document_title: Square root of 2

question_text: who proved that square root of 2 is irrational

text: Square root of 2

text: History[edit]

text: The Babylonian clay tablet YBC 7289 (c. 1800–1600 BC) gives an approximation of √2 in four sexagesimal figures, 1 24 51 10, which is accurate to about six decimal digits,[1] and is the closest possible three-place sexagesimal representation of √2:

text: Another early close approximation is given in ancient Indian mathematical texts, the Sulbasutras (c. 800–200 BC) as follows: Increase the length [of the side] by its third and this third by its own fourth less the thirty-fourth part of that fourth.[2] That is,

text: This approximation is the seventh in a sequence of increasingly accurate approximations based on the sequence of Pell numbers, which can be derived from the continued fraction expansion of √2. Despite having a smaller denominator, it is only slightly less accurate than the Babylonian approximation.

text: Pythagoreans discovered that the diagonal of a square is incommensurable with its side, or in modern language, that the square root of two is irrational. Little is known with certainty about the time or circumstances of this discovery, but the name of Hippasus of Metapontum is often mentioned. For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it.[3][4][5] The square root of two is occasionally called "Pythagoras' number" or "Pythagoras' constant", for example by Conway & Guy (1996).[6]

text: Computation algorithms[edit]

text: There are a number of algorithms for approximating √2, which in expressions as a ratio of integers or as a decimal can only be approximated. The most common algorithm for this, one used as a basis in many computers and calculators, is the Babylonian method[7] of computing square roots, which is one of many methods of computing square roots. It goes as follows:

text: First, pick a guess, a0 > 0; the value of the guess affects only how many iterations are required to reach an approximation of a certain accuracy. Then, using that guess, iterate through the following recursive computation:

text: The more iterations through the algorithm (that is, the more computations performed and the greater "n"), the better approximation of the square root of 2 is achieved. Each iteration approximately doubles the number of correct digits. Starting with a0 = 1 the next approximations are

text:
3/2     = 1.5
17/12   = 1.416...
577/408 = 1.414215...
665857/470832 = 1.4142135623746...

tag: ul

text:
The value of √2 was calculated to 137,438,953,444 decimal places by Yasumasa Kanada's team in 1997. In February 2006 the record for the calculation of √2 was eclipsed with the use of a home computer. Shigeru Kondo calculated 1 trillion decimal places in 2010.[8] For a development of this record, see the table below. Among mathematical constants with computationally challenging decimal expansions, only π has been calculated more precisely.[9]
Such computations aim to check empirically whether such numbers are normal.

text: Rational approximations[edit]

text: A simple  rational approximation 99/70 (≈ 1.4142857) is sometimes used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 6995720000000000000♠+0.72×10−4).  Since it is a convergent of the continued fraction representation of the square root of two, any better rational approximation has a denominator not less than 169, since 239/169 (≈ 1.4142012) is the next convergent with an error of approx. 3004880000000000000♠−0.12×10−4.

text: The rational approximation of the square root of two, 665,857/470,832, derived from the fourth step in the Babylonian algorithm starting with a0 = 1, is too large by approx. 6988160000000000000♠1.6×10−12: its square is 7000200000000000450♠2.0000000000045…

text: Record progression[edit]

text: This is a table of recent records in calculating digits of √2 ( 1 trillion =  1012 = 1,000,000,000,000 ).

text:
Date
Name
Number of digits

June 28, 2016
Ron Watkins
10 trillion

April 3, 2016
Ron Watkins
5 trillion

February 9, 2012
Alexander Yee
2 trillion

March 22, 2010
Shigeru Kondo
1 trillion= 1012

Reference:[10]

text: Proofs of irrationality[edit]

text: A short proof of the irrationality of √2 can be obtained from the rational root theorem, that is, if p(x) is a monic polynomial with integer coefficients, then any rational root of p(x) is necessarily an integer. Applying this to the polynomial p(x) = x2 − 2, it follows that √2 is either an integer or irrational. Because √2 is not an integer (2 is not a perfect square), √2 must therefore be irrational. This proof can be generalized to show that any root of any natural number which is not the square of a natural number is irrational.

text: See quadratic irrational or infinite descent for a proof that the square root of any non-square natural number is irrational.

text: Proof by infinite descent[edit]

text: One proof of the number's irrationality is the following proof by infinite descent. It is also a proof by contradiction, also known as an indirect proof, in that the proposition is proved by assuming that the opposite of the proposition is true and showing that this assumption is false, thereby implying that the proposition must be true.

text:
Assume that √2 is a rational number, meaning that there exists a pair of integers whose ratio is √2.
If the two integers have a common factor, it can be eliminated using the Euclidean algorithm.
Then √2 can be written as an irreducible fraction a/b such that a and b are coprime integers (having no common factor).
It follows that a2/b2 = 2 and a2 = 2b2.   ( (a/b)n = an/bn  )   ( a2 and b2 are integers)
Therefore, a2 is even because it is equal to 2b2. (2b2 is necessarily even because it is 2 times another whole number and multiples of 2 are even.)
It follows that a must be even (as squares of odd integers are never even).
Because a is even, there exists an integer k that fulfills: a = 2k.
Substituting 2k from step 7 for a in the second equation of step 4: 2b2 = (2k)2 is equivalent to 2b2 = 4k2, which is equivalent to b2 = 2k2.
Because 2k2 is divisible by two and therefore even, and because 2k2 = b2, it follows that b2 is also even which means that b is even.
By steps 5 and 8 a and b are both even, which contradicts that a/b is irreducible as stated in step 3.

text: Because there is a contradiction, the assumption (1) that √2 is a rational number must be false. This means that √2 is not a rational number; i.e., √2 is irrational.

text: This proof was hinted at by Aristotle, in his Analytica Priora, §I.23.[11] It appeared first as a full proof in Euclid's Elements, as proposition 117 of Book X. However, since the early 19th century historians have agreed that this proof is an interpolation and not attributable to Euclid.[12]

text: Proof by unique factorization[edit]

text: An alternative proof uses the same approach with the fundamental theorem of arithmetic which says every integer greater than 1 has a unique factorization into powers of primes.

text:
Assume that √2 is a rational number. Then there are integers a and b such that a is coprime to b and √2 = a/b. In other words, √2 can be written as an irreducible fraction.
The value of b cannot be 1 as there is no integer a the square of which is 2.
There must be a prime p which divides b and which does not divide a, otherwise the fraction would not be irreducible.
The square of a can be factored as the product of the primes into which a is factored but with each power doubled.
Therefore, by unique factorization the prime p which divides b, and also its square, cannot divide the square of a.
Therefore, the square of an irreducible fraction cannot be reduced to an integer.
Therefore, √2 cannot be a rational number.

text: This proof can be generalized to show that if an integer is not an exact kth power of another integer then its kth root is irrational. For a proof of the same result which does not rely on the fundamental theorem of arithmetic, see: quadratic irrational.

text: Proof by infinite descent, not involving factoring[edit]

text: The following reductio ad absurdum argument showing the irrationality of √2 is less well-known. It uses the additional information 2 > √2 > 1 so that 1 > √2 − 1 > 0.[13]

text:
Assume that √2 is a rational number. This would mean that there exist positive integers m and n with n ≠ 0 such that m/n = √2. Then m = n√2 and m√2 = 2n.
We may assume that n is the smallest integer so that n√2 is an integer. That is, that the fraction m/n is in lowest terms.
Because 1 > √2 − 1 > 0, it follows from (1) that n > n(√2 − 1) = m − n > 0. So n > m − n > 0.
Also from (1), we have √2 = m/n = m(√2 − 1)/n(√2 − 1) = 2n − m/m − n.
Thus the fraction m/n for √2, which according to (2) is already in lowest terms, is represented by (4) in yet lower terms (which follows from the result (3)). This is a contradiction, so the assumption that √2 is rational must be false.

text: This argument may be tightened as follows.

text: Let b be the least positive integer for which √2 is a rational a/b.  Then b has the property that twice its square is a square, that is, 2b2 = a2.  For a contradiction, we show that a − b is a smaller positive integer with the same property.  Multiply the inequalities 1 > √2 − 1 > 0 by b to show b > a − b > 0.  Now twice the square of a − b is 2a2 − 4ab + 2b2. Rewrite the first and last terms using b's property to yield a2 − 4ab + 4b2, which is just the expansion of (2b − a)2, the promised square. Thus, √2 can also be written as (a − b)/(2 b − a). This procedure can be iterated and understood geometrically, as shown below.

