Zitate von Hermann Weyl

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Hermann Weyl

Geburtstag: 9. November 1885
Todesdatum: 8. Dezember 1955

Hermann Klaus Hugo Weyl war ein deutscher Mathematiker, Physiker und Philosoph, der wegen seines breiten Interessensgebiets von der Zahlentheorie bis zur theoretischen Physik und Philosophie als einer der letzten mathematischen Universalisten gilt.

Zitate Hermann Weyl

„Hiernach wird man verstehen, daß die meisten physikalischen Begriffe, namentlich alle diejenigen, welche die atomistische gebaute Materie betreffen (z. B. die Dichte eines Gases) keine exakten sind im Sinne einer reinen Gesetzesphysik, sondern statistische, mit einem gewissen Grad der Unbestimmtheit behaftete Mittelwerte, und die meisten der geläufigen physikalischen 'Gesetze', namentlich alle, welche die Materie betreffen, nicht als streng gültige Naturgesetze, sondern als statistische Regelmäßigkeiten aufzufassen sind.“

— Hermann Weyl
Philosophie der Mathematik und Naturwissenschaft, München: Oldenbourg Verlag 1927 [= Handbuch der Philosophie, hrsg. von Alfred Baeumler und Manfred Schröter, Teil A], S. 153

Über Ehe, über gesetze

„Ich kann es nun einmal nicht lassen, in diesem Drama von Mathematik und Physik – die sich im Dunkeln befruchten, aber von Angesicht zu Angesicht so gerne einander verkennen und verleugnen – die Rolle des (wie ich genugsam erfuhr, oft unerwünschten) Boten zu spielen.“

— Hermann Weyl
Gruppentheorie und Quantenmechanik, Hirzel, Leipzig 1928, Vorwort

„Die einzig vernünftige Antwort aber auf die Frage: Wie kommt es, daß eine Translation im Äther sich nicht von Ruhe unterscheiden läßt? war die, welche Einstein gab: weil er nicht existiert!“

— Hermann Weyl
Der Äther ist immer eine vage Hypothese geblieben, und noch dazu eine, die sich so schlecht als möglich bewährt hat.

Über Liebe

„Im tatsächlichen Betrieb der physikalischen Forschung spielt heute die Statistik eine ebenso wichtige Rolle wie das strenge Gesetz, sie hat sich immer selbständiger gemacht, und die Versuche, sie auf das Gesetz zurückzuführen, sind allmählich aufgegeben worden. Halten wir uns an die Methodik, wie sie sich aus zwingenden Motiven herausgebildet hat, so müssen wir die statitischen daher als wahrhaft ursprüngliche neben den Gesetzes-Begriffen anerkennen.“

— Hermann Weyl
Philosophie der Mathematik und Naturwissenschaft, München: Oldenbourg Verlag 1927 [= Handbuch der Philosophie, hrsg. von Alfred Baeumler und Manfred Schröter, Teil A], S. 155

Über Gesetze

„Tatsächlich hat nicht nur der Michelsonsche, sondern haben eine ganze Zahl weiterer Versuche, einen Einfluß der Erdbewegung auf kombinierte mechanisch-elektromagnetische Vorgänge festzustellen, ein negatives Ergebnis gehabt. Es wäre also die Aufgabe der Äthermechanik, nicht nur die Maxwellschen Gesetze zu erklären, sondern auch diese merkwürdige Wirkung auf die Materie, die so erfolgt, als hätte der Äther sich ein für allemal vorgenommen: Ihr verflixten Physiker, mich sollt ihr nicht kriegen!“

— Hermann Weyl
Raum, Zeit, Materie - Vorlesungen über Allgemeine Relativitätstheorie, 3. Auflage Springer 1919, S. 144 - Online

Über Krieg, über gesetze

„Einstein's theory of relativity“

— Hermann Weyl
Context: Einstein's theory of relativity has advanced our ideas of the structure of the cosmos a step further. It is as if a wall which separated us from Truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a presentiment. It has brought us much nearer to grasping the plan that underlies all physical happening. From the Author's Preface to First Edition (1918)

„Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.“

— Hermann Weyl
Context: The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space. Ch. 3 "Relativity of Space and Time"

„It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another.“

— Hermann Weyl
Context: It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another. In this interpretation, things of the real world are approximate ideas. From this arises the empirical character of all our knowledge of reality. Introduction

„Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.“

— Hermann Weyl
Context: The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. and certainty Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church... had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico". Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure. Introduction

„Time is the primitive form of the stream of consciousness.“

— Hermann Weyl
Context: Time is the primitive form of the stream of consciousness.... If we project ourselves outside the stream of consciousness and represent its content as an object, it becomes an event happening in time, the separate stages of which stand to one another in the relations of earlier and later. Introduction

„Kant was the first to take the next decisive step“

— Hermann Weyl
Context: In the field of philosophy Kant was the first to take the next decisive step towards the point of view that not only the qualities revealed by the senses, but also space and spatial characteristics have no objective significance in the absolute sense; in other words, that space, too, is only a form of our perception. Introduction

„It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought“

— Hermann Weyl
Context: It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought, a study which is dear to my heart. This could be done only by building up the theory systematically from the foundations, and by restricting attention throughout to the principles. But I have not been able to satisfy these self-imposed requirements: the mathematician predominates at the expense of the philosopher. From the Author's Preface to First Edition (1918)

„It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.“

— Hermann Weyl
Context: Space and time are commonly regarded as the forms of existence of the real world, matter as its substance. A definite portion of matter occupies a definite part of space at a definite moment of time. It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship. Introduction

„A new development began for relativity theory after 1925 with its absorption into quantum physics. The first great success was scored by Dirac's quantum mechanical equations of the electron, which introduced a new sort of quantities, the spinors, besides the vectors and tensors into our physical theories.... But difficulties of the gravest kind turned up when one passed from one electron or photon to the interaction among an indeterminate number of such particles. In spite of several advances a final solution of this problem is not yet in sight and may well require a deep modification of the foundation of quantum mechanics, such as would account in the same basic manner for the elementary electric charge e as relativity theory and our present quantum mechanics account for c and h.“

— Hermann Weyl
Preface to the First American Printing (1950) Note: see Paul Dirac, The Principles of Quantum Mechanics (1947)

„In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.“

— Hermann Weyl
Weyl, Hermann. Invariants. Duke Math. J. 5 (1939), no. 3, 489--502. doi:10.1215/S0012-7094-39-00540-5. http://projecteuclid.org/euclid.dmj/1077491405.

„It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum.“

— Hermann Weyl
Riemanns geometrische Ideen, ihre Auswirkungen und ihre Verknüpfung mit der Gruppentheorie (1925), as quoted/translated by Erhard Scholz, "Philosophy as a Cultural Resource and Medium of Reflection for Hermann Weyl" (2004)

Zitate von Hermann Weyl

Hermann Weyl

Zitate Hermann Weyl

„Ich kann es nun einmal nicht lassen, in diesem Drama von Mathematik und Physik – die sich im Dunkeln befruchten, aber von Angesicht zu Angesicht so gerne einander verkennen und verleugnen – die Rolle des (wie ich genugsam erfuhr, oft unerwünschten) Boten zu spielen.“

„Die einzig vernünftige Antwort aber auf die Frage: Wie kommt es, daß eine Translation im Äther sich nicht von Ruhe unterscheiden läßt? war die, welche Einstein gab: weil er nicht existiert!“

„Einstein's theory of relativity“

„Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.“

„It is the nature of a real thing to be inexhaustible in content; we can get an ever deeper insight into this content by the continual addition of new experiences, partly in apparent contradiction, by bringing them into harmony with one another.“

„Time is the primitive form of the stream of consciousness.“

„Kant was the first to take the next decisive step“

„It was my wish to present this great subject as an illustration of the itermingling of philosophical, mathematical, and physical thought“

„It is in the composite idea of motion that these three fundamental conceptions enter into intimate relationship.“

„In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.“

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