Feast of Orthodoxy

Today is the first Sunday of Great Lent (the Sunday of Orthodoxy), which features a procession of icons in the liturgy. In the 700s, there was a string of three icon-hating emperors (Leo III, Constantine V, Leo IV) who persecuted the faithful who maintained the veneration of the icons. Constantine V in fact attempted to hold an ecumenical council to condemn icons (the pseudo-council of Hiereia, 754) in which 380 bishops participated but no patriarchs. When Leo IV died, his wife St. Irene became Empress and slowly restored the full use of icons and held the Council of Nicaea II (787) which condemned iconoclasm and is notable for its great leniency toward repentent iconoclast bishops. But in 813, another string of three iconclastic Byzantine emperors arose (Leo V, Michael II, Theophilus) – known as the second period of Byzantine iconoclasm. The second period again ended when after Theophilus’s death, a woman became ruler (St. Theodora) and, creating a tradition that has lasted until today, had the icons returned to the churches in a solemn procession on the first Sunday of Lent in 842. For more on history and the tradition behind icon use, see Giakalis, Ambrosios, Images of the Divine: The Theology of Icons at the Seventh Ecumenical Council, 2nd ed. (Leiden: Brill, 2005).

Biblical Notes on Icons
Jesus says that the gold of the Temple is sacred because the Temple is sacred, and the Temple is sacred because God dwells in it (Matthew 23:18, 21). Just so, icons are sacred because the saints they depict are sacred, and the saints are sacred because God dwells in them (1 Corinthians 3:16).

That icons produce miracles is not surprising given that Jews laid out their sick on the street in the hope they would be healed by being covered by St. Peter’s shadow (Acts 5:15), which as St. John Damascene points out, is a type of image. Consider also how the woman with the issue of blood is cured by simply touching Christ’s garment (Matthew 9:20).

Dogmatic and Historical Notes on Icons
The Orthodox position is that icons should always be venerated, but never worshipped with the same worship due to God alone. It may be alleged that such a distinction is ad hoc, but in fact we have an example of a bishop invoking it long before the iconoclast controversy. The sixth-century anti-Chalcedonian Patriarch of Antioch, Severus, who supported veneration of saints, chastises certain Christians who “worship the angels like gods; and again, without moderation, they go forth beyond lawful boundaries” (Homily LXXII.3), and remarks the difference between pious Christians and “those who worship angels and attach to them the glory and worship which are due to God alone” (4).

Another iconoclastic argument is: depictions of Christ are useless because each race depicts Christ differently. St. Photius gives a particularly insightful reply (PG 101:948 ff). Rather than arguing that only the Byzantines have correctly depicted Christ, he says that such differences matter no more than the fact that the Gospel has been translated into many languages. Just as the many translations all point to the same Gospel, so too do the many depictions of Christ all point to the same God-Man. He also add that the widespread use and veneration of icons among all the different races of Christians in fact confirms the antiquity of the practice.

Notes on Icons Today
During Byzantine iconoclasm, iconodules noted that icons help teach the faith and demonstrate our faith in the Incarnation. During the Third Reich in Germany, a racial anti-Semitic theology came into vogue, which denied that God became a Jewish man, thereby essentially denying the incarnation. St. Maria Skobstova (an Orthodox nun in Nazi-occupied Paris, who helped Jews escape), when asked by Nazi officials if she had any Jews in her house, would respond affirmatively and return with all the icons she had of the Theotokos and of Christ.

Not only are icons helpful teaching tools, but they are primarily sacramental. A problem that came up during the controversy in the Byzantine iconoclasm was whether it was fitting for sacraments to be kept outside of the churches – iconoclasts seemed to lean no, while the Orthodox said yes. Even today, icons help ensure that access to God is not limited to the clergy:

It was true that in all Orthodox jurisdictions all but the very lowest formal positions were held exclusively by men. Priests, monks, bishops, etc. could ask for miracles, but they could not make them. Icons, like relics, living (lay) saints, and the earnest prayers of lay believers, were considered effective sources of religious help. More than that, they were independent sources of religious authority. While they were not in competition with structural hierarchs, they are also not subordinate to them. They were accessible and responsive to lay believers, most of whom were female, and therefore gave Orthodox women alternative sources of authority and legitimacy (Weaver, Dorothy C., ‘Shifting agency: male clergy, female believers, and the role of icons’, Material Religion, 7, 3 (2011), p. 417).


