Hi there, Prof. Stroup, I'm not sure what you mean. Perhaps you are thinking of Donatello's David--a sexy adolescent boy in bronze with a long feather from Goliath's helmet gently caressing his leg all the way up to his shapely buttocks? It was commissioned by Cosimo de Medici and certainly testing the boundaries of acceptability. One thing on the male nude in the Renaissance that you could help me with, actually, is this ancient category of the "ephebic" nude, I think is the term? I'm probably spelling it wrong, but it relates to this kind of young male who is to be educated by an older mentor--something I'm remembering from Plato's Phaedrus, too, I think?

The pork thing comes largely from Acts 10 where Peter has a vision where a voice told him to eat non-kosher animals, he refuses and then the voice said, "What God has made clean, you must not call profane."

So that's considered by most Christians to be a signal that anything that was considered ritually unclean is now OK. There are a lot of arguments within Christianity about which rules are considered to be moral issues or whether they were forbidden based on ritual cleanliness rules. That's often (but not always) the driving force behind denominational splits.

Unannounced squads of armed Marines on commercial vessels. I'm dead serious. It would only take a handful of pirate ships with all hands killed and the vessel sunk for them to find the practice no longer economically viable.

It's almost always dangerous to equate historical events with contemporary conditions, for the purposes of shaping current policy. That said, political leaders often do this to inspire and justify political and military actions. For example, Rep. Steven King (R-Iowa) and former Speaker of the House Newt Gingrich, a few years back, were fond of comparing the US-Barbary Wars (waged against North African pirates, during the 18th and 19th centuries) with the War on Terror.

Such comparisons not only typically distort history for self-serving purposes (Several Marine historians pointed out gross factual errors in these comparisons.), but they often result in ineffective and/or counterproductive policy. And the historians who abet these kinds of politically motivated analogies--particularly in the service of justifying asymmetrical, so-called "savage wars of peace"? (I could name names. Several teach at Ivy League universities.) Shame on them.

This question just makes me sad. When I was a kid (and even when I was in college), the Pirates were a very cool team. Willy Stargell, Dave Parker, and company. They had the coolest uniforms and true swagger. Sure there was the occasional drug bust (cocaine, not 'roids), but there was also a lot of community spirit on those teams, and players tended to give back, following in the spirt of the legendary Roberto Clemente. They WERE pirates. Good bad boys.

Likewise, the Mariners (another nautically themed team) seem destined for continuing misery. I love the international flair of the team, and seeing a game at the Safe is almost like being at sea. I've spent a number of lovely evenings there, gazing out over Puget Sound, while eating surprisingly good concession-stand sushi (as the home team gets pounded...again). And the parking situation in SoDo? That's the closest thing to actual piracy that I've encountered.

So, I'm not exactly how to answer your question. I'd like it if both teams returned to their former glory (although I guess the Mariners' was, historically speaking, somewhat short-lived). If I had a better answer to this question, I'd probably be scouting for the MLB, rather than teaching American studies.

If you want to get outside the Western canon, Hawkes' and Minford's translations of "The Story of the Stone" (sometimes also called Dream of the Red Chamber) is a wonderful translation of one of the great classics of Chinese literature. Both Hawkes and Minford are good writers, and the novel is wonderful, even if you don't know the historical and cultural context. It's a little like In Search of Lost Time, in that it is long and not exactly action-packed, but the book is full of subtle social interactions and there's a lot of powerful emotional content. It's also five volumes long, and thus will keep you occupied for a little while.

I've always taken it to mean that the characters are dancing just as fast as they can.

You could just read the play and find out, of course.

Hey Brent-

So.. You are making reference to the Continuum Hypothesis, about which a lot of very trippy shit has been written, most of which sounds like wierdo la-la land to me. Funny how even theoretical mathematics can seem quite hands on and concrete when set against wierd shit like set theory or logic. Ok, I am letting my bias show. Sorry about that.

For anyone else reading this, here is a quick overview of what we are talking about (apologies if it is too brief):

To talk about sizes of sets, when sets are finite, is pretty intuitive. A set with 5 elements has more things than a set with 3 things, though less things than a set with 25 things. From now on, let A and B refer to sets, and let |A| refer to the size of set A.

