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An Interactive Guide To The Fourier Transform

An Interactive Guide To The Fourier Transform
The Fourier Transform is one of deepest insights ever made. Unfortunately, the meaning is buried within dense equations: Yikes. What does the Fourier Transform do? Here's the "math English" version of the above: The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall "cycle recipe" (the strength, offset, & rotation speed for every cycle that was found). Time for the equations? If all goes well, we'll have an aha! This isn't a force-march through the equations, it's the casual stroll I wish I had. From Smoothie to Recipe A math transformation is a change of perspective. The Fourier Transform changes our perspective from consumer to producer, turning What did I see? In other words: given a smoothie, let's find the recipe. Why? So... given a smoothie, how do we find the recipe? Well, imagine you had a few filters lying around: We can reverse-engineer the recipe by filtering each ingredient. Filters must be independent. See The World As Cycles Oh! Related:  Thought

Inceptionism: Going Deeper into Neural Networks Posted by Alexander Mordvintsev, Software Engineer, Christopher Olah, Software Engineering Intern and Mike Tyka, Software EngineerUpdate - 13/07/2015Images in this blog post are licensed by Google Inc. under a Creative Commons Attribution 4.0 International License. However, images based on places by MIT Computer Science and AI Laboratory require additional permissions from MIT for use.Artificial Neural Networks have spurred remarkable recent progress in image classification and speech recognition. But even though these are very useful tools based on well-known mathematical methods, we actually understand surprisingly little of why certain models work and others don’t. So let’s take a look at some simple techniques for peeking inside these networks. So here’s one surprise: neural networks that were trained to discriminate between different kinds of images have quite a bit of the information needed to generate images too. Why is this important?

How to Study and Learn (Part One) All thinking occurs within, and across, disciplines and domains of knowledge and experience, yet few students learn how to think well within those domains. Despite having taken many classes, few are able to think biologically, chemically, geographically, sociologically, anthropologically, historically, artistically, ethically, or philosophically. Students study literature, but do not think in a literary way as a result. They study poetry, but do not think poetically. To study well and learn any subject is to learn how to think with discipline within that subject. To become a skilled learner is to become a self-directed, self-disciplined, self-monitored, and self-corrective thinker, who has given assent to rigorous standards of thought and mindful command of their use. Because we recognize the fact that students generally lack the intellectual skills and discipline to learn independently and deeply, we have designed a Thinker's Guide for Students on How to Study and Learn.

The Art of Learning Summary - Deconstructing Excellence The Art of Learning Summary Josh Waitzkin’s story is a fascinating one, culminating in a book that surpasses any other writing in its insight into how a world champion is made. Everyone in the chess world knew the name Josh Waitzkin by the time he earned the Chess Master designation at the age of twelve, somewhere in the middle of his eight national championship titles. Notoriety in the chess world then morphed into pop culture fame five years later with the movie Searching for Bobby Fischer, which was based on Waitzkin’s life. In seeking an escape from the inner turmoil caused by his child celebrity status, Josh stumbled upon the Tao Te Ching, and was drawn by the Buddhist and Taoist philosophies of inner tranquility. The journey from king of the chess nerds to martial arts legend is astounding in itself, but the real story here is that Josh subsequently accomplished what few have done. Part I: The Foundation Chapter 1: Innocent Moves & Chapter 2: Losing to Win Dr. Part II: My Second Art

geometric double-meanings Jen-chung Chuan Department of Mathematics National Tsing Hua University Hsinchu, Taiwan 300 jcchuan@math.nthu.edu.tw Introduction Why is a geometric figure important? A geometric figure clarifies a theorem, motivates a proof, stimulates the thinking process, sums up a lengthy animation, provides a counterexample to a wild conjecture, or just plainly announces the existence of a significant piece of mathematics. Why is a geometric figure interesting? "Given" and "To Construct" Switched A geometric construction problem has three parts: "Given", "To Construct", and the construction itself. By switching the "Given" and the "To Construct" parts, we see that the picture may have these two interpretations: This tiny example shows that dynamic geometry is at least twice as interesting as the traditional one. The picture carries two messages: Evolute and Involute Involute is the path of a point of a string tautly unwound from the curve. The figure may be interpreted in two ways: Peaucellier Cell