text: Geometric proof[edit]

text: The immediately preceding argument has a simple geometric formulation attributed by John Horton Conway to Stanley Tennenbaum when the latter was a student in the early 1950s[14] and whose most recent appearance is in an article by Noson Yanofsky in the May–June 2016 issue of American Scientist.[15]  Given two squares with integer sides respectively a and b, one of which has twice the area of the other, place two copies of the smaller square in the larger as shown in Figure 1.  The square overlap region in the middle ((2b − a)2) must equal the sum of the two uncovered squares (2(a − b)2).  But these squares on the diagonal have positive integer sides that are smaller than the original squares.  Repeating this process we can find arbitrarily small squares one twice the area of the other, yet both having positive integer sides, which is impossible since positive integers cannot be less than 1.

text: Another geometric reductio ad absurdum argument showing that √2 is irrational appeared in 2000 in the American Mathematical Monthly.[16] It is also an example of proof by infinite descent. It makes use of classic compass and straightedge construction, proving the theorem by a method similar to that employed by ancient Greek geometers. It is essentially the algebraic proof of the previous section viewed geometrically in yet another way.

text: Let △ABC be a right isosceles triangle with hypotenuse length m and legs n as shown in Figure 2. By the Pythagorean theorem, m/n = √2. Suppose m and n are integers. Let m:n be a ratio given in its lowest terms.

text: Draw the arcs BD and CE with centre A. Join DE. It follows that AB = AD, AC = AE and the ∠BAC and ∠DAE coincide. Therefore, the triangles ABC and ADE are congruent by SAS.

text: Because ∠EBF is a right angle and ∠BEF is half a right angle, △BEF is also a right isosceles triangle. Hence BE = m − n implies BF = m − n. By symmetry, DF = m − n, and △FDC is also a right isosceles triangle. It also follows that FC = n − (m − n) = 2n − m.

text: Hence we have an even smaller right isosceles triangle, with hypotenuse length 2n − m and legs m − n. These values are integers even smaller than m and n and in the same ratio, contradicting the hypothesis that m:n is in lowest terms. Therefore, m and n cannot be both integers, hence √2 is irrational.

text: Pythagorean theorem proof[edit]

text: This is another proof by contradiction, supposing that √2 is rational.

text:
That means that we can make a right isosceles triangle where the side lengths are natural numbers and the legs and the hypotenuse do not share any common factors (except 1).
Since the legs are equal, so are their squares. So in order for the Pythagorean theorem to work for this special right triangle, the square of the hypotenuse has to be an even number (and if we cut it in half once then we have the area of the square of the leg).
Recall that the square of an even number is even and the square of an odd number is odd. So if the square of the hypotenuse is even the hypotenuse is even as well.
Remember that a square is a quadrilateral with 2 pairs of parallel sides which are equal in length and has 4 right angles. So both sides of the square of the hypotenuse are even.
So the square of the hypotenuse of this right triangle can be cut in half twice and still have integer area. Since we only want to cut it in half once, then we'll get an even number.
So the square of the leg is even. Now according to (2) the leg must be even.
This contradicts our assumption at (1) that the leg and hypotenuse have no common factors (except 1). Because if they're both even they share a common factor of 2. So the assumption that √2 was rational has to be false. Or in other words √2 is an irrational number. Q. E. D.

text: Analytic proof[edit]

text: Lemma: let α ∈ ℝ+ and p1, p2,… q1, q2,… ∈ ℕ such that |αqn − pn| ≠ 0 for all n ∈ ℕ and

text: √2 is irrational.

text: Constructive proof[edit]

text: In a constructive approach, one distinguishes between on the one hand not being rational, and on the other hand being irrational (i.e., being quantifiably apart from every rational), the latter being a stronger property. Given positive integers a and b, because the valuation (i.e., highest power of 2 dividing a number) of 2b2 is odd, while the valuation of a2 is even, they must be distinct integers; thus |2b2 − a2| ≥ 1. Then[17]

text: the latter inequality being true because we assume a/b ≤ 3 − √2 (otherwise the quantitative apartness can be trivially established). This gives a lower bound of 1/3b2 for the difference |√2 − a/b|, yielding a direct proof of irrationality not relying on the law of excluded middle; see Errett Bishop (1985, p. 18). This proof constructively exhibits a discrepancy between √2 and any rational.

text: Properties of the square root of two[edit]

text: One-half of √2, also the reciprocal of √2, approximately 0.707106781186548, is a common quantity in geometry and trigonometry because the unit vector that makes a 45° angle with the axes in a plane has the coordinates

text: This number satisfies

text: One interesting property of √2 is as follows:

text: since

text: This is related to the property of silver ratios.

text: √2 can also be expressed in terms of the copies of the imaginary unit i using only the square root and arithmetic operations:

text: if the square root symbol is interpreted suitably for the complex numbers i and −i.

text: √2 is also the only real number other than 1 whose infinite tetrate (i.e., infinite exponential tower) is equal to its square. In other words: if for c > 1 we define x1 = c and xn+1 = cxn for n > 1, we will call the limit of xn as n → ∞ (if this limit exists) f(c). Then √2 is the only number c > 1 for which f(c) = c2. Or symbolically:

text: √2 appears in Viète's formula for π:

text: for m square roots and only one minus sign.[18]

text: Similar in appearance but with a finite number of terms, √2 appears in various trigonometric constants:[19]

text: It is not known whether √2 is a normal number, a stronger property than irrationality, but statistical analyses of its binary expansion are consistent with the hypothesis that it is normal to base two.[20]

text: Series and product representations[edit]

text: The identity cos π/4 = sin π/4 = 1/√2, along with the infinite product representations for the sine and cosine, leads to products such as

text: and

text: or equivalently,

text: The number can also be expressed by taking the Taylor series of a trigonometric function. For example, the series for cos π/4 gives

text: The Taylor series of √1 + x with x = 1 and using the double factorial n!! gives

text: The convergence of this series can be accelerated with an Euler transform, producing

text: It is not known whether √2 can be represented with a BBP-type formula. BBP-type formulas are known for π√2 and √2ln(1+√2), however.[21]

text: The number can be represented by an infinite series of Egyptian fractions, with denominators defined by 2nth terms of a Fibonacci-like recurrence relation a(n)=34a(n-1)-a(n-2), a(0)=0, a(1)=6.[22]

text: Continued fraction representation[edit]

text: The square root of two has the following continued fraction representation:

text: The convergents formed by truncating this representation form a sequence of fractions that approximate the square root of two to increasing accuracy, and that are described by the Pell numbers (known as side and diameter numbers to the ancient Greeks because of their use in approximating the ratio between the sides and diagonal of a square). The first convergents are: 1/1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, 577/408. The convergent p/q differs from √2 by almost exactly 1/2q2√2[citation needed] and then the next convergent is p + 2q/p + q.

text: Nested square representations[edit]

text:
The following nested square expressions converge to

2

{\displaystyle {\sqrt {2}}}

:

text: Derived constants[edit]

text: The reciprocal of the square root of two (the square root of 1/2) is a widely used constant.

text:
1

2

=

2

2

=
sin

45

∘

=
cos

45

∘

=
0.70710

67811

86547

52440

08443

62104

84903

928...

