Here’s a thing that struck me the other day about the Anthon Transcript that I thought I ought to mention.

The way that the story has been passed down to us makes it far from easy to reconcile the “Caractors” page…

…with the “singular scrawl” shown to Professor Charles Anthon in 1828:

“It consisted of all kinds of crooked characters disposed in columns, and had evidently been prepared by some person who had before him at the time a book containing various alphabets. Greek and Hebrew letters, crosses and flourishes, Roman letters inverted or placed sideways, were arranged in perpendicular columns, and the whole ended in a rude delineation of a circle divided into various compartments, decked with various strange marks, and evidently copied after the Mexican Calendar given by Humboldt, but copied in such a way as not to betray the source whence it was derived.”

It would seem as though the first page was arranged in horizontal rows, while the second page was arranged in vertical columns and with a compartmentalized circle added after it. It sounds as though we are talking about two quite different things, and so shouldn’t even attempt to reconcile them as one. Yet in the decade up to his death in 1888, David Whitmer repeatedly asserted that this first page was indeed the very same “original paper” that Martin Harris had taken to Charles Anthon.

At this point, any passing Intellectual Historian might gently suggest that all these statements may well have been said in good faith: and that what is actually stopping us seeing them all as descriptions of the same thing is not the evidence itself, but our stubbornly persistent misreading of what is in front of our faces.

Can we do better?

The case of the ‘H’

I suspect that we can: and the giveaway that may well help to point us in the direction of what happened is the capital ‘H’ shape that occurs at least eight times:

How on earth did the person copying this down not notice that this was nothing more than an ornate ‘H’ shape? Though I’ve long wondered about this, reasonable answers have to date always eluded me. But what I noticed here is that perhaps the actual explanation is painfully simple: that the person who originally wrote these down copied the shapes as if they were written in columns, i.e. without seeing them as ‘H’ shapes at all.

The photograph in Clay County Museum directly supports this idea, because the writing on the other side of the fold (“The Book of Generation Adam”) is written sideways:

The two-button mouse

Even though most of the Caractors are evenly inked, the strong downward strokes of one of the three “two-button mouse” shapes also seems to indicate to my eyes that the letters were written ninety degrees rotated from what we see now (though I’d appreciate other people’s palaeographical insights on this particular issue):

I’d have thought the suggestion that these letters were originally written in columns rather than rows would be a palaeographical hypothesis that could be tested out and resolved one way or the other.

Reconstructing the sequence

If the above is basically right, it would seem that the stages that this page went through were:

(1) The shapes were copied in columns from a source that was (wrongly) believed to have also been written in columns.

This caused letters such as the ornate ‘H’ shape to be copied not semantically as letters, but instead as a series of strokes. I would also expect that these columns were copied downwards as per the following image:

I can see how someone who had not grasped the correct orientation of these letters might have considered their rotated versions to be “hieroglyphic”-like. (I can also see how going from “hieroglyphic”-like to reconstructing the 2500 B.C. Jaredite flight from Egypt to America in submarines might seem a little too extreme for some.)

Note that I can easily see how the bottom of this page (beneath the ragged fold in the museum photograph) could have originally contained a “rude delineation of a circle divided into various compartments”: in which case the page was obviously longer. The overall page was also probably folded in half (parallel to the longest edge) at around this time, because only a single crease is apparent in the photograph.

This, then, would have been what was shown to Charles Anthon in 1828.

(2) The circular calendar section was removed, and the ‘Caractors’ word added.

Note that MacKay et al [*1] showed that the “Caractors” lettering at the top and the lettering of the curious letters were all done in the same ink. However, it also seems likely to me (from the orientation) the Caractors word was added in a quite separate construction phase, and their conclusion that this word was added at the same time as the rest of the letters ought to be examined very carefully indeed.

I believe that the circular calendar section was removed around now because of the following phase…

(3) The “Book of Generation Adam” text is added circa 1830, halfway down the reverse side.

Because this text was added right in the middle of the reverse side, it seems likely to me that the circular calendar section had already been removed (or else this text would probably have appeared further up the [slightly longer] page).

We can date this addition to 1830 or after, because that is when the phrase “The Book of Generation Adam” began to be used in the Mormon Church.

(4) The “Book of Generation Adam” half of the page is removed before 1884.

