Disturbances in the Force Ahead for Wordle

Comment on Wordle No. 943

January 19, 2024

Some of you may recall that I wrote software that can play Wordle, the online game owned by and housed at The New York Times. At the outset such software must know what words are accepted by Wordle as guesses and what words might be used as the solution in a game. Thus, the software must employ two word lists.

There is one game every day. The first game in history (before acquisition by The New York Times) was conducted online June 19, 2021. Yesterday (January 18, 2024) was the day of game no. 943. As that game is over, I may reveal its solution, which was "stole". My favorite first guess is the word "roate". After making that guess yesterday, I saw this:

R

O

A

T

E

It's relative rare for me to determine three of the five letters with my first guess. My software, using a list of what I think are words that might reasonably appear as solutions, reported that the possible solutions among the words on my list were "stoke", "stole", "stone", "stove", and "those". At first glance it appears that I have a 20% chance of guessing correctly on my second guess by picking one of those 5 words at random. But I can dig deeper. For each of those words I can hypothesize that that word is the solution, use any one of the words as a guess for that solution, and find the number of words that would still be in play. In this way I can determine for each of those words as a guess the number of words still in play following that word as a guess, and select for my next guess a word for which the number of words still in play is minimum. With this example -- and using my word lists -- each of the four words beginning with 's' is a better second guess than the word "those".

There are two further wrinkles, one helpful and one not helpful. The unhelpful wrinkle is that the solution may not be on the list of words that I imagine as possible solutions. For that list I had a good start because the early game of Wordle had semi-public lists of allowed guesses and possible solutions. As time went by, the list of allowed guesses was significantly expanded but remained semi-public. But the list of possible solutions dropped out of semi-public sight, and, more to the point, there have been four solutions over time -- in games 646 (guano), 659 (snafu), 720 (balsa), and 730 (kazoo) -- that were not on the early list of possible solutions.

The helpful wrinkle is that up through today -- game 944 -- no word has been used as a solution more than once. Quite obviously, unless Wordle is discontinued before, say, its 10th anniversary in 2031, sole use solutions cannot continue forever.

Why do I call that a helpful wrinkle? I expect that the Wordle editor at the New York Times is aware of the history of sole use and is aware that at some point sole use must be discontinued. But for the meanwhile a player can gain advantage by assuming that sole use is still in effect. With game 943 the assumption of sole use narrows the list of 5 words in play to 2, "stoke" and "stole", which means that a random second guess among those has a 50% chance of being correct.

One more example. Suppose the first guess is "least". Then

L

E

A

S

T

That is a remarkably lucky guess yielding 4 letters. The words in play -- using my list of possible solutions -- are "steel", "stole", and "style". The "deeper dig" procedure flags "stole" and "style" as optimal second guesses, but assuming sole use, there is only one optimal second guess, which is "stole".

Yellow vs. Green in "Wordle"

For Wordle haven't we always thought that green was better than yellow?

I find it rather strange that this scored word

S

L

I

M

Y

matches a single word on the purported official list of 2315 possible secret words in original Wordle, but this scoring of the same word

S

L

I

M

Y

matches a dozen.

A Puzzle

This is a Wordle-like puzzle. You are looking at a word evaluated the way Wordle evaluates words. With this one evaluated word you should have all the information you need to deduce the secret word.

A

D

I

E

U

I've posted several of these on Facebook. The thing is that I create the evaluated word in HTML using HTML's ability to provide background coloring. But Facebook seems not to want to accept the snippet of HTML. So I've been posting screenshots of the HTML there. The question as I write this is whether Blogger will accept the HTML for an evaluated word.

It seems to work here. Well, almost. The HTML is coded so that the squares containing the letters should all have the same width, as well as the same height. I guess it's close enough.

From the System Manual

VERB(1) VERB(1)

NAME

verb — Convert any noun to a verb

SYNOPSIS

verb [ -a ] [ -d dictionary ] word

DESCRIPTION

verb generates a dictionary entry for any English noun located in the dictionary as an English verb. By default the dictionary is the system dictionary.

With the -a switch the generated dictionary entry is entered in the dictionary if the user has write permission for the dictionary. Normally the system is configured so that members of the group sysdict have write permission for the system dictionary.

With the -d switch the specified dictionary is used instead of the system dictionary.

EXAMPLES

Generate a dictionary entry for the noun “street” as a verb:

verb street

To perform an action that involves a street. E.g., “Honey, did you remember to street the garbage?”

SEE ALSO

american-english(1), adjective(1), adverb(1), conjunction(1), english-english(1), expletive(1), expletive-deleted(1), grammar(5), noun(1), preposition(1), syntax(1), sysdict(1), sysdict(5), sysdict-daemon(8)

BUGS

There is no guarantee that system dictionary verb entries generated by verb are correct.

