How to Develop a Mindset for Math | BetterExplained

How to Develop a Mindset for Math

Math uses made-up rules to create models and derive relationships. When learning, I ask:

What relationship does this model represent?
What real-world items share this relationship?
Does that relationship make sense to me?
It’s simple, but it helps me understand. If you liked my math posts, this article covers my approach to this oft-maligned subject.

"Prospective memory" in action

"What you are looking at is an pictorialized overhead view of a rat coming to a choice point in the maze. The rat is indicated by the white circle. The colors indicate the firing rates for hippocampal neurons with place fields on the maze with reddish parts indicating high firing rate."

"At the choice point of the maze ... the recorded hippocampal neurons do something very odd. What the rat will do is look down the maze in the direction of each of its two choices. When the rat looks down in one direction place cells that correspond to position down that path will activate. When the rat looks down the other direction place cells corresponding to position in that part of the maze will activate. The important part is though that the rat has not reached that point in the maze yet; the choice point causes a dissociation between the location of the animal and the firing of the place cells. More interestingly, it is as if the rat's brain is simulating what is going to happen if the rat runs in that direction."

From Science Blogs. More good stuff here. Picked up from Andrew Sullivan.

Neuropundits Gone Wild!

An op-ed from Sunday's New York Times, "This Is Your Brain on Politics," proposes to answer what must be the most vexing question of modern American politics: What's going on inside the head of a swing voter? The authors—a team of neuroscientists and political consultants—ran 20 of these undecided volunteers through a brain scanner and showed them pictures and video of the major candidates from both parties. The results, laid out both in print and an online slide show, purport to give us some insight as to how the upcoming primaries will play out: "Mitt Romney may have some potential," the researchers conclude, and Hillary Clinton seems to have an edge at winning over her opponents...
http://www.slate.com/id/2177885/

Sounds of Saturn

This is an audio file of Saturn's radio emissions. Time on this recording has been compressed such that 13 seconds corresponds to 27 seconds. Since the frequencies of these emissions are well above the audio frequency range, we have shifted them downward by a factor of 260. (from NASA, via
Daily Zeitgeist, 11/01/07).

Singing Horses

Check them out!

Sharktopus Sighting!

On January 21, 2007, staff at Awashima Marine Park in Shizuoka, southwest of Tokyo, were alerted by fishermen to a 'strange eel-like fish with razor sharp teeth'. The fish was identified as a female 1.6 m frilled shark and was captured by park staff who were concerned that the shark appeared to be unhealthy. They took it out of the water and put it into a salt water tank where they filmed it and took pictures of it. The shark died a few hours after capture. This rare surface appearance of a frilled shark has been attributed to the animal being unwell and possibly disoriented.[link]

Idolomantis diabolica

Photo by Igor Siwanowicz, thanks to Daily Zeitgeist

Click on image for AWESOME blow-up.

"Haptic Radar"

Thanks to Daily Zeitgeist.

Aye-Aye

Source.

New Spider in Park St Basement

Epeira cinerea and part of her magnificent web.

Funnier than the impersonation

click to watch

Mandelbrot Set

A Cadbury commercial?

Beata forwarded me this link
from Dan Howley, one of her in-laws/neighbors.

giant social spider web!

http://texasento.net/Social_Spider.htm

Goeff's Favorite Poems

Check it out. Some plums among the chestnuts. (I was led to it by following the link to "The book of my enemy has been remaindered" from Andrew Sullivan's blog).

Gastón, el gran depredador del nautilus

Doonesbury: When we cut and run

More here.

Why isn't every physicist a Bayesian?

(Received 1 June 1994; accepted 3 November 1994)

Physicists embarking on seemingly routine error analyses are finding themselves grappling with major conceptual issues which have divided the statistics community for years. While the philosophical aspects of the debate may be endless, a practicing experimenter must choose a way to report results. The results can depend on which of the two major frameworks, classical or Bayesian, one adopts.

This article reviews reasons why most data analysis in particle physics has traditionally been carried out within the classical framework, and why this will probably continue to be the case.

However, Bayesian reasoning has recently made significant inroads in some published work in this field, and many other particle physicists may frequently think in a Bayesian manner without realizing it. I illustrate the issues involved with a few simple, commonly encountered examples which reveal how each framework can sometimes lead to unsatisfying results.

©1995 American Association of Physics Teachers.

Jumping Spider Mating Dance

Click to play

python vs. alligator

http://news.bbc.co.uk/2/hi/americas/4313978.stm

What to do with 66,000 business cards

...Dr. Jeannine Mosely found herself confronted with a gargantuan pile of business cards, rendered useless after the company she worked for changed addresses, she knew what she had to do with them: hand-make a real, live Menger Sponge — creating an actual object from something that had previously been merely a mathematical abstraction — a (sorta nerdy) feat of Guinness Book proportions.

(link)

The quest for radioactive items on eBay.

