Geometry and GeoGebra, Chapter 2

FracTad's Fractopia

Vertical angles

Continuing my incorporation of GeoGebra into my Geometry curriculum (read about my introduction of GeoGebra here), we will start slow and simple. We are learning the basics of proof, and GeoGebra is a great tool for sparking discussion of what we might want to prove.

Example: one of the first exercises every Geometry student does is to prove that vertical angles are congruent. Instead of having them look at static pictures of vertical angles, each of my students will construct two intersecting lines, measure the angles formed, and look for a relationship. They should quickly see that the vertical angles are congruent no matter how much they move the lines around. Hopefully, they will then wonder why is that always the case. And that’s where proof comes in: if they can write a proof using variables, then they have proven it for all cases, not just the one they’re…

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Recommended Reading: September 6-12

Pursuing Veritas

Rocky-Mountain-National-ParkIf you only read one article this week, read America Under Cultural Dhimmitude by Rod Dreher

There are lots of other article worth your read as well, broadly categorized below. Hopefully you find them stimulating for your thinking. And as always, if there’s something you think I should be reading, please let me know in the comments section below. JJP

Theology and Religion

The Achievement of Wolfhart Pannenberg by Michael Root (older, but appropriate this week in memorium of Pannenberg)

From Cain to ISIS by R. R. Reno

InterVarsity Christian Ministry In Trouble for Acting Christian by Andrew Walker

The Perspective of Beauty by Jeff Reid

Resurrecting the Dead in America by Mark Regnerus

Biblical Studies and the History of Christianity

Paul on Jesus’ Resurrection: A New Study by Larry Hurtado

New Testament Studies (Volume 60)

What is Marcionism? by Roger Olson

Early Christians Distinguished from Culture by Michael Kruger

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Terminal Degree – The Middle Of Nowhen


“What if…?” is a qTerminal Degreeuestion that is asked often in progressive rock and metal, sometimes to original and interesting results.  Terminal Degree asked “What if we made a metal album using violins instead of guitars?

Bet you didn’t see that coming.

What if Paganini played lead for a progressive-metal band? What if Heifetz played Carnegie Hall with metal drums and bass? What if we dual-tracked the violin and let it shred over pummeling bass and drums?

What if.

Wonder no more. “The Middle Of Nowhen” is an instrumental album of intense, heavy songs written and performed by a power trio of drums, bass, and violin.


Stanley Chepaitis – acoustic and 5-string electric violins
Nathan Santos – 6-string bass
Mike Barnett – drums

Where guitars usually rule, the violin seriously rocks. This album featured a virtuoso performance from Stanley Chepaitis and a granite-solid back-line of Nathan Santos’…

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Some Dystopian Reading–In the News

Art by one of my favorite artists, South African "Faroutsider."

Art by one of my favorite artists, South African “Faroutsider.”

Some really interesting articles have appeared over the past few weeks dealing with dystopian literature.

Wired has a bit of a spirited debate:


In favor:

While, the London Guardian is worried:

What I strongly disagree with is the notion that dystopian fiction is either right or left.  As a genre, it’s just interesting, and it can be as anti-corporate as it is anti-statist.  What’s left and what’s right?  

Placing it in a left-right category as the Guardian writes does not only diminishes the genre, it diminishes the intelligence of the genre’s audience.

Dystopian Rock: A Request for Ideas


Dear Citizens of the anarcho-Republic of Progarchy,

As some of you might know, in addition to editing this site, I also pretend to be a professor and author during the day.  I’m currently working on a book on the history of dystopias (and dystopic ideas) in fiction, film, and music.  I’m trying to compile a list of dystopian rock albums.  Here’s what I’ve come up with.  If, in the comments section, you’d like to make suggestions of things I’ve missed–PLEASE do so!  I would be exceedingly grateful!

Yours, Brad

"Abandoned" by Craig Farham. “Abandoned” by Craig Farham.

Rush, 2112

Rush, Clockwork Angels

The entire Ayreon series

Arjen Lucassen, Life in the New Real

The Tangent, Not as Good as the Book

Pink Floyd, Animals

Pink Floyd, The Wall

Gary Numan, “Down in the Park”

Radiohead, Kid A

Cosmograf, Capacitor

A few songs by Muse, Oingo Boingo, Coheed and Cambria

Flower Kings, Desolation Rose


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Definitions: Dystopia, etc.


Sewall/Birzer; August 2014


Utopia: from the Greek, meaning “perfect place” and “no where.” Plato used it as a joke.


Republic: from the Latin, “res publica,” meaning “good thing” or “common good.” Based, in large part, on experimentation and adaptation, natural law, inherent struggle and conflict. Also demands something coherent to hold disparate communities together—usually (ideally) virtue.


