Roger Bacon's Voynich Manuscript - Mary D'Imperio and the NSA

Someone just shared a link to this video about Roger Bacon in a comment.

Reminded me that I had looked into him awhile back - this manuscript linked with a Philadelphia-area philologist, Mary D’Imperio, who had been working for the NSA on computer analysis of the Voynich Manuscript.

Germantown, PA = Kelpius and his monks BTW

@stephers this reminds me of the meta-data in that TV show - trying to identify patterns out of something that doesn’t make sense


This volume contains four articles written by personnel of the National Security Agency (NSA) about the Voynich manuscript from 1965 to 1978.

The first essay, by Brigadier John Tiltman, is entitled “The Voynich Manuscript: The Most Mysterious Manuscript in the World” and was presented to the Baltimore Bibliophiles in 1967. It provides a basic summary of facts about the manuscript and its provenance and adds a survey of proposed solutions, most of which it dispenses with quite quickly. I found it interesting to discover that Tiltman was first introduced to the Voynich ms. by William Friedman, founder of the NSA, in 1947 (!) I was also intrigued that Tiltman’s scholarly research into the history of medieval herbalism included consultations with leading English academics, no doubt during visits on “Five Eyes” business.

The second essay, originally classifed Top Secret Umbra, is “An Application of PTAH to the Voynich Manuscript” by Mary D’Imperio - the title itself was unclassified. A few pages in, I came to a full stop when I encountered this:

“PTAH (named for the Egyptian god of wisdom), is a general statistical method developed at IDA (Institute for Defense Analyses), Princeton University. PTAH got its name when a programmer. Mr.Gerry Mitchell, was listening to the opera “Aida” while working on his program. He was struck by the passage “immenso Ptah noi invociam,” and named his program after the Egyptian god. The name was ultimately extended from this program, implementing a particular application of the method, to the method and its mathematical theory as well…”

The technical meaning of PTAH remains classified, although Google helped me find a journal article that suggests PTAH must be some sort of Hidden Markov Model. (Math. Comput. Appl. 2019, 24, 14; doi:10.3390/mca24010014)

D’Imperio used PTAH to analyze the Voynich manuscript and similar works and concluded that “I find the above comparisions quite convincing support for a view that the Voynich text, regarded as a string of single letters, does not ‘act like’ natural language. Instead, it exhibits a clear positional regularity or characters within words. I believe that these findings strengthen the theory of Friedman and Tiltman that an artificial language may underlie the Yoynich text.”

Government interest dating back to 1947 … pharmacology unknown to modern man … artificial languages … the movie “ARRIVAL” based on Ted Chiang’s “Story of Your Life” … hmmm …

The third essay, also by D’Imperio, is “An Application of Cluster Analysis and Multidimensional Scaling to the Question of ‘Hands’ and ‘Languages’ in the Voynich Manuscript.” She uses cluster analytic techniques to examine findings by Captain Prescott Currier, who suggested that the manuscript’s pages can be clustered into groups of multiple authors and styles. D’Imperio’s discussion includes warnings that are still sound today: " The interpretation of cluster analysis results is unavoidably circular; we propose a certain structure in the group of objects under study, we perform the computation, and we are happy if we see what we expected, or at least something that makes sense in terms of our original hypothesis, however revised."

The fourth and final essay, by James Child, takes an important step forward by proposing that “the Voynich Manuscript does not contain an artificial language nor the enciphered text of an underlying text in an unknown language. but is a text in a hitherto unknown medieval North Germanic dialect.”

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I have multiple resources to add to this intriguing topic – a topic that is particularly interesting to me, given my personal interest in ciphers/cryptoanalysis (including my recent interrogation of the show, Severance), as well as my exploration of Voronoi patterns (which curiously connects via Markov models/chains) . . .

Also, my mom was born and raised in Germantown, Pa. It holds a significant place in my memory.

Most synchronously, though, this material overlaps with much of what I have been scrutinizing of late – mainly with regard to cryptography/cryptology and the IDA – with one IDA mathematician/cryptologist in particular – Lee Paul Neuwirth (father of triple threat Bebe Neuwirth) . . .

I will circle back shortly with more links and commentary . . .

