Certainly (remarks Glaukon) Astronomy, besides its usefulness in regard to the calendar, and the seasons, must be admitted by every one to carry the mind upwards, to the contemplation of things not below but on high. I do not admit this at all (replies Sokrates), as Astronomy is now cultivated: at least in my sense of the words, _looking upwards and looking downwards_. If a man lies on his back, contemplating the ornaments of the ceiling, he may carry his eyes upward, but not his mind.[234] To look upwards, as I understand it, is to carry the mind away from the contemplation of sensible things, whereof no science is attainable--to the contemplation of intelligible things, entities invisible and unchangeable, which alone are the objects of science. Observation of the stars, such as astronomers now teach, does not fulfil any such condition. The heavenly bodies are the most beautiful of all visible bodies and the most regular of all visible movements, approximating most nearly, though still with a long interval of inferiority, to the ideal figures and movements of genuine and self-existent Forms--quickness, slowness, number, figure, &c., as they are in themselves, not visible to the eye, but conceivable only by reason and intellect.[235] The movements of the heavenly bodies are exemplifications, approaching nearest to the perfection of these ideal movements, but still falling greatly short of them. They are like visible circles or triangles drawn by some very exact artist; which, however beautiful as works of art, are far from answering to the conditions of the idea and its definition, and from exhibiting exact equality and proportion.[236] So about the movements of the sun and stars: they are comparatively regular, but they are yet bodily and visible, never attaining the perfect sameness and unchangeableness of the intelligible world and its forms. We cannot learn truth by observation of phenomena constantly fluctuating and varying. We must study astronomy, as we do geometry, not by observation, but by mathematical theorems and hypotheses: which is a far more arduous task than astronomy as taught at present. Only in this way can it be made available to improve and strengthen the intellectual organ of the mind.[237] [Footnote 234: Plato, Republic, vii. p. 529 B.] [Footnote 235: Plato, Republic, vii. p. 529 D.] [Footnote 236: Plato, Republic, vii. pp. 529-530.] [Footnote 237: Plato, Republic, vii. p. 530 B. [Greek: Problê/masin a)/ra chrô/menoi ô(/sper geômetri/an, ou(/tô kai\ a)stronomi/an me/timen; ta\ d' e)n tô=| ou)ra/nô| e)a/somen], &c.] [Side-note: Acoustics, in like manner--The student will be thus conducted to the highest of all studies--Dialectic: and to the region of pure intelligible Forms.] In like manner (continues Sokrates), Acoustics or Harmonics must be studied, not by the ear, listening to and comparing various sounds, but by the contemplative intellect, applying arithmetical relations and theories.[238]