Unintended Ramifications

I love this take-down of the Texas State Board of Education (ht):

Let us begin chronologically, considering the contributions of Saint Thomas Aquinas (1224-25-1274). Aquinas is a new addition to the curriculum, added at the insistence of those who would emphasize the important role of Christianity in the development of natural law, political institutions and related ideologies. As the board surely knows, Aquinas was no friend of business or what the new guidelines call “free enterprise.” In his Summa Theologica, he writes of business, “It is devoted to satisfying the desire for profit, and such desire knows no bounds and always strives for more. And so business, absolutely speaking, is wicked, since it does not essentially signify a worthy or necessary objective.” The only possible justification for business, he argues, is to feed one’s family and help the needy. I applaud the board for challenging students in these times to question the moral foundations of the free enterprise system.

It's a little bit misleading (I wouldn't have translated the passage in quite the way it is here), but it's not really far from the truth, which we can crudely summarize here. None of the medieval scholastics are very favorable to usury, but Aquinas is arguably the scholastic who allows the least grey area of all the scholastics: charging interest on loans is contrary to natural law, end of story. And Aquinas also holds that private property is derivative: the natural state of the whole world, so to speak, is to be for the common use of everybody; private property is justified -- and in Aquinas's view is really only justifiable -- as being something that usually best contributes to common use (by encouraging people to take better care of things, by simplifying disputes over use, etc.). Common use still trumps private property if they actually come to an unavoidable conflict, e.g., an emergency situation; the poor can take from the surplus of the rich in dire need and it is not stealing. And even if we aren't in a situation of that sort, if you have more money than you need to feed, clothe, shelter, and educate yourself and your household, you have a moral obligation to use the rest not to satisfy your own tastes but to do what, as far as your best judgment can tell, will do the most good for others. You are merely a steward of anything you have that is more than you actually need in order to meet the essential ends of human life. And, of course, the view that business, insofar as it involves grasping after profit (rather than, saying, doing good things for others in a sustainable way), is wicked is an Aristotelian line of thought that Aquinas also takes up. And the thing of it is, you really do have to understand these sorts of things to understand how Aquinas himself develops and applies the theory of natural law, which, of course, is the (nominal) point.

The rest of the article is good as well -- the knife is put in with Sicilian flair. It highlights a fundamental problem with the TSBOE; these people simply don't understand ideas, and it is shown by almost everything they do. They think that ideas are little snippets that can easily be maneuvered in a textbook to a desired end. But they are really vast, ramifying things that are not easily manipulated. Failure to understand this inevitably leads to the sort of incoherent mess that comes down from these people. They are trying to lead tigers by their tails.

Whewell on Succession of Cause and Effect

The common maxim, that the effect follows the cause, has arisen from the practice of considering, as examples of cause and effect, not instantaneous forces or causes, and the instantaneous changes which they produce; but taking, instead of this latter, the cumulative effects produced in the course of time, and compared with like results occurring without the action of the cause. Thus, if we alter the length of a clock-pendulum, this change produces, as its effect, a subsequent change of rate in the clock: because the rate is measured by the accumulated effects of the pendulum's gravity, before and after the change. But the pendulum produces its mechanical effect upon the escapement, at the moment of its contact, and each wheel upon the next, at the moment of its contact.

William Whewell, History of Scientific Ideas, p. 191

Infinity in Your Room

There is a widespread misconception that the lack of a real counterpart to the idea N is due to N being infinite. On the contrary, Cantor showed that the much 'larger' infinity 2^N is isomorphic as an abstract set with the idealization 'imagine the set of all points in this room.' The latter is an idealization of something that we regard as really there, though of course we can't 'list' all the points in this room by any syntactic process.

F. William Lawvere and Stephen Schanuel, Conceptual Mathematics, (Cambridge 2009) p. 308.

The Rain is Full of Ghosts Tonight

What lips my lips have kissed, and where, and why
by Edna St. Vincent Millay

What lips my lips have kissed, and where, and why,
I have forgotten, and what arms have lain
Under my head till morning; but the rain
Is full of ghosts tonight, that tap and sigh
Upon the glass and listen for reply,
And in my heart there stirs a quiet pain
For unremembered lads that not again
Will turn to me at midnight with a cry.
Thus in the winter stands the lonely tree,
Nor knows what birds have vanished one by one,
Yet knows its boughs more silent than before:
I cannot say what loves have come and gone,
I only know that summer sang in me
A little while, that in me sings no more.

