Everything I Need To Know About Takeoff Speeds I Learned From Air Conditioner Ratings On Amazon

My overall take on this post and comment (after spending like 1.5 hours reading about AC design and statistics): 

Overall I feel like both the OP and this reply say some wrong things. The top Wirecutter recommendation is a dual-hose design. The testing procedure of Wirecutter does not seem to address infiltration in any way, and indeed the whole article does not discuss infiltration as it relates to cooling-efficiency. 

Overall efficiency loss from going to dual to single is something like 20-30%, which I do think is much lower than I think the OP implied, though it also is quite substantial, and indeed most of the top-ranked Amazon listings do not use any of the updated measurements that Paul is talking about, and so consumers do likely end up deceived about that. 

The top-rated AC Wentworth links to is really very weak if you take into account those losses, and I would be surprised if it adequately cooled people's homes. 

My current model: Wirecutter is doing OK but really not great here (with an actively confused testing procedure), Amazon ratings are indeed performing quite badly, and basically display most of the problems that Wentworth talks about. It's unclear whether AC companies are optimizing for the Amazon or the Wirecutter case here, which would require me seeing a trend in SACC over time. I expect many, possibly most consumers, are indeed being fooled into thinking their AC is 20-30% more effective than they think it is, because of infiltration issues. 

Separately, it's possible to me that consumers actually prefer a world where an AC doesn't cool their whole home, but creates a temperature gradient across the home. In the case of heating, I strongly prefer stoves and fireplaces that produce local heating (and substantially radiation heating), despite similar infiltration issues, because I like being able to move closer and farther away from the source of the heat to locally adjust temperature preferences, and I often live/work with people who have substantially different temperature preferences to me.

Overall, If I were to buy a portable AC today, I would choose Wirecutter's top pick, which happens to be a two-hose design. If that wasn't the case, I would probably still just go with the single-hose design, because I actually like temperature gradients. If I cared about cooling a whole building (which historically hasn't been the case), I would probably go with a dual-hose design. Reading Amazon reviews and ratings would have probably made my decision-making here marginally worse. Following the Wirecutter recommendation would have been OK but not great. It mostly would have pointed me towards the SACC as a better rating, and I probably would have figured out to buy an AC with a high SACC rating, and not historical BTU rating. 

My current guess is that most consumers are probably still deceived by non-SACC BTU ratings, but the situation seems to be getting better due to regulations.

↑ comment by johnswentworth · 2022-04-19T00:14:12.418Z · LW(p) · GW(p)

Update: I too have now spent like 1.5 hours reading about AC design and statistics, and I can now give a reasonable guess at exactly where the I-claim-obviously-ridiculous 20-30% number came from. Summary: the SACC/CEER standards use a weighted mix of two test conditions, with 80% of the weight on conditions in which outdoor air is only 3°F/1.6°C hotter than indoor air.

The whole backstory of the DOE's SACC/CEER rating rules is here. Single-hose air conditioners take center stage. The comments on the DOE's rule proposals can basically be summarized as:

• Single-hose AC manufacturers very much did not want infiltration air to be accounted for, and looked for any excuse to ignore it
• Electric companies very much did want infiltration air to be accounted for, and in particular wanted SACC to be measured at peak temperatures
• The DOE did its best to maintain a straight face in front of all this obvious bullshitting, and respond to it with legibly-reasonable arguments and statistics.

This quote in particular stands out:

De’ Longhi [an AC manufacturer] expressed concern that modifying the AHAM PAC-1-2014 method to account for infiltration air would disproportionately impact single-duct portable AC performance and subsequently cause the removal of such products from the market.

So the manufacturers themselves know perfectly well that these products are shit, and won't be viable in the market if infiltration is properly accounted for. However, the DOE responds:

However, as discussed further in section III.C.2, section III.C.3, and III.H of this final rule, the rating conditions and SACC calculation proposed in the November 2015 SNOPR mitigate De’ Longhi’s concerns. DOE recognizes that the impact of infiltration on portable AC performance is test-condition dependent and, thus, more extreme outdoor test conditions (i.e., elevated temperature and humidity) emphasize any infiltration related performance differences. The rating conditions and weighting factors proposed in the November 2015 SNOPR, and adopted in this final rule (see section III.C.2.a and section III.C.3 of this final rule), represent more moderate conditions than those proposed in the February 2015 NOPR. Therefore, the performance impact of infiltration air heat transfer on all portable AC configurations is less extreme. In consideration of the changes in test conditions and performance calculations since the February 2015 NOPR 31 and the test procedure established in this final rule, DOE expects that single-duct portable AC performance is significantly less impacted by infiltration air.

Ok, so how are the test conditions somehow making single-hose air conditioners not look blatantly shitty?

The key piece is that the DOE is using a weighted mix of two test conditions: one at outdoor temperature 95°F/35°C (representing "the hottest 750 hours of the year"), the other at outdoor temperature 83°F/28.3°C (representing some kind of average temperature during times when the AC is used at all). For both cases, the DOE assumes that the indoor temperature (i.e. the air which the single-hose air conditioner is taking in) is at 80°F/26.7°C. So for the average-outdoor-temperature case, they're assuming conditions where there is only a 3°F/1.6°C temperature difference between indoors and outdoors! Obviously infiltration has almost no effect under these conditions... but also do people even bother setting up a portable air conditioner only to bring the temperature from 83°F/28.3°C down to 80°F/26.7°C?

Now for the key question: what weights does the DOE use in the weighted mix of these two conditions? 20% weight on the 95°F/35°C outdoor condition, 80% weight on the 83°F/28.3°C outdoor condition.

Bottom line: the DOE's SACC/CEER rating puts about 80% of its weight on a test condition in which the indoor and outdoor temperatures are only 3°F/1.6°C apart.

This document has a good dense summary of the relevant formulas. In particular, $Q_{s\_95}$ and $Q_{s\_83}$ on page 74038 are the heats lost to infiltration under the two conditions. Those are incorporated into $AC{C}_{95}$ and $AC{C}_{83}$ respectively, which are then combined with the weights on page 74039.

One more interesting observation: if we assume that the efficiency loss from infiltration is basically-zero for the 83°F/28.3°C condition, then in order to get an overall efficiency loss of 20-30% for one-hose vs two, the efficiency under the 95°F/35°C condition would have to be somewhere between zero and negative. (Which is possible, given the way the test is setup - it would mean that running the AC in an 80°F/26.7°C house when it's 95°F/35°C outside makes the house hotter overall. In other words, the equilibrium temperature of the room with that AC cooling it is above 80°F/26.7°C.) I would guess that the efficiency under the 95°F/35°C condition is somewhat higher than this simple estimate implies (since there will be some losses under the the 83°F/28.3°C condition), but I think it is a reasonably-realistic ballpark estimate at the temperatures given.

