A Quote by Georg C. Lichtenberg
All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true.
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The research worker, in his efforts to express the fundamental laws of Nature in mathematical form, should strive mainly for mathematical beauty. He should take simplicity into consideration in a subordinate way to beauty ... It often happens that the requirements of simplicity and beauty are the same, but where they clash, the latter must take precedence.
The beauty to which the Dance ought to aspire is not dependent upon taste or pleasure, but is founded on the immutable laws of Nature.
What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating.
The best laws cannot make a constitution work in spite of morals; morals can turn the worst laws to advantage. That is a commonplace truth, but one to which my studies are always bringing me back. It is the central point in my conception. I see it at the end of all my reflections.
The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.
Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.
When a man and a woman have an overwhelming passion for each other, it seems to me, in spite of such obstacles dividing them as parents or husband, that they belong to each other in the name of Nature, and are lovers by Divine right, in spite of human convention or the laws.
Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework.
If nature leads us to mathematical forms of great simplicity and beauty - by forms I am referring to coherent systems of hypothesis, axioms, etc. - to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature... You must have felt this too: The almost frightening simplicity and wholeness of relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.
Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.
I've spent my life capturing beautiful images. And whether in wilderness or in the downtown of a giant city, I find connections, universal rhythms, patterns and beauty that I recognize as a part of me, a part of all of us that celebrates life. It's my great pleasure to share with you that energy which inspires me; this great visual beauty of our world.
The mere man of pleasure is miserable in old age, and the mere drudge in business is but little better, whereas, natural philosophy, mathematical and mechanical science, are a continual source of tranquil pleasure, and in spite of the gloomy dogmas of priests and of superstition, the study of these things is the true theology; it teaches man to know and admire the Creator, for the principles of science are in the creation, and are unchangeable and of divine origin.
Traditionally, in the Eastern World, man and nature are close: men find happiness and prosperity in the beauty of nature, even if the nature is actually built to match this very need.
You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us.
The refining influence is the study of art, which is the science of beauty; and I find that every man values every scrap of knowledge in art, every observation of his own in it, every hint he has caught from another. For the laws of beauty are the beauty of beauty, and give the mind the same or a higher joy than the sight of it gives the senses. The study of art is of high value to the growth of the intellect.
It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to the understanding of nature ... In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
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