Thursday, October 1, 2020

 Yaunwu said:

"Leaders make the knowledge of the community their knowledge, they make the minds of the community their mind. They are always wary of failing to comprehend the feelings of even one person, or failing to understand the principle of even one thing. 

Leaders should seek only what is good, diligently striving to seek and take advice. They should question right and wrong in principle regardless of whether the matter is great or small. If the principle is right, even thought it involves great expense to carry it out, what is the harm? If the thing is wrong, even though it is a small measure to get rid of it, what is the loss?

The small is a step of the great, the subtle is a sprout of the obvious. This is why the wise are careful of the beginning, sages are mindful of warnings. Even dripping water, if it does not stop, can ultimately turn a mulberry orchard into a lake. A flame, if not removed, will ultimately burn a meadow. 

When the water is streaming and the fire is raging, the disaster is already happening--even if you want to help, there is no way. Of old it has been said, 'If you are not careful about minor actions, ultimately they will encumber great virtue.' This is what is meant here."

Tuesday, September 29, 2020

 "Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler's fallacy. For example, if Kerrich landed, say 44 heads in the first 100 tosses, the coin would not develop a bias towards the tails in order to catch up! That's what is at the root of such ideas as 'Her luck has run out' and 'He is due.' That does not happen. For what it's worth, a good streak doesn't jinx you, and a bad one, unfortunately, does not mean better luck is in store."

Leonard Mlodinow, The Drunkard's Walk, 2008

Monday, September 28, 2020

 "I think scientists have a valid point when  they bemoan the fact that it's socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate." Jennifer Duelette The Calculus Diaries, 2010

Friday, September 25, 2020

"If God were infinity, then divergent series would be His angels flying higher and higher to reach him. Given an eternity, all such angels approach their Creator. For example, consider the following infinite series: 1+2+3+4+... If we add one term of the series each year, in four years the sum would be 10. Eventually, after an infinite number of years, the sum reaches infinity. 

Consider the harmonic series, the first famous example of a divergent series whose terms approach zero: 1+1/2+1/3+1/4+... Of course, this series explodes much more slowly than does the previous example, but it still grows to infinity. In fact, it it grows so incredibly slowly that if we added a term a year, in 10^43 years, we'd have a sum of less than 100. William Dunham writes, '...by adding ever more negligible terms, we nonetheless reach a sum greater than any preassigned quality.'

Jacob Bernoulli published a proof in his 1689 work Tractatus de Seriebus Infinitis, which he closes with: 'So the  soul of immensity dwells in minutia. And its narrowest limits no limits inhere. What joy to discern the minute in infinity! The vast to perceive in the small, what divinity!'"

From The Math Book by Clifford A. Pickover

Wednesday, September 23, 2020

Said of Saint Catharine of Genoa in William James' The Varieties of Religous Experience

"She took cognizance of things, only as they were presented to her in succession, MOMENT BY MOMENT." To her holy soul, "the divine moment was the present moment, ... and when the present moment was estimated in itself and in its relations, and when the duty that was involved in it was accomplished, it was permitted to pass away as if it had never been, and to give way to the facts and duties of the moment which came after."

Friday, September 18, 2020

 Lingyuan quoted a grandee:

"Birds fly away on seeing men of foreboding countenance, and gather after flying beyond the range of arrows. So it is with Master Yuan."

Lingyuan also quoted Master Yuan as saying:

"If you have a good field, why worry that it will mature late? The only thing to fear is lack of ability and equipment."

Wednesday, September 16, 2020

 "I don't believe that math and nature respond to democracy. Just because very clever people have rejected the role of the infinite, their collective opinions, however weighty, won't persuade mother nature to alter her ways. Nature is never wrong." Janna Levin