#Reuben Hersh

[noosphe-re]

One of the great philosophers of mathematics Gottlob Frege made quite an issue of the fact that mathematicians didn't know the meaning of One. What is One? Nobody could answer coherently. Of course Frege answered, but his answer was no better, or even worse, than the previous ones. And so it has continued to this very day, strange and incredible as it is. We know all about so much mathematics, but we don't know what it really is.

Reuben Hersh, What Kind of Thing Is a Number?, A Talk with Reuben Hersh [2.10.97], Edge

[yellowjavkets]

It took a very long time but I've finally completed my favorites shelf!

Pictured here :

ALL TIME TOP SIX

Jurassic Park by Michael Crichton

We Have Always Lived in the Castle by Shirley Jackson

Everything on a Waffle by Polly Horvath

The Last Unicorn by Peter S Beagle

Frankenstein by Mary Shelly

All five books in The Underland Chronicles by Suzanne Collins

OTHERS:

Crying in H Mart by Michelle Zauner

Nature's Numbers by Ian Stewart

Wishful Drinking by Carrie Fisher

Loving and Hating Mathematics by Reuben Hersh and Vera John-Steiner

Nightmare Fuel: The science of horror films by Nina Nesseth

Hyperbole and a Half and Solutions and Other Problems, both by Allie Brosh

The Encyclopedia of the Wonderful and Weird by Milo Rossi

Savvy by Ingrid Law

Jane Eyre by Charlotte Bronte

Little Women by Louisa May Alcott

Pride and Prejudice by Jane Austen

Dracula by Bram Stoker

The Scottish Play by William Shakespeare

The Coldest Girl in Coldtown by Holly Black

[math1089]

Exploring Mathematical Beauties of the Number 108

In mathematical philosophy, formalism is the position that regards mathematics as the study of formal deductive systems. Mathematical truth is simply provability in the system, and there is and can be no ultimate meaning to mathematics other than the operation of naked symbols according to fixed rules.Philip J. Davis & Reuben Hersh Welcome to the blog Math1089 – Mathematics for All. Numbers are…

[whatilistenedtoatwork]

From September 4th to September 8th, 2023

04-09-23

HEAVENLY “Dust To Dust”; WILLIE NELSON “Willie Nelson Sings Kristofferson”; KREATOR “Pleasure To Kill”; TELEVISION PERSONALITIES “…And Don’t The Kids Just Love It”; SKYCLAD “Vintage Whine”; G.I.S.M. “Military Affairs Neurotic”; FRANKIE COSMOS “Vessels”; KRISTIN HERSH “Strange Angels”; THE HANDSOME FAMILY “In The Air”; LAVERN BAKER “LaVern”; THE AQUABATS “The Return Of The Aquabats”; SUN CITY GIRLS “Torch Of The Mystics”; BUTTHOLE SURFERS “Rembrandt Pussyhorse”; TAYLOR SWIFT “Lover”; YOUSSOU N’DOUR & LE SUPER ETOILE DE DAKAR “Immigres”; JOHN LEE HOOKER “Burning Hell”

05-09-23

THE VASELINES “The Way Of The Vaselines”; THE FLAMING LIPS “At War With The Mystics”; BIG DADDY KANE “Looks Like A Job For Big Daddy Kane”; HELLOWEEN “Keeper Of The Seven Keys – Part II”; BOBBY FREEMAN “Do You Wanna Dance?”; MERCURY REV “Yerself Is Steam”; AL GREEN “Have A Good Time”; MOVING HEARTS “The Storm”; THE BLACK KEYS “El Camino”; PRIMAL SCREAM “Sonic Flower Groove”; JENS LEKMAN “I Know What Love Isn’t”; LINKIN PARK “Hybrid Theory”; MARTINA TOPLEY-BIRD “Some Place Simple”

06-09-23

TOM PETTY & THE HEARTBREAKERS “Damn The Torpedoes”; THE OFFSPRING “Americana”; ZION TRAIN “Passage To Indica”; KRISTIN HERSH “Live At Maxwell’s”; KATHRYN TICKELL “Borderlands”; THE AQUABATS “The Fury Of The Aquabats!”; THE PLUGZ “Better Luck”; U-ROY “Dread In A Babylon”; MODEST MOUSE “We Were Dead Before The Ship Even Sank”; HORSLIPS “The Book Of Invasions: A Celtic Symphony”

