My daughter and I were recently playing with python’s square root function. She discovered that if you evaluate an even number of ones, the square root is half that number of three’s on both sides of the decimal. So ?11 is approximately 3.3, and the ?1111 is approximately 33.33, and so forth. We learned that this continues until there are eight three’s on either side of the decimal point, then they reduce in frequency.

The square root of an odd number of ones is also patterned. ?1 is 1, ?111 is 10.5, ?11111 is 105.4, ?1111111 is 1054.0, and so forth.

So we decided to write a python program to generate 20 instances. Here is the program:

#! /usr/bin/env python3
“””Determines the square roots of numbers comprised of ones like 11, 111, 1111, etc.”””
import math
bobby = 10
sue = 1
for x in range(1,20):
   answer = bobby + sue 
   sue = answer
   bobby = bobby*10
   print(x+1, ‘\tThe square root of ‘, answer, ‘ is ‘, math.sqrt(answer))

And here are the answers:

2 The square root of  11  is  3.3166247903554
3 The square root of  111  is  10.535653752852738
4 The square root of  1111  is  33.331666624997915
5 The square root of  11111  is  105.40872829135166
6 The square root of  111111  is  333.333166666625
7 The square root of  1111111  is  1054.0925006848308
8 The square root of  11111111  is  3333.3333166666666
9 The square root of  111111111  is  10540.925528624135
10 The square root of  1111111111  is  33333.33333166667
11 The square root of  11111111111  is  105409.25533841894
12 The square root of  111111111111  is  333333.33333316667
13 The square root of  1111111111111  is  1054092.553389407
14 The square root of  11111111111111  is  3333333.3333333167
15 The square root of  111111111111111  is  10540925.533894593
16 The square root of  1111111111111111  is  33333333.333333332
17 The square root of  11111111111111111  is  105409255.33894598
18 The square root of  111111111111111111  is  333333333.3333333
19 The square root of  1111111111111111111  is  1054092553.3894598
20 The square root of  11111111111111111111  is  3333333333.3333335

Although it looks like the sixes also multiply, they also reduce after reaching eight in a row. Check it out with python’s decimal package. from decimal import Decimal, then in the print statement, add Decimal(math.sqrt(answer)).

Wednesday 6 December: a very exciting discussion about free will put on by the Erasmus Center. Sincere thanks to Jim Holden and to Erasmus for inviting me to respond to Peter Tse, author of The Neural Basis of Free Will (MIT Press, 2013).

My main point during the debate was that standards of proof and acceptable methods of testing are not yet available to neuro-scientists to establish a physiological basis of free will. Study of the neuron is the province of bio-chemistry, which has its own standards of proof and acceptable methods of testing. These standards have been developed over decades, through argument and counter-argument, and through experimentation. They are not optional—not if you seek accurate results. Freedom is a concept discussed for centuries by philosophers, theologians, political scientists, and historians. Each of those fields has its own standards of proof and acceptable methods of argumentation. Those standards are important to ensuring logical results. Will or volition is chiefly the province of psychology, with its own standards of proof and acceptable methods of testing. So bringing bio-chemical evidence to a philosophical debate about a psychological topic seems to me to be like, as Laurie Anderson said, trying to dance architecture.

A secondary point I made was that any logical investigation proceeds from the question that you set. So, setting the question correctly is essential. We would not have had a debate had Dr. Tse written a book entitled, The Neural Basis of Unconstrained Choice. The phrase “free will” connotes something in English that the phrases “unconstrained choice” or “unfettered desire” do not. [It seemed to me an example of the Sapir-Whorf fallacy that the English language should be transparent to physical reality, specifically to neural pathways.] So, I tried to show how desire is different from will in English, how French and Latin are different again, and how investigating free will in English entails different logical assumptions than investigating it in French or Latin. In English, will connotes desire, want, action. In French, arbitre connotes sight, judgment, observation. Different semantic fields with little overlap. Another example: the greatest virtue according to Christians is love. That’s English. In the Latin Bible, the word is caritas. You can also translate caritas as charity (faith, hope, and charity). You can give charity without being in love, such as for tax purposes. So which one is the virtue? Faith in the Latin Bible is fides, which can also be translated as loyalty. Which is it? There’s a big difference between obeying someone that you don’t believe in and believing someone whom you don’t obey. Same for freedom. The French prize Liberté, or liberty. Would Dr. Tse have found the same things if he looked for liberty of desire? A French-speaker who succumbed to Sapir-Whorf would look for la libre volunté in a different part of the brain than an English-speaker. And that makes no sense to me!

