What the &%$#? Election Musings.



In the wake of recent Electoral Events, I will be posting a series of Commentaries, probably beginning next week through early December. I truly hope to contribute to the dialogue, and invite your comments on my posts.

Unlike the Republicans during President Obama’s administration, I do not hope for and will not work for a failed Trump Presidency. I hope he jettisons all of his campaign rhetoric and does a great job, and I support him in any good things he will do.

These blogs will be for perspective, and for going forward.

Note: I have strong opinions and statements, and I back up what I say with evidence. If you share ideas, please back them up with evidence, not just feelings. I’ll outline that in my blogs. You are free to have feelings, but feelings ≠ (do not equal) evidence.

I do not believe—no, I know—that there are not two sides to every story (there are sometimes, but not always). Sometimes one side is true, and one side is false, and no amount of believing will make the other side true: e.g. Earth is round: Case Closed. Our Media must realize this and act accordingly.

God Bless America!

Future topics:

  • Theoretical Methodology. What are facts and Truth, as opposed to Truthiness?
    • A Reading List that will allow you to understand exactly what is taking place
    • The creation of Idiot America where the gut rules, and intellect is despised.
  • The context of this election against the understanding of the Eleven Nations of North America.
  • How I dealing with my stages of grief.
  • How the 2016 Election results happened.
    • How the Republican obstructionist, the Tea Party and Movement Conservatism opened the door.
    • How Trump manipulated the electorate
      • Dog Whistle arguments
      • Enlisting White Rage
      • Enlisting Misogyny
      • Rhetorical techniques
      • Who is Trump after all?
    • How the Democrats were asleep at the switch
    • The Media’s epic failure to cover this election equitably
      • What’s wrong with the media’s approach of two sides to every issue, when there are really not?
    • Extra-campaign factors
      • James Comey and the FBI: motivations
      • Wikileaks
      • Putin and Russia
      • The European phenomenon of whites-first politics (Brexit, Austria, Hungary, Finland, et al.)
  • How Movement Conservatism has bamboozled America (It’s a Con of awesome proportions, let me tell you!)
    • How they have created a state of Invincible Ignorance in almost half of our nation’s people
      • How to invade and conquer Invincible Ignorance
  • Exposing the Right-Wing efforts–successful–to suppress voting
  • The guilt of Fundamentalist and right wing Protestants, and Right-Wing Catholic Bishops in this whole mysoginistic mess as they betray Christ and drive people away from Him and toward the Right-Wing.
  • How we can neutralize the Electoral College without a Constitutional Amendment or Convention, and  enter 21st Century reality.
  • How we progressives can and must work humbly and contritely to convince America that our agenda is good for Everyone!

Steven A. Armstrong


Update: Here’s a posting I sent to friends (real friends) on Facebook:


OK my (real, not FB) friends, since you’ve all been in the discussions.  I’m not going to belabor this, since I am preparing probably a month of Blog Posts putting forth my whole argument. See the preview at www.stevenaarmstrongsf.com . Here are my basic points:


  1. I love you as my friends, and nothing will change that. Bottom line.
  2. The Donald has to prove himself to me. See #9 below for how he’s blowing it so far. The clock is ticking.
  3. I have messaged the poster of the homophobic car note and asked him to verify. He is an Episcopal Priest. I have heard back and the note is genuine. I have verified it. This happened to a real Gay Episcopal married priest, not the poster. Shame!!
  4. I’m sorry the college student lied about the Hijab. That’s wrong, and perhaps actionable. She made a very bad mistake which then plays into the other camp’s hands.
  5. Anything I post, please fact-check. I want to be accurate about facts.
  6. I can assure you—and you know me to be an honorable man—there are millions of us out here who are terrified at the promises DJT made during the Campaign. If you don’t accept that, I don’t know what to say. Talk to people outside your circle.
    1. I must be honest with you. A vote for Trump viscerally feels to me like a repudiation of everything I have worked for my entire life. Sorry, but that what it feels like to me. It doesn’t mean I don’t still like my friends who voted for Trump, but this is personal for me.
    2. We are particularly terrified at the possible effects on SCOTUS. God help us!
  7. I heard a very wise statement the other day: “Those who took Trump seriously, did not take him literally. Those who did not take him seriously took him literally.” I take the man at his word…and it scares the hell out of me.
  8. I cannot for the life of me understand how we listened to the exact same Trump rallies and speeches and tweets, and you don’t see how hate-filled his whole campaign was with Dog Whistles everywhere.
  9. World perspective: White Europeans and their descendants are trying to claw back the power they have lost since they conquered the world in the 16th-19th Centuries: see Brexit, Austria, Hungary, Finland, Russia, and now us. As a Sion of Spain, Ireland, England, Scotland, and Wales, I reject this movement: Anathema Sit!
  10. I cannot for the life of me understand how we listened to the exact same Trump rallies and speeches and tweets, and you don’t see how he either lied or just made stuff up as he went along. No drought in CA, no Climate change, and so forth and so on. No contact with Russia, when Russia affirms his staff was in contact.
  11. I cannot for the life of me understand how when you see the gang of thieves, cut-throats, white supremacists, homophobes, and cronies he is loading his transition team with, you are not as appalled as I am. My heavens, Steve Bannon, the very heart and soul and enabler of the evil Alt-Right! How can you countenance that?
    1. Doesn’t it bother you that White Supremacists and the KKK laud him? They know his true agenda.
  12. I do not care in the slightest that George Soros may be assisting the protests. The Koch Brothers do the same thing with the Tea Party, etc. I’m a Soros fan! Thank God we have some rich guys on the peoples’ side.
  13. One of the ways Trump won was by the racist voter suppression laws in many States which are tantamount to a resurrected Jim Crow. I believe that the US should issue a free National ID Card to all actual citizens, and that all citizens be compelled to vote as in Australia. They can vote a blank ballot if they want. Any one—like Fr. Deacon Paul Weyrich, with whom I served at the Altar, one of the founders of Movement Conservatism and its unholy alliance with Right-wing Christianity—who says “We don’t want everyone to vote” is un-American. I pray for his repose. He died of a terrible illness. A great Deacon, a terrible politician. We both loved trains. You see, I have been at the Heart of the Beast and understand it from the inside.
  14. Some of my basic principles:
    1. There are not two legitimate sides to every story. The media does not have to give time to “both sides” when one is demonstrably false by any valid test. For example, Pence says tobacco doesn’t cause cancer. Sorry Mike, you are just wrong. No justification for listening to you on that. The world is round: No time need be spent on alternate theories.
    2. The greatest evil threatening our nation is “Movement Conservatism,” which is a quasi-religious Cult. I’m not talking about ordinary conservative thinkers. I mean the doctrinaire cult that brought us trickle-down economics, etc., and now has control of Congress. Far more dangerous to us and to the world than Daesh or Al Qaida. And the Republican Party, once the dignified GOP of Eisenhower and Rockefeller, is its biggest victim.
      1. Example: The Left and Right are not equivalent. Liberal think-tanks were created to examine problems from a purely objective standpoint and avoid all partisanship, finding fact-based solutions. Conservative think-tanks eschew all objectivity and were created solely to press for the Movement Conservative agenda. The first is genuine, the second is partisan hogwash.
    3. The New Deal is the greatest achievement of our Nation’s social policy. Of course it had flaws and needs updating over time, but I stand by Our Father and Mother among the Saints, Franklin and Eleanor. I will fight every attempt to destroy it.
    4. The Left, and in particular, the Democratic Party, has made many mistakes. I do not claim infallibility for them at all. In particular, in this election, they did not take account of the rise of White Rage, the disaffection of many of the white middle-class, and the fickleness of minority voters. They did not effectively get out the vote.
      1. The rule by experts of Kennedy and Johnson administrations had many missteps. It’s still the right way, but we need to humbly admit it needs work.
    5. Finally, I intuit very deeply that we are in mid-1930s Germany.
      1. Trump wants to keep holding rallies! Can we say Nuremberg and Reichsparteitag?
      2. He has no concept of how a Democracy works. Ein Volk, ein Reich, ein Führer.
      3. Here are the key notes of Fascism. They sound like DJT to me:

Nationalism: Fascism seeks to solve economic, political, and social problems by achieving a millenarian national rebirth, exalting the nation or race above all else, and promoting cults of unity, strength, and purity

Totalitarianism: It opposes liberal democracy, rejects multi-party systems, and supports a one-party state, which we now have with all the power with the Republicans.

