Comment by jefftk
3 years ago
The article explains it well:
Here’s a thought experiment: Take a 1000 cubic feet room and a purifier that processes 100 cubic feet of air per minute. (I follow Wirecutter in using vulgar imperial units.) Assume pessimistically that all particles are the worst-case size. If you run that purifier with an E12 filter, the fraction of particles that will remain after one minute is
.1 × (1-.995) + .9 = 0.9005.
That’s because 10% of the air goes through the purifier and has 99.5% of particles removed, while 90% of the air doesn’t go through the purifier at all.
Meanwhile, if you run that purifier with an H13 filter instead then the fraction of particles that remain will be
.1 × (1-.9995) + .9 = 0.90005.
If you noticed that 0.9005 and 0.90005 are almost identical then congratulations—you understand air filters better than the Wirecutter. Both 99.5% and 99.95% are close enough to 100% that performance is almost entirely determined by the volume of air they process.
Another application of Amdahl's law.
"the overall performance improvement gained by optimizing a single part of a system is limited by the fraction of time that the improved part is actually used"
Thanks for teaching me the name for this principle!
This is how I feel every time HN suggests rewriting every website in C while ignoring the fact the database takes most of the time for average web apps.
Or the articles about how Python is causing climate disaster while the author continues to drive an oversized SUV.
I really don't like this math, no one actually stops at that point, you take the output, la, "0.9005" and re-run it
and again, and again, etc, point being that over time it does cycle the entire room, due to entropy, and then suddenly the differences start to stack up a bit, not a lot, but when one filter is letting 10x the particles through vs the other filter, it'll show
> suddenly the differences start to stack up a bit, not a lot, but when one filter is letting 10x the particles through vs the other filter, it'll show
It doesn't show: the difference is too small to notice at every stage: https://www.jefftk.com/remaining-particles-by-minute-995-vs-...
Even comparing 95% vs 99.95% it's barely noticeable: https://www.jefftk.com/remaining-particles-by-minute-95-vs-9...
Sheet: https://docs.google.com/spreadsheets/d/1wVIdWR0lWgZRt4gbnVaH...
fair
The idea that the difference between 0.9005 and 0.90005 is "small" is … weird.
The moment I read that I checked out on the rest of the authors opinions.
Why do you feel it is weird? They are both 90%, because 90% * 100% + 10% * "effectively 0%" is completely dominated by the first term.
> The idea that the difference between 0.9005 and 0.90005 is "small" is … weird.
it is. that's one minute of filtration and the difference is minuscule. over time, this would trend to zero. in 10 minutes you'd expect to be near the steady state of the room. (obviously not completely steady state since you are filtering some already filtered air and probably introducing more particulates but close enough for an approximation)
It's a 10x difference. It's not small.
In a sealed environment, you're right, you'd eventually end up with all particles filtered.
But homes are not sealed environments.
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The author explicitly states that it's small in the home use context. If you're talking about medical or cleanroom manufacturing contexts, yes it's a huge difference.
The difference between 0.9005 and 0.90005 is not huge in a medical context, or in a chip fab context, or in any other practical context. We're not talking about the difference between 0.0005 and 0.00005. The numbers in question are 0.9005 and 0.90005, and the point being made is that the 0.9 problem dwarfs the 10x efficiency difference way over in the thousandths place.
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Even in a medical context, the difference, when operated like an air purifier, is negligible.
The genuine HEPA filter in a cleanroom [0] is not sitting in front of a fan in the middle of the room. It’s very carefully installed such that all the air coming into the clean area goes through it once. The calculation is entirely different. (A medical or industrial HEPA filter may well be in the exhaust, in which case the considerations are again different.)
[0] There’s none of this “true HEPA” stuff in a cleanroom. There is a filter that meets a specific standard, and that filter will have a gasket that seals with considerable force against the air handling equipment. The “true HEPA” filter in a Wirecutter-approved air purifier achieves nowhere near 99.97% due to the lack of the aforementioned gasket regardless of how amazing the filter media may be.
Small home or not, homes are not sealed environments. A 10x difference is a 10x difference.
Using one small number or produce another small number, so the difference looks small, doesn't hide the 10x change.
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This is how it works because the room is not sealed, nor is the filter being used to filter outside air into a positive pressure area.
It is (hopefully) easy to see that e.g. a filter that removes 99.5% of particles, but moves twice as much air per minute will remove almost twice as many particles per minute as a filter that removes 99.95% of particles.
Using the numbers from TFA (20% of the room for the 99.5 rather than 10%):
vs
Thus proving the point in TFA that the airflow matters more than E12 vs H13. The fact that the steady state (given that "dirty" air is being introduced somehow) is lower for the filter that moves more air follows from the fact that it removes particles at a faster rate.
Why? It's a 0.05% difference, seems pretty small to me.
The difference between 99.5% and 99.95 is the difference between an event happening 1 in 200 times and happening and 1 in 2000 times.
It's a 10x difference.
The author's "I'll just times .1 by the percent of flow, and produce very small numbers that look fine! See! The numbers are so small!" trick is just … wrong.
The author implies that the difference can be made up by the volume of air being processed, but that would only be true of a sealed environment, where no new pollutants are added to the air.
Setting aside the basic misunderstanding of probability, and ignoring that home purifiers don't operate in sealed environments, the IKEA unit does not process 10x the amount of air as the other units, so the point is mute.
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This entire subthread is the math version of "most programmers can't even do fizz buzz".