07-09-23

VIOLENT FEMMES “Hallowed Ground”; THE FUTUREHEADS “The Chaos”; THE BEAUTIFUL SOUTH “Welcome To The Beautiful South”; CHARLIE RICH “Lonely Weekends With Charlie Rich”; THE JAMES TAYLOR QUARTET “Do Your Own Thing”; ERASURE “The Circus”; BAD RELIGION “Suffer”; fun. “Some Nights”; BRUCE SPRINGSTEEN “Darkness On The Edge Of Town”; THE DECEMBERISTS “Castaways And Cutouts”; LITTLE SIMZ “GREY Area”; BLINK 182 “Enema Of The State”; NIGHTMARES ON WAX “Smoker’s Delight”; REUBEN WILSON “Blue Mode”; THE ONLY ONES “The Only Ones”; THE LEMONHEADS “Come On Feel The Lemonheads”; BRUCE SPRINGSTEEN “The River”; WANDA JACKSON “Wanda Jackson”

08-09-23

JULIAN COPE “Saint Julian”; SCOTT BRADLEE’S POSTMODERN JUKEBOX “OK Crooner”; DAVY SPILLANE “Pipedreams”; GREGORY ISAACS “Willow Tree”; THE JAM “Sound Affects”; CULTURE “Harder Than The Rest”

[exhaled-spirals]

« For many, including myself, mathematics is comforting. In an era of fake news, worldwide illness, and economic uncertainty, mathematics provides proof of another reality which is harmonious, universal, and eternal. Or so it would seem.

In fact mathematics, like all literature, is none of these things. Mathematics is, of course, a human artefact. It is a language which consists of a vocabulary, a grammar, and a community which employs these enthusiastically. Arguably, mathematics is the most refined language ever produced.

[...] The practical [...] usefulness of the work of mathematicians does not concern them. Even a brief exposure to number theory, for example, is sufficient to convince most outside the mathematical community (or even outside the community of number theorists) that the things mathematicians are concerned about are essentially trivial. The strange and often captivating relationships among numbers are simply alien to practical experience. The non-mathematician can only ask ‘Why bother?’.

And the answer to this question must be the same as it is to the issue of literature in general. There is no reason for mathematics other than itself. Mathematics is a form of highly refined, esoteric poetry. Its form and subject matter is not to everyone’s taste. But neither is the Iliad, or The Wasteland, or Finnegans Wake. It takes considerable linguistic skill and aesthetic fortitude to comprehend the content of mathematical poetry. Success in such an endeavour is, as usual, its own reward. »

— From a review of Reuben Hersh’s What is Mathematics, Really?

[historical-nonfiction]

Norbert Wiener of MIT (1894–1964) was well known as an extreme example of someone who could get lost in thought. Once while walking on campus, Wiener met an acquaintance, and after a while he asked his companion: ‘Which way was I walking when we met?’ The man pointed, and Wiener said, ‘Good. Then I’ve had my lunch.’

Quoted from Loving and Hating Mathematics: Challenging the Myths of Mathematical Life, by Reuben Hersh and Vera John-Steiner  (2010)

[sciencebookaday]

What is Mathematics, Really?

What is Mathematics, Really?

What is Mathematics, Really? by Reuben Hersh

Synopsis: Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as…

[mymathematics]

Great book by Reuben Hersh

[plurdledgabbleblotchits]

Is there a way to enlarge our separate tribal loyalties, to include all our fellow humans?

Reuben Hersh

[quadrantexamples47]

four subjects Reuben Hersh Math Really

[quadrantexamples46]

Descartes four rules Reuben Hersh

[noosphe-re]

[camestrosfelapton]

Loved Books: The Mathematical Experience by Philip J. Davis & Reuben Hersh

Loved Books: The Mathematical Experience by Philip J. Davis & Reuben Hersh

I was given this book as a Christmas present as a teenager but I had picked it out in a bookshop. It was part of a bunch of books I was given that included Anarchism by George Woodcock (since lost) and the Norse Myths by Kevin Crossley-Holland (which I still have somewhere).