I also made the case that, as Gertrude Stein said of Oakland, “there’s no there there.” “Free will” is a concept that English speakers use to talk about a whole host of connected ideas and psychological processes. Free will is not a thing. It doesn’t exist the way Plymouth Rock or the Boston Marathon exist. Where do you find free will? I say, in a dictionary.

The public discussion among the guests afterwards was terrific. No one in the room doubted that the brain is essential to thinking. But there seemed a general consensus that thought is not reducible to bio-chemistry. Some people made the point that our morality and personal values depend upon a non-reductive view, on a non-physicalist view, of will. Others said that there are psychological responses that we think are free, but are actually conditioned or instinctive. So we have to distinguish the choices that are free from those that are not. Others asked whether or not free will introduces randomness into science, and if so, to what degree. (I tend to think that decisions are not made randomly, but on the basis of stochastic algorithms that measure optimality by accounting for values, external conditions, imagined results, and so forth.) What was most apparent to me is that neuro-science is not going to trump dozens of disciplines, centuries of carefully thought-out positions, and carefully considered, methodical experimentation. It reaffirmed my faith in the multiplicity of a university, of a fundamental need for diversity of viewpoints, all speaking with each other, with each one grounded in a distinct intellectual tradition.

I just stumbled across Verlaine’s Bonheur, which he described as part of a Catholic triptych. He wrote it in the late 1880s and early 1890s, finishing the manuscript in January 1891. Poem 28 is in the form of an epanaleptic elegy, like Bede’s Hymn to Aethelthryth, modified into an ABABA rhyme. The first line matches the last. Here are the first two stanzas:

Les plus belles voix
De la Confrérie
Célèbrant le mois
Heureux de Marie.
O les douces voix!

Monsiuer le Curé
L’a dit à la Messe:
C’est le mois sacré.
Écoutons sans cesse
Monsieur le Curé.

I’m struck by how tenacious is the poetic form. Not only does the form allude to Latin elegies of the Church, but it also requires the poet to repeat a phrase in different contexts—which is a practice in prayer. Repetition in slightly different contexts allows the poet to restore a reader’s wandering imagination to a fixed narrative while serially enlarging the semantic force of the narrative. So we meet fairly cliché images: voices of monastery, a curate saying Mass. But slight variation and addition of phrases moves our imagination from topic to topic, connotation to connotation, and thereby gives fuller character to otherwise dry words. Verlaine focuses our attention first on superlative beauty, a characteristic we then apply to voices. We follow those voices to a confraternity. The verb célèbrant is in the plural, which places an image of celebration in our minds, but does not assign it to the singular confrérie. Instead, it is the beautiful voices that celebrate.

Next we greet the singular mois ‘month’, which until the /s/ at the end of the line leaves us in suspense, wondering if will end moine ‘monk’. The masculine mois is set in parallel with the previous line’s feminine Confrérie, indicating in part the capaciousness of the community, like a month that contains many days. A natural caesura at the end of the third line interrupts the semantic flow of the Noun + Adjective (mois heureux). This pause sets the initial words of line 3 and 4 in apposition: celebrate and joyful. And now, a bit of genius! Verlaine wraps a singular masculine phrase (le mois hereux) with two singular feminine nouns, confrérie and Marie. Here, one is reminded of Bede’s description of Caedmon’s monastery at Whitby where a community of men is ruled by a woman, Hild, and the Wisdom of God—in Latin, Wisdom is feminine.

After the celebratory kernel, we finish the wrapping with a transformed choir of voices. At first the most beautiful, now, transformed through their celebration of Mary, they are gentle and sweet. Similar transformation will take place with the mois ‘month’ which begins joyfully, then transforms in the second stanza to sacred, sacré.

This is a poem of nine stanzas. The number is not insignificant, as it is the number of months Christ was in the womb, the number of months it takes for the physical body to gain its spiritual soul, and perhaps the number of stanzas it takes for a reader suffused with the physical beauty of Verlaine’s verse to achieve a spiritual understanding.

The Serpentine Lyre.

