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Looking at the Sky: From Pythagoras to Einstein Through Galileo and Newton

No Admission Without Knowledge of Geometry

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Abstract

The idea of universe is not a primitive idea. Legend has it, that was Pythagoras to choose the proper name: cosmos, which opposes itself to chaos and designates order and beauty. It took two millenniums for the evolution of that idea into the modern scientific vision of the world, our vision. The path that led to this vision is extraordinarily fascinating, dramatic and sometimes tragic and has been narrated thousands of times in books that have rightly become classical. We will go over some of its highlights again.

The material world—the reality—is not something given, but is born with us. For the “given” to become reality, it must be resurrected in the literal sense of the word. This is the role of Science, this is the role of Art.

\(^a\)Ossip Mandelstam, Letter to Marietta Shaginyan, April 5, 1933.

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Notes

  1. 1.

    ...And when I gaze upon the stars at night – In thought I ask myself – “Why all these torches bright? – What mean these depths of air, – This vast, this silent sky, – This nightly solitude? And what am I?” – ...– “And all this mighty motion, and this stir – Of things above, and things below, – No rest that ever know, – But as they still revolve, must still return – Unto the place from which they came, – Of this, alas, I find nor end nor aim!”

    Giacomo Leopardi, Canto notturno di un pastore errante dell’Asia (excerpt) 1830.

  2. 2.

    Psalms 90, 4.

  3. 3.

    The original sense of “woman’s ornament” is metaphorically turned into order and beauty, the beauty resulting from order (cosmetics). The usage was for a long time perceived as a metaphor. The “cosmic” unique usage took centuries to emerge. Mundus is the etymological source of the Italian word “monile”.

  4. 4.

    To perceive the logoi in beings is the act known as theoria phusikè, the second of the three stages of the spiritual life distinguished by Evagrius and the tradition that followed him [5].

  5. 5.

    And also on the astronomical data transmitted by the Arabs. Albategnius and some other Arab astronomers are quoted by Copernicus.

  6. 6.

    Philosophy is written in this grand book, which stands continually open before our eyes (I say the ‘Universe’), but can not be understood without first learning to comprehend the language and know the characters as it is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which it is impossible to humanly understand a word; without these one is wandering in a dark labyrinth.

  7. 7.

    But also to the infinite power of God that produces all the infinite effect that it can produce.

  8. 8.

    Curiously, the three great moments of the history of gravitation are all accompanied by a mythical narrative (all three presumably imaginary): Galileo who drops objects from the top of the leaning tower of Pisa, Newton and the apple falling on his head, Einstein and the worker falling off the roof.

  9. 9.

    I have completely abandoned my views, rightfully contested by you, on the degeneration of the metric. I am curious to hear what you will have to say about the somewhat crazy idea I am considering now. A. Einstein. Letter to W. De Sitter of February 2, 1917.

    I have again perpetrated something relating to the theory of gravitation that might endanger me of being committed to a madhouse. A. Einstein. Letter to P. Ehrenfest, February 4, 1917.

  10. 10.

    Sphaera infinita cuius centrum est ubique, circumferentia tamen nullibi : this is the second definition of God that can be read in the Liber XXIV philosophorum, an anonymous medieval treatise attributed to Hermes Trismegistus. Nicolas de Cues applies this definition to the universe: The world machine has, so to speak, its center everywhere and its circumference nowhere (De docta ignorantia, 1440). Bruno at many different places later takes up the definition.

  11. 11.

    Magellan was deceived by his forerunners’ mistake when, upon the warrant of Behaim’s chart, Schoner’s globe, and the unnamed pilots’ story, he formed his great design of circumnavigating the world. The enigma of Magellan is solved as soon as we recognize that he planned and acted in honest error. Let us not underrate the importance of error. Through the promptings of genius, guided by luck, the most preposterous error may lead to the most fruitful of truths. Excerpt from [19].

  12. 12.

    Gérard Nerval - Aurélia ou le Rêve et la Vie (1855).

  13. 13.

    On an excessively clear day, A day when I wanted to work hard not to work on it at all, I saw like a road through the trees, It might have been be the Great Secret, That Great Mystery of which false poets speak. I saw that there is no Nature, That Nature does not exist, That there are hills, valleys, plains,That there are trees, flowers, herbs,That there are rivers and stones. But that there is no whole to which they belong, That a real and true whole Is a disease of our ideas. Nature is parts without a whole.

    This maybe the mystery they are speaking of. This is what without thinking or stopping, I understood should be the truth That everyone is trying to find and does not find, And only I, because I didn’t try, succeeded.

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Moschella, U. (2022). Looking at the Sky: From Pythagoras to Einstein Through Galileo and Newton. In: Streit-Bianchi, M., Catapano, P., Galbiati, C., Magnani, E. (eds) Advances in Cosmology. Springer, Cham. https://doi.org/10.1007/978-3-031-05625-3_1

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