Economics: Some of this does not fit Trump. I am an honest guy. But this part does: Fascists criticized egalitarianism as preserving the weak. They instead promoted social Darwinist views.

Action: Fascism emphasizes direct action, including supporting the legitimacy of political violence, as a core part of its politics. See his rallies.

Age and gender roles: His misogyny, sexual abuse, and a retrograde gender view.

  1. My conversations with my European and other foreign friends confirm that everyone else in the world already sees this. Those who cannot see it here are simply self-deluded. I’m sorry, I must be blunt. There is no American Exceptionalism.
  2. This is my credo. I will not be silent:
                                  First they came for the Socialists, and I did not speak out—

Because I was not a Socialist.

Then they came for the Trade Unionists, and I did not speak out—

Because I was not a Trade Unionist.

Then they came for the Jews, and I did not speak out—

Because I was not a Jew.

Then they came for me—and there was no one left to speak for me. — Pastor Martin Niemöller (1892–1984)



I am doing this for you, to save all of us! You have no idea the evil that has been loosed upon us.

Enough for tonight. I will continue my battle tomorrow and the next, and the next until we have built Jerusalem in America’s green and pleasant lands.


Please God, Truly bless America, and make her The City set on a Hilltop.

My modern adaptation of the Troparion of the Holy Cross in my Byzantine Christian tradition:

“O Lord, save Thy People and Bless Thine Inheritance,
granting to Thy People Victory over any who oppose Justice!
And by the Power of Thy Cross, Preserving Thy Commonwealth!”

Here’s the video:

NB: Some of the accents are wrong in the Greek–not my doing! They forgot the rule about grave accents on the ultima before other words. Ah well!

The sacred meaning is still intact!


Irrational Numbers?


A question from a High School student whom I am tutoring in French, during his tutoring session Saturday morning, inspired today’s Posting: thank you!

First, let me apologize to the mathematicians out there. This won’t be about your irrational numbers.

Rational and Irrational Numbers in Math

Φ: the Golden Section

Φ: the Golden Section

The math whizzes in the audience would tell us, as does Kenneth Rosen in his 2007 Discrete Mathematics and its Applications, that “[i]n mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.” The set of Rational Numbers is designated by the symbol ℚ or Q. All integers are rational numbers. The decimal expression of a rational number always either ends after a finite number of digits or begins a regular series of repetition. (Thank you, Wikipedia!)

An Irrational Number, on the other hand, “is any real number that cannot be expressed as a ratio a/b, where a and b are integers and b is non-zero.” The most famous irrational is π (3.1416……forever, non-repeating), the golden ratio φ (see the Fibonacci Sequence) and the square root of two √2. The first proof of their existence is attributed to a Pythagorean (possibly Hippasus of Metapontum) Ἵππασος, Híppasos; 5th century BCE.

Real Numbers, by the way, are any number that is a quantity along a continuous line. They include Rational and Irrational Numbers, and Transcendent Numbers (π is sometimes called one of these). Surreal Numbers include the Reals, as wells as Infinite and infinitesimal Numbers.

I know very little about higher math, but the terminology and semiotics of math do fascinate me.

But we’re not talking about that today.

“Irrational Numbers” in French!

My jumping off point for another meaning for “irrational numbers” was my student’s question: “Why are the French numbers from 70-99 so strange?”

Ῥωμανία (Romania).  Copyright (c) 1996-2013 Kelley L. Ross, Ph.D. All Rights Reserved

Ῥωμανία (Romania). Copyright (c) 1996-2013 Kelley L. Ross, Ph.D. All Rights Reserved

For non-Francophones, we can quickly summarize. French number names are generally pretty regular Romance Language words, evolved from Latin. We usually think of the Romance Languages as Spanish, French, Italian and Portuguese. Some people know the fun cocktail party fact that Romanian is a Romance Language (notice the name?). But the current and usual count is 23:

Barcelona Cityscape   (c) 2009 Diliff, Wikimedia Commons.

Barcelona Cityscape (c) 2009 Diliff, Wikimedia Commons.

Whether or not you realize it, you heard quite a bit of Catalan spoken in the summer of 1992, as it was the first language for all announcements at the Barcelona Olympics. Barcelona is the capital of Catalonia (CatalanCatalunya, SpanishCataluña)

The evolution of Latin to French numbers went fairly smoothly:

Number Latin numerals Latin Name French Name
1 I ūnus un
2 II duo deux
3 III trēs trois
4 IV quattuor quatre
5 V quīnque cinq
6 VI sex six
7 VII septem sept
8 VIII octō huit
9 IX novem neuf
10 X decem dix
11 XI ūndecim onze
12 XII duodēcim douze
13 XIII trēdecim treize
14 XIV quattuordecim quatorze
15 XV quīndecim quinze
16 XVI sēdecim seize
17 XVII septendecim dix-sept
18* XVIII duodēvīgintī dix-huit
19* XIX ūndēvīgintī dix-neuf
20 XX vīgintī vingt
21 XXI vīgintī   ūnus vingt-et-un
30 XXX trīgintā trente
40 XL quadrāgintā quarante
50 L quīnquāgintā cinquante
60 LX sexāgintā soixante
70* LXX septuāgintā soixante-dix
80* LXXX octōgintā quatre-vingts
90* XC nonāgintā quatre-vingt-dix
100 C centum cent

Notice the number names *starred. In the first case, for 18 and 19, French carried on using the 10+ pattern. Latin, on the other hand, had earlier switched to its subtractive principle that we have spoken about in the past, as evidenced in Roman numerals (IV = 4, that is, 5-1, IX = 9 i.e. 10-1) and their calendar. The Latin 18 and 19 literally mean “two from twenty,” and “one from twenty.”

In the second case, for 70, 80, 90, Latin carries on logically, while French suddenly changes to an additive principle:

70   soixante-dix
71   soixante et onze
72   soixante-douze
73   soixante-treize
74   soixante-quatorze
75   soixante-quinze
76   soixante-seize
77   soixante-dix-sept
78   soixante-dix-huit
79   soixante-dix-neuf

And then from a Base-10 (decimal) system to a Base-20 (vigesimal) system:

80   quatre-vingts
81   quatre-vingt-un
82   quatre-vingt-deux
83   quatre-vingt-trois
84   quatre-vingt-quatre
85   quatre-vingt-cinq
86   quatre-vingt-six
87   quatre-vingt-sept
88   quatre-vingt-huit
89   quatre-vingt-neuf

90   quatre-vingt-dix
91   quatre-vingt-onze
92   quatre-vingt-douze
93   quatre-vingt-treize
94   quatre-vingt-quatorze
95   quatre-vingt-quinze
96   quatre-vingt-seize
97   quatre-vingt-dix-sept
98   quatre-vingt-dix-huit
99   quatre-vingt-dix-neuf

Oh là là là là là là là!! Tiens! Qu’est-ce que se passe?  Oh my, oh my! Look! What’s happening?

Decimal and Vigesimal Systems

The Virgin's Mantle--Vierge au manteau, Ville du Puy-en-Velay, 1417, Musée Croatier

The Virgin’s Mantle–Vierge au manteau, Ville du Puy-en-Velay, 1417, Musée Croatier. For background on this Iconography, read this article!

In the Middle Ages, evolving French had two numbering systems. The decimal system (by 10s) was inherited from Latin, as we have seen above:

Latin: vīgintī (20); trīgintā (30); quadrāgintā (40); quīnquāgintā (50); sexāgintā (60); septuāgintā (70); octōgintā (80); nōnāgintā (90)

French: vingt (20); trente (30); quarante (40); cinquant (50); soixante (60)

The base-20 system (vigesimal) was inherited from the Celtic languages (for example Breton, still spoken in Northwestern France). If we wrote them in modern spelling, they would be:

  • vingt (20)
  • vingt-dix (30)
  • deux-vingts (40)
  • deux-vingt-dix (50)
  • trois-vingts (60)
  • trois-vingt-dix (70)
  • quatre-vingts (80)
  • quatre-vingt-dix (90).

Celts? In France?

Yep! Actually the Celts have been just about everywhere in central to western Europe. Possibly originating in the Caucasus or Carpathian Mountains, by the 6th Century BCE had a flourishing civilization in middle Europe, and by the 5th Century BCE had gone East, West and South, most famously to Iberia, Gaul, Britain, Wales, Scotland and Eire.