Replies from: paulfchristiano, AllAmericanBreakfast

↑ comment by paulfchristiano · 2022-04-20T22:34:26.897Z · LW(p) · GW(p)

I still the 25-30% estimate in my original post was basically correct. I think the typical SACC adjustment for single-hose air conditioners ends up being 15%, not 25-30%. I agree this adjustment is based on generous assumptions (5.4 degrees of cooling whereas 10 seems like a more reasonable estimate). If you correct for that, you seem to get to more like 25-30%.  The Goodhart effect is much smaller than this 25-30%, I still think 10% is plausible.

I admit that in total I’ve spent significantly more than 1.5 hours researching air conditioners :) So I’m planning to check out now. If you want to post something else, you are welcome to have the last word.

SACC for 1-hose AC seems to be 15% lower than similar 2-hose models, not 25-30%:

• This site argues for 2-hose ACs being better than 1-hose ACs and cites SACC being 15% lower.
• The top 2-hose AC on amazon has 14,000 BTU that gets adjusted down to 9500 BTU = 68%.  This similarly-sized 1-hose AC is 13,000 BTU and gets adjusted down to 8000 BTU = 61.5%, about 10% lower.
• This site does a comparison of some unspecified pair of ACs and gets 10/11.6 = 14% reduction.

I agree the DOE estimate is too generous to 1-hose AC, though I think it’s <2x:

The SACC adjustment assumes 5.4 degrees of cooling on average, just as you say. I’d guess the real average use case, weighted by importance, is closer to 10 degrees of cooling. I’m skeptical the number is >10—e.g. 95 degree heat is quite rare in the US, and if it’s really hot you will be using real AC not a cheap portable AC (you can’t really cool most rooms from 95->80 with these Acs, so those can't really be very common). Overall the DOE methodology seems basically reasonable up to a few degrees of error.

Still looks similar to my initial estimate:

I’d bet that the simple formula I suggested was close to correct. Apparently 85->80 degrees gives you 15% lower efficiency (11% is the output from my formula). 90->80 would be 20% on my formula but may be more like 30% (e.g. if the gap was explained by me overestimating exhaust temp).

So that seems like it's basically still lining up with the 25-30% I suggested initially, and it's for basically the same reasons. The main thing I think was wrong was me saying "see stats" when it was kind of coincidental that the top rated AC you linked was very inefficient in addition to having a single hose (or something, I don't remember what happened).

The Goodhart effect would be significantly smaller than that:

• I think people primarily estimate AC effectiveness by how cool it makes them and the room, not how cool the air coming out of the AC is.
• The DOE thinks (and I’m inclined to believe) that most of the air that’s pulled in is coming through the window and so heats the room with the AC.
• Other rooms in the house will generally be warmer than the room being air conditioned, so infiltration from them would still warm the room (and to the extent it doesn’t, people do still care more about the AC’d room).

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-20T22:53:08.419Z · LW(p) · GW(p)

If you wouldn't mind one last question before checking out: where did that formula you're using come from?

↑ comment by DirectedEvolution (AllAmericanBreakfast) · 2022-04-19T12:48:47.733Z · LW(p) · GW(p)

From PickHVAC.com, "What is a good CEER rating?":

From the Pro Breeze single-hose AC product description on Amazon:

a mighty 10,000 BTU cooling capacity...

Super Efficient: This portable AC unit for bedroom boasts a 6.6 CEER Energy Efficiency rating to ensure that blowing cold air in the sweltering summer heat is energy efficient and cost effective.

I haven't looked into the % efficiency loss measurements, but I think it's interesting that you can still figure out that this is a crap AC if you're willing to trust this website.

Replies from: denkenberger

↑ comment by denkenberger · 2022-05-28T02:53:31.663Z · LW(p) · GW(p)

Portable units have to meet a much weaker standard. I actually pushed for a more stringent standard on these products when I was consulting for the Appliance Standards Awareness Project.

Regulation does not fix the problem, just moves it from the consumer to the regulator. A regulator will only regulate a problem which is obvious to the regulator. A regulator may sometimes have more expertise than a layperson, but even that requires that the politicians ultimately appointing people can distinguish real from fake expertise, which is hard in general [? · GW].

It seems like the DOE decided to adopt energy-efficiency standards that take into account infiltration. They could easily have made a different decision (e.g. because of pressure from portable AC manufacturers, or because it's legitimately unclear how to define the standard, or because it makes measurement harder), but it wouldn't be because the issue wasn't obvious (I think it's not even anywhere close to the "failure because the issue wasn't obvious" regime).

Overall I agree with the bottom line that regulation is unlikely to help that much with alignment. But I don't think this seems like the right model of why that is or how you could fix it.

Waiting longer does not fix the problem. All those people who did not notice their air conditioner pulling hot air into the house will not start noticing if we just wait a few years. Problems do not automatically become obvious over time.

I think our understanding of these issues has always been much better than the low baseline you imagine in the OP, but I also think discourse has clearly improved significantly over time. So I'm also not sure that this analogy really says what you want it to say.

Obviously the point about air conditioners doesn't matter

I'd like to remark that, at least for me, the facts-of-the-matter about whether this particular air conditioner works by Goodharting consumer preferences actually affect my views on AI. The OP quite surprised my world model, which did not expect one of the most popular AC units on Amazon to work by deceiving consumers. If lots of the modern world works this way, then John's intuition that advanced ML systems are almost certain to work by Goodharting our preferences seems much more likely. Before seeing the above comment and jbash's comment, I was in the process of updating my views, not because I thought the OP was an enlightening allegory, but because it actually changed what I thought the world was like.

Conversely, the world model "sometimes the easiest way to achieve some objective is to actually do the intended thing instead of Goodharting" would predict that air conditioner example was wrong somehow, a prediction which seems to have been right (if Paul's and jbash's comments are correct, that is). I was quite impressed by this, and am now more confident in the "Goodharting isn't omnipresent" world model.

In any case, my main point is that I actually do care about what's going on in this air conditioning example (and I encourage further discussion on whether the OP's characterization of it is accurate or not).

I can’t believe I’m about to write a comment about air conditioners on a thread about world-ending AI, but having bought one of these one-hose systems for my apartment during a particularly hot summer I can say I was pretty disappointed with its performance.

The main drawback to the one hose system is the cool air never makes it outside the room with the unit. I tried putting a bunch of fans to blow the air to the rest of the house, but as you can imagine that didn’t work very well.

