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Comment by etchalon | Hacker News Reader

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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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.

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.

> 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.

In other words: you miss 100% of the particles you don't circulate

(With apologies to Wayne Gretzky)

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