## Challenge Solution #1

I've posted the solution for the First Challenge Question in the comments section to that post.  St. Jack Spell's comment here is the winner, and my answer key is here, along with some secret knowledge which I promised to "Andrew2" (St. Andrew II?)

Congratulations to Jack---As a prize, he may suggest the topic for a post.  (But no promises about when I would do that post.)

Posted in Challenge Questions | 8 Comments

## Random Santa Fact

Oh, and I meant to include this random piece of information in the previous post but it slipped my mind:

♦  I just got back on Tuesday from a 3 week trip to Europe to go to some physics workshops in Brussels, Belgium and in Benasque, Spain.  While we were in Brussels, Nicole and I saw among many other things the Église St-Nicolas, a strange church near the Grand Place, which actually has privately owned shops built into the walls, completely surrounding the church!  According to our guidebook,

"A market church was built on this site at the end of the 13th century, but, like much of the Lower Town, it was damaged in the 1695 French bombardment.  A cannon ball lodged itself into an interior pillar and in 1714, the bell tower finally collapsed.  Several restoration projects were planned but none came to fruition until 1956, when the west side of the building was given a new Gothic style façade.

Dedicated to St. Nicolas, the patron saint of merchants, this low-lit atmospheric church is known for its choir stalls, dating from 1381, which depict the story of St. Nicolas on medallions..."

So, now you know which side Santa's bread is buttered on!  Explains a lot, doesn't it?

It is now 145 days until Christmas, so you have plenty of time to forget this fact if it is going to ruin your holidays.  Ho ho ho!

## Lots More Random Stuff

♦  A Roman cooking blog: Pass the Garum.

♦  An amazing carved tree trunk.

♦  I have a mild case of synethesia: I associate colors with letters and numbers.  Words tend to be associated primarily with the color of the first letter.  It's not really an actual perception of color, just a really strong association.

One day I made a table of which letters correspond to which colors.  But then I made a table of which numbers were associated with which letters:

## 0123456789

... and at around the time I got to E, I said, hey wait a minute, that's in rainbow order!  The culprit is here, and apparently I am not alone.

However, there appear to have been some mutations which have overcome various aspects of the original letter blocks.  First of all, the purples all seem to have washed out, mostly to browns, though L is a light bamboo. Each letter has differentiated to some degree from the others that were the same color, e.g. A is maroon while S is a lighter red while M is pink; these were all the same pinkish-red color in the magnet set.

I was mathematically inclined from an early age, and the association of 1/I with True/Something and 0/O with False/Nothing seems to have caused them to become white and black respectively.  The whiteness of I is probably also related to Ice.  P became Pink.  4-8 are related numbers, and so are 3-6-9.

My one regret is that, having become hopelessly corrupted by a mass-produced commercial product, my preferences aren't good evidence for what the REAL colors of each letter are.

♦  Having broached the subject of math and mysticism— here is a letter from André Weil (famous mathematician), to his sister St. Simone Weil (mystical writer, activist, and math teacher), explaining the role of analogy in mathematics.  (Not an easy read for non-math people!)

♦  The spoon theory of disease.  Of course, the interesting thing is that it has nothing per se to do with spoons, it just needs to be something concrete with positive associations which you can count.  Counting is one of the most fundamental mathematical analogies: you can use any kind of object to represent any other kind of object, in fact you can even use nonsense words like we were taught to do in kindergarten.  John Baez:

I like to think of it in terms of the following fairy tale. Long ago, if you were a shepherd and wanted to see if two finite sets of sheep were isomorphic, the most obvious way would be to look for an isomorphism. In other words, you would try to match each sheep in herd A with a sheep in herd B. But one day, along came a shepherd who invented decategorification. This person realized you could take each set and "count" it, setting up an isomorphism between it and some set of "numbers", which were nonsense words like "one, two, three, four,..." specially designed for this purpose. By comparing the resulting numbers, you could see if two herds were isomorphic without explicitly establishing an isomorphism!

According to this fairy tale, decategorification started out as the ultimate stroke of mathematical genius. Only later did it become a matter of dumb habit, which we are now struggling to overcome through the process of "categorification".

♦  Which is more important?  Random, low-quality mummy masks, or learning more about early manuscripts of the Gospels and other 1st-3rd century literary documents, by disassembling them into the papayrus fragments from which they were made?