Celts in Europe. For Legend, click the image. Atlas of the Celtic World, by John Haywood; London Thames & Hudson Ltd., 2001, pp.30-37 and other sources. QuartierLatin1968,The Ogre,Dbachmann. Wikimedia Commons.

Celts in Europe. For Legend, click the image. Atlas of the Celtic World, by John Haywood; London Thames & Hudson Ltd., 2001, pp.30-37 and other sources. QuartierLatin1968,The Ogre,Dbachmann. Wikimedia Commons.

That is, they journeyed as far west as they could. St. Brendan may have made it to the New World (several scholars believe his “Voyage” has a real voyage behind its colorful descriptions), but the rest of the Celts had to wait until the re-discovery of the New World by Columbus (on this very weekend, 521 years ago!!) to immigrate to Boston, New York, Chicago, Toronto, San Francisco and other places and begin running them!

United Irish Cultural Center, San Francisco.

United Irish Cultural Center, San Francisco.

The Celts were a force to be reckoned with in Gaul. Just remember that the Romans called them “Gauls,” in France and that they gave Julius Caesar a lot of trouble. Can we say, Vercingetorix ?

Commentarii de Bello Gallico, an account written by Julius Caesar about his nine years of war in Gaul.

Commentarii de Bello Gallico, an account written by Julius Caesar about his nine years of war in Gaul.

Today, there are six surviving Celtic languages. “Speakers” indicates Native Speakers + those with some skills in the language.

  • Galige (Irish) – ca. 1,888,000 speakers – Eire, UK, US
  • Gàidhlig (Scotts) – ca. 92,000 speakers – Scotland & Cape Breton Island (NS, Canada)
  • Cymraeg (Welsh) – ca. 722,000 speakers – Wales, England, Chubut Province Argentina, US, Canada
  • Brezhoneg (Breton) – ca. 356,000 speakers – Brittany, France
  • Kernewek (Cornish) – ca. 3,000 – Cornwall, England
  • Gaelg (Manx) – ca. 1,823 speakers – The Isle of Man (British Crown Dependency)
Celtic Nations today. QuartierLatin1968. One note: The Orkneys and Shetlands should not be shaded as part of Scotland - they were formerly Pict and latterly Norse, but never Celtic.

Celtic Nations today. QuartierLatin1968. One note: The Orkneys and Shetlands should not be shaded as part of Scotland – they were formerly Pict and latterly Norse, but never Celtic.

Wikipedia also correctly reports three “Mixed Languages” influenced by Celtic:

Proto-Celtic is the common ancestor, and comes is part of the Indo-European family of languages. Many other Celtic languages are now extinct, including those spoken in Spain and Portugal.

Vigesimal Celtic Numbering

As it turns out, some of the Celtic Languages use a vigesimal system, base-20, including today, Welsh, Irish and Scots:

  • Welsh: Deugain = 2 times 20 i.e. 40, trigain = 3 times 20 i.e. 60.
  • Irish: 30 = fiche a deich (formerly fiche agus deich), i.e. twenty and ten. 40 = dhá fhichead, i.e. two twenties (still in the decimal system as daichead), trí fichid = 60 (three twenties), ceithre fhichid = 80 (four twenties).
  • Scots: deich ar fhichead = 30 (ten over twenty), dà fhichead = 40 (two twenties), dà fhichead ‘s a deich = 50 (two twenty and ten), trì fichead = 60 (three twenties), up to naoidh fichead = 180 (nine twenties).
Forever 21 Store, San Francisco

Forever 21 Store, San Francisco

Decimal number names are now being taught in the schools in these Countries, but the old names also persist.

Vigesimal systems are fairly wide-spread in human cultures. One of the best known (thanks to the 2012 rumors) is Mayan. In many languages, the name for 20 is “special,” not related to the normal naming convention. Even in Latin, viginti is different. Logically, one would have expected duginti. Greek also has a “special” 20, and we can also see some parallels and variations in the various stages of Greek for all the numbers.

Proto-Indo-European 20 has been variously reconstructed as *wīḱm̥t-; originally perhaps *widḱomt- or *duidḱmti. The first two show where the Latin viginti comes from. The English twenty is cognate with the German zwanzig.

The Celtic 20s in French Numbers

In the 17th century, when the French Academy began to try to standardize the language, they chose the most common usage of

L'Institut de France, including L'Académie française. Nitot, Wikimedia Commons.

L’Institut de France, including L’Académie française. Nitot, Wikimedia Commons.

the best authors of the day for these numbers, which turned out to be decimal up to 60, and then vigesimal from 70-99.

In BelgiumSwitzerland, the Democratic Republic of the CongoRwanda, the Aosta Valley and the Channel Islands, the decimal system is used in French for 70-99, and so you get archaisms (old usages) such as septante (70); octante (80), or huitante (80); nonante (90) or neuvante (90).

The only known photograph of President Lincoln giving his Gettysburg address on November 19, 1863. Library of Congress.

The only known photograph of President Lincoln giving his Gettysburg address on November 19, 1863. Library of Congress.

Believe it or not, we have a similar usage in English. Remember how Lincoln’s Gettysburg address begins “Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal…”? That means 4×20 + 7 = 87 years ago. “Score” was our word for multiples of Twenty. Two Score = 40. Two Score and Ten = 50. This is now archaic in English, but we still see it in historical documents.

 Illustration from Sing a Song for Sixpence (1880) by Randolph Caldecott (d. 1886)

Illustration from Sing a Song for Sixpence (1880) by Randolph Caldecott (d. 1886)

Four and Twenty Blackbirds

While we’re on the subject of language about numbers, how about the old Nursery Rhyme:

Sing a song of sixpence,

A pocket full of rye.

Four and twenty blackbirds,

Baked in a pie.

Even though we normally say Twenty-Four, we can understand what “Four and Twenty” means. It is an echo of our language’s Germanic roots. As speakers and students of modern German know, counting in German is like English, until you get to 21:

eins 1
zwei 2
drei 3
vier 4
fünf 5
sechs 6
sieben 7
acht 8
neun 9
zehn 10
elf 11
zwölf 12
dreizehn 13
vierzehn 14
fünfzehn 15
sechzehn 16
siebzehn 17
achtzehn 18
neunzehn 19
zwanzig 20

Notice now that we have the “Four and Twenty Blackbirds” approach. The ones number is said before the tens number, linked by “und” (and).

21 to 100
einundzwanzig 21
zweiundzwanzig 22
dreiundzwanzig 23
vierundzwanzig 24
fünfundzwanzig 25
sechsundzwanzig 26
siebenundzwanzig 27
achtundzwanzig 28
neunundzwanzig 29
dreißig 30
einunddreißig 31
vierzig 40
einundvierzig 41
fünfzig 50
sechzig 60
siebzig 70
achtzig 80
neunzig 90
hundert 100

German does get a little carried away with its word building procedures. For example, the number 999,999,999 is


neunhundertneunundneunzig  (there is no break in the word, it just won’t fit on the screen!)

Image from

Image from “A Tramp Abroad” (1880) by Mark Twain.

(Kudos to paradoxa4 on the wordreference.com forum for correctly parsing this!) Mark Twain parodied German’s idiosyncracies in his essay “The Awful German Language” in 1880’s A Tramp Abroad.

I have to say that elf (11) and zwölf (12) are my two favorite German numbers, they just sound so cool!

In Austria and Bavaria, zwei becomes zwo, and zwanzig becomes zwozig. Other German speakers will sometimes use these variants to distinguish zwei from drei. In the southern German variant, ja (ya – yes) becomes jo (yo – yes). So Rocky is saying, “Jo, Adrian,” “Yes, Adrian.” (!)

Our Cardinal Numbers

And how about our names for cardinal numbers? Coming from Old English, our number names are from the Germanic family, from one to 999,999 (Nine hundred ninety-nine thousand, nine hundred (and) ninety-nine). These were so commonly used that we kept them, even after the Norman Conquest. The Latin 1,000,000 is attested at decies centena milia, but how many times did the ancient world have to count that high?

Googol. Yot, Hidro, Wikimedia Commons.

Googol. Yot, Hidro, Wikimedia Commons.

In today’s world, however, we need much larger numbers. The “Short Scale” is used exclusively in the U.S., and increasingly in British English:

  • million
  • billion
  • trillion
  • quadrillion
  • quintillion
  • sextillion
  • septillion
  • octillion
  • nonillion

What do you notice? Through Old French, from Italian, we have adopted the Latin names, augmenting them with the suffix –on(e).

