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Will President Dutarte have to resign? Mathematician Euler offered an equation taken as proof of God

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Leonhard Euler.jpg
Leonhard Euler, 1753/Jakob Emanuel Handmann

Recently, Philippines president Rodrigo Dutarte threatened to resign if anyone could prove that God exists. It turns out that the great mathematician Leonhard Euler (1707–1783) offered a proof of the existence of God.

Today, Euler is considered one of the greatest mathematicians of all time. His interests covered almost all aspects of mathematics, from geometry to calculus to trigonometry to algebra to number theory, as well as optics, astronomy, cartography, mechanics, weights and measures and even the theory of music.

Much of the notation used by mathematicians today – including e, i, f(x), ∑, and the use of a, b and c as constants and x, y and z as unknowns – was either created, popularized or standardized by Euler. His efforts to standardize these and other symbols (including π and the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems. More.

Here’s Identity, often taken as a proof of God:

Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as “the most beautiful equation.” It is a special case of a foundational equation in complex arithmetic called Euler’s Formula, which the late great physicist Richard Feynman called in his lectures “our jewel” and “the most remarkable formula in mathematics.”

In an interview with the BBC, Prof David Percy of the Institute of Mathematics and its Applications said Euler’s Identity was “a real classic and you can do no better than that … It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants.”

Some of Euler’s other thoughts about God, offered by a friend, cited by Adam Drozdek, “Leonhard Euler as an Apologist,” Theologische Zeitschrift 66 (2010) pp. 62-82:

He wrote in his Examen d’une controverse sur la loi de refraction des rayons, 1753, that

if other arguments for the existence of God make no impression on the spirit of Atheists, just the consideration of the structure of the eye should convince them about the existence of the supremely wise and powerful Being, in comparison with which the highest wisdom of man is reduced to nothing.

He talks about the human eye in his Letters:

Vision «is without a doubt the most wonderful thing which the human spirit could fathom.» The little that we know about the operation of the eye «is more than sufficient to convince us of the Omnipotence and infinite wisdom of the Creator; and its wonders
should enrapture our spirit to more pure adoration of the supreme being. We discover in the structure of eyes perfections which the most intelligentspirit could never thoroughly examine and the most skilful artist could never construct a machine of such a kind» (Letters 41). Although Euler raised the issue of God’s wisdom, indirectly he also addressed the problem of the existence of God: the eye is a witness of a supremely wise creator who only can be God. Euler was convinced that God «has surely followed in his works the simplest route» and thus the eye cannot be reproduced by a simpler device(Letters 43). Today, the intelligent design proponents use the concept of an irreducible complexity which, as it can be seen, would be endorsed by Euler:

“the eye is complex but it cannot be made any simpler since removing but one element from its construction would render the eye unworkable. Therefore, all the elements of the eye must have been put together at the same time to enable the proper execution of its function.” This is the proof of the existence of God from design, which is the first proof used in European philosophy, namely by Socrates, and was a proof frequently used in the age of Euler, frequently under the name of physicotheology.

And the more we know about the eye, the more complex it is.

But President Duarte may have other stuff to read…

President Rodrigo Roa Duterte 2017.jpg
See also: Philippines president claims he’ll resign if anyone can prove God exists. But leaves himself a fine-tuning loophole.

