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"Turtles all the way down" is a jocular expression of the infinite regress problem in cosmology posed by the "unmoved mover" paradox. The metaphor in the anecdote represents a popular notion of the myth that Earth is actually flat and is supported on the back of a World Turtle, which itself is propped up by a chain of larger and larger turtles. Questioning what the final turtle might be standing on, the anecdote humorously concludes that it is "turtles all the way down".
The phrase was used by Stephen Hawking in 1988, but has been commonly known since at least the early 20th century. A comparable metaphor describing the circular cause and consequence for the same problem is the "chicken and egg problem". The same problem in epistemology is known as the Münchhausen trilemma.
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's tortoises all the way down!"—Hawking, 1988
In John R. Ross's 1967 linguistics dissertation Constraints on Variables in Syntax, the scientist is identified as the Harvard psychologist and philosopher William James. Of the story's provenance, Ross writes:
After a lecture on cosmology and the structure of the solar system, William James was accosted by a little old lady.
"Your theory that the sun is the centre of the solar system, and the earth is a ball which rotates around it has a very convincing ring to it, Mr. James, but it's wrong. I've got a better theory," said the little old lady.
"And what is that, madam?" Inquired James politely.
"That we live on a crust of earth which is on the back of a giant turtle,"
Not wishing to demolish this absurd little theory by bringing to bear the masses of scientific evidence he had at his command, James decided to gently dissuade his opponent by making her see some of the inadequacies of her position.
"If your theory is correct, madam," he asked, "what does this turtle stand on?"
"You're a very clever man, Mr. James, and that's a very good question," replied the little old lady, "but I have an answer to it. And it is this: The first turtle stands on the back of a second, far larger, turtle, who stands directly under him."
"But what does this second turtle stand on?" Persisted James patiently.
To this the little old lady crowed triumphantly. "It's no use, Mr. James---it's turtles all the way down."—J. R. Ross, Constraints on Variables in Syntax 1967
In 1905, Oliver Corwin Sabin, Bishop of the Evangelical Christian Science Church, wrote:
The old original idea which was enunciated first in India, that the world was flat and stood on the back of an elephant, and the elephant did not have anything to stand on was the world's thought for centuries. That story is not as good as the Richmond negro preachers who said the world was flat and stood on a turtle. They asked him what the turtle stood on and he said another turtle, and they asked what that turtle stood on and he said another turtle, and finally they got him in a hole and he said. "I tell you there are turtles all the way down."—Sabin, 1905
The earliest version of the story in its "turtle" form appeared in 1854, attributed by bible skeptic Joseph Barker to preacher Joseph Frederick Berg:
My opponent’s reasoning reminds me of the heathen, who, being asked on what the world stood, replied, “On a tortoise.” But on what does the tortoise stand? “On another tortoise.” With Mr. Barker, too, there are tortoises all the way down.—Barker, 1854
Many 20th-century attributions point to William James as the source. James referred to the fable of the elephant and tortoise several times, but told the infinite regress story with "rocks all the way down" in his 1882 essay, "Rationality, Activity and Faith":
Like the old woman in the story who described the world as resting on a rock, and then explained that rock to be supported by another rock, and finally when pushed with questions said it was "rocks all the way down," he who believes this to be a radically moral universe must hold the moral order to rest either on an absolute and ultimate should or on a series of shoulds "all the way down."
In the form of "rocks all the way down", the story predates James to at least 1838, when it was printed in an unsigned anecdote about a schoolboy and an old woman living in the woods:
"The world, marm," said I, anxious to display my acquired knowledge, "is not exactly round, but resembles in shape a flattened orange; and it turns on its axis once in twenty-four hours."
"Well, I don't know anything about its axes," replied she, "but I know it don't turn round, for if it did we'd be all tumbled off; and as to its being round, any one can see it's a square piece of ground, standing on a rock!"
"Standing on a rock! but upon what does that stand?"
"Why, on another, to be sure!"
"But what supports the last?"
"Lud! child, how stupid you are! There's rocks all the way down!"
How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world.—Hume, 1779
Hawking's suggested connection to Russell may be due to Russell's 1927 lecture Why I Am Not a Christian. In it, while discounting the First Cause argument intended to be a proof of God's existence, Russell comments:
Men are making speeches... all over the country, but each expresses only the thought, or the want of thought, of the multitude. No man stands on truth. They are merely banded together as usual, one leaning on another and all together on nothing; as the Hindoos made the world rest on an elephant, and the elephant on a tortoise, and had nothing to put under the tortoise.
Philosophical allusion to the story goes back at least as far as John Locke. In his 1689 tract An Essay Concerning Human Understanding, Locke compares one who would say that properties inherent in "substance" to the Indian who said the world was on an elephant which was on a tortoise "but being again pressed to know what gave support to the broad-backed tortoise, replied — something, he knew not what."
Despite these accounts, Hindu myths do not actually contain the myth in the form described. Locke appears to have taken the idea from Samuel Purchas. Some accounts involve the earth supported by a single unsupported tortoise, as Jñanaraja argued: "A vulture, which has only little strength, rests in the sky holding a snake in its beak for a prahara [three hours]. Why can [the deity] in the form of a tortoise, who possesses an inconceivable potency, not hold the Earth in the sky for a kalpa [billions of years]?"
The story can also be found in Bernard Nietschmann's "When the Turtle Collapses, the World Ends", Natural History, 83(6):34 (June–July 1974).
A version of the story also appears in Clifford Geertz's, "Thick Description: Towards an Interpretive Theory of Culture", in his 1973 book The Interpretation of Culture, with the scientist and old woman replaced by an Englishman and an Indian respectively.
Carl Sagan recited a version of the story as an apocryphal anecdote in his 1979 book Broca's Brain: Reflections on the Romance of Science, as an exchange between a "Western traveler" and an "Oriental philosopher".
In our favored version, an Eastern guru affirms that the earth is supported on the back of a tiger. When asked what supports the tiger, he says it stands upon an elephant; and when asked what supports the elephant he says it is a giant turtle. When asked, finally, what supports the giant turtle, he is briefly taken aback, but quickly replies "Ah, after that it is turtles all the way down."—Antonin Scalia, Antonin Scalia. "RAPANOS v. UNITED STATES". Cornell Law School Legal Information Institute's Supreme Court collection.
The anecdote has achieved the status of an urban legend on the Internet, as there are numerous versions in which the name of the scientist varies (e.g., Arthur Stanley Eddington, Thomas Huxley, Linus Pauling, or Carl Sagan) although the rest is the same.