Universities overseeing IDA expanded from the five initial members in 1956 — Caltech, Case Western Reserve, MIT, Stanford and Tulane — to twelve by 1964 with the addition of California, Chicago, Columbia, Illinois, Michigan, Pennsylvania, and Princeton.[6] University oversight of IDA ended in 1968 in the aftermath of Vietnam War-related demonstrations at Princeton, Columbia, and other member universities.[7]

Subsequent divisions were established under what became IDA’s largest research center, the Studies and Analyses Center (now the Systems and Analyses Center), to provide cost analyses, computer software and engineering, strategy and force assessments, and operational test and evaluation. IDA created the Simulation Center in the early 1990s to focus on advanced distributed simulation, and most recently, established the Joint Advanced Warfighting Program to develop new operational concepts.[8]

IDA’s support of the National Security Agency began at its request in 1959, when it established the Center for Communications Research in Princeton, New Jersey. Additional requests from NSA in 1984 and 1989 led respectively to what is now called the Center for Computing Sciences in Bowie, Maryland and to a second Center for Communications Research in La Jolla, California. These groups, which conduct research in cryptology and information operations, make up IDA’s Communications and Computing FFRDC.

In 2003, IDA assumed responsibility for the Science and Technology Policy Institute, a separate FFRDC providing technical and analytic support to the Office of Science and Technology Policy and other executive branch organizations.[9]

Throughout its history, IDA also has assisted other federal agencies. Recent work includes research performed in support of the Department of Homeland Security, the National Aeronautics and Space Administration, the Director of National Intelligence, and others.

I am currently in the process of reading Lee Neuwirth’s book (which hauntingly seems to echo the culture and reveals in Apple TV’s Severance):


Wow - the “knots” concept makes me think about maritime stuff, too - speed and rope.
Gerry Lenfest (cable mogul with ties to Navy and Catholic church later education philanthropy) and that WW Smith Foundation and Vanguard all have ocean - shipwright elements.


For some reason this reminded me of the Gordian Knot and Alexander the Great, and the trefoil knot

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Once we can see it, we can cut it and step out of their tempest in a teapot.

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Um, could this be related?


Returning to IDA’s Lee Neuwirth . . .

Note the use of his term “knotty” as a sneaky pun:

On p. 10, the mention of “champagne toasts” to celebrate when an employee solved a cryptology problem/cipher reminds me a whole lot of the “waffle parties” in Severance . . .

@AMcD On p. 18, note the reference to Gerry Mitchell (whom you discussed above) . . .

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Proceeding of the IEEE
International Conference on Robotics and Biomimetics (ROBIO) Shenzhen, China, December 2013

A Hidden Markov Model approach for Voronoi Localization
Jie Song, Ming Liu*
Autonomous Systems Lab, ETH Zurich, Switzerland
Hong Kong University of Science and Technology

Abstract—Localization is one of the fundamental problems for mobile robots. Hence, there are several related works carried out for both metric and topological localization. In this paper, we present a lightweight technique for on-line robot topological localization in a known indoor environment. This approach is based on the Generalized Voronoi Diagram (GVD). The core task is to build local GVD to match against the global GVD using adaptive descriptors. We propose and evaluate a concise descriptor based on geometric constraints around meeting points on GVD, while adopting Hidden Markov Model (HMM) for inference. Tests on real maps extracted from typical structured environment using range sensor are presented. The results show that the robot can be efficiently localized with minor computational cost based on sparse measurements.


So…to me this feels a little like the plot line of “The Magus” you see things on the surface, but you do not see what is going on below (hidden information and motivations).

" The hidden process is a Markov chain going from one state to another but cannot be observed directly. The other process is observable and depends on the hidden states. The goal of HMM is to capture the hidden information from the observables."

Yes - stochastic - the Rockefeller Foundation’s backing of stochastic mathematics feels very important.

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Circling back to “Voynichology” . . .

Here we see mathematical physicist John Baez (father of singer/activist Joan Baez) chiming in . . .

The Voynich Manuscript

John Baez

January 30, 2005

The Voynich manuscript is the most mysterious of all texts. It is seven by ten inches in size, and about 200 pages long. It is made of soft, light-brown vellum. It is written in a flowing cursive script in alphabet that has never been seen elsewhere. Nobody knows what it means. During World War II some of the top military code-breakers in America tried to decipher it, but failed. A professor at the University of Pennsylvania seems to have gone insane trying to figure it out. Though the manuscript was found in Italy, statistical analyses show the text is completely different in character from any European language. Here’s a sample page:

It contains pictures of various things, including plants, stars…

… and most strangely of all, nude maidens bathing in what looks like some very elaborate plumbing:

An interesting puzzle, no? Let me tell you a bit more about it.

Its recent history

It seems that in 1912, the book collector Wilfrid M. Voynich found this manuscript in a chest in the Jesuit College at the Villa Mondragone, in Frascati. He bought it from the Jesuits, and gave photographic copies to a number of experts to have it deciphered. None of them succeeded. In 1961, he sold it to a rare book expert in New York named H. P. Kraus for the price of $24,500. Kraus later tried to sell it for $160,000, but could not find a buyer. In 1969, he donated it to Yale University. It is now in the Beinecke Rare Book Library at Yale, with catalogue number MS 408. They say it’s “very likely” that the book was given to Emperor Rudolph II of the Holy Roman Emperor by British astrologer John Dee… and indeed, that’s one theory, but it’s far from certain. The story of the Voynich is long and complicated.

