Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.
Lord KelvinRead
Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress.
Interpretation
Simplifying proofs shows knowledge growth and readiness for future advancements.
Lord Kelvin's quote emphasizes that as we deepen our understanding of a subject, simplifying the methods of proof not only reflects our advanced knowledge but also indicates that we are prepared to make further progress in that area. This highlights the interplay between clarity in thought and the ability to push the boundaries of knowledge.
In practice
In a lecture about scientific methods, one could use this quote to illustrate the importance of clarity in research.
Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.
We only know God in His works, but we are forced by science to admit and to believe with absolute confidence in a Directive Power-in an influence other than physical, or dynamical, or electrical forces.
In science there is only physics; all the rest is stamp collecting.
There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.
Let nobody be afraid of true freedom of thought. Let us be free in thought and criticism; but, with freedom, we are bound to come to the conclusion that science is not antagonistic to religion, but a help to it.
I need scarcely say that the beginning and maintenance of life on earth is absolutely and infinitely beyond the range of all sound speculation in dynamical science. The only contribution of dynamics to theoretical biology is absolute negation of automatic commencement or automatic maintenance of life.
Our only chance of long-term survival is not to remain lurking on planet Earth, but to spread out into space.
The universe will finally become a ball of radiation, becoming more and more rarified and passing into longer and longer wave-lengths. The longest waves of radiation are Hertzian waves of the kind used in broadcasting. About every 1500 million years this ball of radio waves will double in diameter; and it will go on expanding in geometrical progression for ever. Perhaps then I may describe the end of the physical world as-one stupendous broadcast.
The laws of physics ... seem to be the product of exceedingly ingenious design... The universe must have a purpose.
Not only is science corrosive to religion, but religion is corrosive to science. It teaches people to be satisfied with trivial non-explanations and blinds them to the wonderful real explanations that we have within our grasp.
Psychology, as the behaviorist views it, is a purely objective, experimental branch of natural science which needs introspection as little as do the sciences of chemistry and physics.... The position is taken here that the behavior of man and the behavior of animals must be considered in the same plane.
The human race has a yearning to explore. That's part of our biological and psychological makeup.
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