Why rote memorization is still important for learning

Engineering professor Barbara Oakley explains how she rewired her brain for math at the age of 26:

When learning math and engineering as an adult, I began by using the same strategy I’d used to learn language. I’d look at an equation, to take a very simple example, Newton’s second law of f = ma. I practiced feeling what each of the letters meant—f for force was a push, m for mass was a kind of weighty resistance to my push, and a was the exhilarating feeling of acceleration. (The equivalent in Russian was learning to physically sound out the letters of the Cyrillic alphabet.) I memorized the equation so I could carry it around with me in my head and play with it. If m and a were big numbers, what did that do to f when I pushed it through the equation? If f was big and a was small, what did that do to m? How did the units match on each side? Playing with the equation was like conjugating a verb. I was beginning to intuit that the sparse outlines of the equation were like a metaphorical poem, with all sorts of beautiful symbolic representations embedded within it. Although I wouldn’t have put it that way at the time, the truth was that to learn math and science well, I had to slowly, day by day, build solid neural “chunked” subroutines—such as surrounding the simple equation f = ma—that I could easily call to mind from long term memory, much as I’d done with Russian.

Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.

Full Story: Nautilus: How I Rewired My Brain to Become Fluent in Math

Happy Pi Day

See also:

The real life inspiration behind the movie Pi

Calculus for Kindergarteners

Luba Vangelova reports on a group that believes it may be better to introduce certain elements of, say, calculus to young kids before more route ideas like multiplication tables:

Finding an appropriate path hinges on appreciating an often-overlooked fact—that “the complexity of the idea and the difficulty of doing it are separate, independent dimensions,” she says. “Unfortunately a lot of what little children are offered is simple but hard—primitive ideas that are hard for humans to implement,” because they readily tax the limits of working memory, attention, precision and other cognitive functions. Examples of activities that fall into the “simple but hard” quadrant: Building a trench with a spoon (a military punishment that involves many small, repetitive tasks, akin to doing 100 two-digit addition problems on a typical worksheet, as Droujkova points out), or memorizing multiplication tables as individual facts rather than patterns.

Far better, she says, to start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend “function box” that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).

“You can take any branch of mathematics and find things that are both complex and easy in it,” Droujkova says. “My quest, with several colleagues around the world, is to take the treasure of mathematics and find the accessible ways into all of it.”

Full Story: The Atlantic: 5-Year-Olds Can Learn Calculus

(via Metafilter)

The book Moebius Noodles attempts to put these ideas into practice.

See also:

Punk Rock Mathematics

Computer-Based Math

Hogwarts for Hackers: Inside the Science and Tech School of Tomorrow

Evan, a student at IMSA

I wrote about the Illinois Mathematics and Science Academy, a boarding high school in Aurora, IL, for Wired:

The IMSA Wednesdays are like Google’s “20 percent time” — only better. “At Google, 20 percent time is actually tacked on to the rest of your job. ” says Daniel Kador, another former IMSA student. “At IMSA, it really is built into your schedule.” And though Kador and other students admit that they spent more than a few Wednesdays just goofing off — as high school students so often do — they say the environment at IMSA ends up pushing many of them towards truly creative work. And it pays off.

After teaching himself to program at IMSA, Chu went on to the University of Illinois, where he worked on NCSA Mosaic, the first graphical web browser, following in the footsteps of fellow IMSA alums Robert and Michael McCool. And, eventually, he joined several other IMSA graduates as an early employee at PayPal, where he still works today.

Chu is just one of many tech success stories that have sprung from IMSA over the years (see sidebar, page two). Other IMSA alums have gone on to discover new solar systems, teach neurosurgery, and found such notable tech outfits as YouTube, Yelp, SparkNotes, and OK Cupid. And the spirit that moved Chu to teach himself programming is still very much alive and well. You can think of IMSA as a Hogwarts for Hackers.

Full Story: Wired Enterprise: Hogwarts for Hackers: Inside the Science and Tech School of Tomorrow

Photos by: Greg Ruffing

Mathematicians Predict the Future With Data From the Past


I wrote for Wired:

In Issac Asimov’s classic science fiction saga Foundation, mathematics professor Hari Seldon predicts the future using what he calls psychohistory. Drawing on mathematical models that describe what happened in the past, he anticipates what will happen next, including the fall of the Galactic Empire.

That may seem like fanciful stuff. But Peter Turchin is turning himself into a real-life Hari Seldon — and he’s not alone.

Turchin — a professor at the University of Connecticut — is the driving force behind a field called “cliodynamics,” where scientists and mathematicians analyze history in the hopes of finding patterns they can then use to predict the future. It’s named after Clio, the Greek muse of history.

These academics have the same goals as other historians — “We start with questions that historians have asked for all of history,” Turchin says. “For example: Why do civilizations collapse?” — but they seek to answer these questions quite differently. They use math rather than mere language, and according to Turchin, the prognosis isn’t that far removed from the empire-crushing predictions laid down by Hari Seldon in the Foundation saga. Unless something changes, he says, we’re due for a wave of widespread violence in about 2020, including riots and terrorism. [...]