Its earlier history

When Voynich found the manuscript, there was a letter in it!

The letter was written by Johannes Marcus Marci of Cronland, and addressed to Athanasius Kircher. It is dated 1666. It says that the manuscript was bought by Emperor Rudolph II for the princely sum of 600 ducats. In flattering language, Marci asks Kircher to attempt to decipher the manuscript. He mentions Roger Bacon as a possible author, although there is no clear evidence for this.

If you don’t know these figures, you probably don’t realize how interesting this is. Who are these guys, anyway?

Emperor Rudolph II

Rudolph II (1552-1612) was an emperor of the Holy Roman Empire - which by that time was neither holy, Roman, nor even much of an empire. He moved the imperial court from Vienna to a castle in Prague, in what was then Bohemia. He buried himself in esoteric studies: alchemy, astrology… magico-scientific disciplines of all sorts. Prague became a center for everyone interested in such matters: the infamous British magician John Dee and his henchman Edward Kelley, the monk Giordano Bruno (later burned at the stake for heresy), and even a pair of astrologers by the names of Tycho Brahe and Johannes Kepler. Rudolph II kept a room of curiosities, the Kunstkammer, full of alchemical manuscripts, rhinoceros horns, exotic minerals, scientific instruments, and the like.

In short: the perfect person to buy something like the Voynich Manuscript!

Athanasius Kircher

Athanasius Kircher (~1601 - 1680) was one of the most learned men of his day. He developed an instrument for measuring the magnetic force of the earth, a device for measuring wind speeds, and he designed and built sundials. He studied earthquakes and volcanos. He was an expert on oriental languages, and translated the Emerald Tablet of Hermes, an Arabic alchemical work, into Latin. He also wrote some very popular books on Egyptian antiquities and hieroglyphs. He was the first to correctly conjecture that Coptic was derived from ancient Egyptian. He even received a large gift from the Pope for translating the hieroglyphs on an Egyptian obelisk! When the Rosetta stone was found, quite a bit later, this translation was found to be completely inaccurate. However, during his lifetime he had a reputation for being able to read any text.

In short: the perfect person to decode the Voynich Manuscript!

Roger Bacon

Roger Bacon (1214-1294) was a Franciscan friar and an early advocate of the experimental method. He worked on optics, and at the request of Pope Clement IV he wrote a series of books which amounted to an encyclopedia of science. He also worked on alchemy. He kept much of his work secret from his fellow Franciscans, but nonetheless, in 1278 they imprisoned him on the charge of “suspected novelties” in his teaching. In his Letter on the Secret Works of Art and the Nullity of Magic, he wrote “The man is insane who writes a secret in any other way than one which will conceal it from the vulgar and make it intelligible only with difficulty even to scientific men and earnest students… Certain persons have achieved concealment by means of letters not then used by their own race or others but arbitrarily invented by themselves.”

In short: the perfect person to have written the Voynich Manuscript!

But the story is not so simple…

(To be continued.)


The best books to read on the Voynich manuscript are these:

  • Mary E. D’Imperio, The Voynich Manuscript: An Elegant Enigma, National Security Agency, Fort George G. Meade, Maryland, 1978. Reprinted by Aegean Park Press, Laguna Hills, California, c. 1980.
  • Robert S. Brumbaugh, The World’s Most Mysterious Manuscript, Weidenfeld and Nicholson, London, 1977. Also Southern Illinois University Press, Carbondale, 1978. (This seems to be out of print.)
  • Gary Kennedy and Rob Churchill, The Voynich Manuscript, Orion Press, 2004.

There are also some excellent websites. However, there’s a lot of turnover in these Voynich sites, because nobody can afford to pursue Voynichology as a full-time occupation. If you see a good new site, or find that some of the ones listed here have moved or dissappeared, let me know. You can also see lots of images on Google.

Within that awful volume lies the mystery of mysteries! - Sir Walter Scott

© 2005 John Baez


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As I have been reading through this article, I started thinking about knots and portals because of the connection with knots, the navy and water. With water often associated with portals and gateways to the other world, I wondered if knots were tied into that as well (pun intended).

I found that this interesting lecture by William Thurston who was mathematician who studied at UC Berkley @AMcD and is credited with pioneering Low Dimensional Topology

I found it interesting how he references C.S. Lewis’s Narnia and traveling to other dimensions in this video

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Fascinating. This actually makes sense to me. Consider the various and vast implications of this . . .