As Grindael noted, the part of the page with the “Book of Generation Adam” text was almost certainly “torn off sometime before 1884, because it is described as having the same dimensions then as it did in 1903”.

(5) The remaining fragment is sold to the RLDS Church in 1903.

“This collection of documents [was] eventually given into the care of George Schweich, a nephew of David J. Whitmer, who subsequently sold them to the RLDS Church for $2450 in 1903.”

Is this sequence correct?

I don’t honestly know. But if you were to try – while wearing an Intellectual Historian hat – to reconcile what you see in the RLDS Caractors fragment with the different testimonies assuming they were all given in good faith, then I strongly suspect that this sequence is extremely close to where you would necessarily end up.

And perhaps that’s as good as it gets, at this distance in time. Or… perhaps this is just the start?

[*1] MacKay, Michael Hubbard; Dirkmaat, Gerrit J.; Jenson, Robin Scott. The “Caractors” Document: New Light on an Early Transcription of the Book of Mormon Characters – Mormon Historical Studies, vol. 14, No. 1.

A central pillar of Mormon history is the so-called “Anthon Transcript”, which I have described in reasonable detail on the Cipher Foundations website: this was shown to Professor Charles Anthon in February 1828.

Yet there is a key problem: the description of it given by Anthon in letters dating 1834 and 1841 differs markedly from the image of a “Caractors” page (a document presumably still deep within the LDS’ X-Files-like archive) that is often described as being the “Anthon Transcript”.

In 2012, a better quality image of the same Caractors pages taken around 1884 was discovered in Clay County Museum in Missouri: and this image shows that the full piece of paper then had “The Book of Generation Adam” written on it, which would date it to not earlier than (and probably very close to) 1830.

This implies clearly and unambiguously that there is now no good reason for anyone to think that this “Caractors” sheet is related to the “Anthon Transcript”, simply because it would appear to have been written some two years after Charles Anthon was shown the Anthon Transcript. So there is no logical way that the two items can be the same thing: sorry but they just can’t, and that’s that.

Caractors

I therefore see no possible theological objection if anyone tries to decrypt the letters on the Caractors sheet: and given that we now have a far higher quality image to work with than we ever did with the original Caractors image, there’s no obvious reason not to give it a go.

So if anyone wants to try, I’ve created a worksheet you can print out and work with (by inserting blank space between the seven lines of text) – just click on the following image to get a reasonable resolution (a higher quality source image would be even nicer, if anyone happens to be passing Clay County Museum in Missouri with a digital camera *hint* *hint*):-

caractors-line-by-line

I should caution that it’s hard to be sure what is going on in this page. Though it at first looks like the ungainly mixture of semi-fast shorthand and foolhardily slow-to-write extras (that Isaac Pitman derided as “arbitraries”) that was typical of English shorthands deriving from Jeremiah Rich’s system (e.g. Addy’s etc) and which were still popular circa 1800, further examination makes it clear to me that it’s actually a bit of an improvised mess. As such, its shorthand-like symbols now seems more likely to me to be shapes in a mildly homophonic cipher alphabet than actually shorthand per se.

As always, there’s room for a certain amount of overlap between the two types of writing: but probably not enough to stop anyone from actually breaking it using broadly the same kind of cryptological toolkit.

The Last Sixteen Words

Interestingly, the last three lines (where the text gets smaller and smaller) seem to be written far more systematically than the first four lines. Indeed, there also appears to be a regular use of dashes or hyphens, very possibly as word separators. If you use this to turn the last two-and-a-half lines into a series of sixteen words, this is what you get (click on the following for a much higher resolution image):

last-sixteen-words

Decrypting The Caractors

There is plenty of old-fashioned codebreaking meat to get your cryptological teeth into here: though I’m still trying to resolve the numerous ambiguous / miscopied letter-shape issues, I thought it would be good to give a work-in-progress update on where I’ve got to, in case this inspires someone to crack this (as Marco Ponzi did for the Paris 7272 cipher here the other day).

Word #10 is almost identical to Word #6 (though with a letter inserted), which makes the pair of words look like “ONE / ONCE” or some similar phrase (no doubt there are lists of similar ABC / ABDC pairs on the Internet somewhere, please tell me if you know where they are).