Lonergan on Eschatology

I have transcribed some handwritten notes the Canadian theologian Bernard Lonergan SJ left on some New Testament verses generally considered eschatological. He is brilliant as usual. Square brackets are mine, round brackets are Lonergan’s.

Textes Eschatologiques

Matt 1023
NB. Discourse partly particular partly referring to general mission of disciples esp 1017 onwards.
cf. Dan 713f the 5th kingdom. not eschatological. Refers to “cette magnifique et soudaine extension du règne messianique que constitutera la conversion des gentiles” [“this magnificent and sudden extension of the messianic reign that the conversion of the gentiles will constitute”] cf. Dan 714

Matt 1627, 28 Mc 91 Lc 927       2 Pet 116
Eschatological Matt 1627 Mc 838 Lc 926
No separation in Matthew. In Mc, new chapter καὶ ἔλεγεν αὐτοῖς [And he said to them]. In Lc, λέγω δὲ ὑμῖν ἀληθῶς [But I tell you truly].
Mt.  donec videant Filium hominis venientem in regno suo
Mc.  donec videant regnum Dei veniens in virtute
Lc.   donec videant regnum Dei
Apparently cf. Dan 713, 14 Matt means no more than Mk + Lc.
virtute = spiritual power cf. St. Paul δύναμις (?)

Matt 2663f, Mc 1461f, Lc 2267f
Lc. No question of eschatology.
Are you Xt? Yes but my present appearance does not confirm it. I cannot convince you by argument. However you shall see the kingdom prophesied by Daniel. Moreover I am Son of God. “seated at right hand” which is not in Daniel cf. stoning of Stephen.
Mc. Mt. ὄψεσθε [you will see] Lc. ἔσται [will be] equivalent. Question is “who are you?” answer in apocalyptic style.

Matt 2338, Lc 1335 (Rom 1125)
Luke puts the λογιον before triumphal entry into Jerusalem
ἰδοὺ ἀφίεται ὑμῖν ὁ οἶκος ὑμῶν Jer 225 127.
οὐ μὴ ἴδητέ με ἕως ἥξει ὅτε εἴπητε·
Εὐλογημένος ὁ ἐρχόμενος ἐν ὀνόματι κυρίου. Ps 11726
1° Does not seem to refer to entry into Jerusalem. Context too general.
2° Addressed to “Jerusalem”
3° You would not receive me
  You will lose your inheritance of grace
You will not have another chance till your final conversion
4° The verse “Εὐλογημένος ὁ ἐρχόμενος” is a Messianic prophesy cf Ps 11722,23 “The stone which the builders rejected; the same has become the head of the corner. This is the Lord’s doing and it is wonderful in our eyes.”
5° Therefore οὐ μὴ ἴδητέ με ἕως κτλ simply means this is your last chance; you will not be asked again; the “Kingdom” will come but you will not be the Kingdom; you will say εὐλογημένος = you will have just grounds for saying ∵ the Kingdom is a fact, a fait accompli; the gentiles will receive of the inheritance

N.B. Mt 2335 quem occidistis inter templum et altare [whom you killed between the sanctuary and the altar]. solidarity of the present generation with the whole Jewish race.
cf. Dan 926,27 occidetur Xtus [the Antointed/Christ will be cut off/killed] etc. Lc 2123,24 separate destruction of Jerusalem + end of world
Mt. 2422-28 Prophetic confusion of destruction of Jerusalem + end of world.
II Pet. 116 on “Transfiguration”




Shading Candles

You are sitting in a room and it is dusk. Candles have been brought in that you may see to get on with the work in hand. Then you try to look up and out to the garden which lies beyond; and all you can see is the reflection of the candles in the window. To see the garden the candles must be shaded.
Now that is what philosophy does. It prevents us from being dazzled by what we know. It is a form of thinking which ends by saying, don’t think – look.

Maurice O’Connor Drury, The Danger of Words and Writings on Wittgenstein (Bristol: Thoemmes, 2003), p. 114.

Maurice O’Connor Drury was a friend of Wittgenstein from the late 1920s right up to the latter’s death. His book The Danger of Words is a collection of five essays originally prepared as speeches for various audiences. The above passage comes from the fourth, ‘Hypotheses and Philosophy’, which begins with a hypothetical scenario from the Francis Bacon scholar Thomas B. Macaulay. The emperor Justinian, upon his closure of the school of Athens, decides to ask its teachers (e.g., Simplicius, Isidore) what abiding results philosophy has achieved for humankind. Macaulay’s response is that ancient philosophy has had no lasting contribution to human knowledge. Modern philosophy (i.e., natural science), on the other hand, has cured disease, facilitated business, increase men’s powers, and so on. Drury responds, however, that the point of philosophy was never to add to human knowledge or human skill. It is to make us like Socrates and always be aware of what we do not know, to make “people say only just as much as they really know; that when, as happens in every generation, new advances in knowledge are made, they are not taken to be more important than they really are”, ensuring that human wonder remains secure.



