The boiling frog story is a widespread anecdote describing a frog slowly being boiled alive. The premise is that if a frog is placed in boiling water, it will jump out, but if it is placed in cold water that is slowly heated, it will not perceive the danger and will be cooked to death. The story is often used as a metaphor for the inability of people to react to significant changes that occur gradually. According to contemporary biologists the premise of the story is not literally true; an actual frog submerged and gradually heated will jump out. However, 19th century research experiments appear to corroborate one underlying premise; that a submerged frog will stay still when heated, but only as long as the heating is gradual enough.
If you drop a frog in a pot of boiling water, it will of course frantically try to clamber out. But if you place it gently in a pot of tepid water and turn the heat on low, it will float there quite placidly. As the water gradually heats up, the frog will sink into a tranquil stupor, exactly like one of us in a hot bath, and before long, with a smile on its face, it will unresistingly allow itself to be boiled to death.
The boiling frog story is generally told in a metaphorical context, with the upshot being that people should make themselves aware of gradual change lest they suffer eventual undesirable consequences. This may be in support of a slippery slope argument. It is also used in business to illustrate the idea that change needs to be gradual to be accepted. The expression "boiling frog syndrome" is sometimes used as shorthand for the metaphor.
The story has been retold many times and used to illustrate many different points. It has been used to warn about diverse phenomena, for example: in 1960 about sympathy towards the Soviet Union during the Cold War, in 1980 about the impending collapse of civilization anticipated by survivalists, and in the 1990s about inaction in response to climate change and staying in abusive relationships. It has also been used by libertarians to warn about slow erosion of civil rights.
In the 1989 book The Age of Unreason, management author Charles Handy begins with this metaphor to illustrate how the business world is changing and how we will require upside-down thinking to continue to organise our work and daily lives effectively. In the 1996 novel The Story of B, environmentalist author Daniel Quinn spends a chapter on the metaphor of the boiling frog, using it to describe human history, population growth and food surplus. Al Gore used a version of the story in his presentations and the 2006 movie An Inconvenient Truth to describe ignorance about global warming. In his version the frog is rescued before it is harmed.
In September 2009, TV personality Glenn Beck did a demonstration on his show in which he seemingly threw a frog into a pot of boiling water. He explained shortly afterward that the stunt was faked, but an edited video not containing this explanation later began circulating on the internet.
In philosophy the boiling frog story has been used as a way of explaining the Sorites paradox. This paradox describes a hypothetical heap of sand from which individual grains are removed one at a time, and asks if there is a specific point when it can no longer be defined as a heap.
Several experiments involving recording the reaction of frogs to slowly heated water took place in the 19th century. In 1869, while doing experiments searching for the location of the soul, German physiologist Friedrich Goltz demonstrated that a frog that has had its brain removed will remain in slowly heated water, but his intact frogs attempted to escape the water.
Other experiments showed that frogs did not attempt to escape gradually heated water. An 1872 experiment by Heinzmann demonstrated that a normal frog would not attempt to escape if the water was heated slowly enough, and this was corroborated in 1875 by Fratscher.
Goltz raised the temperature of the water from 17.5°C to 56°C in about ten minutes, or 3.8°C per minute, in his experiment which prompted normal frogs to attempt to escape, whereas Heinzmann heated the frogs over the course of 90 minutes from about 21°C to 37.5°C, a rate of less than 0.2°C per minute. One source from 1897 says, "in one experiment the temperature was raised at a rate of 0.002°C. per second, and the frog was found dead at the end of 2½ hours without having moved." 
In 1888 William Thompson Sedgwick explained the apparent contradiction between the results of these experiments as a consequence of different heating rates used in the experiments: "The truth appears to be that if the heating be sufficiently gradual, no reflex movements will be produced even in the normal frog ; if it be more rapid, yet take place at such a rate as to be fairly called "gradual," it will not secure the repose of the normal frog under any circumstances..."
Contemporary scientists have described the story as inaccurate. In 1995, Professor Douglas Melton, of the Harvard University Biology department, said, "If you put a frog in boiling water, it won't jump out. It will die. If you put it in cold water, it will jump before it gets hot — they don't sit still for you." Dr. George R. Zug, curator of reptiles and amphibians at the National Museum of Natural History, also rejected the suggestion, saying that "If a frog had a means of getting out, it certainly would get out."
In 2002 Dr. Victor H. Hutchison, Professor Emeritus of Zoology at the University of Oklahoma, with a research interest in thermal relations of amphibians, said that "The legend is entirely incorrect!". He described how the critical thermal maximum for many frog species has been determined by contemporary research experiments: as the water is heated by about 2°F, or 1.1°C, per minute, the frog becomes increasingly active as it tries to escape, and eventually jumps out if the container allows it.
Law professor and legal commentator Eugene Volokh commented in 2003 that regardless of the behavior of real frogs, the boiling frog story is useful as a metaphor, comparing it to the metaphor of an ostrich with its head in the sand. Economist Paul Krugman used the story as a metaphor in a July 2009 column, while pointing out that real frogs behave differently. Journalist James Fallows has been advocating since 2006 for people to stop retelling the story, describing it as a "stupid canard" and a "myth". But following Krugman's column, he declared "peace on the boiled frog front" and said that using the story is fine as long as you point out it's not literally true.