Animation Movie Meme

(From here)

X what you’ve seen
O what you saw some but not all of
Bold what you particularly liked
Strike-through what you hated

CLASSIC DISNEY
——————————-
[ X ] 101 Dalmatians (1961)
[ X ] Alice in Wonderland (1951)
[ X ] Bambi (1942)
[ X ] Cinderella (1950)
[ X ] Dumbo (1941)
[ X ] Fantasia (1940)
[ X ] Lady and the Tramp (1955)
[ X ] Mary Poppins (1964)
[ X ] Peter Pan (1953)
[ X ] Pinocchio (1940)
[ X ] Sleeping Beauty (1959)
[ X ] Snow White and the Seven Dwarfs (1937)
[ O ] Song of the South (1946)

DISNEY’S DARK AGE
——————————-
[X] The Aristocats (1970)
[O] The Black Cauldron (1985)
[X] The Fox and the Hound (1981)
[X] The Great Mouse Detective (1986)
[X] The Jungle Book (1967)
[ ] The Many Adventures of Winnie the Pooh (1977)
[ ] Oliver and Company (1986)
[O] Pete’s Dragon (1977)
[X] The Rescuers (1977)
[X] Robin Hood (1973)
[X] The Sword In The Stone (1963)

THE DISNEY RENAISSANCE
——————————-
[X] Aladdin (1992)
[X] Beauty and the Beast (1991)
[ ] A Goofy Movie (1995)
[O] Hercules (1997)
[X] The Hunchback of Notre Dame (1996)
[X] The Lion King (1994)
[X] The Little Mermaid (1989)
[X] Mulan (1998)
[O] Pocahontas (1995)
[ ] The Rescuers Down Under (1990)
[O] Tarzan (1999)

DISNEY’S MODERN AGE
——————————-
[ ] Atlantis: The Lost Empire (2001)
[X] Bolt (2008)
[ ] Brother Bear (2003)
[O] Chicken Little (2005)
[ ] Dinosaur (2000)
[O] The Emperor’s New Groove (2000)
[ ] Fantasia 2000 (2000)
[ ] Home on the Range (2004)
[ ] Lilo & Stitch (2002)
[X] Meet the Robinsons (2007)
[ ] Treasure Planet (2002)

PIXAR
——————————-
[X] A Bug’s Life (1998)
[X] Cars (2006)
[X] Finding Nemo (2003)
[X] The Incredibles (2004)
[ ] Monsters Inc. (2001)
[X] Ratatouille (2007)
[X] Toy Story (1995)
[ ] Toy Story 2 (1999)
[X] Wall-E (2008)
[X] Up (2009)

DON BLUTH
——————————-
[X] All Dogs Go to Heaven (1989)
[X] An American Tail (1986)
[O] An American Tail: Fievel Goes West (1991)
[X] Anastasia (1997)
[X] The Land Before Time (1988)
[ ] The Pebble and the Penguin (1995)
[X] Rock-a-Doodle (1991)
[X] The Secret of NIMH (1982)
[ ] Thumbelina (1994)
[O] Titan AE (2000)
[ ] A Troll in Central Park (1994)

CLAYMATION
——————————-
[ ] The Adventures of Mark Twain (1986)
[X] Chicken Run (2000)
[ ] Coraline (2009)
[ ] Corpse Bride (2005)
[ ] James and the Giant Peach (1996)
[X] The Nightmare Before Christmas (1993)
[ ] The Puppetoon Movie (1987)
[ ] Wallace & Gromit: The Curse of the Were-Rabbit (2005)

CGI GLUT
——————————-
[X] Antz (1998)
[ ] Happy Feet (2006)
[ ] Kung Fu Panda (2008)
[O] Madagascar (2005)
[X] Monster House (2006)
[X] Over the Hedge (2006)
[X] The Polar Express (2004)
[X] Shrek (2001)
[ ] Shrek 2 (2004)
[ ] Shrek The Third (2007)
[ ] Monsters vs. Aliens (2009)
[ ] How to Train Your Dragon (2010)