Cacotopia or cacao-topia: first used in the English language in 1715, meaning a nightmare society in which morals mean nothing and the average citizen worships Mammon and proclaims atheism, but is obsessed with theological discussion. The worse in society—the unethical and depraved—rule. As far as is known, no one employed the word again until 1817 and 1818, when the Utilitarian English philosopher Jeremy Bentham used it in his Plan of Parliamentary Reform.


Dystopia or dys-topia: first used in the English language by Bentham’s most famous follower, John Stuart Mill in 1868. In his own writings, Mill used dys-topia as a synonym for “cacao-topia.” When Glenn Negley and J. Max Patrick used the term dystopia in their anthology of over thirty utopian visions (Quest for Utopia, 1952), they incorrectly assumed they were coining the term for the first time in recorded history. Since 1952, in no small part due to Negley’s and Patrick’s usage of it, dystopia has become an accepted and common part of the English language.


Cacotopia vs. Dystopia. Recent scholars, such as Matthew Beaumont and Eric D. Smith, have attempted to distinguish cacotopia and dystopia. The former, they claim, deals far more with the moral decline of a society while the latter deals with the increased intrusion of government in the lives of ordinary citizens. I (Brad—your prof) am less than convinced by this hairsplitting, but the argument as presented is certainly a viable one and one with the potential to make a permanent mark on dystopian studies.


Ustopia. One of the foremost scholars and writers of dystopian fiction, Canadian Margaret Atwood, claims that the separation of utopia and dystopia, itself, is a false one. All Utopias must contain dystopian elements, and all dystopians must possess utopian ones. “But scratch the surface a little, and—or so I think—you see something more like a yin and yang pattern; within each utopia, a concealed dystopia; within each dystopia, a hidden utopia, if only in the form of the world as it existed before the bad guys took over” (Atwood, In Other Worlds, 85) Why is this the case? Because utopians must always stop human progress and ingenuity, thus creating a false stability based on the notion of one person, group, or generation. “There is always provision made for the renegades those who don’t or won’t follow the rules: prison, enslavement, exile, exclusion, or execution,” Atwood continues (In Other Worlds, 86)

A Beginner’s Guide to Dystopia



Mark Twain, Connecticut Yankee in King Arthur’s Court (1889)

G.K. Chesterton, Napoleon of Notting Hill (1904)

Robert Hugh Benson, Lord of the World (1907)

Jack London, The Iron Heel (1908)

G.K. Chesterton, Man Who Was Thursday (1908)

Aldous Huxley, Brave New World (1931)

Sinclair Lewis, It Can’t Happen Here (1935)

Murray Constantine [Katherine Burdekin], Swastika Night (1937)

C.S. Lewis, That Hideous Strength (1945)

George Orwell, Animal Farm (1945)

George Orwell, 1984 (1949)

Ray Bradbury, Martian Chronicles (1950)

Ray Bradbury, Fahrenheit 451 (1953)

Arthur Bestor, Demolished Man (1953)

Walter Miller, A Canticle for Leibowitz (1960)

Kurt Vonnegut, Mother Night (1963)

Pierre Boulle, Planet of the Apes (1963)

Philip K. Dick, Do Androids Dream of Electric Sheep? (1968)

Kurt Vonnegut, Slaughter-House Five (1969)

Ira Levin, This Perfect Day (1970)

Stephen King, The Stand (1970)

  1. Neil Schulman, Alongside Night (1979)

Margaret Atwood, The Handmaid’s Tale (1985)

P.D. James, Children of Men (1992)

Michael O’Brien, Father Elijah (1996)

Michael O’Brien, Eclipse of the Sun (1998)

Margaret Atwood, Oryx and Crake (2003)

Suzanne Collins, Hunger Games (2008)

Ernest Cline, Ready Player One (2011)


Graphic Novels

Frank Miller, The Dark Night Returns (1986)

Alan Moore and David Lloyd, V for Vendetta (1998)

Brian Vaughan, Y: The Last Man (2002)

Paul Pope, Batman: Year 100 (2006)

Brian Wood, DMZ (2006)



[Including movies made from the above forms of fiction]

The Island; Blade Runner; 12 Monkeys; Dark City; Logan’s Run; Idiocracy; Soylent Green; Gattaca; Batman Begins; Equilibrium; Brazil

Syllabus: CWC4000: American Founding and the Classics

CWC4000: “The Classical Origins of the American Founding”

Instructor: Dr. Bradley Birzer (

Class time: MWF: 12-12:50PM; KTCH 118

Office Hours: 9:30-1:00 and by appointment (Woodbury 302)

Autumn 2014

Assignments/messages/note will appear at:



Required Reading: The Lineage

  • Livy, The Early History of Rome (Book 1: 1:1-1:26; Book 3: 3:16-3:35)