The presence of the “6L6” shape in word #1 and word #4 makes it look as though the similar (but slightly malformed) shape in word #15 was the same shape in the original but miscopied: this makes it look to me that much of what we are up against here is miscopying of a simple-ish cipher rather than a genuinely complicated cipher. As such, I suspect that the first letter of word #4 is ther same backwards-crossed-C-C character in words #14 and #15 (and which is the first letter of the top line on the whole page).

Word #12 looks like it may well be a name: but without higher quality scans, I suspect it will be difficult to parse the symbols definitively (some may well be pairs, so it is hard to be sure how many letters we are looking at).

Word #14 and word #15 also offers a cryptographic oddity that might yield a way in: if we use letters to denote patterns rather than actual letters, the two consecutive words would seem to be ABCDE and FGEHAC. Given that there’s a high chance that the plaintext of this page is in some way related to the Bible, I suspect a keenly observant codebreaker with a side interest in Biblical studies might possibly be able to crack these two words alone.

Finally, for those we are interested by the possible connection between the various Whitmers and the Caractors document that has been suggested in recent years, I found a 1989 article that mentioned where the Whitmer family had been to church: “In Fayette [near Seneca Lake, NY], the Whitmers drew closer to God by working the soil and worshipping at Zion’s Church, a German-speaking Presbyterian church“. So there is also a (small) possibility that the plaintext of what we are looking at here might possibly be German. I just thought I’d mention this in passing. 🙂

Good luck!

As part of the long slow process of fleshing out the Cipher Foundation’s website, I’ve added a new page there laying out the core evidence relating to the Anthon Transcript, a cipher-like document that sits right at the heart of the foundation history / mythology of the Mormon Church.

The short (non-TL;DR) version is that even though it has long been claimed that the Anthon Transcript (shown to Professor Charles Anthon in 1828) and the Caractors fragment are one and the same, a photograph that was unearthed in Clay County Museum in Missouri in 2012 seems to disprove this whole notion. Hmmm.

All the same, people continue to build high-rise cipher theories on top of this unsupportive sandy loam. Most recently, Jerry Grover announced his own fairly epic (251 pages of argument) Caractors translation, that renders the first four lines as:

In the nineteenth regnal year of Mosiah I, the Nephites traveled over the mountains to the foreign speaking people of Mulek. These twenty thousand ‘children of Mosiah’ traveled downriver on the east side of the River Sidon [Grijalva] for eighty days and reached Zarahemla. And then it came to pass that after ten years thus began the period of the Seven Tribes. After the space of twenty-one more years had passed, Zeniff, with sixty of his people, departed. Fifty-three more years then passed; then the Limhiites obtained twenty-four plates from the west in the Land of Desolation, returning upriver on the River of Lamanite Possessions [Usumacinta]. After their return upriver, seven years later, the Limhiites traveled west, bringing the pure gold Jaredite plates to Mosiah (II), which he translated. Previous to the arrival of the Limhiites, Benjamin was made King in the second month of the four hundred and thirty-sixth year after Lehi left Jerusalem. At the age of eighty-three, King Benjamin ascended to eternity, which was four hundred seventy nine years after Lehi left Jerusalem. King Benjamin’s death occurred one and one third years before the arrival of the Limhites. Four years before the arrival of the Limhites, the period of the Seven Tribes ended in conjunction with the Jubilee Year.

Personally, I’d assess the probability that this is correct is roughly the same as a truck load of lobsters falling out of a clear blue sky into my garden: in that I can conceive that it is (just about) possible and (broadly) consistent with the laws of physics, but (etc etc etc).

More generally, I’d offer this as a stark warning to idiot Voynich linguists such as Stephen Bax, as the kind of ultimate destination their foolish non-theorizing will ultimately lead them to.

The Anthon Transcript was a document shown to Professor Charles Anthon by Martin Harris in New York in February 1828: Harris claimed that it was a copy of the “reformed Egyptian” letters used to write the Golden Plates. The story goes that these Plates had been hidden in a hill near where Mormon founder Joseph Smith lived; that the Angel Moroni first directed Smith to them in 1823 (though he only took them away in 1827); and that Smith claimed to have translated the Book of Mormon from these Plates.

It is normally reported that the Anthon Transcript is the same as the “Caractors” document widely shown on the Internet, and which was first supplied by David Whitmer…

800px-Caractors_large

…but since reading an essay called The Anthon Affair by Jerome J. Knuijt, I’m really not so sure any more.

