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## Introdução

• Durante Milênios o ser humano tem relacionado a matemática Deus, com o sagrado e com a prória base da realidade.
• Este livro explora essa relação da matemática com Deus. Este livro não afirma que Deus usa a matemática ou que Deus é a matemática, ele so instiga o leitor e pensar nessa relação entre Deus e a matemática
• hoje em dia varias teorias colocam a matematica como a base da realidade
• The ancient Greek study of mathematics was closely related to that of religion. Plato is quoted as saying "God ever geometrizes" and Pythagoras as saying "numbers rule the Universe".
• A number of famous mathematicians have made connections between mathematics and God, often likening God to a mathematician.

O ganhador do Prémio Nobel Eugene Wigner, uma vez perguntei sobre a "a eficácia sem razoável aparente da matemática na formulação das leis da natureza". Deus é um matemático? investiga por que a matemática é tão poderosa como ela é.

• Desde os tempos antigos até hoje, cientistas e filósofos têm se maravilhado com a forma de como uma disciplina aparentemente abstrata pode tão perfeitamente o mundo natural.

Mais do que isso - a matemática tem frequentemente feito previsões, por exemplo, sobre as partículas subatômicas ou fenômenos cósmicos que eram desconhecidas na época, mas mais tarde foi provado ser verdade.

--- Matemática mathematics product of human study and manipulation, rather than something fixed and eternal produzido por uma mente inteligente e superior?

math is how God (or nature) organizes the world, or it is simply a human tool to understand that world.

the eternal truth contained in the geometry formulated by Euclid 2,400 years ago.

By the 19th century, however, iconoclasts had posited and established a whole new world of non-Euclidian geometry. Livio writes about the symmetries of the universe: the immutable, if incompletely understood, laws of math and physics that make a hydrogen atom, for instance, behave in the same way on Earth as it acts 10 billion light years away. Another sign of universal structure, as teased apart with the help of math?

Why does math describe reality so well? A scientist offers tentative answers.Livio (The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, 2005, etc.), an astrophysicist at the Hubble Space Telescope Science Institute, frames his investigation with a history of math, beginning with the key question: Are mathematical truths discovered or invented? Pythagoras came down firmly on the side of discovery. His argument convinced Plato, and thus almost every ancient philosopher of note. The default assumption throughout most of history was that numbers, geometric figures and other mathematical truths are real. Galileo was the first to argue that scientific truth was necessarily expressed in mathematical terms. Newton's highly accurate calculations of the gravitational force drove the point home, implying that math and physical reality were two sides of the same coin. Even probability and statistics, which seem fuzzier than the hard equations of physics, give useful answers in the world of quantum interactions. But then math began to explore realms of thought that had no obvious relation to the world as we experience it: non-Euclidean geometry, or the paradoxes of set theory and symbolic logic. The idea that math was a game invented by mathematicians rather than something inherent in reality became fashionable, perhaps even inescapable. Also, it became clear that certain undeniably useful scientific disciplines—Darwinian evolution, to name one salient example—resisted mathematical treatment. Even so, Livio shows that correspondences between mathematical discoveries and physical phenomena continued to crop up, often in abstract mathematics created without any idea of practical applications, such as Einstein's use of non-Euclidean geometry. Knot topology, devised to explain a long-discredited model of the atom, turned out to have application to string theory. The author gives no final answer to the central question of math's relationship to reality. There are physical phenomena that are modeled by math, he asserts, but we also understand reality with a brain wired to find mathematical relations all around it.The conclusion falls a bit flat, but Livio's trip through mathematical history is thoroughly enjoyable and requires no special training to follow it.

### Johannes Kepler

At University, Kepler had learned about Copernicus' system and had immediately accepted heliocentrism as a real picture of the world: 'I have attested it as true in my deepest soul,' he later wrote. Nevertheless, he did not exhibit much interest in the subject until the day in Gratz when the figure on the blackboard suggested to him that he could explain the details of the heliocentric cosmos in terms of a beautiful underlying geometric pattern. Copernicus had discovered the general arrangement of the heavens - the sun at the center and the planets revolving around it. Now Kepler would explain precisely the orbital sizes and spacings. That there was a precise mathematical explanation for the cosmic plan was an article of faith with Kepler, because for him the world was a reflection of the supremely Pythagorean God. Following Nicholas of Cusa, Kepler saw the world as the material embodiment of mathematical forms present within God before the act of creation. 'Why waste words?' he wrote, 'Geometry existed before the Creation, is co-eternal with the mind of God, is God himself ... geometry provided God with a model for the Creation.' Thus, 'where matter is, there is geometry.' Because he believed that the world was a reflection of God, who was a perfect being, according to Kepler it must necessarily be a perfect world, and therefore the manifestation of sublime geometric principles. 'It is absolutely necessary that the work of such a perfect creator should be of the greatest beauty.' (Kepler) (Wertheim, Pythagoras' Trousers, 1997)

### Citações de Grandes Mentes

Antes de começar o livro exponho aqui um lista de citações de grandes mentes que relacionam Deus e a matemática

## Matemática e a natureza

### Mathematical universe hypothesis - Max Tegmark

Em física e cosmologia, a hipótese do universo matemático (MUH), é uma 'teoria de tudo' especulativa , proposta por Max Tegmark [1].