The difference with this book was that maths was a new and surprising interest. I had never liked mathematics and for much…

[stopkingobama]

Arguments why God (very probably) exists

Photo credit: Pixabay, ddouk, CC0 Public Domain, https://pixabay.com/en/bath-abbey-chair-stained-glass-561789/

The question of whether a god exists is heating up in the 21st century. According to a Pew survey, the percent of Americans having no religious affiliation reached 23 percent in 2014. Among such “nones,” 33 percent said that they do not believe in God – an 11 percent increase since only 2007.

Such trends have ironically been taking place even as, I would argue, the probability for the existence of a supernatural god have been rising. In my 2015 book, “God? Very Probably: Five Rational Ways to Think about the Question of a God,” I look at physics, the philosophy of human consciousness, evolutionary biology, mathematics, the history of religion and theology to explore whether such a god exists. I should say that I am trained originally as an economist, but have been working at the intersection of economics, environmentalism and theology since the 1990s.

Laws of math

In 1960 the Princeton physicist – and subsequent Nobel Prize winner – Eugene Wigner raised a fundamental question: Why did the natural world always – so far as we know – obey laws of mathematics?

As argued by scholars such as Philip Davis and Reuben Hersh, mathematics exists independent of physical reality. It is the job of mathematicians to discover the realities of this separate world of mathematical laws and concepts. Physicists then put the mathematics to use according to the rules of prediction and confirmed observation of the scientific method.

But modern mathematics generally is formulated before any natural observations are made, and many mathematical laws today have no known existing physical analogues.

Einstein Memorial, National Academy of Sciences, Washington, D.C. Wally Gobetz, CC BY-ND

Einstein’s 1915 general theory of relativity, for example, was based on theoretical mathematics developed 50 years earlier by the great German mathematician Bernhard Riemann that did not have any known practical applications at the time of its intellectual creation.

In some cases the physicist also discovers the mathematics. Isaac Newton was considered among the greatest mathematicians as well as physicists of the 17th century. Other physicists sought his help in finding a mathematics that would predict the workings of the solar system. He found it in the mathematical law of gravity, based in part on his discovery of calculus.

At the time, however, many people initially resisted Newton’s conclusions because they seemed to be “occult.” How could two distant objects in the solar system be drawn toward one another, acting according to a precise mathematical law? Indeed, Newton made strenuous efforts over his lifetime to find a natural explanation, but in the end he could say only that it is the will of God.

Despite the many other enormous advances of modern physics, little has changed in this regard. As Wigner wrote, “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”

In other words, as I argue in my book, it takes the existence of some kind of a god to make the mathematical underpinnings of the universe comprehensible.

Math and other worlds

In 2004 the great British physicist Roger Penrose put forward a vision of a universe composed of three independently existing worlds – mathematics, the material world and human consciousness. As Penrose acknowledged, it was a complete puzzle to him how the three interacted with one another outside the ability of any scientific or other conventionally rational model.

How can physical atoms and molecules, for example, create something that exists in a separate domain that has no physical existence: human consciousness?

It is a mystery that lies beyond science.

Plato. Elizabethe, CC BY-NC-ND

This mystery is the same one that existed in the Greek worldview of Plato, who believed that abstract ideas (above all mathematical) first existed outside any physical reality. The material world that we experience as part of our human existence is an imperfect reflection of these prior formal ideals. As the scholar of ancient Greek philosophy, Ian Mueller, writes in “Mathematics And The Divine,” the realm of such ideals is that of God.

Indeed, in 2014 the MIT physicist Max Tegmark argues in “Our Mathematical Universe” that mathematics is the fundamental world reality that drives the universe. As I would say, mathematics is operating in a god-like fashion.

The mystery of human consciousness

The workings of human consciousness are similarly miraculous. Like the laws of mathematics, consciousness has no physical presence in the world; the images and thoughts in our consciousness have no measurable dimensions.

Yet, our nonphysical thoughts somehow mysteriously guide the actions of our physical human bodies. This is no more scientifically explicable than the mysterious ability of nonphysical mathematical constructions to determine the workings of a separate physical world.

Until recently, the scientifically unfathomable quality of human consciousness inhibited the very scholarly discussion of the subject. Since the 1970s, however, it has become a leading area of inquiry among philosophers.

