself. Archimedes is one of the secondary sources but not in a work on astronomy or cosmology. Archimedes wrote a work on calculating and expressing large numbers, The Sand Reckoner, in which he calculated the number of grains of sand needed to fill the cosmos. He used Aristarchus’ heliocentric model, which he only mentions in passing, because the heliocentric cosmos is considered to be larger the than the geocentric one.

Siegel now moves onto Copernicus and once again delivers up historical rubbish:

Copernicus was frustrated to discover that his model gave less successful predictions when compared against Ptolemy’s. The only way Copernicus could devise to equal Ptolemy’s successes, in fact, relied on employing the same ad hoc fix: by adding epicycles, or small circles, atop his planetary orbits!

As stated, this is rubbish. From the very beginning Copernicus used deferent/epicycle models for the planetary orbits. He didn’t add epicycles as an ad hoc solution because his model gave less successful predictions when compared against Ptolemy’s. In fact, Copernicus didn’t produce any planetary tables before he died in the year that his De revolutionibus was published, so he couldn’t know about the comparative predictive powers of his and Ptolemy’s system. When Erasmus Reinhold (1511–1553) did produce his Prutenic Tables (1551), the first ones based on Copernicus’ model, it turned out that in some cases the predictions were better than in tables based on Ptolemy and in some cases worse. This was because Copernicus used the same, in the meantime corrupted through frequent copying, basic data for his models as Ptolemy. This problem was recognised by Tycho Brahe, which is why he set up his massive astronomical observation programme, on the island of Hven, in order to provide new basic data. It is to Tycho that Siegel now turns.

Tycho Brahe, for example, constructed the best naked eye astronomy setup in history, measuring the planets as precisely as human vision allows: to within one arc-minute (1/60th of a degree) during every night that planets were visible towards the end of the 1500s. His assistant, Johannes Kepler, attempted to make a glorious, beautiful model that fit the data precisely.

This is Siegel’s introduction to Kepler’s Mysterium Cosmographicum published in 1596, four years before he even met Tycho and began to work with him! Siegel now gives a brief description of the model presented in the Mysterium Cosmographicumand follows it up with a pile of absolute garbage.

Maybe our astrophysicist author has slipped into a parallel universe because what he presents here is hyperbollocks, an assorted collection of made-up “facts” thrown together in a narrative that bears absolutely no relation to what really happened in history. As a Kepler fan when I read this and the following paragraphs eight days ago, I began banging my head against the wall and haven’t stopped since. No pain can blot out the stupidity presented here. 

Kepler formulated this model in the 1590s, and Brahe boasted that only his observations could put such a model to the test. But no matter how Kepler did his calculations, not only did disagreements with observation remain, but Ptolemy’s geocentric model still made superior predictions.

Tycho made no such boast, that is simply made up and in fact he was not in any way interested in Kepler’s model. Kepler wanted to work with Tycho to get access to his data to fine tune his model, Tycho wanted to employ Kepler to do the mathematics necessary to turn his data into models for the planets orbits in his own geo-heliocentric model. When Kepler arrived in Prague, Tycho refused him access to the data he wanted out of fear of being plagiarised. Instead, he set Kepler to write a paper proving that Ursus had plagiarised him. The resulting essay is brilliant, was however first published in the nineteenth century, and has been described by Cambridge historian of science, Nicholas Jardine as The Birth of History and Philosophy of Science (CUP, 2nd rev. ed. 1988). Following this he was given the task of determining the orbit of Mars using Tycho’s data, to which I will return in a minute. 

At this point in his life Kepler made no attempt to improve his geometrical model. The phrase, Ptolemy’s geocentric model still made superior predictions is quite simple mind boggling for anybody who knows what they are talking about. The geometric model that Kepler presents in his Mysterium Cosmographicum is his answer to the question, why are there exactly six planets? Kepler argues that his completely rational God, who is a geometer, designed his cosmos rationally and geometrically and there are exactly six planets because there are only five regular Platonic solids to fill the spaces between them. Not our idea of rational but Kepler was mighty pleased with his “discovery.” This model makes no predictions of any kind!

Now we get to the crux of Siegel’s whole argument, Kepler admitting he was wrong:

In the face of this, what do you think Kepler did?

  • Did he tweak his model, attempting to save it?
  • Did he distrust the critical observations, demanding new, superior ones?
  • Did he make additional postulates that could explain what was truly occurring, even if it was unseen, in the context of his model?

No. Kepler did none of these. Instead, he did something revolutionary: he put his own ideas and his own favored model aside, and looked at the data to see if there was a better explanation that could be derived from demanding that any model needed to agree with the full suite of observational data.

Kepler didn’t tweak his model, at this time, attempting to save it, he certainly didn’t mistrust Tycho’s data, and he didn’t at this time add any postulates. He did put his model aside but not to look at the data to see if there was a better explanation that could be derived from demanding that any model needed to agree with the full suite of observational data. He was too busy doing other thing, things that served other purposes. 

If only we could all be so brave, so brilliant, and at the same time, so humble before the Universe itself! Kepler calculated that ellipses, not circles, would better fit the data that Brahe had so painstakingly acquired. Although it defied his intuition, his common sense, and even his personal preferences for how he felt the Universe ought to have behaved — indeed, he thought that the Mysterium Cosmographicum was a divine epiphany that had revealed God’s geometrical plan for the Universe to him — Kepler was successfully able to abandon his notion of “circles and spheres” and instead used what seemed to him to be an imperfect solution: ellipses.

Here without explicitly naming it, Siegel is referencing Kepler’s work on the orbit of Mars that he published in his Astronomia Nova in 1609. It was during the many years of his “War with Mars”, his own description, that he finally discovered his first two laws of planetary motion: 1: Planetary orbits are ellipses with the Sun at one focus of the ellipse 2: A line from the Sun to the planet sweeps out equal areas in equal periods of time. For a good description of the route to the Astronomia Nova, I recommend James R. Voelkel’s excellent The Composition of Kepler’s Astronomia nova (Princeton University Press, 2001). 

Siegel apparently thinks that this refutes Kepler’s Mysterium Cosmographicum, it doesn’t. The Mysterium Cosmographicum doesn’t deal with the shape of orbits at all. His model has the Platonic solids filling the spaces between the spheres. In the Ptolemaic deferent/epicycle system the orbits are not simple circle because of the epicycle. Ptolemy in his Planetary Hypothesis embedded the deferent/epicycle in a sphere but the book that got lost and was only rediscovered in the 1960s in a single Arabic copy. However, Peuerbach (1423–1461) revived this model in his Theoricae Novae Planetarum (written in 1454, published by Regiomontanus in 1472), which is almost certainly based on a now lost copy of the Planetary Hypothesis, with illustrations. 

Peuerbach’s illustration of a sphere containing a deferent/epicycle Source: Wikimedia Commons

Copernicus’ heliocentric system, which also uses the deferent/epicycle models would suffer from the same problem and it is between these spheres that Kepler places his Platonic solids, irrespective of the orbit inside the sphere. The system would work equally well for elliptical orbits, so Kepler’s discovery of them had no effect on his Mysterium Cosmographicum

Siegel gives a table of Tycho’s Mars observations with the following caption:

Tycho Brahe conducted some of the best observations of Mars prior to the invention of the telescope, and Kepler’s work largely leveraged that data. Here, Brahe’s observations of Mars’s orbit, particularly during retrograde episodes, provided an exquisite confirmation of Kepler’s elliptical orbit theory. [my emphasis]

Kepler used Tycho’s Mars data to derive his first two laws, so they can’t be used by him as confirmation. In fact, at the beginning he didn’t actual confirm his theory, simple assuming it applied to all the planets. It wasn’t until his Epitome Astronomiae Copernicanae published in three volumes from 1618 to 1621, after he had discovered his third law and done a substantial amount of the work reducing Tycho’s observational data to planetary tables, the Rudolphine Tables published in 1627 and on which he had begun to work as Tycho was still alive, that he demonstrated all three laws for all the known planets.