What is specifically odd is that, when later quizzed about the meetings he had with Martin Harris, Anthon wrote that the transcript “consisted of all kinds of crooked characters disposed in columns” (1834), “like the Chinese mode of writing” (1841). Moreover, “the whole ended in a rude delineation of a circle divided into various compartments;“, and that this resembled “a rude representation of the Mexican zodiac“, “evidently copied after the Mexican Calendar given by Humboldt“.

Incidentally, the 24-ton Aztec Calendar Stone (to which Anthon was undoubtedly referring) had been rediscovered not long before (in 1790), and looks like this:-

Aztec-Calendar-Stone-enhanced

LDS writers typically downplay any connection with von Humboldt’s writing, by (for example) saying that that Joseph Smith was but a “poorly educated farmboy“, who could not possibly have amassed a “frontier library”. It seems far more likely to me that von Humboldt’s writings (e.g. about Indians writing in hieroglyphics etc) or similar ideas about Mesoamerican history instead made their way to Joseph Smith via the cracked mirror of newspaper summaries. But that’s the kind of argument that can be (and indeed often is) batted back and forth ad nauseam: it really doesn’t interest me.

So it turns out that the central mystery of the Anthon Transcript is not only why a document so intensely central to the claims of Mormonism is not only absent from the archives, but why it is also so clearly misrepresented as being the “Caractors” document. The latter may well also be a document connected to early Mormons (notes from a shorthand Bible? The 1823 Detroit Manuscript?), but it is now hard for me to see how the Caractors page could in any obvious way be the same one described so specifically by Charles Anthon.

Knuijt seems to have his doubts that David Whitmer – one of the Three Witnesses to the Golden Plates – was an altogether reliable source for the Caractors to have come from: and reading Whitmer’s Wikipedia page (ha!), this scepticism seems to be reasonably justified. All I know is that until the actual Anthon Transcript or the actual Detroit Manuscript turns up (someone must surely have taken a copy of the latter, right?), this is probably a debate that cannot be settled anywhere apart from a pub car park. 🙂

* * * * * * *

Note: the two letters from Professor Charles Anthon (to Eber D. Howe, 17th Feb 1834; and to Reverend Coit, 3rd April 1841) can be found transcribed here.

Here’s yet another cipher-tinged literary genre I wasn’t previously aware of – the ex-Mormon novel. As a just-released exemplar,  “Latter-Day Cipher” by ex-Mormon Latayne Scott (author of “The Mormon Mirage”, so her overall position should be no great surprise) appears to do a pretty good job of tackling contentious Mormon issues – along the lines of ‘if certainty is God-given, why do His interpreters on earth keep changing their minds?’

Her novel has a socialite killed with “strange markings carved into her flesh and a note written in a 19th Century code“: and so, of course, it is to the alphabet of the Anthon Transcript that her title appears to refer [Update: it actually refers to the phonetic Deseret Alphabet, developed in the 1850s to teach English to immigrants. Thanks for the correction, Latayne!] Sounds like quite a fun read to me (though perhaps 12 million Mormons may beg to differ).

Actually, this all reminds me of an unexpected parallel I forgot to mention in that previous post… between the golden plates and the Anthon Transcript (that signalled the founding of the Mormon Church) and the Golden Dawn Cipher Manuscripts (that signalled the founding of the Hermetic Order of the Golden Dawn). How similar yet dissimilar!

Incidentally, everyone knows about famous Mormons (such as the Osmond family, Matthew Modine, and Ted Bundy) but what about famous Golden Dawn members? Well… Aleister Crowley aside, the GD had as members [according to Wikipedia, so be ready with your pinch of salt] the poet Yeats, Bram Stoker, Gustav Meyrink, Arnold Bennett, and Edith Nesbit (yes, she of “The Railway Children” fame). Just so you’re prepared for the next pub quiz! 🙂

At the heart of the founding mythology of the Mormon Church sits a small fragmentary document called the Anthon Transcript. The claim linked with it is that it was copied from gold plates revealed by angels to the 18-year-old Mormon prophet Joseph Smith Jr in 1823, and that its “Caractors” were written in the “reformed Egyptian” of the (otherwise unknown) “Nephite” people, who had (allegedly) emigrated to America from Jerusalem two and a half millennia earlier.

