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Is God a Mathematician? Quotes by Mario Livio

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Is God a Mathematician?

Is God a Mathematician?

by

Mario Livio

1,329 ratings, 3.82 average rating, 183 reviews

Is God a Mathematician? Quotes Showing 1-19 of 19
“For Newton, the world’s very existence and the mathematical regularity of the observed cosmos were evidence for God’s presence.”
Mario Livio,

Is God a Mathematician?

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“Put simply, the cosmological argument claims that since the physical world had to come into existence somehow, there must be a First Cause, namely, a creator God.”
Mario Livio,

Is God a Mathematician?

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“Indeed, the quality that made Newton’s theories truly stand out-the inherent characteristic that turned them into inevitable laws of nature-was precisely the fact that they were all expressed as crystal-clear, self-consistent mathematical relations.”
Mario Livio,

Is God a Mathematician?

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“Imagine what would have happened had the logicist endeavor been entirely successful. This would have implied that mathematics stems fully from logic-literally from the laws of thought. But how could such a deductive science so marvelously fit natural phenomena? What is the relation between formal logic (maybe we should even say human formal logic) and the cosmos? The answer did not become any clearer after Hilbert and Godel. Now all that existed was an incomplete formal “game,” expressed in mathematical language. How could models based on such an “unreliable” system produce deep insights about the universe and its workings?”
Mario Livio,

Is God a Mathematician?

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“The legendary inscription above the Academy’s door speaks loudly about Plato’s attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried out by people associated in one way or another with the Academy. Yet Plato himself was not a mathematician of great technical dexterity, and his direct contributions to mathematical knowledge were probably minimal. Rather, he was an enthusiastic spectator, a motivating source of challenge, an intelligent critic, an an inspiring guide. The first century philosopher and historian Philodemus paints a clear picture: “At that time great progress was seen in mathematics, with Plato serving as the general architect setting out problems, and the mathematicians investigating them earnestly.” To which the Neoplatonic philosopher and mathematician Proclus adds: “Plato…greatly advanced mathematics in general and geometry in particular because of his zeal for these studies. It is well known that his writings are thickly sprinkled with mathematical terms and that he everywhere tries to arouse admiration for mathematics among students of philosophy.” In other words, Plato, whose mathematical knowledge was broadly up to date, could converse with the mathematicians as an equal and as a problem presenter, even though his personal mathematical achievements were not significant.”
Mario Livio,

Is God a Mathematician?

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“Tegmark argues that “our universe is not just described by mathematics-it is mathematics” [emphasis added]. His argument starts with the rather uncontroversial assumption that an external physical reality exists that is independent of human beings. He then proceeds to examine what might be the nature of the ultimate theory of such a reality (what physicists refer to as the “theory of everything”). Since this physical world is entirely independent of humans, Tegmark maintains, its description must be free of any human “baggage” (e.g., human language, in particular). In other words, the final theory cannot include any concepts such as “subatomic particles,” “vibrating strings,” “warped spacetime,” or other humanly conceived constructs. From this presumed insight, Tegmark concludes that the only possible description of the cosmos is one that involves only abstract concepts and the relations among them, which he takes to be the working definition of mathematics.”
Mario Livio,

Is God a Mathematician?

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“Unfortunately, I do not find Tegmark’s line of reasoning to be extremely compelling. The leap from the existence of an external reality (independent of humans) to the conclusion that, in Tegmark’s words, “You must believe in what I call the mathematical universe hypothesis: that our physical reality is a mathematical structure,” involves, in my opinion, a sleight of hand. When Tegmark attempts to characterize what mathematics really is, he says: “To a modern logician, a mathematical structure is precisely this: a set of abstract entities with relations between them.” But this modern logician is human! In other words, Tegmark never really proves that our mathematics is not invented by humans; he simply assumes it. Furthermore, as the French neurobiologist Jean-Pierre Changeaux has pointed out in response to a similar assertion: “To claim physical reality for mathematical objects, on a level of the natural phenomena we study in biology, poses a worrisome epistemological problem it seems to me. How can a physical state, internal to our brain, represent another physical state external to it?”
Mario Livio,

Is God a Mathematician?

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“Mind-boggling, isn’t it? Centuries before the question of why mathematics was so effective in explaining nature was even asked, Galileo thought he already knew the answer! To him, mathematics was simply the language of the universe. To understand the universe, he argued, one must speak this language. God is indeed a mathematician.”
Mario Livio,

Is God a Mathematician?

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“The teleological argument, or argument from design, attempts to furnish evidence for God’s existence from the apparent design of the world.”
Mario Livio,

Is God a Mathematician?