I will now return to that third law and the Harmonice mundi (1619) in which it first appeared. Kepler had already suggested the possibility of fine tuning the Mysterium Cosmographicum model with the Pythagorean concept of a harmony of the spheres and this is what his magnus opus Harmonice mundi was. He had already conceived it in the late 1590s but because of other commitments didn’t actually get round to writing it until the second decade of the seventeenth century. 

Having created his harmony of the spheres, in 1621 Kepler published an expanded second edition of Mysterium Cosmographicum, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication, so far from abandoning his first theory to produce his elliptical orbits as Seigel claims, Kepler spent his whole life working to improve it.

What is truly bizarre is that Siegel appears to be aware of this fact. He writes:

It cannot be emphasized enough what an achievement this is for science. Yes, there are many reasons to be critical of Kepler. He continued to promote his Mysterium Cosmographicum even though it was clear ellipses fit the data better. He continued to mix astronomy with astrology, becoming the most famous astrologer of his time.

As already explained in detail, he didn’t just promote his Mysterium Cosmographicum, he worked very hard for many years to improve it. The statement, becoming the most famous astrologer of his time is another example of hyperbollocks. Kepler was a well-known astrologer in Southern Germany and Austria but the most famous astrologer of his time I hardly think so. I would also note that the modern astro-scientists disdain for astrology, as displayed here by Seigel, displays their ignorance of the history of their own discipline. Astrology was the driving force behind the developments in astronomy for its first three thousand years of its existence. 

Siegel, like many scientists, who think they can write history of science without doing the detailed research, has taken a set of half facts, embroidered them with stuff that he simply made up and created a nice fairy tale that has very little to do with real history of science. A fairy tale that will be swallowed by his large fan base, who will believe it and make life difficult for real historians of science. 


Filed under History of Astronomy, Myths of Science

I expect better of you Beinecke

The Beinecke Rare Book & Manuscript Library is the rare book library and literary archive of the Yale University Library. Yesterday their Twitter account posted a tweet entitled GalileoSiderius Nunc, which linked to a blog post from July 11, 2022, by Raymond Clemens, Curator, Early Books & Manuscripts. 

It featured one of Galileo’s famous washes of the Moon from his Sidereus Nuncius (1610) followed by a short text.

Above: Detail, p. 18. Galileo, Siderevu nvncivs, QB41 G33 1610, copy 2. 

Our mini-exhibits end with the vitrine holding several copies of Galileo’s first printed images of the moon, the first ever made with the benefit of the telescope. For the first time, most Europeans were shown the dark side of the moon. Galileo’s sketches also emphasize its barren and rocky nature—well known to us today, but something of a revelation in the sixteenth century, when most people thought of the moon as another planet, thus generating its own light. Galileo was the first person to accurately depict the moons of Jupiter (which he called “Medicean stars,” after his patron, the Florentine Medici family). A photograph at the back of the vitrine was taken in 1968, before humans landed on the moon. It shows Earth as seen from the moon—the first time we saw our own planet from another astronomical body. This rough black and white image eerily resembles Galileo’s lunar landscape.

It is a mere 152 words long, not much room for errors, one might think, but one would be wrong.

We start with the heading. The title of Galileo’s book is Sidereus Nuncius and there one really shouldn’t shorten Nuncius to Nunc, as this actually changes the meaning from message or messenger to now! Also, it is Sidereus not Siderius!

Addendum: A reader on Twitter, more observant than I, has pointed out, correctly, that 1609 and 1610 are in the seventeenth century and not the sixteenth century as stated by Clemens.

In the first line Clemens writes: Galileo’s first printed images of the moon, the first ever made with the benefit of the telescope. I shall be generous and assume that with this ambiguous phrase he means first ever printed images made with the benefit of the telescope. If, however, he meant first ever images made with the benefit of the telescope, then he would be wrong as that honour goes Thomas Harriot.

The real hammer comes in the next sentence, where he writes:

For the first time, most Europeans were shown the dark side of the moon.

The first time I read this, I did a double take, could a curator of the Beinecke really have written something that mind bogglingly stupid? By definition the dark side of the moon is the side of the moon that can never be seen from the earth. The first images of it were made, not by Galileo in 1609, after all how could he, but by the Soviet Luna 3 space probe in 1959, 350 years later. 

The problems don’t end here, he writes:

Galileo’s sketches also emphasize its barren and rocky nature—well known to us today, but something of a revelation in the sixteenth century, when most people thought of the moon as another planet, thus generating its own light.

In the geocentric system the moon was indeed regarded as one of the seven planets, but in the heliocentric system, which Galileo promoted, it had become a satellite of the earth and was no longer considered a planet. There was a long and complicated discussion throughout the history of astronomy as to whether the planets generated their own light or not. However, within Western astronomy there was a fairy clear consensus that the moon reflected sunlight rather than generating its own light. A brief sketch of the history of this knowledge starts with Anaxagoras (d. 428 BCE). The great Islamic polymath Ibn al-Haytham (965–1039) clearly promoted that the moon reflected sunlight. In the century before Galileo, Leonardo (1452–1519) in his moon studies clearly stated that the moon was illuminated by reflected sunlight. However, he never published. 

Maybe, Clemens is confusing this with the first recognition of the true cause of earth shine, the faint light reflected from the earth that makes the whole moon visible during the first crescent, a recognition that is often falsely attributed to Galileo. However, here the laurels go to Leonardo but who, as always, didn’t publish. The first published correct account was made by Michael Mästlin (1550–1631)

 Clemens’ next statement appears to me to be simply bizarre:

Galileo was the first person to accurately depict the moons of Jupiter (which he called “Medicean stars,” after his patron, the Florentine Medici family).

Galileo was the first to discover the moons of Jupiter, just one day ahead of Simon Marius, but to state that he accurately depicted them is somewhat more than an exaggeration. For Galileo and Marius, the moons of Jupiter were small points of light in the sky, the positions of which they recorded as ink dots on a piece of paper. To call this accurate depiction is a joke.

Somehow, I expect a higher standard of public information from the Beinecke Library, one of the world’s leading rare book depositories. 

Addendum 18:30 CEST: The post on the Beinecke blog that this post refers to has now been heavily edited. Everything I criticised has been either removed or corrected but without acknowledgement anywhere!

Renaissance Mathematicus 1 Beinecke Library 0!


Filed under History of Astronomy, Myths of Science


Today the Renaissance Mathematicus officially became a teenager, although I think it’s been one since it first emerged into the digital world thirteen years ago, snotty-nosed, stroppy, belligerent, argumentative, anti-authority, whilst at the same time oscillating between bursting with energy and sloth like behaviour. Did I mention self-opinionated and convinced it knows better than everybody else?

Thirteen is, in the Germanic languages, the first number with a compound name, three plus ten, eleven and twelve having single names. It is the sixth prime number and the second two-digit prime forming a twin prime with eleven, the first two digit prime. 