Possible early fragment of St. Mark's Gospel from before 90 AD, but we'll have to wait for it to be published to assess the credibility of this.  (Some claim the earliest fragment of Mark's Gospel is 7Q5 (mid-1st century) from the Dead Sea Scrolls, but in my opinion the reconstruction of that text fragment is far too speculative to be convincing.

♦  Longtime commenter St. Jack Spell is currently writing a series on the historical evidence for the Resurrection: parts 1 2 3 4, with I think more to come 5, 6, 7, 8.  I found particularly noteworthy his argument that certain critical facts surrounding the Resurrection (the burial of Jesus, that the tomb was found empty, dating the earliest claims to have seen Jesus to very early on) are accepted even by most skeptical New Testament scholars.

♦  From the Wikipedia article on the origins of the University of Bologna.  The first university was run by the students:

The University arose around mutual aid societies of foreign students called "nations" (as they were grouped by nationality) for protection against city laws which imposed collective punishment on foreigners for the crimes and debts of their countrymen. These students then hired scholars from the city to teach them. In time the various "nations" decided to form a larger association, or universitas—thus, the university. The university grew to have a strong position of collective bargaining with the city, since by then it derived significant revenue through visiting foreign students, who would depart if they were not well treated. The foreign students in Bologna received greater rights, and collective punishment was ended. There was also collective bargaining with the scholars who served as professors at the university. By the initiation or threat of a student strike, the students could enforce their demands as to the content of courses and the pay professors would receive. University professors were hired, fired, and had their pay determined by an elected council of two representatives from every student "nation" which governed the institution, with the most important decisions requiring a majority vote from all the students to ratify. The professors could also be fined if they failed to finish classes on time, or complete course material by the end of the semester. A student committee, the "Denouncers of Professors", kept tabs on them and reported any misbehavior. Professors themselves were not powerless, however, forming a College of Teachers, and securing the rights to set examination fees and degree requirements. Eventually, the city ended this arrangement, paying professors from tax revenues and making it a chartered public university.

In some ways it makes a lot of sense that the people paying for the product should set the terms for what they would get in exchange.

♦  But maybe college kids shouldn't be allowed to run universities... apparently about half of college students believe that we see because of rays that come out of our eyes.  The extramission theory of vision strikes back!  Original article here (behind paywall).

♦  Then again, maybe we shouldn't let the people running them now be in charge either...

♦  The educational philosophy of mistakes.

♦  Why we should Radically Simplify Law.  On the Cato Institute website, but really both conservatives and liberals should be able to go along with this.  No one wins when the law is a complicated mess.

♦  Don't let fear stop you from travelling, a charming comic.

♦  A frank discussion by a gay adoptive father on the emotionally tragic consequences for a girl growing up without her mother.

In light of my previous post on gay marriage, I should probably say that—while I think that growing up with parents of both genders is the ideal situation (and having sexually unusual role models can be very confusing)—I still think being adopted by a gay couple is probably better than being in some large institutional setting, with little or no individual attention and affection provided.  So on balance I am not fundamentally opposed to same-sex couples adopting children, assuming that there aren't enough qualified opposite-sex adoptive parents to go around.  Adoption is all about coping with non-ideal situations.

But I do think it is wrong for a couple to deliberately create a new human being in any natural or artificial way, if the intention is to withdraw them from either of their biological parents.  Part of the point of the virtue of Chastity is to make sure that children come into existence in optimal environments for their physical, moral, and spiritual development.  The emotional needs of adults should come second.

♦  Speaking of the difference between ideal and non-ideal marriage partners, an erie piece about an unusual wedding.  The testimony of this saint is also well worth reading, and also her apocalyptic experience.

## Reflections on Gay Marriage

[I was going to present a list of links, but my commentary on one of them ballooned out of control.  Now it is a post.  Also, if any people in gay relationships are reading this, I don't hate you; I want only good things to happen to you.  It's just we don't agree on which things are in fact good.]

In light of the recent Supreme Court decision in which Justice Kennedy (a man whose fundamental job description is to interpret a written Constitution in light of precedent, remember) overturned thousands of years of precedent in light of few decades of liberal opinion concerning alternative sexualities, I begin by presenting:

Judaism's Sexual Revolution

This article explains, from a Jewish perspective, why the Torah's prohibition of (male) homosexuality wasn't just based on mere bigotry.  Some good insights in here; though some of the statements about historical causation seem oversimplistic, in broad outline I think the narrative is true.  Christians will need to make a few obvious corrections.  For example, we believe that celibacy is not only permissible, but—for those able to accept it—an even higher calling than marriage.  (And, since we don't accept double standards of chastity between the two genders, we believe that lesbianism is also wrong.)

