You can't prove it's impossible!

[reddragdiva]

A common sophistry which really annoys me is the one that conflates an utterly negligible probability with a non-negligible one. The argument goes:

1. There is technically no such thing as certainty.
2. Therefore, [argument I don't like] is not absolutely certain.
3. Therefore, the uncertainty in [argument I don't like] is non-negligible.

Step 3 is the tricky one. Humans are, in general, really bad at feeling the difference between epsilon uncertainty and sufficient uncertainty to be worth taking notice of — they can't tell a nonzero chance from one that's worth paying attention to ever. (This is why people buy lottery tickets.)

It’s a terrible, terrible argument, and an unfortunately common one. It needs to be bludgeoned to death every time it’s brought up.

Comments

[vatine]

Part of the problem is that even low-probability events may be worth paying attention to.

High-probability, low-danger (or low-payout) scenarios are easy to reason about. Low-probability high-danger (or high-payout) scenarios are much harder to reason about.

Then there's the wonders of "how frequently are we testing this probability". If we test something once a second, you'd expect a once-in-a-million event to occur about once every two weeks. If we try it once a year, not so much.

On the gripping hand, when I get gut-feelings one way or another, I do tend to return to the whiteboard and start working from first principles, because I am (probably) over- or under-estimating badly. So, I guess, one can learn to live with one's cognitive limitations.

[reddragdiva]

I would boggle at anyone who raises this argument doing the actual numbers, ever.

[blue_cat]

This seems to me to be akin to the known issue of people failing to understand, or choosing not to understand, statistical likelyhood especially as associated to the level of control.

When a person is in control of the situation (e.g. driving a car) the perceived risk of an accident is low and the tolerance of risk is high.

When a person is not in control (e.g. flying) the perceived risk is high and tolerance of risk is low.

As for actual numbers, reminding myself that more people are killed in car accidents yearly than plane accidents does kinda work (your 'returning to numbers' idea) but still only partially works.

Regarding Reddragdiva's original issue, it is a bit difficult to identify the scenario's other than the above without an example?

[vatine]

To continue with the "frequency of trials", for a 1-in-14M repeated trial (1-in-14M every time), you have 50% chance to win after somewhere between 9.7M and 9.8M trials. For something repeating once a week, really not worth expecting to walk away with the price (that's, what, couple of hundred thousand years), but for something repeating once a second, that's about 100 days.

FWIW, the 1-in-1M "number of trials to make it 50% give or take" is on the order of ~700k trials, still not worth it for a once-in-a-week event, but for a once-in-a-second...