IMPORTS
——————————-
[ ] Arabian Knight
[ ] Back to Gaya
[X] The Last Unicorn (1982)
[ ] Light Years (1988)
[ ] The Triplets of Belleville (2003)
[ ] Persepolis (2007)
[ ] Planet 51 (2009)
[ ] Waltz With Bashir (2008)
[O] Watership Down (1978)
[ ] When the Wind Blows (1988)
[ ] Yellow Submarine (1968)

STUDIO GHIBLI/MIYAZAKI
——————————-
[ ] The Cat Returns (2002)
[ ] Grave of the Fireflies (1988)
[ ] Howl’s Moving Castle (2004)
[ ] Kiki’s Delivery Service (1989)
[ ] Laputa: Castle in the Sky (1986)
[ ] Lupin III: The Castle of Cagliostro (1979)
[ ] My Neighbors The Yamadas (1999)
[ ] My Neighbor Totoro (1993)
[ ] Nausicaä of the Valley of the Wind (1984)
[ ] Only Yesterday (1991)
[ ] Pom Poko (Tanuki War) (1994)
[ ] Porco Rosso (1992)
[ ] Princess Mononoke (1999)
[ ] Spirited Away (2002)
[ ] Whisper of the Heart (1995)
[ ] Ponyo on a Cliff by the Sea (2009)
[ ] Panda! Go Panda!
[ ] Tales from Earthsea
[ ] Horus, Prince of the Sun

SATOSHI KON
——————————-
[ ] Millennium Actress (2001)
[ ] Paprika (2006)
[ ] Perfect Blue (1999)
[ ] Tokyo Godfathers (2003)

SHINKAI MAKOTO
——————————-
[ ] She and Her Cat (1999)
[ ] Voices of a Distant Star (2001)
[ ] The Place Promised in Our Early Days (2004)
[ ] 5 Centimeters per Second (2007)

OTHER ANIME FILMS
——————————-
[ ] Akira (1989)
[ ] Appleseed (2004)
[ ] Appleseed: Ex Machina (2007) -
[ ] Arcadia of My Youth (U.S. Title – Vengeance of the Space Pirate) (1982)
[ ] Cowboy Bebop: The Movie (2003)
[ ] The Dagger of Kamui (U.S. Title – Revenge of the Ninja Warrior) (1985)
[ ] Dirty Pair: Project Eden (1987)
[ ] End of Evangelion (1997)
[O] Gundam Wing: Endless Waltz (1998)
[ ] Fist of the North Star (1986)
[ ] Galaxy Express 999 (1979)
[ ] Ghost in the Shell (1996)
[ ] The Girl Who Leapt Through Time (2006)
[ ] Lensman (1984)
[ ] Macross: Do You Remember Love (U.S. Title – Clash of the Bionoids) (1984)
[ ] Metropolis (2001)
[ ] Neo-Tokyo (1986)
[ ] Ninja Scroll (1993)
[ ] Origin: Spirits Of The Past
[ ] Patlabor the Movie (1989)
[ ] The Professional: Golgo 13 (1983)
[ ] Project A-ko (1986)
[ ] Robot Carnival (1987)
[O] Robotech: The Shadow Chronicle (2006)
[ ] Silent Möbius (1991)
[ ] Space Adventure Cobra (1982)
[ ] Steamboy (2004)
[ ] Sword of the Stranger (2007)
[ ] Unico and the Island of Magic (1983)
[ ] Urotsukidoji: The Movie (1987) Never will I see this of my own volition.
[ ] Vampire Hunter D (1985)
[ ] Vampire Hunter D Bloodlust (2000)
[ ] Wings of Honneamise: Royal Space Force (1987)

CARTOONS FOR GROWN-UPS
——————————-
[ ] American Pop (1981)
[ ] The Animatrix (2003)
[ ] Beavis & Butthead Do America (1996)
[ ] Cool World (1992)
[ ] Final Fantasy: The Spirits Within (2001)
[ ] Final Fantasy: Advent Children (2005)
[ ] Fire & Ice (1983)
[ ] Fritz the Cat (1972)
[ ] Heavy Metal (1981)
[ ] Heavy Metal 2000 (2000)
[ ] Hey Good Lookin’ (1982)
[ ] Lady Death (2004)
[ ] A Scanner Darkly (2006)
[X] South Park: Bigger, Longer & Uncut (1999)
[ ] Street Fight (Coonskin) (1975)
[ ] Waking Life (2001)