Higher still, the most common counting scheme is given by Robert Munafo (in some very interesting pages! ) as

N N in Latin 3,18 103N+3 name for 103N+3
10 decem 1033 decillion
11 undecim 1036 undecillion
12 duodecim 1039 duodecillion
13 tredecim 1042 tredecillion
14 quattuordecim 1045 quattuordecillion
15 quindecim 1048 quindecillion, quinquadecillion
16 se(x)decim 1051 sexdecillion, sedecillion
17 septemdecim 1054 septendecillion
18 duodeviginti24 1057 octodecillion
19 undeviginti24 1060 novemdecillion, novendecillion
20 viginti 1063 vigintillion
10100 “googol” = ten duotrigintillion
100 centum 10303 centillion
1000 mille 103003 millillion
1000000 decies centena milia 103000003 milli-millillion
1010 to the 100 “googolplex” (i.e. 10 to a googol.

As Munafo explains, Googol and Googolplex were invented just for the expression of these huge numbers:

“In 1938, mathematician Edward Kasner asked his nephew Milton Sirotta (who was 9 years old at the time) to invent a name for the number 1 with a hundred zeros written after it, and the nephew chose the name googol. As Kasner’s telling of the story goes, ‘He was very certain that this number was not infinite, and therefore equally certain that it had to have a name.’

“The name googolplex was invented at the same time, and also by Milton Sirotta if we trust the grammatical implication of the wording in [his account]. An article by Carl Bialik indicates that relatives and ‘family archives’ point to the invention of these words being in the 1920’s, and gives more details.

“Regarding its definition, Kasner wrote: ‘It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. […] It would never do to have [contemporary boxing champion Primo] Carnera [be] a better mathematician than Dr. Einstein, simply because he had more endurance. [and so it was decided that googolplex should be] a specific finite number, with so many zeros after the 1 that the number of zeros is a googol.’

“A generation later, googol had been popularized enough to be able to reach audiences of the widely-distributed Peanuts comic strip in which Schroeder estimates Lucy’s odds of eventually marrying him as ‘Oh, I’d say about ‘googol’ to one’:”

Schroeder and Lucy discuss googol.

Schroeder and Lucy discuss googol. Charles Schultz.

If you love language about numbers, please treat yourself to Robert Munafo’s pages (© 1996-2013 Robert P. Munafo) !

Scientists and Mathematicians usually just use the exponent notation system (10100). But the words are fun to play with!

Illustration, anonyme Chronik, „Von der Schöpfung der Welt bis 1384 / From the Creation of the World until 1384“

Illustration, anonyme Chronik, „Von der Schöpfung der Welt bis 1384 / From the Creation of the World until 1384“

I should note that this post comes on the day of perhaps the most infamous number in the western world, 13! It was not a happy day in 1307: On Friday, 13 October, King Philip IV (the Fair) of France rounded up the Knights Templar in his realm, and arrested them on trumped-up charges of Heresy. They were subsequently tortured into “confessing,” or died. Pope Clement V later disbanded the Order. Philip’s motives were primarily economic, as he wanted their “treasure” which vanished with their persecution.

Today, with the recent discovery and publication of the Chinon Parchment by Barbara Frale, which details Clement V’s exoneration of the Templar leadership and attempts to thwart Philip’s villainy, the Roman Church admits that the arrest, murder and disbanding of the Templars was a mistake.

We usually pat ourselves on the back and think how lucky we are not to live in those benighted times. A quick look around the world, however, and even in our own country, will show that people are still persecuted for their differences in religious belief, and religion is still used as a mask for economic and political oppression. O Tempora! O Mores!

We’ve taken quite a journey around the world of numbers and the words that represent them. I hope it has been fun! See you next time!

Steven A. Armstrong
Tutor, Editor, Consultant

Enough is Enough!


US Capitol


The manufactured crisis of Governmental Shutdown has pushed me over the line. I have to come out of the Political Closet. Enough is enough.

English: George Bernard Shaw, Nobel laureate i...

George Bernard Shaw, Nobel laureate in Literature 1925. (Photo credit: Wikipedia)

Enough, by the way, is a prime example of our twisted legacy of historic spellings in English. George Bernard Shaw is credited with the quip that Fish should be spelled Ghoti…“gh” from enough, “o” from women, and “ti” from nation. Historical spellings plague both French and English, and to some extent, German. Wikipedia has excellent sections on English spelling peculiarities, French Orthography, and German Orthography.

I apologize in advance if this edition seems overly political or partisan. One of these days, I’ll do what I hope will be an equally biting Blog entry on “When Liberals Go Bad.” I have plenty of ammunition for that too. But the current state of affairs leads me in another direction today.

Elephant and donkey in Luna Park, Coney Island, N.Y., prior to race to Washington to decide the bet of Joseph Cannon and Luna Park creator Frederic Thompson. 1911

Elephant and donkey in Luna Park, Coney Island, N.Y., prior to race to Washington to decide the bet of Joseph Cannon and Luna Park creator Frederic Thompson. 1911.

The Two Parties

OK, back to the topic. A friend of mine, Fr. Tom Allender, S.J. and I came up with a pithy way of talking about our current U.S. political landscape:

“We have two parties: The Stupid Party and The Evil Party.” Thanks Tom!

As a life-long Democrat, I sadly concede that my party is the Stupid Party. We had full control of the Government at the beginning of the Obama Administration and couldn’t get much done.  The old joke is unfortunately true:

“Do you belong to an Organized Political Party?”

“No. I’m a Democrat.”

Contemporary Republicans

Kareem Abdul-Jabbar (center), Stephen Colbert to the left and Jon Stewart to the right.

Kareem Abdul-Jabbar (center), Stephen Colbert to the left and Jon Stewart to the right.

But the other side of the Aisle has now become The Evil Party. Taken over by religious fanatics and the Astroturf “Tea Partiers” (The Tea Party is a fake creation of the Koch Brothers and their allies), the GOP now just lies and obstructs any progress at all. Its media voice is Roger Ailes’ (mis)led Fox News, who wouldn’t know a fact if they stumbled over one in the dark. Fox “newscasts” are simply one long propaganda stream without any attempt at fairness or balance. It is such a parody of itself that only a comedian as talented as Stephen Colbert can mock them, while his colleague Jon Stewart holds their feet (as well as CNN’s, MSNBC’s and other Media’s feet) to the fire.

This has not always been true. When I was growing up, The Grand Old Party was a dignified group of people whom I didn’t

President Eisenhower

President Eisenhower

particularly agree with, but they were (in the language of the day) Statesmen. Pres. Eisenhower, Vice-President Nelson Rockefeller, Pres. Ford are good examples. Even (gasp!) Pres. Nixon was a remarkably progressive in social reform and international politics. He just had a deadly problem of his personal morality and honesty that doomed his administration. Sen. Barry Goldwater was a fine Senator for my home state of Arizona, although I didn’t want to see him President.

Beginning with the administration of Pres. Reagan, however, things shifted, and the Neocons and Religious Right took over. Chaney, Rumsfeld, Gingrich, and their ilk took over behind the scenes, and eventually, under Pres. G.W. Bush and since, have led the party.  There are some Republicans who hearken back to the better days of the GOP, such as Gov. Chris Christie.

The Shutdown of 2013

The current Republican Shutdown of the National Government and the statements of Speaker of the House John Boehner (R-OH) and Sen. Ted Cruz (R-TX) are prime examples of the bald-face lying—or completely being out-of-touch and believing one’s own fictions—that now typify the current Republicans.

Now let me be fair. Democratic Politicians lie when it suits them, and spin things to their advantage. They just aren’t very good at it, being generally liberal progressives, since it makes them feel (and look) guilty. The “hand in the cookie-jar” look. Just think “Gov. Rod Blagojevich”!

The Shutdown-Anti-Affordable Healthcare talk of Congressional Republicans is a perfect example for us to subject to submit to rhetorical analysis. Cruz is backed in this effort by the rather Conservative Heritage Foundation.

Fr. Protodeacon Paul Weyrich

Fr. Protodeacon Paul Weyrich

As a side note, I was a colleague of Heritage and Free Congress founder Fr. Protodeacon Paul Weyrich who was a good man, and a fellow supporter of Amtrak. I just disagreed very very much, respectfully, with his politics and social views. I served the Divine Liturgy with him in the Holy Place, and trust that he is with God now.

