Essential Subjects= Astronomy Icon

September 10, 2015

The Patterns of Geometry Can Be Seen In Astronomy*

*Superphysics Note: As later proven by Isaac Newton who invented calculus from geometric patterns through the observation of heavenly bodies

Socrates We propose geometry as a second branch of knowledge which our youth will study. We make astronomy the third. I am strongly inclined to it. The observation of the seasons, months, and years is as essential to the general as it is to the farmer or sailor.
Glaucon I am amused, at your fear of the world.

It makes you guard against insisting on useless studies. I admit that it is difficult to believe that in every man there is an eye of the soul that can be purified and re-illumined with astronomy, after it has been lost and dimmed by other pursuits.

Astronomy is far more precious than 10,000 bodily eyes because truth is seen by it alone.

Glaucon There are two classes of persons. One class will believe you. Another class will not believe you. They will naturally deem them to be idle tales, for they see no profit from them. Therefore, you must decide which of the two are you proposing to argue with. You will very likely say that your chief aim is your own improvement and not to argue with others. At the same time, you do not bear a grudge on any benefit that others may receive.

Then take a step back, for we have gone wrong in the order of the sciences. After plane geometry, we proceeded at once to solids in revolution, instead of taking solids in themselves.

The third dimension should have followed the second. The third dimension is concerned with cubes and depth.

Little is known about those sciences because:

  • No government patronises them.
    • This leads to a lack of energy in pursuing them, in addition to them being difficult.
  • Students cannot learn them unless they have a director.

But even if a director could be found, the conceited students would not attend to him. But this would not happen if the whole State became the director of these studies and gave honour to them.

Then, disciples would want to come, and there would be continuous and earnest search, and discoveries made. The third dimension is disregarded by the world and maimed of their fair proportions. Their followers are unable to tell of their usefulness. However, these studies still force their way by their natural charm. If they had the help of the State, they would some day emerge into light.

Glaucon Yes, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces. Then you placed astronomy next, and then you made a step backward.

Three-dimensional solid geometry should have naturally followed two-dimensional geometry.

But three-dimensional solid geometry is in such a ludicrous state. It made me pass over it, and go on to astronomy as the motion of solids. If encouraged by the State, the science of solid geometry [physics] would exist and be the third science that we must study. Astronomy will be the fourth.

Glaucon The right order. Socrates, you rebuked the vulgar way that I praised astronomy. I think that everyone must see that astronomy compels the soul to look upwards and lead us from this world to another.

On the contrary, I think that those who elevate astronomy into philosophy make us look downwards and not upwards. A man cannot learn the unseen knowledge of being by gaping at the heavens or by blinking on the ground.

If he does these, then his soul is looking downwards, not upwards, whether his way to knowledge is by water or by land, whether he floats, or only lies on his back. Only the knowledge of being and of the unseen can make the soul look upwards.

Glaucon I acknowledge the justice of your rebuke. Still, how can astronomy be learned to be more conducive to that knowledge of being?

The starry heaven is wrought on a visible ground.

The most perfect of visible things is far inferior to the true motions of absolute swiftness and slowness which are relative to each other*.

They carry with them that which is contained in them**.

These are to be apprehended by reason and intelligence, but not by sight.

The spangled heavens should be used as a pattern and with a view to that higher knowledge.

*Superphysics Note: This is similar to General Relativity.

**Superphysics Note: Unlike General Relativity, the cause of the motions of heavenly bodies are inherent. I call this “gravitational signatures”. Socrates implies that photons cannot directly measure such inherent signatures. The pattern of such signatures can then be used to make a locational map that Einstein refers to as the fabric of spacetime and can be used to predict the motions of heavenly bodies.


Their beauty is like the beauty of pictures excellently wrought by the hand of Daedalus or some other great artist.

Any geometrician who saw them would appreciate the exquisiteness of their workmanship. But he would never think that there is a true equal, true double, or true proportion in the spangled heavens*.

Likewise, a true astronomer will have the same feeling when he looks at the movements of the stars.

*Superphysics Note: Socrates rejects a cosmological constant

Glaucon He will think that heaven and the things in heaven are framed by the Creator in the most perfect way.

But the true astronomer will never imagine that the following can also be eternal and subject to no deviation:

  • the proportions of:
    • night and day,
    • night and day to the month,
    • the month to the year,
    • the stars to these and to one another.

It is equally absurd to take so much pains in investigating their exact truth*.

Then, in astronomy, as in geometry, we should employ problems, and leave the heavens alone if we would approach the subject in the right way. This would make the natural gift of reason useful.

*Superphysics Note: Socrates discourages the search for a universal constant.


That is a work infinitely beyond our present astronomers.

Yes, our legislation will be more valuable if it can give a similar extension to many other things.

The study of motion is the most suitable study to extend.