"Geometry and Experience"
Albert Einstein (1921)
An expanded form
of
an Address to the Prussian Academy of Sciences
in
Berlin on January 27th, 1921
ONE reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain.
At this point an enigma presents itself which in all ages has agitated inquiring minds. 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? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things.
***
"She
talks about a network of energy
that
flows through all living things.
She
says all energy is only borrowed,
and
one day you have to give it back."
~(Jake Sully's Describing His Teacher of the Navi Ways)~
***
“A human being is a part of the whole called by us universe,
a part limited in time and space.
He experiences himself,
his thoughts and feeling as something separated from the rest,
a kind of optical delusion of his consciousness.
This delusion is a kind of prison for us,
restricting us to our personal desires and to affection for a few persons nearest to us.
Our task must be to free ourselves from this prison
by
widening our circle of compassion to embrace all living creatures
and
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