In some countries, including the UK and the USA, thirteen is considered an unlucky number, with people going as far as to not having a thirteenth floor in a building or a room 13 in a hotel. This superstition has been given the wonderful name Triskaidekaphobia from the Ancient Greek treiskaídeka for thirteen and phóbos meaning fear. There are various attempts to explain the historical origins of this phobia but none of them can actually be substantiated. Friday 13th is considered particularly unlucky in these cultures and has the equally splendid name paraskevidekatriaphobia from the Greek Paraskevi for Friday, reiskaídeka for thirteen, and phóbos meaning fear. In the Gregorian calendar, Friday 13th occurs at least once every year and can occur up to three times. Although there is evidence of both Friday and thirteen being considered unlucky, the earliest reference to Friday 13th as unlucky is in the nineteenth century. Once again, the origin of the superstition is a mater of speculation. 

One common occurrence of the number thirteen in the English language is the baker’s dozen. Whereas a dozen is a group of twelve, a baker’s dozen is a group of thirteen. The term dates back to the fifteenth century and refers to the habit of baker’s selling their wares in units of thirteen rather than twelve as the law required. As bakers could be fined for selling their wares underweight, it is thought that they included an extra item to avoid the risk of a fine.

As usual the Renaissance Mathematicus blog anniversary is an occasion for reflection, looking inward and questioning, a period of introspection. Why do I do this at all? What is my motivation? What do I hope to achieve? 

I’ve actually been thinking about these questions for sometime now. I am a self-confessed music junkie, who has spent a large part of my life working as a very small cog in the music business, as a stagehand, club live sound man, jazz club manager and chief cook and bottle washer. I also possess an obscenely large album collection, which I relativise by pointing out that other music junkies I know have much larger collections. One of my favourite rock guitarists is Robert Fripp, the genius behind King Crimson. Fripp is very philosophical for a rock musician and one of his sayings is, “don’t become a professional musician unless you can’t do anything else.” This statement is of course ambiguous. It could mean, if you are physically or mentally incapable of doing anything else or on the other hand you are so obsessed that nothing else comes into question. 

I prefer the second interpretation and it neatly sums up my relationship to history in general and the history of science in particular. I have been addicted to history for as long as I can remember, history in general, history of mathematics, history of science, history of food… What ever else I’ve done in my life, I’ve always studied history simply because. However, as I have revealed in the past, I am an AD(H)Dler and this means I tend to get easily distracted in my studies, research, and readings. Oh look, there’s another aspect I could follow up over there and isn’t this fact interesting, maybe I could find out something about that! This means I have in my life a strong tendency never to get anything finished, because there are always twenty other different pathways I want to go down first. Forcing myself to write a weekly blog post helps me to stay focused, to concentrate, and get at least one thing finished.  When I’m not writing blog posts my mind still wanders off in twenty different directions at once, but that’s OK; that’s have I come up with new topics for blog posts. 

All of the above basically covers the first two of my questions, why and motivation and there isn’t really any other explanation. This still leave the third question open; what do I hope to achieve? I don’t really have a general answer to this. I don’t actually think I want to achieve anything in particular. Initially, as I have said in the past, I wanted to teach myself to write, and I think I fulfilled that aim some time ago. I wrote my, The emergence of modern astronomy – a complex mosaic series to prove to myself that if I wrote in slices; I could write a book. Another aim that I think I successfully fulfilled. I might even get around to turning it into a proper book manuscript and trying to find a publisher this summer! The Renaissance Science series was just, you’ve written one long series, what could you write a second one about? 

On the whole I try not to think about potential readers but to write just for myself. This is a safety mechanism to stop me putting myself under any sort of pressure, will I fill my readers expectations!? Of course, I’m happy that people do read my scribblings and some of them even appear to enjoy them. Truth be told, the actual number of people who regularly read this blog scares me somewhat, in particular the successful professional historians of science, who I know do so. Imposter syndrome, what moi? As I have been known to say on occasions, even my imposter syndrome has imposter syndrome. One very concrete thing that I have aimed to achieve with my scribblings since the day I started this blog, is to try and clear away at least some of the myths that plague the popular perception of the history of science. It’s a Sisyphus task but it helps to keep me motivated and focused. 

Having mentioned my readers, I will close this anniversary post by saying I’m grateful for every person, who takes the time to read my weekly outpourings and I hope they gain something for the time taken. I’m also grateful to all those, who take the time to provide feedback, through comments: I thank all of you both readers and commentors and hope you stay on bord for the next twelve months.


Filed under Autobiographical, Myths of Science

Rants, Rage, Rudeness, and Respect

A man that I’ve never come across before, Brett Hall, has taken me to task in, what he terms, a newsletter on YouTube for being rude to Neil deGrasse Tyson. Before somebody drew my attention to his comments, I had absolutely no idea who or what Brett Hall was. It appears he is an Australian, who, it seems, studied about seventeen degrees, I might be exaggerating somewhat, I lost count somewhere down the line in his litany of all the wonderful things he had studied. Anyway, if I understand him correctly, he now regards himself as a science communicator and has a podcast where he explicates and propagates the philosophies of Karl Popper and David Deutsch. He also has a blog and apparently, has recently added a newsletter, in the first edition of which he chose to criticise me. 

I am well acquainted with the works of Karl Raimund Popper, he being one of my first two introductions to the philosophies of mathematics and science, the other was Stephen Körner. I read my first philosophy of science books by both of them in the same week many, many moons ago. I read a large amount of Popper’s oeuvre and a decade later studied him at university. Popper led me to Imre Lakatos, the biggest influence on my personal intellectual development. 

I must admit, because I gave up trying to keep up with all the developments in modern physics quite some time ago, that until about two weeks ago I had never heard of David Deutsch. So that you don’t have to go look, he’s a big name in quantum physics and especially in the theory of quantum computing. Purely by chance, the German news magazine, Der Spiegel, had a long interview with him a couple of weeks ago about his views on epistemology and what he sees as the correct approach to the future and development of scientific thinking. Mr Hall will probably come down on me like a ton of bricks for saying this but, for me, it came across as fairly vacuous, a lot of waffle and pie in the sky. But I’m probably just too stupid to understand the great maestro!  

But back to Mr Hall and good old Neil deGrasse Tyson. Mr Hall bemoaned what he saw as increasing rudeness in debate in the Internet age, a common and widely spread trope, and cited my latest diatribe against NdGT, as an example, misquoting the title of my piece, claiming that I had said that Tyson “knows nothing”, whereas I in fact wrote “knows nothing about nothing”, a wordplay on Tyson’s topic the history of zero. There is a substantial difference between the two statements. He then went on to quote correctly that I accused Tyson of “spouting crap.” Strangely, Mr Hall calls me a science historian, whereas the correct term is historian of science. There is a whole debate within the discipline, as to why it’s the latter and not the former. Even more bizarrely, he states that he is not going to name me and then provides a link to the post on my blog that of course contains my name! I have no problems in being named, I’m old enough and ugly enough to defend myself against all comers.

Mr Hall goes on to explain that he also does not always agree with the theories of NdGT, but that there is no reason not to treat him with respect when stating your disagreement. I have no objection to this statement; however, it misses the point entirely. NdGT is not stating a theory in astrophysics, which is, or rather was, his academic discipline. If he had, I almost certainly would not have commented in any way whatsoever, as I’m not an astrophysicist and so not qualified to pass judgement. No, NdGT was doing something entirely different. On a commercial podcast, for which, given his popularity, he is almost certainly extremely well paid, he was mouthing off extemporaneously about the history of mathematics, a topic about which he very obviously knows very little. He was, as I put it, and there really is no polite way to express, spouting crap, with all the assurance and authority that his prominent public persona gives him. He was literally lying to his listeners, who, I assume, mostly not knowing better believe the pearls of wisdom that drip from his lips. That is serious abuse of his status and of his listeners and deserves no respect whatsoever. 

