In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.
Shiing-Shen ChernRelated topics
concerning connection curvature example fact infinitesimal metric parallelism preserving product result salient scalar tangent transportation riemannianRelated quotes
It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another.
Freeman Dyson
The growth and maintenance of new synaptic terminals makes memory persist. ...The ability to grow new synaptic connections as a result of experience appears to have been conserved throughout evolution. As an example... the cortical maps of the body surface are subject to constant modification in response to changing input from sensory pathways.
Eric Kandel
A host of positive psychological changes inevitably will result from widespread economic security. The dignity of the individual will flourish when the decisions concerning his life are in his own hands, when he has the means to seek self-improvement. Personal conflicts among husbands, wives and children will diminish when the unjust measurement of human worth on the scale of dollars is eliminated.
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It is much more accurate to identify the factors of production as know-how (that is genetic information structure), energy, and materials, for, as we have seen, all processes of production involve the direction of energy by some know-how structure toward the selection, transportation, and transformation of materials into the product.
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There are in fact four very significant stumbling blocks in the way of grasping the truth, which hinder every man however learned, and scarcely allow anyone to win a clear title to wisdom, namely, the example of weak and unworthy authority, longstanding custom, the feeling of the ignorant crowd, and the hiding of our own ignorance while making a display of our apparent knowledge.
Roger Bacon