This highlights one of the most important things missing from the Right’s verbage. They have lost the concept of “the Loyal Opposition.” Fr. Dn. Paul (of Eternal Memory) and I are both loyal Americans with very different viewpoints. In the current hyper-partisanship of the Republicans, if you criticized Pres. G.W. Bush, you were being disloyal to the Country. Today, if you criticize Pres. Obama, you are a patriot. Point-of-View has become the absolute standard instead of a reasoned, balanced debate among loyal citizens. As we will see later, this must change.

The “Argument”

The Anti-Affordable Healthcare talk goes like this: “Obama care will hurt Americans. They don’t understand it and don’t want it. This was forced on the American People by the President and the Democrats.”

The reality: The Affordable Health-Care Act is not perfect, and like so much of government, is confusing. Some of its inadequacies stem from the opposition of Republicans during its creation. Nevertheless, it is a very long-overdue reform of a health-care system that is incredibly out of line with those in most Western Industrialized Nations. As of 10-2-13, the second day site was open, 6.1 million people have visited the registration site, overwhelming the resources of the website. We want this. We need this.

What Boehner, Cruz and other nay-sayers are doing is like this:



You are standing with a friend next to a civic auditorium, the (former HP Pavilion) SAP Center in San Jose where a concert by Justin Timberlake is about to take place. Fans of every age, gender and ethnicity are lined up by the thousands up and down Santa Clara Street and into the Parking Lot waiting to get in. CalTrains continue to disgorge more attendees every few minutes. The marquee flashes “sold out.”

You turn to your friend and say, “Man, nobody listens to Justin Timberlake any more. Who would go to a concert of his?”

Your friend points to the crowd, a puzzled look on his face.

You reply, “Oh, they don’t count, those kind of people have no taste! I mean real, ordinary people.”

QED (quod erat demonstrandum=that which was to be demonstrated)

This is what Boehner, Cruz and their colleagues are doing, ignoring the clear facts in front of their faces, and instead, following their own ideology.

Rhetorical Analysis

Let’s apply some rhetorical analysis.

First, they have demonized the Affordable Health Care act by calling it exclusively “Obamacare,” (just as Christians “demonized”

Winged snake-tailed daimon in an animal frieze, gecko on the right near the handle. Oversized Corinthian kylix, ca. 620 BCE.

Winged snake-tailed daimon in an animal frieze, gecko on the right near the handle. Oversized Corinthian kylix, ca. 620 BCE.

the word δαίμων (daimon), originally benevolent nature spirits in Greek Religion). This implies that this health-care legislation is something dreamed up by, and imposed by, one man, instead of the result of decades of effort by lots of people. Hyper-partisans are very good at this tactic, and media are like sheep in using the handy terms. They are attractive because they are pithy, catchy and convenient, while “Affordable Health Care Act” is none of these, being government-speak.

Next, their propaganda relies on fear, and misinformation. For decades, since Pres. Reagan, Republicans have been scaring the daylights out of middle America (what we now call the Red Areas) and gaining power by doing it. When the big bogeyman of Communism fell, it became liberals, latte-drinking, yogurt-eating urbanites, feminists, and LGBT people, immigrants, and hybrid-drivers that the great middle was told to fear.

Let’s be honest: On the other side, urban progressives often (secretly) look down on their fellow Americans from the Red Areas as benighted, ignorant hicks.

I say “Red Areas,” by the way, instead of Red States, because the reality is far more complex. If we examine a map of voting by counties, we see the real divide.

2008 Counties

Mark Newman at The University of Michigan has done an excellent analysis of the voting patters in the 2008 Presidential Election. What we see is generally a divide between Urban America and Rural America. The little blue spots are areas of higher population density. This is a bit oversimplified as there are some regional divisions as well, but I believe we see the problem.

A note is due on how easily we can debunk the partisan stereotypes. A friend had an old stockbroker in Oklahoma who was making fun of those who drive Hybrids. “Can’t see one of those puny hybrids having enough power to be of use on a farm!” he quipped.

My friend, whose family includes trainmen like mine, held back from reminding him that railroad trains are hybrid diesel electric. And Superman is the only one more powerful than a locomotive!

That’s how silly this all is, funny, if it weren’t destroying us.

Bangkok during the Riots

Bangkok during the Riots

The deep roots of the fear-mongering can be summed up as “Fear those who are different from you.” This is the tribal mentality that fuels the Balkans conflicts, the massacres in Africa, the civil unrest in Thailand, and so many other tragedies. Ideologues routinely use this strategy to divide and conquer.

When I was an undergraduate at Yale, the New York Times did an investigative report on the Boston Bussing controversies, which set poor blacks and poor Irish at one another’s throats. As it turns out, this manufactured conflict was created by the wealthy “Boston Brahmans” to keep these potential partners in reform from making common cause in reform and civic progress. To this day, an African-American takes his life in his hands if he walks into Irish Southie, and the reverse is somewhat true of Roxbury.

Invincible Ignorance

Finally, the Congressional Republicans are practicing the “Invincible Ignorance Fallacy.” This is a state of mind that is ideologically based, refusing to admit of the possibility of any evidence opposing your position, and deliberately refuses to listen to any facts and evidence that would counter your argument. It is, in fact, a sham argument, since real argument necessitates facts and evidence, along with reasoning. They are either knowingly or unknowingly caught in this Fallacy.

Ultra-Extreme Creationists (not the Intelligent Designers) follow this approach. The most extreme think this way:

The Devil planting Fossils to fool us!

The Devil planting Fossils to fool us!

God made the world exactly the way it says in the “Christian” (actually Jewish) Bible. It was created about 4004 BC (sic).

  • What about the fossil record, the geological record, the archeological record, and evolutionary theory that all show a much different picture?

The Devil planted all that evidence to tempt us to disbelieve the Bible, which is literally inerrant.

(Note: the vast majority of Christian Churches have never taught inerrancy on the literal level of the Judeo-Christian Scriptures. We will do another Blog post on the uses and interpretation of Sacred Scriptures, featuring the Integumentum: the Four Levels of Meaning!)

You probably think I’m joking about the devil and dinosaur bones. Try Googling “Devil plants fossils.” You’ll be amazed. This is the same Invincible Ignorance Fallacy that the Congressional GOP is using on Affordable Health Care and other issues (think Gun Control—not even shooting up a bunch of little kids could get through to them). This is also what fuels hate groups like the Westboro “Baptist Church.”

What Can We Do?

Pope Francis and Patriarch Bartholomew

Pope Francis and Patriarch Bartholomew

Pope Francis, God bless him, is working to bring his Church back into balance, and restore the spirit of Vatican II. He has the charism of both St. Ignatius Loyola and St. Francis of Assisi to inspire his Christianity. We have to restore balance in our Country, too, using the tools we have at hand.

Papa Francisco

Papa Francisco

So what are we going to do about this state of affairs?

  1. In the short-run, Boehner, Cruz, et al. just need to give up, and end the shutdown and co-operate to raise the debt limit.
  2. Our national conversation must restore the concept of The Loyal Opposition.
  3. We have to reach out across the Urban-Rural and regional divides to recognize that we are all Americans, and we are this together.
  4. We must sadly give up on trying to convince the Invincibly Ignorant. Let’s concentrate on building a reasonable majority coalition.

Now, we are going to enter my own personal fantasyland. If we really, really want to restore balance to our national political life, here’s my wish list. I know it’s “out there,” but keep an open mind.

