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You started this subthread with the comment:

> The idea that the difference between 0.9005 and 0.90005 is "small" is … weird.

When you use the author's numbers, 0.9005 and 0.90005, the implication is that you're taking the parameters of they hypothetical as given. You then go on to say that the difference between those numbers is significant. Remember that in this abstract, idealized scenario, the air filters are only able to process 1/10th of the air in the room (hence the shared 0.9, the dominant portion of the magnitude). Perhaps the room reciculates with its environment at the rate of one room volume per day, and the filters can only process 1/10th of the room per day. Given that, do you still think the difference is significant? Or are you just outright refusing to participate in the thought experiment at all? Because that's what it seems like now that you're trying to broaden the scope of your contention to the other sections of the article.

I started the subthread with the comment because saying the difference between those numbers is small is weird, … because it is.

Those numbers represent percentages (90.005% and 90.0005%) and those two inputs, especially when applied to a chaotic system, will produce outsized differences over time.

And the data shows that the two filters produced outsized differences over time.

I'm not broadening the scope of my contention. I'm pointing out that my contention (there is a large difference in those numbers that is hidden by the way the author presents them) is confirmed by the data.

The data have nothing to do with the hypothetical where the air filters process 10% of the air in the room. They also have nothing to do with the air filters in the thought experiment, which are simplified, ideal filters that have the exact characteristics we say they do. Nobody is applying the numbers in question to any "chaotic system", because this is just a simple framing designed to illustrate exactly one, utterly banal point: If you don't process most of the air, it doesn't matter how efficient you are. In fact, that's all the section should have been. That one sentence. No numbers (it doesn't need them), and very little detail. Just, "if you don't process most of the air, the efficiency doesn't matter". You can't disagree with that conditional statment. You can argue that the premise is flawed, or irrelevant, or unrealistic to the point of uselessness, but you can't argue with the totally boringly obvious statement that if you aren't processing 90% of the air at all, then your efficiency doesn't matter. It's not more controversial than saying that "if your air filters are turned off, their efficiency doesn't matter."

> That, for a single minute, as a percentage of total air, a 99.5% and a 99.95% purifier produce a minor difference in total air quality is deeply irrelevant to the overall performance of the purifier over any length of time. The 10x difference, however, will matter over time.

Can you explain, with actual math, what you’re trying to say?

There are plenty of plausible explanations for Wirecutter’s unexpected results. They could have messed up (quite likely). The difference in the behavior of the fans could be circulating the air differently (also seems reasonably likely). The conditions of the test could be such that the difference in CADR was relevant (possible but doesn’t seem likely). They could have failed to set up the IKEA filter correctly (I once failed to set up a Conway filter correctly — it was somewhat embarrassing). Or, by pure magic, the fact that the extremely clean outgoing air from the IKEA filter was less extremely clean than the extremely clean outgoing air from the other filter made a difference (seems very unlikely).

> the original WireCutter article showed such stark differences between the performance of the Förnuftig and the Levoit Core 300, over a 30 minute span. If you were correct, over those 30 minutes, the amount of particulate in the test room would have been roughly equal for both purifiers. It wasn't. The Förnuftig removed only 64.5% of the particulate while the Levoit removed 97.4%.

Note that you are talking about the 0.3 micron measurements: if we look at larger particles the difference is smaller. But that's fine!

There are two big ways that that comparison is different from what we're talking about here:

* Those two purifiers have very different capacities: 135 CFM (CADR) for the Levoit, 82 for the Förnuftig

* The filter on the Förnuftig is much less effective against very small particles. The math above is comparing filters that are 99.5% vs 99.95% effective, while in this case it's more like 70% vs 99.97%.

We're talking about 0.3 micron measurements because the input value for his numbers is the efficiency of the filters in removing 0.3 micron particles (99.5 vs 99.95).

The author claimed the difference between the purified air, as a percentage of total air volume, was small. He used percentages expressed as a decimal to make that difference look small (0.9005 vs 0.90005). But a clever observer would translate those numbers back into their percentages (90.05 vs 90.005), start applying some math (i.e. 100000 x 0.9005 vs 0.90005), see the 10x difference, understand how that 10x different is going to multiply over time in a chaotic system, check the data to see if that's true, and then throw away the author's point.

Multiplying .9005 and .90005 by 10000 does not actually cause a 10x difference to appear. No, really, try it!

If your goal is to play with numbers, you could raise them both to a large power. You would discover that the ratio between them increases exponentially, but this would pale in comparison to the fact that both results would exponentially approach zero much faster than the ratio would increase.

10000 x .9005 is 9,005. 10000 x .90005 is 9,000.5.

Meaning that the first filter left 5 particles vs the second filter leaving .5 particles.

A 10x difference.

The goal isn't to "play with numbers" but to understand why/if the relative effectiveness of a filter results in a substantive difference in air quality.

The data shows it does.

> The data shows it does

As I described above [1] the data show that the difference between 70% and 99.95% matters, not that the difference between 99.5% and 99.95% does. (And that's ignoring difference in flow rates, which is also very large.)

[1] https://news.ycombinator.com/item?id=31823047

The 70% and 99.95% difference is because of the 10x filtration efficiency difference, combined with the CADR difference.

This is very straight-forward.

The "10x" you've been referring to is about the difference in how many particles make it through filters of 99.5% vs 99.95% efficacy [1], not 70% vs 99.95%, which would be 600x [2].

[1] (1−.995)÷(1−.9995)

[2] (1−.7)÷(1−.9995)

"CADR" is a word I included for a reason.

Extraordinary claims require extraordinary evidence. The data shows a huge difference which cannot be explained by the difference between 5 particles and 0.5 particles.

As noted in the article, the Wirecutter does not explain its methodology or give particularly complete data, and what explanations they do give about filtration make no sense.

It's a 10x difference in filtration efficiency, combined with a CADR difference between the two units.

I don't understand why you think more of an explanation is required?

There is a 10x difference between (1-efficiency) for the two filter media choices. Explanation needed as to why this is at all relevant.

Your comment is like observing that car A burns 87 octane gasoline and another burns 89 octane gasoline and claiming, without explanation, that one of them accelerates faster because (90-octane) is 3x lower.

hint: the bigger purifier wins because it has a more powerful, more power hungry fan pushing air through it. Its performance might be further improved (depending on the fan and motor characteristics) by putting a less efficient, lower pressure drop filter in because more air would go through it per unit time.

Meanwhile, two IKEA filters will outperform it in every measure, including cost, noise, and power consumption. But their efficiency will still be lower.