

Monday, December 28, 2009

Why did Eutychus fall asleep? The physics of heating and ventilation

Acts 20:8-9 (NRSV) reads: "[Paul] continued speaking until midnight. There were many lamps in the room upstairs where we were meeting. A young man named Eutychus, who was sitting in the window, began to sink off into a deep sleep while Paul talked still longer. Overcome by sleep, he fell to the ground three floors below..."

Why does Luke mention the lamps? Did they contribute to the accident in some way? Some have suggested that the lamps made the air 'heavy' and that this made Eutychus sleepy, but I am not aware of any scientific assessment. Larkin suggests that "the boy must have tried to catch the night air by sitting on a windowsill". Haenchen and F.F.Bruce assumed that the air would be freshest by the window. But if the air was freshest there, why did he fall asleep?

I will argue that the lamps would have made the room comfortably warm and may have caused a soporific concentration of carbon dioxide in the air. I will also argue that the air may well have been more sleep-inducing at the window than elsewhere in the room.

Lamps produced a lot of heat and relatively little light. In a scientific experiment an oil lamp produced 60W of heat and only 10 lumens of light. A modern incandescent 60W light bulb produces the same heat, but gives 870 lumens of light. Along with its 60W of heat, the oil lamp produces 0.0084 cubic meters of carbon dioxide per hour. This is the same amount of heat and carbon dioxide as a typical person (modern adults produce 75W of sensible heat).

From what I can gather, upper floor rooms in insulae (apartment blocks) were typically 4m by 5m. We can imagine there being 20 people in the room and 30 oil lamps (or equivalent). The lamps would give a third of the light of a modern 60W bulb, so the room would still be dimly lit by our standards. Now, the people would then emit 1.2kW of heat and the lamps would produce 1.8kW, making a total of 3kW. Now, the incident occurred at the end of April or the beginning of May. At this time of year in nearby Istanbul the average daytime maximum temperature is 18C, and the nighttime minimum is 10C. Now, we do not know whether the room in question was constructed of brick or wood, so let us consider each case in turn.

Brick construction
Brick has a high volumetric heat capacity so the building's temperature will have varied little between day and night. The room will therefore have been at about 14C before the arrival of the large number of people and lamps. I have performed a computer simulation to calculate how much the room would warm with 3kW of heat starting at dusk (8pm). The model predicts that by midnight the effective temperature in the room would be a cozy 23C. Therefore the people and lamps are sure to have made the room comfortably warm and this may have contributed to Eutychus's drowsiness.

It is reasonable to suppose that they would have kept the door(s) and window(s) closed (for privacy and to avoid disturbing the neighbors) until the room had warmed up. I do not have a good estimate of what the natural air infiltration rate would have been. Well sealed modern buildings can give as little as 0.4 air changes per hour. If the room in question had 2 air changes per hour, the 30 lamps would have created a carbon dioxide (CO2) concentration of 4800 parts per million (ppm). This much CO2 could well have contributed to Eutychus's sleep since complaints of drowsiness occur at concentrations as low as 1000-2500 ppm. Also, since warm air rises, we should expect the CO2 concentration to be higher for Eutychus at the window, than for the others, who would have been at a lower level. Thus, it seems plausible that CO2 was a factor in inducing Eutychus's sleep. CO2 buildup would be possible only if the window was closed, but Eutychus would still fall out if the shutters or window covering were not secured. The image above is of carbonized wooden shutters in Herculaneum.

Wood construction
If the room in question was made of wood it is likely to have started the evening at a temperature above 14C since it would have gained heat from the outside during the day. It would also have warmed up quickly after the people and lamps arrived. By midnight the occupants would have needed to open the window(s) and perhaps door(s) to induce a considerable amount of ventilation to prevent over-heating. This ventilation would prevent a CO2 problem, but the temperature distribution in the room would be an issue. The through-draught needed to prevent over-heating would make the room cool at the end of the room where the fresh air entered, and warm at the end where the air left. Someone sitting at the warm end of the room might well start to feel sleepy and move to the nearest open window in search of cool air. Unfortunately the air in that window would be warmer, not cooler. To find the cool, fresh air, Eutychus would have needed to cross to the other side of the room where the cool air entered. Now, by midnight the ambient temperature will have been lower than the temperature of the air in the building, so there would have been a tendency for air to enter the building on the ground floor and rise by buoyancy and exit through the window on the third floor where Eutychus sat. Therefore, Eutychus is unlikely to have found fresh air at the window.