Money Out of Politics

  1. Take all money out of Politics.
    1. No private or corporate campaign spending or donations. All elections, at every level, are publically financed. You can’t use your own money to run for office.
    2. Outlaw PACs and the like.
    3. All broadcast time for campaigns is free, donated by the Networks. We do own the airwaves, you know. A reasonable equation can be worked out for how much support you need to get TV/radio time.
    4. Restrict Lobbying to merely sharing your opinion/position with elected officials. No goods/services/perks may be given, not even buying a Congress member a cup of coffee. No Gifts. No writing bills for Congress to use. No junkets. None.
    5. Limit Campaigns to six weeks or maybe two months. No campaigning allowed before the kickoff date.
    6. Voting on Saturday and Sunday to maximize participation. All voting machines must either use a scanned paper ballot or issue a printed receipt showing the vote, with two copies, one for the voter and one for the polling place. A paper re-count can always be done. No computer-only paperless voting, as this is too easy to manipulate.
    7. Non-Partisanship strictly enforced on Non-Profits, e.g. Churches. They can advocate for positions, but absolutely for no candidates or parties. Tax Exemption of the Parish/Congregation or offending body will be removed on the first offense for a reasonable amount of time.
    8. Once this is done and in place, we can then proceed to remove Personhood from Corporations by a Constitutional Amendment. Corporate officials are now personally liable for the decisions they make, and their consequences. If I drive drunk and kill someone, I am found guilty of vehicular manslaughter. If a corporate official signs off on a product/policy that he/she knows is demonstrably dangerous to life (as in substandard car part), and someone dies as a direct result, he or she should be tried for—say—negligent homicide. Let’s get serious about personal responsibility. What do you say, William Bennett? Put that in your Book of Virtues!
      1. Corporate Secrecy is limited to proprietary secrets that are necessary to protect their copyrights, patents, etc. All other materials (emails, audits, board meeting minutes, etc.), are open to Public scrutiny. A Court, using in camera sessions, can even scrutinize the proprietary secrets if needed for a criminal or civil case.
      2. Think of how this will change our Financial Institutions,
        Big Pharma, Big Tobacco (!), et al.
President Teddy Roosevelt

President Teddy Roosevelt

We have a great deal to accomplish, and we are a great country and a great people. We have to tackle

Our Mother and Father among the Saints, Franklin and Eleanor (Thank you AZ Club and Uncle Dan!)

Our Mother and Father among the Saints, Franklin and Eleanor (Thank you AZ Club and Uncle Dan!)

poverty, homelessness, a crumbling infrastructure, millions who need meaningful work, sustainable and renewable energy independence, continuing racism and classism, and so forth. We have to get past this partisan blockade and move forward together.

I think this is perhaps our last chance to break the power of the corporations and big money at this stage in history. We did this at the beginning of the 20th century. We need to return to updated versions of the Square Deal of President Teddy Roosevelt and the New Deal of Pres. Franklin Delano Roosevelt and Eleanor Roosevelt. Neither President Roosevelt was perfect (Teddy held some pretty offensive racial opinions, for example), but their economics were pretty good.

My Inspiration

The Three Satellites of the Holy Trinity: Sts. Basil the Great, John Chrysostom and Gregory the Theologian.

The Three Satellites of the Holy Trinity: Sts. Basil the Great, John Chrysostom and Gregory the Theologian.

What is my inspiration for my positions? Well, first, my Eastern Christianity. Christianity which is always socially and economically progressive. Many Church Fathers, such as St. Basil the Great, St. John Chrysostom, St. Gregory the Theologian (Nazianzen), and St. Gregory of Nyssa were economically progressive. St. Basil taught that if you have two cloaks in your closet, you have stolen one from the poor.

Tri Sviatitelia (Russian: Три Святителя meaning the Three Holy Satellites) was a pre-dreadnought battleship built for the Imperial Russian Navy during the 1890s.

Tri Sviatitelia (Russian: Три Святителя meaning the Three Holy Satellites) was a pre-dreadnought battleship built for the Imperial Russian Navy during the 1890s.

Entrepreneurship in Byzantine Christian thought is the same as a talent for metalworking, or any other skill. An Entrepreneur has been given that skill by God:

  1. To Provide honorable employment with a living wage
  2. To Produce good and useful products and/or services at a reasonable and fair price

If he or she makes a tidy sum doing this, that is fine, as long as he/she also is very generous in Philanthropia. God is Ὁ Φιλάνθρωπος, The Philanthrōpos, The Lover of Humanity par excellence. We must image God in this quality.

Roerich Museum, New York (1931); Louis & Nettie Horch col., New York (1935); Katherine Campbell col., USA (1940s); Nicholas Roerich Museum (on loan since 1949; acquisition, 1963).  Пантелеймон Целитель.

St. Panteleimon. Roerich Museum, New York (1931); Louis & Nettie Horch col., New York (1935); Katherine Campbell col., USA (1940s); Nicholas Roerich Museum (on loan since 1949; acquisition, 1963). Пантелеймон Целитель.

One of the concrete ways in which the Christian Roman Empire did this was in its health-care system in the capital of Constantinople. By the 6th century reign of St. Justinian as Emperor, the Health Center there gave the best medical care available in Europe until the 18th century, and this continued throughout the life of the Empire, until its fall in 1453. Health care was free, and open to all. Doctors and Nurses (we have copies of their notes for rounds) worked at the Center for 6 months of the year, and there were no fees paid by the patients. During the off 6 months, medical professionals could conduct their private practice for fees.

The system was supported by the Imperial Family,

St. Luka

St. Luka

wealthy Romans, and the Church. Parenthetically, there is a class of Saints in Eastern Christianity called “The Holy Unmercenary Physicians,” who healed miraculously without charge. These were the Ἅγιοι Ανάργυροι, Hagioi Anárgyroi, such as St. Panteleimon, Sts. Cosmas and Damian, and a modern Saint, Валенти́н Фе́ликсович Во́йно-Ясене́цкий, Valentin Felixovich Voyno-Yasenetsky, later Archbishop Luka (Luke), Архиепи́скоп Лука́ (1877-1961). An outstanding surgeon, he served as Archbishop of Simferopol and of the Crimea.

Fr. David serving Divine Liturgy at Emmaus House

Fr. David serving Divine Liturgy at Emmaus House

A friend and colleague of mine, Melkite Greek Catholic priest Fr. David Kirk edited a little volume called Quotations from Chairman Jesus, demonstrating Christ’s love of the poor and revolutionary spirit. He is one of many progressive Christians, like Dorothy Day, Ekaterina Fyodorovna Kolyschkine (Екатерина Фёдоровна Колышкина) Catherine Doherty, Archbishop Joseph Raya, and Jim Wallis.

Another inspiration for my views and approaches is the Rosicrucian Utopia, probably

Rosicrucian Cultural Center of NYC, Harlem

Rosicrucian Cultural Center of NYC, Harlem

best known through the vision of the Federation in Gene Rodenberry’s Star Trek. One can learn more about the Rosicrucian Utopia in the 4th Rosicrucian Manifesto, Positio Fraternitatis (2000).

Let’s get to work. We have a lot to do!

Thank you for listening!

Steven A. Armstrong
Tutoring, Editing and Consulting

Dorothy Day

Dorothy Day

Catherine Doherty

Catherine Doherty

Archbishop Raya

Jim Wallis
Jim Wallis

Gloriously Wacky English–Part 4: Grammar 2: Parts of Speech

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To continue our discussion of the peculiarities of English, I thought it might be good to look at our “Parts of Speech.”

Parts of Speech in World Languages

The rather odd term Part of Speech is the common name for a word class, a lexical class, or a lexical category. It divides our vocabulary up into groups of words that have the same function in syntax (Greek: σύνταξις “arrangement”). Syntax includes the rules, norms, etc., for the arrangement of words to form sentences in a language.

Virtually all human languages have nouns and verbs, but there are many variations after that. For example, Japanese has three classes of adjectives, which are thought of as separate parts of speech. Japanese, Korean and Chinese have Nominal Classifiers.

Noun Classifiers

Noun Classifiers are words that indicate what kind of thing is being referred to. Here are some examples from Wikipedia of Mandarin Chinese classifiers:

  • 3-ge xuesheng (三個學生) lit. “3 human-classifier of student” — 3 students
  • 3-ke shu (三棵樹) lit. “3 tree-classifier of tree” — 3 trees
  • 3-zhi niao (三隻鳥) lit. “3 bird-classifier of bird” — 3 birds
  • 3-tiao he (三條河) lit. “3 long-wavy-shape of river” — 3 rivers
Pien Wen-chi, Three Friends and A Hundred Birds

Pien Wen-chi, Three Friends and A Hundred Birds (1413)

English does not have this part of speech, but there are a few nouns that fill this function in specialized cases:

  • Ranchers say: “Three head of cattle”  (head = Cattle classifier)
  • Florists say:  “Five stem of roses”  (stem = Rose classifier)
  • We all say:  “Three pair(s) of pants/socks/gloves/shorts/glasses/ear-muffs.” (pair = apparel classifier for items that come in twos for our feet, legs, hands, arms, eyes, ears–everything we have two of). It is also used for other things that come in pairs: scissors, chopsticks, etc.
Six Head of Cattle

Six Head of Cattle

French is similar in this regard:

  • Une tête de bétail (= a head of cattle)
  • Une paire de lunettes/jumelles/gants/chaussures/baguettes (a pair of glasses/binoculars/gloves/shoes/chopsticks…things that come in pairs)
  • Une botte de radis (= a boot) of radishes)
  • Un pied de roses (a foot [for trees/berries] of roses)

Related to this is our rather lengthy (and sometimes humorous) list of Collective Nouns for all kinds of things. The most common are  “a brood of chickens,” “a flock of birds,” “a herd of sheep/cattle, etc.” These are actually rudimentary Noun Classes rather than Classifiers.

