Sunday, December 27, 2020

Heller Coins of Medieval Hall in Swabia

For about 300 years, these small silver coins, nominally worth half a penny were an important medium of daily commerce in central Europe. They originated in the town of Hall in Swabia and were therefore called Häller (Haeller or Heller). 

In response to an advertisement from my longtime friends at Liberty Coin Service of East Lansing, I bought 12 medieval hellers to give out at Christmas. The 2x2 inserts from Liberty Coins say, “Silver Hand heller / City of Hall / 1189-1500.” Denied access to the University of Texas libraries because of Covid-19, I went looking online for references and found very little information. 


Five typical häller. 
Hands top center and bottom left.

The American Numismatic Society lists about two dozen, giving them all the same general descriptions, although their fabrics—diameter, weight, fineness—speak of historical complexity. The attributions depend on who worked the coins when they were donated to the ANS. The ones acquisitioned in 1927 are dated 1240-1437; the acquisitions of 1953 are dated 1300-1400. German haeller are catalogued from Württembergische Münz- und Medaillenkunde by Christian Binder (Stuttgart, 1846) because the free city of Hall in Swabia was entered into the Württemberg hegemony in 1802.

The Bohemian heller are listed in Beschreibung der sammlung böhmischer münzen und medaillen originally catalogued by Max Donebauer and then privately published by Eduard Fiala; Prague, 1888-1889. In each case, all häller are given the same catalog numbers. Clearly, the small half-pennies, lacking legends or inscriptions, easily with no mint control marks—little crosses or mullions, stars, etc.—are difficult to date or place. The 24 coins catalogued with pictures range in weight from 0.3 to 0.817 grams: median 0.525; modes 0.52 and 0.53; mean 0.546. The diameters all seem within 16.5 to 17.5 mm. Some of the coins are torn in the fields, a common flaw among Medieval coins which tended to be larger rather than thicker. 

Civic Coat of Arms

The American Numismatic Association provides even less data.  The ANA Numismatist has one entry for “Hall am Kocher.” (The river is often an identifier in German, for instance, to differentiate Frankfurt-am-Rhein from Frankfurt-am-Main). That citation is in an article from February 1961 by Dr. John Davenport: “European States Issuing Dollar Size Coins” clearly, not about the half-penny. More recently, Usula Kampmann’s “Around the World” column for September 2020 centered on the coins of Schwäbische Hall. Unfortunately, it was as light as the coin itself on facts. She said only that the heller was originally worth half a pfennig.


I attribute them to the rise of Friedrich Barbarossa.  Whether the western half of the Roman empire actually “fell” or “collapsed” can be debated. Clearly, many aspects of society had changed slowly, almost imperceptibly one generation after another. And just as slowly, the Holy Roman Empire became a new cultural context. Low points of chaos punctuated a general trend toward production and trade, technology, literacy, art, and (ultimately) science. 


Friedrich, the duke of Swabia, was the son of two powerful local families. Born in 1122, he died in 1190 on a Crusade. Friedrich inherited the title of duke of Swabia. Hall’s position as a center of exchange dated back to the salt trade of the Celts. 


Friedrich consolidated his central European realms and was crowned a king in 1152 and then Holy Roman Emperor in 1155. During his wars of expansion, Italians gave him the soubriquet “Barbarossa.” In his lifetime, he increased the royal mints from two to 28. 


Numismatists can often distinguish the genuine English pennies of good sterling silver (0.925 fine) from copies made elsewhere, such as the Papacy, which were also of sterling silver. To my knowledge, no one has attempted this for the haeller. The fact is that like English pennies, gold florins, and other popular issues, the haeller could have been copied in many places and likely were. That fact speaks to a fundamental principle of economics: trade crosses borders. As long as the coins were good, they were accepted prima facie.


