Spectroscopy and poetry

Linkdump from today's mathematical explorations

Review of Cosmos Episode 5 "Hiding in the light" with lots of links to the scientists mentioned in the show.
http://www.latimes.com/entertainment/tv/showtracker/la-et-st-cosmos-recap-20140404,0,259862.story#axzz2yCyoagkI

Spectrosopy information:
http://loke.as.arizona.edu/~ckulesa/camp/spectroscopy_intro.html
http://www.ipac.caltech.edu/outreach/Edu/Spectra/spec.html


lunchbreak reader feed notes:
The Wikipedia article on Homer pretty drat awful...
This comment thread  illustrates why this page  is really a mess, from a historian's viewpoint. Taking everything with a grain of salt, but it seems that wikipedia has some policies that do not agree with what is commonly viewed as good academic practice. The particular article on Homer gets ~ 100k views a week, so this is a problem.

Will the social sciences ever become hard science? (very likely no, and with good reason.)
http://backreaction.blogspot.com/2014/04/will-social-sciences-ever-become-hard.html


The poetry that moves men to tears The comments of this article are full of thoughtful, insightful poems.
Anthony Holden's new anthology celebrates the poems that move men – with revealing contributions from the likes of Ian McEwan, Jonathan Franz...

From the comments section (which is just as fascinating as the article itself):
Those Winter Sundays by Robert Hayden

Those Winter Sundays

Sundays too my father got up earlyand put his clothes on in the blueblack cold,then with cracked hands that achedfrom labor in the weekday weather madebanked fires blaze. No one ever thanked him.

I`d wake and hear the cold splintering, breaking.When the rooms were warm, he`d call,and slowly I would rise and dress,fearing the chronic angers of that house,

Speaking indifferently to him,who had driven out the coldand polished my good shoes as well.What did I know, what did I knowof love`s austere and lonely offices?

Tilt and rotation of the planets.

Missing 20th century physicist, gorgeous maps

Linkdump from today's explorations

Disappearing physicist: http://www.futilitycloset.com/2014/04/02/night-crossing/ Who was Ettore Majorana? http://en.wikipedia.org/wiki/Ettore_Majorana

From an excellent stats blog: http://andrewgelman.com/2014/03/29/agree-comment/

The problem is simple, the researchers are disproving always false null hypotheses and taking this disproof as near proof that their theory is correct.

Beautiful maps made with d3.js. https://www.jasondavies.com/maps/

Beautiful graphs and beautiful monsters

Linkdump from today's mathematical explorations

Beautifully graphs with clear explanations and interpretations are one of my favorite things.  This blog post by the 538 blog is a prime example of just that.

http://fivethirtyeight.com/features/four-strikes-and-youre-out/

While discussing counterexamples with a student today I mentioned the Weierstrass function. Here is an great blog post which gives some backstory to the development of and reaction to the function that is everywhere continuous and nowhere differentiable. A thumb on the nose to Newton.

http://nautil.us/issue/11/light/maths-beautiful-monsters
http://www.math.washington.edu/~conroy/general/weierstrass/weier.htm

The Weierstrass function is just one of many "Pathological Functions": http://en.wikipedia.org/wiki/Pathological_%28mathematics%29

There are many here http://math.stackexchange.com/questions/740/useful-examples-of-pathological-functions and here http://mathoverflow.net/questions/22189/what-is-your-favorite-strange-function.  There is also an excellent book titled Counterexamples in Analysis which covers even more of these pathological functions in great detail. http://www.amazon.com/Counterexamples-Analysis-Dover-Books-Mathematics/dp/0486428753

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.