BCE) to claim that the world is made upof atoms. According to these two and their successors, atoms cannot be subdivided. These scientists disagreed over the question whether all atoms were the same or if there were different types of atoms, but they all agreed that the way the atoms are formed into more complex materials gives those materials their different properties, including their form, color, degree of hardness, and so on. They did not base this claim on only mathematical analogy but also gave other explanations. One was the principle of the preservation of matter, which they inherited from their predecessors from Miletus. If matter can be subdivided endlessly, at the end of the process it will disintegrate into particles without volume, and how can such particles reform into a real substance? It was only twentieth century mathematics that solved this dilemma; namely, it gave a mathematical framework in which a measurable length consisted of points, each of which was of zero length.
Another argument used by the atomists was the need to explain motion. If a substance is continuous and there is no space between one particle and the next, how can there be movement? They also claimed that the atoms, which our senses cannot perceive because of their very small size, are constantly in random and purposeless motion. A similar type of motion, Brownian motion (named after its discoverer, Robert Brown), relating to the irregular motion of minute particles suspended in a fluid, was discovered in the eighteenth century; it was later found that the movement of atoms is similar to Brownian motion. It was Albert Einstein, at the beginning of the twentieth century, who gave mathematical expression to the movement of atoms. In time, the Greek theory of atomism was recognized as being the forerunner of the atomistic approach to nature as it developed toward the end of the nineteenth century and the beginning of the twentieth. Stamps and banknotes issued by Greek governments in modern times carry an image of Democritus and the symbol of an atom. Nevertheless, the recognition of Leucippus and Democritus as the prophets of the modern atomistic approach ascribes to the Greeks greater merit than is warranted. The Greek atomists based themselves solely on philosophical study and mathematical analogies, with no supporting evidence. Aristotle rejected the claim of the Greek atomists for reasons we will discuss later, and his theory of the continuum was accepted by most of the Greek scientistsand philosophers, although supporters of the theory of atomism were active until the first century CE. The atomic structure of the world reappeared and was accepted after thousands of years, but this time it was based on reliable physical evidence.
Another example of the construction of a pattern based on mathematical knowledge and adapting it to physical reality is the conformity of the perfect geometric solid shapes with basic components of nature. A geometric solid is called perfect if all its faces are identical in shape and size. A cube is an example of a perfect solid. Perfect solids were known thousands of years before the Greeks, but they were the only ones who tried to identify all of them. Later Greek writers attributed the discovery of perfect solids to Pythagoras, while others credited Theaetetus, a contemporary of Plato, with the discovery. In any event, in Plato's time it was known that there were only five perfect solids: the triangular pyramid, the cube, the octahedron, the dodecahedron, and the decahedron (see the diagram). On the one hand were five perfect solids, and on the other was the Greek's belief that nature had five basic elements: water, air, earth, fire, and the world. What could be more natural than to conclude that the perfect shapes reflect the main elements of nature? The matching is attributed to Plato himself: the pyramid is fire, the cube is earth, the octahedron reflects air, the dodecahedron reflects the world, and the
Another argument used by the atomists was the need to explain motion. If a substance is continuous and there is no space between one particle and the next, how can there be movement? They also claimed that the atoms, which our senses cannot perceive because of their very small size, are constantly in random and purposeless motion. A similar type of motion, Brownian motion (named after its discoverer, Robert Brown), relating to the irregular motion of minute particles suspended in a fluid, was discovered in the eighteenth century; it was later found that the movement of atoms is similar to Brownian motion. It was Albert Einstein, at the beginning of the twentieth century, who gave mathematical expression to the movement of atoms. In time, the Greek theory of atomism was recognized as being the forerunner of the atomistic approach to nature as it developed toward the end of the nineteenth century and the beginning of the twentieth. Stamps and banknotes issued by Greek governments in modern times carry an image of Democritus and the symbol of an atom. Nevertheless, the recognition of Leucippus and Democritus as the prophets of the modern atomistic approach ascribes to the Greeks greater merit than is warranted. The Greek atomists based themselves solely on philosophical study and mathematical analogies, with no supporting evidence. Aristotle rejected the claim of the Greek atomists for reasons we will discuss later, and his theory of the continuum was accepted by most of the Greek scientistsand philosophers, although supporters of the theory of atomism were active until the first century CE. The atomic structure of the world reappeared and was accepted after thousands of years, but this time it was based on reliable physical evidence.
Another example of the construction of a pattern based on mathematical knowledge and adapting it to physical reality is the conformity of the perfect geometric solid shapes with basic components of nature. A geometric solid is called perfect if all its faces are identical in shape and size. A cube is an example of a perfect solid. Perfect solids were known thousands of years before the Greeks, but they were the only ones who tried to identify all of them. Later Greek writers attributed the discovery of perfect solids to Pythagoras, while others credited Theaetetus, a contemporary of Plato, with the discovery. In any event, in Plato's time it was known that there were only five perfect solids: the triangular pyramid, the cube, the octahedron, the dodecahedron, and the decahedron (see the diagram). On the one hand were five perfect solids, and on the other was the Greek's belief that nature had five basic elements: water, air, earth, fire, and the world. What could be more natural than to conclude that the perfect shapes reflect the main elements of nature? The matching is attributed to Plato himself: the pyramid is fire, the cube is earth, the octahedron reflects air, the dodecahedron reflects the world, and the
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