A genius explains | From the Guardian Daniel Tammet is talking. As he talks, he studies my shirt and counts the stitches. Ever since the age of three, when he suffered an epileptic fit, Tammet has been obsessed with counting. Now he is 26, and a mathematical genius who can figure out cube roots quicker than a calculator and recall pi to 22,514 decimal places. Tammet is calculating 377 multiplied by 795. Tammet is a "savant", an individual with an astonishing, extraordinary mental ability. There are many theories about savants. Scans of the brains of autistic savants suggest that the right hemisphere might be compensating for damage in the left hemisphere. Tammet is creating his own language, strongly influenced by the vowel and image-rich languages of northern Europe. Professor Simon Baron-Cohen, director of the Autism Research Centre (ARC) at Cambridge University, is interested in what Mänti might teach us about savant ability. Tammet has never been able to work 9 to 5. He was born on January 31 1979.

List of cognitive biases Cognitive biases are systematic patterns of deviation from norm or rationality in judgment, and are often studied in psychology and behavioral economics.[1] There are also controversies over some of these biases as to whether they count as useless or irrational, or whether they result in useful attitudes or behavior. For example, when getting to know others, people tend to ask leading questions which seem biased towards confirming their assumptions about the person. However, this kind of confirmation bias has also been argued to be an example of social skill: a way to establish a connection with the other person.[8] Although this research overwhelmingly involves human subjects, some findings that demonstrate bias have been found in non-human animals as well. Decision-making, belief, and behavioral biases[edit] Many of these biases affect belief formation, business and economic decisions, and human behavior in general. Social biases[edit] Memory errors and biases[edit] See also[edit] [edit]

Uncertain Certainty: The Nihility Of Knowing... "Last week, I jokingly asked a health club acquaintance whether he would change his mind about his choice for president if presented with sufficient facts that contradicted his present beliefs. He responded with utter confidence. "Absolutely not," he said. "No new facts will change my mind because I know that these facts are correct." I was floored. In the current presidential election, a major percentage of voters are already committed to "their candidate"; new arguments and evidence fall on deaf ears. Perhaps the single academic study most germane to the present election is the 1999 psychology paper by David Dunning and Justin Kruger, "Unskilled and Unaware of It: How Difficulties in Recognizing One's Own Incompetence Lead to Inflated Self-Assessments." On average, participants placed themselves in the 66th percentile, revealing that most of us tend to overestimate our skills somewhat. In other words, we are as bad at judging ourselves as we are at judging others.

Review of 2008: 100 great articles Centre for Learning & Performance Technologies The Library Top down implementation of social learning won't work It's time to encourage people to use public social media tools - not ban them! What is social learning? An explanation using Twitter I was taking a look at all the resources that I had collected during 2008 in my Library as well as those that I had posted about in my blogs, etc, to identify those that I particularly enjoyed, that inspired me, made me think and/or I just found useful. I then fed all the titles into Wordle to generate a word cloud and identify trends in this collection of my favourite resources. Here are the resources listed chronologically by the month in which they appeared. 13 tips for virtual world teaching , Matt Villano, Campus Technology Thanks to YouTube, professors are finding more audiences , Jeffrey R Young, Chronicle of Higher Education Seven strategies for implementing a successful corporate wiki , Brad Kenney, Information Week

The Fermi Paradox: Advanced civilizations do not… This article is partly adapted from my TransVision 2007 presentation, “Whither ET? What the failing search for extraterrestrial intelligence tells us about humanity's future.” As I stated in my previous article, “The Fermi Paradox: Back with a vengeance”: The fact that our Galaxy appears unperturbed is hard to explain. So, let’s try to figure out what’s going on. But rather than describe the possible developmental trajectories of extraterrestrial intelligences (ETI's) (a topic I’ll cover in my next article), I’m going to dismiss some commonly held assumptions about the nature of advanced ETI’s – and by consequence some assumptions about our very own future.Advanced civilizations do not… …advertise their presence to the local community or engage in active efforts to contact As SETI is discovering (but is in denial about), space is not brimming with easily detectable radio signals. This problem is not as simple as it sounds. …colonize the Galaxy …sterilize the Galaxy Finally, some good news.

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