{\displaystyle {\frac {1}{\sqrt {2}}}={\frac {\sqrt {2}}{2}}=\sin 45^{\circ }=\cos 45^{\circ }=0.70710\,67811\,86547\,52440\,08443\,62104\,84903\,928...}

 (sequence A010503 in the OEIS)

text: Paper size[edit]

text: The (approximate) aspect ratio of paper sizes under ISO 216 (A4, A0, etc.) is 1:√2. This ratio of lengths of the shorter over the longer side guarantees that cutting a sheet in half along a line parallel to its shorter side results in the smaller sheets having the same (approximate) ratio as the original sheet.

text:
Proof:
Let

S
=

{\displaystyle S=}

 shorter length and

L
=

{\displaystyle L=}

 longer length of the sides of a sheet of paper, with

text:
Let

R
′

=

L
′

S
′

{\displaystyle R'={\frac {L'}{S'}}}

 be the analogue ratio of the halved sheet, then


document_title: List of islands of the Federated States of Micronesia

question_text: how many islands are included in the federated states of micronesia

root

text: List of the islands of the Federated States of Micronesia, in the central and western Caroline Islands Archipelago of the Western Pacific Ocean. The islands are within the Micronesia cultural and ecological region of Oceania.

tag: p

text: There are 607 islands and islets in the Federated States of Micronesia.[1]

text: List[edit]

text: Entries in boldface italics are atolls consisting of several islands, not single islands.

text:
Ant Atoll (12 islands)[2]

Dienpwahlek
Imwinyap (on Mapcarta)
Muniteate
Nahlos
Nikalap Aru (on Mapcarta)
Pahnwasank (on Mapcarta)
Pamuk Imwintiati (on Mapcarta)
Pasa
Wolauna (on Mapcarta)

Chuuk Atoll (98 islands)[3]
Eauripik[4]

Eauripik
Oao

Elato[4]

Falipi
Kari
Oletel

Eot (island) (on Google Maps)
Etal Atoll (on Google Maps)

Etal Island
Parang (on Google Maps)
Unon

Eten Island (on Google Maps)
Faichuk
Falalop (de)
Farafor (on Google Maps)
Faraulep (on Google Maps)
Fayu Atoll

East Fayu Island[5]

Fefan (on Google Maps)
Ferit (on Google Maps)
Fono (on Google Maps)
Front Island (on Geographic.org)
Gaferut (on Google Maps)
Hall Islands
Ifalik
Kapingamarangi
Kosrae (on Google Maps)
Kuop
Kutu (island)
Lalang (on Google Maps)
Lamotrek
Lelu Island
Losap
Lukunor
Magur (island)
Mokil Atoll

Urak
Kahlap (Mokil)
Manton

Murilo
Nama
Namoluk
Namonuito Atoll
Ngulu Atoll
Nomwin
Nukuoro Atoll (46 islands)[6] (on Google Maps)

Moduilalo
Olomanga
Deahua
Moduilodo
Gausema
Senugudai
Masabu
Masagumani-ingage
Dagamanga
Ladi
Demodu
Haisisi
Ngaligi
Sungaulohu
Tuija
Haduganae
Balaiasi
Moduovega
Baonga
Ahuloloa
Moduodula
Ahuedolu
Moduovae
Deahu
Deahu
Deahu
Sabinimadogo
Modubodai
Moduidua
Ahuilodo
Dahangahaino
Dahangadabu
Ahulegalega
Masagumani-ilalo
Niulegida
Ahulanui
Dolungahale
Dalagivao
Moduia
Modunui
Namooilodoa
Hauosiga
Gabinivele
Dalainamo
Deungagelegele
Guam
Saipan
Tinian
Rota

Olimarao (2 islands)

Olimarao Island
Falipi Island

Oroluk Atoll (1 island)

Oroluk Island

Pakin Atoll
Piagailoe

West Fayu Island

Pingelap
Pis (on Google Maps)
Pohnpei (on Google Maps)
Poluwat

Aaru To (on Geographic.org)
Alet Island (on Google Maps)

Pulap

Pollap
Tamatam
Fanadik

Sapwuahfik (on GeoNames, on Mapcarta)
Satawal
Satawan
Sorol
Tonowas
Ulithi
Uman Island
Weno (on Google Maps)
Winipirea (on Google Maps)
Woleai

Falalus
Pial
Luisaga
Faluelemariete
Faluelepalape
Faluelegalao
Elingarik
Woteggai
Sileap
Falamalok
Taramat
Farailes
Jalangigereil
Tahoilap
Mariyang
Falalop
Paliau
Raur
Motegosu


document_title: Christian cross

question_text: when did the cross become a christian symbol

text: Christian cross

text: History of use[edit]

text: Pre-Christian[edit]

text: This section may stray from the topic of the article. Please help improve this section or discuss this issue on the talk page. (July 2016)

tag: table

text: The cross-shaped sign, represented in its simplest form by a crossing of two lines at right angles, greatly predates the introduction of Christianity, in both East and West. It goes back to a very remote period of human civilization. It is supposed to have been used not just for its ornamental value, but also with religious significance.[3] It may have represented the apparatus used in kindling fire, and thus as the symbol of sacred fire or as a symbol of the sun, denoting its daily rotation. It has also been interpreted as the mystic representation of lightning or of the god of the tempest, or the emblem of the Aryan pantheon and the primitive Aryan civilization.[3]

text: Ankh

tag: div

text: Another associated symbol is the ansated cross (ankh or crux ansata) used in ancient Egypt. It was often depicted in the hands of the goddess Sekhmet, and as a hieroglyphic sign of life or of the living. Egyptian Christians (Copts) adopted it as the emblem of the cross.[3] In his book, The Worship of the Dead, Colonel J. Garnier wrote: "The cross in the form of the 'Crux Ansata' ... was carried in the hands of the Egyptian priests and Pontiff kings as the symbol of their authority as priests of the Sun god and was called 'the Sign of Life'."[4]

text: Ndj & nfr

text: Another Egyptian symbol is the Ndj (Cross-ndj (hieroglyph)) - Uses for the hieroglyph: 1— "to protect, guard, avenge", and "protector, advocate, avenger" 2— "homage to thee", (a form of salutation to gods) 3— "discuss a matter with someone", "to converse", "to take counsel". Yet another Egyptian symbol is the nfr - meaning: beauty or perfect.

text: In the Bronze Age a representation of the cross as conceived in Christian art appeared, and the form was popularised. The more precise characterization coincided with a corresponding general change in customs and beliefs. The cross then came into use in various forms on many objects: fibulas, cinctures, earthenware fragments, and on the bottom of drinking vessels. De Mortillet believed that such use of the sign was not merely ornamental, but rather a symbol of consecration, especially in the case of objects pertaining to burial. In the proto-Etruscan cemetery of Golasecca every tomb has a vase with a cross engraved on it. True crosses of more or less artistic design have been found in Tiryns, at Mycenæ, in Crete, and on a fibula from Vulci.[3]

text: According to W. E. Vine, the cross was used by worshipers of Tammuz, an Ancient Near East deity of Babylonian origin who had the cross-shaped taw (tau) as his symbol.[5]

text: Instrument of execution[edit]

text: John Pearson, Bishop of Chester (c. 1660) wrote in his commentary on the Apostles' Creed that the Greek word stauros originally signified "a straight standing Stake, Pale, or Palisador", but that, "when other transverse or prominent parts were added in a perfect Cross, it retained still the Original Name", and he declared: "The Form then of the Cross on which our Saviour suffered was not a simple, but a compounded, Figure, according to the Custom of the Romans, by whose Procurator he was condemned to die. In which there was not only a straight and erected piece of Wood fixed in the Earth, but also a transverse Beam fastned unto that towards the top thereof".[6]

text: Early Christian[edit]

text: During the first two centuries of Christianity, the cross was rare in Christian iconography, as it depicts a purposely painful and gruesome method of public execution and Christians were reluctant to use it.[1] A symbol similar to the cross, the staurogram, was used to abbreviate the Greek word for cross in very early New Testament manuscripts such as P66, P45 and P75, almost like a nomen sacrum (nomina sacra).[7] The extensive adoption of the cross as Christian iconographic symbol arose from the 4th century.[8]

text:
However, the cross symbol was already associated with Christians in the 2nd century, as is indicated in the anti-Christian arguments cited in the Octavius[9] of Minucius Felix, chapters IX and XXIX, written at the end of that century or the beginning of the next,[10] and by the fact that by the early 3rd century the cross had become so closely associated with Christ that Clement of Alexandria, who died between 211 and 216, could without fear of ambiguity use the phrase τὸ κυριακὸν σημεῖον (the Lord's sign) to mean the cross, when he repeated the idea, current as early as the apocryphal Epistle of Barnabas, that the number 318 (in Greek numerals, ΤΙΗ) in Genesis 14:14 was interpreted as a foreshadowing (a "type") of the cross (T, an upright with crossbar, standing for 300) and of Jesus (ΙΗ, the first two letters of his name ΙΗΣΟΥΣ, standing for 18).[11]
His contemporary Tertullian rejected the accusation of Christians being "adorers of the gibbet" (crucis religiosi).[12]
In his book De Corona, written in 204, Tertullian tells how it was already a tradition for Christians to trace repeatedly on their foreheads the sign of the cross.[13] The crucifix, a cross upon which an image of Christ is present, is not known to have been used until the 6th century AD.[14]