  • A Time article on the link between smartphone use and adolescent depression. The article shows that researchers have not reached consensus on the nature of the link. One thing seems clear from my own experience: new technologies end up distracting us from each other and from nature, and ultimately from our own self.
  • Patriarch Ilia has caused a baby-boom in Georgia by promising to baptize and sponsor the third (or higher) child of married couples.
  • A Guardian article detailing the work of Jan Banning, who photographs communist parties around the world. Outside of the one in Kerala, India, they are pretty weak, but, Banning says, their motives are perhaps not without reason: “We drove some 5,000km in western Russia, saw quite a lot of these villages and small towns. It’s a disaster. You can clearly see the effects of neo-liberalism – public space has been dismantled, the roads are a mess, there are few shops left, the people are on their own.”
  • I went searching on Google to see how common it was for Christian mothers who have lost their children to take comfort in the pieta. I ended up coming across this remarkable article by Michele Chronister about how miscarriage grief is like (and unlike) other forms of loss of children.
  • David Bentley Hart has recently released new articles: ‘Human Dignity Was a Rarity Before Christianity’ at Notre Dame’s Church Life Journal, ‘Are Christians Supposed to Be Communists?’ at the New York Times, and ‘The Illusionist’, a review of Daniel Dennett’s new book on mind at The New Atlantis.

Contraception Failure

There is a New York Times article showing cumulative contraceptive failure rates over time, i.e., if you use a certain contraceptive method for five years, how likely is it that you would have become pregnant in that time? Here is how the values were calculated: “The probability that a woman doesn’t get pregnant at all over a given period of time is equal to the success rate of her contraceptive method, raised to the power of the number of years she uses that method.” By “success rate,” they mean percentage of women who avoid pregnancy in one year. However, it is important to remember that these rates are in fact only for the first year of use. The question becomes whether these rates can reasonably be applied to later years.

I have found a possible answer in a 2004 article by James Trussell, ‘Contraceptive failure in the United States’:

We confine attention to the first-year probabilities of pregnancy solely because probabilities for longer durations are generally not available. There are three main points to remember about the effectiveness of contraceptive methods over time. First, the risk of pregnancy during either perfect or typical use of a method should remain constant over time for an individual woman with a specific partner (providing that her underlying fecundity and frequency of intercourse do not change). Second, in contrast, the risk of pregnancy during typical use of a method will decline over time for a group of users, primarily because those users prone to fail do so early, leaving a pool of more diligent contraceptive users or those who are relatively infertile or who have lower coital frequency. This decline will be far less pronounced among users of those methods with little or no scope for imperfect use. Risk of pregnancy during perfect use for a group of users should decline as well, but this decline will not be as pronounced as that during typical use, because only the relatively more fecund and those with higher coital frequency are selected out early. For these reasons, the probability of becoming pregnant during the first year of use of a contraceptive method will be higher than the probability of becoming pregnant during the second year of use. Third, probabilities of pregnancy cumulate over time.

As the final sentence indicates, what the New York Times authors have done is mathematically correct. However, they should not have been so quick to take the first-year “success rate” and assume it is the same in the following years. The first-year rate includes women who, for one reason or another, were unsuited to use that kind of contraception (e.g., due to difficulty in regimen adherence, physiological reasons, etc.) and became pregnant and stopped using it. It follows that the second-year “success rate” will be greater, since it no longer includes these users. However, one might predict the reverse: perhaps the second-year “success rate” will actually be lower, since users who did not get pregnant in the first year might become more complacent about adherence.

Quickly searching, I was able to locate one study that measured non-injection hormonal contraceptive failure rate over three years (this category includes not just oral contraceptives, but also patches and rings). The cumulative failure rate was 4.8%, 7.8%, and 9.4%, after one, two, and three years, respectively. As one can see, the failure rates after two and three years were lower than what would be predicted based solely off the first year number (predicted: year 2, 9.3%; year 3, 13.7%). Although a look at the numbers for injectable (DMPA) contraception might give us caution: 0.1% after year 1, 0.7% after year 2, 0.7% after year 3. The number after the second year is in fact higher than the predicted value based on the failure rate after one year (predicted: 0.2%), but then after that, there were no additional contraceptive failures. I am not sure what the answer for this is, but it should give us pause about relying too much on this study. While I can admit that the study suggests that it’s common for contraceptive success rates to rise after one year of use, I cannot say this is certain. Finally, the cumulative failure rates for IUDs and implants over three years were: 0.3%, 0.6%, 0.9%. This matches up with the predicated values based off the first year (predicted: after year 2, 0.5991%; after year 3, 0.897%), probably because user adherence is hardly an issue here.

