Albert Einstein

In your schooldays most of you who read this book made acquaintance with the noble building of Euclid’s geometry, and you remember—perhaps with more respect than love—the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers.

It is only with reluctance that man’s desire for knowledge endures a dualism of this kind.

We cannot ask whether it is true that only one straight line goes through two points.

The laws were clear and simple, the mechanical interpretations clumsy and contradictory.

Every description of the scene of an event or of the position of an object in space is based on the specification of the point on a rigid body (body of reference) with which that event or object coincides.

For the theoretician such an asymmetry in the theoretical structure, with no corresponding asymmetry in the system of experience, is intolerable.

Every description of events in space involves the use of a rigid body to which such events have to be referred.

To deny the ether is ultimately to assume that empty space has no physical qualities whatever.

A pedestrian who observes the misdeed from the footpath notices that the stone falls to earth in a parabolic curve.

The existence of the gravitational field is inseparably bound up with the existence of space.

In the first place we entirely shun the vague word “space,” of which, we must honestly acknowledge, we cannot form the slightest conception, and we replace it by “motion relative to a practically rigid body of reference.”

Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things.

I stand at the window of a railway carriage which is travelling uniformly, and drop a stone on the embankment, without throwing it.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

Every child at school knows, or believes he knows, that this propagation takes place in straight lines with a velocity c = 300,000 km./sec.

In my opinion the answer to this question is, briefly, this:—As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Lightning has struck the rails on our railway embankment at two places A and B far distant from each other.

These axioms are free creations of the human mind.

Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

The matter of which geometry treats is first defined by the axioms.