By our modern measures, the nominal häller weighed 0.546 grams and were 0.545 pure silver. In their time, they were valued against the standard Köln (Cologne) mark which at 233.8 grams modern was about half a medieval (not ancient) Roman pound. Each unze was divided in to 32 pfennig. The haeller was accepted as half a pfennig or a twelfth of a schilling.  


The fact that it was debased to just over 50% pure is the reason why it survived in daily commerce: it had more utility as a coin in local trade, wherever it was used, rather than being exported for exotic goods. 


(Both images Wikimedia Commons)
The Hand is taken to be a sign of blessing, perhaps the Hand of God, according to some modern interpretations, epigraphic evidence being lacking. This is assumed to be the obverse. The Cross on the reverse is easy. However, some are the only element while others are within a Shield. Most are saltier crosses, often with at a pellet in two of the noches. In some the reverse exergue has pellets separated by bars. While these details can differentiate varieties, no numismatist has attempted to decode them. In the exergue of one coin that I had, two pellets are in one field and could look like the crossed bishop’s staffs known, for instance from the coat of Basel. But Hall was never a seat. So, if this coin was issued by a bishop’s mint, that was someplace else.


Into modern times, the word “heller” continued as a generic term for any small coin, whether or not it was a lawful denomination as a fraction, for example, of a silver thaler (“dollar”). The currency reform of Austria-Hungary in 1892 re-established the heller as 1/100 of a corona in Austria. (The Hungarian korona was divided into 100 filler.) Germany used the heller as a fraction (1/100) of a colonial East African rupie on the Indian standard of 1 rupee = 2 UK sterling shillings. Therefore the  rupie and rupee were about the same as 50 cents US silver of the time. So, the East African heller was about the same as half a US cent. The heller denomination was last struck by the former Czechoslovakia up to 1993. The separate Czech and Slovak republics kept the denomination – Czech plural haléřů; Slovak plural haliers. 

 In German, anything from the town of Hall would be a häller. The plural is the same word, rather than hällerer or hällern or hälleren. (In English we still have the archaic deer not “deers” for a plural.) The umlaut double-dots are a medieval convention to represent a little e over the a to show the vowel shift upward. So häller becames haeller and then heller.


Additional Sources:

I now wish that I had seen earlier this most excellent write-up Common Medieval Coins: Info Thread by Orielensis (Apr 23, 2019) on CoinTalk here:

“Frederick I Barbarossa and Political Legitimacy,” poster by Brian Sebetic; Faculty Mentor: Dr. Monique O’Connell; Wake Forest University online atäbisch_Hall,_Holy_Roman_Emperor

Previously on Necessary Facts

City Air Makes You Free 

The Cure for a Failing Empire 

Numismatics Informs Economics

Science in the Middle Ages 

Rescuing Aristotle and the Church 

Astronomical Symbols on Ancient and Medieval Coins 

Friday, December 25, 2020

Jupiter-Saturn Conjunction 2020

I have them in my notebook going back months, of course. They are finally slipping behind the roofs and trees. See the previous post. But with some exceptions, conjunctions are only aesthetically important to us: we do not learn more about anything. Occulations do offer opportunities to compare and contrast observations and measurements.

Mostly, it was a social event. I took the occasion to post on-topic at discussion boards that I visit: Cloudy Nights, The Sky Searchers, the British Astronomical Society, the Society for Amateur Astronomy, and Star Gazers. Astronomy has long been an international community of amateurs and professionals. I met someone from Houston on a British forum.

I purposely put the 70-mm National Geographic
to work because any telescope is better than none.

Back in the 1970s, I participated in a fanzine called The Libertarian Connection. We sent in two pages (mimeographed until about 1976, then photo-offset) and the hosts printed them off, bound them, and mailed them out every six weeks. In 1977, while working at a computer terminal at Michigan State University where I had hacked some time, I got a message on my screen from a friend on a computer at Lansing Community College. In 1983, I joined a bulletin board, and connected with a 300 baud modem. So, the online discussion board is a medium that I understand. 



