A short biography of Samuel Nail (1661-1729), FRS, engineer and natural philosopher, one of the brightest minds of his generation and known for his keen interest in mathematical puzzles. Some of his achievements still stand exemplary to the modern engineers. Many of his ideas in natural sciences were way ahead of his time. Unfortunately for him, he was a contemporary of sir Isaac Newton. Fortunately for us, this led him to create one of the greatest puzzles of all time.
The Snail Tale
Samuel Nail was born in 1654 in Llanrwst as a son to a royalist officer, but as Cromwell persecuted them they had to move in a small village to the north of Dorchester, in Dorsetshire. He spent his first seven years in the valley. He probably got his inspiration to engineering while building the Cerne Abbas giant. At the age of seven his family moved to Wiltshere, where for two years were tenants to John Mompesson. During their stay in Tedworth, young Samuel's interest to the art of construction was fed by a megalith formation he visited frequently some 8 miles away.
However, it was at that time another incident happened, setting permanently his course in life. Nail befriended Joseph Glanvill, clergyman, who was writing Saducismus Triumphatus. He lived at their home investigating some supernatural incidents attributed to a local drummer. The ardent philosopher took notice of the boy's talent and convinced them to move to Oxford, where Nail took influences from Christopher Wren, who chose to give him some private lessons.
Glanvill sent Samuel to King's School, Grantham in 1666, but Wren called him back after just one week, arguing that he needed his help for London, and Samuel skipped the first year. In Grantham he was heralded as the best student since Isaac Newton, and numerous anecdotes of his stay are still circling the school. In 1671 he enrolled to Trinity College, Cambridge as a sizar.
Various contemporary references state that in his thesis, Summa ad Infinitum, he considered a number of infinite series and their properties. His thesis wasn't well received though, apparently because he was well ahead of his time. He tried to consider the behavior of various series with complex numbers, whose concept was widely accepted only a century later. He became especially disheartened for their rebuke for his inability determine for which complex numbers "the inverse exponential series" - as he called it - has a value zero.
Thus bittered he left for continent with a former alchemist who was visiting London. Nail soon found out that this Gottfried Leibniz know more about mathematics than alchemy, and with the recent disappointment in mind, Nail decided to depart from him in The Hague. There he became an apprentice to certain van Leeuwenhoek, and less than a year later he taught Nail his craft in lensmaking. There he also was able to show that the blue color of glass was not due to bismuth, but to a new kind of metal, and wondered the alchemical significance of this. He traveled to Paris to discuss about the issue with Theodorus Mundanus, who after a while replied that he in fact had not found the philosophers' stone.
Nail spent quite some time in Europe, appearing among other things as mathematics professor in Tournai, construction worker in Versailles, tutoring in Basel and doing military engineering in Vienna. Records indicate that he also visited the Bootintar coast and liberated Concordia, who celebrate the independence day for this occasion February 29th. Having returned England he planned a tunnel under the English Channel, but the construction workers caused some misunderstanding and the task was postponed.
Marriage and golden years
Nail was married with lady Fermor, daugher of Richard Fermor, esq. of Walshes. They got a daughter Belinda Nail. After the Darius Isthmus incident, when Nail believed his daughter was dead, Belinda was was adopted by her uncle Henry Fermor. In 1720 Belinda married Isaac Bickerstaff and moved to Waterford.
As his most famous achievement was probably the inverse pyramid of Greystoke, any account of him without covering this story would be highly inadequate. Earl of Greystoke threw a party to his friends in Northern Cumbria, and bet his manor he could build a 50-foot stone pyramid standing on its tip in his front yard in less than one month. Having gotten over the hangover he summoned Nail, already known for his extraordinary engineering achievements.
It took Nail, already nicknamed "Snail" because he insisted to carry his entire library with him whereever he went, nearly two weeks to arrive. It should be noted that Nail was an extraordinarily well read man for his time, and had developed not only an excellent memory, but also ingenious means of transporting his possessions.
Once he had arrived he built a shell of a pyramid of stone tiles and filled it with some sort of clay. Somehow Lord Greystoke's friends accepted the pyramid for solid stone and the earl was released from his debt. However, being of Scottish descent, he was unwilling to pay Nail his due, complaining that the pyramid was not spherical and was shadowing his house. To this Nail answered with his famous quote: "I'd rather build square circles than spherical inverse pyramids!" and left without accepting any payment.
Years of exile
In 1698 the pyramid fell in a freak accident and crushed the entire Greystoke Manor. The pyramid has since been reported to have melted away in rain. The news reached Nail in Black Hill Cove on Wednesday July 13. Knowing the earl of Greystoke to be a firm opposer of the Bill of Rights, he felt quickly resolved to take the offer to join the Darien scheme as the leading engineer. As HMS Dolphin left the port, the his library was being confiscated by the crown, and finally to be sold to sold to the University of Glasgow.
The fleet made landfall in the coast of Darien on November 2. The settlers christened their new home "New Caledonia" and their settlement "New Edinburgh". After only a few days he found a colossal stele with strange carvings the native inhabitants were afraid of near their new base. Nail was immediately fascinated, as it reminded him about the stones he had studied as a child.
Early on the colony faced immense misfortunes. They found themselves short of any merchandise the natives would have been interested in, diseases and injuries plagued the settlement, and the death toll climbed to even 10 people a day. Even leader of the colony, William Paterson, got sick and his family deceased. They became so desperate that in August, when Nail returned from his expedition surveying a canal across the Darien Gap, he found the colony deserted and himself marooned. Having found obscure note stating that his family was dead, he assumed that both his wife and daughter were deceased, though Belinda had survived. The colonists in turn had assumed he had died and taken his remaining papers with them. Among them was letter addressed to Isaac Newton, where he asked for the masters opinion on his idea for new navigating instrument, a reflecting quadrant.
