How to increase my concentration and focus?. Please give me tips or useful research materials so that I may use it in studying. Thank you very much for your kind patience.
maths bros, I have an idea
to show intuitively that irrational numbers is pure bullshit, what if we made a small video game where we would drive a car or something, and the goal would be to chase an irrational numbers, say PI
the idea is that "advancing the car" would be automatic, but that instead of going forward, we would go further and further "down" the REAL line, toward the infinitessimal.
We would converge further and further of PI, but would never attain it, because we can't.
The "movement" "down" the real line would correspond to Dedekind cut or something, so this why we could never arrive.
The further we go, the more obstacles there will be, which will inevitably entrave us, and thus, make us fail in our quest to reach the unreachably irrational pi.
do northern grasses (scotland etc) grow slowly? Are there any examples of northern grasses that grow very fast?
I ask because my lawn has two different types of grasses. One is thin like paper and the blades are broad, the other is more like a tiny straw, and the blades are thin (although it has a thicker cross section area)
The first type grows very fast in the summer, the second doesn't. The first one turns white in the winter (dormant), the second stays green. The first one also has a lighter green color, the second is darker.
It seems like the second type of grass is somehow "winter adapted". The dark color means it absorbs more light (useful in north latitudes). The slow growth means it's not adapted to take advantage of a rich sunny climate. And it stays green all year long so it can take advantage of light energy even when it's cold.
>at the age of six or seven Kurt suffered from rheumatic fever; he completely recovered, but for the rest of his life he remained convinced that his heart had suffered permanent damage. >He developed paranoid symptoms, including a fear of being poisoned, and spent several months in a sanitarium for nervous diseases >Gödel had confided in them that he had discovered an inconsistency in the U.S. Constitution that could allow the U.S. to become a dictatorship >He studied and admired the works of Gottfried Leibniz, but came to believe that a hostile conspiracy had caused some of Leibniz's works to be suppressed >Later in his life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would eat only food that his wife, Adele, prepared for him. Late in 1977, she was hospitalized for six months and could no longer prepare her husband's food. In her absence, he refused to eat, eventually starving to death >Gödel was a convinced theist, in the Christian tradition