Ground Truth 

Jupiter-Mars Conjunction

Defending the Hobby-Killer Telescope

In Support of the Entry-Level Telescope


Sunday, December 20, 2020

Merry Newtonmas 2020

For about 1500 years, the story of the Star of Bethlehem was accepted as historically accurate because it was divine truth. Miracles were not questioned. With the Renaissance, a new way of looking at the world evolved. 

The scholarly tradition of explaining the Star of Bethlehem with scientific evidence apparently began with Johannes Kepler who identified a triple conjunction as the likely event.

13 December 2020 scale drawing

In 1604, he published The New Star in the Foot of the Serpent (De stella nova in pede serpentarii: et qui sub ejus exortum de novo iniit, trigono igneo…). In that tract, he examined a triple conjunction, as well as a nova, which he identified as the cause of the conjunction. He was not alone in that kind of a belief. Others expected the conjunction to cause a comet. Reviewing the facts in 1614, Kepler said that the Star of Bethlehem was a nova in 4 BCE caused by a triple conjunction in 7 BCE. (See “Common Errors in ‘Star of Bethlehem’ Planetarium Shows,” by John Mosley, The Planetarian, Third Quarter 1981.)

19 December 2020
Scale drawing
Over the centuries, the Christmas Star has been explained as a comet, a meteor or meteor shower, but the conjunction theory has been the most popular. 

In science, a good problem takes us far beyond the results of a single observation. The Christmas Star has been debated on many levels. The International Planetarium Society website ( lists over 100 citations to the Star of Bethlehem. Some of those articles and letters were part of a multifaceted decades-long argument among at least five astronomers and one editor. Writing in Archaeology Vol. 51, No. 6 (Nov/Dec 1998), Anthony F. Aveni cited 250 “major scholarly articles” about the Star of Bethlehem. 

The sciences here are psychology and sociology, not astronomy. People want to believe. The need for religion derives from a more basic need for certainty. I like it when my own plans come together. Beyond that, I observe that most other people do not find freedom in the unknown, the unplanned, or the spontaneous response to unforeseen events. As with a spontaenous choice, an effective response is based on a rational understanding of experiential circumstances. For myself, an invention is a kind of discovery. Right now, my instrument is a telescope. But I also own two microscopes. For myself, the Christmas conjunction is no more or less special than the structure of a poinsettia, something I have not investigated at all, but which is pretty easy to find. Conjunctions happen all the time. And they happen at all only because of our inertial frame of reference. Standing on the spinning Earth orbiting a focus of an ellipse, we see arrangements come and go with -- I confess -- comforting predictability.



Merry Newtonmas 2019 

Reminders of Newtonmas Past 

Atheists in Foxholes 

Saturday, December 12, 2020

Turing Never Said That

“I think that sometimes it is the people who no one imagines anything of who do the things that no one can imagine.” The line is spoken twice, first by Knightley qua Clarke and then by Cumberbatch qua Turing. But they never said it. It should be attributed to a different genius, the screenwriter, Graham Moore.

I never accepted the quote as genuine, but it came up again when a colleague used it in their signature block. I wanted to warn them about that; so I did another Google search for an authoritative reference to debunk the false citation. I found the work of Sir John Dermot Turing.  

Dermot Turing – like his celebrated uncle Alan Turing – was educated at Sherborne School and King’s College, Cambridge. After doing a D.Phil in Genetics at Oxford, he concluded that scientific research was not for him, and moved into the legal profession. … His specialism was financial sector regulation, particularly the problems associated with failed banks, and financial market infrastructure.  -- More at

In a blog on his website, Sir John explains: “Fake quotes - July 30, 2019 - We all know about fake news, but only recently I discovered fake quotes. I was asked where Alan Turing’s famous quotation ‘Those who can imagine anything can create the impossible’ had come from. After a lot of digging, the answer was ‘It didn’t.’ Not in his broadcasts. Not in his published papers. Not in his unpublished speeches.” 

