A priori comprehensive judgment-woodmam

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In the careers of great scientists, it was often at a young age that they were exposed to information by chance that inspired their great minds and thus had a major impact on their destinies. In his "Autobiography," Albert Einstein said

  At the age of 12, I experienced another kind of surprise of an entirely different nature: this was experienced at the beginning of a school year when I was given a small book on Euclidean plane geometry. This book contained many assertions, such as that the three heights of a triangle intersect at a point, which in themselves, although not obvious, could be proved so reliably that any doubt seemed impossible. This clarity and reliability created an indescribable impression on me. As for having to admit axioms without proof, this matter did not disturb me. If I could prove them on the basis of propositions whose validity seemed to me to be beyond doubt, then I would be perfectly satisfied. I remember, for example, that before this sacred little book on geometry came into my hands, an uncle had told me about the Pythagorean theorem. After a great effort, I succeeded in "proving" this theorem based on the similarity of triangles. In doing so, I felt that the relationship between the sides of a right triangle was "obviously" determined entirely by one of its acute angles. In my opinion, only what is not "obvious" in a similar way needs to be proved. Moreover, the object of geometric study seems to be the same type of thing as those objects of sensory perception that "can be seen and touched. The origin of this primitive idea is naturally due to the unconscious existence of the relationship between the geometric concept and the object of direct experience, and this primitive idea is probably the basis for Kant's famous question about the possibility of "a priori synthesis".

  At the age of 12-16, I became familiar with basic mathematics, including the principles of calculus. At this time, I was fortunate to have access to books that were not too rigorous in terms of logical rigor, but that highlighted the basic ideas in a clear and simple way. Overall, the study was truly fascinating. It impressed me no less than elementary geometry, culminating several times in the basic ideas of analytic geometry, infinite series, differential and integral concepts. I was also fortunate to know the main results and methods in the whole field of natural sciences from a remarkable popular book, which was almost entirely limited to qualitative accounts, a work that I read with great attention. When I entered the Technical University of Zurich as a student of mathematics and physics at the age of 17, I had already studied some theoretical physics.

  This rather long autobiography is an important source for our understanding of the development of Einstein's scientific ideas. The wonders of thinking that geometry brought to Einstein made it too late for him to follow the steps, and he managed to get to the last page of the Little Book of Sacred Mean Geometry in one sitting.

  In Einstein's first steps into the field of natural science, one person was important, and although it is difficult to say that he had any great influence on Einstein in his thinking, it was he who handed Einstein the first key to the door of the temple of natural science. He was Talmay, the Russian university student who gave Einstein the "Little Book of Sacred Geometry" that he would never forget. At first, Talmeh always talked to Einstein about mathematics, and the more he talked, the more he aroused Einstein's interest in mathematics. Bored with the boring teaching methods at school, Einstein simply taught himself calculus. Talmay, who studied medicine, was soon no longer Einstein's mathematical rival either, but he still enthusiastically introduced Einstein to the various natural science books and Kant's philosophical works that were popular at the time, such as Buchner's Force and Matter and Bernstein's Popular Reader in Natural Science.

  The most effective thing for great minds is often not to directly try to teach them how to learn. What is most helpful is information and resources that will inspire their thinking.

  2. Cultivating the Essentials

  Developing the habit of active learning begins with forming a need to be hungry for learning. Only by forming a hunger and thirst for learning can you actively seek and find learning resources that interest you and actively challenge any learning difficulties.

  Fermi, the 1938 Nobel Prize winner in physics, was a very receptive reader as a child, and the school curriculum could not "feed" him. He went to find "snacks" - extracurricular books to read. The famous open-air market opened every Wednesday at the Parade, where collectors often found antique books, prints, art and all kinds of antiques. Fermi joined the ranks of collectors, and his short head traveled through the square every Wednesday. He collected a lot of "treasures" here, and bought a lot of books on physics.

  One day, Fermi brought back two books on mathematical physics from Hundred Flowers Square, and he told his sister that he would read them right away. When the excitement of reading, he said to himself: "How interesting this book is, you can not imagine at all. I am learning about the propagation of various waves!" "Wonderful, it explains the motion of the planets!" His emotions reached a peak when he read the chapter on the circulation of ocean tides.

  When he finished reading the whole book and came to his sister again, he said, as if he had found a "new world": "Did you know, sister, that this book is written in Latin, which I had not noticed?" My sister shook her head and laughed.

  Fermi's diligence, good learning and motivation deeply touched his neighbor, Professor Amidi. The professor soon saw that the boy was a good "material" and liked Fermi very much.

  Once the professor said half-jokingly, "Fermi, can I give you a few questions?"

  "That's great, come on!" Fermi jumped at the chance.

  The professor knew that the questions were obviously above Fermi's level and did not expect him to answer them all. But to the professor's surprise, in a few moments Fermi had all the answers. He pestered the professor to come up with some more difficult questions to "try"; the professor gave some questions to Fermi that he himself had not yet solved. By some miracle, Fermi was able to solve all of them again! The professor nodded his head in admiration and exclaimed that there was a lot of talent. The professor gave Fermi all his books on physics and mathematics, one by one, in a reasonable order. Fermi was like a fish in water, swimming in the ocean of knowledge consisting of physics and mathematics to his heart's content.

  The careful nurturing and assistance of the old professor Amidi provided Fermi with the opportunity to make his debut in the academic world. At the end of his secondary school, he wrote his thesis "On the vibration of strings". This thesis baffled the professors of the Roman Academy of Engineering who were examining it, unable to explain how such a young Fermi could be so knowledgeable and insightful.

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