On the other hand, how should one distinguish between sets of infinite size? Is it even possible to distinguish? Well, the approach taken by Georg Cantor at the end of the 19th century was to consider set maps: If there is a 1-1 map from A to B (namely, a way of pairing elements of A with elements of B, in such a way that no two elements from A have the same partner), then we will say |A| <= |B|. Sets A and B have the same size (|A|=|B|) if |A| <= |B| and |B| <= |A|. (You should read <= as 'less than or equal to'). You can check that the set of the even integers has the same size as the set of odd integers, or as the set of all integers. If, in addition, it is not possible to match pairs so each element of B has a partner from A, then we write |B| > |A|.

You can also check that, for any set A, |A|<|P(A)|, where P(A) is the set of subsets of A (referred to as 'the power set'). For any finite set A, |P(A)|=2^|A| (a simple exercise), and, by properly interpreting 2^|A| as the size of the set of maps from A to {0,1}, we have |P(A)|=2^|A| for any set A. By the above, |A| < 2^|A|, for any set A.

Let's let N refer to the set of positive integers {1,2,3,4,...}. ("Countable infinity" means |N|, i.e. can be counted one by one). Let's also let R refer to the set of all real numbers (all decimals of any size, large or small).

The above skeleton of an argument shows that there is a chain of set sizes |N| < 2^|N| < 2^(2^|N|) < ... This is of course a rather strange thing to get used to. It means that there are arbitrarily many infinities that are all different from each other.

It is not hard to see, by writing the real numbers in binary notation, that 2^|N|=|R|. This means we must have |R| > |N|, so |R| cannot be countably infinite. This is why |R| is called "uncountable". Cantor showed this fact by a now classic argument referred to as diagonalization. It is pretty stunning if you think about it.. Ok this is getting long.

So, one issue with the way you've stated the question is that "uncountably infinite" by definition means any set A with |A| > |N|. In that sense, every infinite set is either countable or uncountable, so the simple answer to your question is no, there is nothing between countable and uncountable.

Of course, I know what you meant. Cantor asked the straightforward question: If |N| < 2^|N|, is there anything inbetween? That is, is there a set A so that |N| < |A| < 2^|N|? A negative answer is called the Continuum Hypothesis (CH), while a positive answer would be the negation of CH. Apparently it drove Cantor into the insane asylum, so.. Caution!

So finally to the point: Kurt Godel and Paul Cohen together showed sixty years ago that CH is independent of ZFC. That is: If you start with the basic set axioms from Zermelo-Fraenkel set theory, and throw in the Axiom of Choice (together this is ZFC-- if you are curious about the details you can read about it online, but you can just think of this as a basic logical framework to talk about sets), then you may either assume the continuum hypothesis as an axiom, or assume its contradiction as an axiom, and your logical world will still be consistent. Let me say that again: you can ASSUME CH or ASSUME NOT CH, and still everything from the standpoint of truth verifiability is totally gravy. Holy shit!

Did I mention this shit is tripped out?

This means the only way to prove or disprove CH would be to come up with a stronger set of axioms for sets, that mathematicians agree are an accurate intuitive framework for doing set theory, and then doing your proof from there. So.. good luck with that. Apparently wikipedia says some people still work on this stuff, and have various proposals for what axioms one should use.. I have no idea, but take the advice of people much wiser than me to avoid like the plague trying to answer this one way or the other.

Anyway, all that aside, I like your idea! I can't think of such a function after thinking about it a few minutes.. And the business of finding Q seems like it would be the truly difficult part. Though, of course, as I pointed out above, unless your constructions will use some set axioms beyond the ones of ZFC (which I am not well acquainted with, but to my naive understanding seem to be the ones one does work with), then your goal is hopeless.

You need to read up on Georg Cantor.

He thought about all that stuff a long time ago and then went nuts.

Whoa, I just read an article about the subject earlier today:

http://www.nybooks.com/articles/archives/2010/oct/14/pirates-are-winning/?pagination=false

A summary:

Pirating is the way of life in Somalia--entire local/regional economies are based on it. For example, pirating groups are organized into various "corporations," and people can essentially buy stock into these ventures. Also, they pay people to work for them. The whole notion is based on getting money from holding hostages, and the pirates try not to kill anyone, since they know that would only make the world angrier at them and more likely to retaliate. Once they get their ransom, they grab the money and flee. They are strongly motivated by money, even with the threat of death.

Companies/organizations prefer to deal with a pirate/hostage situation the easy way, which means paying off the pirates and writing off the losses, rather than organize a good number of countries/mercenaries/etc to go in and try to reorganize a whole country.