If the room was crowded, the window may have been the only available spot for Eutychus to sit. Alternatively, when he started to feel sleepy he may well have moved to the window in search of fresh air. Like Haenchen and Bruce, he may not have thought through the physics of air movement in a three floor building, for the air was probably warmer and richer in carbon dioxide at the window than elsewhere in the room. The heat produced by the lamps, and perhaps the carbon dioxide, will have helped to induce Eutychus's sleep and this may be why Luke mentions them.

To do a more thorough study we really need someone with expertise in ancient building architecture to collaborate with someone who is expert in thermal modeling of buildings and computational fluid dynamics (CFD). Any volunteers?

Friday, December 18, 2009

Epaenetus, Stephanas, and inscriptions









Wednesday, December 16, 2009







Saturday, December 12, 2009

Paul's visits to Troas

How Acts 16:6-11 explains 2 Cor 2:12-13
In Acts 16:6-11 we read that Paul and his companions were not permitted to preach in the province of Asia, which included Troas. They arrived in Troas but immediately are called to Macedonia. Evidently, they did not evangelize Troas or indeed its region, the Troad.

In 2 Cor 2:12-13 we learn that Paul's anxious desire to meet Titus drove him from the Troad to Macedonia. Paul had presumably communicated his Ephesus-Troad-Macedonia travel plan to Titus, who was to leave Corinth and travel to wherever Paul was scheduled to be at the time. Paul therefore knew that Titus would not arrive in Troas after the date that Paul had been due to leave. Paul, proceeded to Macedonia when this date passed because he was anxious to meet Titus as soon as possible. Paul had to stick to his original schedule to meet Titus the soonest. Now, Paul writes that he had gone to the Troad to evangelize and that a door was opened for him. The implication is that an unexpected opportunity for evangelism had arisen and that, had it not been for his anxiety, he would have extended his stay in the Troad beyond his scheduled departure date to exploit this opportunity. This makes it rather likely that Paul had not previously evangelized the Troad. If he had done so, he would have known what to expect and he would have been better able to judge how long he would wish to devote to that region. The opening of the door was unexpected because he had not tried that door before.

So, there is a minor point of agreement here between Acts and 2 Corinthians. Both imply that Paul did not preach in the Troad on his way to Macedonia.

How 2 Cor 2:12-13 explains Acts 20:6
When Paul went to Troas for the third time his desire to preach there was so strong that he spoke until midnight (Acts 20:7) and continued to converse until dawn (Acts 20:11), when he left for a full day's journey to Assos without having slept at all. He also devoted o fewer than 7 days to Troas (Acts 20:6), even though he was in a hurry to reach Jerusalem (Acts 20:16)? Haenchen thought that Paul had difficulty finding a ship, and Pervo also suggests that the delay in Troas was involuntary, but this extended stay in Troas is simply explained by the priority that Paul placed on preaching in Troas.

All this agrees well with 2 Cor 2:12-13, which tell us that, a few months earlier, Paul had had to leave the Troad in a hurry, leaving preaching opportunities unexploited. It makes sense that Paul would want to spend a week in Troas to complete the work that he had cut short the previous year.

Acts and 2 Corinthians are in harmony here too.

The commentators seem to have missed these points.

Friday, December 11, 2009

Acts 24:17, the collection, and Ananias

Acts 24:17 reads:






Saturday, December 5, 2009

The plot against Paul (Acts 20:3)

We read in Acts 20:3 that the Jews made a plot against Paul when he was about to set sail for Syria. I will argue that the plot is historical and that it consisted of the decision by the Jews to intercept Paul if he attempted to deliver the collection. Points 3, 4, 5, and 8, are new.