text: The oldest extant depiction of the execution of Jesus in any medium seems to be the second-century or early third-century relief on a jasper gemstone meant for use as an amulet, which is now in the British Museum in London. It portrays a naked bearded man whose arms are tied at the wrists by short strips to the transom of a T-shaped cross. An inscription in Greek on the obverse contains an invocation of the redeeming crucified Christ. On the reverse a later inscription by a different hand combines magical formulae with Christian terms.[15] The catalogue of a 2007 exhibition says: "The appearance of the Crucifixion on a gem of such an early date suggests that pictures of the subject (now lost) may have been widespread even in the late second or early third century, most likely in conventional Christian contexts".[16][17][18]

text: The Jewish Encyclopedia says:[19]

text: The cross as a Christian symbol or "seal" came into use at least as early as the second century (see "Apost. Const." iii. 17; Epistle of Barnabas, xi.-xii.; Justin, "Apologia," i. 55-60; "Dial. cum Tryph." 85-97); and the marking of a cross upon the forehead and the chest was regarded as a talisman against the powers of demons (Tertullian, "De Corona," iii.; Cyprian, "Testimonies," xi. 21–22; Lactantius, "Divinæ Institutiones," iv. 27, and elsewhere). Accordingly the Christian Fathers had to defend themselves, as early as the second century, against the charge of being worshipers of the cross, as may be learned from Tertullian, "Apologia," xii., xvii., and Minucius Felix, "Octavius," xxix. Christians used to swear by the power of the cross

text: In contemporary Christianity[edit]

text: Catholics, Orthodox Catholic, Oriental Orthodox, members of the major branches of Christianity with other adherents as Lutheranism and Anglicans, and others often make the Sign of the Cross upon themselves. This was already a common Christian practice in the time of Tertullian.[20]

text: The Feast of the Cross is an important Christian feast. One of the twelve Great Feasts in Orthodox Catholic is the Exaltation of the Cross on September 14, which commemorates the consecration of the basilica on the site where the original cross of Jesus was reportedly discovered in 326 by Helena of Constantinople, mother of Constantine the Great. The Catholic Church celebrates the feast on the same day and under the same name (In Exaltatione Sanctae Crucis), though in English it has been called the feast of the Triumph of the Cross.

text: Roman Catholic, Eastern Orthodox and Anglican bishops place a cross [+] before their name when signing a document. The dagger symbol (†) placed after the name of a dead person (often with the date of death) is sometimes taken to be a Christian cross.[21]

text: Rejection in Protestantism[edit]

text: Although Christians accepted that the cross was the gallows on which Jesus died,[22] they had already begun in the 2nd century to use it as a Christian symbol.[23] During the first three centuries of the Christian era the cross was "a symbol of minor importance" when compared to the prominence given to it later,[24] but by the second century it was  closely associated with Christians, to the point where Christians were mocked as "adorers of the gibbet" (crucis religiosi), an accusation countered by Tertullian.[12] and it was already a tradition for Christians to trace repeatedly on their foreheads the sign of the cross.[25] Martin Luther at the time of the Reformation retained the cross and crucifix in the Lutheran Church. Luther wrote: "The cross alone is our theology." He believed one knows God not through works but through suffering, the cross, and faith[need quotation to verify].[26]

text: The Protestant Reformation spurred a revival of iconoclasm, a wave of rejecting sacred images, which in some localities (such as England) included polemics against using the cross in worship. For example, during the 16th century, a minority of theologians in the Anglican and Reformed traditions Nicholas Ridley,[27] James Calfhill,[28] and Theodore Beza,[29] rejected practices that they described as cross worship. Considering it a form of idolatry, there was a dispute in 16th century England over the baptismal use of the sign of the cross and even the public use of crosses.[30] There were more active reactions to religious items that were thought as 'relics of Papacy', as happened for example in September 1641, when Sir Robert Harley, pulled down and destroyed the cross at Wigmore.[31] Writers during the 19th century indicating a pagan origin of the cross included Henry Dana Ward,[32] Mourant Brock,[33] and John Denham Parsons.[34] David Williams, writing of medieval images of monsters, says: "The disembodied phallus is also formed into a cross, which, before it became for Christianity the symbol of salvation, was a pagan symbol of fertility."[35] The study, Gods, Heroes & Kings: The Battle for Mythic Britain states: "Before the fourth century CE, the cross was not widely embraced as a sign of Christianity, symbolizing as it did the gallows of a criminal."[36]

text: Jehovah's Witnesses do not use the symbol of the cross in their worship, which they believe constitutes idolatry.[37] They believe that Jesus died on a single upright torture stake rather than a two-beam cross, arguing that the Greek term stauros indicated a single upright pole.[38] Although early Watch Tower Society publications associated with the Bible Student movement taught that Christ was executed on a cross, it no longer appeared on Watch Tower Society publications after the name Jehovah's witnesses was adopted in 1931,[39] and use of the cross was officially abandoned in 1936.[40]

text: The Church of Jesus Christ of Latter-day Saints teaches that Jesus died on a cross, however, their prophet Gordon B. Hinckley stated that "for us the cross is the symbol of the dying Christ, while our message is a declaration of the living Christ." When asked what was the symbol of his religion, Hinckley replied "the lives of our people must become the only meaningful expression of our faith and, in fact, therefore, the symbol of our worship."[41][42] Prophet Howard W. Hunter encouraged Latter-day Saints "to look to the temple of the Lord as the great symbol of your membership."[43] Images of LDS temples and the Angel Moroni (who is found in statue on most temples) are commonly used to symbolize the LDS faith.[44]

text: Notable individual crosses[edit]

text:
The Ruthwell Cross, a stone Anglo-Saxon cross located in Ruthwell, Dumfriesshire (8th century)

Easby Cross (9th century)

Muiredach's High Cross (10th century)

Victory Cross, Cathedral of San Salvador of Oviedo (10th century)

Holly Cross with which the city of Santa Cruz de Tenerife was founded in Spain (1496).

Cross of Sacrifice or War Cross, from a Commonwealth War Graves Commission cemetery (1920)

A wooden cross at Coventry Cathedral, constructed of the remnants of beams found after the Coventry Blitz

Cross in Valle de los Caídos near Madrid, the highest cross in the world (Juan de Ávalos 1959)

The Millennium Cross in Skopje, Republic of Macedonia, one of the biggest crosses in the world (2000)

The World Trade Center Cross rises from the World Trade Center wreckage.


document_title: Gulliver's Travels

question_text: where does gulliver travel to in part 1

question_tokens: where does gulliver travel to in part 1

text: Gulliver's Travels

text: Plot[edit]

text: Part I: A Voyage to Lilliput[edit]

text: The travel begins with a short preamble in which Lemuel Gulliver gives a brief outline of his life and history before his voyages.

text: During his first voyage, Gulliver is washed ashore after a shipwreck and finds himself a prisoner of a race of tiny people, less than 6 inches (15 cm) tall, who are inhabitants of the island country of Lilliput. After giving assurances of his good behaviour, he is given a residence in Lilliput and becomes a favourite of the Lilliput Royal Court. He is also given permission by the King of Lilliput to go around the city on condition that he must not harm their subjects.

text: At first, the Lilliputians are hospitable to Gulliver, but they are also wary of the threat that his size poses to them. The Lilliputians reveal themselves to be a people who put great emphasis on trivial matters. For example, which end of an egg a person cracks becomes the basis of a deep political rift within that nation. They are a people who revel in displays of authority and performances of power. Gulliver assists the Lilliputians to subdue their neighbors the Blefuscudians by stealing their fleet. However, he refuses to reduce the island nation of Blefuscu to a province of Lilliput, displeasing the King and the royal court.

text: Gulliver is charged with treason for, among other crimes, "making water" in the capital though he was putting out a fire. He is convicted and sentenced to be blinded. With the assistance of a kind friend, "a considerable person at court", he escapes to Blefuscu. Here, he spots and retrieves an abandoned boat and sails out to be rescued by a passing ship, which safely takes him back home.