The Barbary Pirates of the olden days were ultimately defeated on land. The ocean is too large to be patrolled adequately, and this remains true today. In order to defeat pirating, a force would have to go into Somalia and establish order/government, which hasn't been in place for decades. Past efforts at trying to organize the country haven't gone so well (think Black Hawk Down), and it would be a huge undertaking to get in there and eradicate piracy.

If you've already got Math Type or Equation Editor, you should be able to just use them directly from Word. Just click Insert>Object in Word, and scroll down to Microsoft Equation Editor. Then you get the little toolbar on screen in your document without having to leave Word.

A: Specifically in regards to Tennessee Williams' play, I've appreciated when directors (and cast) ignore the temptation to literally assign Margaret as the aforementioned 'cat', and instead use the title to describe the absolute jumpingbean hailstorm of LIES inherent in 'polite' Southern society (regarding cancer, fertility, bisexuality, greed, birth control, the after-effect racism still in play from slavery (and the shameless greed in pursuing that ill-got treasure from the dying cotton industry), etc etc), as well as the doubt/mistrust and downright trouble that this breeds.

I've also heard it described as not terribly unlike The Tempest in it's commentary about dreams diverted, death and what different people's views may be of "rightful inheritance".
(also tied to that would be the idea of being stranded: the MS delta has 'islands', and Brick is nothing if not stranded without his crutch, and islands and far away lands (Peter and Jack's decor) are mentioned, the bed in the bedroom is essentially an island...).

Written in 1955, when lies of a 'denial' nature were catching on all over the nation, Williams' play was an especially-contrasting punch-in-the-gut view of american society. Especially postwar, when everyone wanted to believe "all is well, nothing to see here". Tennessee was a master of stirring the shit.

The very last thing the 'cat' can refer to is perhaps better described as a "fish -violently- out of its water" - the South itself.
You see, Big Daddy's vast wealth is highly unlikely - it's the biggest fantasy in the whole play. The North was growing fat on southern misfortune and their continuation of social inequity and legal mistakes. The contrast illustrated may be between the agri-centered primal old south (the cat) out of its element and in pain in a inhospitable, industrial-based and therefore hostile (hot tin roof) nation and world, with no forseeable way back to 'comfort'. (But the cat got its damn fool self up there to begin with, you know).

You may also want to see: http://www.xmission.com/~emailbox/phrases.htm#Like_a_cat_on_hot_bricks

As in you don't want it to look something like

a = (v^2) / r

or t = sqrt( [delta]v / [1/2]a )?

ie - you want your powers, roots, etc to actually 'look right'?

I'd try and familiarize myself with one of the programs designed for exam generation (there's a bunch).

I've always found that particular bit interesting, as many cultures have actually fetishized the sacrifice of a virgin, rather than prohibiting it. I can find almost no references to any societal strictures against murder of a virgin as opposed to murder of a deflowered girl.

It does make that particular episode of I, Claudius a bit more dramatic, though.

Read Acts 15. The key part is the letter to gentile believers.

"15:28 It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: 29You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things. Farewell."

As Peter says:
"15:10 Now then, why do you try to test God by putting on the necks of the disciples a yoke that neither we nor our fathers have been able to bear? 11No! We believe it is through the grace of our Lord Jesus that we are saved, just as they are."

The context being the issue of whether converts need to follow Jewish law. They basically boil it down to the key things that Christians must do (avoid idolatry, sexual immorality and animal cruelty).

Also, read Galatians. Paul gives a similar account and says explicitly man is not justified (made right with God) by following the law of Moses, but by faith. In Romans 5-7 he talks more extensively about this and says, Theologically, Christians have died in Christ and are therefore no longer bound to follow the law.

This doesn't mean immorality is now okay, but that "morality" proceeds out of God's love and grace and forgiveness and is not a means to earn his love, grace and forgiveness.

Basil is correct. Such a war would be unwinnable, since they have a vast country the size of Texas to hide in, and there are no other economic options, so there will always be young men looking for it. We've gone into Somalia before, with horrific results.

When the pirates complain about foreign ships fishing in their waters, and dumping toxic waste they don't want to take care of legally, they have a point. Countries really do do those things.

The pirates support the entire economy. One pirate haul might support a thousand people for a year. It's their whole economy.

For the West, it's just a cost of doing business. You run boats through the Red Sea, you're going to pay some pirate money and lose a few people now and then.

Where Basil goes wrong is where he says "in the long run the only way to really solve the problem is education, infrastructure, and stability." These things will never take hold in Somalia; the Somalis have been famously quarrelsome and rebellious for as long as non-Somalis have been aware of their existence, a thousand years or more.