The statement is insightful, powerful, and empowering. It deserves repetition and popularization. The author was Graham Moore. Moore received an Academy Award and a Golden Globe for his screenplay of Imitation Game. He understood Turing. 

“I had been this huge computer nerd my entire life. I went to space camp and computer programming camp. I was that kid. From a very young age, I knew about the legend of Alan Turing - among awkward, nerdy teenagers, he is a patron saint. He never fit in, but accomplished these wonderful things, as part of a secret queer history of computer science. And so I always dreamt of writing something about him, and I thought that there had never been a proper narrative treatment of his life, that he deserved. I by chance met the producers of the film at a party, and one of them told me they had optioned a biography. When I asked who it was, they said, 'it's a mathematician that you've never heard of.' When they told me it was Alan Turing, I almost tackled them, and I told them I'd do anything to write this film, I'd write it for free. It was all about luck and passion. That is how it started, and I felt that everyone else involved was just as committed to the story.” -- Graham Moore via IMDB at


Dermot Turing has developed an interest in his uncle’s work, publishing several books about the wartime projects at Bletchley Park. I bought two of them through Amazon UK. For myself, that was evocative on several levels. 

First, I am a globalist and I love global commerce. Unlike my conservative comrades who have fallen into the abyss of nationalism, I find an overarching  vista in Ayn Rand’s warnings against the Balkanization of western society. (See the Ayn Rand Institute here.) To be able to buy a product from across the Atlantic ocean with a few clicks is a tribute to human ingenuity in a open market.  

Second, my money was exchanged from dollars to pounds automatically and at a trivial cost. On the one hand a global society needs a global currency. On the other hand, an open market allows a plethora of monetary media. Friedrich A. Hayek called gold “the wobbly anchor.” (On NecessaryFacts here.) At the American Numismatic Association convention in Chicago in 2019, I spoke on the future of money and predicted a world coming soon with personal currencies. (See a version on Necessary Facts here.) During the Middle Ages, bankers rationalized the variegated fabric of local coinages with an abstract system of “pounds-shillings-pence”; and when they met at great fairs, using the new Arabic numbers and algebraic methods, they cleared their books without ever touching a coin.


Third, the transaction was secured with public key cryptosystems. Software agents shook hands and established trust in order to safely carry my money and order the transport of the seller’s product. 


A final note on Turing from Turing: “One scene in the movie which had puzzled me is the one where a young Alan Turing is pinned beneath the floorboards at his boarding-school and jumped on by his schoolmates. That’s bizarre, in many ways, not least because there is no evidence that Turing was bullied at school, and certainly none in Hodges’s book. Oho, it turns out that this scene is lifted from another book altogether – A Madman dreams of Turing machines, a novel by Janna Levin. So what started as fiction has been recycled as biography.” – Sir John Dermot Turing.



A Successful Imitation of Alan Turing 

Turing’s Cathedral 

Variations on Enigma 

BASIC: Turing’s Truth 

The Code Book 

Coins and Codes 

Sunday, December 6, 2020

Focus on Simon Georg Ploessl

The Ploessl ocular (“eyepiece”) is easily the most popular design in the hobby of astronomy. Regardless of focal length, from 40 mm to 4 mm, they are common because they are inexpensive and they reasonably support the limits of the largest amateur instruments. Better designs are available, but at a greater cost. A modest instrument under city skies usually will not benefit from the improved optics of an orthoscopic ocular. Thus, the Ploessl is the first choice, whether for a refractor, reflector, or catadioptric telescope. For all of its ubiquity, its inventor, Viennese optician Simon Georg Ploessl is not widely known among astronomers. 

Say it Right


Lithograph by Kriehuber
First of all, he spelled his name Plößl and that almost rhymes with the English word “vessel.” 