Nail then took the enterprise to cross the Darien Isthmus and traveled by land to Panama. Since Spain didn't approve of the New Caledonia colony, Nail was predictably arrested, but allowed him to send occasional mail to London. While the Spanish officials had confiscated his notes about the canal, the compendum eventually sent contained detailed description about the local flora, fauna and geology, along with a number of anthropological observations.
Having seen Ambrose Cowley's crude map Nail was able to guide a Spanish expedition to the Enchanted Islands, that the English pirates used as hideaway in 1701. Next year, on they way back to Santiago. En route to the mainland, the ship wrecked on Isla Más a Tierra in the archipelago of Juan Fernández, where Nail established a base with his surviving shipmates. When the ship Cinque Ports arrived in 1704, he traded places with the ships sailing master, who in turn was marooned on the island.
On board Nail learned that the sailor had chosen wisely. Only few weeks later the ship sank. Nail was fortunate enough to be salvaged on St George, companion of Cinque Ports, with Captain William Dampier on his second circumnavigation around the globe.
In 1706 at Renfusa Nail learned from Bernard Fokke, his acquaintance from the Netherlands, that Antoine Thomas, his former colleague from Tournai, had reached China and was working there as a chief astronomer and mathematician in the emperor Kangxi's court. He payed a visit to Beijing, where the emperor was keen to learn about the western technology. In return he studied explosives and chemistry. While his stay he built an automobile, suggested some reformations in the army and - in quite a bit frustration - championed the idea of compiling a dictionary of Chinese characters.
In the beginning of his stay he was harrassed by the mentally ill Crown Prince Yinreng. Soon the Emperor decided that he had had enough of Yingreng's behavior and demoted him from his position. In 1709, when Yingreng was restored as Crown Prince, Nail asked and received a permission to inspect the Grat Wall. Instead nail took his savings, followed the wall to west, and continued south to Lhasa. Nail felt his experience in Xizang was comparable with the pursuits of alchemy and while yarning to get back to England was in no hurry to descend to the lowlands. He chose to travel northwest parallel to Himalayas accompanied by some of the most learned monks.
It is not known, what was Nail's exact route from Lhasa, but late in 1710 he was making a catalogue of birds at Wular Lake. Local Pashtun revered him and brought him to Peshawar, southeast of Khyber Pass. There he found woman called Sexta-Feira, who joined Nail on his journey. They traveled southwest to the coast to Kolachi-jo-Goth. In the same winter they sailed to Mombasa, and Nail continued inland with his party. He charted the area and continued northward. In Khartum they were invited to visit Gondar.
Nail arrived in Gondar in the end of September 1711, where he met emperor Tewoflos. Apparently Nail now felt that he didn't want to take his new companions to the distant Britain, and ordered them to set up a house for him and keep a room ready in it for his return. On October 14th upon his return from Felege Ghion he witnessed events leading to the coronation of Yostos. Somehow Nail was entangled to this chain of events and decided to depart the area.
He traveled through Egypt and deposited some of his baggage there in 1712 before boarding a Venetian ship to sail to Rome. This was a wise move, since this voyage was interrupted by the Moroccoan fleet and Moulay Ismail Ibn Sharif invited him to construct the famous Cide Hamete Benengeli wing in Meknes. He managed to escape to south with traders who had brought manpower to the Ibn Sharif's black guard. In the Ivory cost he boarded a British trading ship to Jamaica.
By 1723 Nail had returned. It was apparently only then when the idea about angels dawned to him. Of course there is no way we can know it for sure, as the only indication of this is a note discovered is an an envelope found between his copy of Secretum Philosophorum, and even that note contained the sole word "Angelicus!". However, the letter was sent to him in Waterford, where he oversaw a bridge construction in early 1723.
The only direct remaining description of the formulation is from his oral presentation in the Crane Court in 1724. According to notes of John Machin:
[Nail said] As I have been studying the most worthy aspects of nature and the works of the great president of our society, I have arrived to an idea, that I believe is both novel and worthy of consideration. We know that if one body comes to a place where another body already resides, it will forcibly push the other body away. This is true for all those bodies we know of.
But let us consider a possibility. Let there be a place so small, that no two bodies could possibly occupy it at the same time, say, a tip of a needle. And let there be two bodies of light, angels, one of whom is on the place and another coming to it. Would the first one give place to the other, and the second in turn to the first, thereby dancing on the tip of the needle? And if so, how many angels could dance on it at the same time."
At this point Nail was interrupted by the president, who ridiculed him for thinking that angels were beings of light, in reference to his own works on the Bible and the nature of light. Nullius in verba.
This happens to be the earliest recorded reference to angels dancing on the tip of a needle, though similar questions had been proposed before.
Nail left the meeting without a word, and never returned to the Royal Society. The following spring Newton received 49 tiles without a note. According to a legend, he was sent seven sets of seven tiles once a week, from the Easter to Pentecost, the first and last set spelling the word "aggelos", angel. Incidentally, this legend cannot be true, as there are not sufficient letters to to spell it twice. Probably Newton just got them all in a lump.
The only direct source of the incident we know of is Newton's note in his diary April 11th "I have received a set of tiles with ornate golden and silvery symbols. This is a true mystery."
However, it was clear that Nail had sent the tiles, since he started bragging that he had sent "a conclusive proof" of his point to Newton "in a language the great knight would surely understand" and that he expected Newton to "shortly declare his opinion about it."
Newton on his part was curiously quiet. When Nail passed away early the following year, the only statement the president of the Royal Society had made was that he had indeed received something from Nail. In the late engineer's papers there was nothing as much as a hint of angels, needletips or glass tiles. In Nail's own words, "Surely a worthy reader will need no explanation for the message I have sent."