I would also point out that he is a serial offender and regularly delivers totally ignorant speeches about the history of science and/or mathematics. For example, he regularly repeats, with emphasis, that Newton invented calculus in a couple of weeks, on a dare, which, not to put to finer point on it, is total codswallop. Newton developed his contribution to the evolution of calculus over several years having first read, studied, and digested the work of Descartes, Fermat, Wallace, and Barrow. One can point these things out to NdGT but he simply ignores them and carries on blithely spreading the same tired out falsehoods. He has long ago wilfully squandered any right to be treated with respect, when talking about the history of science and/or mathematics.

Returning to Brett Hall’s basic thesis that academics have jettisoned common decency, politeness, and good manners in the computer age as a result of social media, he expounds on this for the whole of his newsletter, claiming that this behaviour from academics put young people off from entering academia to study the sciences. Like NdGT, Mr Hall appears to have very little knowledge of the history of science. Academics/scholars/scientists, or whatever you want to call them, have been slagging each other off, both publicly and privately, since the first Egyptians put brush to papyrus and the first Babylonians wedge to clay.

Just to take the era in which I claim the most expertise, the emergence of modern astronomy in the Early Modern Period. The two Imperial Mathematici, Tycho Brahe and Nicolaus Reimers Baer laid into each other in a way that makes the HISTSCI_HULK look like a cuddly kitten. A half generation later the next generation, Kepler and Longomontanus, attacked each other with slightly less expletives, but just as much virulence. Galileo laid into anybody and everybody, that he perceived as his enemies and there were many, with invective that would cause a drunken sailor to blush. Moving to the other end of the seventeenth century. Isaac Newton, Lucasian Professor, treated John Flamsteed, Astronomer Royal, like a doormat. In turn, Flamsteed refused to even utter the name of Edmond Halley the Savilian Professor of geometry. Newton and Robert Hooke, demonstrator of experiments at the Royal Society, abused each like a couple of fishwives. Hooke had blazing public rows with virtually every notable scientist in Europe. You get the picture?

In case Mr Hall should argue that modern academics weren’t like that before the advent of the Internet, I could entertain him for hours with anecdotes about the invectives that leading academic archaeologist launched at each other in the early 1970s. One stated that an excavation report by another was about as useful of a mid-Victorian museum guide. The offended party then opened legal proceedings for libel but withdrew them when the offender expressed joy at the prospect of being able to prove his statement under oath in a court of law. I could go on but…

Let us return to myself and my alter ego the HISTSCI_HULK, why do I launch my notorious rants? 

One of my favourite musicians, Robert Fripp, says that one shouldn’t become a professional musician unless one can’t do anything else. This statement is, to say the least, ambiguous. It could mean you lack the ability to do something else, or the compulsion to create music is so great that nothing else comes into question. I have always assumed he intended the second meaning, and this is exactly why I’m a historian of science. The fascination with numbers, number systems, and their origins started very early, at most about five years old, and has simply grown ever since. I can’t explain rationally why I’m fascinated, intrigued, even obsessed by the history of science, I simply am. I have a compulsion to investigate, discover and learn about the history of science so great that nothing else comes into question. 

On a personal level I have always been taught, more by example than anything else, that if one is going to do something then learn to do it properly and then do so. I am from nature a pedant, and I don’t regard pedantry as bad, and a perfectionist. Over the years I have had the good fortune to meet and learn from several excellent teachers, who have helped me to channel that pedantry and perfectionism into my studies and not to accept anything but the best possible.

The history of science is very much a niche discipline within the academic hierarchy and has to battle constantly to justify its existence. There have been and are many excellent historians of science, many of whose books line the walls of my humble abode and nourish my unquenchable thirst for a depth of understanding in the history of science. As I have documented elsewhere, I have a multiple addictive personality and my greatest addiction is without doubt the history of science.

The commercial world of books and television is not interested in the complex and difficult web that is the real history of science, but pop history of science sells well, so they commission not historians of science but scientists to produce pop books and television programmes about the history of science. I mean, after all they are scientists so they must know about the history of their discipline. The results are all to often a disaster. There are exceptions, my friend Matthew Cobb is a professional scientist, who also writes excellent history of science books, several of which adorn my bookshelves. However, the majority of popular history of science books and television programmes are badly researched, shallow perpetuators of myths and inaccuracies–in the Middle Ages the Church opposed science and people believed the world was flat, Newton had an Annus mirabilis and created calculus, and modern optics, physics and astronomy all in one year during the plague, Galileo was persecuted by the Church because he proved that the Earth goes around the Sun, which contradicted the Bible, Ada Lovelace created computer science, and, and, and… A classic example was the original Cosmos television programme from Carl Sagan in which his presentation of the history of astronomy and cosmology was a total and utter cluster fuck, which influenced his tens of million viewers in a very bad way. Whenever I say this on the Internet, I get screamed at by Sagan groupies.

Because I love and live for the discipline, the abuse that it suffers at the hands of these popularises hurts my soul and sets me in a rage causing the HISTSCI_HULK to emerge and go on a rampage. One of the reasons that I do this is because established historians of science are very reluctant to subject these perversions of their discipline to public review. Somehow, they seem to think it is beneath them to engage and point out that the product in question is so much bovine manure. Nobody pays me to be a historian of science, I have no position, no status, and no academic reputation to lose, so I weigh in with all guns blazing and say what I really think. I have a message for Mr Hall and anybody else, who feels offended by my approach, nobody says you have to read it! 


Filed under Autobiographical, Myths of Science

NIL deGrasse Tyson knows nothing about nothing

They are back! Neil deGrasse Tyson is once again spouting total crap about the history of mathematics and has managed to stir the HISTSCI_HULK back into butt kicking action. The offending object that provoked the HISTSCI_HULK’s ire is a Star Talk video on YouTube entitled Neil deGrasse Tyson Explains Zero. The HISTSCI_HULK thinks that the title should read Neil deGrasse Tyson is a Zero!

You simple won’t believe the pearls of wisdom that NdGT spews out for the 1.75 million Star Talk subscribers in a video that has been viewed more than one hundred thousand times. If there ever was a candidate in #histSCI for cancellation, then NdGT is the man.

 Before we deal with NdGT’s inanities, we need some basic information on number systems. Our everyday Hindu-Arabic number system is a decimal, that’s base ten, place value number system, which means that the value of a number symbol is dependent on its place within the number. An example:

If we take the number, 513 it is actually:

 5 x 10+ 1 x 101 + 3 x 100

A quick reminder for those who have forgotten their school maths, any number to the power of zero is 1. Moving from right to left, each new place represents the next higher power of ten, 100, 101, 102, 103, 104, 105, etc, etc. As we will see the Babylonians [as usual, I’m being lazy and using Babylonian as short hand for all the cultures that occupied the Fertile Crescent and used Cuneiform numbers] also had a place value number system, but it was sexagesimal, that’s base sixty, not base ten. It is a place value number system that requires a zero to indicate an empty place. There are in fact two types of zero. The first is simply a placeholder to indicate that this place in the number is empty. The second is the number zero, that which occurs when you subtract a number from itself.