text: Part II: A Voyage to Brobdingnag[edit]

text: Gulliver soon sets out again. When the sailing ship Adventure is blown off course by storms and forced to sail for land in search of fresh water, Gulliver is abandoned by his companions and is left on a peninsula on the western coast of the North American continent.

text: The grass of that land is as tall as a tree. He is then found by a farmer who was about 72 ft (22 m) tall, judging from Gulliver estimating a man's step being 10 yards (9 m). He brings Gulliver home and the farmer's daughter Glumdalclitch cares for Gulliver. The giant-sized farmer treats him as a curiosity and exhibits him for money. After a while the constant shows make Gulliver sick, and the farmer sells him to the queen of the realm. Glumdalclitch (who accompanied her father while exhibiting Gulliver) is taken into the Queen of Brobdingnag's service to take care of the tiny man. Since Gulliver is too small to use their huge chairs, beds, knives and forks, the Queen of Brobdingnag commissions a small house to be built for him so that he can be carried around in it; this is referred to as his "travelling box".

text: Between small adventures such as fighting giant wasps and being carried to the roof by a monkey, he discusses the state of Europe with the King of Brobdingnag. The King is not happy with Gulliver's accounts of Europe, especially upon learning of the use of guns and cannons. On a trip to the seaside, his traveling box is seized by a giant eagle which drops Gulliver and his box into the sea where he is picked up by some sailors who return him to England.

text: Part III: A Voyage to Laputa, Balnibarbi, Luggnagg, Glubbdubdrib and Japan[edit]

text: Setting out again, Gulliver's ship is attacked by pirates and he is marooned close to a desolate rocky island near India. He is rescued by the flying island of Laputa, a kingdom devoted to the arts of music, mathematics, and astronomy but unable to use them for practical ends. Rather than use armies, Laputa has a custom of throwing rocks down at rebellious cities on the ground.

text: Gulliver tours Balnibarbi, the kingdom ruled from Laputa, as the guest of a low-ranking courtier and sees the ruin brought about by the blind pursuit of science without practical results, in a satire on bureaucracy and on the Royal Society and its experiments. At the Grand Academy of Lagado in Balnibarbi, great resources and manpower are employed on researching completely preposterous schemes such as extracting sunbeams from cucumbers, softening marble for use in pillows, learning how to mix paint by smell, and uncovering political conspiracies by examining the excrement of suspicious persons (see muckraking). Gulliver is then taken to Maldonada, the main port of Balnibarbi, to await a trader who can take him on to Japan.

text: While waiting for a passage, Gulliver takes a short side-trip to the island of Glubbdubdrib which is southwest of Balnibarbi. On Glubbdubdrib, he visits a magician's dwelling and discusses history with the ghosts of historical figures, the most obvious restatement of the "ancients versus moderns" theme in the book. The ghosts consist of Julius Caesar, Brutus, Homer, Aristotle, René Descartes, and Pierre Gassendi.

text: On the island of Luggnagg, he encounters the struldbrugs, people who are immortal. They do not have the gift of eternal youth, but suffer the infirmities of old age and are considered legally dead at the age of eighty.

text: After reaching Japan, Gulliver asks the Emperor "to excuse my performing the ceremony imposed upon my countrymen of trampling upon the crucifix", which the Emperor does. Gulliver returns home, determined to stay there for the rest of his days.

text: Part IV: A Voyage to the Land of the Houyhnhnms[edit]

text: Despite his earlier intention of remaining at home, Gulliver returns to sea as the captain of a merchantman, as he is bored with his employment as a surgeon. On this voyage, he is forced to find new additions to his crew whom he believes to have turned the rest of the crew against him. His crew then commits mutiny. After keeping him contained for some time, they resolve to leave him on the first piece of land they come across, and continue as pirates. He is abandoned in a landing boat and comes upon a race of hideous, deformed and savage humanoid creatures to which he conceives a violent antipathy. Shortly afterwards, he meets the Houyhnhnms, a race of talking horses. They are the rulers while the deformed creatures that resemble human beings are called Yahoos.

text: Gulliver becomes a member of a horse's household and comes to both admire and emulate the Houyhnhnms and their way of life, rejecting his fellow humans as merely Yahoos endowed with some semblance of reason which they only use to exacerbate and add to the vices Nature gave them. However, an Assembly of the Houyhnhnms rules that Gulliver, a Yahoo with some semblance of reason, is a danger to their civilization and command him to swim back to the land that he came from. Gulliver's "Master," the Houyhnhnm who took him into his household, bought him time to create a canoe to make his departure easier. After another disastrous voyage, he is rescued against his will by a Portuguese ship. He is disgusted to see that Captain Pedro de Mendez, a Yahoo, is a wise, courteous, and generous person.

text: He returns to his home in England, but he is unable to reconcile himself to living among "Yahoos" and becomes a recluse, remaining in his house, largely avoiding his family and his wife, and spending several hours a day speaking with the horses in his stables.

text: Composition and history[edit]

text: It is uncertain exactly when Swift started writing Gulliver's Travels (much of the writing was done at Loughry Manor in Cookstown, County Tyrone, whilst Swift stayed there) but some sources[which?] suggest as early as 1713 when Swift, Gay, Pope, Arbuthnot and others formed the Scriblerus Club with the aim of satirising popular literary genres. According to these accounts, Swift was charged with writing the memoirs of the club's imaginary author, Martinus Scriblerus, and also with satirising the "travellers' tales" literary subgenre. It is known from Swift's correspondence that the composition proper[clarification needed] began in 1720 with the mirror-themed Parts I and II written first, Part IV next in 1723 and Part III written in 1724; but amendments were made even while Swift was writing Drapier's Letters. By August 1725 the book was complete; and as Gulliver's Travels was a transparently anti-Whig satire, it is likely that Swift had the manuscript copied so that his handwriting could not be used as evidence if a prosecution should arise, as had happened in the case of some of his Irish pamphlets (the Drapier's Letters). In March 1726 Swift travelled to London to have his work published; the manuscript was secretly delivered to the publisher Benjamin Motte, who used five printing houses to speed production and avoid piracy.[8] Motte, recognising a best-seller but fearing prosecution, cut or altered the worst offending passages (such as the descriptions of the court contests in Lilliput and the rebellion of Lindalino), added some material in defence of Queen Anne to Part II, and published it. The first edition was released in two volumes on 28 October 1726, priced at 8s. 6d.[9]

text: Motte published Gulliver's Travels anonymously, and as was often the way with fashionable works, several follow-ups (Memoirs of the Court of Lilliput), parodies (Two Lilliputian Odes, The first on the Famous Engine With Which Captain Gulliver extinguish'd the Palace Fire...) and "keys" (Gulliver Decipher'd and Lemuel Gulliver's Travels into Several Remote Regions of the World Compendiously Methodiz'd, the second by Edmund Curll who had similarly written a "key" to Swift's Tale of a Tub in 1705) were swiftly produced. These were mostly printed anonymously (or occasionally pseudonymously) and were quickly forgotten. Swift had nothing to do with them and disavowed them in Faulkner's edition of 1735. Swift's friend Alexander Pope wrote a set of five Verses on Gulliver's Travels, which Swift liked so much that he added them to the second edition of the book, though they are rarely included.

text: Faulkner's 1735 edition[edit]

text: In 1735 an Irish publisher, George Faulkner, printed a set of Swift's works, Volume III of which was Gulliver's Travels. As revealed in Faulkner's "Advertisement to the Reader", Faulkner had access to an annotated copy of Motte's work by "a friend of the author" (generally believed to be Swift's friend Charles Ford) which reproduced most of the manuscript without Motte's amendments, the original manuscript having been destroyed. It is also believed that Swift at least reviewed proofs of Faulkner's edition before printing, but this cannot be proved. Generally, this is regarded as the Editio Princeps of Gulliver's Travels with one small exception. This edition had an added piece by Swift, A letter from Capt. Gulliver to his Cousin Sympson, which complained of Motte's alterations to the original text, saying he had so much altered it that "I do hardly know mine own work" and repudiating all of Motte's changes as well as all the keys, libels, parodies, second parts and continuations that had appeared in the intervening years. This letter now forms part of many standard texts.