William Thurston’s son . . . Followed in his low-dimensional topology (and knotted) foot steps . . .

About Dylan Thurston

Main Research Group: Topology

Affiliated Groups: Logic / Complex Analysis / Geometry

Research Interests: geometric and quantum low-dimensional topology and related fields; including Heegaard Fleor homology and its extension to 3-manifolds with boundary; rigidity of graphs in space; cluster algebras; geometric intersection numbers for curves on surfaces; finite-type invariants

Math Genealogy

Dylan Paul Thurston

March, 2016

Interests Experience

Department of Mathematics
University of Indiana, Bloomington

Low-dimensional topology and related fields.


Fellowships and awards

Professor, Indiana University, Bloomington, Spring 2013–present. Chancellor’s Professor, University of California at Berkeley, Fall 2012. Visiting Professor, Tokyo Institute of Technology, Spring 2012. Visiting Professor, Cornell University, Fall 2011.

Assistant Professor, Barnard College, Columbia University, 2005–2012.
Benjamin Peirce Assistant Professor, Harvard University, 2002–2005.
NSF Postdoctoral Research Fellow, Harvard University, 2000–2002.
JSPS Postdoctoral Fellowship (Short Term), Research Institute for Mathematical Sciences,

Kyoto University, Japan, Sept–Nov 2001.

Ph.D., University of California at Berkeley, 2000. Dissertation: “Wheeling: A diagrammatic analogue of the Duflo isomorphism” under Vaughan Jones. arXiv:math.QA/0006083.

A.B. cum laude, Harvard University, 1995. Thesis: “Integral expressions for the Vassiliev knot invariants”, under Raoul Bott. arXiv:math.QA/9901110.

NSF grant DMS-1507244, “Rubber Bands to Rational Maps”, 2015–present.
NSF grant DMS-1358638, “Homology theories for tangles and bordered 3-manifolds”, 2010–

Presidential Research Award, Barnard College, 2009. Project: “Homology theories of knots and links”.
Most Cited Paper Award for Computer Aided Geometric Design, 2009, for “Discrete one-forms on meshes and applications to 3D mesh parametrization” with Steven Gortler and Craig Gotsman.
Sloan Research Fellow, 2006–2010.
NSF Postdoctoral Research Fellow, Harvard University, 2000–2002.

Bordered Heegaard Floer homology: Invariance and pairing. With R. Lipshitz and P. Ozs- váth. Memoirs of the American Mathematical Society, accepted for publication, 2016. arXiv:0810.0687.

Bimodules in bordered Heegaard Floer homology. With R. Lipshitz and P. Ozsváth. Geometry and Topology, 19:525–724, 2015. arXiv:1003.0598.

A tour of bordered Floer theory. With R. Lipshitz and P. Ozsváth. Proceedings of the National Academy of Sciences, 108(20):8085–8092, May 17, 2011. arXiv:1107.5621.

Slicing planar grid diagrams: a gentle introduction to bordered Heegaard Floer homology. With R. Lipshitz and P. Ozsváth. Proceedings of Gökova Geometry-Topology Conference 2008, Gökova, 2009. arXiv:0810.0695.

Heegaard Floer homology as morphism spaces. With R. Lipshitz and P. Ozsváth. Quantum Topology, 2(4):381–449, 2011. arXiv:1005.1248.

A faithful linear-categorical action of the mapping class group of a surface with boundary. With R. Lipshitz and P. Ozsváth. Journal of the European Mathematical Society, 15(4):1279–1307, 2013. arXiv:1012.1032.


Bordered Floer homology

Heegaard Floer homology: Other papers

Geometric topology

Conformal geometry and rational maps

Finite type and quantum invariants

Computing HF by factoring mapping classes. With R. Lipshitz and P. Ozsváth. Geometry and Topology, 18:2547–2681, 2014. arXiv:1005.2550.

Bordered Floer homology and the spectral sequence of a branched double cover I. With R. Lipshitz and P. Ozsváth. Journal of Topology, 7(4):1155–1199, 2014. arXiv:1011. 0499.

Notes on bordered Floer homology. With R. Lipshitz and P. Ozsváth. In Contact and Symplectic Topology, 275–355, Bolyai Society Mathematical Studies 26, 2014. arXiv: 1211.6791.

Relative Q-gradings from bordered Floer theory. With R. Lipshitz and P. Ozsváth. Preprint, 2012. arXiv:1211.6990.

Bordered Floer homology and the spectral sequence of a branched double cover II: The spectral sequences agree. With R. Lipshitz and P. Ozsváth. Journal of Topology, accepted for publication, 2015. arXiv:1404.2894.