I had no idea why until I zoned out one day while thinking about the air conditioner and realized it was sucking the cold air into the intake and blowing it out of the house. And I did indeed read a bunch of reviews from Costco customers before I bought the unit, none of which mentioned the problem.

I apologize if this is piling on, but I would like to note that this error strikes me as very similar to another one made by the same author in this comment [LW(p) · GW(p)], and which I believe is emblematic of a certain common failure mode within the rationalist community (of which I count myself a part). This common failure mode is to over-value our own intelligence and under-value institutional knowledge (whether from the scientific community or the Amazon marketplace), and thus not feel the need to tread carefully when the two come into conflict.

In the comment in question, johnswentworth asserts, confidently, that there is nothing but correlational evidence of the role of amyloid-β in Alzheimer's disease. However, there is extensive, strong causal evidence for its role: most notably, that certain mutations in the APP, PSEN1, and PSEN2 genes deterministically (as in, there are no known exceptions for anyone living to their 80's) cause Alzheimer's disease, and the corresponding proteins are well understood structurally and functionally to be key players in the production of amyloid-β. Furthermore, the specific mutations in question are shown through multiple lines of evidence (structural analysis, in vitro experiment, and in vivo experiments in transgenic mice) to lead directly (as opposed to indirectly, via a hypothetical other Alzheimer's-causing pathway) to greater production of amyloid-β.

A detailed summary of this and further evidence can be found in section 1.1 "Rationale for targeting Aβ and tau" of Plotkin and Cashman (2020). Passive immunotherapies targeting Aβ and tau in Alzheimer's disease. A good general survey on amyloid-β production is Haass et al (2012). Trafficking and Proteolytic Processing of APP.

(My background: I have a family member with Alzheimer's and as a result I spent five months studying the scientific literature on the subject in detail. I am posting under a pseudonym to protect my family member's privacy.)

After this comment there was a long thread about AC efficiency.

Summarizing:

• I said: "In practice I think the actual efficiency loss relative to a 2-hose unit is more like 25-30%" (For cooling from 85 to 70.)
• John said [LW(p) · GW(p)] that this was ridiculous.
• After the dust settled, our best estimate on paper is 40% rather than 25-30%.

The reason for the adjustments were roughly:

• [x2] I estimated exhaust temperature at 130 degrees, but it's more like 100 degrees if the indoor air is 70.
• [x1/2] I thought that all depressurization was compensated for by increased infiltration. But probably half of depressurization is offset by reduced exfiltration instead (see here [LW(p) · GW(p)])
• [x3/2] I only considered sensible heat. But actually humidity is a huge deal, because the exhaust is heated but not humidified (see here [LW(p) · GW(p)])

John also attempted to measure the loss empirically [LW(p) · GW(p)], but I'd summarize as "too hard to measure":

• With 1-hose the indoor temp was 68 vs 88 outside, while with 2-hose the indoor temp was 66 vs 88 outside (using the same amount of energy).
• We both agree that 10% is an underestimate for the efficiency loss (e.g. due to room insulation, other cooling in the building, and the improvised 2-hose setup).
• I don't think we have a plausible way to extract a corrected estimate.

On the physics: to be clear, I'm not saying the air conditioner does not work at all. It does make the room cooler than it started, at equilibrium.

I also am not surprised (in this particular example) to hear that various expert sources already account for the inefficiency in their evaluations; it is a problem which should be very obvious to experts. Of course that doesn't apply so well to e.g. the example of medical research replication failures. The air conditioner example is not meant to be an example of something which is really hard to notice for humanity as a whole; it's meant to be an example of something which is too hard for a typical consumer to notice, and we should extrapolate from there to the existence of things which people with more expertise will also not notice (e.g. the medical research example). Also, it's a case-in-point that experts noticing a problem with some product is not enough to remove the economic incentive to produce the product.

It's particularly jarring to notice a huge conflict between a clever argument and a lot of people's reported experiences, and then to have the confidence to not only believe the clever argument but to not even think the conflict is worth acknowledging or exploring.

When the argument specifically includes reasons to expect people to not notice the problem, it seems obviously correct to discount reported experiences. Of course there are still ways to gain evidence from reported experience - e.g. if someone specifically said "this unit cooled even the far corners of the house", then that would partially falsify our theory for why people will overlook the one-hose problem. But we should not blindly trust reports when we have reasons to expect those reports to overlook problems.

In this particular case, I indeed do not think the conflict is worth the cost of exploring - it seems glaringly obvious that people are buying a bad product because they are unable to recognize the ways in which it is bad. Positive reports do not contradict this; there is not a conflict here. The model already predicts that there will be positive reports - after all, the air conditioner is very convenient and pumps lots of cool air out the front in very obvious ways.

↑ comment by paulfchristiano · 2022-04-15T22:31:51.567Z · LW(p) · GW(p)

In this particular case, I indeed do not think the conflict is worth the cost of exploring - it seems glaringly obvious that people are buying a bad product because they are unable to recognize the ways in which it is bad.

The wirecutter recommendation for budget portable ACs is a single-hose model. Until very recently their overall recommendation was also a single-hose model.

The wirecutter recommendations (and other pages discussing this tradeoffs) are based on a combination of "how cold does it make the room empirically?" and quantitative estimates of cooling that take into account infiltration. This issue is discussed extensively, with quantitative detail, by people who quite often end up recommending 1-hose designs for small rooms (like the one this AC is advertised for).

One AC unit tested by the wirecutter is convertible between 2-hose and 1-hose. They write:

The best thing we took away from our tests was the chance at a direct comparison between a single-hose design and a dual-hose design that were otherwise identical, and our experience confirmed our suspicions that dual-hose portable ACs are slightly more effective than single-hose models but not effective enough to make a real difference

The 2-hose model they recommend probably wins in part because design improvements lower the complexity of the 2-hose setup:

Unlike the single-hose portables we typically recommend, the Duo has a unique “hose-in-hose” setup where the exhaust and intake are split into two separate conduits contained within a single larger tube, making it even more efficient.

(Amusingly, I think this means that the only 2-hose model recommended by the wirecutter also looks like it has just 1 hose in pictures.)

I think it's correct that consumers probably overweight setup simplicity relative to efficiency. But I think their subjective sense of "how cold does this make the room" is roughly accurate and your argument doesn't undermine that as much as you suggest (because infiltration affects the room as well as the house, and on top of that they care most about the room), and the quoted numbers for AC efficacy also take this consideration into account.