text: Lindalino[edit]

text: The five-paragraph episode in Part III, telling of the rebellion of the surface city of Lindalino against the flying island of Laputa, was an obvious allegory to the affair of Drapier's Letters of which Swift was proud. Lindalino represented Dublin and the impositions of Laputa represented the British imposition of William Wood's poor-quality copper currency. Faulkner had omitted this passage, either because of political sensitivities raised by an Irish publisher printing an anti-British satire, or possibly because the text he worked from did not include the passage. In 1899 the passage was included in a new edition of the Collected Works. Modern editions derive from the Faulkner edition with the inclusion of this 1899 addendum.

text: Isaac Asimov notes in The Annotated Gulliver that Lindalino is generally taken to be Dublin, being composed of double lins; hence, Dublin.[10]

text: Major themes[edit]

text: This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (October 2017) (Learn how and when to remove this template message)

text: Gulliver's Travels has been the recipient of several designations: from Menippean satire to a children's story, from proto-science fiction to a forerunner of the modern novel.

text: Published seven years after Daniel Defoe's wildly successful Robinson Crusoe, Gulliver's Travels may be read as a systematic rebuttal of Defoe's optimistic account of human capability. In The Unthinkable Swift: The Spontaneous Philosophy of a Church of England Man, Warren Montag argues that Swift was concerned to refute the notion that the individual precedes society, as Defoe's novel seems to suggest. Swift regarded such thought as a dangerous endorsement of Thomas Hobbes' radical political philosophy and for this reason Gulliver repeatedly encounters established societies rather than desolate islands. The captain who invites Gulliver to serve as a surgeon aboard his ship on the disastrous third voyage is named Robinson.

text: Scholar Allan Bloom points out that Swift's critique of science (the experiments of Laputa) is the first such questioning by a modern liberal democrat of the effects and cost on a society which embraces and celebrates policies pursuing scientific progress.[11]

text: A possible reason for the book's classic status is that it can be seen as many things to many different people. Broadly, the book has three themes:

text:
A satirical view of the state of European government, and of petty differences between religions
An inquiry into whether men are inherently corrupt or whether they become corrupted
A restatement of the older "ancients versus moderns" controversy previously addressed by Swift in The Battle of the Books

text: In storytelling and construction the parts follow a pattern:

text:
The causes of Gulliver's misadventures become more malignant as time goes on—he is first shipwrecked, then abandoned, then attacked by strangers, then attacked by his own crew.
Gulliver's attitude hardens as the book progresses—he is genuinely surprised by the viciousness and politicking of the Lilliputians but finds the behaviour of the Yahoos in the fourth part reflective of the behaviour of people.
Each part is the reverse of the preceding part—Gulliver is big/small/wise/ignorant, the countries are complex/simple/scientific/natural, and the forms of government are worse/better/worse/better than England's.
Gulliver's viewpoint between parts is mirrored by that of his antagonists in the contrasting part—Gulliver sees the tiny Lilliputians as being vicious and unscrupulous, and then the king of Brobdingnag sees Europe in exactly the same light; Gulliver sees the Laputians as unreasonable, and his Houyhnhnm master sees humanity as equally so.
No form of government is ideal—the simplistic Brobdingnagians enjoy public executions and have streets infested with beggars, the honest and upright Houyhnhnms who have no word for lying are happy to suppress the true nature of Gulliver as a Yahoo and are equally unconcerned about his reaction to being expelled.
Specific individuals may be good even where the race is bad—Gulliver finds a friend in each of his travels and, despite Gulliver's rejection and horror toward all Yahoos, is treated very well by the Portuguese captain, Don Pedro, who returns him to England at the novel's end.

text: Of equal interest is the character of Gulliver himself—he progresses from a cheery optimist at the start of the first part to the pompous misanthrope of the book's conclusion and we may well have to filter our understanding of the work if we are to believe the final misanthrope wrote the whole work. In this sense Gulliver's Travels is a very modern and complex novel. There are subtle shifts throughout the book, such as when Gulliver begins to see all humans, not just those in Houyhnhnm-land, as Yahoos. However, a feminist perspective of Gulliver's Travels argues that it is misogyny, and not misanthropy, that is shown in Gulliver.[12]

text: Throughout, Gulliver is presented as being gullible; he believes what he is told, never perceives deeper meanings, is an honest man, and expects others to be honest. This makes for fun and irony; what Gulliver says can be trusted to be accurate, and he does not always understand the meaning of what he perceives.

text: Also, although Gulliver is presented as a commonplace "everyman", lacking higher education, he possesses a remarkable natural gift for language. He quickly becomes fluent in the native tongue of any strange land in which he finds himself, a literary device that adds verisimilitude and humour to Swift's work.

text: Despite the depth and subtlety of the book, it is often classified as a children's story because of the popularity of the Lilliput section (frequently bowdlerised) as a book for children. One can still buy books entitled Gulliver's Travels which contain only parts of the Lilliput voyage.

text: Misogyny[edit]

text: A well-known underlying theme in Gulliver's Travels is misogyny. Swift uses satire to openly mock misogyny throughout the book, with one of the most cited examples of this coming from Gulliver's description of a Brobdingnagian woman:

text: "I must confess no Object ever disgusted me so much as the Sight of her monstrous Breast, which I cannot tell what to compare with, so as to give the curious Reader an Idea of its Bulk, Shape, and Colour.... This made me reflect upon the fair Skins of our English Ladies, who appear so beautiful to us, only because they are of our own Size, and their Defects not to be seen but through a magnifying glass...."

text: This open critic towards aspects of the female body is something that Swift often brings up in other works of his, particularly in poems such as The Lady's Dressing Room and A Beautiful Young Nymph Going To Bed.[13]

text: A well known criticism of Swift's misogyny by Felicity A. Nussbaum proposes the idea that “Gulliver himself is a gendered object of satire, and his antifeminist sentiments may be among those mocked.” Gulliver’s own masculinity is often mocked, seen in how he is made to be a coward among the Brobdingnag people, repressed by the people of Lilliput, and viewed as an inferior Yahoo among the Houyhnhnms.[12]

text: Another criticism of Swift's use of misogyny delves into Gulliver's repeated use of the word 'nauseous,' and the way that Gulliver is fighting his emasculation by commenting on how he thinks the women of Brobdingnag are disgusting.

text: "Swift has Gulliver frequently invoke the sensory (as opposed to reflective) word "nauseous" to describe this and other magnified images in Brobdingnag not only to reveal the neurotic depths of Gulliver's misogyny, but also to show how male nausea can be used as a pathetic countermeasure against the perceived threat of female consumption. Swift has Gulliver associate these magnified acts of female consumption with the act of "throwing-up" — the opposite of and antidote to the act of gastronomic consumption."[14]

text: This commentary of Deborah Needleman Armintor relies upon the way that the giant women do with Gulliver as they please, in much the same way as one might play with a toy, and get it to do everything one can think of. Armintor's comparison focuses on the pocket microscopes that were popular in Swift's time. She talks about how this instrument of science was transitioned to something toy-like and accessible, so it shifted into something that women favored, and thus men lose interest. This is similar to the progression of Gulliver's time in Brobdingnag, from man of science to women's plaything.

text: Comic Misanthropy[edit]

text: Misanthropy is a theme that scholars have identified in Gulliver's Travels. Arthur Case, R.S. Crane, and Edward Stone discuss Gulliver's development of misanthropy and come to the consensus that this theme ought to be viewed as comical rather than cynical.[15][16][17]

text: In terms of Gulliver's development of misanthropy, these three scholars point to the fourth voyage. According to Case, Gulliver is at first averse to identifying with the Yahoos, but, after he deems the Houyhnhnms superior, he comes to believe that humans (including his fellow Europeans) are Yahoos due to their shortcomings.  Perceiving the Houyhnhnms as perfect, Gulliver thus begins to perceive himself and the rest of humanity as imperfect.[15]  According to Crane, when Gulliver develops his misanthropic mindset, he becomes ashamed of humans and views them more in line with animals.[16] This new perception of Gulliver's, Stone claims, comes about because the Houyhnhnms' judgement pushes Gulliver to identify with the Yahoos.[17] Along similar lines, Crane holds that Gulliver's misanthropy is developed in part when he talks to the Houyhnhnms about mankind because the discussions lead him to reflect on his previously held notion of humanity.  Specifically, Gulliver’s master, who is a Houyhnhnm, provides questions and commentary that contribute to Gulliver’s reflectiveness and subsequent development of misanthropy.[16] However, Case points out that Gulliver's dwindling opinion of humans may be blown out of proportion due to the fact that he is no longer able to see the good qualities that humans are capable of possessing.  Gulliver’s new view of humanity, then, creates his repulsive attitude towards his fellow humans after leaving Houyhnhnmland.[15] But in Stone's view, Gulliver’s actions and attitude upon his return can be interpreted as misanthropy that is exaggerated for comic effect rather than for a cynical effect.  Stone further suggests that Gulliver goes mentally mad and believes that this is what leads Gulliver to exaggerate the shortcomings of humankind.[17] Over time, though, Gulliver is able to get used to humanity again.[15]