Just another aggressive & confident church - nothing more, nothing less.

"A church that borrows imagery, music and speech tied to a culture it opposes and wants to change?"

You mean like Christianity did with the Pagans?

see also: Easter; Xmas...

(Or, to a lesser degree, 80's evangelical TV pastors (adopting music video formats to preach with, while at the same time denouncing music videos and cable television)?)

If we did, it would be yet another instance of our vast and mighty forces engaging in assymetrical warfare. We could win any battle, yes, but winning the war is another matter.

The fact is, the shipping lanes are busy, and consist of a very large space, and the pirates are small and mobile enough in their little inflatable skiffs that they can wait to attack until they're absolutely sure the coast is clear. They will never, ever allow themselves to get into a situation in which they are confronting a naval warship head-on.

I suppose we could send our ships out there and just start firing at people who looked like they were up to no good... but that would backfire.

No.

And no, it's not human nature so much as a bad choice repeated over and over again (like murder, for example).
I'd say the root might be:
Fear of the poorly understood by the ignorant, and a distinct lack of confidence in self/misunderstanding of humanity are at the root.

hmm.... I foresee a military operation dubbed "Operation Peter Pan".

Dan, the thing is, those ye olde tyme blasting of pirates never eradicated the industry of pirating (any more than jails eradicate burglary, or capital punishment eradicates murder).
Greed exists, therefore pirating will continue to manifest in some form.

But yes, I'd like to see the UN / major nations whoop some pirate ass. Televised for a nation (or several) hungry for pride in their homeland(s), please. Could possibly even be a bonding experience for nations otherwise at odds (imagine a Iranian/British/American joint venture...?).

I mean, it's a much better use of our military and tax dollars than the bullshit deja vu FAIL-fest going on in Afghanistan & less-so-now in Iraq. Right?

I would say the pirates are simply a side-effect of long standing economic depression, exploitation and war. To actually solve the problem, one would have to actually solve the cultural and economic problems of the region.

Otherwise, blowing up some pirate bases and boats probably won't stop people who are willing to go to such extremes, and really have no other options.

Kind of like fighting terrorism. You don't exactly win by killing more of them. It might work, but in the long run the only way to really solve the problem is education, infrastructure, and stability.

How about pharmacology? Pharmacists are in high demand and make good money, and there are many different fields to work in, besides at the local drug store, like working in hospital, in training or quality control. Some of that is working on the insurance or big pharma side, but it's work, and the money is good.

That particular detail was, I believe, created first by Hawthorne in 1852. Nothing about that in the classical texts, but it's a nice romantic Victorian twist.

The ancients believed in their gods the same way you and I believe in gravity.

"But we see gravity every day," you might say to me. But we don't, not really. We see behavior that is adequately explained by our understanding of gravity, as taught to us by people who know more about it than we do. And like most people, we don't understand gravity fully and are content to know that there are specialists out there who do, and they have a good handle on it.

If you replace "gravity" with "the gods," I think that's a pretty good explanation of how the ancients interacted with their notion of the divine. It was a different form of understanding the world, of building a rough-and-ready framework for understanding how the world works. Was it totally accurate? Certainly not. But is the understanding of science that you and I have totally accurate? Just as certainly not, and yet we can recognize that and still not reject it and still get along fine every day.

What's more, I think if you managed to convey to an ancient Hellene that you "don't believe in the gods," their reaction might be very similar to if I told you that I don't believe in gravity: puzzlement, perhaps a response that, well, something makes the grain grow every year, and maybe bemused curiosity or dismissive indifference.

Off the top of my head, I'd agree with your prof: this stands out as a shock-value account, perhaps referring to an older law indicating that a child could not be put to death. It could be a total fiction (not the law, which sounds reasonable, but the account of Livilla's rape) intended to underline the severity of Sejanus' crimes, and the severity of the response.

As cruelty to children is often used in narratives to make a larger or more dramatic point (I am thinking of the accounts of Paullus' triumph over Perses in 160 [he display's the conquered king's children, and the next day one of his sons dies: he is left childless]), I would guess that is what this is doing. I've not thought about this specific case, however, and now I am wondering about other examples of such (I know of none off the top of my head).

I would guess that the root source of homophobia would go back to small in-group and tribal societies, where reproduction was essential for the tribes survival. I could see how some of these cultures would ostracize a person who refused to reproduce with someone of the opposite sex.

It seems like for something like homophobia to start its existence, there would need to be a compelling social value that was served by it. From there, it was just tradition that carried it on.