Words with Many Anagrams

Of course, the question of what words are the (single-word) anagrams of other words depends on having a reference list of all words. For this purpose I am using a list of 466,378 words gathered over time. The list has grown by about one-third over the last few years. Some of the additions are actually new words such as covid. On the other hand, I have the impression that many of the added words may be viewed as misspellings of standard words that have come into use. For example abcess appears now to be in use as an alternate spelling of abscess. Other words on the list are archaic spellings of standard words. Regardless, my list may not be regarded as definitive in any way. The following table lists by rows all words having 11 or more anagrams. The first column contains the common length of the words in that row, and the second column gives the number of words in the row.

5	11	adret ardet dater derat detar drate rated tarde tared trade tread
5	11	airts arist astir raits sitar stair stria tarsi tiars tisar trias
5	11	akers asker eskar kaser kesar rakes reaks reask saker sekar skear
5	11	almes amsel lames leams males meals melas mesal salem samel selma
5	11	apert apter parte pater peart petar prate preta taper terap trape
5	11	arles arsle earls laers lares laser lears rales reals seral slare
5	11	armet artem marte mater merat metra ramet tamer terma trame trema
5	11	aspen napes neaps panes panse peans penas snape sneap spane spean
5	11	enols lenos losen noels noles nosel nosle olsen selon slone solen
5	11	ertop opter petro poret porte poter prote repot tepor toper trope
5	12	abest abets baste bates beast beats besat betas esbat estab sebat tabes
5	12	agron angor argon garon goran grano groan nagor orang organ rogan ronga
5	12	caret carte cater cerat certa crate creat creta ecart react recta trace
5	12	epris espri peris piers presi pries prise ripes siper speir spier spire
5	14	acost actos ascot atocs catso coast coats costa octas scoat tacos tacso tasco tosca
5	14	elaps lapse leaps lepas pales peals pelas pleas salep saple sepal slape spale speal
5	15	acers acres arces cares carse caser ceras cesar crase escar races sacre scare scrae serac
5	15	apers apres asper pares parse pears peras prase presa rapes reaps repas spaer spare spear
5	15	erste ester estre reest reset reste retes steer stere stree teers teres terse trees tsere
5	15	inest inset neist niste nites seint senit senti sient snite stein stine tiens tines tsine
5	17	astel laste lates least leats salet satle setal slate stael stale steal stela taels tales teals tesla
5	19	arest arets artes aster astre earst rates reast resat serta stare stear strae tares tarse taser tears teras treas
6	11	agrest gaster gaters graste grates greats resgat retags stager strage targes
6	11	aidmen amined daimen damine demain dieman dimane maiden mained median medina
6	11	arrest arrets astrer rarest raster raters sartre starer tarres terras treasr
6	11	capers casper crapes escarp pacers parsec recaps scarpe scrape secpar spacer
6	11	enters ernest nester renest rentes resent streen strene tenser ternes treens
6	11	nestor noster noters rontes sterno stoner strone tenors tensor toners trones
6	11	palest palets pastel peltas petals plaste plates pleats septal staple tepals
6	12	estrin inerts insert inters niters nitres sinter sterin strein strine triens trines
6	12	hepars phares phaser phrase raphes seraph shaper sharpe sherpa shrape sphaer sphear
6	13	aretes asteer easter eastre eaters reates reseat saeter seater staree steare teaser teresa
6	17	alerts alters artels estral laster lastre rastle ratels relast resalt salter slater staler stelar strale talers tarsel
7	11	angries earings erasing gainers graines reagins regains reginas searing seraing seringa
7	11	aridest asterid astride diaster disrate restiad setarid staider staired tardies tirades
7	11	atenism estamin etamins inmates inmeats insteam mainest manties samnite tameins tamines
7	11	cantier centiar ceratin certain citrean creatin cretian crinate nacrite nectria tacrine
7	11	parties pastier piaster piastre pietras pirates praties raspite spirate tapiser traipse
7	12	easting eatings gainest gainset genista ingates ingesta seating signate tangies teasing tsigane
7	12	estrous oestrus ousters sestuor sourest souters stoures toruses tousers trouses trousse tussore
7	14	anestri antsier asterin eranist nastier ratines resiant restain retains retinas retsina stainer starnie stearin
9	11	actioners anoretics atroscine certosina creations narcotise ostracine reactions secration tinoceras tricosane

David Brooks goes to church

— Probably not yet a Bonhoffer moment,
but an Exodus moment

New York Times columnist David Brooks, who, according to Wikipedia, is not religiously observant, spoke from the pulpit at the Washington National Cathedral on February 12, 2017.

He suggested that chaos in the Trump White House and the moral bankruptcy of the Trump Administration make it unlikely that President Trump will be able to serve for the duration of his first term.

