## Profile

Dan Christensen
Works at University of Western Ontario, London, Canada
Attended Massachusetts Institute of Technology
10,035 followers|322,993 views

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### Dan Christensen

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Not only does Mike Bostock's web page provide a great visual introduction to various algorithms, the source code to that web page provides a great introduction to producing beautiful animations using javascript and d3js.

Visualising Algorithms
by +Mike Bostock

If you haven't seen it elsewhere in this comprehensive article Mike Bostock explains the value of using our highly evolved visualisation skills to augment our intellect and evaluate and debug algorithms.  In doing so he delights the reader with numerous fascinating animations, code, images and so many related mathematical, visualisation and programming rabbit holes that it looks like Fibonacci's rabbits (http://goo.gl/bzyRI1) have been here.

Algorithms are a fascinating use case for visualization. To visualize an algorithm, we don’t merely fit data to a chart; there is no primary dataset. Instead there are logical rules that describe behavior. This may be why algorithm visualizations are so unusual, as designers experiment with novel forms to better communicate. This is reason enough to study them.

But algorithms are also a reminder that visualization is more than a tool for finding patterns in data. Visualization leverages the human visual system to augment human intellect: we can use it to better understand these important abstract processes, and perhaps other things, too.

Sampling

Shuffling

Sorting

Maze Generation

Using Vision to Think

Related Work

More here: http://goo.gl/sTNLFf

Image: Retinal Microscopy http://goo.gl/v2DMVB here http://goo.gl/O52N1Q﻿
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Nice﻿

### Dan Christensen

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An easy to use python interface to the POV-ray ray tracing software allows you to generate beautiful images and animations with a small amount of code.
This post presents Vapory, a library I wrote to bring POV-Ray’s 3D rendering capabilities to Python. POV-ray is a popular 3D rendering software which …
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I found it feeling so massing in Google webpage not sure which ways to prevent or get to know people or which cold shear﻿

### Dan Christensen

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Much better than the original!

Casey Fiesler replaced the text in this stupid book so it's not completely demeaning.

From Fiesler's description:

The problematic part is that, as far as I can tell, the steps for becoming a computer engineer if you’re Barbie are:

- Design a videogame.
- Get a boy to code it for you.
- Accidentally infect your computer with a virus.
- Get a boy to fix it for you.
- Take all the credit for these things yourself.

And the problem isn’t even that Barbie isn’t a “real” computer scientist because she isn’t coding. ﻿
I am a PhD student in a computing department, so I guess it's not surprising that my social media feeds have been full of outrage over Barbie's "computer engineering" skills. The blog post that originally went viral appears to be sporadically down due to heavy traffic, but The Daily Dot also has a good summary…
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I am sure He-Man would need help with coding, too. ﻿

### Dan Christensen

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David Mumford has a great description of how you can directly relate the low zeros of the Riemann zeta function to the distribution of small prime numbers.

http://www.dam.brown.edu/people/mumford/blog/2014/RiemannZeta.html

He also mentions a book that Barry Mazur and  are writing called "What is Riemann's Hypothesis", which looks like an excellent introduction to the topic for people who aren't afraid of a bit of mathematics.  A draft is freely available here:

http://wstein.org/rh/

It contains lots of beautiful graphs.﻿
Barry Mazur and William Stein are writing an excellent book entitled What is Riemann's Hypothesis? The book leads up to Riemann's 'explicit formula' which, in von Mangoldt's form, is the formula for the discrete distribution supported at the prime powers:  \sum_{\text{primes }p} \sum_{n \ge 1} ...
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### Dan Christensen

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Interesting information about the techniques Snowden and journalists used to communicate securely.

"Micah," the email read, "I'm a friend. I need to get information securely to Laura Poitras."
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What is this jaff

﻿

### Dan Christensen

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There are five elementary problems on this list.  Knowing Conway, the $1000 reward will probably come in a box that you have to spin and tap appropriately to open... [...] John Conway is offering$1,000 for solutions (either positive or negative) to any of the  following problems. If you solve one of these, you can reach him by sending snail mail  (only) in care of the Department of Mathematics at Princeton University.

Problem 1.  ‘Sylver’ coinage game (named after Sylvester, who proved it  terminates):

The game in which the players alternately name positive integers that are not sums of  previously named integers (with repetitions being allowed). The person who names 1  (so ending the game) is the loser. The question is: If player 1 names ‘16’, and both players play optimally thereafter, then  who wins? [...]﻿
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### Dan Christensen

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Great simulations illustrating how mild individual preferences can lead to segregation.

"Parable of the Polygons" is a playable post on how harmless choices can make a harmful world.﻿
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The number theory behind why you can't have both perfect fifths and perfect octaves on a piano keyboard. There's a lot more where this comes from, related to lattice theory and diophantine approximation; see for instance https://en.wikipedia.org/wiki/Fokker_periodicity_block﻿
The integers are a unique factorization domain, so we can’t tune pianos. That is the saddest thing I know about the integers. I talked to a Girl ...
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I was wrong to say it has nothing to do with it; if we have a UFD with at least two primes, then problems like this arise.﻿

### Dan Christensen

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A great animation and a great description of the accomplishment!

Yesterday, the Philae lander successfully landed on a comet. (You can follow its landing as live-cartooned by  at xkcd1446.org) It's a little bit hard to understand just how insane a task that was, so let me try to give you a bit of context.

First, there's the  problem of simply getting there. Comet 67P is about 4km across on its long side, and the Rosetta mission had to travel about 6.4 billion kilometers in order to reach it. For a sense of scale, this is sort of like being able to throw a rock to the other end of a football field and correctly hit the leftmost edge of a particular red blood cell. Not the center, mind you, but a particular dot on its surface.