1. Paul nowhere identifies anyone who helped with the collection. The two 'brothers' in 2 Cor 8:18-24 and the 'brother' of 2 Cor 12:18 are strangely anonymous, and Paul conspicuously uses Timothy's lesser-known name (Titus) when discussing him in connection to his missions to organize the collection. These silences are explicable if Paul was aware of opposition to the collection and was worried that it would be endangered if the identities of the helpers would leak out.

2. The plot was when Paul was about to sail. This is historically plausible since only at that time would it have been possible for the Jews to attempt to intercept the collection. Before that time the collection was dispersed in the homes of the individual donors (see 1 Cor 16:2).

3. If the plot was to attack Paul's person, it is surprising that he found out about it. If, on the other hand, Paul had been publicly forbidden from delivering the collection, he would have had reason to suspect that he would be under surveillance. Paul's knowledge of the "plot" is then explicable.

4. If the Jews (who had been given jurisdiction by Gallio) had declared the collection illegal, it would have been too dangerous for Paul to return to the Aegean after delivering the collection, and this would explain why Paul knew that he would not see the Ephesians again (Acts 20:25). The collection's illegality also explains why Acts does not mention it (for Luke is always careful to avoid giving any hint that the Christians do anything illegal).

5. We read that to avoid the plot Paul went north to Macedonia (Acts 20:3) and he sailed from Philippi and stayed in Troas (Acts 20:5). Why Philippi and Troas, rather than, for example, Beroea, Thesssalonica, or Ephesus? This was a long diversion, given his tight schedule (Acts 20:16). Well, it occurs to me that Philippi and Troas are the cities where he would have been safest from the plot of the Jews. We have no evidence of a synagogue in Philippi, and Acts records no Jewish opposition to Paul there. Also, there is no evidence that there were Jews in Troas in the first century.

6. Jewett argues that the boat that Paul took from Philippi to Patara was probably a coastal freighter that he had obtained for his exclusive use. This would have avoided the risk of being betrayed by fellow-passengers or port officials.

7. Paul's decision to split the party (Acts 20:5) will have served to protect the collection (so Gilchrist). The delegates (who were not under suspicion) would have been able to carry the collection with little risk of ambush, while Paul and Luke travelled separately with their empty pockets hanging out. Paul also travelled independently to Assos (Acts 20:13-14) and this also makes sense as a precaution against being arrested or ambushed while boarding a boat with the collection.

8. At first sight it seems that this "we" passage gives a surprisingly detailed and boring account of the journey. However, if the intended readers were expected to know that Paul was in danger of arrest or ambush, this passage is a gripping account of a daring escape and its inclusion is explicable.

It seems to me that the contents of this "We passage" comport well with the preceding mention of the plot (Acts 20:3). It is hard to imagine that Luke has inserted someone else's travel diary into his text at this point, as many suppose.

In summary: Paul, knowing that the collection would be opposed by synagogue Jews, chose to protect the identities of those who were to deliver it. The Jews in Achaia forbid Paul from delivering the collection, but he chose to do so anyway, even though he knew that he would be arrested if he ever returned to the Aegean. He was aware that he was under suspicion and that if he took a boat heading east he could be betrayed by crew or fellow passengers. He therefore headed north to Philippi, where there were few, if any, Jews who opposed him. Knowing that he was under more suspicion than the delegates, he sent them ahead to Troas with the money. Later, he walked from Troas to Assos, as a diversionary tactic, while the others took the money in the boat. To avoid being betrayed by fellow passengers they chartered a coastal freighter for their private use. Luke did not want to mention the collection in writing because of its illegality (Acts might fall into the hands of opponents), but his intended readers probably already knew about it. He wrote a dramatic account of how he and the others smuggled the collection out of the Aegean.