Of course, extraordinary claims need at least some kind of evidence – and so the key historical question is whether or not the Transcript provides that. The other pages of the transcript (if they existed at all) have long disappeared, while the eponymous Professor Anthon (who had originally been said to have somehow verified Smith’s translation) later reported “that the marks in the paper appeared to be merely an imitation of various alphabetical characters, and had, in my opinion, no meaning at all connected with them“. After the Transcript had been shown to Charles Anthon, its “translation” was carried out by Joseph Smith who acted as a “seer” to channel it: to do this, Smith used either a giant pair of golden spectacles (that had been found with the golden plates), or one or two stones placed in the bottom of an upturned tall hat, the latter a scrying technique he used before and after 1823 when searching for buried treasure.

Regardless of all that, my particular interest in the Anthon Transcript is as a cipher historian looking at a single contentious document. Back in 2004, I exchanged a number of emails with Richard Stout, who has researched extensively on this subject to build up his own (very specific) claims. However, what follows below relates to my own opinion of what we can learn about the Transcript purely from its alphabet, and is competely independent of Richard’s ideas and interpretations. (And no, I’m neither a Christian, a Mormon, nor even an ex-Mormon.)

anthon-transcript-small

What kind of document is this? Much as people ask of the Voynich Manuscript, is it shorthand, cipher, a lost ancient language, or some kind of deception? Furthermore, is it an original document, a copy of a document, a copy of some letter-shapes from a real document, or a purely made-up thing? The hope here is that we can use its alphabet to help resolve any of these open questions: so let’s see what we find…

Are the letters shorthand? Just about anyone who has grasped the history of shorthand would quickly conclude that it is not a tachygraphic (“fast writing”) system, insofar as it is (as can be seen from the many fussy and overflourished letter-shapes) clearly not optimized for writing speed. Because it appears neither concise, memorizable, speedy, nor unambiguous, it’s a pretty poor match for the whole idea of shorthand.

It should be clear, then, that the Transcript itself was not written in a shorthand system: yet I do hear what Richard Stout says when he suggests links between individual Anthon Transcript letters and letters taken from a whole range of shorthand systems (apparently including many Tironian notae).

Yet I must caution that even an apparently well-defined character can trace out multiple independent paths through time. As a prime example, Stout notes that the filled-in box shape (which appears three times in the Anthon Transcript) appears in William Addy’s (1618-1695) shorthand system, where it denotes the word “altogether“. Addy’s system (first printed in 1684) was based on Jeremiah Rich’s earlier system: curiously, Addy later published a shorthand version of the Bible (1687), though this was perhaps stenographic oneupmanship to trump Rich’s shorthand version of the New Testament (1673-1676). The problem we have is that, as we saw here only a few days ago, Cod. Pal. Germ. 597 also includes a solid square in its first alchemical cipher alphabet… some 250 years before Addy. So, what was the actual source for the Transcript’s filled square shape – 15th century alchemy, or late 17th century stenography?

All the same, Isaac Pitman’s “History of Shorthand” (I own a copy of the 3rd edition) describes Jeremiah Rich’s system as being “encumbered with long lists of arbitrary characters to represent words which could not be written in any moderate space of time by their respective letters” (p.22), an “absurdity” whose “practice seems to have been at its height in the days of Rich” (p.23), with its 300 “arbitraries“. To Pitman’s roving historical eye, Rich’s follower Addy merits only a single paragraph (p.26). But helpfully, Pitman continues with a long list of people who produced related systems: Nathaniel Stringer (1680), William Addy (1695), Dr Doddridge (published in Oxford in 1805!), Farthing (1654), George Delgarno (1656), Everardt (1658), Noah Bridges (1659), William Facy (1672), William Mason (1672), John West (1690), Thomas Gurney (1751) [though Gurney finally dropped the arbitraries!]… and notes that Rich’s system (and/or its many variants and descendants) were still being taught early in the 19th century.

So it would seem that Stout is broadly on target with comparisons with the over-complex systems initially devised by Rich and Addy. I think it would be fair to say that if the Anthon Transcript’s alphabet can at all be said to have a parentage, it lies in the family of overcomplex shorthand systems deriving from Jeremiah Rich, and specifically in the ornate (and occasionally impractical) arbitrary signs added to them.