Now on to the horror that is NdGT’s attempt to tell us the history of zero:

HISTSCI_HULK: Not suitable for those who care about the history of maths

 NdGT: I pick these based on how familiar we think we are about the subject and then throw in some things you never knew

HISTSCI_HULK: All NildGT throws in, in this video, is the contents of the garbage pail he calls a brain.

NdGT: For this segment, we’re gonna talk about zero … so zero is a number, but it wasn’t always a number. In fact, no one even imagined how to imagine it, why would you? What were numbers for?

Chuck Nice, Star Talk Host: Right, who counts nothing?

NdGT: Right, numbers are for counting … nobody had any use to count zero … For most of civilisation this was the case. Even through the Roman Empire…

 Here NdGT fails to distinguish between ordinal numbers, which label the place that object take in a list and cardinal numbers which how many things are in a collection or set. A distinction that at one point later will prove crucial.

HISTSCI_HULK: When it comes to the history of mathematics NildGT is a nothing

CN: They were so sophisticated their numbers were letters!

In this supposedly witty remark, we have a very popular misconception. Roman numerals were not actually letters, although in later mutated forms they came to resemble letters. Roman numbers are collections of strokes. One stroke for one, two strokes for two, and so one. To save space and effort, groups of strokes are bundled under a new symbol. The symbol for ten was a crossed or struck out stroke that mutated into an X, the symbol for five, half of ten, was the top half of this X that mutated into a V; originally, they used the bottom half, an inverted V.  The original symbol for fifty was ↓, which mutated into an L and so on. As the Roman number system is not a place value number system it doesn’t require a place holder symbol for zero. If Romans wanted to express total absence, they did so in words not numbers, nulla meaning none. This was first used in a mathematical context in the Early Middle Ages, often simply abbreviated to N. 

NdGT: [Some childish jokes about Roman numeral] … I don’t know if you’ve ever thought about this Chuck, you can’t write zero with Roman numerals. There is no symbol for zero.

The Roman number system is not a place value number system but a stroke counting system that can express any natural number, that’s the simple counting numbers, without the need for a zero. The ancient Egyptian number system was also a stroke counting system, whilst the ancient Greeks used an alpha-numerical system, in which letters do represent the numerals, that also doesn’t require a zero to express the natural numbers.

NdGT: It’s not that they didn’t come up with it, it’s the concept of zero was not yet invented. 

HISTSCI_HULK: I wish NildGT had not been invented yet

This is actually a much more complicated statement than it at first appears. It is true, that as far as we know, the concept of zero as a number had indeed not been invented yet. However, the verbal concept of having none of something had already existed linguistically for millennia. Imaginary conversation, “Can I have five of your flint arrowheads?” Sorry, I can’t help you, I don’t have any at the moment. Somebody came by and took my entire stock this morning.” 

Although the Egyptian base ten stroke numeral system had no zero, by about 1700 BCE, they were using a symbol for zero in accounting texts. Interestingly, they also used the same symbol to indicate ground level in architectural drawings in much the same way that zero is used to indicate the ground floor in European elevators. 

Also, the place holder zero did exist during the time of the Roman Empire. The Babylonian sexagesimal number system emerged in the third millennium BCE and initially did not have a zero of any sort. This meant that the number 23 (I’m using Hindu-Arabic numerals to save the bother of trying to format Babylonian ones) could be both 2 x 601 + 3 x 600 = 123 in decimal, or 2 x 602 + 3 x 600 = 7203 in decimal. They apparently relied on context to know which was correct. By about 700 BCE the first placeholder zero appeared in the system and by about 300 BCE placeholder zeros had become standard. 

During the Roman Empire, the astronomer Ptolemaeus published his Mathēmatikē Syntaxis, better known as the Almagest, around 150 CE, which used a weird number system. The whole number part of numbers were written in a ten-base system in Greek alphanumerical symbols, whereas fractional parts were written in the Babylonian sexagesimal number system, with the same symbols, with a placeholder zero in the form of small circle, ō.

HISTSCI_HULK NildGT now takes off into calendrical fantasy land.

NdGT: So, when they made the Julian calendar, that’s the one that has a leap day every four years, … That calendar … that anchored its starter date on the birth of Jesus, so this obviously came later after Constantine, I think that Constantine brought Christianity to the Roman Empire. So, in the Julian calendar they went from 1 BC, BC, of course, stands for before Christ, to AD 1, and AD is in Latin, Anno Domini the year of our Lord 1, and there was no year zero in that transition. So, when would Jesus have been born? In the mythical year between the two? He can’t be born in AD 1 cause that’s after and he can’t be born in 1 BC, because that’s before, so that’s an issue.

CN: I’ve got the answer, it’s a miracle.

The Julian calendar was of course introduced by Julius Caesar in AUC 708 (AUC is the number of years since the theoretical founding date of Rome) or as we now express it in 44 BCE. The Roman’s didn’t really have a continuous dating system, dating things by the year of the reign of an emperor. Constantine did not bring Christianity to the Roman Empire, he legalised it. Both Jesus and Christianity were born in Judea a province of the Roman Empire, so it was there from its very beginnings. For more on Constantine and Christianity, I recommend Tim O’Neill’s excellent History for Atheists Blog. 

To quote myself in another blog post criticising NdGT’s take on the Gregorian calendar

The use of Anno Domini goes back to Dionysius Exiguus (Dennis the Short) in the sixth century CE in his attempt to produce an accurate system to determine the date of Easter. He introduced it to replace the use of the era of Diocletian used in the Alexandrian method of calculating Easter, because Diocletian was notorious for having persecuted the Christians. Dionysius’ system found very little resonance until the Venerable Bede used it in the eight century CE in his Ecclesiastical History of the English People. Bede’s popularity as a historian and teacher led to the gradual acceptance of the AD convention. BC created in analogy to the AD convention didn’t come into common usage until the late seventeenth century CE. [Although BC does occur occasionally in late medieval chronicles.]

As NdGT says Anno Domini translates as The Year of Our Lord, so Jesus was born in AD 1 the first year of our Lord, simple isn’t it. 

I wrote a whole blog post about why you can’t have a year zero, but I’ll give an abbreviated version here. Although we speak them as cardinal numbers, year numbers are actually ordinal numbers so 2022 is the two thousand and twenty second year of the Common Era. You can’t have a zeroth member of a list. The year zero is literally a contradiction in terms, it means the year that doesn’t exist. 

HISTSCI_HULK You can’t count on NilDGT

NdGT: So now, move time forward. Going, it was in the six hundreds, seven hundreds, I’ve forgotten exactly when. In India, there were great advances in mathematics there and they even developed the numerals, early versions of the numerals we now use, rather than Roman numerals. Roman numerals were letters [no they weren’t, see above], these were now symbolic shapes that would then represent the numbers. In this effort was the hint that maybe you might want a zero in there. So, we’re crawling now before we can walk, but the seeds are planted. 

We have a fundamental problem dating developments in Hindu mathematics because the writing materials they used don’t survive well, unlike the Babylonian clay tablets. The decimal place value number system emerged some time between the first and fourth centuries CE. The symbols used in this system evolved over a long period and the process is too complex to deal with here. 

The earliest known reference to a placeholder zero in Indian mathematics can be found throughout a commercial arithmetic text written on birch bark, the Bakhshali manuscript, the dating of which is very problematical and is somewhere between the third and seventh centuries CE. 