OTHER ANIMATED MOVIES
——————————-
[O] Animal Farm (1954)
[ ] Animalympics (1980)
[ ] Aqua Teen Hunger Force Colon The Movie (2007)
[ ] Batman Beyond: Return of the Joker
[ ] The Brave Little Toaster (1988)
[ ] Bravestarr: The Movie (1988)
[ ] Cats Don’t Dance (1997)
[X] Care Bears: The Movie (1985)
[X] Charlotte’s Web (1973)
[X] Fern Gully (1992)
[X] G.I. Joe: The Movie (1987)
[ ] Gobots: Battle of the Rock Lords (1986)
[O] He-Man & She-Ra: The Secret of the Sword (1985)
[X] The Hobbit (1977)
[O] The Iron Giant (1999)
[ ] Justice League: The New Frontier (2008)
[ ] Lord of the Rings (1978)
[ ] Little Nemo: Adventures in Slumberland (1992)
[ ] My Little Pony: The Movie (1986)
[ ] Pink Floyd’s The Wall (1982)
[X] The Prince of Egypt (1998)
[ ] Powerpuff Girls: The Movie (2002)
[ ] Quest For Camelot (1999)
[ ] Ringing Bell (1978)
[ ] The Road to El Dorado (2000)
[ ] Rock & Rule (1983)
[ ] Space Jam (1996)
[ ] Starchaser: The Legend of Orin (1985)
[ ] Superman: Doomsday (2007)
[ ] The Swan Princess (1994)
[O] Transformers: The Movie (1986)
[ ] Wizards (1977)
[X] Who Framed Roger Rabbit (1988)
[ ] Wonder Woman (2009)
[X] Balto (1995)
[ ] Spirit: Stallion of the Cimarron (2002)

ADDENDUM
[ ] 9 (2009)
[ ] The Ant Bully (2006)
[ ] Batman: Mask of the Phantasm
[ ] Bee Movie (2007)
[ ] Beowulf (2007)
[ ] The Chipmunk Adventure (1987)
[ ] Cloudy With a Chance of Meatballs (2009)
[ ] Felix the Cat: The Movie (1988)
[ ] Flushed Away (2006)
[ ] Happily N’Ever After (2007)
[ ] Hoodwinked (2005)
[ ] Horton Hears a Who (2008)
[X] Ice Age (2002)
[X] Ice Age: The Meltdown (2006)
[ ] Ice Age: Dawn of the Dinosaurs (2009)
[ ] Jimmy Neutron: Boy Genius (2001)
[ ] Madagascar: Escape 2 Africa (2008)
[ ] Open Season (2006)
[ ] Pokemon: The First Movie (1999)
[ ] The Princess and the Frog (2009)
[ ] Robots
[ ] The Rugrats Movie (1998)
[X] Shark Tale (2004)
[ ] Shrek Forever After (2010)
[X] The Simpsons Movie (2007)
[ ] Sinbad: Legend of the Seven Seas (2003)
[ ] Space Chimps (2008)
[X] The Spongebob Squarepants Movie (2004)
[ ] The Tale of Despereaux (2008)
[ ] Valiant (2005)
[ ] We’re Back! A Dinosaur’s Story (1993)

ADDENDUM II
[ ] Mind Game
[ ] The Secret of Kells
[ ] Shonen Sarutobi Sasuke (U.S. title “Magic Boy”)
[ ] Princess Arete
[ ] Urusai Yatsura: Beautiful Dreamer
[O] Cat Soup
[ ] Summer Wars

On David Layman on Aquinas on Conscience

David Layman is puzzling over Aquinas's account of conscience. The ground for the distinction is itself fairly easy to clear up; by the time we get to Aquinas the distinction had already been made, although there was some variation as to details. And the argument, which Aquinas is explicitly making, is that while synderesis and conscience are often treated as if they were synonyms, in fact this cluster of terms serves two distinguishable roles or functions. And this is true even of the English word 'conscience' today; one can easily distinguish between two general ways we use the term and can easily find cases where confusing these two usages leads to even greater confusion down the road.

But the more interesting puzzle is the second puzzle. Aquinas holds that it is wrong to violate conscience; he mentions in this context Romans 14:23, in which Paul says that everything that is not of faith is of sin. David then asks:

Remember that for Aquinas, conscience is an “act” arising out of the “disposition,” synderesis (ST I, Q 79, A. 13). This disposition is an universal ordering of all humans to the good. According to the glossary in LMP, conscience is “the dictate of reason that one should or should not do something.”