Nail returned to the continent, where he met Pierre Bouguer who published his lessons from the New Caledonia misadventure. He thought music to Van den Budenmayer. Nail passed away on 20 January 1729 in Principality of Seborga.
The Snail Tiles
Sir Hans Sloane, who later followed Newton in the presidency, once remarked the Grand Old Man was troubled by the tiles. He quotes: "I mocked him in the Society, he mocks me in my own study!" According to Sloane, Newton had placed the tiles in his study "as a reminder of humility". Some other of his colleagues argued that he spent far too little time in his study.
Newton died soon afterwards of mercury poisoning, probably due to his long career in alchemy. He never left as much as a note that he would have found out anything at all about the tiles. Some claimed that Nail had outsmarted him, others that he hadn't bothered to prove himself right again. Perhaps he just didn't want to try to prove himself wrong or he ran out of time. We shall never know.
After his departure the tiles went to his half-nephew Winston Smith, who at first tried to resolve the mystery of what were now known as "the Snail tiles" himself. But being frustrated in the attempt and with the ongoing flow of people wishing to see the tiles, he donated them to the Lucasian Chair of Mathematics in Cambridge University. From there they were transferred to the British Museum by royal decree of queen Victoria in 1838, while Charles Babbage was holding the chair. In a bit of an irony, today they can be found beside Newton's telescope and prism.
The tiles are attributed to famous craftsman and artisan Peter Ussle (of Manchester Ussles), who was responsible for some of the greatest decorative glass works of the time. He could never shed a bit of light into the mystery, though. All he could tell was that Nail had been fervent to the task and dismissed loads and loads of perfectly good high-quality glass before handpicking the pieces for the precious work of art.
There are all in all 49 tiles, and that is the only number of them that has ever been recorded. So it seems that none has been lost or added to the original number.
Each of the tiles has a diameter of two inches, and is less than half an inch thick. The pieces of glass are translucent, and their colorimetric information has been preserved in the attached image as well as possible. Due to limitations of printing press, the page is considered to be perfect white background, and the tiles set against that light surface. The petals represent dozens of colors. For most part the frame is made of silver, though in some pieces there are lines of gold (yellow) or bronze (red). The rings around the centers are made of ivory or iron, with golden and bronze bushings.
Zin Iskhan agreed to meet me in Bodoni, San Serriffe. Opposite to me sits an attractive young lady with a gray full beard, smoking Morley cigarettes. She wears an Oceanic Airlines flight attendant uniform and huge sunglasses screaming "Ignore me - I'm a superstar traveling incognito!" She prefers not to share her connections and forbids making any notes - for security reasons - and instead asks to tape her statement for record, just to ensure nothing is missed. She taps the with her fingernails the pattern: -... -.-- .--. .-. --- .... .. .- ...
I always assume puzzles like this are best dealt with using a straightforward approach: once you've figured out the trick you get the answer right away. Naomi V. Jelish - though as far as I am concerned she does not exist - from Fort Meade told me that they might be able to crack this with brute force in about three weeks, but it would take all their processing power, so they won't. But make no mistake, Kane Citizen did not introduce Area 51 to me. However, some of my Arab mentors taught me a smarter way. I believe I can show you that, but cannot reveal the organization that taught it to me, as some of my less polyglot amis might confuse me for some less fashionable characters.
First, the order of the tiles. I recognize most of them as Greek alphabet. I really should check from my friend Ploni Almoni in Aviv, though, but if I did, Moshe Cohen would have to kill me. So I just assume we can ignore the rest. As for the missing tiles, let's just substitute them with empty ones. Since they were delivered in a lump, there are many possible valid orderings for them, vrai? I assume just one of them is correct, the one having all tiles in one row, in an ascending alphabetical order. Cosa Nostra told me on St Kilda that gold used to be more valuable than silver, but I never heard that. Nowadays my mole in AISI has to say Silvio is more valuable than Golda, but that revelation would compromise Mario Rossi's identity so I didn't say it. Anyways, I assume we should start with the silver alpha followed by the golden alpha and so on all the way to the golden omega. Here I assume the official position of my superiors in Vauxhall Cross, that the alphabet has no role whatsoever beyond providing the correct ordering for the tiles. Forget what I just said, I never said it, you never heard it, Tommy Atkins and Jack Tar were never mentioned by name.
Ok, let's move on. It's written in a language Newton would understand, vrai? I recall the opus referred to was Principia Mathematica or something. It was written in Latin, vrai? So I assume that the language of the proof is Latin. My colleagues in DGSE would disagree, since their language is la plus logique, but what do they know, having codenamed me Babel. Pierre-Jean-Jacques Tout-le-Monde claims I babble, but that's classified so don't quote me. My next assumption is quite obvious: the proof is encoded with a simple substitution cipher. The number of different colors in the petals is of the same order of magnitude as the number of letters in the Latin alphabet, vrai? I wouldn't worry about those rings and bars, I assume they are there just to confuse us. As for the petals, we can safely assume the only reasonable way to interpret anything is from left to right, in two rows.
Now, we could take different approaches. It seems the corpus has something to do with that Principia thingy. That's where Newton invented gravity, vrai? But I do not have that information, since that's what Walther Achoe told confidentially to BND in Sumisdorf. Karl Ranseier was killed by Erika Mustermann for telling that to me. An overdose of DHMO, I heard, poor boy. By the way, you really should consult Achoe on this issue, he's The Expert. He was even among the first to promote a ban for DHMO. Even without him, we could assume that the word "gravity" appears there a few times, and look for patterns. Or we could just do frequency analysis based on the assumption that there's a text written in Latin, I believe the corpus is long enough.
