To Explain the World: The Discovery of Modern Science

by Steven Weinberg

By the same reasoning, as far as we can tell from surviving fragments, it appeared to Zeno to be impossible ever to travel any given dist...

Of course, Zeno’s reasoning...

As pointed out later by Aristotle,11 there is no reason why we cannot accomplish an infinite number of steps in a finite time, as long as the time needed for each su...

but the infinite series ½ + ¼ + ⅛ + . . . has a finite sum, in t...

What is most striking is not so much that Parmenides and Zeno were wrong as that they did not bother to explain why, if motion i...

Indeed, none of the early Greeks from Thales to Plato, in either Miletus or Abdera or Elea or Athens, ever took it on themselves to explain in detail how their theories about ultimat...

There was a strain of intellectual snobbery among the early Greeks that led them to regard an understanding of appearances as not worth having.

At various times it has been thought that circular orbits are more perfect than elliptical orbits, that gold is more noble than lead, and that man is a higher being than his fellow simians.

Are we now making similar mistakes, passing up opportunities for scientific progress because we ignore phenomena tha...

Biologists who are interested in chromosomes or nerve cells study animals like fruit flies and squid, not noble eagles and lions.

Elementary particle physicists are sometimes accused of a snobbish and expensive preoccupation with phenomena at the highest attainable energies,

but it is only at high energies that we can create and study hypothetical particles of high mass, like the dark matter particles that astronomers tell us make u...

In any case, we give plenty of attention to phenomena at low energies, like the intriguing mass of neutrinos, about a m...

Today, for instance, we expect to find that our deepest physical laws satisfy principles of symmetry, which state that physical laws do not change when we change our point of view in certain definite ways.

With Socrates, in the late fifth century BC, and Plato, some forty years later, the center of the stage for Greek intellectual life moved to Athens, one of the few cities of Ionian Greeks on the Greek mainland.

Almost all of what we know about Socrates comes from his appearance in the dialogues of Plato, and as a comic character in Aristophanes’ play The Clouds.

it is useful to look at the theorem as an instance of the scope of Greek knowledge of geometry before the time of Euclid.

Consider any circle, and any diameter of it.

Let A and B be the points where the diameter intersects the circle. Draw lines from A and B to any...

Thales’ Theorem tells us that this is a right triangle: the angle of triangle ABP at P is a right angle, or in other terms, 90°.

The trick in proving this theorem is to draw a line from the center C of the circle to point P.

Both of these are isosceles triangles, that is, triangles with two sides equal.

In triangle ACP, sides CA and CP are both radii of the circle, which have the same length according to the definition of a circle.

The sum of the angles of any triangle is two right angles,* or in familiar terms 180°,

2α + αʹ = 180° 2β + βʹ = 180°

Adding these two equations and regrouping terms gives 2(α + β) + (αʹ + βʹ) = 360°

Now, αʹ + βʹ is the angle between AC and BC, which come together in a straight line, and is therefore half a full turn, or 18...

and therefore α +...

Figure 1. Proof of Thales’ theorem.

The theorem states that wherever point P is located on the circle, the angle between the lines from the ends of the diameter to P is a right angle.