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Comment by api_or_ipa | Hacker News Reader

Reminds me of a lesson about misleading statistics I tell my nephews. We've all see the hand sanitizers that advertize killing 99.99% of germs, but what does that actually mean? 99.99% equates to 1/10,000 survivors and assuming for each generation the population doubles means it takes just 14 generations for the original colony to be back at full strength again. For extra creepy effect, e coli can reproduce in optimal conditions as fast as every 20 minutes which buys you only a couple hours of hygiene[0].

Given this drug kills 99/100 HIV virus units, then this really only helps you for log2(100) or ~7 generations

The math is pretty easy, but the results are something that always surprise me: it turns out humans are pretty bad at estimating exponential growth.

0: real life conditions are probably slower than this, I concede.

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> which buys you only a couple hours of hygiene

Which is long enough for you to complete your lunch! :-)

Is that even the claim they are making? I honestly never thought about it, but the claim could easily be "we kill 99.99% of germ strains" or "we kill 99.99% of germ cells".

I think the problem is that people tend to focus on the size of the numeric probability, as if it was intrinsically meaningful. And don't think to consider contextual details like in the example you give. It's the combination of the probabilities to the contextual details they're applied to that really matter.

Another illustration of that is, if 99.99% equates to 1/10000 survivors, the meaning of it depends on how many bacteria exist on the area in the first place. It has quite a different meaning if the typical number is 10000 vs if it's 100000000

> e coli can reproduce in optimal conditions

Then avoid dipping your hand into beef stew for too long. Most of time, germs grow like sigmoid function.

The idea is that it kills 99% of them, and then your immune system is up to the task of killing the remaining 1%.

the marketing idea?

But it's not a simple, linear battle.

That most virulent 1% then multiplies and infects systemwide... and adds new mutations all the time.

It's not the most virulent 1%, it's 1% which have unusual mutations that cause them to be resistant to this treatment, but which usually reduce their fitness in other respects. (This can be seen in humans as well, e.g. malaria resistance->sickle-cell). The fastest-multiplying viruses are also (obviously) going to be the most common, in the absence of treatment.

Interesting point. I hadn't considered unusual but useful mutations they accrued might come with reduced fitness in other regards.

It's like having superpowers, but with physical abnormalities. Like so many things, this was explored in the comics!

This is really fascinating how being really good at something often correlates with being less good at other things (in this case antibiotic resistance seems to be inversely proportional to the potency of the bacteria).

This is true not just for bacteria but also for other living creatures; for example animals that have lots of children have very short average lifespans.

It makes me think that every living species must be at the absolute cutting edge of its capabilities genetically-speaking.

Natural selection tends to work on traits that are relevant till the ability to reproduce ends. If the trait can dominate by rapid reproduction, life span does not matter and robustness is not selected for. Generally it is not an inherent trade-off between certain traits, apart from energy consumption.

My physics brain is now imagining some conserved quantity like the fitness density of a bacteria population. Lol

hand sanitizers aren't to replace soap, where as soap kills and washes surviving germs away

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