Cellular Automata

Linkdump from today's explorations

This reminded me of Cellular Automata and Conway's game of life.

Post by Olya Petrakova.

There are 128 rules with last digit "1" 000 1 I'll have to experiment, maybe finally learn some processing, to list them all here. While searching differential equations, I found an interesting discussion about why the Navier Stokes equation is so difficult. This fits nicely into the blog post yesterday about equations. http://physics.stackexchange.com/questions/56496/what-is-the-mystery-of-turbulence/66917#66917 The solution to the equation is an open question in mathematics and you can read a very precise (2 page) description of it here: http://www.claymath.org/millenium-problems/navier%E2%80%93stokes-equation It basically describes how fluids flow.

Compressible flow (air)
Incompressible flow (water)
 

Chile Earthquake Facts

Linkdump from today's explorations.

All items taken from this reddit thread: http://www.reddit.com/r/worldnews/comments/21yyig/an_80_magnitude_earthquake_has_struck_offshore/

USGS website info: http://earthquake.usgs.gov/earthquakes/eventpage/usc000nzvd#summary
USGS Summary report: http://earthquake.usgs.gov/earthquakes/eqarchives/poster/2014/20140401.php

Wave propagation map: http://i.imgur.com/RRmDfnQ.png
Wave propagation video: https://www.youtube.com/watch?v=hhvfbjCIiXo
Hear the sound of the quake! (well, the sound of its seismic waveform) http://www.iris.edu/dms/nodes/dmc/tools/event/4597319

Pasta analogy which nicely explains the logarithmic nature of the strength of earthquakes: https://pbs.twimg.com/media/Bj_DmNbCIAErl1C.jpg

Old Math Books

Sometimeshttp://www.reddit.com/r/math turns has some wonderful curiosities on its frontpage. Several users have math texts from the mid to late 1800s and posted a few images. As it turns out, each text has been digitally archived and can be viewed for free by anyone with an internet connection and a PDF reader. The discussions about typesetting, mathematical notation, and mathematical exposition (writing style), was interesting.  Below are some highlights.

Plane and solid geometry by George Wentworth (1899)
imgur gallery
discussion thread
full text on Internet Archive

A treatise on differential equations by George Boole & Isaac Todhunter (1865)
imgur gallery
discussion thread
full text on Internet Archive

Elements of Algebra By George Roberts Perkins (1852)
imgur gallery
discussion thread
full text on Google Books

BBC -- Beautiful Equations

 

Artist Matt Collings chats openly with scientists as he takes a tour of some of the most important equations in physics. Equations are explained to be an unambiguous generalized shorthand for expressing relationships about physical quantities. "A little increase in mass means a gigantic increase in energy." How much, exactly? Well, the details are actually worked out in a way that anyone can follow.

This documentary is well worth watching as it gives an approachable and concrete explanation of what all the symbols on the page actually mean and how truly remarkable it is that such universal truths, which literally apply to all objects in the universe, can be expressed in such a compact manner. 

The concept of "Mathematical Beauty" is explored and (spoiler alert) it basically means that a single, compact equation can very simply and very generally express the relationship between quantities (mass, energy, time, velocity, force, etc.).

BBC Page for "Beautiful Equations" http://www.bbc.co.uk/programmes/b00wltbm

Matt Collings's website: http://www.emmabiggsandmatthewcollings.net/recent

The five equations presented: 

1) The relationship between mass and energy: E = mc^2 
(E = energy, m = mass of an object, c = the speed of light)

2) The force of gravity between two bodies: F = (G * m1*m2)/(r^2)
(G = the gravitational constant, m1 and m2 = "the first object having mass m1, the second object has mass 2" and r = the distance between the two objects)

3) Time dilation: t' = t*sqrt[ 1 - (v/c)^2 ]
 t = time in your frame of reference, as you move at velocity v.
t' = time according to someone watching you from another frame of reference at rest to the first. c = the speed of light. 

4) Dirac Equation: (i*gamma*del - m)*phi = 0 
Difficult to summarize without getting into complicated mathematics. Essentially it predicted that all matter has anti-matter components and it described how the most elementary of particles behaved. More here.

 "What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating." Paul Dirac 1969 full speech here

5) Hawking Equation:  S = A/4
S = entropy (disorder) , A = the area of the black hole

It is worth mentioning another blog post which goes nicely with this theme.

"Math doesn't use fancy words and weird notations because mathematicians are trying to confuse non-mathematicians. It’s not done out of spite, or out of some desire to exclude non-mathematicians from the club. It’s about precision."

http://www.goodmath.org/blog/2014/03/24/yet-another-cantor-crank-size-vs-cardinality/

As a particularly nice example, I offer up the equation for the Fourier Transformation.



At first, it can seem intimidating and overwhelming -- so many symbols, fractions within superscripts, what does it all mean? Well, each symbol has a very specific and unambiguous meaning, quite a lot of punch is packed into this array of symbols!


The image above was originally seen here and explained for the lay reader in this blog.

Government shutdown -- information and perspective from one online educator

Here are four short ( apolitical ) webpages regarding shutdowns previous and current.