Recognizing that he could not reconcile his own scientific materialism with the existence of a nonphysical world of human consciousness, a leading atheist, Daniel Dennett, in 1991 took the radical step of denying that consciousness even exists.

Finding this altogether implausible, as most people do, another leading philosopher, Thomas Nagel, wrote in 2012 that, given the scientifically inexplicable – the “intractable” – character of human consciousness, “we will have to leave [scientific] materialism behind” as a complete basis for understanding the world of human existence.

As an atheist, Nagel does not offer religious belief as an alternative, but I would argue that the supernatural character of the workings of human consciousness adds grounds for raising the probability of the existence of a supernatural god.

Evolution and faith

Evolution is a contentious subject in American public life. According to Pew, 98 percent of scientists connected to the American Association for the Advancement of Science “believe humans evolved over time” while only a minority of Americans “fully accept evolution through natural selection.”

As I say in my book, I should emphasize that I am not questioning the reality of natural biological evolution. What is interesting to me, however, are the fierce arguments that have taken place between professional evolutionary biologists. A number of developments in evolutionary theory have challenged traditional Darwinist – and later neo-Darwinist – views that emphasize random genetic mutations and gradual evolutionary selection by the process of survival of the fittest.

From the 1970s onwards, the Harvard evolutionary biologist Stephen Jay Gould created controversy by positing a different view, “punctuated equilibrium,” to the slow and gradual evolution of species as theorized by Darwin.

In 2011, the University of Chicago evolutionary biologist James Shapiro argued that, remarkably enough, many micro-evolutionary processes worked as though guided by a purposeful “sentience” of the evolving plant and animal organisms themselves. “The capacity of living organisms to alter their own heredity is undeniable,” he wrote. “Our current ideas about evolution have to incorporate this basic fact of life.”

A number of scientists, such as Francis Collins, director of the U.S. National Institutes of Health, “see no conflict between believing in God and accepting the contemporary theory of evolution,” as the American Association for the Advancement of Science points out.

For my part, the most recent developments in evolutionary biology have increased the probability of a god.

Miraculous ideas at the same time?

For the past 10,000 years at a minimum, the most important changes in human existence have been driven by cultural developments occurring in the realm of human ideas.

In the Axial Age (commonly dated from 800 to 200 B.C.), world-transforming ideas such as Buddhism, Confucianism, the philosophies of Plato and Aristotle, and the Hebrew Old Testament almost miraculously appeared at about the same time in India, China, ancient Greece and among the Jews in the Middle East, groups having little interaction with one another.

Many world-transforming ideas, such as Buddhism, appeared in the world around the same time. Karyn Christner, CC BY

The development of the scientific method in the 17th century in Europe and its modern further advances have had at least as great a set of world-transforming consequences. There have been many historical theories, but none capable, I would argue, of explaining as fundamentally transformational a set of events as the rise of the modern world. It was a revolution in human thought, operating outside any explanations grounded in scientific materialism, that drove the process.

That all these astonishing things happened within the conscious workings of human minds, functioning outside physical reality, offers further rational evidence, in my view, for the conclusion that human beings may well be made “in the image of [a] God.”

Different forms of worship

In his commencement address to Kenyon College in 2005, the American novelist and essayist David Foster Wallace said that: “Everybody worships. The only choice we get is what to worship.”

Even though Karl Marx, for example, condemned the illusion of religion, his followers, ironically, worshiped Marxism. The American philosopher Alasdair MacIntyre thus wrote that for much of the 20th century, Marxism was the “historical successor of Christianity,” claiming to show the faithful the one correct path to a new heaven on Earth.

In several of my books, I have explored how Marxism and other such “economic religions” were characteristic of much of the modern age. So Christianity, I would argue, did not disappear as much as it reappeared in many such disguised forms of “secular religion.”

That the Christian essence, as arose out of Judaism, showed such great staying power amidst the extraordinary political, economic, intellectual and other radical changes of the modern age is another reason I offer for thinking that the existence of a god is very probable.

Robert H. Nelson, Professor of Public Policy, University of Maryland

This article was originally published on The Conversation. Read the original article.