If that is true, then how can Aquinas equate an evil “conscience” with the Pauline phrase “everything not of faith?” If a human can know the dictate of reason, “I ought not commit suicide”, through reason–apart from faith–then how can an evil conscience be the absence of faith? The dictate of conscience (according to the Aquinas) does not arise either within faith or apart from faith. It arises from practical reason, determined by synderesis, the disposition (again quoting the glossary of LMP) that all humans “should seek the good proper to their human nature….” But the absence or presence of faith does not bear on this issue. I do not see how Aquinas can properly cite the apostolic text as authority for his claim.

In other words, “conscience” in Paul (and the entire New Testament canon) is a state of moral knowledge known in and through the living (in technical terms, “existential”) reality of a specific community that enacts and expresses a new experience of life and moral reasoning. Aquinas reappropriates this concept and redefines it as a state of moral knowledge known by, and accessible to all humans, apart from that new life.

But a little thought shows that this puzzle is unknotted easily enough. Just as reason, although universal, can be examined specifically in a Christian context, so can universal moral dispositions. That everyone has something in the way of conscience doesn't mean that it is formed in the same way for everyone. And in the Summa Theologiae, which David is considering, Aquinas is not considering conscience "apart from that new life"; the ST is a work of sacred doctrine, not ethical philosophy. Philosophy is a handmaid here, a queen attending on an empress. Thus he sets up the general framework solely in order to see how it works in the context of Christian life. Thus it is false in context to say that the absence or presence of faith has no bearing on the issue of these universal capacities of the mind; faith is not irrelevant to moral life, and the ST throughout presupposes faith. It explicitly says this, right at the beginning, in fact.

The point is actually generally important for interpreting much of Aquinas's moral theory in the Summa. The long, detailed discussion of virtue in the ST is a discussion of infused virtue. What reason says about acquired virtue comes up quite a bit, of course; but it comes up solely as a starting-point for understanding its infused and charity-formed counterpart. The Summa moves from God ruling over us to God working in us to God being with us; it is, as it says, a work of Christian theology.

Chesterton on Politics

The whole modern world has divided itself into Conservatives and Progressives. The business of Progressives is to go on making mistakes. The business of Conservatives is to prevent mistakes from being corrected. Even when the revolutionist might himself repent of his revolution, the traditionalist is already defending it as part of his tradition. Thus we have two great types—the advanced person who rushes us into ruin, and the retrospective person who admires the ruins.

The Illustrated London News, April 19, 1924

Columcille

Today is the feast of St. Columba of Iona, Enlightener of Scotland, Wolf against Sin, Dove of the Church, one of the Twelve Apostles of Ireland and patron saint of poets. The hymn Altus Prosator, often recognized as one of the richest and most powerful theological poems of the sixth century despite its very unclassical Latin, is often attributed to him. It is abecedarian -- that is, each stanza starts with a letter of the alphabet; for instance, Capitulum A begins with the line from which the hymn takes its name, Altus Prosator. Here are Capitulum A and B in Samuel John Stone's translation:

High Creator, Unbegotten,
Ancient of Eternal days,
Unbegun ere all beginning,
Him, the world's one source, we praise:
God who is, and God who shall be :
All that was and is before:
Him with Christ the Sole-Begotten,
And the Spirit we adore,
Co-eternal, one in glory,
Evermore and evermore:—
Not Three Gods are They we worship,
But the Three which are the One,
God, in Three most glorious Persons :—
Other saving Faith is none.

All good angels and archangels,
Powers and Principalities,
Virtues, Thrones, His will created—
Grades and orders of the skies,
That the majesty and goodness
Of the Blessed Trinity
In its ever bounteous largesse
Never might inactive be;
Having thus wherewith to glory,
All the wide world might adore
The high Godhead's sole-possession
Everywhere and evermore.