The second lyre is named for the interlace pattern on its headstock. The last lyre had two dragon heads, so it’s the Dragon-head lyre. Simple. Number Two is made completely of mahogany. The Sutton Hoo lyre was oak and had no sound holes. So, it seems as if the original makers relied on the sonority of the box itself to carry the sound waves. That means paying close attention to grain direction and keeping the joints tight. I decided on a frame, much like a tortion box, but with the head stock exposed.

The frame is 3/4″ x 3/4″ mahogany. There are two main points of potential warp: torque on the cross-beam and tilt on the base. The headstock is so heavy and the string pins so thick that tilt is unlikely there. So, joinry type will be chosen to account for that.

Click on any picture to enlarge it.

The main crossbrace is joined with a through-tenon. If it is seated in the mortise well, then the brace won’t tilt (or roll) forward or backward, causing the lyre’s skin to buckle.

You can see that it’s pretty well seated. There’s a little daylight, but I filled that with epoxy. All the main structural joints are epoxied. The base of the lyre is going to anchor the force of the strings, like the anchorage of the Brooklyn Bridge. So the main counterforce, it seems, has to be against tilt (or roll). So I decided on a bridle joint. I also wanted a lot of exposed long grain for glue.

I kept the proportions of the joint to thirds, which left enough wood to sustain the pressure. Even with as hard a wood as mahogany, I wouldn’t make the frame any thinner. Next, I wanted to reinforce the base with a secondary brace that would also support the bridge. To counteract both tilt and torque, I decided on a half-lap dovetail to secure the brace to the sides, and mortise and tenon to secure the stiles.

Here you can see the seating for the half-lap dovetail:

It’s a lot of chisel work! But mahogany is gorgeous to work with. Here is the entire base architecture just before glue-up:

I used regular wood glue for the crossbrace assembly, since the joints are doing most of the work.

But just to be sure, I added dowels:

In the picture above, you can also see the mahogany skin. I skinned one side with 1/16″ mahogany veneer. It was too thin to support anything structurally, so I put nto a series of very thin supports. These were walnut. I wanted something with closer grain than mahogany, both to avoid splintering and to carry high-frequency sound more efficiently.

Here is the frame with one side of skin:

After all that work and all those beautiful joints, one is tempted to show it off–very Greene & Greene! But a clean aesthetic demands otherwise, so I hid the joinery. I don’t have pictures of carving the headstock, but you can see it in the following video. (I made the video so you can hear the sound.) The saddle is a strip of walnut that spans the mahogany skin and supports a mahogany bridge. The tailpiece is mahogany and clutches the body like a c-clamp. The strings are sent through holes and their ends are tied, like a classical guitar. The tuning pegs are zither pegs, tuned with a handle.

The tuning is CDGCDG. I came up with the rhythm and melody so that the music would match the syllabification of Caedmon’s Hymn, caesurae included. Here are the first four lines (click link to watch video):

SerpentineLyre Small

Trinity College Library

Thanks to the generosity of the College of Humanties and Fine Arts at UMass, the parser is now working at a very basic level. Here it is: http://www.bede.net/misc/dublin/parse.html

Mark Faulkner of Trinity College Dublin aided by the generosity of the Irish Research Council brought me to Trinity in July to describe the parser. He hosted a terrific conference where a wide variety of scholars and scientists presented big-data projects. One conclusion from my perspective was that medieval texts (as well as all ancient languages) are as subject to the Law of Large Numbers as are network packets, social media posts, and traffic patterns. One surprise was how few samples were needed.

Specifically, texts (that is, generically similar sets of syntactically correct utterances) will approach audience expections as defined by genre, language, and period. These expectations are in turn characterized by sets of related vocabulary items. For example, a sermon employs certain words to indicate to an audience that it is indeed a sermon—or conversely, it is by virtue of certain vocabulary items that we classify a text as a sermon. (See Michael Drout, Lexomics.) Moreover, those vocabulary items tend ot come in serially-arranged chunks so that, as an extreme example, an adventure story may use words to describe setting and character before using words that describe dying.

Consequently, a parser that seeks to classify for genre or for aesthetic particulars considers not only vocabulary, but related vocabulary items, and the order in which those items appear over the span of the text. That parser will also consider phrases and phrase structure. Old English poetry, once recognized through its combination of rhetorical tropes (alliteration, hypotaxis, etc.), can be parsed metrically. More importantly, word combinations and clusters can be searched for and a stochastic algorithm applied in order to yield high-frequency clusters. That algorithm is the challenge. Although Google has developed similar algorithms to rank websites and to effect advertiser auctions, deciding on the likelihood of a grammatical claim is a different problem. My challenge over the next year or so is to break down the assumptions a fluent reader of Old English makes when reading a text. The biggest roadblock will be the desire to put in my own grammatical knowledge. A Natural Language Parser does not rely on a grammarian’s parse of a text. It relies instead on all texts ever written in that language.