Comments
polistra – //This is silly. Math is a complex system of thought invented by humans.// That was silly. The relationships always existed, we just symbolized and articulated them so that we could understand them.Celad
July 16, 2018
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To illustrate with a simple example, I would conjecture that it is/was impossible for God to create a world in which one cannot prove that the square root of 2 is irrational.
Can you imagine a world that has a different kind of mathematics? Or is our symbolic understanding the only one possible, as you see it?Silver Asiatic
July 16, 2018
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jerry,
Would God create a world where one could prove He exists?
Interesting question. This immediately raises the following question:
Does/did God have any choice in the matter?
To illustrate with a simple example, I would conjecture that it is/was impossible for God to create a world in which one cannot prove that the square root of 2 is irrational.daveS
July 16, 2018
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I think a better question would be
Would God create a world where one could prove He exists?
The implications of a definitive proof for God is that our behavior would change dramatically if our certainty that God existed was the same as the sun will rise in the morning. Would there be free will? Would there be faith? Would there be virtue? All our behaviors would be constricted to a very narrow range of what would be PC behaviors. But PC in terms of what we thought God wanted. We would be anything but human. We would be automatons. It would thwart His reason for creating us.jerry
July 16, 2018
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Of related note, some atheists believe that mathematics and/or logic, all by itself, can make God dispensable. Yet, Godel, with his incompleteness theorems, proved that "we cannot construct an ontology that makes God dispensable".
THE GOD OF THE MATHEMATICIANS - DAVID P. GOLDMAN - August 2010 Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel's critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes. http://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians Taking God Out of the Equation - Biblical Worldview - by Ron Tagliapietra - January 1, 2012 Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties. 1. Validity ... all conclusions are reached by valid reasoning. 2. Consistency ... no conclusions contradict any other conclusions. 3. Completeness ... all statements made in the system are either true or false. The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem. Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation. Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3). http://www.answersingenesis.org/articles/am/v7/n1/equation#
As Bruce Gordon stated, The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
The atheist simply has no explanation for why the universe should be describable by mathematics. Of supplemental note: The resurrection of Jesus Christ from death provides a very credible reconciliation between General Relativity and Quantum Mechanics into the much sought after "Theory of Everything"
Gödel, Infinity, and Jesus Christ as the Theory of Everything - video https://youtu.be/x1Jw5Y686jY Quantum Mechanics, Special Relativity, General Relativity and Christianity - video https://www.youtube.com/watch?v=gKggH8jO0pk
Verse:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
bornagain77
July 14, 2018
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As to this quote I cited in post 8:
"The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,,"
Finding 'unexpected order' where it shouldn't be found is a recurring theme.,, For instance, the inverse square law,,,
"Newton proposed that Gravitational force is inversely proportional to the Square of the distance between two masses (Inverse Square Law). For an orderly, designed universe, this makes sense – why wouldn’t it be something nice and even, like the square of the distance? For someone who believes in a random universe though – why the Square? Why not r ^ 2.148273.. or r ^ 1.932157.. The universe is full of nice, neat relationships like this, at very fundamental levels – moreso than not. I find the ability of the atheist to accept so many coincidences nothing short of astonishing." drc466 - UD blogger Inverse Square Law http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html Designer gravity - Don DeYoung The force F between two masses m1 and m2, when separated by a distance r, can be written as F = (G m1 m2)/r2 Where G is the gravitational constant, first measured by Henry Cavendish in 1798.(1) This equation shows that gravity decreases as the separation distance, r, between two objects becomes large but never quite reaches zero. The inverse-square nature of this equation is intriguing. After all, there is no essential reason why gravity should behave in this way. In a chance, evolving universe, some random exponent like r1.97 or r2.3 would seem much more likely. However, precise measurements have shown an exact exponent out to at least 5 decimal places, 2.00000. As one researcher put it, this result seems ‘just a little too neat.’2 http://creation.com/gravity-the-mystery-force
In regards to mathematics describing the physical universe, the atheist simply has no explanation for why such 'unexpected order' should be found. Einstein himself stated that, "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles."
On the Rational Order of the World: a Letter to Maurice Solovine - Albert Einstein - March 30, 1952 Excerpt: "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles." -Albert Einstein http://inters.org/Einstein-Letter-Solovine
It is also very interesting to note that the very belief that there is some type of unity, an overriding connection, of the laws of physics, i.e. a theory of everything, is itself a belief that arises from the presupposition of Design in the universe. i.e. A Theistic presupposition.