On combinatorial link Floer homology. With C. Manolescu, P. Ozsváth, and Z. Szabó. Geometry and Topology, 11:2339–2412, 2007. arXiv:math.GT/0610559.

Legendrian knots, transverse knots and combinatorial Floer homology. With P. Ozsváth and Z. Szabó. Geometry and Topology, 12:941–980, 2008. arXiv:math.GT/0611841.

Transverse knots distinguished by knot Floer homology. With L. Ng and P. Ozsváth. Journal of Symplectic Geometry, 6:461–490, 2008. arXiv:math.GT/0703446.

Grid diagrams and Heegaard Floer invariants. With C. Manolescu and P. Ozsváth. Preprint, 2009. arXiv:0910.0078.

Naturality and mapping class groups in Heegaard Floer homology. With A. Juhász. Preprint, 2012. arXiv:1210.4996.

The algebra of knotted trivalent graphs and Turaev’s shadow world. In Invariants of knots and 3-manifolds (Kyoto 2001), 337–362, Geometry and Topology Monographs 4, 2002– 2004. arXiv:math.GT/0311458.

Appendix to “The volume of hyperbolic alternating link complements” by M. Lackenby. With I. Agol. Proc. London Math. Soc., 3d ser., 88(1):204–224, 2004. arXiv:math.GT/ 0012185.

A random tunnel number one 3-manifold does not fiber over the circle. With N. Dunfield. Geometry and Topology, 10:2431–2499, 2006. arXiv:math.GT/0510129.

3-manifolds efficiently bound 4-manifolds. With F. Costantino. Journal of Topology, 1(3): 703–745, 2008. arXiv:math.GT/0506577.

Grid diagrams, braids, and contact geometry. With L. Ng. Proceedings of Gökova Geometry- Topology Conference 2008, Gökova, 2009. arXiv:0812.3665.

A shadow calculus for 3-manifolds. With F. Costantino. Draft available online. On geometric intersection of curves in surface. Draft available online.

From rubber bands to rational maps: A research report. Research in the Mathematical Sciences, accepted for publication, 2016. arXiv:1502.02561.

Conformal surface embeddings and extremal length. With J. Kahn and K. Pilgrim. Preprint, 2015. arXiv:1507.05294.

Wheels, wheeling, and the Kontsevich integral of the unknot. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Israel J. Math. 119:217–237, 2000. arXiv:q-alg/9703025.

The Århus invariant of rational homology 3-spheres I: A highly non-trivial flat connection on S3. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 8(3):315–339, 2002. arXiv:q-alg/9706004.

Cluster algebras, representation theory

Discrete geometry

The Århus invariant of rational homology 3-spheres II: Invariance and universality. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 8(3):341–371, 2002. arXiv:math.QA/9801049.

The Århus invariant of rational homology 3-spheres III: The relation with the Le-Murakami- Ohtsuki invariant. With D. Bar-Natan, S. Garoufalidis, and L. Rozansky. Selecta Math., n.s., 10(3):305–324, 2004. arXiv:math.QA/9808013.

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants. With D. Bar-Natan and T. Le. Geometry and Topology 7(1):1–31, 2003. Published version of my Ph.D. dissertation. arXiv:math.QA/0204311.

On the existence of finite type link homotopy invariants. With B. Mellor. J. Knot Theory Ramifications 10(7):1025–1039, 2001. arXiv:math.GT/0010206.

Hyperbolic volume and the Jones polynomial. Lecture notes from a series at summer school “Invariants des nœuds et de variétés de dimension 3”, Grenoble, France, 1999. Notes available online.

Perturbative 3-manifold invariants by cut-and-paste topology. With G. Kuperberg. Preprint, 1999. arXiv:math.GT/9912167.

The F4 and E6 families have only a finite number of points. Draft available online.

From dominoes to hexagons. Preprint, 2004. arXiv:math.CO/0405482.
Cluster algebras and triangulated surfaces. I. Cluster complexes. With S. Fomin and M.

Shapiro. Acta Mathematica, 201:83–146, 2008. arXiv:math.RA/0608367.
Cluster algebras and triangulated surfaces. Part II: Lambda lengths. With S. Fomin. Memoirs of the American Mathematical Society, accepted for publication, 2016. arXiv:1210.

Positive basis for surface skein algebras. Proceedings of the National Academy of Sciences,

111(27):9725–9732, 2014. arXiv:1310.1959.
The complex volume of SL(n, C) representations of 3-manifolds. With S. Garoufalidis and

C. Zickert. Duke Mathematical Journal, 164(11):2099–2160, 2015. arXiv:1111.2828.

Discrete one-forms on meshes and applications to 3D mesh parametrization. With S. Gortler and C. Gotsman. Computer Aided Geometric Design, 23:83–112, 2006.

