Comment by etchalon
3 years ago
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.
3 years ago
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.
(0.9005 - 0.90005) / 0.90005 = 0.00049997222
It's a 0.049997% difference, not a 10x difference.
In an unsealed environment, the steady state will be related to amount filtered * % filtered / amount exchanged for any given time period. The difference in % filtered is not a significant factor in the above ratio.
What? Where are you getting the 10x from? Both numbers are about 0.9 and the difference is about 0, not 10. If you are refering to the sticker number, yeah the whole point of that calculation is that a 10x sticker number does absolutely not translate to a 10x difference.
> but homes are not sealed.
Correct, but neither are they ultra high throughput (at which point any filter sitting in the room would be useless anyway, since you never get the filtered air). So "not sealed" is too vague to make any conclusion.
No, a 10x difference would be between 0.9 and 0.09. What was given was about a 1.0005x difference. If you had a child that was .9005 meters tall and one that was .90005 meters tall, you couldn't tell which was taller without a precision ruler.
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in practice the filtration in a room goes down exponentially and quite quickly even with budget filters that only filter out 90%. even in shops where you are sanding.
https://woodgears.ca/dust/dylos.html
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.
That difference is from his comments on the toy model of 1000 cubic feet room and 100 cubic feet per minute recirculating air.
In an operating room or chip fab, the room would be over pressure and the new air coming into the room would be filtered. The cleanliness of that air would be determined by the quality of the filter.
Also, if you need air that clean, you need to have strategies for all sorts of things besides filtering.
The point is, you need to be very careful when you put numbers on the internet, and when you read numbers on the internet. Numbers make things feel more real than they are.
For me to actually trust the numbers here, I would need to see the graphs for multiple runs of each filter.
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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.
0.90005 times 10 is 9.0005, not 0.9005 (I.e. the two fractions presented are 90.005% and 90.05%). Even if you look at the complement you get 9.995% vs 9.95% which is small. One could imagine that these differences could also arise from eg obstructions to airflow or positioning in the room or the direction of the wind outside. The point is that the difference is dominated by air flow in a typical environment rather than filtering differences.
How is there a 10x change? I see a 0.1% change.
Is it a 10x difference? If you used the better filter, you would still have 99.95% of the particles you would have had if you used the worse filter
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.
Probabilities and amounts are not comparable even though they both use % notation.
In this case they are measuring the % of particles captured (an amount), not the likelihood a particle is captured (a probability). The parent is right, it’s a tiny difference.
Consider a purifier that purifies 99.995%. According to your "probabilities", that's a 100x improvement. Now consider this purifier purifies 1 cubic millimeter of air per hour. That is to say, each hour 1 cubic millimeter of air is 99.995% purified (no probability). Would you say that this purifier is 100x better than the IKEA one with 99.5% purification at 1 cubic feet of air per minute? Considering air flow is not a trick.
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This entire subthread is the math version of "most programmers can't even do fizz buzz".