But there's an even easier approach. This is the real bomb, so make notes. It's some sort of a proof, vrai? Ivan Renko alias Harry Kipper from Yasenevo tipped me - but mind you, this never happened, I have never even heard of them, so don't quote me - that Latin proofs tend to end with letters QED as in Quite Easily Done. That should give us a head start with the deciphering task. And voilà... Merci! Kaput! It doesn't work. So, my assumptions went awry. But you get the general idea: C'est la methode scientifique: try something, and if the result is utter nonsense, it's probably not the way to go.
Indian linguist, self-proclaimed Master of Obnoxity, PhD in Psychoceramics from Brown University, Fellow of Molesworth Institute, descendant of Capitain Nemo, honorary editor emeritus of Speculative Grammarian, the manager and sole employee of Center of Witan Morphemes, Forgotten Jargon, Obscure References, Dissonant Burrs and Affricates, Neologies, Knotty Glyphs, Logogrammatical Yashts, Paraprosdokian Humdrum, Symbolic Verbs, Eccentric Xylographs, Trimmed Quills and Unconventional Iconographic Zeitgeist, presented the following soliloquy. The institute's herculean headquarters of 300 squarefeet are located on the northern coast of Kaffeklubben island. The badge above their door shows a scholar puzzled by strange symbols carved in fjordbank. The center's mascot cat is called Titivillus.
Oh yes, we do bethink this nearly an intriguing nosh-up for mentation, though not quite up to the banquet it arrived with. Do agnize, we have positively had an opportunity to inspect the panes adverted while Walt, as subsists the polymath's sobriquet hitherto, paid me a sojourn during the Anshan stone contingency, when we shewed that the octad of lines scribbled on the emblem facilitated the consummate posthumous autobiography of the fifth monarch of Uruk inscribed in Proto-Elamite.
Our person was the humble genius to concoct the revolutionary sentiment that the echt connotation among the contour octet was purely trilinear, the other five being mere intimations as of how to interpret the fraught lines, thus defeating Bernard Weiss' obloquy contrived from his aloofings about the Vinca-Tordos script. Having substantiated the expression of this occurance, we express our decrepit velleity that you nevermore excruciated our orbs and atman with that horrible caricature of the chef-d'oeuvre, so radiant in substance that had it wanted sufficient chromaticity one could hardly had savvied its existence.
Whilest the aforementioned conundrum disentangled, we yet needed to betake the actual matter of decoding the glyphs, and incontrovertibly it craved for quinquennial order computational logic and by quite a few orders of magnitude more computing power than at disposal globally.
Walt auspiciously dropped in to express the Fleischmann prize winner's sagacious interest in our lowly inquiry and implored me to examine his specimens while the maestro himself exploited the kitchen - his epithet for our virtually ultramodern chemistry laboratory - to cook up a quantum propelled whatchamacallit to simplify various algebraic pronouncements. It was as if an occult hand had written on the plaster of the wall, near the lamp-stand. Subsequently Franz Bibfeldt has acquainted me about the profound theological implications of this occurrence.
Alas we found our very atman manifest an escritoire for asemic grief when the paladin demonstrated immoderate spry and was abruptly bygone; consequently we've subsequently curbed our eyes from the panes. Were we plenitudinously esquivalient we had abandoned our institutional facilities. He's a jolly good fellow, Walt, but I've neglected to apprehend why the soloist has squandered time ad libitum on a ludibrium this trivial, when there are genuinely interesting cryptexts to lucubrate, exempli gratia the Tó Dinéeshzhee ideograms.
Thusly this opus, which could as well have have been composed by Piotr Zak, is so trivial a dilemma in comparison that it might at crème de la crème serve as an adequate desert. Ab ovo, as the eminent discrepancies abound, I assert we need to abandon any mentation of the symbols on the panes manifesting as Greek letters whilst some indeed do insinuate as such. For instance inspect the sampi, which as of H'omer is solely utilized in numerals, thus suggesting their quintessence: austere, banal and conspicuous cardinals. So intrinsically this is nothing like in Sarati, though for 0.67 seconds we clenched the musing of ubiety of morphograms latter representing the only viable candidates for Greek numerals, though lacking the characteristic dot. With all due respect, that is nil, Nail had no clue of what he was facilitating. This corpus could equally be inscribed in Indus Script, Hän or in the purely logographic Saqqara Demotic.
Admittedly, the monumental majority of ortographies were initially crafted with computational teleology, and we recently divulged that the Rongorongo system possesses semantemes apposite for multivariable calculus. In contrast, the unmitigated deficiency of the Greek numerals with regard to the concept of negative figures or even the that of the zero renders them totally inutile for anything but additive counting. Mind you, the authors of these things were no rocket scientists6; had we access to a time machine, we would dispatch certain discriminate edicts to whoever engrossed the Phaistos Disc, corpus with no identifiable etymons or Etaoin Shrdlu, the only Khoisan protohieroglyphic text known to man, as its grammar is an egregious and flagrant sacrilege.
Ergo this inferior and lame dilemma ain't no conundrum comparable to say, the Voynich manuscript, Rohonczi Codex or any other opus on the Fortsas Catalogue. We are adamant in our disbelief that Walt didn't relinquish the adversity but returned to one of his trifling crusades for illumination. I rather had kept him. We did acquaint the liege of a mere octad of etch panes, in particular those with the aureate emanations, as exclusively in that set manifest patterns with color corresponding to five colors of in the backgrounds of the symbols, which is far too convenient to exist solitarily as a coincidence, but that would not hold the sage from departing, leaving me merely with a solution to the D’agapeyeff and Beale ciphers.