The most exciting possibility to my mind is using glosses to tie OE literature into its Latin and Celtic analogues. A gloss is a single-word translation of one language into another. For example, French eau can be glossed by English water. Old English scribes glossed many Latin words. They wrote them in tiny letters above the Latin. Using these glosses, we could connect OE texts to Latin texts more closely and trace the migration and adaptation of images and collocations over time. Paired with information about the movement of manuscripts, we could map the dispersal of ideas, images, and metaphors over time and space.

Because some of these metaphors constitute a defining characteristics of a genre (such as lyric), we can watch the evolution of genre over time. And by examining the structure and constitution of these text in multiple languages, we could observe the interrelation and mutual influence of written culture.

The bottom line? In the next stage, I have to treat a text like an organism. Ask what other organisms are like it. Then try to dissect their DNA and determine which genetic markers came from where.

This perl script generates the HTML for a simple 12-month calendar. Run it in Terminal: it will ask which day of the week is the first of January. Then, copy-and-paste the results to your HTML code. Modify the script as you like.

#usr/bin/perl -w

# generate a calendar for HTML
# sharris@umass[dot]edu 2017

# ___________________________________________ declarations

my $start = 0;
my @monthNames = qw(January February March April May June July August September October November December );
my @month = qw(31 28 31 30 31 30 31 31 30 31 30 31);
my @dayNames = qw(Su M Tu W Th F Sa);

my $table = “<table width=’200′ border=’1′ cellpadding=’2′ cellspacing=’1′ bordercolor=’#000000′>”;
my $tr = “<tr align=’center’ valign=’middle’>”;

my $weekday = 0; # which day of the week is it?
my $date = 1; # what date is it?
my $m = 0; # total months for giant loop offset by 1
my $offset = 0; # offset counter
my $i = 7; # 7 days in a week

# ____________________________________________ setup
print “\nOn which day of the week is the first of January? (M T W H F S U)”;
$start = <STDIN>;

# now we set the week-counter to the day of the week minus 1 as offset

if ($start == “M”){$offset = 1;}
if ($start == “T”){$offset = 2;}
if ($start == “W”){$offset = 3;}
if ($start == “H”){$offset = 4;}
if ($start == “F”){$offset = 5;}
if ($start == “S”){$offset = 6;}
if ($start == “U”){$offset = 0;}

# ___________________________________________ BIG LOOP

foreach (@monthNames) {
print “<p><b>”.$_.”</b></p>\n”;
print $table;
print $tr;

foreach (@dayNames){
print “\n<td bgcolor=’#CCCCCC’><b>”.$_.”</b></td>”;
}
print “</tr>\n”;

$date = $month[$m] – ($month[$m] + $offset) + 1;

until ($date > $month[$m]){
for ($i = 7; $i > 0; $i–){
if ($i == 7){print “<tr align=’center’ valign=’middle’>”;}
print “<td bgcolor=’#CCCCCC’>”;
if ($date > 0 && $date <= $month[$m]){print $date;} else {print “\&nbsp\;”;}
print “</td>\n”;
if ($i == 1){print “</tr>”;}

if ($date == $month[$m]){$offset = 8 – $i;}
$date++;
} # weekly loop

} # fill loop
print “</table>”;
$m++;
} # monthly loop

Update 5/2017. Now that the static state parser is working, time to move on to the syntax. The next big issue is language. So far, I’ve written in PERL. Love it. Works brilliantly. But much of the available open-source code is in python. NLTK is in python. You can tokenize with it. Parse with it. The Helsinki parsed OE corpus is in it. And it loads into a script easy-peasy. Very tempting to switch horses in mid stream.

Second issue: I’m moving the parser from UNIX to LINUX.

I’m putting the parser on a sandboxed Dell that’s about 10 years old and about $150 on Amazon. Fine computer that still runs Ubuntu! As an aside, I can configure the IP tables to reject traffic from China, which cuts back significantly on lost processor time spent dealing with robot hack attempts every 2 seconds. Here hacker “tomcat” is calling from 106.39.44.0, which is Chinanet, No.31, Jingrong Street, Beijing

Two seconds later, the next caller, 116.31.116.7 at port 36116:11, is from the same server. Between this sort of nonsense and the spam, it’s a wonder academic computing can do anything else.