ETA: I also think it's possible that consumers have historically underestimated the importance of infiltration (especially 5+ years ago when discussion was less good, when people may have leaned more on "what it says on the tin" vs recommendations, and when legally-mandated efficiency numbers would not have included infiltration) and this made it harder for two-hose designs to compete. On this story slow institutional progress is gradually fixing this problem, and two-hose designs will be clearly better once enough of them are made (rather than right now where they still aren't better at small room / low price point). But the total upside will be like 5-10% efficiency, and it's kind of small potatoes that can't even easily be pinned on individual irrationality given that in fact the best existing AC units for these conditions do seem to have one hose right now.

Replies from: habryka4, johnswentworth

↑ comment by habryka (habryka4) · 2022-04-16T23:15:59.242Z · LW(p) · GW(p)

The best thing we took away from our tests was the chance at a direct comparison between a single-hose design and a dual-hose design that were otherwise identical, and our experience confirmed our suspicions that dual-hose portable ACs are slightly more effective than single-hose models but not effective enough to make a real difference

After having looked into this quite a bit, it does really seem like the Wirecutter testing process had no ability to notice infiltration issues, so it seems like the Wirecutter crew themselves is kind of confused here? 

The... Wirecutter article does also not seem to discuss the issue of infiltration of hot air in any reasonable way. Instead it just says that: 

This produces a slight vacuum effect, which pulls in “infiltration air” from anywhere it can in order to equalize the pressure. In the presence of a gas-powered device such as a furnace, that negative pressure creates a backdraft or downdraft, which can cause the machine to malfunction—or worse, fill the room with gas fumes and carbon monoxide. We don’t think that most people plan to use their portable AC in such a room, but if your home is set up in such a way that you’re concerned about ventilation, skip the rest of our recommendations

Which... seems to misunderstand the actual problem of infiltration as it relates to heating efficiency? This is the only mention of the word infiltration in the whole article, and I can't find any other section that discusses infiltration problems in other words. 

Indeed, the article says directly: 

Although our testing has shown that dual-hose models tend to outperform some single-hose units in extremely hot or muggy weather, the difference is usually minimal, and we don’t think it outweighs the convenience of a single hose.

Based on a testing methodology that is very unlikely to be able to measure the primary issue with single-hose vs. double-hose designs. This seems like Wirecutter is directly falling prey to the exact problem the OP is describing. 

I feel a bit confused how the official SACC measures account for infiltration, but assuming they are doing it properly, the overall difference between single-hose and dual-hose designs does only seem to be something like 20%. I do expect the current Wirecutter tests to fail to measure that difference, but am also not sure that 20% is really worth the loss of convenience from having a single hose.

Replies from: paulfchristiano

↑ comment by paulfchristiano · 2022-04-16T23:25:24.670Z · LW(p) · GW(p)

They measure the temperature in the room, which captures the effect of negative pressure pulling in hot air from the rest of the building. It underestimates the costs if the rest of the building is significantly cooler than the outside (I'd guess by the ballpark of 20-30% in the extreme case where you care equally about all spaces in the building, the rest of your building is kept at the same temp as the room you are cooling, and a negligible fraction of air exchange with the outside is via the room you are cooling).

Which... seems to misunderstand the actual problem of infiltration as it relates to heating efficiency? This is the only mention of the word infiltration in the whole article, and I can't find any other section that discusses infiltration problems in other words. 

I think that paragraph is discussing a second reason that infiltration is bad.

Replies from: habryka4

↑ comment by habryka (habryka4) · 2022-04-16T23:32:09.168Z · LW(p) · GW(p)

I think that paragraph is discussing a second reason that infiltration is bad.

Yeah, sorry, I didn't mean to imply the section is saying something totally wrong. The section just makes it sound like that is the only concern with infiltration, which seems wrong, and my current model of the author of the post is that they weren't actually thinking through heat-related infiltration issues (though it's hard to say from just this one paragraph, of course). 

↑ comment by johnswentworth · 2022-04-15T22:50:08.641Z · LW(p) · GW(p)

The best thing we took away from our tests was the chance at a direct comparison between a single-hose design and a dual-hose design that were otherwise identical, and our experience confirmed our suspicions that dual-hose portable ACs are slightly more effective than single-hose models but not effective enough to make a real difference

I roll to disbelieve. I think it is much more likely that something is wrong with their test setup than that the difference between one-hose and two-hose is negligible.

Just on priors, the most obvious problem is that they're testing somewhere which isn't hot outside the room - either because they're inside a larger air-conditioned building, or because it's not hot outdoors. Can we check that?

Well, they apparently tested it in April 2022, i.e. nowish, which is indeed not hot most places in the US, but can we narrow down the location more? The photo is by Michael Hession, who apparently operates near Boston. Daily high temps currently in the 50's to 60's (Fahrenheit). So yeah, definitely not hot there.

Now, if they're measuring temperature delta compared to the outdoors, it could still be a valid test. On the other hand, if it's only in the 50's to 60's outside, I very much doubt that they're trying to really get a big temperature delta from that air conditioner - they'd have to get the room down below freezing in order to get the same temperature delta as a 70 degree room on a 100 degree day.

If they're only trying to get a tiny temperature delta, then it really doesn't matter how efficient the unit is. For someone trying to keep a room at 70 on a 100 degree day, it's going to matter a lot more.

So basically, I am not buying this test setup. It does not look like it is actually representative of real usage, and it looks nonrepresentative in the basically the ways we'd expect from a test that found little difference between one and two hoses.

Generalizable lesson/heuristic: the supposed "experts" are also not even remotely trustworthy.

(Also, I expect it to seem like I am refusing to update in the face of any evidence, so I'd like to highlight that this model correctly predicted that the tests were run someplace where it was not hot outside. Had that evidence come out different, I'd be much more convinced right now that one hose vs two doesn't really matter.)

Replies from: paulfchristiano

↑ comment by paulfchristiano · 2022-04-15T23:06:30.713Z · LW(p) · GW(p)

(Also, I expect it to seem like I am refusing to update in the face of any evidence, so I'd like to highlight that this model correctly predicted that the tests were run someplace where it was not hot outside. Had that evidence come out different, I'd be much more convinced right now that one hose vs two doesn't really matter.)

From how we tested:

Over the course of a sweltering summer week in Boston, we set up our five finalists in a roughly 250-square-foot space, taking notes and rating each model on the basic setup process, performance, portability, accessories, and overall user experience.

ETA: it's not clear that's the same testing setup used in the other tests they described. But they do talk about how the 1-vs-2 convertible unit "struggled to make the room any cooler than 70 degrees" which sounds like it was probably reasonably hot.

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-15T23:26:56.519Z · LW(p) · GW(p)

Alright, I am more convinced than I was about the temperature issue, but the test setup still sounds pretty bad.