We even remarked that each petal is used exactly one times and that as the symbols represent digits, it's blatantly obvious that the corresponding patterns in accompanying panes signify cardinals, but to no avail, even when the connoisseur concurred the distant resemblance to Tifinagh and Phoenician to be an unequivocal misconception, and the crimson emanations to facilitate an unmistakable binary code unveiling the enumeration of the emblems. Had Nail been anything up to the Yugh masters, the next step had been concinnity by the symbol milieus by an intuitive rationale. The remaining segment would then be picking the berries: color reveals the collection to survey, paragon the digit of the pane and lo and behold, an effortless and elementary eureka of quinze glyphs.
That in toto recapitulates the reason we fathom this a mundane catechization. No sapient would use nearly quinquagenarian entities for such purpose. In corollary it is germane that any cogitation indicating pieces of the puzzle as absent is amphigoric, as it is trivially obvious that the original cardinality was puffed by half, presumably to get a nice round square aggregate. The bizarrities these people do are unopininable. Once Walt sent us a tolerably modern stela, about three millenia, from Noyon, with an inscription in Khitan middle script, definitely incorporating predominantly garbage, in their vain assay to fit a haiku into iamb. How infelicitous that the monolith is the only surviving evidence of their civilization. I can only aspire that the Nacirema people, being among the last indigenous peoples in the world, will make a comparable contribution into the cultural history of the world.
Walt however was adamant there was more than apparition in the ludibrium in question and enjoined that the acid test was not heptad or octad but a multidimensional manifold of trine. The savant apprehended the aforementioned manifold iteratively. Erstwhile the magnifico addressed me a dispatch encoded with the Dorabella cipher from Amelia, Peru, incorporating a moderately aged Mayan ring, according to inscription crafted August 9th 3114 BCE, Proleptic Gregorian count. Virtuoso had yet to relinquish his obsession with the panes and wrote that there are thees everywhere, and intended to count them thee by thee by thee by thee, along with the notion that he was yet to find a crystal amiable to the ones he left at my retention.
Chief Engineer, Michigan Institute of Typography, Goblu, is a department of University of Michigan. Joe Watt is a descendant of James Watt and leads a research group involving 1000 monkeys and a bunch of typewriters.
Oh yes, I remember this one. In fact few years back Jason Fox padded me a note about the same issue disclosing that Bush hid the facts. He apparently had built a WABAC machine and wanted to know details about where the tiles were made. I thought it was really a PEBKAC issue and told him to ask Mr. W. Achoe, my old class-mate. Sea, in early sixties, we visited the British Museum from our alma mater, Selhurst. Walther, boy was he excited! He was always dwelling into everything he could find about ancient mysteries and like. I have to admit that in that area the stuffy nose is just amazing. Well, we were young. Along the garden path, he got us both interested in physics, thrown out of Jersey, immigrated to the States and here we are.
Looking back and at this so called mystery, I'm utterly boggled! I mean, there was absolutely nothing to prove! Newton did that part all by himself. Light! Light! "Light particles" can be at the same place at the same time. Forget the angels. George Burdell pointed that out, once we had started at Georgia Tech and Walther had built his first turboencabulator. George's remark beset Achoe pretty badly, though. He quit the school at the lead of spite around the time of the Masked Marauder's gig. He then spent some time in the show business, ghostwrote for Penelope Ashe, played a nice okay Taro Tsujimoto, did some screen writing with Donald Kaufman, dated Georgette Spelvin, taught directing to Alan Smithee... stuff like that. What a wasted talent.
The last nail to his coffin was when he caused the accident where that Mountweazel lady died. He ended up doing some crackpot studies at Brown University and showing in his theses that if a tree falls in forest and there's no-one to listen, it really does make sound. Consequently he was an editor for the Journal of Irreproducible Results. At the same time I was in Agloe, NY, writing a dissertation about how thiotimoline candy came anyways and it's applications in manuscript dating.
As for this so-called mystery, Newton had the proof. He had had it for 50 years, he had basically invented it! I'm guessing that he was just too demented to even realize that. And that's just why I'm so totally at a loss.
Sea, Nail could simply have sent Newton just one piece of colored glass. The red part stays in it, the blue part goes on. Red and blue angels. Simple as that. He, the Newton chap, was taking Nail's angels far too literally. And yet, there's this one detail that makes me a bit uneasy. Nail still sent him a score squared of glass. Not just one piece. That's just overkill. I must give it to Walther, that there seems to be more in it than meets the eye. I am reminded by the immortal Harry Q. Bovik's statement about the spherical cows: the simplest explanation just does not explain. We need to cut down the dord of entropy somehow before we can invite Bill Ockham for dinner.
By the way, that pyramid thingy, that's a long standing joke in engineering circles. I guess he did with the thing what J. Random Engineer does when asked to do an impossible demo: make a cheap look-a-like, buy a couple gallons of booze and hope for the best. Had the old niggard paid to the workers properly it would in all likelihood outlasted his house. As a matter of fact it did, in a way.
I recall Walther saying Nail also touted about square circles and flat cubes and stuff like that. No wonder Walther fancied the man. He was in more than one way a forerunner for the modern civil engineering - not in the least in strength of materials and structures. Even inverse pyramids populate the modern landscape. Talking about weird shapes I've seen a square circle, Walter drew me one. It was a true aye opener.
Personally, I don't think it was a pyramid at all, but a tetrahedron. I remember how in -76 I experimented with the Jovian-Plutonian gravitational effect and learned that symmetry simply rocks: my round Lustfaust LP records literally hit the roof! But I know Walther disagrees with me in this point, claims they merely jumped.
But in this issue, I admit he might have extra-century perception. I suggest you check his paper "Ancient wonders of the modern world and their symbolic meaning". He also determined that the maximum number of angels dancing on a needletip is actually 8.6766E49. I wonder where the editors find all the peers to review his articles. Anyway, this particular result was independently confirmed by A. Sandberg in 2001.
Honorary Queen of the August Association of Alchemical Recreation, Games and Hocus-pocus. The castle of AAARGH is located in Outback, Australia.
