It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex.
Freeman DysonRelated topics
algebra appropriate complex course division field ground mechanics numbers quantum real theorem frobeniusRelated quotes
The university is a vast public utility which turns out future workers in today's vineyard, the military-industrial complex. They've got to be processed in the most efficient way to see to it that they have the fewest dissenting opinions, that they have just those characteristics which are wholly incompatible with being an intellectual. This is a real internal psychological contradiction. People have to suppress the very questions which reading books raises.
Mario Savio
We have said that consciousness is an operation rather than a thing, a repository, or a function. It operates by way of analogy, by way of constructing an analog space with an analog ‘I' that can observe that space, and move metaphorically in it. It operates on any reactivity, excerpts relevant aspects, narratizes and conciliates them together in a metaphorical space where such meanings can be manipulated like things in space.
Julian Jaynes
The new paradigm may be called a holistic world view, seeing the world as an integrated whole rather than a dissociated collection of parts. It may also be called an ecological view, if the term "ecological" is used in a much broader and deeper sense than usual. Deep ecological awareness recognizes the fundamental interdependence of all phenomena and the fact that, as individuals and societies we are all embedded in (and ultimately dependent on) the cyclical process of nature.
Fritjof Capra
In this situation, it becomes vital that our own country orient its policies in consonance with this basic evolutionary condition rather than pursue a course blind to the reality that the colonial era is now past and the Asian peoples covet the right to shape their own free destiny. What they seek now is friendly guidance, understanding, and support - not imperious direction - the dignity of equality and not the shame of subjugation.
Douglas MacArthur
Can a physicist visualize an electron? The electron is materially inconceivable and yet, it is so perfectly known through its effects that we use it to illuminate our cities, guide our airlines through the night skies and take the most accurate measurements. What strange rationale makes some physicists accept the inconceivable electrons as real while refusing to accept the reality of a Designer on the ground that they cannot conceive Him?
Wernher von Braun