Tegmark's sole postulate is: All structures that exist mathematically also exist physically. This is in the sense that "in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically 'real' world". [2]

O postulado é: Todas as estruturas que existem matematicamente ainda existe fisicamente. Isto é no sentido de que "naqueles complexos o suficiente para conter auto-conhecimento subestruturas (SAS), estes SAS vai subjetivamente se percebem como existente em um" mundo físico "real". [2]

The MUH can be considered a physico-mathematical expression of the philosophy known as modal realism, which treats physical reality as indexical, or self-referent, rather than absolute. The MUH suggests that not only should worlds corresponding to different sets of initial conditions or to different physical constants be considered real, but also worlds ruled by altogether different equations.

O MUH pode ser considerada uma expressão físico-matemático da filosofia conhecido como realismo modal, que trata da realidade física como indexical, ou auto-referente, ao invés de absoluto. O MUH sugere que não só devem mundos correspondentes a diferentes conjuntos de condições iniciais ou diferentes das constantes físicas ser considerada real, mas também mundos governados por equações completamente diferente.


Tegmark claims that the MUH has no free parameters and is not observationally ruled out, and is therefore to be preferred over all other TOE's by Occam's Razor. He envisages conscious experience as taking the form of "self-aware substructures" of mathematical structures, which will subjectively perceive themselves as existing in a physically "real" world.

afirma que o Tegmark MUH não tem parâmetros e não é livre observacionalmente descartada, e, portanto, deve ser dada preferência sobre todos os outros TOE por Navalha de Occam. Ele prevê a experiência consciente como sob a forma de "auto-conhecimento subestruturas" das estruturas matemáticas, que subjetivamente se percebem como existente em um fisicamente "mundo real".

The MUH is related to the anthropic principle, to theories hypothesizing a multiverse, and to Jürgen Schmidhuber's ultimate ensemble of all computable universes.[3].

O MUH está relacionado com o princípio antrópico, as teorias hipótese em um multiverso, e ensemble final Jürgen Schmidhuber de todos os universos computável. [3].

### Física Digital

Digital Physics ("DP") is a suitably neutral scientific term for a breathtaking philosophical concept. It refers to the hypothesis that all of physics -- which is to say, all of our universe -- can be rendered by a digital computer. Everything from melting ice in our backyard to black holes in the cosmos should be expressible as a computer program, according to digital physics. The reason this should be so is that our universe itself is the manifestation of a computer program, being run on some ultimate computer -- not so very different, in principle, from our own computer games and virtual reality simulations.

Digital physics arose at the intersection of physics and computer science. Physicists have long noted that, at the most elementary level, our universe operates according to mathematical principles. In many respects, the fundamental behaviors observed on the quantum level defy common sense when interpreted as tiny specks of matter. The interpretation that seems best to fit the facts is that these behaviors are related to the mathematical principles in some unimaginably fundamental way. As the science popularizer John Gribbon puts it, "nature seems to 'make the calculation' and then present us with an observed event."

Meanwhile, computer science has demonstrated ever greater success at "modeling" the behaviors of natural phenomena. That is, by programming a computer with a series of step-by-step instructions for taking one set of information (say, the position of an electron) and changing that information according to a mathematical formula, computer scientists have been able to reproduce on the computer monitor the same puzzling behaviors observed by the physicists in the laboratory.

At some point in the development of both physics and computer science we could begin to speak of a convergence. Physicists became more and more convinced of the essential mathematical nature of "particle" behavior, and computer scientists became more and more confident of their ability to model the natural world through the strict mathematical rules of computer programming.

### Multiverse

• AND MATH RULING

### String_theory

• WITH MATH RULING

### The Unreasonable Effectiveness of Mathematics in the Natural Sciences

The Unreasonable Effectiveness of Mathematics in the Natural Sciences is the title of an article published in 1960 by the physicist Eugene Wigner[1]. In it, he observed that the mathematical structure of a physics theory often points the way to further advances in that theory and even to empirical predictions, and argued that this is not just a coincidence and therefore must reflect some larger and deeper truth about both mathematics and physics.

