6 ms·

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.

bramblerose 4y ago
Why do you feel it is weird? They are both 90%, because 90% * 100% + 10% * "effectively 0%" is completely dominated by the first term.
1986 4y ago
Why? It's a 0.05% difference, seems pretty small to me.
- etchalon 4y ago
  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.
  - snowwrestler 4y ago
    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.
  - rootlocus 4y ago
    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.
    - etchalon 4y ago
      A E12 filter filters out 99.5% of particles above 0.3 microns. An H13 filter filters out 99.95% of particles above 0.3 microns. Assuming a volume of 10000 particles above 0.3 microns: An E12 filter will leave 50 particles. An H13 filter will leave 5 particles. The "rootlocus" filter would leave 0.5 particles. So yes, I would say your filter is 100x better because it literally is.
      - rootlocus 4y ago
        > Assuming a volume of 10000 particles above 0.3 microns: That volume is not the same volume processed by all filters in the same amount of time. In the first minute: E12 filters 10000 particles @ 99.5% performance -> removes 9950, leaves 50 H13 filters 10000 particles @ 99.95% performance -> removes 9995, leaves 5 RLv1 filters 10 particles @ 99.995% performance -> removes 10, leaves 0 RLv2 filters 1000000 particles @ 99% performance -> removes 990000, leaves 10000 RLv1 only filters a tiny amount of air each minute, while RLv2 filters a lot of air each minute (I've improved the flow, but drastically botched the performance) By your method, RLv2 is 2000x slower than H13, but in the same ammount of time filtered 99x more particles. RLv1 needs to run 99000 minutes to filter the same amount of particles RLv2 does in one minute. The example is meant to show air flow totaly dominates performance, and it's not "a trick" to multiply by it. I also want to point out that comparing the amount of particles "left" (50 vs 5 vs 0 vs 10000) is nonsense and absolutely no indication of performance in any way.
        hexane360 4y ago
        In other words: you miss 100% of the particles you don't circulate (With apologies to Wayne Gretzky)
weaksauce 4y ago
> 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)
- etchalon 4y ago
  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.
  - deleted 4y ago
    [deleted]
  - diffeomorphism 4y ago
    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.
  - hexane360 4y ago
    (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.
  - kbelder 4y ago
    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.
csours 4y ago
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.
- etchalon 4y ago
  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.
  - jefftk 4y ago
    How is there a 10x change? I see a 0.1% change.
  - dan-robertson 4y ago
    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.
  - infinityio 4y ago
    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
- rcoveson 4y ago
  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.
evancox100 4y ago
This entire subthread is the math version of "most programmers can't even do fizz buzz".
aidenn0 4y ago
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%): .2 × (1-.995) + .8 = 0.801 vs .1 × (1-.9995) + .9 = 0.90005 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.

bramblerose 4y ago

Why do you feel it is weird? They are both 90%, because 90% * 100% + 10% * "effectively 0%" is completely dominated by the first term.

1986 4y ago

Why? It's a 0.05% difference, seems pretty small to me.

etchalon 4y ago
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.
- snowwrestler 4y ago
  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.
- rootlocus 4y ago
  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.
  - etchalon 4y ago
    A E12 filter filters out 99.5% of particles above 0.3 microns. An H13 filter filters out 99.95% of particles above 0.3 microns. Assuming a volume of 10000 particles above 0.3 microns: An E12 filter will leave 50 particles. An H13 filter will leave 5 particles. The "rootlocus" filter would leave 0.5 particles. So yes, I would say your filter is 100x better because it literally is.
    - rootlocus 4y ago
      > Assuming a volume of 10000 particles above 0.3 microns: That volume is not the same volume processed by all filters in the same amount of time. In the first minute: E12 filters 10000 particles @ 99.5% performance -> removes 9950, leaves 50 H13 filters 10000 particles @ 99.95% performance -> removes 9995, leaves 5 RLv1 filters 10 particles @ 99.995% performance -> removes 10, leaves 0 RLv2 filters 1000000 particles @ 99% performance -> removes 990000, leaves 10000 RLv1 only filters a tiny amount of air each minute, while RLv2 filters a lot of air each minute (I've improved the flow, but drastically botched the performance) By your method, RLv2 is 2000x slower than H13, but in the same ammount of time filtered 99x more particles. RLv1 needs to run 99000 minutes to filter the same amount of particles RLv2 does in one minute. The example is meant to show air flow totaly dominates performance, and it's not "a trick" to multiply by it. I also want to point out that comparing the amount of particles "left" (50 vs 5 vs 0 vs 10000) is nonsense and absolutely no indication of performance in any way.
      - hexane360 4y ago
        In other words: you miss 100% of the particles you don't circulate (With apologies to Wayne Gretzky)

weaksauce 4y ago

> 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)

etchalon 4y ago
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.
- deleted 4y ago
  [deleted]
- diffeomorphism 4y ago
  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.
- hexane360 4y ago
  (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.
- kbelder 4y ago
  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.

csours 4y ago

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.

etchalon 4y ago
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.
- jefftk 4y ago
  How is there a 10x change? I see a 0.1% change.
- dan-robertson 4y ago
  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.
- infinityio 4y ago
  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
rcoveson 4y ago
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.

evancox100 4y ago

This entire subthread is the math version of "most programmers can't even do fizz buzz".

aidenn0 4y ago

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%): .2 × (1-.995) + .8 = 0.801 vs .1 × (1-.9995) + .9 = 0.90005 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.