[americanlibertypac]

Arguments why God (very probably) exists

Photo credit: Pixabay, ddouk, CC0 Public Domain, https://pixabay.com/en/bath-abbey-chair-stained-glass-561789/

The question of whether a god exists is heating up in the 21st century. According to a Pew survey, the percent of Americans having no religious affiliation reached 23 percent in 2014. Among such “nones,” 33 percent said that they do not believe in God – an 11 percent increase since only 2007.

Such trends have ironically been taking place even as, I would argue, the probability for the existence of a supernatural god have been rising. In my 2015 book, “God? Very Probably: Five Rational Ways to Think about the Question of a God,” I look at physics, the philosophy of human consciousness, evolutionary biology, mathematics, the history of religion and theology to explore whether such a god exists. I should say that I am trained originally as an economist, but have been working at the intersection of economics, environmentalism and theology since the 1990s.

Laws of math

In 1960 the Princeton physicist – and subsequent Nobel Prize winner – Eugene Wigner raised a fundamental question: Why did the natural world always – so far as we know – obey laws of mathematics?

As argued by scholars such as Philip Davis and Reuben Hersh, mathematics exists independent of physical reality. It is the job of mathematicians to discover the realities of this separate world of mathematical laws and concepts. Physicists then put the mathematics to use according to the rules of prediction and confirmed observation of the scientific method.

But modern mathematics generally is formulated before any natural observations are made, and many mathematical laws today have no known existing physical analogues.

Einstein Memorial, National Academy of Sciences, Washington, D.C. Wally Gobetz, CC BY-ND

Einstein’s 1915 general theory of relativity, for example, was based on theoretical mathematics developed 50 years earlier by the great German mathematician Bernhard Riemann that did not have any known practical applications at the time of its intellectual creation.

In some cases the physicist also discovers the mathematics. Isaac Newton was considered among the greatest mathematicians as well as physicists of the 17th century. Other physicists sought his help in finding a mathematics that would predict the workings of the solar system. He found it in the mathematical law of gravity, based in part on his discovery of calculus.

At the time, however, many people initially resisted Newton’s conclusions because they seemed to be “occult.” How could two distant objects in the solar system be drawn toward one another, acting according to a precise mathematical law? Indeed, Newton made strenuous efforts over his lifetime to find a natural explanation, but in the end he could say only that it is the will of God.

Despite the many other enormous advances of modern physics, little has changed in this regard. As Wigner wrote, “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”

In other words, as I argue in my book, it takes the existence of some kind of a god to make the mathematical underpinnings of the universe comprehensible.

Math and other worlds

In 2004 the great British physicist Roger Penrose put forward a vision of a universe composed of three independently existing worlds – mathematics, the material world and human consciousness. As Penrose acknowledged, it was a complete puzzle to him how the three interacted with one another outside the ability of any scientific or other conventionally rational model.

How can physical atoms and molecules, for example, create something that exists in a separate domain that has no physical existence: human consciousness?

It is a mystery that lies beyond science.

Plato. Elizabethe, CC BY-NC-ND

This mystery is the same one that existed in the Greek worldview of Plato, who believed that abstract ideas (above all mathematical) first existed outside any physical reality. The material world that we experience as part of our human existence is an imperfect reflection of these prior formal ideals. As the scholar of ancient Greek philosophy, Ian Mueller, writes in “Mathematics And The Divine,” the realm of such ideals is that of God.

Indeed, in 2014 the MIT physicist Max Tegmark argues in “Our Mathematical Universe” that mathematics is the fundamental world reality that drives the universe. As I would say, mathematics is operating in a god-like fashion.

The mystery of human consciousness

The workings of human consciousness are similarly miraculous. Like the laws of mathematics, consciousness has no physical presence in the world; the images and thoughts in our consciousness have no measurable dimensions.

Yet, our nonphysical thoughts somehow mysteriously guide the actions of our physical human bodies. This is no more scientifically explicable than the mysterious ability of nonphysical mathematical constructions to determine the workings of a separate physical world.

Until recently, the scientifically unfathomable quality of human consciousness inhibited the very scholarly discussion of the subject. Since the 1970s, however, it has become a leading area of inquiry among philosophers.

Recognizing that he could not reconcile his own scientific materialism with the existence of a nonphysical world of human consciousness, a leading atheist, Daniel Dennett, in 1991 took the radical step of denying that consciousness even exists.