I'm not going to analyse the legal reasoning of the Supreme Court decision right now, nor do I wish to explain in detail, in this particular post, why homosexual relationships are morally problematic.  Instead I would like to focus on the implications of gay marriage for the culture.  (It should go without saying to any reader of Plato, that it's a huge philosophical mistake to talk about the cultural effects of gay marriage without first discussing the morality of gay relationships!  But I'm going to do it anyway.)

God loves all of us, and his rules are not based on hate and contempt for any person.  They are based on his knowledge about what is genuinely best for us, "the perfect law that gives freedom" (James 1:25).  It really only takes a mustard seed of faith to believe that an omniscient being just might know a bit more about healthy sexual boundaries than we do.

Even nonreligious people should have the humility to realize that we aren't the first generation to gather experience about how the world works.  We live in a culture which is shockingly unrooted from the past.  Those who seek to normalize gay relationships should start by taking a long and hard look at previous cultures in which it was culturally tolerated for many generations, and ask whether they would really want to live in a society like those.

Mind you, history never repeats itself exactly.  Even those cultures which endorsed same-sex relationships have viewed them as an obviously distinct cultural category from Marriage.  That is because they were in tune with basic biological facts which we prefer to ignore, but still, it presents a new situation.  For the first time, gay relationships are being modelled on the norms and practices of heterosexual married couples, possibly leading to a more wholesome set of relationship norms.

Except for that annoying rule about not having sex with other people; apparently half of gay couples (not necessarily married) are in explicitly open relationships.  (Edit: the underlying study is available here, and some limitations of this study are discussed here.)  While I am sure that a small minority of gay couples follow all the rules of traditional sexual morality (no premarital sex, adultury, or divorce) except for the gender of the other partner (and the exclusive use of unnatural sex acts, which necessarily goes along with that choice), let's be honest and admit that, if there were still legal penalties for adultery, Marriage is the last thing that the Gay Rights Movement, taken as a whole, would have wanted.  (Not all gay people are on board with this; one of my friends from college is gay and sarcastically pointed out to me that too many gay people regard it as a "license for promiscuity.")

Like anyone else, what gay people need is to turn to Christ and learn to live in freedom from the harmful fleshly desires which are indeed part of the human condition for everyone.  But if they cannot accept this, it is far better that they should live in a committed exclusive relationship, than that they should live the notoriously promiscuous, reckless, and obscene lifestyle characteristic of the cultural venues of the gay community.  (Note: I do not identify all gay individuals or couples as being members of this "gay community"; those are different things.)

Recently several supposedly Christian denominations have also come out in favor of gay commitment ceremonies.  If they are really, really serious about "Marriage Equality", the first step is to emphasize that gay people are otherwise subject to the exact same rules about chastity as everyone else.  I have a feeling most of them will welch, saying something about how the "dynamics of oppression" and "homophobia" have made it so that they are "triggered" by hard words like "sin", and that what they really need is "affirmation and welcoming" and some vague talk about "committing to respect the other person for their unique personhood".  Bosh.  Real love is willing to lay down specific boundaries, the boundaries which are necessary for genuine love to thrive.  You simply can't extend an institution like Democracy or Marriage to a new group of people without first giving them a crash course in what the necessary working rules for that institution are.  Institutions can't exist without rules, any more than animals can exist without skeletons.

To be clear, a conservative Christian like myself cannot actually endorse any relationship which is forbidden by God.  But we can hope and pray that Gay Marriage is at least a step towards a more wholesome life for our friends who are gay, as compared to the likely alternatives.  It is a relationship which requires work, sacrifice, and commitment to another person.  Perhaps some diluted reflection of God's holiness can shine through a little.

But early signs are not all encouraging.  At the most recent Episcopal General Convention in Salt Lake City, in which the U.S. bishops endorsed new commitment ceremonies for gay couples, the following prayer was offered at an LGBT celebratory Eucharist:

“Spirit of Life, we thank you for disordering our boundaries and releasing our desires as we prepare this feast of delight: draw us out of hidden places and centers of conformity to feel your laughter and live in your pleasure.”