A efetividade irracional da Matemática nas Ciências Naturais é o título de um artigo publicado em 1960 pelo físico Eugene Wigner [1]. Nela, ele observou que a estrutura matemática de uma teoria física freqüentemente aponta o caminho para avanços nessa teoria e até mesmo as previsões empíricas, e argumentou que esta não é apenas uma coincidência e, portanto, devem reflectir alguns dos maiores e mais profunda verdade sobre a matemática e física.

#### The miracle of mathematics in the natural sciences

Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says "it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena." He then invokes the fundamental law of gravitation as an example. Originally used to model freely falling bodies on the surface of the earth, this law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets, where it "has proved accurate beyond all reasonable expectations."

Wigner começa seu trabalho com a crença, comum a todos os que estão familiarizados com a matemática, que os conceitos matemáticos têm aplicabilidade muito além do contexto em que foram originalmente desenvolvidos. Baseado em sua experiência, ele diz que "é importante salientar que a formulação matemática de experiência muitas vezes grosseiro o físico leva a um número] [[uncanny] de casos para uma descrição espantosamente precisa de uma grande classe de fenômenos." Ele então chama o fundamental lei da gravitação como um exemplo. Originalmente usada para modelar corpos em queda livre na superfície da Terra, esta lei foi prorrogado em função do que termos Wigner "observações muito escassa" para descrever o movimento dos planetas, em que "provou precisa ultrapassar todas as expectativas razoáveis."

Another oft-cited example is Maxwell's equations, derived to model the elementary electrical and magnetic phenomena known as of the mid 19th century. These equations also describe radio waves, discovered by Heinrich Hertz in 1887 a few years after Maxwell's death. Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it." He concludes his paper with the same question with which he began:

Outro exemplo muito citado é equações Maxwell, derivado do modelo para os fenômenos elétricos e magnéticos elementares conhecidas como de meados do século 19. Essas equações descrevem também as ondas de rádio, descobriu por Heinrich Hertz em 1887, poucos anos depois da morte de Maxwell. Wigner resume seu argumento dizendo que "a imensa utilidade da matemática nas ciências naturais é algo que beira o misterioso e que não há explicação racional para isso." Ele conclui seu artigo com a mesma pergunta com que começou:

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

O milagre da adequação da linguagem da matemática para a formulação das leis da física é um dom maravilhoso que nos entender nem merecem. Nós devemos ser gratos por isso e espero que ele permanecerá válido em pesquisas futuras e que se estenderá, para melhor ou para pior, para nosso prazer, embora talvez também a nossa perplexidade, a variedade de ramos de aprendizagem. </ Blockquote>

Many forms observed in nature can be related to geometry (for sound reasons of resource optimization). For example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms. But scientists generally see such phenomena as the logical outcome of natural principles.

eye horus

## pitagorismo

### Sacred geometry

Luca Pacioli

Sacred geometry may be understood as a worldview of pattern recognition and a complex system of religious symbols and structures involving space, time and form. According to this belief, the basic patterns of existence are perceived as sacred. By connecting with these, a person contemplates the Mysterium Magnum, and the Great Design. By studying the nature of these patterns, forms and relationships and their connections, insight may be gained into the mysteries – the laws and lore of the Universe.

The golden ratio, geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of mandala and yantra. For examples of sacred geometry in art and architecture refer:

### platonismo=

Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. The term Platonism is used because such a view is seen to parallel Plato's belief in a "World of Ideas" (typified by Plato's cave): the everyday world can only imperfectly approximate an unchanging, ultimate reality. Both Plato's cave and Platonism have meaningful, not just superficial connections, because Plato's ideas were preceded and probably influenced by the hugely popular Pythagoreans of ancient Greece, who believed that the world was, quite literally, generated by numbers.

The major problem of mathematical platonism is this: precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One answer might be Ultimate ensemble, which is a theory that postulates all structures that exist mathematically also exist physically in their own universe.

Gödel's platonism postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly. (This view bears resemblances to many things Husserl said about mathematics, and supports Kant's idea that mathematics is synthetic a priori.) Davis and Hersh have suggested in their book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism (see below).

Some mathematicians hold opinions that amount to more nuanced versions of Platonism. These ideas are sometimes described as Neo-Platonism.

### ONTOLOGY AND Matemática

${\displaystyle e^{i\pi }+1=0\,\!}$
${\displaystyle e\,\!}$ is E (mathematical constant), the base of the natural logarithm,
${\displaystyle i\,\!}$ is the imaginary unit, which satisfies i2 = −1, and
${\displaystyle \pi \,\!}$ is pi, the ratio of the circumference of a circle to its diameter.