“So you think of physics in search of a “Grand Unified Theory of Everything”, Why should we even think there is such a thing? Why should we think there is some ultimate level of resolution? Right? It is part, it is a consequence of believing in some kind of design. Right? And there is some sense in which that however multifarious and diverse the phenomena of nature are, they are ultimately unified by the minimal set of laws and principles possible. In so far as science continues to operate with that assumption, there is a presupposition of design that is motivating the scientific process. Because it would be perfectly easy,, to stop the pursuit of science at much lower levels. You know understand a certain range of phenomena in a way that is appropriate to deal with that phenomena and just stop there and not go any deeper or any farther.”,,, You see, there is a sense in which there is design at the ultimate level, the ultimate teleology you might say, which provides the ultimate closure,,” Professor of philosophy Steve Fuller discusses intelligent design in Cambridge - Video - quoted at the 17:34 minute mark https://uncommondescent.com/news/in-cambridge-professor-steve-fuller-discusses-why-the-hypothesis-of-intelligent-design-is-not-more-popular-among-scientists-and-others/
As David Klinghoffer noted, Why in the world would a scientist blithely assume that there is or is even likely to be one unifying rational form to all things, unless he assumed that there is a singular, overarching intelligence that has placed it there? Why shouldn't the world be chaotic, utterly random, meaningless? Why should one presume that something as orderly and rational as an equation would describe the universe's structure?
Stephen Hawking's "God-Haunted" Quest - David Klinghoffer - December 24, 2014 Excerpt: Why in the world would a scientist blithely assume that there is or is even likely to be one unifying rational form to all things, unless he assumed that there is a singular, overarching intelligence that has placed it there? Why shouldn't the world be chaotic, utterly random, meaningless? Why should one presume that something as orderly and rational as an equation would describe the universe's structure? I would argue that the only finally reasonable ground for that assumption is the belief in an intelligent Creator, who has already thought into the world the very mathematics that the patient scientist discovers. http://www.evolutionnews.org/2014/12/stephen_hawking092351.html
Moreover, when throwing the reductive materialism that undegirds Darwinian evolution into the mix, the insurmountable problem of mathematics describing the physical universe becomes all the more intractable for the atheist. Darwinian evolution is based on a materialistic view of reality which denies that anything beyond nature exists. On the other hand, Mathematics exists in a transcendent, beyond space and time, realm which is not reducible any possible material explanation. This transcendent mathematical realm has been referred to as a Platonic mathematical world.
Platonic mathematical world - image https://image.slidesharecdn.com/quantuminformation2-120301000431-phpapp01/95/quantum-information-14-728.jpg?cb=1330561190 Naturalism and Self-Refutation – Michael Egnor – January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”? It seems a stretch. What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,, https://evolutionnews.org/2018/01/naturalism-and-self-refutation/
Simply put, Mathematics itself, contrary to the materialistic presuppositions of Darwinists, does not need the physical world in order to exist. And yet Darwinists, although they deny that anything beyond nature exists, need this transcendent world of mathematics in order for their theory to be considered scientific in the first place. The predicament that Darwinists find themselves in regards to denying the reality of this transcendent, immaterial, world of mathematics, and yet needing validation from this transcendent, immaterial, world of mathematics in order to be considered scientific, should be the very definition of self-refuting.
For many years I have thought that it is a mathematical scandal that we do not have a proof that Darwinian evolution works. (Chaitin 2012, 53).
bornagain77
July 14, 2018
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Nonlin.org, I don't think he invented the identity; if there are aliens that can do math, then I suspect it's likely they know of this identity (or one equivalent to it). It has some existence independent of our minds. How do you think Euler determined this identity to be true? I know it's true because if you calculate the left hand side, using the usual definitions, you get 0.daveS
July 14, 2018
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daveS@7, Euler observed this equation to be true. Did you think he "invented" it? https://en.wikipedia.org/wiki/Euler%27s_identityNonlin.org
July 14, 2018
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Benjamin Peirce, a noted American 19th-century philosopher, mathematician, and professor at Harvard University, after proving Euler’s identity during a lecture, stated that the identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”.[8] Per Wikipedia
Here are some very well done videos showing the stringent 'mathematical proofs' for Euler's Identity:
Euler's Formula and Euler's Identity: Rationale for Euler's Formula and Euler's Identity - video http://www.youtube.com/watch?v=mgNtPOgFje0 Euler's identity - video http://www.youtube.com/watch?v=zApx1UlkpNs
Of related note:
One of the most frequently mentioned equations was Euler's equation, e^pi*i+1 = 0, Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" The equation contains nine basic concepts of mathematics — once and only once — in a single expression. These are: e (the base of natural logarithms); the exponent operation; ?; plus (or minus, depending on how you write it); multiplication; imaginary numbers; equals; one; and zero. - Robert P. Crease, in "The greatest equations ever" at PhysicsWeb (October 2004) Euler's identity - Mathematical beauty Excerpt: Euler’s identity is often cited as an example of deep mathematical beauty.