There are also many more colorful and fanciful ones which have various origins, sometimes alliterative. These originate in the Mediaeval English hunting tradition, called venery. We have:

  • A Congregation of Alligators
  • An Army of Ants
  • A Troop of Apes
  • A Cloud of Bats
  • A Bench of Bishops — I didn’t know they hunted Bishops…well I guess the Romans before Constantine did, Henry VIII did, and the Communists did, tragically.
  • A Hastiness of Cooks — Gordon Ramsey hunts cooks!
  • A Murder of Crows
  • A Gaggle of Geese
  • An Exaltation of Larks
  • A Pod of Pelicans
  • A Nest of Vipers
  • A Pack of Wolves
  • And so forth…
Tree With Crows

Caspar David Friedrich (1774–1840), Tree With Crows

The system has been expanded several times in history, notably:

Lists of Parts of Speech

The first mention of Parts of Speech that we know of comes from the work of the Sanskrit grammarian Yāska in the 5th-6th Centuries BCE. He defined four classes of words:

  • Nouns
  • Verbs
  • Words Expressing the relationships between nouns and verbs
  • Words qualifying nouns or verbs

Plato refers only to nouns and verbs in the Cratylus, and Aristotle adds Conjunctions, which included our conjunctions, pronouns and the article–Greek has only one. Dionysius Thrax’s work, Art of Grammar (Τέχνη Γραμματική) (2nd Century BCE) introduces 8 categories:

  • Noun
  • Verb
  • Participle (Verbal Nouns/Adjectives)
  • Interjection
  • Pronoun
  • Preposition
  • Adverb
  • Conjunction

Surprisingly to us today, the Adjective was not recognized as a separate part of speech until Nicolas Beauzée did so in 1767 in his Grammaire générale, ou exposition raisonnée des éléments nécessaires du langage (General Grammar, or a Rational Explanation of the Necessary Elements of Language).

Grammar School, Milpitas CA

Grammar School, Milpitas CA

The traditional list of English parts of speech follows the European model, with the 8 parts of speech we all learned in school:

  • Noun
  • Pronoun
  • Adjective (includes Articles)
  • Verb
  • Adverb
  • Preposition
  • Conjunction
  • Interjection/Exclamation

How the Parts of Speech Are Effective…

We also teach Latin, Greek and many other languages using the same categories. They work well for Latin and Greek for example. In Latin, a noun is a noun is a noun. The same word is never a verb. The root of the word (its meaning) can be transformed by inflections into other parts of speech, but they are distinct. Let’s look at Lux “light.”

If you recall one of our previous discussions, Lux comes from the Proto-Indo-European root *lewk- “white, light, bright.” Lux is always a noun. The related verb is luceo “to shine.” The derived adjective is lūcidus, “clear, bright, shining.” In other words, the root is turned into different parts of speech by modifying its form. In Latin, only adjectives can be used as another part of speech, when they are employed as Substantives:  Boni:  “the good men,” “Bonae: “the good women,” Bona: “the good things” (nominative plural M/F/N). Latin can do this because of the grammatical categories of gender and number.

…And Not So Effective!

Not so in English! Let’s take the word “Baby.” We would usually think of this as a noun:  “Take care of the Baby.” But it can also exercise the function of an adjective, with no change in form:  “Baby Carriage.” It can also be a verb:  “Don’t Baby me!”  This could mean, “Don’t treat me like a Baby,” or “Don’t say ‘Baby…’ to me as if everything is OK!” The latter would be more clearly stated in writing as “Don’t ‘baby’ me!” In speech, the first meaning would be indicated by normal inflection of the voice for “Baby” in the verb function and position. The second would probably be indicated by a short pause before and after “Baby” and perhaps a slight raising of the voice.

Claus Ableiter, Historical Baby Carriage

Claus Ableiter, Historical Baby Carriage

English is remarkably flexible in this regard, making it even more difficult for non-native speakers to master, but also probably contributing to its popularity as a second language. We make verbs, adjectives, and sometimes other parts of speech out of many nouns. It’s not always considered “proper” English, but it works.

  • We will grandfather him in.  (Here, “grandfather” is a bare infinitive.)
  • Isn’t that a beautiful Grandfather Clock! (= Adjective)

We also inflect the noun with verb, adjective, or adverb endings, more like Latin:

  • Grandfatherly = adverb
  • Grandfatherish = adjective
  • “We’ve Grandfathered in as many as we can.” = verb / participle

We can also get very playful in informal speech:

“‘Yikes! We’ve been Enron-ed!’ exclaimed the people of the West Coast when their lights went out.”

The adults in the room will recognize this as an analogy with the kind of language we don’t use in front of our Mothers…but this is a family-friendly blog and we won’t go into that.

The Real Scoop

They don’t teach all this in schools, unless you take university courses in Linguistics. This is the real structure of English (and other languages) in which words are categorized by function rather than by rigid Parts of Speech. Although there are disputes, the Wikipedia list of Function categories is fairly good. These include Open Word Classes, those which are susceptible to modification of function, either by position or by changes in form, and also can and are added to on a regular basis.

Open word classes:

For example, we have recently brought new words into English. “Truthiness,” (Thank you Stephen Colbert!), the “Buffyverse” (the universe where Buffy and Angel take place). The Oxford English Dictionary regularly alerts us of new additions, including recently, dataveillance, geotagging, and the Australian boofy (describing big, strong but not very bright men–”Strong as an Ox, and as bright as one too!”).

David Shankbone, Stephen Colbert in NYC

David Shankbone, Stephen Colbert in NYC

Then there are the Closed Word Classes, ones that are not normally susceptible to modification or addition:

Closed word classes:

These form the core of the language, and change only very slowly. So we don’t add new conjunctions, we stick with the ones we have (and, or, but, etc.). We do create portmanteau words like Juneteenth–which looks like an Ordinal Number, but it really isn’t: it’s the celebration of June 19, 1865, the Abolition of Slavery in the State of Texas after the Civil War, now celebrated in many areas. A portmanteau–pronounced as in French, approximately port-man-toe–word is one made up of two or more words or morphemes.

Whew! (An onomatopoeic Interjection) So that’s why when we learn the Parts of Speech in Grammar School, we aren’t really getting the full scoop. I can understand why, I’m not sure a first grader needs to understand Open and Closed Word Groups, etc. Unlike in Math, however, where we first learn Euclidian geometry, and then later learn that it can be transcended, or in Science where for all intents and purposes we learn classical Physics, and then graduate to Relativity and Quantum Physics, we don’t progress in the understanding of how our own language works or other languages work, for real. And that makes learning other languages harder.

More to come!

Steven A. Armstrong
Tutor, Editor, Consultant

Gloriously Wacky English–Part 2: Grammar 1: Inflection

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Gloriously Wacky English: Part 2–Grammar 1: Inflection

A while back, we surveyed some of the reasons English has such a large and varied vocabulary, and why its spelling is nothing if not irregular.

Today, let’s take a quick look at some of the peculiarities of something sometimes not well studied in our “Grammar” Schools and High Schools: Grammar.

What is Grammar?

Grammar is one of the components of natural, human language. Others include spelling and punctuation, although punctuation can also be considered part of Grammar. Grammar itself is the set of structural rules that govern how words are arranged and formed into phrases, clauses, and sentences.

In English, we derive meaning using two primary structures: fusion (inflection) and analysis (position indicating the role of the word in its sentence. English is less fusional than most Indo-European languages (especially those like Latin, Greek, Russian, and German, among many others, who use prefixes, suffixes and infixes to convey the role of many types of words.

For example, the noun “human being” in Latin is listed in the dictionary as Homo. Depending on its role in the sentence, its form will change. These changes are called cases, and the list falls into five basic patterns, called declensions:

Singular, Plural

  • Subject (Nominative): homo, homines the human(s)
  • Possessive (Genitive): hominis, hominum of the human(s)
  • Indirect Object (Dative): homini, hominibus to the human(s)
  • Direct Object (Accusative): hominem, homines the human(s)
  • Adverbial (Ablative): homine, hominibus by/from the human(s)
  • Direct Address (Vocative): homo, homines O Human(s)

The Genitive, Dative, Accusative and Ablative Cases are also used as objects of prepositions, and some verbs take other direct objects than the Accusative.

