Source: WSJ, Apr 2017
Source: Fast Company. Apr 2017
If you want to become more creative, the answer may lie in becoming more courageous.
The Improvisational Leadership class is designed to expose students to new experiences, making them more creative by expanding their frames of reference. The class is 100% experiential, with no tests, textbook, or papers. Creativity can be learned, but not through lectures or reading, says Cook. “It has to be learned through doing,” he says.
And that can take a nudge. Each week, Cook, chairman of the global PR firm Golin and author of Improvise: Unorthodox Career Advice from an Unlikely CEO, challenges students to push their personal limits by trying new things.
“Trying new things gives you the courage you need to experiment with your life and not be worried about whether or not you fail,” says Cook.
In another exercise, students pulled a topic out of a hat and were given five minutes to prepare a presentation that positions them as an expert. “The idea is that you’re sometimes not given much time to prepare for something, and you have to sound knowledgeable and confident,” says Cook. “These real-life skills and experiences help you think on your feet.”
And in another, students must negotiate something. “They’re often very nervous about asking for something, but people respect you for negotiating,” says Cook. “They expect and respect it, especially when you’re standing up for your values.”
“What surprised me most was how much life opens up when you’re willing to get out of your comfort zone,” she says. “You never know where a door leads, and you can only find out if you go through it,” she says.
Becoming courageous and creative doesn’t happen overnight, says Cook. “It builds up a little at a time by doing new things and trying things you’ve never done before,” he says. “Every little step pushes you out of your comfort zone. I’ve seen students do things they never thought they could do before. They’re nervous, but they do it because it’s an assignment. The next time is easier. The goal is to become more creative, courageous leaders.”
Source: Gizmodo, Oct 2013
I. J. Good happened to invent the idea of an intelligence explosion, and if it really was possible. The intelligence explosion was the ﬁrst big link in the idea chain that gave birth to the Singularity hypothesis.
In the 1965 paper “Speculations Concerning the First Ultra-intelligent Machine,” Good laid out a simple and elegant proof that’s rarely left out of discussions of artiﬁcial intelligence and the Singularity:
Let an ultraintelligent machine be deﬁned as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion,” and the intelligence of man would be left far behind. Thus the ﬁrst ultraintelligent machine is the last invention that man need ever make . . .
Thus the ﬁrst ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control (emphasis mine).
In a 1996 interview with statistician and former pupil David L. Banks, Good revealed that he was moved to write his essay after delving into artiﬁcial neural networks. Called ANNs, they are a computational model that mimics the activity of the human brain’s networks of neurons. Upon stimulation, neurons in the brain ﬁre, sending on a signal to other neurons. That signal can encode a memory or lead to an action, or both. Good had read a 1949 book by psychologist Donald Hebb that proposed that the behavior of neurons could be mathematically simulated.
In 1998, Good was given the Computer Pioneer Award of the IEEE (Institute of Electrical and Electronics Engineers) Computer Society. He was eighty-two years old. As part of his acceptance speech he was asked to provide a biography. He submitted it, but he did not read it aloud, nor did anyone else, during the ceremony. Probably only Pendleton knew it existed.
[The paper] “Speculations Concerning the First Ultra-intelligent Machine” (1965) . . . began:
“The survival of man depends on the early construction of an ultra-intelligent machine.” Those were his [Good’s] words during the Cold War, and he now suspects that “survival” should be replaced by “extinction.” He thinks that, because of international competition, we cannot prevent the machines from taking over. He thinks we are lemmings. He said also that “probably Man will construct the deus ex machina in his own image.”
Source: American Mathematical Monthly, Jan 2003
When he received his doctoral degree in 1866, Georg Cantor (1845-1918) followed the custom of the day by defending certain theses that he had advanced. (Hilbert was four years old at the time.) The third of these reads [9, p. 8]: “In mathematics the art of asking questions is more valuable than solving problems.”
Indeed, it is precisely by the identification of concrete problems that mathematics has been able to and will continue to develop. That is the deeper reason why Hilbert took the risk of offering a list of unsolved problems.
For the axiomatization of a theory one needs its completion. On the other hand, for the development of a mathematical theory, one needs problems. In addition to the completion of a theory, Hilbert insisted on problems and therefore on the development of a theory. In other words, Hilbert was not at all the pure formalist he is often taken to be.
In Hilbert’s formalistic view, mathematics is to be replaced by mechanical derivations of formulas, without any reasoning concerning their specific content. Recall the words of Griffith [32, p. 3]:
“A mathematical proof is a formal and logical line of reasoning that begins with a set of axioms and moves through logical steps to a conclusion …. A proof confirms truth for the mathematics.” In such a formal system, in proof theory, the subject of research is the mathematical proof itself [48, p. 413], [58:3, p. 155]. To master this subject (in the object language), one must control the field of proofs (in a metalanguage).
How many proofs do mathematicians publish each year? A back of-the-envelope calculation yields a rough approximation: multiplying the number of journals by the number of yearly issues by the number of papers per issue by the average number of theorems per paper, someone has arrived at an estimated lower bound of two hundred thousand theorems a year!
“Simplicity … is simplicity of ideas, not simplicity of a mechanical sort that can be measured by counting equations or symbols,” declared the Nobel Laureate physicist Steven Weinberg
Hilbert’s twenty-fourth problem is a mathematical problem that was not published as part of the list of twenty-three problems known as Hilbert’s problems but was included in David Hilbert‘s original notes. The problem asks for a criterion of simplicity in mathematical proofs and the development of a proof theory with the power to prove that a given proof is the simplest possible.
The 24th problem in my Paris lecture was to be: Criteria of simplicity, or proof of the greatest simplicity of certain proofs. Develop a theory of the method of proof in mathematics in general. Under a given set of conditions there can be but one simplest proof.