Thursday, April 27, 2017

Number Theory

Asking why:
Douge Clarke - (1:20): "What are you doing? Why are you doing it? How is it helping?"
Carene Umubyeyi - (0:10): "One of the most important things to do as a critical thinker is to question everything." (0:34): "The process of using what you know to be generally true in order to make an inference about something specific." (1:10): "First, you note down your givens, your observations, things you can see from the problem. Second, you reason using deductive reasoning, using general statements to infer specifics. And thirdly, you reach your evidence based conclusion." (3:52): "It is crucial to ask why. Ask the reasoning behind the concept."

Alan Dove - (2:43): "The point is that science and only science lets us find facts that are true for everybody, everywhere." (3:20): "It doesn't matter what country you're in, what language you speak, or what religion you are. You can reproduce the result. In fact (and this is a really important point), it will work even if you don't believe it will. You can deny Newton's laws until you are blue in the face. Gravity will still apply to you. Science gives us facts. Statements about the world that are true for everyone."
Steven Strogatz - (22:23): "If you are pure [mathematician], you are mathematician as poet. That is, you love your own subject and you're looking inward. You want to understand the structure of math itself with no reference to the outside world." (29:02): "All these people were simultaneously scientists and mathematicians and engineers. And it's a 20th century conceit - well, maybe because of the age of specialization - that we're only one at a time. But, to me, I'm a mathematician who's really interested in science, as well as the arts, honestly, and humanities. So I don't really like those distinctions." (29:47): "She doesn't really care what medium she's in. It could be painting, it could be sculpture, it could be charcoal. But she's interested in solving a problem. That is, she has some artistic thing in her head she wants to express. And then she thinks about what medium will help her best express it." (50:33): "Math is a language. But it's much more than a language. And it's because we don't have a word for what it is." (51:46): "So it is a language. But it's a language with an incredibly powerful machine built inside of it." (52:13): "It's not just a language. It's a language that let's you predict the future." (52:37): "It's more like math is the operating system of the universe."

Sustainability, adaptability, modern learning, and application:
Adam Bly - (1:55): "Science is butressed by it's instability. It's in fact the ability for science to be overturned and constantly proved wrong and for theories to only last as good as they are, until someone comes along and overturns them, that gives it one of its greatest sources of stability."'
Conrad Wolfram -  (4:05): "The first step is posing the right question. If you ask the wrong question about a situation, you're almost always going to get the wrong answer." (7:47): "Well one of the things they say is 'You need to get the basics first.' I think what they mean by this is you have to work stuff out on paper before you do it on a computer. But you really got to ask 'basics of what exactly?'  Are the basics of learning how to drive a car learning how to service it, or engineer it for that matter? Are the basics of photography today loading a film into your camera or coating a plate with chemicals? I don't think so. I think those are the machinery of the moment."  (9:08): "Just because paper was invented before computers, it doesn't mean it gets you closer to the basics of the subject." (9:40): "What we should be doing is problem-centric mathematics... They should be problems that the kids involved, or the adults for that matter, are keen to solve at that point, that they find interesting." (10:40): "So you can actually use the computer to experience some of the things that you're interested in." (11:28): "If you use computers correctly to do the calculation you can do much harder problems, you can go further, you can get people more experience. That's the crucial thing." (13:23): "Programming allows you to write down your understanding of the subject. And of course the great advantage is that you can then run the program and actually do things with it. So programming is a crucial part of early maths education. It should be part of primary maths education, just as a way to express oneself." (13:40): "I'm arguing for a mathematics that is both more practical and more conceptual. The thing that is exciting at the moment is that we don't have to choose. The mathematics of the real world is far more intellectual and conceptual than the mathematics we're teaching right now. By mimicking the real world, we will improve both practical use and conceptual understanding." (20:19): "There's also the ability to use real data. Actually pull in real examples from the world. Don't do statistics with five data points. Do it with 10,000 real data points that came in yesterday from the financial markets. That's the kind of thing we can do with modern computing environment."

And of Course Neil deGrasse Tyson, modern day science's PR man, came up multiple times in the search:

Neil deGrasse Tyson - (0:22): "We look up and say, I wonder what that is. Let me go find out. Let me poke it. Let me turn it around.
Neil deGrasse Tyson - (1:44): "At some point, you have to step away from the exam and say 'I have a new thought that no one has had before. And it's not a thought that you told me to regurgitate on this exam that you just wrote.' "  (3:03): "The success of those people is not measured by how they performed on the exam that you wrote as a professor. Because they are thinking in ways that you have yet to think. Because they're inventing tomorrow." (4:02): "The system of education rewards high GPA. But the system of life rewards tenacity. Rewards your urge to tackle something you've never seen before. And even if you don't succeed, in that tenacity, to have the energy to go back and try it again. Knowing how to fail."
Neil deGrasse Tyson - (3:33): "If you're an employer and two candidates come up looking for a job. And you're interviewing the two candidates. And you say 'For part of this interview I just want to ask you what's the height of the spire on this building that we're in? ' And the candidate says 'Oh, I was an architect. I majored in architecture for a while and I memorized the heights of all the buildings on campus. I know the height of that spire is 150 feet. In fact, 155 feet tall.' Turns out that's the right answer. And the person came up with it in seconds. That person goes away. The next candidate walks in. 'Do you know the height of the spire?' The candidate says 'No, but I'll be right back.' Person runs outside. Measures the length of the shadow of that spire on the ground. Measures the length of his or her own shadow. Ratios the height to the shadows. Comes up with a number. Runs back inside. 'It's about 150 feet.' Who are you gonna hire? I'm hiring the person who figured it out. Even though it took that person longer. Even though the person's answer is not as precise. I'm hiring that person. Cuz that person knows how to use the mind in a way not previously engaged. You realize when you know how to think, it empowers you far beyond those who know only what to think.