The character that looks like a capital-B ß is a double-s. It is called an “Eszet” or “sharp-ess” (scharfes-Ess) from a time when German orthography spelled words like der Fuss (the foot) as der Fusz to show that it had a hissing-s sound, not the unvoiced fricative that we know in English as “sh” in “shoe” or “push.” 

The umlaut-o ö is sounded by rounding your lips to say English long-o, but instead, saying English long-a. If you did not grow up speaking German, then “Plessl” is close enough. That is because three consonants follow the vowel. Each one clips some time off the sounding. The word for “height” die Höhe sounds like an American calling their friend from across a room “hey-ya” not the short laugh “heh.”

The double-dots are a medieval shorthand for a little letter e that was placed over the o to show the shifted sound. Thus, the questionably undead cat is not as if in English long-o “Shro-din-jer’s” but umlaut-ö as if in English like “Shray-ding-er’s.” Ploessl also used the ligature œ (oe), a less common flourish.

If your typewriter has no umlaut vowels (ä ö ü) or a sharp-s (ß), you can use an e and a double-s. Thus, Plößl (which is how he spelled it) is accepted as Plössl or Ploessl, but spelling the name Plossl or saying it that way is wrong.


From the Microscopic to the Macroscopic


Georg Simon Plößl (1794-1868) was born in Wieden which had been an independent villa in the Middle Ages but by the 18th century already lay within Vienna’s shadow. He was the son of a cabinetmaker. And therefore an apprentice in his father’s shop, beginning as a lathe operator (turner). When he was 18, he left for the optical firm Voigtländer, starting on May 9, 1812 [5].


In 1823, he moved back to his father’s home and began his own laboratory and workshop for investigations into the production of optical instruments.[1] In 1828 he was open for sales [2]. At first, Ploessl made microscopes, and he soon became famous for them.


His company took off (and took a new direction) when he sold a microscope to Joseph Franz von Jacquin, professor of botany and chemistry at the University of Vienna. Von Jaquin introduced Ploessl to the astronomer Joseph Johann von Littrow for whom he built a telescope in 1830. 


Three-inch "dialytic" Refractor by Simon Georg Plößl

At Viennese industrial fairs in 1835, 1839, and 1845, Ploessl was granted gold medals in recognition of the exemplary products of his workshop. In 1847 another gold medal was bestowed by the Emperor Ferdinand. The emperor also commissioned him to build a telescope which was gifted to the Vizier of the Ottoman Empire.[6] (Some sources say that it was for the Sultan.) [5]


By 1850,  in addition to the microscopes which were the primary production of his firm Ploessl had delivered refractors to observatories in Romania (Iasi; 6.4 inches), Hungary (Biczke; 8.5 inches), Greece (Athens; 8 inches), and Russia (Pulkovo; 6.4 inches). In 1851 the firm delivered an 11-inch f/11.8 refractor to the Vizier. Delivering up to 610x magnification, it was said to divide gamma Coronae Borealis: 0.6 seconds of arc at 4th and 7thmagnitudes. (The above is from 19th century reports. A modern paper identifies the Athens instrument as 162-mm (6.37 inches) [1].) Other Ploessl instruments have been identified. He also built dipleidoscopes for determining the moment of high noon, 12 o’clock post meridian. 


All of his telescopes had objectives of crown glass. They followed the Fraunhofer design of a concave and convex lens pair, but did not use flint glass which was rarer in large, high-quality blanks. Consequently, the essential element in the design was the secondary lens system, a flint glass ocular that minimized chromatic aberration. That was Ploessl’s stellar achievement. 


The Ploessl Ocular Lens System

Two pairs of lenses, match convex and concave curves, and the pairs are separated by a gap. The concave lenses are at the extremes, the convex face each other in the center. This design was not a happenstance. The Voigtländer firm was founded in 1763 when Johann Christoph Voigtländer received a monopoly charter (“protection decree”) from the Austrian monarchy to produce mathematical instruments. Fifty years later, Ploessl studied mathematics and optical theory while rising from apprentice to journeyman. 

