Gauss’s Pythagorean right triangle proposal | Wikipedia audio article


Gauss’s Pythagorean right triangle proposal
is an idea attributed to Carl Friedrich Gauss for a method to signal extraterrestrial beings
by constructing an immense right triangle and three squares on the surface of the Earth. The shapes would be a symbolical representation
of the Pythagorean theorem, large enough to be seen from the Moon or Mars. Although credited in numerous sources as originating
with Gauss, with exact details of the proposal set out, the specificity of detail, and even
whether Gauss made the proposal, have been called into question. Many of the earliest sources do not actually
name Gauss as the originator, instead crediting a “German Astronomer” or using other nonspecific
descriptors, and in some cases naming a different author entirely. The details of the proposal also change significantly
upon different retellings. Nevertheless, Gauss’s writings reveal a belief
and interest in finding a method to contact extraterrestrial life, and that he did, at
the least, propose using amplified light using a heliotrope, his own 1818 invention, to signal
supposed inhabitants of the Moon.==Proposal==
Carl Friedrich Gauss is credited with an 1820 proposal for a method to signal extraterrestrial
beings in the form of drawing an immense right triangle and three squares on the surface
of the Earth, intended as a symbolical representation of the Pythagorean theorem, large enough to
be seen from the Moon or Mars. Details vary between sources, but typically
the “drawing” was to be constructed on the Siberian tundra, and made up of vast strips
of pine forest forming the right triangle’s borders, with the interior of the drawing
and exterior squares composed of fields of wheat. Gauss is said to have been convinced that
Mars harbored intelligent life and that this geometric figure, invoking the Pythagorean
theorem through the squares on the outside borders (sometimes called a “windmill diagram”,
as originated by Euclid), would demonstrate to such alien observers the reciprocal existence
of intelligent life on Earth and its grounding in mathematics. Wheat was said to be chosen by Gauss for contrast
with the pine tree borders “because of its uniform color”.==Attribution==
The specificity of the proposal’s details as it appears in most later sources—even
its attribution to Gauss—is called into question in University of Notre Dame Professor
Michael J. Crowe’s 1986 book, The Extraterrestrial Life Debate, 1750–1900, in which he surveys
the origins of the Gauss proposal and observes that:The history of this proposal … can
be traced through two dozen or more pluralist writings reaching back to the first half of
the nineteenth century. When this is done, however, it turns out that
the story exists in almost as many forms as its retellings. Furthermore, these versions share one characteristic:
Never is reference supplied to where in the writings of Gauss … the [proposal] appear[s]!Some
early sources explored by Crowe for the attribution and form of Gauss’s proposal include Austrian
astronomer, Joseph Johann Littrow’s statement in Wunder des Himmels that “one of our most
distinguished geometers” proposed that a geometric figure “for example the well known so-called
square of the hypotenuse, be laid out on a large scale, say on a particular broad plain
of the earth”. and Patrick Scott’s Love in the Moon, in which a “learned man” is described
as proposing a signal formed by a “great plantation of tree” in the form of “47th Proposition
of Euclid” in “the great African dessert [sic]”. In Chambers’s Edinburgh Journal it was written
that a Russian savant had proposed to “communicate with the moon by cutting a large figure of
the forty-seventh proposition of Euclid on the plains of Siberia, which, he said, any
fool would understand”.In the writings of astronomers Asaph Hall and of Norman Lockyer,
each refer separately to a “German Astronomer” who proposed the method of contact be by “fire
signals” from Siberia. Writing in 1902, Simon Newcomb placed the
origin of a Siberian triangle “several hundred miles in extent” not with Gauss, but at the
feet of German astronomer Franz Xaver von Zach. In lectures presented by François Arago at
the Paris Observatory, he named Siberia as the location of an extraterrestrial signaling
project advanced by an unnamed “German geometer”, but that the signaling method was to be through
the use of mirrors, rather than any large symbol drawn upon the Earth. Despite this version’s departure from a geometric
figure, the appearance of mirrors as a signaling device has a connection with Gauss’s background. Gauss invented the Heliotrope in 1818, an
instrument that uses a mirror to reflect sunlight in a manner allowing a 1-inch (2.5 cm) square
mirror to be seen 8 miles (13 km) away even in sunny weather.Gauss wrote of the heliotrope’s
potential as a celestial signaling device in a March 25, 1822 letter to Heinrich Olbers,
by which he reveals a belief and interest in finding a method to contact extraterrestrial
life: “With 100 separate mirrors, each of 16 square feet, used conjointly, one would
be able to send good heliotrope-light to the moon …. This would be a discovery even greater
than that of America, if we could get in touch with our neighbors on the moon.” Finally, in the October 1826 issue of the
Edinburgh New Philosophical Journal an unnamed author wrote that in a conversation with Franz
von Gruithuisen, Gauss stated words to the effect that “the plan of erecting a geometrical
figure on the plains of Siberia corresponded with his opinion, because, according to his
view a correspondence with the inhabitants of the moon could only be begun by means of
such mathematical contemplations and ideas, which we and they have in common.” Crowe concluded in sum that his review of
earliest sources failed to confirm the detail of the proposal and Gauss as its author, but
that his origination of the idea was not unlikely given the existing evidence

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