Some hit antique stalls with their CDV-700s cranked, hoping to spook dealers into a discount. Others surreptitiously palm an RM-60 while listening on earphones for telltale clicks from cheap old candy dishes and sickly pale-green milk pitchers. These mysterious men are a most obscure group of antique collectors, and they seek an invisible prize scorned by all others: radiation.
(link)

Totally awesomely incredible photo spftware demo

This is mindblowing.

http://www.maniacworld.com/amazing-image-technology.html

Dr Quantum - Double Slit Experiment

My weekend at the Grand Hyatt

I'm quite proud of this picture (from my room on the 31st floor). It's a composite of 2 cell-phone pix. You can see the top of the south facade of Grand Central Terminal, and the little bridge that takes Park Ave through the station. One hotel entrance is right off that ramp.

Women In Art

Jesus Shark

Captive shark had 'virgin birth'

Female hammerhead sharks can reproduce without having sex, scientists confirm.

The evidence comes from a shark at Henry Doorly Zoo in Nebraska which gave birth to a pup in 2001 despite having had no contact with a male.

Genetic tests by a team from Belfast, Nebraska and Florida prove conclusively the young animal possessed no paternal DNA, Biology Letters journal reports.

Seth Cooke took this article and ran with it...

"The shark story (the first of those two linked to above) is fantastic for two reasons. Firstly it's extremely heartening to know that our evil ocean dwelling distant relatives aren't such vile alien killers after all and enjoy a bit of kinky eat me/beat me sex. Biting in the bedroom is great and I'm glad they think so too. Thus bridges are built between species that otherwise seemed irreconcilable. Everyone can be happy.

Secondly, the notion of a virgin hammerhead giving birth has filled my mind with reimagined Synoptic Gospels in which Jesus is a shark. Exactly the same stories, everything identical, just that one detail altered. It'd be like Porco Rosso only instead of an idealised post WWI Mediterranean it'd be all up in your Nazareth, Bethlehem and Jerusalem, and instead of a pig biplane pilot bounty hunter you'd have Jesus as a fucking evil shark."

That's my paper!

Corrections, May 25, 2007

View from my window (door, actually)

5/25/07, 2PM. I sent this to Andrew Sullivan. Come visit, y'all.

TSA Confiscates Congressman’s Last Meal During Food Stamp Challenge

Today, four members of Congress conclude the Congressional Food Stamp Challenge, in which lawmakers chose to live “on three dollars of food per day, the same amount an average participant in the Food Stamp Program receives.”

One of the participants, Rep. Tim Ryan (D-OH), “stuck to the challenge” even as he traveled to speak at his alma mater’s commencement exercises, bringing along his “pasta and sauce, as well as the last of my jelly, peanut butter, and bread.” After the ceremony and late for his plane, he rushed through the airport choosing not to check his bags to save time. He writes:

I step up to the metal detector, take my shoes off, place my bag through the scanner and come out the other side to the most dreaded words in travel, “Bag Check!” […]

As the agent sifted though my bag, I tried to recount what could possibly be in there that was threatening… my mouthwash? Toothpaste? Yeah, it was those two, but it was also my peanut butter and jelly. […]

He politely put the peanut butter and jelly to the side, closed my bag and gave it back to me. I was too astonished to talk. I took my bag and walked towards the gate thinking about the 4 or maybe 5 meals that she had taken from me. What am I going to do now? It’s not like I can just go to Safeway and grab another jar. I have .33 cents and a bag of cornmeal to last today and tomorrow.

While Ryan took the loss in stride, comforted by the fact that he could soon lift his $21/week spending limit come Tuesday, one in 10 Americans constantly live with such restrictions and “over 80 percent of food stamp benefits go to families with children.”

Rep. James McGovern (D-MA) explained that “nearly 36 million Americans” do not “consistently have enough food to feed themselves or their families.”

He added that on such a low budget there’s “no organic foods, no fresh vegetables, we were looking for the cheapest of everything.” “We got spaghetti and hamburger meat that was high in fat — the fattiest meat on the shelf. … It’s almost impossible to make healthy choices on a food stamp diet.”

You can read more about the Food Stamp Challenge and H.R. 2129, Feeding America’s Families Act HERE.

– Ryan Powers

http://thinkprogress.org/2007/05/21/food-stamp/

Let math help pick your music

MUSIC INTELLIGENCE: 2012

MAY 7, 2007

Mike McCready’s company, Platinum Blue, uses computers to analyze the mathematical patterns in songs. McCready and Malcolm Gladwell discuss how this technology can help the music business identify potential hits, and what Gladwell should listen to next. From “2012: Stories from the Near Future,” the 2007 New Yorker Conference.

Click here to hear it. About
10-15 minutes, but worth it.

Congresscritters try to survive on $21 in food stamps for a week

Rep. Tim Ryan (D-Ohio) and Rep. Jim McGovern (D-Mass.) are among a handful of congresscritters participating in an experiment in which they must subsist on standard US food stamp rations for one week.

The shocking conclusion, so far? $21 worth of stamps a week doesn't add up to much, and it's "almost impossible" to maintain a healthy diet for $1 a meal (huh, wonder why America's poor suffer obesity in such great numbers?).