Star Ware: The Amateur Astronomer's Guide
to Choosing, Buying, and Using Telescopes
and Accessories, 4th ed.,
by Philip S. Harrington, John Wiley and Sons, 2007.

Three factors kept this system from becoming widely accepted. First, telescopes are durable goods. Better ones have been built since 1610, but the old ones still work. The Ploessl refractor in Athens served the university until 1940. Second, astronomy was a private pursuit for intellectuals of independent means. While Britain had its Royal Astronomer, few such public posts existed elsewhere. Ploessl built telescopes for state enterprises in Greece and Russia, but he built more for wealthy patrons in Hungary, Romania, and Italy. Only with the explosion of science in the 20th century was there any broad consumer demand for the instruments of empirical discovery. Third, as prosperous as the Ploessl firm was, it was a sole proprietorship. When Simon Ploessl was killed by a falling sheet of glass in 1868, there was no one to step into leadership. The firm continued until 1905, but there was no visionary to drive the effort.[*]


Enter Al Nagler


Al Nagler founded TeleVue. He gave an extensive interview to Astronomy magazine, which posted it as a blog and it is archived at The story is enjoyable and edifying. Briefly, he said:

While the Nagler was the first eyepiece I designed for Tele Vue, I feared entering the astronomy market as an unknown “kitchen-table” company with such an expensive eyepiece. This caution led me to produce a Plössl eyepiece first, to gain reputation, experience, and capital.[7]

References and Further Reading

[1] The Hellenic Archives of Scientific Instruments at


[3] Looking at the Skies for 175 Years: The 162-mm Ploessl Refractor and the 400-mm Gautier Refractor of National Observatory of Athens, Panagiotis, Lazos and Tsimpidas, Dimitrios; XXXVII Scientific Instrument Symposium, 3-7 September 2018, Leiden and Haarlem.


[5] “Plössl-Mikroskope - ein Vergleich mit modernen Geräten,” by E. Steiner and P. Schulz, ©Naturhistorisches Museum Wien, download from

 [6] “The Achromatic Telescope, Dialytes, and Fluid Lenses--Nebula--Double Stars—Occultations” by the Rev. T. W. Webb, A.M., F.R. A. S., The Intellectual Observer, Groombrdige and Sons, London, No. XLIX, February 1866, 

[7] “The evolution of eyepiece developments at Tele Vue,” Posted by Michael Bakich on Tuesday, October 13, 2015, A guest blog by Al Nagler. Astronomy.

[*] Addendum 14 December 2020. I found evidence of this. To make a short story long, I borrowed a Meade 10-inch Ritchey-Chretien catadioptric telescope from the local club. Researching it, I discovered a legal kerfluffle among Meade and some others. A discussion on Cloudy Nights took me to the website of retired telescope maker R. F. Royce ( At the top of one of his pages is this quote: "If the pure and elevated pleasure to be derived from the possession and use of a good telescope of three, four, five, or six inches aperture were generally known, I am certain that no instrument of science would be more commonly found in the homes of intelligent people." - Garrett P. Serviss, Pleasures of the Telescope, 1901. So, I followed that track. In his time, Serviss was famous as a popularizer of science, especially astronomy. When he was a night editor at The Sun of New York, one of his lecture tours was subsidized by Andrew Carnegie. His passing was noted in a long obituary in Popular Astronomy (August-September 1929). The Pleasures of the Telescope was first published by Putnam in 1901, and then went through several re-publications. Google Books and Hathi Trust provide the 1915 printing by D. Appleton and Company. Serviss described two kinds of eyepieces: positive (Ramsden) and negative (Huygens). He does not mention the Ploessl. 


The Genius of Design

Raymond Loewy

The Perfect Machine

The Christmas Star