Needless to say, "disordering our boundaries and releasing our desires" sounds more like a pagan orgy than something a Christian priest should say.  "For God is not a God of disorder but of peace" (1 Cor 14:33).  The Holy Spirit does instill in us the desire for holiness and peace and submission.  If a spirit instead releases the desire for sensuality and lawlessness, that's a different kind of spirit, which comes from below, not above.  These are ordained Christian clergy, who theoretically believe that gay marriage is required based on justice (due to being the same as straight marriage), but who still can't help but portray it, in their own liturgical ceremonies, as being about transgressive wildness.  (Why not celebrate the newfound ability of gay couples to lead honorable and respectable lives of chaste decency, in obedience to God's commandments?  Becuase, deep down, they know that's not what they're doing!)

Intellectually, the libertine faction of gay activism (which really wants to destroy marriage) is strictly incompatible with the faction that wants those rules and boundaries (because that's what marriage is), but now for gay people as well as straight people.  And yet these two factions are in bed with each other.  (Uh, politically, I mean.)  Until the "conservative" faction excommunicates the "libertine" faction, even religiously sanctioned gay marriage simply won't approximate to the same thing that it means for straight people.

Many people scoff when conservatives claim that Gay Marriage will harm the institution of Ordinary Marriage, since obviously a small minority of people falling in love with each other can't really affect the majority culture.  Unless, of course, the effect on Straight Marriage is positive, then it could totally happen!  (Ironically, one of the benefits cited by this article is learning from gay and lesbian relationships that—guess what?men and women are different and therefore bring different things to a relationship!  The obvious next step, of asking whether the "male" traits might naturally complement or balance the "female" traits in some way that produces a more stable and wholesome union, does not seem to occur to them.)  Yet, when reading the writings of gay activists, it doesn't take very long to find claims that gay couples can help straight couples break out of the straightjackets of faithfulness and traditional gender roles.  Exactly the conservative claim, but now portrayed as a good thing!

But the conservative activists do have it backwards.  Gay marriage will not and cannot destroy straight marriage.  Straight marriage was already on the rocks, and its boundaries had become disordered to the point where many people could no longer tell what was the difference between it, and another union based primarily on romantic thrills.  The existence of gay marriage will accelerate certain harmful trends in how straight people percieve marriage, but not by very much.  For the most part, it hurts only the gay couple themselves, and anyone who cares about their well-being.

In any case, there is no need to panic.  God's law remains the same as before, and he still works in people's hearts to lead them to repent and follow Jesus.  Praise be to the Lord for his unsearchable riches and grace, and may he have mercy on me—a sinner.

Posted in Ethics, Politics | 29 Comments

## Physics Challenge #1: Nonrelativistic Metric

This is a new feature which I'd like to try out.  I will ask a question about concepts in theoretical physics, and the readers will try to answer it.  It may be a straightforward question, or it may be a trick question.  I figure this will give me a better idea of what my readership does and does not understand about what I've written, and give readers a chance to show off their skills.

Challenge #0 happened kind of accidentally in the comment section of this post, and there it was suggested that this might be a cool regular feature.  So let's give Challenge #1 a whirl, and see what happens.

The metric of special relativity in Cartesian coordinates, in units where the speed of light $c = 1$, is

(The d's are just a calculus notation to indicate that you can use this metric to measure infinitesimal distances between nearby points, something which is very useful in general relativity where the metric is a function of position.  Here, however the metric is constant in space and time, so you could replace the d's with $\Delta$'s if you like.)

It has a ten dimensional group of symmetries, called the Poincaré group, which preserve the metric.  These are the set of transformations acting on the t, x, y, and z coordinates which preserve the metric.  (See the link for details.)

Suppose that instead we want to do nonrelativistic Newtonian mechanics.  These are the laws of physics which people believed were true before St. Maxwell and Einstein came along, and which are still valid for describing objects travelling much slower than the speed of light.

1. What is the appropriate metric to use when describing the geometry of spacetime in non-relativistic physics?

2. What is the symmetry group of this metric?  How many dimensions does it have?

3. Are these the same as the symmetries of Newtonian physics, which this metric is supposed to describe?  Why or why not?

The correct answer to these questions reveals something surprising about the way in which relativity is an improvement on nonrelativistic physics.

You need not answer all of these questions, but the answers to one may help confirm that the answers to the others are correct.  Experts (e.g. those with graduate education in physics) are requested to wait a while before attempting an answer, in order to give others a chance to respond.

Posted in Challenge Questions | 31 Comments