Incidentally, the Proto-Indo-European root from which homo comes is *dʰǵʰm̥mō, a derivative of *dʰéǵʰōm, that is, “earth.” Homines are “Earthlings,” in the language of Science Fiction.

In Latin, Adjectives and Pronouns follow similar patterns of change, while Verbs are quite different, as would be expected.

A quick example from Greek will illustrate the role of prefixes, suffixes and infixes in the formation of verbs:

Λύω  “to loose” has the typical Classical Greek 6 principal parts:

We can see all three types of change operative. From these six forms, all the rest of the verb forms can be built, over 200 for most verbs! Some reasons for so many forms is because Classical Greek has more moods than we do, and also a dual number (together with singular and plural).

Inflection in English

We don’t think about it much, but English does have some remaining inflections. That is why we are (partly) a fusional language. For example, in nouns we have some inflection:

Singular, Plural

  • Subject/Object: human, humans
  • Possessive: human’s, humans’

In Personal Pronouns, more cases have survived. The declension of “I” yields the following:

Singular, Plural

  • Subject: I, we
  • Object: me, us
  • Reflexive*: myself, ourselves
  • Possessive: mine, ours
  • Possessive Determiner: my, our

*While the Reflexive is not precisely a grammatical case, it is an inflected form.

Verbs also have conjugations in English, and these show the Germanic ancestry of our language. We have two ways we vary verbs, called “strong” and “weak” by analogy with German.

The “weak” verbs in English are those that form the past and the past participle by adding “-ed” at the end of the verb:

Bare Infinitive, Past, Past Participle

  • Look, looked, looked
  • Like, liked, liked

“Strong” verbs have internal or other changes:

  • See, saw, seen
  • Do, did, done
  • Take, took, taken

The bare infinitive is the infinitive without “to.” It is used in some situations: we say “I can see,”  but “I like to see.” Both are infinitives.

There are also suppletive verbs, which I like to call sandwich verbs. This is a linguistic phenomenon in which two or more verb roots are blended together to form a complete conjugation. English has two: “to be” and “to go.” As an example, “to go” has these three principal parts:

Go, went, gone

Clearly, “went” is not cognate with go, gone. Go (gone) is from the Proto-Indo-European *ǵʰēh₁-

For the past tense, Old English used another verb, ēode “he went.” By the 15th century, another verb, wenden, had become synonymous with “go.” Its past tense “went” replaced ēode in the conjugation of “to go.” We also have wend and wended from wenden, perhaps not as common today as previously: I wended my way home. She wends her way home.

There is more, but that’s enough for today! Wacky English is a big subject!

— Steven A. Armstrong
Tutor, Editor, Consultant

An update on the Late Latin, “Cattus/Gattus.”

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An update on the Late Latin, “Cattus/Gattus.” 

As you may recall, I mentioned that Martial (Marcus Valerius Martialis–March 1, 40 CE-ca. 102/104 CE), the original Insult Comic, according to Wikipedia (and I think it’s a good call), is credited with the first use of a form of the word “cattus” around 75 CE. I finally tracked it down. It is from his Epigram 13.69, and also, surprisingly, from the Jerome & Company Vulgate translation of the Septuagint (Greek version of the Hebrew Scriptures completed under Ptolemy II in Alexandria) text of Baruch 6:21 (in Catholic Bibles). Chapter 6 is known as the Letter of Jeremiah in Orthodox Christian Bibles and is printed separately. There is no surviving manuscript evidence that either has a Hebrew antecedent; however, some scholars theorize that the differences between the Greek Septuagint and the Hebrew Masoretic Text stem from the use of different Hebrew source-texts. Some passages from the Dead Sea Scrolls seem to indicate that there were variant Hebrew texts in existence.

Cattus in Martial

Martial’s Epigram 13.69 reads as follows:


Pannonicas nobis numquam dedit Vmbria cattas:
mavult haec domino mittere dona Pudens.

Umbria has never supplied us with Pannonian [Cattae]:
these are the gifts Pudens prefers to send to his lord.

Apparently Martial was ticked off that his friend the Centurion Aulus Pudens (from Umbria) never sent him any Pannonian Cattae, but rather sent these directly to the Emperor.

(In some manuscripts, cattae and cattas are transmitted as caltae and caltas.)

Now “here’s the rub.” No classical scholar knows what catta was in 75 CE! There are theories that it is an unknown species of bird. The fundamental Latin Dictionary by Lewis and Short defines it as that. In 1931 John Phelps argued for that theory based on his reading of the 4th Century Latin Vulgate’s translation of Baruch 6:21.

Cattus in Baruch

Let’s look at the Latin Vulgate (=people’s) translation from the late 4th Century CE. The Greek of the Septuagint, followed by the Latin, and then English is

ἐπὶ τὸ σῶμα αὐτῶν καὶ ἐπὶ τὴν κεφαλὴν αὐτῶν ἐφίπτανται νυκτερίδες, χελιδόνες καὶ τὰ ὄρνεα, ὡσαύτως δὲ καὶ οἱ αἴλουροι.

Supra corpus eorum et supra caput eorum volant noctuæ, et hirundines, et aves etiam similiter et cattæ.

Owls, and swallows, and other birds fly upon their bodies, and upon their heads, and cats in like manner.

The only problem with Phelps’ theory is that the Greek αἴλουροι really means “Domestic Cats.” There was even a Non-Chalcedonian Pope of Alexandria in the 5th century known as Timothy Aelurus (Αἴλουρος), Timothy the Cat.

In the absence of an original Hebrew text to compare the Septuagint version with, we are hard pressed to come to any other conclusion. Cattus/Catta seems to mean “cat.”

If anyone out there knows if Pannonia was known for its cats, please comment!

Steven A. Armstrong
Tutor, Editor, Consultant

Dog Language…Some Quick Thoughts

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Dog Language…Some Quick Thoughts

Of course, my boss Angus had several things to say about my most recent post!

This is fodder for several more posts, and I really encourage readers to let us know their experiences.

Dog Speak

Researchers have cataloged the fairly large number of different kinds of Dog Barks. We’ll take another post to talk about how human world languages represent these barks. Right now, I am interested in the dog side.

Dog Barks

The major types of Barks are

Warning Bark

Alarm Bark

Barking on Command

Playful Bark

Need Bark

I can testify that Angus has several variants on this repertoire. My boyhood Ridgeback Rex Dino Armstrong had a very specific, staccato, “Scorpion in the House” Bark. He was fearless! He was a great dog for a kid to walk around the neighborhood with. He was gentle (praus in Greek…we’ll have a whole post on that adjective one of these days), but who’s going to mess with a boy or girl walking with her/his Rhodesian Ridgeback West African Lion Hound‽ (Do you recognize that punctuation mark? A Free first Latin lesson for the first five who identify it!)

Please, let us all know what kinds of Barks your dog has! If you have another animal companion, let us know what she/he sounds like!

We can then compile this into a Post. I’m not sure that dogs have gerunds, phrasal verbs, predicate compliments, etc. Someday we’ll know.

What We Say: What Dogs Hear!

Gary Larson highlighted this phenomenon in his famous Far Side Comic:


© Gary Larson. Used for commentary purposes only.

You know, we find that Angus has a wider vocabulary. He certainly knows his name, but he also knows “Park” (we live next to Golden Gate Park, which he considers “Angus-Land”), “Let’s Go!” “Treat,” “Biscuit,” and even “Bath” (which he doesn’t like), and a few more. His ears go up, and he responds appropriately to these stimuli. I don’t know if he is reading our minds, or listening to our intonation, or what, but it is pretty consistent.

I would love to have our readers compile the human terms that your animal companions respond to. I mean, if plants can respond to harsh or pleasant talk, shouldn’t animals? My correspondents such as Rev. Martha Del Rio in Sacramento always remind me: animals are perfect in themselves, and have everything they need to be fulfilled. Please comment.


Angus on his Throne Pillows!

That’s all for tonight, but please contribute, here and on our sites. As I was writing this, Angus came up for a chin rub. He knew I was writing about him!

Peace to all!

Steven Armstrong
Tutor, Editor, Consultant