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“This development had dramatic philosophical consequences. As in the case of the non-Euclidean geometries in the nineteenth century, there wasn’t just one definitive set theory, but rather at least four! One could make different assumptions about infinite sets and end up with mutually exclusive set theories. For instance, once could assume that both the axiom of choice and the continuum hypothesis hold true and obtain one version, or that both do not hold, and obtain an entirely different theory. Similarly, assuming the validity of one of the two axioms and the negation of the other would have led to yet two other set theories.

This was the non-Euclidean crisis revisited, only worse. The fundamental role of set theory as the potential basis for the whole of mathematics made the problem for the Platonists much more acute. If indeed one could formulate many set theories simply by choosing a different collection of axioms, didn’t this argue for mathematics being nothing but a human invention? The formalists’ victory looked virtually assured.”
Mario Livio,

Is God a Mathematician?

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“So mathematics is indeed extraordinarily effective for some descriptions, especially those dealing with fundamental science, but it cannot describe our universe in all its dimensions. To some extent, scientists have selected what problems to work on based on those problems being amenable to a mathematical treatment.”
Mario Livio,

Is God a Mathematician?

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“On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt-mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician-mathematics was God!

The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent the agenda, for the next generation of philosophers-Plato in particular-the Pythagoreans established a commanding position in Western thought.”
Mario Livio,

Is God a Mathematician?

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“In his book Opticks, Newton made it clear that he did not believe that the laws of nature by themselves were sufficient to explain the universe’s existence-God was the creator and sustainer of all the atoms that make up the cosmic matter: “For it became him [God] who created them [the atoms] to set them in order. And if he did so, it’s unphilosophical to seek for any other Origin of the World, or to pretend that it might arise out of a Chaos by the mere Laws of Nature.” In other words, to Newton, God was a mathematician (among other things), not just as a figure of speech, but almost literally-the Creator God brought into existence a physical world that was governed by mathematical laws.”
Mario Livio,

Is God a Mathematician?

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“Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind.”
Mario Livio,

Is God a Mathematician?

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“Our mathematics is a combination of invention and discoveries. The axioms of Euclidean geometry as a concept were an invention, just as the rules of chess were an invention. The axioms were also supplemented by a variety of invented concepts, such as triangles, parallelograms, ellipses, the golden ratio, and so on. The theorems of Euclidean geometry, on the other hand, were by and large discoveries; they were the paths linking the different concepts. In some cases, the proofs generated the theorems-mathematicians examined what they could prove and from that they deduced the theorems. In others, as described by Archimedes in The Method, they first found the answer to a particular question they were interested in, and then they worked out the proof.

Typically, the concepts were inventions. Prime numbers as a concept were an invention, but all the theorems about prime numbers were discoveries. The mathematicians of ancient Babylon, Egypt, and China never invented the concept of prime numbers, in spite of their advanced mathematics. Could we say instead that they just did not “discover” prime numbers? Not any more than we could say that the United Kingdom did not “discover” a single, codified, documentary constitution. Just as a country can survive without a constitution, elaborate mathematics could develop without the concept of prime numbers. And it did!

Do we know why the Greeks invented such concepts as the axioms and prime numbers? We cannot be sure, but we could guess that this was part of their relentless efforts to investigate the most fundamental constituents of the universe. Prime numbers were the basic building blocks of matter. Similarly, the axioms were the fountain from which all geometrical truths were supposed to flow. The dodecahedron represented the entire cosmos and the golden ratio was the concept that brought that symbol into existence.”
Mario Livio,

Is God a Mathematician?

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“himself, then according to the sign he should be one of those he does not shave. On the other hand,”
Mario Livio,

Is God a Mathematician?

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“Không thể nghi ngờ gì rằng định luật vạn vật hấp dẫn của Newton chính là sản phẩm của một thiên tài. Song thiên tài ấy không thể hoạt động trong chân không được. Một số nền tảng đã được lát đặt một cách cẩn thận bởi các nhà khoa học trước đó.”
Mario Livio,

Is God a Mathematician?

tags:

nền-tảng

,

thiên-tài

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“Các công cụ toán học không được lựa chọn một cách tuỳ tiện mà đúng hơn phải thật chính xác dựa trên khả năng tiên đoán đúng đắn của chúng đối với kết quả của các thí nghiệm hoặc quan sát có liên quan.”
Mario Livio,

Is God a Mathematician?

tags:

công-cụ-toán-học

,

hiệu-quả-đến-phi-lý

,

thí-nghiệm

,

tiên-đoán

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“Vấn đề là thông qua sự ham hiểu biết cháy bỏng, sự cố chấp bướng bỉnh, trí tưởng tượng sáng tạo và một quyết tâm mạnh mẽ, loài người đã tìm ra những hình thức luận toán học thích hợp cho việc lập mô hình một số lượng lớn các hiện tượng vật lý.”
Mario Livio,

Is God a Mathematician?

tags:

hiếu-học

,

hình-thức-luận

,

loài-người

,

sáng-tạo

,

tưởng-tượng

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