The Aryasiddhanta a mathematical and astronomical work by Āryabhaṭa (476–550 n. Chr.) uses a decimal place value number system but written with alphanumerical symbols and without a zero. The Āryabhaṭīyabhāṣya another mathematical and astronomical work by Bhāskara I (c. 600–c. 680 n. Chr.) uses a decimal place value number system with early Hindu numerals and a zero. With the Brāhmasphuṭasiddhānta an astronomical twenty-four chapter work with two chapters on mathematics by Brahmagupta (c. 598–c. 668 n. Chr.) we arrive out our goal. Brahmagupta gives a complete set of rules for addition, subtraction, multiplication, and division for positive and negative numbers, as well as for zero as a number. The only difference between his presentation and one that one might find in a modern elementary arithmetic text is that Brahmagupta tried to define division by zero, which as we all learnt in school is not defined, didn’t we? Far from being “hint that maybe you might want a zero in there” this was the real deal. 

HISTSCI_HULK: NildGT would be in serious trouble with the Hindu Nationalist propagators of Hindu science if they found out about his garbage take on the history of Hindu mathematics.

NdGT: These [sic] new mathematics worked their way to the Middle East. Baghdad specifically, a big trading post from all corners of Europe and Asia, and Africa and there it was. Ideas were put across the table. This was the Golden Age of Islam, major advances were made in all…in engineering, in astronomy, in biology, physiology, and vision. The discovery that vision is a passive phenomenon not active. So, all of this is going on and zero was perfected. They called those numerals Hindu numerals; we today call them Arabic numerals. 

What NdGT doesn’t point out is that the Golden Age of Islam lasted from about 700 to 1600 CE and took place in many centres not just in Baghdad. The Brāhmasphuṭasiddhānta was translated into Arabic by Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (ges. 777 n. Chr.), Muhammad ibn Ibrahim ibn Habib ibn Sulayman ibn Samura ibn Jundab al-Fazri (ges. c. 800 n. Chr.), and Yaʿqūb ibn Ṭāriq (ges. c. 796 n. Chr.) in about 770 CE. This meant that Islamicate[1] mathematical scientists had a fully formed correct theory of zero and negative numbers from this point on. They didn’t develop it, they inherited it. 

Today, people refer to the numerals as Hindu-Arabic numerals!

NdGt: So, this is the full tracking because in the Middle East algebra rose up, the entire arithmetic and algebra rose up invoking zero and you have negative numbers, so mathematics is off to the races. Algebra is one of the very common words in English that has its roots in Arabic. A lot of the a-l words, a-l is ‘the’ in Arabic as I understand it. So, algebra, algorithm, alcohol these are all traceable to that period. … So, I’m saying just consider how late zero came in civilisation. The Egyptian knew nothing of zero [not true, see above]. 

The Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī (c. 780–c. 850) wrote a book on the Hindu numeral system of which no Arabic text is known, but a Latin translation Algoritmi de Numero Indorum was made in the twelfth century. The word algorithm derives from the Latin transliteration Algoritmi of the name al-Khwārizmī. He wrote a second book al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah (c. 82O), the translation of the title is The Compendious Book on Calculation by Completion and Balancing. The term al-Jabr meaning completion or setting together became the English algebra. 

The first time I heard this section I did a double take. “The entire arithmetic and algebra rose up invoking zero and you have negative numbers, so mathematics is off to the races”, you what! Ancient cultures had been doing arithmetic since at least three thousand years BCE and probably much earlier. I can’t do a complete history of algebra in this blog post but by the early second millennium BCE the Babylonians could solve linear equations and had the general solution to quadratic equations but only for positive solutions as they didn’t have a concept of negative numbers. The also could and did solve some cubic equations. In the middle of the first millennium BCE they had astronomical algorithms to predict planetary orbits, as well as lunar and solar eclipses. Brahmagupta’s work includes the general solution of linear equations, and the full general solution of quadratic equations, as we still teach it today. NdGT’s statement is total rubbish.

Of historical interest in the fact that although Islamicate mathematical scientists acquired negative numbers from Brahmagupta, they mostly didn’t use them, regarding them with scepsis 

HISTSCI_HULK: NildGT is off with the fairies

CN: What is this that I hear about the Mayans and zero?

NdGT: I don’t fully know my Mayan history other than that they really worshipped Venus, so their calendar was Venus based. The calendar in ancient Egypt was based on the star Sirius [something unintelligible about new year]. It’s completely arbitrary when you say the new year’s just began. Pick a date whatever matters in your culture and call it new year. Even today when is the Chinese New Year, it’s late January, February. Everybody’s got a different starter date.

The Mayan culture developed a vigesimal, base twenty, place value number system, which included a placeholder zero, independent of the developments in the Middle East and India. The Dresden Codex, one of the most important Maya written documents contains a mixture of astronomy, astrology, and religion, in which observations of Venus play a central role. The first day of Chinese New Year begins on the new moon that appears between 21 January and 20 February

HISTSCI_HULK: I’d worship Venus, she was a very beautiful lady

CN: The Jewish New Year is another new year that…

NdGT: Everybody’s got another new year. The academic calendar’s got a new year that’s September the first…

I assume that NdGT is referring to the US American academic calendar, other countries have different academic years. In Germany where I live, each German state has a different academic year, in order to avoid that the entire population drive off into their summer holidays at the same time. 

NdGT: …and by the way one quick question you’ve got a hundred dollars in your bank account, and you go and withdraw a hundred dollars from the cash machine and the bank tells you what?


So, here’s the thing, you have no money left in the bank and that’s bad, but what worse is to have negative money in the bank and so this whole concept of negative numbers arose and made complete sense once you pass through zero. Now instead of something coming your way, you now owe it. The mathematics began to mirror commerce and the needs of civilisation, as we move forward, because we are doing much more than just counting. 

CN: So, this is like the birth of modern accounting. Once you find zero that’s when you’re actually able to have a ledger that shows you minuses and pluses and all that kind of stuff.

One doesn’t need negative numbers in order to do accounting. In fact, the most commonly used form of accounting, double entry bookkeeping, doesn’t use negative numbers; credits and debits are both entered with positive numbers. 

Numbers systems and arithmetic mostly have their origin in accounting. The Babylonians developed their mathematics in order to do the states financial accounting. 

HISTSCI_HULK: There’s no accounting for the stupidity in this podcast

NdGT: So now we’re into negatives and this keeps going with math and you find other needs of culture and civilisation, where whole other branches of math have to be developed and we got trigonometry. All those branches of math where you thought the teacher was just being angry with you giving you these assignments, entire branches of math zero started it all. Where it gives you deeper insights into the operations of nature. 

I said I did a double take when NdGT claimed that arithmetic and algebra first took off when the Islamic mathematicians developed zero and negative numbers, which of course they didn’t, but his next claim completely blew my mind. So now we’re into negatives and this keeps going with math and you find other needs of culture and civilisation, where whole other branches of math have to be developed and we got trigonometry. I can hear Hipparchus of Nicaea (c. 190–c. 120) BCE, who is credited with being the first to develop trigonometry revolving violently in his grave.

HISTSCI_HULK: I could recommend some good books on the history of trigonometry, do you think NildGT can read?