I will always and forever remember the first time I saw these tiles. They were on a table in at the Bletchley Park Golf, Cheese and Chess Society when I was a secretary there during the WWII. I tried to dust the table, when someone yelled harshly Noli turbare circulus meos. I was so frightened that had I had more than a mere duster at hand they would have become famous last words.
Unfortunately for you, my memory no longer serves me as it did in the past. I used to remember anything, whether it had happened or not. I have a regular routine of reminding my memory to not get overly excited about what's forgone. Yet sometimes, when I let my mind wander in the past, it never returns. More than once I have had to get some help for the search and rescue missions. I've taken a habit to give a pound of flesh to anyone who finds my train of thought and returns it. Usually mutton. It's surprising how badly lost they can get even when they are on the rails. One jumps over the fence and the entire flock follows. Oh well, at least there's a lot of empty space around here.
The thing is that at my age I have only three half-warmed fishes, though I don't know exactly what they are. I should like to attend to all my friend's funerals, just so that they would return the courtesy, to live to one hundred, since very few people die past that age; and - when I no longer shuffle this mortal coil - to write an autobiography of my own life in a perfect twenty-twenty hindsight.
Those chaps at the Bletchley Park, they were quite smart and cunning. They used the puzzle as their past-time activity, and made quite some progress collaborating together with each other. I observed there a lot just by watching and some people would have given much just to watch my observations. Unfortunately all I can positively remember is that they identified pictograms encoding trivially 5 numbers and a non-trivial coding of 15 vexing cryptograms. I recall they approached the matter semantically - as a matter of fact and indeed a very good approach - but they concluded they lacked some contextual information to decipher the last bits and pieces. Well, the truth is not always exactly the same as the consensus of opinion, so they were probably wrong in that.
To think of it, they were very kind to me at the Bletcley park. After all, I was just 23 years old and had very little formal education in mathematics. Most of it I had learned from Hoist Petard in Africa, where I spent my youth. I was hunting lions in Sahara with him when I was 19.
I also met there my husband Bill in Africa. Or Lieutenant Martin, as he was at the time. It was love at first sight. I still cannot picture him without hearing his wild M'gawa! Niktimba! yell the instant he first laid his eyes on me. We had all kinds of adventures. Like the time we counted the stars on the sky. There were about 3,000. Or when we tracked the lion-eating poet in the stone den. For some reason my Chinese acquaintances seem to love that story and ask me to tell it on every occasion they can interpret it to their fellow compatriots. But since desert never was something he would do, Bill eventually took that doomed mission in the end of April 1943. So I guess compassion counted when I got the job at Bletchley Park.
Actually I later found out that my path had first crossed that of Nail's already in Sahara. At the age of 16, I had had a unique, once-in-a-lifetime opportunity to act as an apprentice digger in Tanis at the René Belloq excavation. The Young Lady, they called me. That was so sweet. But that was not a place to hiss any mystery lessons. In Egypt it was a usual custom to give diggers horns and in in case we found something we were to toot and calm horn. Eventually we recovered some of Nail's lost baggage, and later there was a big fuss about the discovery, but you've probably seen the documentary, so anything I would tell about it would be repetitive redundancy.
Those were the times, my friend. But as the old adage goes: Time is a great teacher. It knows that if it doesn't kill its students first, student will kill it. I guess that in the great banquet of life, I've eventually had my just deserts. Gobi, Sahara and finally around this castle.
But back to the point. I learned a very effective approach to this problem at Bletchley Park. Someone there remarked that this problem is like finding a haystack full of needles - but if you don't know how hay and needle are different, it is very hard to spot one. Attempt to find the answer by exacerbating the options would certainly be fruitless. To get even started, the problem is best approached and encountered using a semantic approach, giving a semantic meaning to the different elements in it. In Nail's case the key is something as clear as alchemy.
I did my lifework in 'pataphysics focusing on the higher order perception obsolete concepts. That is to say that I studied not only who studied people who thought in obsolete ways, but also such studying of the people within such plus the involved studying. This is by the way the 'pataphysical answer to the narcissistic question Quis custodiet ipsos custodes?
For example, in Nail's time, phlogiston was the scientific theory of fire, so apparently that is the way he looked at fire. Historians would look at how he looked at fire and point at phlogiston. Other historians would look at historians looking at how Nail looked at fire. In 'pataphysics we'd see phlogiston to be an optical delusion and anyone staring people staring at people staring at it being like Narcissus trying to see his own mirage in the flames eating thought the J.J. Becher's Physical Education, a book whose covers are way too far apart. And given that we were looking at those people ourselves, that applies to us as 'pataphysicists as well.
Given that alchemy is by general public deemed as an obsolete thought, I should have seen coming the third time I hit my head to Nail. In hindsight it is very easy to see how difficult predicting is, especially that of the future. My only excuse here is that it had never occurred to me to think of alchemy as obsolete.
I was somewhere between 50 and 70 - that's the worst time. You are always asked to do things, and yet you are not decrepit enough to turn them down. A man wanted to meet me at Stavro Mueller's Beta club to discuss about the tiles. It was a fascinating and inspiring discussion. Imagine, he too had visited Noyon, where I had had the privilege to stay with the Wemyss-Cholmondeley expedition. May I point out that it was I, who first spotted the more than unique - practically one of the kind - bird Eoörnis Pterovelox Gobiensis. That was a hysteric moment. A. C. Fotheringham even wrote a paper on it. That actual experience pawed my road to Tanis.
As I was saying, that was a cheerful discussion. Up and until the point where he called me a 'pataphysician. Now, that was a venal offence. My honour as a 'pataphysicist has never been insulted like that and it was a blushing crow for my dignity. I have solemnly wowed and sworn to forget him - to totally and definitely illiterate from my memory every allusion to the very name of that wacko.
