Sciences

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (There are 25 prime numbers below 100.)

2, 3, 5, 13, 89, 233, 1597, 28657, 514229, and 433494437.  (Fibonacci Primes, numbers that are BOTH Fibonacci and Prime. There are only 10 of these less than 1 billion. )

Numbers seem simple, and they represent order. We can see nature through numbers, but numbers themselves already create astonishment: 111,111,111 x 111,111,111 = 12,345,678,987,654,321. 

1. 1. The essence of mathematics is never in the particular way it is represented, but in the concept that it brings forth, and the unification of particulars that it embodies. One might hypothesize that any mathematical system will find natural realizations. This is not the same as saying that the mathematics itself is realized. The point of an abstraction is that it is not, as an abstraction, realized. The set { { }, { { } } } has 2 elements, but it is not the number 2. The number 2 is nowhere “in the world”. ~ Louis Kauffman

   2. It is not the victory of science that distinguishes our nineteenth century, but the victory of scientific method over science. Nietzsche, The Will to Power

   3. Georg Cantor: The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though in its highest form it has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds. 

   4. "Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of the mystery that we are trying to solve." ~ Max Planck

   5. Roger Penrose, (from The Road to Reality): “… no one, not even Benoit Mandelbrot himself [...] had any real preconception of the set’s extraordinary richness. The Mandelbrot set was certainly no invention of any human mind. The set is just objectively there in the mathematics itself. If it has meaning to assign an actual existence to the Mandelbrot set, then that existence is not within our mind, for no one can fully comprehend the set’s endless variety and unlimited complication.”

   6. “The past tells us who we are, without it, we lose our identity.”  ” Stephen Hawking

   7. We had this old idea, that there was a universe out there, and here is man, the observer, safely protected from the universe by a six-inch slab of plate glass. Now we learn from the quantum world that even to observe so minuscule an object as an electron we have to shatter the plate glass; we have to reach in there…. John Wheeler, A Question of Physics. 

   8. "Science, understood as the discoverer of absolute truth, remains therefore, naturally, a source of disillusion for its lack of absolute truths. If the cold marble idol of a perfect, eternal and universal science that we could only seek to better understand falls and shatters, it is there that suddenly alongside it we find a living creature, a science that our thought freely creates. A living entity: flesh of our flesh, the fruit of our torment, our companion in the struggle . . ." ~ Bruno de Finetti 

   9. “I cannot resist the formation of a hypothesis for every subject. But no matter how good I think any hypothesis is, I must not fall in love with it, for it may show itself to be contrary to the facts.” --- Charles Darwin 

   10. 'The problem is that scientists are supposed to know, but they do not. Science is helpless and covers up this helplessness with a deceptive screen of expert assurance.' Žižek, Slavoj. 'Joe Public v the volcano.' in: New Statesman. April 29, 2010. (English).

   11. It is easier to perceive error than to find truth, for the former lies on the surface and is easily seen, while the latter lies in the depth, where few are willing to search for it. ~ (Johann Wolfgang von Goethe, MuR, §166)