Finding this altogether implausible, as most people do, another leading philosopher, Thomas Nagel, wrote in 2012 that, given the scientifically inexplicable – the “intractable” – character of human consciousness, “we will have to leave [scientific] materialism behind” as a complete basis for understanding the world of human existence.

As an atheist, Nagel does not offer religious belief as an alternative, but I would argue that the supernatural character of the workings of human consciousness adds grounds for raising the probability of the existence of a supernatural god.

Evolution and faith

Evolution is a contentious subject in American public life. According to Pew, 98 percent of scientists connected to the American Association for the Advancement of Science “believe humans evolved over time” while only a minority of Americans “fully accept evolution through natural selection.”

As I say in my book, I should emphasize that I am not questioning the reality of natural biological evolution. What is interesting to me, however, are the fierce arguments that have taken place between professional evolutionary biologists. A number of developments in evolutionary theory have challenged traditional Darwinist – and later neo-Darwinist – views that emphasize random genetic mutations and gradual evolutionary selection by the process of survival of the fittest.

From the 1970s onwards, the Harvard evolutionary biologist Stephen Jay Gould created controversy by positing a different view, “punctuated equilibrium,” to the slow and gradual evolution of species as theorized by Darwin.

In 2011, the University of Chicago evolutionary biologist James Shapiro argued that, remarkably enough, many micro-evolutionary processes worked as though guided by a purposeful “sentience” of the evolving plant and animal organisms themselves. “The capacity of living organisms to alter their own heredity is undeniable,” he wrote. “Our current ideas about evolution have to incorporate this basic fact of life.”

A number of scientists, such as Francis Collins, director of the U.S. National Institutes of Health, “see no conflict between believing in God and accepting the contemporary theory of evolution,” as the American Association for the Advancement of Science points out.

For my part, the most recent developments in evolutionary biology have increased the probability of a god.

Miraculous ideas at the same time?

For the past 10,000 years at a minimum, the most important changes in human existence have been driven by cultural developments occurring in the realm of human ideas.

In the Axial Age (commonly dated from 800 to 200 B.C.), world-transforming ideas such as Buddhism, Confucianism, the philosophies of Plato and Aristotle, and the Hebrew Old Testament almost miraculously appeared at about the same time in India, China, ancient Greece and among the Jews in the Middle East, groups having little interaction with one another.

Many world-transforming ideas, such as Buddhism, appeared in the world around the same time. Karyn Christner, CC BY

The development of the scientific method in the 17th century in Europe and its modern further advances have had at least as great a set of world-transforming consequences. There have been many historical theories, but none capable, I would argue, of explaining as fundamentally transformational a set of events as the rise of the modern world. It was a revolution in human thought, operating outside any explanations grounded in scientific materialism, that drove the process.

That all these astonishing things happened within the conscious workings of human minds, functioning outside physical reality, offers further rational evidence, in my view, for the conclusion that human beings may well be made “in the image of [a] God.”

Different forms of worship

In his commencement address to Kenyon College in 2005, the American novelist and essayist David Foster Wallace said that: “Everybody worships. The only choice we get is what to worship.”

Even though Karl Marx, for example, condemned the illusion of religion, his followers, ironically, worshiped Marxism. The American philosopher Alasdair MacIntyre thus wrote that for much of the 20th century, Marxism was the “historical successor of Christianity,” claiming to show the faithful the one correct path to a new heaven on Earth.

In several of my books, I have explored how Marxism and other such “economic religions” were characteristic of much of the modern age. So Christianity, I would argue, did not disappear as much as it reappeared in many such disguised forms of “secular religion.”

That the Christian essence, as arose out of Judaism, showed such great staying power amidst the extraordinary political, economic, intellectual and other radical changes of the modern age is another reason I offer for thinking that the existence of a god is very probable.

Robert H. Nelson, Professor of Public Policy, University of Maryland

This article was originally published on The Conversation. Read the original article.

[matematicaposititva]

Matematicas Una Historia De Amor | Hersh Reuben Y John Steiner Vera RESEÑA: Las matemáticas tienen para muchos mala fama: frías, complicadas, ajenas a todo aquello que no sea «racional».