First, Boston does not usually get all that sweltering. I grew up in Connecticut (close to Boston and similar weather), summer days usually peaked in the low 80's. Even if they waited for a really hot week, it was probably in the 90's. A quick google search confirms this: typical July daily high temp is 82, and google says "Overall during July, you should expect about 4-6 days to reach or exceed 90 F (32C) while the all-time record high for Boston was 103 F (39.4C)".

It's still a way better test than April (so I'm updating from that), but probably well short of keeping a room at 70 on a 100 degree day. I'm guessing they only had about half that temperature delta.

Second, their actual test procedure (thankyou for finding that, BTW):

Over the course of a sweltering summer week in Boston, we set up our five finalists in a roughly 250-square-foot space, taking notes and rating each model on the basic setup process, performance, portability, accessories, and overall user experience.

The makers of portable air conditioners are required to list their performance and efficiency statistics, and our research and our previous testing have proven these numbers to be accurate. By prescreening for these stats, we got the impression that every model we tested would cool a room capably. We confirmed that they did by taking measurements with two Lascar temperature and humidity data loggers—we placed one 3 feet away, directly in front of the unit, and placed the other one 6 feet away on a diagonal. With each AC set to its lowest setting (between 60 and 64 degrees Fahrenheit, depending on the unit) and the highest fan/compressor setting, we measured the temperature and humidity in the room every 15 minutes for three hours to see how well each unit dispersed the coolness and dehumidification process across the space.

Three feet and six feet away? That sure does sound like they're measuring the temperature right near the unit, rather than the other side of the room where we'd expect infiltration to matter. I had previously assumed they were at least measuring the other side of the room (because they mention for the two-hose recommendation "In our tests, it was also remarkably effective at distributing the cool air, never leaving more than a 1-degree temperature difference across the room"), but apparently "across the room" actually meant "6 feet away" based on this later quote:

In our tests, it [a two-hose air conditioner] produced some of the most even and consistent cooling across the room, never registering more than a 1-degree difference between our monitors positioned at 3 feet directly in front of the AC and 6 feet away on a diagonal.

... which sure does sound more like what we'd expect.

So I'm updating away from "it was just not hot outside" - probably a minor issue, but not a major one. That said, it sure does sound like they were not measuring temperature across the room, and even just between 3 and 6 feet away the two-hose model apparently had noticeably less drop-off in effectiveness.

Replies from: paulfchristiano

↑ comment by paulfchristiano · 2022-04-16T14:09:45.175Z · LW(p) · GW(p)

Boston summers are hotter than the average summers in the US, and I'd guess are well above the average use case for an AC in the US. I agree having two hoses are more important the larger the temperature difference, and by the time you are cooling from 100 to 70 the difference is fairly large (though there is basically nowhere in the US where that difference is close to typical).

I'd be fine with a summary of "For users who care about temp in the whole house rather than just the room with the AC, one-hose units are maybe 20% less efficient than they feel. Because this factor is harder to measure than price or the convenience of setting up a one-hose unit, consumers don't give it the attention it deserves. As a result, manufacturers don't make as many cheap two-hose units as they should."

Replies from: Benito

↑ comment by Ben Pace (Benito) · 2022-04-16T23:49:20.465Z · LW(p) · GW(p)

Does anyone in-thread (or reading along) have any experiments they'd be interested in me running with this air conditioner? It doesn't seem at all hard for me to do some science and get empirical data, with a different setup to Wirecutter, so let me know.

Added: From a skim of the thread, it seems to me the experiment that would resolve matters is testing in a large room with temperature sensors more like 15 feet away in a city or country that's very hot outside, and to compare this with (say) Wirecutter's top pick with two-hoses. Confirm?

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-17T00:25:09.264Z · LW(p) · GW(p)

... I actually already started a post titled "Preregistration: Air Conditioner Test (for AI Alignment!)". My plan was to use the one-hose AC I bought a few years ago during that heat wave, rig up a cardboard "second hose" for it, and try it out in my apartment both with and without the second hose next time we have a decently-hot day. Maybe we can have an air conditioner test party.

Predictions: the claim which I most do not believe right now is that going from one hose to two hose with the same air conditioner makes only a 20%-30% difference. The main metric I'm interested in is equilibrium difference between average room temp and outdoor temp (because that was the main metric relevant when I was using that AC during the heat wave). I'm at about 80% chance that the difference will be over 50%.

(Back-of-the-envelope math a few years ago said it should be roughly a factor-of-two difference, and my median expectation is close to that.)

I also expect (though less strongly) that, assuming the room's doors and windows are closed, corners of the room opposite the AC in single-hose mode will be closer to outdoor temp than to the temp 3 ft away from the AC, and that this will not be the case in two-hose mode. I'd put about 60% on that prediction.

These predictions are both conditional on the general plan I had, and might change based on details of somebody else' test plan. In particular, some factors I expect are relevant:

• The day being hot enough and the room large enough that the AC runs continuously (as opposed to getting the room down to target temperature easily, at which point it will shut off until the temperature goes back up).
• The test room does not open into an indoor room at lower temperature (I had planned to open the outside door and windows in the rest of the apartment).
• Test room generally not in direct sun, including outside of walls/ceiling. If it is in full sun, then I'd strengthen my probability for the second prediction.

Also, in case people want to bet, I should warn that I did use this AC during a heat wave a few years ago (with just the one hose), so e.g. I have seen firsthand how it tends to only cool the space right in front of it. On the other hand, it could turn out that was due to factors specific to the apartment I was in back then - for instance, the roof in that apartment was uninsulated and in full sun, so a lot of heat came off the ceiling.

Replies from: paulfchristiano, Raemon, Benito

↑ comment by paulfchristiano · 2022-04-17T02:32:58.628Z · LW(p) · GW(p)

I would have thought that the efficiency lost is roughly (outside temp - inside temp) / (exhaust temp - inside temp). And my guess was that exhaust temp is ~130.

I think the main way the effect could be as big as you are saying is if that model is wrong or if the exhaust is a lot cooler than I think. Those both seem plausible; I don't understand how AC works, so don't trust that calculation too much. I'm curious what your BOTEC was / if you think 130 is too high an estimate for the exhaust temp? 

If that calculation is right, and exhaust is at 130, outside is 100, and house is 70, you'd have 50% loss. But you can't get 50% in your setup this way, since your 2-hose AC definitely isn't going to get the temp below 65 or so. Maybe most plausible 50% scenario would be something like 115 exhaust, 100 outside, 85 inside with single-hose, 70 inside with double-hose.