Characterizing generic global rigidity. With S. Gortler and A. Healy. American Journal of Mathematics, 132(4):897–939, 2010. arXiv:0710.0926.

Sensor network localization using sensor perturbation. With Y. Zhu and S. Gortler. Transactions on Sensor Networks, 7(4), Article 36, 2011.

On affine rigidity. With S. Gortler, C. Gotsman, and L. Liu. Journal of Computational Geometry 4(1):160–181, 2013. arXiv:1011.5553.

Generic global rigidity in complex and pseudo-Euclidean spaces. With S. Gortler. In Rigidity and Symmetry, 131–154, Fields Institute Communications 70, 2014. arXiv:1212.6685. Characterizing the universal rigidity of generic frameworks. With S. Gortler. Discrete and

Computational Geometry, 51(4):1017–1036, 2014. arXiv:1001.0172.
Measurement isomorphism of graphs. With S. Gortler. Preprint, 2012. arXiv:1212.6551.

A bulk inflaton from large volume extra dimensions. With B. Greene, D. Kabat, and J. Levin. Physics Letters B, 694(4):485–490, 2011. arXiv:1001.1423.

Markup optimisation by probabilistic parsing. With C.-c. Shan. Draft available online.

Other papers

Selected invited talks

“Elastic graphs and degenerations of complex structures”
Special session on Holomorphic Dynamics, AMS sectional meeting, Stony Brook, March 2016

“Discrete measured foliations”
Oberwolfach workshop on Computational Geometric and Algebraic Topology, Oct 2015 Tech Topology Conference, Georgia Tech, Oct 2015

“Rubber bands, square tilings, and rational maps”
Dynamical Developments: a conference in Complex Dynamics and Teichmüller theory, Bremen University, Aug 2015
Invited address, AMS sectional meeting, University of Wisconsin—Eau Claire, Sept 2014

“Bordered Heegaard-Floer homology”
Lecture course at XIXth Oporto meeting on Geometry, Topology and Physics, Faro, Por- tugal, July 2010

“Combinatorial Heegaard-Floer homology and transverse knots.” Notes available online. Workshop on Cluster Algebras and Related Topics (4 lectures), Morelia, Mexico, Decem- ber 2008

“Wheels and wheeling” and “Hyperbolic volume and the Jones polynomial”
Summer school at conference Invariants des nœuds et de variétés de dimension 3, Greno- ble, France, June 1999.

Topology II, graduate course, IU Bloomington, Spring 2016.
Complex Analysis, upper-level undergraduate course, Harvard, Fall 2003; Barnard, Fall

2009; IU Bloomington, Spring 2016.
Geometric Topology, graduate course, IU Bloomington, Fall 2016; Harvard, Spring 2005. Rational Maps, graduate topics course, IU Bloomington, Spring 2015.
Topology, upper-level undergraduate course, IU Bloomington, Spring 2015; Harvard, Spring

Geometric Topology II, graduate course, IU Bloomington, Spring 2014.
Metric Geometry, graduate course, IU Bloomington, Fall 2013.
Intuitive Topology, undergraduate course, IU Bloomington, Spring 2013.
Curves on Surfaces, graduate topics course, Berkeley, Fall 2012.
Calculus I, Cornell, Fall 2011; Calculus II, Harvard, Spring 2003; Calculus III, Barnard,

Fall 2005, Spring 2006, Fall 2010.
Graph rigidity undergraduate research project, Barnard, Summer 2009–2011. Led to sev-

eral papers by the students, including S. Frank and J. Jiang, “New classes of counterexamples to Hendrickson’s global rigidity conjecture”>, Discrete and Computational Ge- ometry, 45(3):574–591.

Honors Linear Algebra, introductory course for majors, Barnard, Fall 2009.
Perspectives in Mathematics, introductory course for non-majors, Barnard, Fall 2009, Fall

  1. With D. MacDuff and D. Bayer.
    Algebraic Topology I, Harvard, Fall 2004; Algebraic Topology II, Barnard, Spring 2008,

Spring 2009, Spring 2011.
Introduction to Algebraic Topology, undergraduate course, Barnard, Spring 2009. Symmetry, first-year seminar, Barnard, Fall 2006 and Spring 2008.
Geometry and Topology seminar, Barnard, multiple semesters, Spring 2007–present. Combinatorics, undergraduate course, Barnard, Spring 2007.
Undergraduate seminar, Barnard, Spring 2007.
Modern Analysis II, undergraduate course, Barnard, Spring 2006.

