Werner Heisenberg

Can you, or anyone else, reach the central order of things or events, whose existence seems beyond doubt, as directly as you can reach the soul of another human being? I am using the term 'soul' quite deliberately so as not to be misunderstood. If you put your question like that, I would say yes. ... the word 'soul' refers to the central order, to the inner core of a being whose outer manifestations may be highly diverse and pass our understanding.

The first thing we could say was simply: ‘I believe in God, the Father, the almighty creator of heaven and earth.

"Any concepts or words which have been formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning: that is to say, we do not know exactly how far they will help us in finding our way in the world. We often know that they can be applied to a wide range of inner or outer experience, but we practically never know precisely the limits of their applicability. This is true even of the simplest and most general concepts like "existence" and "space and time". Therefore, it will never be possible by pure reason to arrive at some absolute truth.
The concepts may, however, be sharply defined with regard to their connections. This is actually the fact when the concepts become part of a system of axioms and definitions which can be expressed consistently by a mathematical scheme. Such a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. But the limits of the applicability will in general not be known, at least not completely."

An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.

The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached.

But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

"[The probability wave] meant a tendency for something. It was a quantitative version of the old concept of "potentia" in Aristoelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."

Quantum theory provides us with a striking illustration of the fact that we can fully understand a connection though we can only speak of it in images and parables.

The positivists have a simple solution: the world must be divided into that which we can say clearly and the rest, which we had better pass over in silence. But can anyone conceive of a more pointless philosophy, seeing that what we can say clearly amounts to next to nothing? If we omitted all that is unclear, we would probably be left completely uninteresting and trivial tautologies.

I am firmly convinced that we must never judge political movements by their aims, no matter how loudly proclaimed or how sincerely upheld, but only by the means they use to realize these aims.

There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality.

This [chaotic environment,] I felt, was only possible because all these types of order were partial, mere fragments that had split off from a central order; they might not have lost their creative force, but they were no longer directed toward a unifying center. Its absence was brought home to me with increasingly painful intensity the longer I listened. I was suffering almost physically, but I was quite unable to find a way towards the center through the thicket of conflicting opinions. ...There was a hush as, high above us, [a young violinist] struck up the first great D minor chord of Bach’s Chaconne. All at once, and with utter certainty, I had found my link with the center….The clear phrases of the Chaconne touched me like a cool wind, breaking through the mist and revealing the towering structures beyond. There has always been a path to the central order in the language of music, in philosophy and in religion, today no less than in Plato’s day and in Bach’s. That I now knew from my own experience.

One evening I reached the point where I was ready to determine the individual terms in the energy table, or, as we put it today, in the energy matrix, by what would now be considered an extremely clumsy series of calculations. When the first terms seemed to accord with the energy principle, I became rather excited, and I began to make countless arithmetical errors. As a result, it was almost three o'clock in the morning before the final result of my computations lay before me. The energy principle had held for all terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and I felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me. I was far too excited to sleep, and so, as a new day dawned, I made for the southern tip of the island, where I had been longing to climb a rock jutting out into the sea. I now did so without too much trouble, and waited for the sun to rise.

Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word 'understanding.

Modern positivism...expresses criticism against the naïve use of certain terms... by the general postulate that the question whether a given sentence has any meaning... should always be thoroughly and critically examined. This... is derived from mathematical logic. The procedure of natural science is pictured as an attachment of symbols to the phenomena. The symbols can, as in mathematics, be combined according to certain rules... However, a combination of symbols that does not comply with the rules is not wrong but conveys no meaning.
The obvious difficulty in this argument is the lack of any general criterion as to when a sentence should be considered meaningless. A definite decision is possible only when the sentence belongs to a closed system of concepts and axioms, which in the development of natural science will be rather the exception than the rule. In some case the conjecture that a certain sentence is meaningless has historically led to important progress... new connections which would have been impossible if the sentence had a meaning. An example... sentence: "In which orbit does the electron move around the nucleus?" But generally the positivistic scheme taken from mathematical logic is too narrow in a description of nature which necessarily uses words and concepts that are only vaguely defined.