I doubt you'll see effects that big. I also expect the improvised double hose will have big efficiency losses. I think that 20% is probably the right ballpark (e.g. 130/95/85/82). If it's >50% I think my story above is called into question. (Though note that the efficiency lost from one hose is significantly larger than the bottom line "how much does people's intuitive sense of single-hose AC quality overstate the real efficacy?")

Your AC could also be unusual. My guess is that it just wasn't close to being able to cool your old apartment and that single vs double-hoses was a relatively small part of that, in which case we'd still see small efficiency wins in this experiment. But it's conceivable that it is unreasonably bad in part because it has an unreasonably low exhaust temp, in which case we might see an unreasonably large benefit from a second hose (though I'd discard that concern if it either had similarly good Amazon reviews or a reasonable quoted SACC).

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-17T17:11:59.587Z · LW(p) · GW(p)

I'm curious what your BOTEC was / if you think 130 is too high an estimate for the exhaust temp?

I don't remember what calculation I did then, but here's one with the same result. Model the single-hose air conditioner as removing air from the room, and replacing with a mix of air at two temperatures: $T_C$ (the temperature of cold air coming from the air conditioner), and $T_H$ (the temperature outdoors). If we assume that $T_C$ is constant and that the cold and hot air are introduced in roughly 1:1 proportions (i.e. the flow rate from the exhaust is roughly equal to the flow rate from the cooling outlet), then we should end up with an equilibrium average temperature of $\frac{T_C+T_H}{2}$. If we model the switch to two-hose as just turning off the stream of hot air, then the equilibrium average temperature should drop to $T_C$.

Some notes on this:

• It's talking about equilibrium temperature rather than power efficiency, because equilibrium temperature on a hot day was mostly what I cared about when using the air conditioner.
• The assumption of roughly-equal flow rates seems to be at least the right order of magnitude based on seeing this air conditioner in operation, though I haven't measured carefully. If anything, it seemed like the exhaust had higher throughput.
• The assumption of constant $T_C$ is probably the most suspect part.

Replies from: paulfchristiano, ADifferentAnonymous

↑ comment by paulfchristiano · 2022-04-17T17:56:17.971Z · LW(p) · GW(p)

Ok, I think that ~50% estimate is probably wrong. Happy to bet about outcome (though I think someone with working knowledge of air conditioners will also be able to confirm). I'd bet that efficiency and Delta t will be linearly related and will both be reduced by a factor of about (exhaust - outdoor) / (exhaust - indoor) which will be much more than 50%.

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-17T22:34:28.852Z · LW(p) · GW(p)

... and will both be reduced by a factor of about (exhaust - outdoor) / (exhaust - indoor) which will be much more than 50%.

I assume you mean much less than 50%, i.e. (T_outside - T_inside) averaged over the room will be less than 50% greater with two hoses than with one?

I'm open to such a bet in principle, pending operational details. $1k at even odds?

Operationally, I'm picturing the general plan I sketched four comments upthread. (In particular note the three bulleted conditions starting with "The day being hot enough and the room large enough that the AC runs continuously..."; I'd consider it a null result if one of those conditions fails.) LMK if other conditions should be included.

Also, you're welcome to come to the Air Conditioner Testing Party (on some hot day TBD). There's a pool at the apartment complex, could swim a bit while the room equilibrates.

Replies from: denkenberger

↑ comment by denkenberger · 2022-05-28T04:07:18.079Z · LW(p) · GW(p)

I studied the impact of infiltration because of clothes dryers when I was doing energy efficiency consulting. The nonobvious thing that is missing from this discussion is that the infiltration flow rate does not equal the flow rate of the hot air out the window. Basically absent the exhaust flow, there is an equilibrium of infiltration through the cracks in the building equaling the exfiltration through the cracks in the building. When you have a depressurization, this increases the infiltration but also decreases the exfiltration. If the exhaust flow is a small fraction of the initial infiltration, the net impact on infiltration is approximately half as much as the exhaust flow. The rule of thumb for infiltration is it produces about 0.3 air changes per hour, but it depends on the temperature difference to the outside and the wind (and the leakiness of the building). I would guess that if you did this in a house, the exhaust flow would be relatively small compared to the natural infiltration. So roughly the impact due to the infiltration is about half as much as the calculations indicate. But if you were in a tiny tight house, then the exhaust flow would overwhelm the natural infiltration and the increase in infiltration would be close to the exhaust flow. 

Another factor is the dehumidification load on the air conditioner. This is a really big deal in the southeastern US, though it would be less of a deal in the Bay Area. Basically, if it is very humid outside, the additional infiltration air has to be de-humidified, and that can double how much heat the air conditioner needs to remove from the infiltration air. So this could counteract the benefit of the net infiltration being smaller than the exhaust flow.

The exhaust temperature of 130°F sounds high to me for regular air conditioner, but heat pumps designed to heat hot water and dry clothing to go even higher than that. So it is possible they increase it more than a regular air conditioner to increase the overall efficiency (because the fan energy is significantly larger with the hose as compared to a typical window unit). Still, I am confident that the reduction in efficiency of one hose versus two hose is less than 50% unless it is very hot and humid outside.

Replies from: paulfchristiano

↑ comment by paulfchristiano · 2022-06-23T22:09:13.742Z · LW(p) · GW(p)

Thanks! It's amusing that we had this whole discussion and the one commenter who knew what they were talking about got just one upvote :)

It sounds very plausible that exhaust is small relative to natural infiltration and I believe you that (extra infiltration) = 50% (exhaust).

In the other direction, it looks like I was wrong about 130 degrees and we're looking at more like 100 [LW · GW] (alas, googling random forum comments is an imperfect methodology, though I do feel it's plausible that John's AC has unusually cold exhaust).

If the building is ending up around 70, that means I'm underestimating the exhaust quantity by about 2x. But then apparently the extra infiltration is only about half of the exhaust. So sounds like the errors cancel out and my initial estimate happens to be roughly right?

↑ comment by ADifferentAnonymous · 2022-04-18T17:31:26.443Z · LW(p) · GW(p)

$T_c$ does seem like a bad assumption. I tried instead assuming a constant difference between the intake and the cold output, and the result surprised me. (The rest of this comment assumes this model holds exactly, which it definitely doesn't).