Teaching and undergraduate research


Lie Algebras, upper-level undergraduate course, Harvard, Fall 2002.
Algebra, informal upper-level undergraduate course, Harvard, Fall 2002.
Elliptic Functions, upper level undergraduate course, Geneva, Fall 1998. With P. de la


Co-organizer, Special Session on Random Spaces, AMS sectional meeting, University of Wisconsin—Eau Claire, Sept 2014.

Co-organizer, Conference “What’s next? The mathematical legacy of Bill Thurston”, at Cornell University, June 2014.

Organizer of semester on “Homology Theories of Knots and Links” at MSRI, Spring 2010, including organizing the introductory workshop.

Founding editor, Quantum Topology, 2009–present.
Referee for Acta Mathematica, Algebraic Geometry and Topology, Compositio Mathemat-

ica, Duke Mathematical Journal, Experimental Mathematics, Geometry and Topology,

Topology, National Science Foundation, inter alia. Member, Association for Women in Mathematics. Member, American Mathematical Society.

Sensor Network Localization Using Sensor Perturbation

Yuanchen Zhu Harvard University

Steven J. Gortler Harvard University

Dylan Thurston Columbia University

Back to the Voynich Manuscript conundrum . . .

I think perhaps one of the most intriguing – and potentially revealing – aspects of this seemingly un-solvable mystery is that Voynich was married to Ethel Boole – daughter of mathematician George Boole (father of Boolean logic). Something tells me that Voynich did not just happen to stumble upon this manuscript, as has been commonly portrayed. He certainly seems to have been an Intel agent/spook (as was John Dee who preceded him in this woven tale).

Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.[5]

In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole’s algebra in this setting,[8] and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Shannon already had at his disposal the abstract mathematical apparatus, thus he cast his switching algebra as the two-element Boolean algebra. In modern circuit engineering settings, there is little need to consider other Boolean algebras, thus “switching algebra” and “Boolean algebra” are often used interchangeably.[9][10][11]

Newbold also had a great interest in puzzles, codes, and cryptography. This interest led to the last major undertaking of his professional life. He worked to decipher a famous coded text, commonly referred to as the Voynich Manuscript. He believed it had been written by Roger Bacon, a thirteenth century English monk, scientist, astrologer, and inventor. According to Newbold’s complex system for deciphering the code, Bacon had made numerous scientific discoveries which no one else would “rediscover” for centuries. Newbold died before he could decipher the whole manuscript, but the partial decipherment was published posthumously as The Cipher of Roger Bacon (1928). In the years immediately following Newbold’s death, his version of the meaning of the code in the Voynich Manuscript was seen as the truth. Several years later, however, other experts began to look at Newbold’s method with a critical eye. They correctly noted that his system was faulty as it was based on a number of unproven assumptions. Newbold’s interpretation of the Voynich Manuscript was eventually completely disregarded, with experts questioning if Roger Bacon was the author of the manuscript. None of these questions regarding the validity of his decipherment surfaced during his lifetime.

I found this fictional story, and I can’t help but wonder if there are any clues embedded . . .

As friends draw Edward into a peculiar and addictive computer game, his obsession deepens as he discovers surprising parallels between the game’s virtual reality and the mystery of the codex. An accomplished and entertaining thriller, Codex explores the mysterious power of books in the medieval and modern ages.

From Voynich → we get to Boole (Boolean logic/digital circuits) and
John Baez → both of whom lead us to Claude Shannon (Shannon entropy/information theory) → who links us back to the Voronoi → strangely connecting us to crystalline polymers . . .

This type of self-organization is inherent in the melt-crystallized polymers, such as polypropylene [30,31]. Suppose a molten linear polymer (such as polypropylene or polyethylene) is cooled down slowly. In that case, some polymer chains take on a certain orderly configuration: they align themselves in semicrystalline plates called lamellae [30,31].

I have a weird hunch that all of these narratives intersect at militarized mixed reality gaming . . . No matter which way we turn, it continually feels as though we are literally in someone’s game . . . In fact, I am beginning to think there is no real chaos in this reality/matrix, but rather, order and manufactured chaos leading to increased order/precision control . . .

I found this book today:

Gordon Rugg

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Gordon Rugg (born 1955) is a British academic, head of the Knowledge Modelling Group at Keele University and a visiting Senior Research Fellow at the Open University, known for his work on the Voynich manuscript.[1]


Born in Perth, Scotland, Rugg has a first degree in French and Linguistics and a PhD in Psychology, both from Reading University, UK.

His background includes working as a timberyard worker, a field archaeologist and an English lecturer. He became the focus of media attention in 2004 for his work on the Voynich manuscript.