[1] Metros Where A Government Shutdown Could Hurt Most

#  Metro                 % of Local Wages Going to Federal Workers

1  Washington, DC-VA-MD-WV                  18.5%

2  Bethesda-Rockville-Frederick, MD         12.6%

3  Virginia Beach-Norfolk, VA-NC            11.8%

[2] Visualization of previous shutdowns where each year is a horizontal bar  (click the “hi-res” button for a larger image)

[3] Explanation and context of each previous shutdowns (via Washington Post)

[4] Who has been most shut down by the shutdown? (via Slate)

NASA                               97%
Housing and Urban Development      96%
Education                          94%
EPA                                94%
Securities and Exchange Commission 91%

Commerce                           87%
Smithsonian                        84%
Labor                              82%
Treasury                           82%
Interior                           81%

The Department of the Interior is responsible for the National Park Service. More information about how the shutdown will impact our national parks can be found here.

------ sources ------

[1] http://trends.truliablog.com/2013/09/metros-that-could-suffer-most-from-a-federal-government-shutdown/

[2] http://vizual-statistix.tumblr.com/post/62731422207/given-that-were-on-the-verge-of-a-possible

[3] http://www.washingtonpost.com/blogs/wonkblog/wp/2013/09/25/here-is-every-previous-government-shutdown-why-they-happened-and-how-they-ended/?print=1

[4] http://www.slate.com/articles/news_and_politics/slate_labs/2013/10/federal_government_shutdown_agencies_with_the_most_furloughs.html

------ Personal note ------

This past weekend, I was invited to the Davidson Institute Fellow award ceremony by one of my previous students who earned a $10,000 scholarship for his mathematical work. While I was there I had the opportunity to chat with him and his mother about mathematics, his research, and general thoughts about the next steps in his education and study.

If I could send a message to anyone in congress is this: 

I feel it is shameful to our nation that such a phenomenal student  personally feels apprehensive in any way about funding his continuing education.  Admittedly, some of his concern can be attributed to “teenage jitters” which will surely pass and he will very likely have scholarships to whatever institution he chooses to attend. But the simple fact is, the more he is concerned about funding, the less his mind is able to focus on his studies.  My concern extends to all of my students, even (especially!) those who I taught as a public school teacher many years ago. I have genuine fear that in the coming decades, there will be a gigantic collapse caused by our nation’s inability to educate its youth and properly fund scientific research.   

Current high school students are panicking about funding college education, current undergrad & grad students must fight even harder for grant monies… all of this leaves less and less time and energy for clear and creative thinking.

Weekend of poetry, hooping, juggling, and great food

Dan Waber and Jennifer Hill are both poets, writers, and all-round creative people in addition to being very hospitable hosts. They are lifelong learners who are always engaged in some sort of creative activity. It was refreshing and energizing to break out of my usual work- and math-minded cycle. I feel like I have plenty of new ideas for juggling, reading, cooking and even computer programming.

Interactive poetry & computer programming
Saturday night Dan was showing me some of his very interesting sketches made with processing.js. Some of my favorites are:

• love me don't love me (a clever interactive poem about their cat)
• death of my mother (My father died 3 years ago so this one really struck a chord with me.)
• a tool for discovering your favorite letter and another tool for discovering your favorite letter. (This reminded me of the design principle behind the Museum of Math Logo. Dan's tools are monochrome and focus on movement while Wolfram's are colored and static. It would be interesting to see the two combined.)

Dan's letter explorer (letter d) 

Wolfram's letter explorer (letter d)

Wolfram's letter explorer ( letter j)

Dan's other letter explorer (letter j)

• the blurbinator (hilarious tool that constructs a blub about your own book of poetry, example below)

Non-math books

Their bookshelves were lined with all sorts of interesting titles. Here are a few which I either read while there or are presently reading: 

• The Transitive Vampire: A Handbook of Grammar for the Innocent, the Eager, and the Doomed
• The Dot and the Line: A Romance in Lower Mathematics,  video (great early Disney animation!)
• Accelerando

Delicious, delicious food
I had one of the most delicious dinners I've ever eaten at Maison. I felt like this was the first time in my life I finally understood, on a sensory level, what exactly people mean when they talk about the importance of natural ingredients of high-quality food. Every single meal was a gustatory delight. Dan is a highly skilled chef. He showed me how to spatchcock a chicken and even makes his own cereal. Every dish was made from entirely fresh ingredients -- from the earth to the table without processing beyond preparation in the kitchen. 

Juggling, Hooping, Poi!

Walking around on First Friday after dinner at Maison I visited a handful of art galleries and even had the chance to witness some lovely glow-in-the-dark poi swinging (and try my hand at it).

All the cool kids were swinging poi, so I thought I'd try.

 Pianos were scattered about town for people to play and the whole place felt very alive. I went to a yoga class on Saturday that really tested my limits. I do like a challenge, but I wasn't quite up for trying to stand on my head just yet... I got to juggle in and around town http://www.tellus360.com/ is juggler-friendly. The Marriott... not so much. While waiting for Jenn's friend to check out, I was politely asked to stop juggling by the security, the rest of the staff didn't seem to mind, though.

Juggling in Tellus 360 which hosts rooftop yoga on Saturdays!

There were lots of great parks in and around town and everywhere I juggled and Jen hooped, people would stop by and watch, sometimes even trying out juggling and/or hooping.  Jenn's mother visited on Sunday afternoon and had a show with dinner, as we demonstrated some of the new moves we were developing over the weekend.

Here are a few quick juggling clips.

contact juggling with one ball

three club backcrosses

four club singles

Last but not least, their cat Steve has the quirky habit of jumping up on the sink so that he can dip his head under the tap and sip up water.

I feel very fortunate to have such friends and I hope that I can return the hospitality some day when they visit Baltimore. 

Webinar on the mathematics of juggling for CTY Online

I did a 1 hour webinar on the mathematics of juggling. It was a lot of fun! Fortunately it was recorded. 

Webinar link