Chapter 1

Thia was written by the great man in German and translated to English. For me understanding this is hard as, for the dolphin who is trapped in a fisherman's net, been asked by a fish to breath deeply. I shall survive!

Physical Meaning of Geometrical Propositions

First you have to think about mathematical axioms. A 'point', 'Straight Line', 'plane', which we can call axioms. From these we prove the rest of the propositions to be true.

A proposition is then correct ("true") when it has been derived in the recognised manner from the axioms.

The question of "truth" of the individual geometrical propositions is thus reduced to one of the "truth" of the axioms.

Take the case of: if there are two 'points' the closest distance between them is a 'straight line'.

So you can say that if there are two points the shortest distance (time Interval) between them is a straight line.

But you cannot say that only one straight line passes through two points.

(Now is it the same as: If given the statement "Buddhist monks are shaven headed". Shown a shaven headed man, and asked the question "Is he a Buddhist monk?". Then the answer should be,"Yes". Does not matter otherwise. You cannot think that the person is a thug who is not dressed in saffron robes and he is a murderer. I sit and think.)

The concept "true" does not tally with the assertions of pure geometry, because by the word "true" we are eventually in the habit of designating always the correspondence with a "real" object; geometry, however, is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

The word true is a concept associated with a real object in nature. But in geometry is not concerned with the relation of the ideas involved in it to objects of experience, but only with the logical connection of these ideas among themselves.

We still call the propositions of geometry "true." Though the geometric ideas are derived from the exact objects of nature, Geometry should keep to its logical unity.

At a distance we can easily see two points on a straight line. And if we look with one eye we can easily fool ourselves to put tree points on a straight line, depending on the point of observation.

If we make one proposition that on a practically rigid body two points exists with a certain distance (line interval) between them independently of any changes in position to which we may subject the body, the propositions of Euclidean geometry then resolve themselves into propositions on the possible relative position of practically rigid bodies. A branch of Physics is born.

It follows that a natural object is associated also with a straight line. Three points A, B and C on a rigid body thus lie in a straight line when the points A and C being given, B is chosen such that the sum of the distances AB and BC is as short as possible. This incomplete suggestion will suffice for the present purpose.

Of course the conviction of the "truth" of geometrical propositions in this sense is founded exclusively on rather incomplete experience. For the present we shall assume the "truth" of the geometrical propositions, then at a later stage (in the general theory of relativity) we shall see that this "truth" is limited, and we shall consider the extent of its limitation.