Now that the basic parser is working, it needs fine-tuning. First, the lists of closed-class words need to be improved. Pronouns are especially difficult to differentiate, and I wonder if I need to. Relative, interrogative, demonstrative—are these required to assemble phrases?

Second, the list of PRP is too short. Mitchell & Robinson have a good list in their textbook.

Third, the order of assembly for the syntax portion needs some thought. Obviously, closed class words must come first. After pronouns, prepositional phrases might be easiest to isolate. The trick is to try to think like an undergrad: what were the first steps? Small closed-class words (PRN, CNJ, PRP), then obvious inflections (-um, -ode, -ost, etc).

Update 6/20/2017. It’s working. Parser finds possible inflections and declensions based on suffixes, then cheks for closed class, then checks for prepositional phrases. Still a long way to go. Noun phrases, the right bounary of PP, suboptimal parses, and so on. But it’s working. Here it is: http://www.bede.net/misc/dublin/parse.html

Once the parser delivers all possibilities to the calling function, it’s time to decide what’s what. What is a verb, what is  noun, and so on. Because language is not mathematics, there is rarely a single answer. Instead, there are better and worse answers. In short, all possible answers need to be ranked. The best answer(s) are called “optimal.”

As far as I know, current iterations of the parsed corpora of OE treat all OE utterances as equivalent. In other words, the syntax of a sentence from the poem Beowulf is as grammatical as a sentence from Aelfric’s sermons. Bruce Mitchell, the greatest of OE syntacticians, compiled his conclusions from an undifferentiated variety of sources: “I have tried to select a variety of relevant examples or to illustrate the phenomenon from Aelfric and Beowulf, as best suited my purpose” (OE Syntax, p. lxiii). Although he noticed distinctions in syntax between authors, he attempted to derive from them a single form. For example, swelc ‘such’ is a strong, demonstrative pronoun in most OE writing; but it is used in a weak form “in ‘Alfredian’ prose” (sec. 504). Mitchell chased an abstract description of syntactic phenomena, whose instantiated form in language he illustrated with examples. Variants were classed as deviations from a norm. His was a Platonic quest. Mine, much impoverished by comparison, shall be a touch more Aristotelian.

Syntax will be subdivided generically. What is optimal in a prose chronicle may not be optimal in a poem.

Syntax will be subdivided temporally. What was optimal in Alfred’s court may not have been optimal in Cnut’s.

And syntax will be subdivided spatially, or rather, geographically. What was optimal in Anglian may not have been optimal in Kentish.

These subdivissions will have to be rough-and-ready, since we lack diplomatic editions of manuscripts. Editors have already elided much of the information that distinguishes one scribe’s work from another’s. For example, I noted in a manuscript of Aelfric an instance of OE faðer ‘father’, which was not supposed to exist at the time. As diplomatic editions come available, I will be able to account for them. For the moment, any dated or datable text will be marked as such. The “syntaxer” (program that parses syntax) will prefer texts of similar genre, locale, and time.

INDICES. The major component to the project is a set of massive indices.

Like a Google search, this parser operates on tables of frequencies. Google digests the raw web daily, at least. The web is then sifted through algorithms at Google’s massive data centers. That sifting process results in massive indices of frequencies. An index will record searches, links, and clicks. A search for Silly Putty is recorded. A second search. Then a third. Three users click on a single link. That link is recorded and marked as the top link. The next user to search for Silly Putty is sent the top link first.

An Aelfric index. By parsing the works of Aelfric, the computer can build a list of most-used words and their usual grammatical function in Aelfric’s sentences. So, someone searching for heald in Aelfric will prompt the retun of pre-parsed sentences, rather than invoking a new search. The sentences will come in order: the most usual use of heald first, the least usual last. (It seems most often to be in participial form.)

Other indices are obvious. A Wulfstan index. The works of King Alfred’s court. Benedictine books. The Chronicle. Poetry. And so forth.

PROGRESS:

Meanwhile, the parser is taking a sentence and parsing it!

The first test sentence was, of course, “Hello, World!” Here is the screen grab of the first Old English sentence to work:

Se man wæs god. The correct forms are listed in each cluster.