Let $T_r$ be the temperature of the room (also intake temperature for a one-hose model). Then at equilibrium,

$T_r=(T_c+T_h)/2$

$T_r=\left(\right(T_r-\Delta )+T_h)/2$

$2T_r=T_r+T_h-\Delta$

$T_r=T_h-\Delta$

i.e. no loss in cooling power at all! (Energy efficiency and time to reach equilibrium would probably be much worse, though)

In the case of an underpowered $(\Delta =15)$ one-hose unit handling a heat wave ($T_h=100$), you'd get $T_r=85$ and $T_c=70$—nice and cool in front of the unit but uncomfortably hot in the rest of the room, just as you observed. Adding a second hose would resolve this disparity in the wrong direction, making $T_r=T_c=85$. So if you disproportionately care about the area directly in front of the AC, adding the second hose could be actively harmful.

↑ comment by Raemon · 2022-04-17T02:21:42.167Z · LW(p) · GW(p)

Also, like, Berkeley heat waves may just significantly different than, like, Reno heat waves. My current read is that part of the issue here is that a lot of places don't actually get that hot so having less robustly good air conditioners is fine.

Replies from: johnswentworth, paulfchristiano

↑ comment by johnswentworth · 2022-04-17T17:14:24.900Z · LW(p) · GW(p)

I bought my single-hose AC for the 2019 heat wave in Mountain View (which was presumably basically similar to Berkeley).

When I was in Vegas, summer was just three months of permanent extreme heat during the day; one does not stay somewhere without built-in AC in Vegas.

↑ comment by paulfchristiano · 2022-04-17T02:33:48.713Z · LW(p) · GW(p)

I think labeling requirements are based on the expectation of cooling from 95 to 80 (and I expect typical use cases for portable AC are more like that). Actually hot places will usually have central air or window units.

↑ comment by Ben Pace (Benito) · 2022-04-17T01:32:03.312Z · LW(p) · GW(p)

Sweet! I could also perform a replication I guess.

Replies from: johnswentworth

↑ comment by johnswentworth · 2022-04-17T22:22:12.532Z · LW(p) · GW(p)

Or you could get to it before I do and I could perform a replication.

A 2-hose unit will definitely cool more efficiently, but I think for many people who are using portable units it's the right tradeoff with convenience. The wirecutter reviews both types of units together and usually end up preferring 1-hose units.

It is important to note that the current top wirecutter pick is a 2-hose unit, though one that combined the two hoses into one big hose. I guess maybe that is recent, but it does seem important to acknowledge here (and it wouldn't surprise me that much if Wirecutter went through reasoning pretty similar to the one in this post, and then updated towards the two-hose unit because of concerns about infiltration and looking at more comprehensive metrics like SACC). 

A/Cs primarily work by using electricity to drive a pressure differential between the cool, low-pressure indoor refrigerant and the hot, high-pressure outdoor refrigerant. It's not just moving air around. PV = nRT! Here's a video explainer.

Read carefully, the post doesn't ignore the effect of the evaporator and condenser...

Here’s how this air conditioner works. It sucks in some air from the room. It splits that air into two streams, and pumps heat from one stream to the other - making some air hotter, and some air cooler. The cool air, it blows back into the room. The hot air, it blows out the window.

... But it is written in such a way that the reader might come away with the impression that the single-hose A/C has zero net effect on the household temperature. Even the edited-in caveat makes it sound like it might be cooling off the room in which it's located, at the expense of heating up the rest of the house.

The actual effect of this air conditioner is to make the space right in front of the air conditioner nice and cool, but fill the rest of the house with hot outdoor air. Probably not what one wants from an air conditioner!...

... I want to clarify that it will still cool down a room on net. If the air inside is all perfectly mixed together, it will still end up cooler with the air conditioner than without. The point is not that it doesn't work at all. The point is that it's stupidly inefficient in a way which I do not think consumers would plausibly choose over the relatively-low cost of a second hose if they recognized the problems.

This reading is reinforced by using the A/C as an analogy for a truly zero-value or destructive AI:

It’s “Potemkin village world”: a world designed to look amazing, but with nothing behind the facade. Maybe not even any living humans behind the facade - after all, even generally-happy real humans will inevitably sometimes appear less-than-maximally “good”.

We'd need to imagine an A/C that does nothing to net temperature, or that actively heats up the house on net for this analogy to work. Given that I expect more readers here will know about this hypothesis than about the practical details of how an A/C work, I worry they're more likely to see AI as a metaphor for this A/C than this A/C as a metaphor for AI!

Note also that regulation could totally fix this particular problem. We could ban single-hose A/Cs; there's a whole nation of HVAC experts who could convey this information, and they're licensed in the USA, so there's already a legal framework for identifying the relevant experts.

Waiting also might fix the problem, especially if these people have metered electricity. It's easily possible that they'll notice their high summer electric bill, consider efficiency improvements, look into the A/C, do 10 seconds of research, and invest in the two-hose unit the next time around.

When discussing AI, it seems valuable to distinguish more clearly between three scenarios:

• Individual AI products truly analogous to an A/C. They are specific services, which can indeed be more or less efficient, and can be chosen badly by ill-informed consumers. We might handle these in a similar way to how conventional products are regulated.
• An AI-driven world in which human decisions made in collaboration with individual AI products drive Molochian metrics at the expense of actual wellbeing. Bad results, but debuggable, and occurring for essentially the same reason as all the other institutional coordination failures we're already dealing with.
• A fast-takeoff superintelligent AI that is actively attempting to seize control of the observable universe in order to maximize paperclip production. I think this is not analogous to A/C, partly because it assumes that the AI itself isn't Goodharting itself as it chases world domination. And, come to think of it, I haven't seen this possibility discussed before (which means next to nothing, I am not well informed). Why wouldn't a self-improving AI have the same Goodharting problem in achieving its world-domination designs that we face in creating that AI in the first place?

Ok, I want to say thank you for this comment because it contains a lot of points I strongly agree with. I think the alignment community needs experimental data now more than it needs more theory. However, I don't think this lowers my opinion of MIRI. MIRI, and Eliezer before MIRI even existed yet, was predicting this problem accurately and convincingly enough that people like myself updated. 15 years ago I began studying neuroscience, neuromorphic computing, and machine learning because I believed this was going to become a much bigger deal than it was then. Now the general gist of the message has absolutely been proven out. Machine learning is now a big impressive thing in the world, and scary outcomes are right around the corner. Forecasting that now doesn't win you nearly as many points as forecasting that 15 or 20 years ago. Now we are finally close enough that it makes sense to move from theorizing to experimentation. That doesn't mean the theorizing was useless. It laid an incredible amount of valuable groundwork. It gave the experimental researchers a server of what they are up against. Laid out the scope of the problem, and made helpful pointers towards important characteristics that good solutions must have. A call to action for an army of experimentalists to put the theory to test us not evidence against MIRI. Their theory is still useful and helpful, it's just no longer where we need the most rapid expansion of effort. We are entering a new phase now, gathering experimental data, and we still need MIRI, and others like them, to update and refine the theory in response to the experimental data. Theory used to be 95% of the work going into AGI alignment. Now it needs to become more like 5%. Not by decreasing the work going into theory. We need to increase that! But rather, because now it is time to throw open the floodgates of evidence and unleash the army of experimenters. Engineering work is easier than pure theory to get right, so thankfully, lots more people are qualified to contribute. This is good, because we need a lot. There is so much work to be done.

