After years of finding mathematics easy, I finally reached integral calculus and came up against a barrier. I realized that this was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way.
Interpretation
This quote reflects the struggle and limitations one may face in learning complex subjects like mathematics.
Isaac Asimov shares his experience of encountering a significant challenge in his study of mathematics, specifically integral calculus. Despite previously finding mathematical concepts accessible, he reached a point where he recognized the limits of his understanding, illustrating that even for those who excel in certain areas, there can be hurdles that signify the end of their mastery in a subject.
In practice
In a classroom setting when discussing the challenges of learning new subjects.
Democracy cannot survive overpopulation. Human dignity cannot survive it. Convenience and decency cannot survive it. As you put more and more people into the world, the value of life not only declines, but it disappears. It doesn't matter if someone dies.
Science does not promise absolute truth, nor does it consider that such a thing necessarily exists. Science does not even promise that everything in the Universe is amenable to the scientific process.
Democracy cannot survive overpopulation.
Although the time of death is approaching me, I am not afraid of dying and going to Hell or (what would be considerably worse) going to the popularized version of Heaven. I expect death to be nothingness and, for removing me from all possible fears of death, I am thankful to atheism.
A subtle thought that is in error may yet give rise to fruitful inquiry that can establish truths of great value.
During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But by 1800, this had become entirely impracticable.
Let the American youth never forget, that they possess a noble inheritance, bought by the toils, and sufferings, and blood of their ancestors; and capacity, if wisely improved, and faithfully guarded, of transmitting to their latest posterity all the substantial blessings of life, the peaceful enjoyment of liberty, property, religion, and independence.
For the speedy reader paragraphs become a country the eye flies over looking for landmarks, reference points, airports, restrooms, passages of sex.
I much prefer working with kids whose life could be completely upended by a reading of a book over a weekend. You give them a book to read - they go home and come back a changed person. And that is so much more interesting and exciting.
The more you read, the more you will write. The better the stuff you read, the better the stuff you will write.
I cannot read a single word of the Hindoos without being elevated.
Therefore, teaching, talk and tale, however lucid or fascinating, effect nothing until self-activity be set up; that is, self-education is the only possible education; the rest is mere veneer laid on the surface of a child's nature.
Subscribe for the occasional hand-picked quote. No noise.