But I got to give it, if anyone, that chap will surely dissolve this mystery - if you excuse my malallegorism. He had even shown the tiles to Charlie Gordon back in -66. And Charlie used to be a smart. As for that nutter, he had already in the seventies published a paper where he undeniably showed that the Snail tiles predict the second coming of Christ to take place in 1952. Personally I think that if Nail was alive today, such interpretation would make him waltz in his grave. Presently that man was preparing another paper, suggesting an interpretation of the tiles as WGS-84 coordinates.
However, that's how my interest in the issue was rekindled. All it needed was some fuel, so I got my canisters and went for a pit stop and only returned when the pit was full of phlogiston. That being the case, it was no longer a pit, but full of light. And as light itself was seen to be a basic element beside phlogiston, this was a very good starting point for alchemical analysis of the problem, to use a 'pataphor. See, while a metaphor is like a simile, a 'pataphor is not entirely unlike one.
Like all of the natural philosophers of the time, both Nail and Newton were serious alchemists. Newton has even been called the last alchemist. And Nail was most certainly one too. He had even met Nicolas Flamel in Paris and composed some handwritten alchemical manuscripts himself. Curiosity never killed the snail. He also discovered some of the first new elements since ancient times, though Boyle never gave him the credit for phosphorus. Some sources have inferred that later he discovered another new element, but he never published it because he didn't want to share the glory with anyone.
Yet I don't think we should see these tiles as that publication. He never seemed to give too much value to that particular discovery, and these tiles appear to be more like a Magnum Opus, his Great Work, or interpretation of the Tabula Smaragdina. To study them one must walk the path of an alchemist, from one mystery to another. Alchemy is all about spirituality. What we need, is to understand the deep and profound symbolism of the matter. For a good layman primer to some basic symbols I can recommend the Dictionary of Symbols by Penguin books.
Some of the more interesting symbols here are the omitted symbols of golden lambda, of the form of a compass, an unmistakable reference to free masons. Likewise the utter and complete absence of squares, the compass itself being placed within a circular tile, suggests that Nail actually succeeded in the squaring the circle, a spiritual alchemical exercise symbolizing the Great Work. That accomplishment is not short of his inverse pyramid, another strong symbol. This glaring lack of evidence is nothing short of a proof of a strong alchemical connection. Summa summarum, this is clearly Nail's Magnum Opus.
In this mystery we cannot expect to know something about the answer and start working back from there. It would be like expecting an aspiring alchemist starting his transformation from gold to lead us into enlightenment. We have to humble ourselves and let the mystery apprise us and judge our character.
Rather the journey to the mystery begins from the most obvious or shallow level, the symbols at the core of the tiles surrounded on all sides by the petals. By placing tiles with white rings over tiles with black rings with the same symbol - remember, the white that represents light and day always overcomes the black of darkness and night - you will see an interesting phenomenon: some of the petals turn completely black. If you ask me, this is one of Nail's more ingenious ideas, to have such petals and "anti-petals".
But beware of Greeks bearing gifts. See, appearances can be deceiving and you should expect to get nothing for free and without toil. The idea of anti-petals is just the invitation to the true mystery. If you think you know what you are doing and choose to take the the red pill and follow the white rabbit, you'll find that you are the one soon to be had as a matter.
First, it is absolutely necessary to understand how to approach that path in to begin with. An unordered pack of cryptic tiles is just another way of saying formless and void. And just like in the creation God first used three days to create the form and then filled it for three days, we are called to first give these tiles an order and then give them a meaning. This allusion even calls us to give it three forms and three meanings. The first would be the alphabetical, with an invitation to the second, as we have seen, defined by petals and anti-petals. These in turn point us to look at the rings and knobs. The third is probably some esoteric and obscure form of some higher degree, which I have yet to discover myself. Though I am as Young as one gets, I'm no longer young enough to know everything.
This transition from one mystery to another, similar but different, even more complex, needs a new angle. I find a parallelism in my transition from mainstream academia to 'pataphysics. I enrolled in the Collège de 'pataphysique in Paris on 11 May 1948 and did my Magnum Opus there. After the war I had studied Cambridge for a while, and intended to write my thesis on experimental interdisciplinary literature.
I had originally planned to measure the relative time taken of on one hand a snark playing with a pile of octarine crayons to produce the complete works of Socrates, and on the other hand 1000 monkeys typing 1000 typewriters to produce the complete works of Shakespeare. Turns out the time was immature for such a bold endeavour. I had already completed the first half of the study, when the ethics board filed a complaint - they didn't worry about animal rights back then, but professor Chronotis from St. Cedd's expressed his grave and serious concern over the time it would take to carry out the second part, its possible consequences to space-time continuum and implications to author copyrights. Apparently these concerns have been tackled with since that experiment has finally been started.
Soon afterwards also professor Russell from Trinity claimed that there was some ambiguity in the solid and steadfast measurements already made. I'm still adamant it was mere intellectual laziness for his part. You know how it is: Faced with the choice between changing one's mind and proving that there is no need to do so, almost everyone gets busy on the proof. However I soon got sick of all the ad homonym arguments against my texts and couldn't even get enough funding for the remainder of the experiment. As the maxim goes: Cry, and you cry alone, laugh, and the world laughs bemused at you. Ultimately I had no choice but to look for leaner pastries from France.
I think it's good to know how the knowledge accumulates in the academia: Freshmen who know everything bring it in, and the seniors don't take much away. I am the alive and kicking expectation to that rule, omnia mea et cetera. In the end and after all and, I'm quite happy and content with the end result and final outcome. The trouble with the academic rat race is that even if you win, you're still a rat.