[3] Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:[4] The number 0, the additive identity. The number 1, the multiplicative identity. The number pi, which is ubiquitous in the geometry of Euclidean space and analytical mathematics (pi = 3.14159265…) The number e, the base of natural logarithms, which occurs widely in mathematical analysis (e = 2.718281828…). The number i, the imaginary unit of the complex numbers, a field of numbers that contains the roots of all polynomials (that are not constants), and whose study leads to deeper insights into many areas of algebra and calculus. (Both pi and e are transcendental numbers.) Furthermore, the equation is given in the form of an expression set equal to zero, which is common practice in several areas of mathematics. Stanford University mathematics professor Keith Devlin has said, “like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence”.[5] And Paul Nahin, a professor emeritus at the University of New Hampshire, who has written a book dedicated to Euler’s formula and its applications in Fourier analysis, describes Euler’s identity as being “of exquisite beauty”.[6] The mathematics writer Constance Reid has opined that Euler’s identity is “the most famous formula in all mathematics”.[7] And Benjamin Peirce, a noted American 19th-century philosopher, mathematician, and professor at Harvard University, after proving Euler’s identity during a lecture, stated that the identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”.[8] A poll of readers conducted by The Mathematical Intelligencer in 1990 named Euler’s identity as the “most beautiful theorem in mathematics”.[9] In another poll of readers that was conducted by Physics World in 2004, Euler’s identity tied with Maxwell’s equations (of electromagnetism) as the “greatest equation ever”.[10] http://en.wikipedia.org/wiki/Euler%27s_identity#Mathematical_beauty God by the Numbers - Connecting the constants Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.",,, The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,, Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3
Alexander Vilenkin comments on the beauty of mathematics being ideally suited for describing our physical universe (particularly e^ipi+1=0)
Quote: "It appears that the Creator shares the mathematicians' sense of beauty." - Alexander Vilenkin http://rfforum.websitetoolbox.com/post?id=3754268
Leonhard Euler, the son of a Christian pastor, and a fervent Christian all his life,,,, the brilliant mathematician Leonhard Euler stated this about atheism:
A DEFENSE OF THE (Divine) REVELATION AGAINST THE OBJECTIONS OF FREETHINKERS, BY MR. EULER Excerpt: "The freethinkers (atheists) have yet to produce any objections that have not long been refuted most thoroughly. But since they are not motivated by the love of truth, and since they have an entirely different point of view, we should not be surprised that the best refutations count for nothing and that the weakest and most ridiculous reasoning, which has so often been shown to be baseless, is continuously repeated. If these people maintained the slightest rigor, the slightest taste for the truth, it would be quite easy to steer them away from their errors; but their tendency towards stubbornness makes this completely impossible." http://www.math.dartmouth.edu/~euler/docs/translations/E092trans.pdf
bornagain77
July 14, 2018
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Nonlin.org, How do you know that Euler's identity actually is true?daveS
July 14, 2018
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daveS, polistra, No, Euler’s Identity is NOT "true by definition", and math was NOT "invented by humans". "Mathematics is the language in which God has written the universe" Galileo Galilei Italian astronomer & physicist (1564 - 1642)Nonlin.org
July 14, 2018
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Mathematics is to explain God's wisdom in human wisdom. He studied mathematics with this idea. He thought his wisdom was nothing compared to the design of the eye. The Bible says that God created this world with wisdom. That wisdom is called creativity in today's term. Euler alone achieved more than 30% of 18th-century mathematics. There are no mathematicians who surpass him in human history. His reasoning ability is about 10 times more than the reasoning ability of a well-behaved scientist. What Euler points out is that when he sees the structure and function of the eye, no one can make it, except the Creator, the Almighty. Moreover, he can not even imagine that the eye was accidentally created by itself. He saw this as a definite proof that there is an Almighty. He thought that humans who do not believe in this proof are stupid. Is there anyone who believes that the eye has been built on an evolutionary basis for an extended period of time? Some of us have blamed the design of the eye with our insignificant creativity.KD Jung
July 14, 2018
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Some see God in this equation as in everything around us, while others - unfortunately - see nothing. Just telling them "you should see" doesn't quite do the trick.Nonlin.org
July 14, 2018
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“the eye is complex but it cannot be made any simpler since removing but one element from its construction would render the eye unworkable. Therefore, all the elements of the eye must have been put together at the same time to enable the proper execution of its function.” This is the proof of the existence of God from design, which is the first proof used in European philosophy, namely by Socrates, and was a proof frequently used in the age of Euler, frequently under the name of physicotheology.
Was Euler the first to give us the notion of "irreducible complexity"?PaV
July 14, 2018
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This is silly. Math is a complex system of thought invented by humans. The fact that we CAN invent such systems leads to considerations of design, but nothing INSIDE such systems proves anything about any part of the universe except our minds.polistra
July 14, 2018
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My answer: I would first want to see a formal argument that Euler's Identity implies the existence of God written out explicitly (as opposed to an array of statements marveling over the beauty of the equation). Moreover, that argument should be clearly valid at a minimum. I don't expect such to appear, however. The basic problem is that Euler's Identity is simply true by definition. How does one bootstrap such a truth into a proof that God exists?daveS
July 14, 2018
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