There is another aspect to the whole history of zero that NdGT doesn’t touch on, and often gets ignored in other more serious sources. The ancient cultures that didn’t develop a place value number system, didn’t actually need zero. Almost all people in those cultures, who needed to do and did in fact do arithmetical calculations, didn’t do their calculation by writing them out step for step as we all learnt to do in school, they did them using the oldest analogue computer, the abacus or counting board. The counting board was the main means of doing arithmetical calculation from some time a couple of thousand years BCE, we don’t know exactly when, all the way down to the sixteenth century CE. An experienced and skilled user of the counting board could add, subtract, multiply, divide and even extract square roots much faster than you or I could do the same calculations with paper and pencil. 

The lines or column on a counting board represent the ascending powers of ten in a decimal place value number system, powers of sixty on a Babylonian counting board. During a calculation, an empty line or column represents an implicit zero. In fact, there is one speculative theory that realising this led someone to make that zero explicit when writing out the results of a calculation and that is how the zero came into existence. Normally, when using a counting board only the initial problem and the result are recorded in writing and if one is using a stroke collection, ancient Romans and Egyptians, or an alphanumerical, ancient Greeks, as well as ancient Indian and Arabic cultures before they adopted Hindu numerals, number system, then, as already noted above, you don’t need a zero to express any number. 

This blog post is already far too long but before I close a personal statement. I am baffled as to why a supposedly intelligent and highly educated individual such as Neil deGrasse Tyson chooses to pontificate publicly, to a large international audience, on a topic that he very obviously knows very little about, without taking the trouble to actually learn something about the topic before he does so. Maybe the fact that the podcast is heavily sponsored and littered with commercial advertising is the explanation. He’s just doing in for the money.

His doing so is an insult to his listeners, who, thinking he is some sort of expert, believe the half-digested mixture of half-remembered half-facts and made-up rubbish that he spews out. It is also a massive insult to all the historian of mathematics, who spent their lives finding, translating, and analysing the original documents in order to reconstruct the real history. 

HISTSCI_HULK: If I were a teacher and he had handed this in as an essay, I wouldn’t give him an F, I would give it back to him, tell him to burn it, and give him a big fat ZERO!

[1] Islamicate is the preferred adjective used by historians for mathematics and science produced under Islamic hegemony and published mostly in Arabic. It is used to reflect that fact that those producing it were by no means only Arabs or indeed Muslim


Filed under History of Mathematics, Myths of Science

A terrible fortnight for the HISTSCI_HULK

It’s been a tough two weeks for my old buddy the HISTSCI_HULK, who has now packed his bags and departed for pastures unknown screaming, “you can all kiss my posterior!” That not what he actually said but you get the message. 

So, what has upset the #histSTM pedant this time and what was the straw that finally broke the poor monsters back? It all started with Nicolaus Copernicus’ birthday on 19 February. As per usual this year, numerous people, including myself, posted on social media to mark the occasion. Our attention was drawn to the post on Twitter by the Smithsonian National Air and Space Museum, so we followed the link to their website and were less than happy about what we found there:

A rigid code of respect for ancient cultures and thought governed the early Renaissance, a period during which resistance to traditional concepts was met with hostility. Therefore, the Polish astronomer, Nicolaus Copernicus, whose ideas changed the course of astronomy forever, did not release his manuscript for publication until he was on his deathbed.

De revolutionibus Source: Wikimedia Commons


The early Renaissance was a period of lively scientific debate characterised by clashes of contrasting, conflicting, and even contradictory theories, and ideas. The debate in astronomy, to which Copernicus contributed, had been rumbling on since at least the middle of the fifteenth century. Also, it is not true that he “didn’t release his manuscript for publication until he was on his deathbed”. Rheticus published his Narratio Prima, as a trial balloon, in 1540. Following its relatively positive reception, Copernicus gave the manuscript of De revolutionibus to Rheticus to take to Petreius in Nürnberg to be published. At the time, as far as we known, he was still healthy. Printing and publishing a book takes time and by the time the book was finished, Copernicus had suffered a stroke and lay on his deathbed. Finally, the reason why Copernicus held De revolutionibus back for so long was because he couldn’t deliver. In the Commentariolus, Copernicus stated he would prove his hypothesis that the cosmos was heliocentric, but he had failed in this endeavour and so was reluctant to publish, a reluctance that was dissolved by the positive reception of the Narratio Prima.

Looking further on the Smithsonian National Air and Space Museum website, under Ancient Times and the Greeks, we find the following: 

Plato wondered why the starlike planets moved relative to the stars. Trying to answer the question was to occupy the attention of astronomers for many centuries.

Plato was more interested in the how rather than the why. Astronomers sought a mathematical explanation for the celestial movements. 

Under Ptolemy’s Planetary System we find the following

In the theory of Ptolemy, the planets moved in small orbits while revolving in large orbits about the Earth. This theory, although incorrect, could explain the apparent motions of the planets and also account for changes in their brightness.

This is an attempt to explain the deferent–epicycle model of planetary motion that Ptolemaeus presented. If one didn’t already know how Ptolemaeus’ system functioned, one certainly would have no idea after reading this. 

This is what is being described: The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Source: Wikimedia Commons


Already more than somewhat miffed the HISTSCI_HULK had the misfortune fourteen days later to view the article posted by the magazine History Today to acknowledge the birthday of Gerard Mercator on 5 March, he flipped out completely, thundering:


Let us examine the offending object, the opening paragraph truly is a stinker:

The age of discovery that began with Christopher Columbus, along with Ferdinand Magellan’s conclusive demonstration that the Earth is round, created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface. Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today. It was also Mercator who first used the term ‘atlas’ for a collection of maps.

In my opinion the age of discovery is an unfortunate misnomer, as I pointed out in a fairly recent blog post on the subject, preferring the term, Contact Period. It didn’t start with Columbus but was well underway by the time he found backing for his first voyage. 

… along with Ferdinand Magellan’s conclusive demonstration that the Earth is round …!!

Where to start? 1) Nobody of significance in Europe need a demonstration that the Earth was round in 1521, it had been an accepted fact for around a thousand years by then. 2) Ferdinand Magellan didn’t demonstrate anything, he died on route on the island of Mactan, waging imperialist war against the indigenous inhabitants. 3) Any nineteenth century flat earther would counter the claim that he “conclusive demonstration that the Earth is round” by stating that he merely sailed in a circle around the flat Earth disc.

… created a demand for new maps and confronted cartographers with the problem of how to depict the spherical Earth on a flat surface.

This statement would have historians of mapmaking and map projection tearing their hair out, that’s if they have any to tear out. The problem of how to project a spherical earth onto a flat surface had been extensively discussed by Ptolemaeus in his Geographia in the second century CE, a book that re-entered Europe at the beginning of fifteenth century more than one hundred years before Magellan undertook his fateful voyage. 

Of the various solutions, or ‘projections’, the one accepted as the best was that of Gerardus Mercator, which is still in use today.

Ignoring for a moment that “accepted as the best” is total rubbish, which of Mercator’s projections? He used at least two different ones and his son a third. Our author is, of course, referring to the so-called Mercator Projection. First off there is no such thing as “the best projection.” All projections have their strengths and weaknesses and, which projection one uses is dependent, or should be, on the task in hand. The Mercator projection allows a mariner to plot a course of constant compass bearing as a straight line on a sea chart. 

Yes, it was Mercator who first used the term atlas for a collection of maps. Our author at least got that right.