But a flight like this isn't a simple throw, and the animation below shows you why. To efficiently get out to distant parts of the solar system requires a manoeuver called a "gravitational assist," or a "slingshot." It turns out that if you fly close by an object that's pulling you in with gravity, and you fire your engines hard and forward just as you're at the closest point, you get a much bigger speed boost than you would if you fired your engines at any other time. So interplanetary flight paths will often do things like boost into an orbit around the Sun, swing back around some other convenient planet -- sometimes the Earth, sometimes Venus, sometimes Mars -- and use it to speed up. More complicated flight paths might do more than one swing. Rosetta did four gravitational assists, flew close enough to two asteroids to take pictures, and then pulled into orbit around a comet. This had to basically be planned out from the beginning, and re-planned hastily when the original launch window slipped: it turns out that a many planet-route that you plan on one day isn't much use on a different day.

Once it encountered the comet, Rosetta put itself into orbit around it, and dropped the Philae lander. Landing was an even more interesting challenge, because comets lack the one thing that we most often use to land, namely gravity. On Earth or Mars or the Moon, if a lander drops, it will generally go "thud," and your biggest problem is not going "thud" very quickly and being smashed to bits. On a comet, if a lander drops, it will generally bounce off and then fly back into space. Worse, you can't assume that you can just hit hard and embed yourself in the surface of the comet: we had no idea what surface we would be landing on, whether it be nearly-impenetrable rock, gravel, ice, dust, level, sloped, cratered, or something completely different.

So Philae's landing plan had a few steps. It would fly up to the comet, then fire harpoons into the surface, while firing a thruster engine to stabilize itself. It would then reel itself in, and fire that thruster to push itself hard towards the surface, and then screw itself down to the rock. The idea was that hopefully one of these would work.

In practice, the one turned out to be the screws, because both the thruster and the harpoons failed to work, for reasons still unknown. But somehow it appears to have landed anyway.

And what do we get for all of this? Our first chance to study a comet from really up close. Comets are made from the matter at the farthest reaches of our Solar System, and carry in them a snapshot of what our solar system was made of in its earliest days.

You can see more about the mission planning here: http://www.esa.int/Our_Activities/Space_Science/Rosetta/The_long_trek  and at http://en.wikipedia.org/wiki/Rosetta_(spacecraft) .
More about Comet 67P at http://en.wikipedia.org/wiki/67P/Churyumov%E2%80%93Gerasimenko .﻿
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### Dan Christensen

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David Mumford has a new blog, and one of his first posts is about understanding Feynman path integrals in a finite-dimensional setting. I had seen a nice treatment of this topic that treats time and space as both being discrete, but this approach treats time as being continuous, and leads to a formula for exp(tH) for any matrix H.

http://www.dam.brown.edu/people/mumford/blog/2014/FeynmanIntegral.html

I can't seem to find an RSS feed for this blog, though...﻿
Like many pure mathematicians, I have been puzzled over the meaning of Feynman's path integrals and put them in the category of weird ideas I wished I understood. This year, reading Folland's excellent book Quantum Field Theory -- A Tourist Guide for Mathematicians, I got a glimmer of what was ...
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Cool!   But it's interesting that Feynman got a blog before Mumford.﻿

### Dan Christensen

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Tor is a network that can forward your data through volunteer relay hosts in a way that lets you avoid internet censorship and hide your online activity from people who may want to monitor you.  Your connection is encrypted, so none of the volunteers can access your data, and your data goes through many relays, so none know the source and destination of the traffic.

It is very easy to access the Tor network for web browsing.  You can download a self-contained browser and Tor client at

https://www.torproject.org/projects/torbrowser.html.en

for Linux, OS X and Windows, and run it directly from the download or a USB key without installing anything.  It comes with a version of firefox that has extra privacy protection.  I got it running in under a minute, and am using it to author this post.

My challenge to you is to do the same and +1 this post through the Tor network!

https://www.torproject.org/﻿
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Have a look at the work by the https://guardianproject.info/﻿

### Dan Christensen

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Facebook now allows direct access through the Tor network, which allows people to avoid internet censorship:

Does Google+ have anything similar?  This message was posted via Tor, but using the standard Google+ website, so my connection has to leave the Tor network before reaching Google.

Via  ﻿
In the battle against Internet censorship, this matters.
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10,035 people
Work
Occupation
Mathematics Professor (Algebraic Topology, Representation Theory and Mathematical Physics)
Employment
• University of Western Ontario, London, Canada
Professor, 2000 - present
• Johns Hopkins University, Baltimore
Assistant Professor, 1997 - 1999
• Institute for Advanced Study, Princeton
Member, 1999 - 2000
Places
Currently
Previously
Lisbon, Portugal - Princeton, NJ - Baltimore, MD - Boston, MA - Waterloo, Ontario - Montreal, Quebec - Zurich, Switzerland - Toronto, Ontario
Other profiles
Story
Tagline
Interested in math, physics, computation and more.
Introduction
Professor of Mathematics at the University of Western Ontario in London, Ontario, Canada.  Interested in mathematics, physics, computation, technology, the outdoors, the environment, and more.

Education
• Massachusetts Institute of Technology
PhD, Mathematics, 1992 - 1997
• University of Waterloo
BMath, Mathematics, 1987 - 1992
• Malvern Collegiate Institute, Toronto
1983 - 1987
Basic Information
Gender
Male
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