Both lawmakers are blogging about the experience: McGovern here, Ryan here. Snip from Ryan's latest post:

My biggest concern today is running out of food before the end of the week.

One loaf of bread doesn’t make as many sandwiches as you’d think, and I’m running through my cottage cheese pretty fast as well.

The budgeting was hard enough, rationing what I do have will present another challenge.

Link to Washington Post story (thanks, Rebecca).

(From Boing Boing)

High-Dynamic-Range Photography: A Guide

If you've seen a particularly eye-popping, out-of-this-world night photograph of a city skyline, or a particularly apocalyptic cloudscape with cartoonish color saturation making the rounds on blogs lately, there's a good chance it was made using high-dynamic-range imaging, or HDR software. And while these images may look like the work of a pro photographer, or at least a seasoned digital-imaging or special-effects expert, the tools to easily make your own amazing HDR images are widely (and in some cases freely) available.

(more of the how-to)
(more HDR images)


Oh! And here's a guide to how to fake HDR in photoshop if you didn't take three pictures...

Loan tiny sums to micro-enterprises in the developing world

Kiva.org is the world’s first peer-to-peer, distributed microloan website. A great idea where PayPal meets Gates Foundation. The site allows you to lend a small amount of money, say $25, to needy microenterprises in developing countries. You receive repayment at the end of the loan period . This sounds like a great idea



read more | digg story

Bayeux Tapestry Animated

A terrific animation of an 11th century artwork. Some details of the tapestry's history and construction here.

Holy Smokes.

Top Hedge Fund Managers Earn Over $240 Million

James Simons, a 69-year-old publicity shy former math professor, uses complex computer-driven mathematical models to make bets on stocks, bonds and commodities, among other things.

Skip to next paragraph

J.N. Bowles/Bloomberg News, right

James Simons, left, earned $1.7 billion in 2006, more than any other hedge fund manager. Kenneth Griffin, right, made $1.4 billion.

Crow IQ - a new wrinkle

Click to activate.

Kaye effect - dancing shampoo

WARNING: Turn sound down. Music extremely obnoxious.

Andrew Sullivan on Blacksburg and Baghdad

One Reminder 17 Apr 2007 10:48 am Imagine that this kind of massacre happened every day. Imagine a police force that was far too small to even respond to most of them. Imagine this occurring repeatedly for years until the perpetrators and their accomplices became the de facto power-brokers throughout the land. Imagine the shootings also being accompanied by the brutal torture of victims. Imagine families never having finality on whether their own siblings or parents or children have been murdered or not. This is Iraq today. Now think of the justified rage many feel at the VT campus police chief and university president for misjudgments. Now imagine them presiding over several more massacres in the same place. Ask yourself: why do we not feel as enraged by those responsible for security in Iraq? Are those victims not human beings too? Are they not children and mothers and fathers and sons? Are we not ultimately responsible for them, having destroyed the institutions of order in their country? Now go watch John Bolton tell the victims to go help themselves.

Medieval tech support

Animaris Rhinoceros Transport

And go here to see it in motion.

Lovesick swan

"The swan that fell in love with a pedal boat is back courting its plastic lover after spending the winter in a local zoo.

Swans choose a partner for life but the rare Black Australian swan nicknamed Petra made the mistake of falling for a pedal boat designed to look like a swan.

And when Petra's pedal boat lover refused to fly south for the winter Petra also remained, a move that could have killed her as the cold weather arrived.

In the end though local zoo chiefs took pity on the swan and gave her and her boat boyfriend a place to spend the winter, and this week the pair were once again on the lake together.

According to biologists in Muenster, north-western Germany, Petra has been circling its plastic lover, staring endlessly at it and making crooning noises, all the typical signs of a swan in love.

The boat in the meantime is still being hired out to families who want to picnic on the Aasee lake - where the star-crossed lovers have become a tourist attraction.

Zoo director Joerg Adler said: "This arrangement could go on for ever, the swan obviously believes it has found a partner for life."

http://www.ananova.com/news/story/sm_2264994.html?menu=

Now you know

From the Times Sky Watch, Week of April 8 (4/8/07)

"... reddish Betelgeuse, orangish Aldebaran and yellowish Pollux ...
brilliant topaz Arcturus ... Even as you observe these stellar colors,
do you notice that they are only recognizable in the brightest stars?
That is because of the physiology of the eye -- more specifically,
the fact that the color sensors on the retina, the cones, are
insensitive to faint light. Under dim light the rods in the retina
take over. But their greater light sensitivity is offset by their
colorblindness. That is why we see all faint stars as white. But
if we look at them through binoculars or a telescope, their
amplified brightness stimulates the cones, which detect their
color.

Channelling Tatouine

(Ethiopian tanks in Somalia. New York Times, April 8 2007)

That's my paper!

(Wednesday March 14, 2007)

Birds of Paradise

!!!

The N Y Times Strikes Again (3/20/07)

The dangers of vivid writing.