Open Letter to GTS Trustees (October 21, 2015)

Be Servant Leaders

An Open Letter to the GTS Board of Trustees

William F. Hammond

San Diego

October 21, 2015

Mark 10:42-45
So Jesus called them and said to them, “You know that among the Gentiles those whom they recognize as their rulers lord it over them, and their great ones are tyrants over them. But it is not so among you; but whoever wishes to become great among you must be your servant, and whoever wishes to be first among you must be slave of all. For the Son of Man came not to be served but to serve, and to give his life a ransom for many.”

It was a dark day in 1962 when I saw my long time friend, a priest who had graduated from The General Theological Seminary, fired from his post for daring to call out the congregation on its racially segregated status. The darkness was that of institutional power subverting the Gospel in the name of the Church.

Fortunately I find most days in The Episcopal Church to be days of light.

But a year ago October 1 was another dark day when the New York Times published an article entitled “Seeking Dean's Firing, Seminary Professors End Up Jobless”.

An eight member majority of the Faculty had found that the new Dean, far from being a servant leader, was making it impossible for them to carry out their duties conscientiously. The conflict was complicated because your leaders had refused meaningful dialogue and had become a party to the conflict.

The eight members of the Faculty had written a letter to Bishop Sisk, then your Chair, beginning “We the majority of the Faculty,” saying that the hostile authoritarian posture of the Dean was making it impossible for them to continue and listing the changes they thought essential for them to be able to continue. In reply on behalf of the Board's Executive Committee, Bishop Sisk sent individual letters to the eight disingenuously dismissing them by “accepting their resignations” apparently without bothering to check whether individually any of them had intended to resign.

Several weeks later you ratified that decision with a majority vote and then insensitively and dishonestly “made it unanimous” with a second vote where nay voters were pressured into abstaining.

Another priest friend, a teacher on the staff of a seminary, said: “The Dean was mean, and the Board sacked the Faculty.” My friend along with more than 900 seminary professors, theological scholars, and academically-oriented preachers signed a petition in protest of an inappropriate abuse of institutional power by your leaders, who, with your cooperation, had recently revised the Bylaws so as to make the Seminary an earthly kingdom with the Dean as king.

A year after the event, it is clear, as many had predicted, that dismissing eight of ten members of the Faculty was a nearly fatal blow.

It is not insignificant that since the Dean arrived a dozen members of the professional staff other than Faculty members, including three librarians, have left the Seminary.

According to grapevine information, this fall there were only 14 students (though fewer than 14 full-time-equivalent students) in the entering class. Of those only six are seeking the M.Div., among whom four are postulants.¹

The latest newsletter from the Seminary indicates that giving in the past year, including giving by Board members, has greatly declined relative to the previous year.

There was a suddenly scheduled “focused visit” last December by an accreditation team from the Association of Theological Schools (ATS), which identified a number of issues: the broken state of the Faculty, confused theological vision, questions about workplace ethics, and a dysfunctional system of shared governance.

The Seminary faces a second focused visit from an ATS accreditation team before the end of the current term. As far as church observers from outside can see, there will be little progress to report on the concerns raised in the focused visit last year.

Last spring the Seminary submitted a canonically required triennial report to General Convention. That report neglected to mention the pending loss of a majority of the Faculty. In response to the inadequate report and spurred by complaints the 2015 meeting of General Convention passed Resolution D075 ordering the formation of a committee to review the relationship of The Episcopal Church with The General Theological Seminary.

Those of you who were angered and outraged by what you called the ultimatums of the Faculty were contributors to a stifling authoritarianism that has choked the Seminary nearly to death. That is not your calling nor the calling of your leaders. You are called to serve.

I think you should take heroic efforts to preserve the Close. That will take money. But that is far less important than preserving the Community whose beating heart is the Faculty. The Seminary could survive a move from the Close, but it cannot survive without a strong core Faculty of sufficient breadth. Rebuilding the core Faculty will be difficult because of the reputation you presently have in the community from which you will need to hire. You will need to dispel that.

It is time for the Board to apologize to the Church.

It is time for new leadership.

It is time for the Board to restore a proper role for the Faculty in the governance of the Seminary² — not only because that will remove one of the accreditation issues but also because leadership at the Seminary can then more closely match the Kingdom standard of servant leadership rather than the worldly standard of authoritarian leadership.

It is time to separate the positions of Dean and President, with the latter position focused primarily on fund raising (and not operating from a different city).

It is time for the Board to reconsider its size. To the extent that its present large size might have been established in the 1990s toward the end of raising funds, it now seems that end has not been met.

Finally, it is time for The Episcopal Church to find better ways to help support the seminaries that are able to survive and their students.

---

Footnotes

1. * Previous information given to me, which had been in an early draft, was five entering M.Div. enrollees with one postulant.
2. * For example, by reverting the Bylaws to the end of the year 2006.