He is co-author with Marian Petre of two books for students which focus on semi-tacit skills in research. He is head of the Knowledge Modelling Group at Keele University and a visiting Senior Research Fellow at the Open University.


His main research theme is elicitation methods – techniques for eliciting information from people, for purposes such as market research and requirements gathering for software development. His main work in this field includes the following.

  • A series of co-authored papers on card sorts.
  • A series of co-authored papers on laddering, including one which integrates laddering with graph theory.
  • A paper co-authored with Neil Maiden, describing a framework for choosing the appropriate methods to elicit various types of semi-tacit and tacit knowledge.

This work formed one main strand in the Verifier method which he developed with Joanne Hyde. This is a method for critically re-assessing previous research into difficult problems. The initial stage uses a range of elicitation methods to gain an accurate picture of the assumptions and normal working practices used in the previous work. The next stage uses a knowledge of experts’ behaviour and a range of error taxonomies to identify the places where human error is most likely to have occurred. The final stage uses various formalisms to assess whether or not an error actually has occurred. There is no guarantee that this method will catch every error – it is not a method for proving the correctness of a piece of previous work – but it improves the chances of finding key errors.

Rugg’s other work is multidisciplinary, including theoretical archaeology and teaching methods.

Voynich manuscript[edit]

Main article: Voynich manuscript

The Voynich manuscript is written in an unknown script.

Rugg used an informal version of the Verifier method to re-assess previous work on the Voynich manuscript, a manuscript widely believed to be a ciphertext based on a code which had resisted decipherment since the manuscript’s rediscovery by Wilfrid Voynich in 1912. Previous research had concluded that the manuscript contained linguistic features too complex to be readily explicable as a hoax, and too strange to be explicable as a transliteration of an unidentified language, leaving an uncracked cipher as the only realistic explanation.

Rugg suggested that these assessments of complexity were not based on empirical evidence. He examined a range of techniques known in the late sixteenth century, and found that, by using a modified Cardan grille combined with a large table of meaningless syllables, it was possible to produce meaningless text that had qualitative and statistical properties similar to those of “Voynichese”. Rugg replicated the drawings from a range of pages in the manuscript, accompanying each with the same quantity of text as found in the original page, and discovered that most pages could be reproduced in one to two hours, as fast as they could be transcribed. This suggested that a meaningless hoax manuscript as long and as apparently linguistically complex as the Voynich manuscript could be produced, complete with coloured illustrations, by a single person in between 250 and 500 hours.

However, there is debate about the features of the manuscript which Rugg’s suggested method was not able to emulate. The two main features are lines showing different linguistic features from the bulk of the manuscript, such as the Neal keys, and the statistical properties of the text produced. Rugg argues that these linguistic features are trivially easy to hoax using the same approach with a different set of tables, and would add about five minutes to the time to produce each page; the counter-argument is that this makes the hoax too complex to be plausible. Regarding statistics, Rugg points out that text produced from the same set of initial nonsense syllables but using different table structures shows widely different statistical properties. Since there are tens of thousands of permutations of table design, he argues that it would simply be a question of time to find a design which produced the same statistical properties as “Voynichese”. Whether or not this would prove anything useful is another issue, since it could either be used to support Rugg’s argument, or dismissed as coincidence.

Further counterarguments are:

  • There is no historical evidence showing that Cardan grilles were used for this kind of purpose at any time in history
  • The radiocarbon dating, codicology and palaeography all indicate that the manuscript was constructed roughly a century before Cardan grilles were devised
  • The mathematical concept of randomness was not yet fully formed in the time period proposed

The debate continues.

Selected publications[edit]

  • Petre, Marian, and Gordon Rugg. The unwritten rules of PhD research. McGraw-Hill International, 2010.

Articles, a selection:


  1. ^ Schinner, Andreas. “The Voynich manuscript: evidence of the hoax hypothesis.” Cryptologia 31.2 (2007): 95-107.

In our first test of concept, Gordon applied a ‘light’ version of Verifier to a problem which had defied the world’s best codebreakers for almost a century, a document known as the Voynich Manuscript. Within a few weeks he found a solution which previous researchers had missed. His findings were published in the leading peer-reviewed journal of historical cryptography Cryptologia , and in Scientific American.

Fascinating that I found that rope on the mudflat on Friday.

These loops remind me of the Celo logo @leo.


Apologies I realized I got his name wrong, I meant C.S. Lewis not Lewis Carol, my bad.

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Do you see any resemblance to what Viviane Fischer is wearing here (her most recent appearance, since “splitting” apart from Fuellmich) and the Voynich Manuscript? Are these people always speaking in code?

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I hadn’t seen that - what - she has ties to the manuscript? I missed that.

Are those dandelions? The toothed leaves…