text: Another aspect that Crane attributes to Gulliver’s development of misanthropy is that when in Houyhnhnmland, it is the animal-like beings (the Houyhnhnms) who exhibit reason and the human-like beings (the Yahoos) who seem devoid of reason; Crane argues that it is this switch from Gulliver’s perceived norm that leads the way for him to question his view of humanity.  As a result, Gulliver begins to identify humans as a type of Yahoo.  To this point, Crane brings up the fact that a traditional definition of man – Homo est animal rationale (Humans are rational animals) – was prominent in academia around Swift’s time.  Furthermore, Crane argues that Swift had to study this type of logic (see Porphyrian Tree) in college, so it is highly likely that he intentionally inverted this logic by placing the typically given example of irrational beings – horses – in the place of humans and vice versa.[16]

text: Stone points out that Gulliver's Travels takes a cue from the genre of the travel book, which was popular during Swift's time period. From reading travel books, Swift’s contemporaries were accustomed to beast-like figures of foreign places; thus, Stone holds that the creation of the Yahoos was not out of the ordinary for the time period. From this playing off of familiar genre expectations, Stone deduces that the parallels that Swift draws between the Yahoos and humans is meant to be humorous rather than cynical.  Even though Gulliver sees Yahoos and humans as if they are one and the same, Stone argues that Swift did not intend for readers to take on Gulliver’s view; Stone states that the Yahoos’ behaviors and characteristics that set them apart from humans further supports the notion that Gulliver's identification with Yahoos is not meant to be taken to heart. Thus, Stone sees Gulliver’s perceived superiority of the Houyhnhnms and subsequent misanthropy as features that Swift used to employ the satirical and humorous elements characteristic of the Beast Fables of travel books that were popular with his contemporaries; as Swift did, these Beast Fables placed animals above humans in terms of morals and reason, but they were not meant to be taken literally.[17]

text: Character analysis[edit]

text: Pedro de Mendez is the name of the Portuguese captain who rescues Gulliver in Book IV. When Gulliver is forced to leave the Island of the Houyhnhnms, his plan is "to discover some small Island uninhabited" where he can live in solitude. Instead, he is picked up by Don Pedro's crew. Despite Gulliver's appearance—he is dressed in skins and speaks like a horse—Don Pedro treats him compassionately and returns him to Lisbon.

text: Though Don Pedro appears only briefly, he has become an important figure in the debate between so-called soft school and hard school readers of Gulliver's Travels. Some critics contend that Gulliver is a target of Swift's satire and that Don Pedro represents an ideal of human kindness and generosity. Gulliver believes humans are similar to Yahoos in the sense that they make "no other use of reason, than to improve and multiply...vices" [18] Captain Pedro provides a contrast to Gulliver's reasoning, proving humans are able to reason, be kind, and most of all: civilized. Gulliver sees the bleak fallenness at the center of human nature, and Don Pedro is merely a minor character who, in Gulliver's words, is "an Animal which had some little Portion of Reason."[19]

text: Cultural influences[edit]

text: From 1738 to 1746, Edward Cave published in occasional issues of The Gentleman's Magazine semi-fictionalized accounts of contemporary debates in the two Houses of Parliament under the title of Debates in the Senate of Lilliput. The names of the speakers in the debates, other individuals mentioned, politicians and monarchs present and past, and most other countries and cities of Europe ("Degulia") and America ("Columbia") were thinly disguised under a variety of Swiftian pseudonyms. The disguised names, and the pretence that the accounts were really translations of speeches by Lilliputian politicians, were a reaction to an Act of Parliament forbidding the publication of accounts of its debates. Cave employed several writers on this series: William Guthrie (June 1738 – November 1740), Samuel Johnson (November 1740 – February 1743), and John Hawkesworth (February 1743 – December 1746).

text: The astronomers of Laputa have discovered "two lesser stars, or satellites, which revolve about Mars".[20] This may have influenced Voltaire, whose 1750 story Micromégas also refers to two moons of Mars. In 1877, Asaph Hall discovered the two real moons of Mars, Deimos and Phobos; in 1973 craters on Deimos were named Swift and Voltaire,[21] and from 2006 numerous features on Phobos were named after elements from Gulliver's Travels, including Laputa Regio, Lagado Planitia, and several craters.[22]

text: The term Lilliputian has entered many languages as an adjective meaning "small and delicate". There is even a brand of small cigar called Lilliput. There is a series of collectable model houses known as "Lilliput Lane". The smallest light bulb fitting (5mm diameter) in the Edison screw series is called the "Lilliput Edison screw". In Dutch and Czech, the words Lilliputter and liliput(á)n respectively are used for adults shorter than 1.30 meters. Conversely, Brobdingnagian appears in the Oxford English Dictionary as a synonym for very large or gigantic.

text: In like vein, the term yahoo is often encountered as a synonym for ruffian or thug. In the Oxford English Dictionary it is considered a definition for "a rude, noisy, or violent person" and its origins attributed to Swift's Gulliver's Travels.[23]

text: In the discipline of computer architecture, the terms big-endian and little-endian are used to describe two possible ways of laying out bytes in memory. The terms derive from one of the satirical conflicts in the book, in which two religious sects of Lilliputians are divided between those who crack open their soft-boiled eggs from the little end, and those who use the big end, the "Big-endians".

text: Dostoevsky references Gulliver's Travels in his novel Demons (1872): 'In an English satire of the last century, Gulliver, returning from the land of the Lilliputians where the people were only three or four inches high, had grown so accustomed to consider himself a giant among them, that as he walked along the Streets of London he could not help crying out to carriages and passers-by to be careful and get out of his way for fear he should crush them, imagining that they were little and he was still a giant....'

text: Reception[edit]

text: The book was very popular upon release and was commonly discussed within social circles.[24] Public reception widely varied, with the book receiving an initially enthusiastic reaction with readers praising its satire, and some reporting that the satire's cleverness sounded like a realistic account of a man's travels.[25] James Beattie commended Swift’s work for its “truth” regarding the narration and claims that “the statesman, the philosopher, and the critick, will admire his keenness of satire, energy of description, and vivacity of language,” noting that even children can enjoy the novel.[26] As popularity increased, critics came to appreciate the deeper aspects of Gulliver’s Travels. It became known for its insightful take on morality, expanding its reputation beyond just humorous satire.[25]

text: Despite its initial positive reception, the book faced backlash. One of the first critics of the book, referred to as Lord Bolingbroke, criticized Swift for his overt use of misanthropy.[25] Other negative responses to the novel also looked towards its portrayal of humanity, which was considered inaccurate. Swifts’s peers rejected the novel on claims that its themes of misanthropy were harmful and offensive. They criticized its satire for exceeding what was deemed acceptable and appropriate, including the Houyhnhnms and Yahoos’s similarities to humans.[26] There was also controversy surrounding the political allegories. Readers enjoyed the political references, finding them humorous. However, members of the Whig party were offended, believing that Swift mocked their politics.[25]

text: British journalist William Makepeace Thackeray described Swift’s novel as “blasphemous,” citing its critical view of mankind as ludicrous and overly harsh. He concludes his critique by remarking that he cannot understand the origins of Swift’s critiques on humanity.[26]

text: In other works[edit]

text: Sequels and imitations[edit]