  • Cicero, On the Laws (Book 1) [I’ll lecture from On Duties and On the Republic]

  • Tacitus, Germania (all of it)

  • Virgil, The Aeneid (Books 1-3; 8; 12) [I’ll lecture from the Eclogues and Georgics]

  • Magna Carta [I’ll lecture from Bede, King Alfred, Aquinas, Sydney, and Coke]


Required Reading: The Revolution (or close, give or take a century)[1]

  • Catos Letters: 72-76, 85
  • Thomas Gordon, “A Discourse of Standing Armies”
  • Demophilus, “The Genuine Principles of the Ancient Saxon, or English Constitution”
  • Addison, Cato: A Tragedy
  • Dickinson, Letters from a Pennsylvania Farmer: 1, 3, 8-10, 12
  • CX Letters (will be emailed to you)
  • Articles of Confederation
  • Declaration of Independence (Jefferson’s version; will be emailed to you)
  • Northwest Ordinance, Articles 1-6
  • James Wilson, “Speech to the Pennsylvania Convention” (December 1787)
  • John Dickinson as “Fabius,” letters 10-3
  • Noah Webster, “A Citizen of America”
  • Tench Coxe, “An American Citizen”
  • James Wilson, “Of the Law of Nature”
  • James Wilson, “Of the Natural Rights of Individuals”



Why did the Federalists take the name Publius?  Why is the American Capitol (the same name as the temple to Jupiter) modeled on Roman republican architecture?  How was Washington the American Cincinnatus?  Why is the upper body of Congress named the Senate?  Why did the Revolutionary Army have “Cato: A Tragedy” performed seven times during the winter at Valley Forge?  Why is the symbol of the House of Representatives the Roman fasces. Over the past 100 years a number of traditions have emerged to explain the American Founding, variously labeled: Whig, neo-Whig, Commonwealth, Liberal/Enlightenment, neo-Liberal, and Protestant.  All of these schools of thought are correct, but only within their contexts. First and foremost, the authors and signers of the Declaration of Independence, the Articles of Confederation, the Constitution, and the Bill of Rights saw themselves in a western tradition that ran from Leonidas and his Spartans at Thermopylae to the English Common Law tradition of King Alfred to the modern constitutional theories of Blackstone.  They did, after all, create ares publica, Latin for the “good thing” or “common good.” Western Civilization 4000 considers the republicanism of the ancients—especially as understood by Cicero, Virgil, Tacitus, and Livy—as it influenced the American Founders.  In particular, the course will focus on the revolutionary thought of John Adams, Thomas Jefferson, John Dickinson, James Wilson, and Mercy Otis Warren.



  • Semester-long Research Paper: 30%
  • Midterm Examination: 30%
  • Final Examination: 40%


Research Paper

Worth 30% of your grade, your research paper can cover any topic dealing with the subject matter of the course: the classical and medieval influences on the American Founding. The paper should be in normal 12-point font (Cambria, Times, etc.), double spaced, footnoted, and with 1-inch margins on the top, bottom, and sides; roughly 10-15 pages total. I encourage you to own a (real; tangible—not just e-version) of a good dictionary and thesaurus. As to computer programs/apps, I suggest Endnote as the best for bibliographical reference and formatting, and Scrivener as the best writing program. Our library possesses excellent primary document collections, on the shelves as well as online. While I do not mind you using secondary sources, I would encourage you strongly to use as many primary sources as possible. Frankly, it is very difficult to find satisfactory secondary sources on almost any aspect of the founding, as almost every author comes at the topic with some agenda. Every writer (especially American writers)—left, right, above, below, next to—desires to co-opt and use the founders for personal goals. Hence, the desire to teach and learn almost exclusively from primary documents.



[1] Unless otherwise stated, all available at:


Syllabus: Dystopian Literature and the Moral Imagination

SEWL 1020-172R: “Dystopian Literature and the Moral Imagination”

Instructor: Dr. Bradley Birzer (

Class time: MWF: 10-10:50AM

Office hours: Tuesday, 9:30-1:00, and by appointment (Woodbury 302)

Autumn 2014


Required Reading

  • Aldous Huxley, Brave New World
  • George Orwell, Nineteen Eighty-Four
  • Walter Miller, Canticle for Leibowitz
  • Margaret Atwood, Handmaid’s Tale
  • Suzanne Collins, Hunger Games
  • Plus additional handouts (probably via email or dropbox)