Mandelbrot Set

I like this video. (Note that the song has some foul language here and there. But it too still has some nice points.) Wikipedia has some nice articles on the fractals mentioned, although I can't guarantee accuracy of all details (the first is from a different website, though, which has a nice applet showing the construction of the Peano Curve):

Peano Space-Filling Curve
Koch Curve
Cantor Ternary Set
Sierpinski Gasket
Mandelbrot Set
Julia Set

Stewart-Williams on Human Dignity

Stewart-Williams has a somewhat muddled argument (hat-tip) that evolutionary theory undermines the foundations on which a thesis of human dignity rests. One of the things that makes his argument muddled is that he fails to distinguish three completely distinct kinds of theses (there are slight variations of each of the following, but the variations are not important here because Stewart-Williams is mixing together entire families):

I. Human Dignity: Human beings ought to have a role in moral reasoning such that they are treated as transcending in value and importance any price and, as such, should be treated with respect and responsibility.

II. Human Uniqueness: No other animals have the sort of feature in light of which people attribute this dignity to human beings.

III. Human Supremacy: All other animals have their value wholly in being instrumental to human ends.

These are all three completely different ideas; although they are consistent with each other, none of the three actually entails any of the others. You can hold that human beings have transcendent dignity without committing to the claim that they are the only ones that do, or that other animals have no value in themselves. You can hold that some feature usually used as a ground for this dignity, e.g., rationality, is unique to human beings without holding that it actually gives the dignity people think it does; and you can hold that it is unique but that there are many other features, available to many other animals, that are valuable in themselves. And you can hold that other animals have value wholly in being instrumental to human ends without holding that human beings are beyond price or that they have unique features. Failing to recognize this comes well nigh to making Stewart-Williams's argument incoherent; he argues against I at one point by arguing against III, and argues against III at one by arguing against II. That is, almost his entire argument consists of rejecting claims by giving arguments against claims that are not the claim he is arguing against at a given moment.

Moreover, even if we take a position which holds I, II, and III, Stewart-Williams misses the mark somewhat. His rejection of II makes the false assumption that the only features that are used to ground human dignity are the image of God thesis -- that human beings are in the image of God -- and the rationality thesis -- that human beings are animals; to give just one example of another feature that has been given as such a ground, some have suggested creative will. His rejection of the image of God thesis is less than adequate; it makes the assumption (again, false) that the only reason for accepting such a thesis is the belief that God created human beings in accordance with a pre-existing design; but this is to confuse questions of how we come to be in the image of God with questions of what it is that makes us like God, and therefore of divine worth, regardless of how we came to have it. His rejection of the rationality thesis is equally weak. He assumes that the primary sense of rationality in this context is "the ability to work things out about the world"; this is vague enough that perhaps it includes everything, but the primary sense in which rationality is relevant to this question is usually understood to be our capacity to engage in abstract moral reasoning -- to reason out moral principles, communicate them, and act according to them. Unlike more technical cognition about tools and coordination, this is not obviously distributed in different degrees throughout the animal kingdom. But even if it were, all this would do is cause problems for II, not I. To hold that all animals should be regarded as having dignity like human dignity in the degree that they are regarded as having rationality is a coherent position.

His rejection of the claim that even if rationality were unique to humans it still would not be a supreme adaptation seems to me to be more muddled still. It is simply wrong to say that after Darwin biology has anything to say at all about what constitutes a "supreme adaptation" or not; it lacks the tools entirely for doing it, since it only deals with the degree of reproductive and survival success. But it's difficult to find cases where people justify the supremacy of rationality in terms of its superior contribution to our survival or reproductive fitness; we usually evaluate rationality as important because it is valuable for moral ends. So the fact that, in biological terms, rationality is just one adaptation among many -- if it really is even quite right to consider it an adaptation at all rather than, from a biological point of view, something of an accident -- is irrelevant to the question. Multiply adaptations as you please; it still remains a question of how valuable any of them are for human valuing, which is, after all, what we are talking about when we are talking about human dignity.

And this is all in the course of one short passage of a few paragraphs; I have to say I don't think it bodes well for the book from which it is excerpted.

Represent!

If I were a Springer-Verlag Graduate Text in Mathematics, I would be J.-P. Serre's Linear Representations of Finite Groups. My creator is a Professor at the College de France. He has previously published a number of books, including Groupes Algebriques et Corps de Classes, Corps Locaux, and Cours d'Arithmetique (A Course in Arithmetic, published by Springer-Verlag as Vol. 7 in the Graduate Texts in Mathematics). Which Springer GTM would you be? The Springer GTM Test

(ht)

My knowledge of this field is so slight that the sum total of what I know is that it's part of a more general field, representation theory for groups, and that it's the part that represents finite groups using linear algebra. Or something like that.