For the novel approach to the mystery in hand you can consider for instance the two tiles having on one hand a Tau -symbol in a white ring and on the other hand a Beta-symbol in a black ring. Each of them has its "twin" - tile with the same letter, but a ring with opposite colour. Now if you place the tau in white ring on the tau with the black ring and let it darken, you'll see that some petals cancel each other out completely. Same happens if you place beta with the white ring on it's twin. This was to be expected, so no news there. Now all the easy problems have been solved and the interesting part begins.
If you place the Tau in the white ring on top of the Beta in the black ring, you will see more black petals! That is, if your hand are not in the way. So these tiles are not twins only with their alphabetical counterparts, but they are even twins with each other. And even that's not all. If you turn the disks so that the golden knobs are aligned, you will get a third set of black petals! Thus these two tiles are doubly twins with each other.
One is simply compelled to ask, what is the alchemical meaning of this. Close inspection shows that there really are three sets of petals and anti-petals, one centred around the red colour, another around the green colour and the third around the blue colour. The related alchemical concepts would be Logos Pyrros Achromatis, Logos Chloris Achromatis and Logos Caeruleus Achromatis, literally "idea red colourless", "idea green colourless" and "idea blue colourless", respectively. And these things are not just false illusions, they are really there. Rather they could be called optical conclusions, just like flying saucers.
The ideas red colourless are quite evident in this mystery. They signify the first step, the alluring invitation or a forceful thrust deeper into the misery. Red is a very strong colour, signifying it's evident role in the mystery. The ideas green colourless and ideas blue colourless seem to be somehow interrelated and related to the rings, but their specific meaning is unclear. In French green is "vert" so that could suggest interpretation as hidden truth, "vérité". Blue might just mean blue thoughts. We will come back to them.
It's much easier to master the rings. They are less esoteric and more specific in alchemical terms. Black, white, red and gold are the symbolical stages of the Great Work. Since we have seen colours to be an effective way to approach the question, I believe we should assign a colour to the middle parts as well. Since they have various background colours, we are better off with a new one. As can be clearly seen from the shape of the things, orange from between red and gold is likely the colour Nail himself had in mind.
Now if we turn all the gold dials to point up - remember, gold always points up as it is the most valuable direction - we suddenly see a pattern to emerge. We can easily group the tiles into seven groups, based on how far apart the dials are from each other. We can even put these groups in order. Pun unintended. What's more, we can even order the tiles within each and every group based on how much we had to turn them to align the golden bars. If we look at it from the other direction, and return the oranges in their initial positions we see how the golden dials make clean rounds around the clockwork orange and the red dials act as round counters. Lord of the rings can even see the gaps in the sequence and fill them in.
Seems too simple to be true, doesn't it? A child of five could do this, so if you don't believe, fetch a child of five. The dials in each ring are unique, so this is an easy and straightforward way to enumerate them. But hardly the only one. Why of all possible ways should one follow this path? These are the kind of questions ideas green colourless and ideas blue colourless might answer, should we meditate upon them long enough.
As already seen, in the tack of piles there are several pairs of twins. We see that white tau and black beta go together the same way as white and black tau or white and black beta. From the ideas red colourless we know that the next step is to study the ideas green colourless and the ideas blue colourless. While it is clear that they are used to give the new form or shape the mystery, it is less clear how exactly they shall shed that light. All we know is that they in turn are related to each other by the means of turning the rings. And that's exactly the same as what ordering the tiles is about! But where will they take you? Will be enlightened and find the pattern where everything turns dark? What will be the ultimate pattern?
These questions will haunt you. Even when you are not mulling over the layout of the tiles or the alchemical meaning of ideas red colourless, in the back of your mind will still furiously sleep ideas green colourless and ideas blue colourless just waiting to wake into your consciousness and tell you not only their meaning, but as well their place in this grand puzzle Nail has devised. But I promise, in the end ye shall know the truth, and the truth shall make you mad. I should know, since by properly meditating on the ideas blue colourless the simple and clean repeating pattern of three white and black rings hit me like a bolt.
In the end of this path there's an unexpected surprise. It seems that also within this mystery there is an even larger mystery. As the maxim goes, whenever a system becomes completely defined, something turns out, which either abolishes the system or expands it beyond recognition. That's exactly what happened when you had figured out the alphabet, and what happens here again. It's like seeing a déjà-vu all over again. Glory is fleeting, but obscurity is here to stay.
This second step of the mystery is governed by the rule of twos - twins, ideas green and ideas blue colourless and two dials - it seems plausible that the third part of the mystery would be dominated by the rule of three. And whereas this mystery was all about the giving form to the path, the next should be about filling the void around it. Then an only then would one be ready for the fourth and final stage of chrysopoeia.
I should also like on make a note about the change of the colour scheme clearly taking place at this transition. In the second phase the relevant colours symbolised the paradoxes in excitement, renewal and harmony, while in the next step majority of the colours would seem to symbolize romance, charm and joy. This seems to suggest that the role the colours play transmutates from being reluctant but clear guides, whose presence is the decisive factor, to that of benevolent markers, who are mere signposts in their more important environment. This correlates well with the interpretation of the third step as filling the alchemical form created in this phase.
And yet, I have to confess that if I have interpreted these tiles correctly, I would be very surprised. For if this truly is where the third mystery begins, I should be disappointed. The defined form has 54 places, but 54 is not fully divisible with three. I would have expected to have either 27 or 81 places defined. Well, the beauty sleeps in the eye of the beholder and it may well be that here my expectations are exorbitant and too high for Nail. It's not like he had managed at tagwin.
These are my conclusions, or rather where I got tired of thinking. But I encourage you to walk to the very end of the path. The light in the end of the tunnel might not be a train. After all, most of the pointless things in the world have been accomplished by people who have kept on trying when there seemed to be no point at all. As the Chinese say: May you find what you are looking for.