The next paragraph is a potted biography, which is OK but is littered with small inaccuracies:

He was born Gerhard Kremer at Rupelmonde in Flanders (now in Belgium), the seventh and last child of an impoverished German family which had recently moved there. His father was a cobbler, but the surname meant ‘merchant’ and Gerhard turned it into Latin as Mercator after his father and mother died when he was in his teens. A great-uncle who was a priest made sure that he got a good education and after graduating from the University of Louvain in 1532 he studied mathematics, geography and astronomy under Gemma Frisius, the Low Countries’ leading figure in these fields. He learned the craft of engraving from a local expert called Gaspar Van der Heyden and the three men worked together in the making of maps, globes and astronomical instruments for wealthy patrons, including the Holy Roman Emperor Charles V.

When Mercator was born his parents were only visiting his uncle or great-uncle, it is not known for certain whether he was the brother or uncle of Mercator’s father, in Rupelmonde. Following his birth, they returned to Gangelt in the Duchy of Jülich. Whether the family was German, or Flemish is not known for certain. They first moved permanently to Rupelmonde when Mercator was six years old. He adopted the Latin name of Mercator, meaning merchant as does Kremer, not when his parents died but when his uncle/great-uncle sent him to a Latin school. In the school he became Gerardus Mercator Rupelmundanus. After graduating MA on the liberal arts faculty of the University of Louvain in 1532, he left the university and only returned two years later, in 1534, to study geography, mathematics, and astronomy under the guidance of Gemma Frisius. He learnt the art of globe making when he assisted Frisius and Gaspar Van der Heyden to construct a terrestrial globe in 1535. This is followed by another paragraph of biography:

In 1538 Mercator produced a map of the world on a projection shaped like a pair of hearts. His inability to accept the Bible’s account of the universe’s creation got him into trouble with the Inquisition in 1544 and he spent some months in prison on suspicion of heresy before being released. John Dee, the English mathematician, astrologer and sage, spent time in Louvain from 1548 and he and Mercator became close friends.

The sentences about the cordiform projection (heart shaped, devised by Johannes Stabius before Magellan “sailed around the world” by the way) world maps and about John Dee are OK.  Why he refers to Dee as an astrologer but not Frisius or Mercator, who were both practicing astrologers, puzzles me. I’m also not sure why he calls Dee a sage, or what it’s supposed to mean. However, his account of Mercator’s arrest on suspicion of heresy is simply bizarre. He was arrested in 1543 on suspicion of being a Lutheran. Whilst in prison he was accused of suspicious correspondence with the Franciscan friars of Mechelen. No evidence was found to support either accusation, and he was released after four months without being charged. Nothing to do with, “His inability to accept the Bible’s account of the universe’s creation.”

We are now on the home straight with the final paragraph. Mostly harmless biography but it contains a real humdinger!

In 1552 Mercator moved to Duisburg in the Duchy of Cleves in Germany, where he enjoyed the favour of the duke. He set up a cartographic workshop there with his staff of engravers and perfected the Mercator projection, which he used in the map of the world he created in 1569. It employed straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point and proved a boon to sailors, though he never spent a day at sea himself [my emphasis]. In the 1580s he began publishing his atlas, named after the giant holding the world on his shoulders in Greek mythology, who was now identified with a mythical astronomer-king of ancient times. Strokes in the early 1590s partly paralysed Mercator and left him almost blind. A final one carried him off in 1594 at the age of 82 and he was buried in the Salvatorkirche in Duisburg.

I studied mathematics at university and have been studying/teaching myself the history of map projections for maybe the last thirty years and I have absolutely no idea what the phrase, straight lines spaced in a way that provided an accurate ratio of latitude and longitude at any point, is supposed to mean. I’m certain the author, when he wrote it, didn’t have the faintest clue what he was saying and tried to bluff. I also pity any reader who tries to make any sense out of it. It’s balderdash, hogwash, gobbledygook, poppycock, mumbo-jumbo, gibberish, baloney, claptrap, prattle, or just plain total-fucking-nonsense! What it definitively isn’t, in anyway whatsoever, is a description of the Mercator projection.

This wonderful piece of bullshit caused the HISTSCI_HULK to flip out completely. Imitating Charles Atlas, he tore his facsimile edition of the Mercator-Hondius Atlas in half with his bare hands and threw it out of the window. It’s a hard back by the way.

The term Atlas, as used by Mercator had nothing to do with the mythological Greek Titan Atlas, who by the way, holds the cosmos on his shoulders and not the Earth, but rather bizarrely the equally mythical King Atlas of Mauritania, who according to legend was a wise philosopher, mathematician, and astronomer, who is credited with having produced the first celestial globe. As Mercator explains: “I have set this man Atlas, so notable for his erudition, humaneness, and wisdom as a model for my imitation.”

Bizarrely, the article is illustrated, not by Mercator’s 1569 world map based on his projection, but the double planisphere world map from 1587 created by his son Rumold Mercator (1541–1599), which was based on it, and which first appeared in Isaac Casaubon’s edition of Strabo’s Geographia, published in Geneva. It was incorporated into later editions of the Atlas. 

Source: Wikimedia Commons

History Today is a popular English monthly history magazine, which according to Wikipedia, and I quote, “presents serious and authoritative history to as wide a public as possible.” Judging by this article, you could have fooled me. History Today has more than 300,000 followers on Twitter, that’s more than 300,000 potential readers for this garbage. The article was written by Richard Cavendish (1930–2016), an Oxford graduate, who specialised in medieval studies. Most well known as a historian of the occult his work, quoting Wikipedia once more, “is highly regarded for its depth of research and agnostic stance towards its sometimes controversial subject matter,” and, “He also wrote regularly for the British journal History Today.” The article was written in 2012, but the editor, Paul Lay, who considered it “serious and authoritative history” then, is the same editor, who thought it suitable to trot out again in 2022. 

Having within a fortnight been confronted by two horrible examples of how not to write popular #histSTM, the HISTSCI_HULK was more than somewhat mentally fragile when he stumbled on the offending object that finally caused him to snap, pack his bag, and depart, vowing never to read another word ever again. The offending object? A page from the book of the four-year-old daughter of a historian, who I know on Twitter:


“He made an amazing discovery.” As we obviously have to do with Galileo’s telescopic discoveries, there were more than one, we will restrict ourselves to those. All of Galileo’s telescopic discoveries were made independently, in the same time period, by other astronomers and they were also confirmed by the Jesuit astronomers of the Collegio Romano, so in fact anybody, who had anything to say on the topic, not only believed him but also congratulated him for having made them. 

“Galileo changed how people think about the Sun and Earth.” If any single person is going to be given credit for that then surely it should be Copernicus. In fact, it is, in my opinion, wrong to credit any single person with this. The shift in perception from a geocentric cosmos to a heliocentric one was a gradual accumulative process to which a fairly number of people contributed.

“He built a new telescope to study space.” I have difficulties with the new in this sentence. Galileo, like quite a large number of people built a so-called Dutch telescope with which to make astronomical observations. He was by no means unique in doing this and not even the first to do so. What should be expressed here is that Galileo was one of a number of people, who constructed telescopes, after it was invented in 1608, in order to make astronomical observations.

“He proved that Earth travels around the Sun.” Apart from the fact that the sentence isn’t even grammatically correct, it should read “the Earth”, it’s simple false. The problem that faced all the early supporters of a heliocentric model of the cosmos was that they simply couldn’t prove the hypothesis.

“People thought it was the other way around.” Of course, they did because that’s what our senses tell us. We all have to learn that it’s not true!

I have a very simple question. Why do people present young, impressionable children with garbage like this?

In case anybody is concerned, I’m sure the HISTSCI_HULK will return when he’s calmed down.  


Filed under History of Astronomy, History of Cartography, Myths of Science