I mostly agree with that relying on real world data is necessary for better understanding our messy world and that in most cases this approach is favorable. 

There's a part of me that thinks AI is a different case though, since getting it even slightly wrong will be catastrophic. Experimental alignment research might get us most of the way to aligned AI, but there will probably still be issues that aren't noticeable because the AIs we are experimenting on won't be powerful enough to reveal them. Our solution to the alignment problem can't be something imperfect that does the job well enough. Instead is has to be something that can withstand immense optimization pressure. My intuition tells me that the single-hose solution is not enough for AGI and we instead need something that is flawless in practice and in theory. 

The Waterfall approach to software development gave way to Agile. Space X's fast iterations let it run rings around Boeing's "we carefully design it once and then it will fly".

This is fine for other fields, but the problem with superintelligent alignment is that the things in "move fast and break things" is, like, us. We only have one chance to get superhuman alignment right, which is why we have to design it carefully once. Misaligned systems will try to turn you off to make sure you can't turn them off. I think Eliezer has even said that if we could simply revert the universe after each time we mess up alignment, he would be way less pessimistic.

Further, experiments with systems that are not capable enough to kill us yet can provide us with valuable information, but the problem is that much of the difficulty comes up around superintelligence levels. Things are going to break in weird ways that we couldn't have anticipated just by extrapolating out the trends from current systems. So if we just wait for evidence that less robust solutions are not enough, then we will see that less robust solutions seem to work really well on weak current models, pat ourselves on the back for figuring out that actually alignment wouldn't be that hard in X area and then as we approach superintelligence we start noticing X break down (if we're lucky! if X is something like deception, it will try to hide from us and actively avoid being caught by our interpretability tools or whatever) and at that point it will be too late to try and fix the problem, because none of the technical or political solutions are viable in a very short time horizon.

Again, to be very clear, I'm not arguing that there is no use at all for empirical experiments today, it's just that there are specific failure cases that are easy to fall into whenever you try to conclude something of the form "and therefore this is some amount of evidence that superintelligence will be more/less likely to be Y and Z"

Just added a clarification to the post:

EDIT: several commenters seem to think that I'm claiming this air conditioner does not work at all, so I want to clarify that it will still cool down a room on net. The point is not that it doesn't work at all. The point is that it's stupidly inefficient in a way which I do not think consumers would plausibly choose over the relatively-low cost of a second hose if they recognized the problems.

I do believe the analysis in the post is in fact correct, and the success of this air conditioner is primarily due to consumers not recognizing the problem. Would you have spent an extra, say, $30 on a two-hose air conditioner if you had noticed the issue in advance?

(BTW, I also bought a one-hose air conditioner off amazon a few years back, which is where this example came from. When I realized there was only one hose, I was absolutely flabbergasted that anyone would even bother to build such an obviously stupid thing. And it indeed did a pretty shitty job cooling my apartment!)

The fact that you chose to use your superior knowledge to buy the much better air conditioner, while also choosing to not leave a review explaining this, is an illustration of OP's point, and not a refutation.

Just added this clarification to the post:

EDIT: several commenters seem to think that I'm claiming this air conditioner does not work at all, so I want to clarify that it will still cool down a room on net. The point is not that it doesn't work at all. The point is that it's stupidly inefficient in a way which I do not think consumers would plausibly choose over the relatively-low cost of a second hose if they recognized the problems.

EER does not account for heat infiltration issues, so this seems confused. CEER does, and that does suggest something in the 20% range, but I am pretty sure you can't use EER to compare a single-hose and a dual-hose system.

With two hoses, the air sucked in never mixes with the cool air in the room; it's kept completely separate. Only heat is exchanged by the AC, not air.

There is an important difference here between "obvious in advance" and "obvious in hindsight", but your basic point is fair, and the virus example is a good one. Humanity's current state is indeed so spectacularly incompetent that even the obvious problems might not be solved, depending on how things go.

No, they're trying to avoid generalizing from fictional evidence. John is offering the Fable of the Air Conditioners as an example of a particular phenomenon that he says also applies to the AI alignment problem. If his chosen example of this phenomenon is not in fact a good example of the phenomenon, then one might reasonably be less inclined to believe that the phenomenon is as common and as important as he suggests it is, and/or less inclined to believe what he says about the phenomenon.

It's a hard problem – a recapitulation of the difficult problem of describing or specifying human values generally.

Toy model: we have some system with a bunch of problems. A group of people with some fixed skills/background will be able to find 80% of the problems given enough time; the remaining 20% are problems which they won't find at all, because it won't occur to them to ask the right questions. (The air conditioner pulling in hot air in the far corners of the house is meant to be an example of such a problem, relative to the skills/background of a median customer.) For the 80% of problems which the group can find, the amount of time required to find them has a wide tail: half the problems can be found in a week, another 25% in another two weeks, another 12.5% in another four weeks, etc.

(The numbers in this setup aren't meant to be realistic; the basic idea I want to illustrate should occur for a fairly wide range of distributions.)

In this toy model:

• the group is more likely to find any given problem if given more time
• 'nonobvious' is not all-or-nothing; there are problems which won't be found in a week but will be found in a year.

So this toy model matches both of your conditions.

What happens in this toy model? Well, after a bit over two years, 79.5% of the problems have been found. Almost all of the remaining 20.5% are problems which the group will not find, given any amount of time, because they do not have the skills/background to ask the right questions. They will still keep improving things over time, but it's not going to make a large quantitative difference.

Point is: you are arguing that there exist problems which will be found given more time. That is not the relevant claim. In order to argue that alignment is importantly easier in slow takeoff worlds, you need to argue that there do not exist fatal problems which will not be found given more time.

I am saying that the probability is roughly constant and doesn't depend on $T$ much. The vast majority of problems which will be noticed during iteration will be noticed in 6 months; another 49.5 years might catch a few more, but those few will be dwarfed by the problems which will not be noticed during iteration approximately-regardless of how much time is spent.

Somebody who did not notice the air conditioner problem in 6 months is unlikely to notice it in the next 49.5 years. The examples of charities with mediocre impact and low replication rates in medicine have both been ongoing for at least a century. Time is just not the main relevant variable here.