Cumulative contraception failure is an important area of research that seems neglected, given that “[t]he typical woman who uses reversible methods of contraception continuously from age 15 to age 45 would experience 1.8 contraceptive failures. If we consider both reversible methods and sterilization, the typical woman would experience only 1.3 contraceptive failures from age 15 to 45” (from the Trussell article). While it may be mentioned that there are much more effective methods (e.g., IUDs or implants) than what is commonly used, I find it very unfortunate that the one method with a perfect success rate often gets ignored or dismissed as impractical, especially given its role in developing certain virtues.



At the long term care facility at which I used to volunteer, bingo is played every other week or so. In the room in which it is held, there are six tables (numbered 1-6 in the sketch below), each holding about four players. There are also some individual seats for extra players. Each player receives two bingo cards, and bingo is usually played according to normal rules, with the exception that getting four corners on one of the bingo cards counts as a bingo as well.


Among other things, I was often responsible for distributing bingo cards to the players. I noticed that the two bingo cards I gave to a player typically carried a very similar series of numbers. I began to wonder if I could increase a player’s chances of winning if I gave them two cards with as minimal overlap as possible (and perhaps by doing so, decrease the number of balls the caller has to draw in order to reach bingo). I figured wins would occur more quickly with a diverse pair of cards, for the same reason that you gain no advantage in the lotto when having two identical sets of numbers.

Running the numbers
I made a simulation using Java, which I checked by comparing the numbers it generated with the probabilities calculated on this site. After verifying, I set up a game with thirty players, each having two randomly generated cards. I then ran 10,000 games to determine the most likely ways to reach bingo. The 10,000 games resulted in 12,051 bingos (more than one bingo can occur per game if two or more players reach bingo at the same time). The data is as follows:
running the numbers

Note the following:

  • 59% of bingos used the free space. This is especially notable since there are more ways to get a bingo without a free space (9) than there are with a free space (4). If we exclude from the analysis the numbers from four corners bingo, the percentage of bingos that did not use the free space falls from 41% to 32.5%.
  • Approximately 25% of games resulted in multiple bingos.

Is a lack of card overlap advantageous?
Next I made sure one of the thirty players had no overlap whatsoever between his cards (call him player X). All the other members had randomly generated cards, which almost always contained some overlap, usually 4 or 5 numbers overlapping between cards on average. I ran one million games. The percentage of winning bingos belonging to player X was, on average, 3.37%. To be more specific about the method, I ran 100,000 games at a time, with player X having the same pair of cards for all 100,000 games, and all other players getting randomly generated cards each match. I ran this ten times for a total of 1,000,000 games. The upshot of all this is that there is no practical benefit for a player to have no overlap between his cards, as any given player has a 1/30 = 3.33% chance of winning a game of chance involving 30 players.

Does card overlap increase time needed to reach bingo?
The above results suggest that card overlap has little effect on time to reach bingo. To confirm, I ran 100,000 games where all players had a purely randomly generated set of cards and another 100,000 where each player had zero overlap between his cards (though this doesn’t rule out the inevitable overlap among different players’ cards). The results showed no difference in number of balls drawn to reach bingo (approximately 18.0 turns in either case).

The answer to all my initial questions was “no.” Practically speaking, overlap on the cards has no effect on the outcome of the game. One reason for this is that, unlike the example of the lotto numbers, the location of the number matters. Having the same number on both cards is not always a mere repetition because the ‘value’ of a bingo number depends on the numbers around it and, also, an overlapped number may fall on a different spot in the two cards.

I think the simulation is solid, given that I verified it independently. The only possible limitation I can think of is that, in the real life situation, there are only a limited set of cards, whereas the simulation randomly generates each pair – but I do not see how that would affect my results. Another possible issue is that player X’s cards were not randomized every game, but, again, I do not see how this would be a big issue, since the balls were randomly drawn each game and all the other players had cards randomly generated each game. It does raise an interesting question though: when we want a random simulation, should we make all parts random, or is it enough to have just one part random? I can share the source code for the simulation with anyone who wants it.