Utilizing lecture as well as discussion, this course will explore the rise and power (and faults) of twentieth-century dystopian literature. In particular, we’ll explore the power of imagination, the essence of words and language, the fears of conformity, the deadliness of ideologies (right, left, capitalist, communist, fascist) and fundamentalisms, the dignity and complexity of the human person; and the realities of equality and hierarchy in the social as well as the political spheres of life . Though we 21st-century types throw around the term “dystopia” in a relatively easy fashion, it did not enter the English language with any steadiness until 1952. Prior to this, some had spoken of false utopias, broken utopians, dark utopias, or, most frequently, cacotopias. For our purposes, then, we must ask why the concept and genre (possibly a sub-genre of science fiction; this is debatable) came into common usage in the second half of the twentieth century.   The books assigned will consider four types of dystopias: a managerial capitalist/socialist one; a fascistic/communist one; a post-apocalyptic one; and a Puritan one. I will also lecture on Plato, Augustine, Thomas More, and Francis Bacon; the French Revolution; the rise of Marxism, Darwinism (social and biological), and Freudianism as “progress”; fascism and futurism; eugenics and racialism; and fabulism in twentieth-century literature. We will also discuss dystopia in film, computer games, and graphic novels.



  • Five Book Response Papers (one per book, 1000-1200 words each): 50% total
  • Final exam: 30%
  • Participation and discussion: 20%


Response papers

Each of your five response papers should be 1,000-1,200 words in length. As to formatting, please use a reasonable 12-point font, one-inch margins, and footnotes. Additionally, please double space the paper. Feel free to use published book reviews as sources. Plagiarism (the use of another’s work without proper recognition/attribution) will result in an immediate F for the paper. I encourage you to own a real dictionary and thesaurus—not just an e-version. As to computer programs/apps, I suggest Endnote as the best for bibliographical reference and formatting, and Scrivener as the best writing program.



Here’s hoping you WANT to attend, of course. Sewall language on the matter (with which I concur): “You may miss only 7 class periods in a MWF class.  Upon your 8th absence, you will automatically fail the course.  If there are extenuating circumstances (e.g. hospitalization or extended illness), they will be taken into account on a case-by-case basis in implementing the automatic failure provision, providing that you can present evidence/documentation.”


Seven Impale – Basking in the City of the Sun


sevenimpaleOne of the many strands of the golden hair of art rock is rooted in John Coltrane’s epic India, where the mighty ‘Trane and Eric Dolphy so caught the attention of a young Roger McGuinn that the Byrd lifted the song’s theme whole, filtering it through his twelve-string Ric and overlaying it on his band’s psych pop masterpiece, Eight Miles High. It was a sincere embrace, in spirit, of modal jazz, and helped launch rock into territories beyond the blues, to points further east, to lands that Coltrane remapped as an astral plane. Four years later and three after Coltrane’s death, the Soft Machine’s album Third became the purest rock expression, from what remains art rock’s best “fusion” record, of what Coltrane had been searching for. Side-long pieces of heavy fuzz bass, driving organ, wailing horns, and Robert Wyatt’s inimitable drumming. This kind of music, like Coltrane’s, is hard, riffy…

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A Love of Lingering: Salander’s STENDEC (2014)


A review of Salander, “STENDEC” (2014, independent release). Tracks: Pearls Upon a Crown; Book of Lies; Ever After; Hypothesis 11/8; Situation Disorientation; Controlled Flight Into Terrain; and Zeitgeist. Total time: 65 minutes.  Recommendation: HIGHEST; MUST OWN

Salander's second album of 2014: STENDEC.  Even better than the amazing first album. Salander’s second album of 2014: STENDEC. Even better than the amazing first album.

From the moment I first heard “CRASH COURSE FOR DESSERT” by Salander, I knew I not only loved the music, but I also knew I would love the musicians as well.

And, so it came to pass.

A rather significant part of my 2014 has been the sheer joy of getting to know Dave Smith, one of the two Daves who make up Salander. Sadly, I’ve not had the chance to get to know Dave Curnow, the other Dave, but I trust the judgment of the first Dave. So, per my respect of Dave, Dave must also be great.

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Take a big paper bag. Got one? Good – now toss in some 1970s King Crimson, some Frank Zappa, a bit of the 1969 ‘Crims, a healthy dose of their 80’s classic “Discipline“, a large amount of 90s-era ‘Crims, some Steely Dan, a bit of Toto, a very healthy quantity of the 1970s ECM catalog, a pinch of Edvard Grieg, a modicum of Steve Reich, a soupcon of Ulrich Schnauss’ textures, and some 50’s and 60s Blue Note Records for good measure. Got it all? Great. Now shake.

Keep shaking. Shake hard.

Right. That’s enough shaking. Now: Dump our the contents of your paper bag, and you should get the music of Seven Impale – “City Of The Sun”. Seven Impale - City Of The Sun

“WHO?” I heard someone in the back ask. 

Lest turn to their label, Karimsa Records, for some details:

SEVEN IMPALE consists of Stian Økland on vocals and guitars, Fredrik…

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