text:
Many sequels followed the initial publishing of the Travels. The earliest of these was the anonymously authored Memoirs of the Court of Lilliput,[27] published 1727, which expands the account of Gulliver's stays in Lilliput and Blefuscu by adding several gossipy anecdotes about scandalous episodes at the Lilliputian court.
Abbé Pierre Desfontaines, the first French translator of Swift's story, wrote a sequel, Le Nouveau Gulliver ou Voyages de Jean Gulliver, fils du capitaine Lemuel Gulliver (The New Gulliver, or the travels of John Gulliver, son of Captain Lemuel Gulliver), published in 1730.[28] Gulliver's son has various fantastic, satirical adventures.
Donald Grant Mitchell retold part one of the novel in the form of a short story for children, published in St. Nicholas magazine in 1874.[29]
Hungarian author Frigyes Karinthy wrote two science fiction novellas that continue the adventures of Gulliver: Voyage to Faremido (1916) is an early examination of artificial intelligence, with a pacifist theme,[30] while Capillaria (1921) is a satire on the 'battle of the sexes'.[30]
Soviet science fiction writer Vladimir Savchenko published Gulliver's Fifth Travel—The Travel of Lemuel Gulliver, First a Surgeon, and Then a Captain of Several Ships to the Land of Tikitaks (Russian: Пятое путешествие Гулливера – Путешествие Лемюэля Гулливера, сначала хирурга, а потом капитана нескольких кораблей, в страну тикитаков), a sequel to the original series in which Gulliver's role as a surgeon is more apparent. Tikitaks are people who inject the juice of a unique fruit to make their skin transparent, as they consider people with regular opaque skin secretive and ugly.
Gulliver's Travels Beyond the Moon (ガリバーの宇宙旅行, Garibā no Uchū Ryokō, Gulliver's Space Travels) is a 1965 Japanese animated film, portraying an elder Gulliver taking part in a space travel, joined by a boy, a crow, a talking toy soldier and a dog. The film, although being a children's production generally fascinated by the idea of space travelling, portrays an alien world where robots have taken power. Thus it continues in Swift's vein of critical approach on themes in current society.
Hanna-Barbera produced two adaptations of Gulliver's Travels, one was an animated TV series called The Adventures of Gulliver from 1968 to 1969 and another was a 1979 animated television special titled Gulliver's Travels.
American physician John Paul Brady published in 1987 A Voyage to Inishneefa: A First-hand Account of the Fifth Voyage of Lemuel Gulliver (Santa Barbara: John Daniel), a parody of Irish history in Swift's manner.
In 1998 the Argentine writer Edgar Brau published El último Viaje del capitán Lemuel Gulliver (The Last Voyage of Captain Lemuel Gulliver), a novel in which Swift's character goes on an imaginary fifth journey, this time into the River Plate. It satirises ways and customs of present-day society, including sports, television, politics, etc. To justify the parody, the narrative is set immediately after the last voyage written by Swift (precisely, 1722), and the literary style of the original work is kept throughout the whole story.

text: Adaptations[edit]

text: Music[edit]

text:
In 1728 the Baroque composer Georg Philipp Telemann composed a 5-movement suite for two violins based on Swift's book. Telemann's piece is commonly known as Gulliver's Travels, and depicts the Lilliputians and the Brobdingnagians particularly vividly through rhythms and tempos. The piece is part of Telemann's Der getreue Musik-meister (The Steadfast Music Teacher).
The ambient band Soufferance based and themed their 2010 concept album on the book. Titled "Travels into Several Remote Nations of the Mind", the album featured a single, 65 minute song, bearing the title "The Thoughts and Memoirs of Mike Lachaire, First a Strange Individual, and then a Philosopher", referencing the full title of the original book.[31]

text: "Polygondwanaland" 13th studio album by King Gizzard and the Lizard Wizard draws many connections among thematic interpretations thought the book and album.

text: Film, television and radio[edit]

text: Gulliver's Travels has been adapted several times for film, television and radio. Most film versions avoid the satire completely.

text:
Guliver's Travels Among the Lilliputians and the Giants (1902): A French silent film by Georges Méliès, a pioneer of early film. Gulliver is played by Méliès himself in this version.
Gulliver Mickey (1934): is a black and white Mickey Mouse short, produced by Walt Disney and released by United Artists in 1934.
The New Gulliver (1935): this Soviet retelling of the travel to Lilliput was lauded for the ground-breaking animation work by director Aleksandr Ptushko.
Gulliver's Travels (1939): Max Fleischer's animated feature-length classic of Gulliver's adventures in Lilliput. This was the first full-length animated cartoon after Walt Disney's Snow White and the Seven Dwarfs. The film was spun off into two cartoon short series: the Gabby cartoons about a Lilliputian sidekick of the film, and the Animated Antics cartoons starring Sneak, Snoop and Snitch (the three villains) and Twinkletoes (the carrier pigeon).
The Three Worlds of Gulliver (1960): a loose adaptation starring Kerwin Mathews and featuring stop motion effects by Ray Harryhausen.
Case for a Rookie Hangman (1970): A satirical movie by the Czech Pavel Juráček, based upon the third book, depicting indirectly the Communist Czechoslovakia, shelved soon after its release.[32]
Gulliver a törpék országában (1974): Directed by András Rajnai for Hungarian Television (MTV), this show deals with the trip to Lilliput.[33]
Gulliver's Travels (1977): Part live-action and part-animated. Stars Richard Harris.
Gulliver's Travels (1979): An animated TV movie adaptation of the first two parts made in Australia. It was produced by Southern Star Group for Famous Classic Tales, with the voice cast being Julie Bennett, Regis Cordic, Ross Martin, Don Messick, Hal Smith, John Stephenson, and Janet Waldo.[34]
Gulliver az óriások országában (1980): The second adaptation by András Rajnai for Hungarian Television (MTV), this hour-long show is an adaptation of Gulliver's voyage to Brobdingnag.[35]
Gulliver in Lilliput (1981): BBC Classics Television. Stars Andrew Burt and Elisabeth Sladen.[36]
Gulliver's Travels: It was produced by Saban Entertainment. It was aired from September 8, 1992 to June 29, 1993. It is an adaptation of the Gulliver's Travels novel by Jonathan Swift, and spanned a total of 26 episodes.
Gulliver's Travels (1996): Live-action, 2 part, TV miniseries with special effects starring Ted Danson and Mary Steenburgen, also featuring a variety of film stars in cameo roles.[37] This version includes all four voyages.
Crayola Kids Adventures: Tales of Gulliver's Travels (1997): Live-action direct-to-video film starring children with Adam Wylie as Gulliver.[38]
Jajantaram Mamantaram (2003): Live-action Indian children's film, starring Javed Jaffrey.[39]
Gulliver's Travels (2010): Modernized, live-action version of Gulliver's adventures in Lilliput, starring Jack Black, also featuring Billy Connolly, James Corden, Amanda Peet, Chris O'Dowd, Catherine Tate, Jason Segel, Emily Blunt and Olly Alexander.[40]
Gulliver's Travels was produced by Golden Films. This is an animated short version of the story. It is part of a larger series known as "Enchanted Tales."

text: Bibliography[edit]

text: Editions[edit]

text: The standard edition of Swift's prose works as of 2005[update] is the Prose Writings in 16 volumes, edited by Herbert Davis et al.[41]

text:
Swift, Jonathan Gulliver's Travels (Harmondsworth: Penguin, 2008) ISBN 9780141439495. Edited with an introduction and notes by Robert DeMaria Jr. The copytext is based on the 1726 edition with emendations and additions from later texts and manuscripts.
Swift, Jonathan Gulliver's Travels (Oxford: Oxford University Press, 2005) ISBN 9780192805348. Edited with an introduction by Claude Rawson and notes by Ian Higgins. Essentially based on the same text as the Essential Writings listed below with expanded notes and an introduction, although it lacks the selection of criticism.
Swift, Jonathan The Essential Writings of Jonathan Swift (New York: W. W. Norton, 2009) ISBN 9780393930658. Edited with an introduction by Claude Rawson and notes by Ian Higgins. This title contains the major works of Swift in full, including Gulliver's Travels, A Modest Proposal, A Tale of a Tub, Directions to Servants and many other poetic and prose works. Also included is a selection of contextual material, and criticism from Orwell to Rawson. The text of GT is taken from Faulkner's 1735 edition.
Swift, Jonathan Gulliver's Travels (New York: W. W. Norton, 2001) ISBN 0393957241. Edited by Albert J. Rivero. Based on the 1726 text, with some adopted emendations from later corrections and editions. Also includes a selection of contextual material, letters, and criticism.