Will stay in water till boiled

Often, you'll hear people describing the pattern of a set of small, incremental changes being made to something, without that something realising they all add up to unnoticed disaster, as the "boiling frog" scenario. Examples might be many small tax changes or laws introduced by a government, which, if it were to do them all at once, would cause panic. Instead it does them slowly, with each change having very little effect on it's own.

This is said to be how a frog behaves in cold water when you slowly heat it up. The frog stays in until it's too late, whereas if it were to have jumped in when the water was getting warmer, it would have jumped out immediately having seen the danger.

Except it's not true.

Experiments, hopefully which never actually got to hot for our little green friends, show in fact they jump out very early in any case.

It's a useful analogy

Wikipedia describes the effect, but it is unfortunately a myth. In 1869 Friedrich Goltz conducted the experiment which shows this to be the case. It's been used a great deal by politicians, a notable example being Al Gore, and some places you'd have thought would have been more careful checking the truth of it, such as The Canadian Medical Association Journal. In the 1960's US politicians often invoked it as a warning against the Soviet Union during the Cold War. Climate change activists are also fond of the idea for obvious reasons, and it's also been raised in cases of domestic abuse.

It's been compared to the story of an ostrich putting it's head in the sand when in danger, completely false but still serving a purpose in language today. There's even been a movement since 2006 for people to stop using these metaphors because they are not scientifically corrent, but that doesn't seem to be changing anything.