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Book: Is God a Mathematician?
Quotes of Book: Is God a Mathematician?
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  1. Mario Livio _ Is God a Mathematician?

    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.
    book-quotehình-thức-luậnloài-ngườisáng-tạo

  2. Mario Livio _ Is God a Mathematician?

    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.
    book-quotehiệu-quả-đến-phi-lýthí-nghiệmtiên-đoán

  3. Mario Livio _ Is God a Mathematician?

    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.
    book-quotethiên-tài

  4. Mario Livio _ Is God a Mathematician?

    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.
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  5. Mario Livio _ Is God a Mathematician?

    The teleological argument, or argument from design, attempts to furnish evidence for God's existence from the apparent design of the world.
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  6. Mario Livio _ Is God a Mathematician?

    Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind.
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  7. Mario Livio _ Is God a Mathematician?

    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.
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  8. Mario Livio _ Is God a Mathematician?

    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.
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  9. Mario Livio _ Is God a Mathematician?

    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.
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  10. Mario Livio _ Is God a Mathematician?

    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?
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  11. Mario Livio _ Is God a Mathematician?

    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.
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  12. Mario Livio _ Is God a Mathematician?

    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.
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