There must have been more than a hundred subtly different (usually plagiarised) shorthand systems based on Jeremiah Rich’s original, with many of them still in surprisingly active use circa 1823: and so I would predict that finding the closest match to the source of (or the inspiration for) the Anthon Transcript would likely be a perfectly possible (if painstaking) job, given a copy of Pitman’s book as a starting point.

Are the letters Tironian notae? Stout suggest comparisons between various individual Transcript letter-shapes and the sprawling array of Tironian notae accumulated over the centuries. However, my judgment is that you could construct visual correlations between just about any non-pictographic alphabet and Tironian notae: and so I’m very far from convinced that there is any immediate causality implicit in the choice of letter shapes.

Are the letters “reformed hieroglyphics”? Given that I place the Anthon Transcript’s alphabet firmly within the visual & stylistic tradition of arbitrary-loaded shorthands (which themselves all ultimately derive from Jeremiah Rich’s mid-seventeenth century shorthand system, even if the Anthon Transcript’s text is apparently not written in a shorthand system), I have to say that I am at a loss to see any conceivable connection with hieroglyphics (or even with Demotic, for that matter).

Are the letters written in an Old Irish shorthand? Richard Stout points to one shape in particular (you can see an example on line 2 of the Anthon Transcript, two glyphs to the right of the filled square) comprising two left-curving lines joined by a horizontal line: he points to a resemblance with an Irish glyph used on “page 311” of the late fourteenth century Book of Ballymote, and continues by pointing to resemblances between rows of dots elsewhere in the same manuscript and in the Anthon Transcript.

Yet dots were used by medieval monks across Europe to encipher vowels: so I’m far from sold on the idea that rows of dots (which, in any case, were used a quite different way in the Transcript) link this to the Book of Ballymote at all.

Stout’s proposed Irish manuscript connection seems to be an apologium for other Mormon cipher claim, in which the other main source document was allegedly written in some kind of old Irish writing. But I don’t really see that connection here at all: before I get too excited about a single letter-shape, I’d want to have trawled through the relevant shorthand archives first.

Are the letters a cipher alphabet? The Anthon Transcript seems quite ill-judged for this, too: what on earth would any cipher alphabet be doing with a nine-vertical-strokes-plus underline shape (line 2)? This seems to be unnecessarily showy – and in fact, I would suggest that this sort of “prison-cell counting” shape is more the kind of thing you would see in a child’s made-up cipher to denote ’10’ (or possibly ‘X’).

Regardless, the whole document could possibly be written in a cipher: and so I think it would be a good idea to subject a transcription of the Transcript to some statistical tests. It would be more credible were this to be done by someone outside of the Mormon Church (in contrast to previous attempts, according to Wikipedia). It’s true that there are some repeated patterns inside the Transcript, sure: but might these amount to complete words, phrases, or even sentences? Right now, I’m not sure: it looks fairly fragmentary to me.

Are the letter-shapes all fake? I don’t think so: to my eyes, they do give the impression of forming a moderately coherent set of “characters” copied from one or more existing shorthand documents, but with child-like cipher shapes added, very probably to give the whole thing slightly more of an ‘exotic’ feel. More than anything else, I think it is this awkward blend of the nuanced and the naive that makes it seem unconvincing as a real piece of text.

Because the ratio of arbitraries to simple strokes also seems quite high to my eyes, I would also be unsurprised if the author had cherry-picked the interesting-looking letter-shapes from a shorthand source.

In summary, probably the least controversial inference you can draw from the lettershapes is their post-1650 dating: the embellished “H” shape and the probable links with Rich-family shorthand letter-shapes indicate that this is in no way ancient.

In the absence of any other credible information, the most likely story I can reconstruct is that the “caractors” in the Anthon Transcript were copied in no particular order from a shorthand Bible (or possibly a shorthand diary), with various other letter-shapes added to make the overall alphabet look more ‘exotic’, or even “hieroglyphic” (even though, to our modern eyes, these singularly fail to have the desired effect). I would also be fairly unsurprised if the same shorthand Bible itself was subsequently used as a prop to convince skeptics – in short, that this was the Detroit Manuscript itself (but which, like the rest of the Anthon Transcript, subsequently disappeared from sight).

Of course, a single good piece of evidence could well refute all of this… but I haven’t seen it yet.

What do you think?


Post update: a very big thank you! to Richard Stout for suggesting corrections to the first two paragraphs – much appreciated! 🙂