There are competing theories as well. A group of researchers at the New England Complex Systems Institute — who practice a discipline called econophysics — have built their own model of political violence and concluded that one simple variable is sufficient to predict instability: food prices. In a paper titled “The Food Crises and Political Instability in North Africa and the Middle East,” they explain that although many other grievances may be aired once the violence begins, the cost of food is the primary trigger. They make a similarly grim prediction: large-scale riots over food, beginning around October of this year.

Full Story: Wired Enterprise: Mathematicians Predict the Future With Data From the Past

I’d actually recommend reading journal articles I cite before reading my article:

Dynamics of political instability in the United States, 1780–2010 by Peter Turchin

The Food Crises and Political Instability in North Africa and the Middle East by Marco Lagi, Karla Z. Bertrand and Yaneer Bar-Yam.

Also check out Turchin’s blog.


Revolution – history and praxis. Technoccult interviews Johnny Brainwash

The Rise of Predictive Policing: Police Using Statistics to Predict Crime

Are We On the Verge of the Next Psychedelic Explosion?

Meteorologists: The Original Data Scientists?

Rock star data scientist Nate Silver wrote a long article on meteorology for the New York Times:

Why are weather forecasters succeeding when other predictors fail? It’s because long ago they came to accept the imperfections in their knowledge. That helped them understand that even the most sophisticated computers, combing through seemingly limitless data, are painfully ill equipped to predict something as dynamic as weather all by themselves. So as fields like economics began relying more on Big Data, meteorologists recognized that data on its own isn’t enough.

The New York Times: The Weatherman Is Not a Moron

(via Abe)

A New Theory of Everything

Technology Review covers Stuart Kauffman‘s work to find a mathematical model for autocatalytic sets, the process by which life may emerge from molecules:

What makes the approach so powerful is that the mathematics does not depend on the nature of chemistry–it is substrate independent. So the building blocks in an autocatalytic set need not be molecules at all but any units that can manipulate other units in the required way.

These units can be complex entities in themselves. “Perhaps it is not too far-fetched to think, for example, of the collection of bacterial species in your gut (several hundreds of them) as one big autocatalytic set,” say Kauffman and co.

And they go even further. They point out that the economy is essentially the process of transforming raw materials into products such as hammers and spades that themselves facilitate further transformation of raw materials and so on. “Perhaps we can also view the economy as an (emergent) autocatalytic set, exhibiting some sort of functional closure,” they speculate.

Could it be that the same idea–the general theory of autocatalytic sets–can help explain the origin of life, the nature of emergence and provide a mathematical foundation for organisation in economics?

Full Story: MIT Technology Review: The Single Theory That Could Explain Emergence, Organisation And The Origin of Life

(via Social Physicist)

I find this very interesting, but don’t get too excited. These sorts of grand unification theories are extremely elusive. I’m also skeptical of these sorts of models which try to find universal rules for all types of systems.

See also:

Social Physics with Kyle Findlay

Guest Post: Some resources for thinking about systems

Researchers Trying to Build a Functioning Babbage’s Analytical Engine

 A photo of the Difference Engine constructed by the Science Museum based on the plans for Charles Babbage's Difference Engine No. 2

A photo of the Difference Engine constructed by the Science Museum based on the plans for Charles Babbage’s Difference Engine No. 2 by geni

Forget big data:

The project follows the successful effort by a group at the museum to replicate a far less complicated Babbage invention: the Difference Engine No. 2, a calculating machine composed of roughly 8,000 mechanical components assembled with a watchmaker’s precision. That project was completed in 1991.

The new effort — led by John Graham-Cumming, a programmer, and Doron Swade, a former curator at the museum — has already digitized Babbage’s surviving blueprints for the Analytical Engine. But the challenges of building it are daunting.

In the case of the Difference Engine, a complete set of plans existed. The Analytical Engine, by contrast, was a work in progress, as Babbage continually refined his thinking in a series of blueprints. Thus, the hope is to “crowd-source” the analysis of what should be built; plans will be posted online next year, and the public will be invited to offer suggestions.

New York Times: It Started Digital Wheels Turning

Punk Mathematics Author Tom Henderson to Keynote EsoZone Portland 2011

Tom Henderson, author of the forthcoming book Punk Mathematics, will keynote EsoZone Portland 2011 on November 18th at p:ear. Admission is free. Tom’s talk is tentatively titled “Time, Space, and the Self are Illusions – So Do ‘You’ Wanna Go ‘Out’ with ‘Me’ ‘Tonight’?” He’ll cover:

    • Mining your history for strategy
    • Virtual paranoia
    • Your eigenself and “you”
    • Using the howling void beyond your epsilon of consciousness for a good time

Tom has a masters in mathematics from Portland State University. According to the Kickstarter page for his book:

Punk Mathematics will be a series of mathematical stories. It is written for readers who are interested in having their minds expanded by the strange metaphors and implications of mathematics, even if they’re not always on friendly terms with equations. Better living through probability; the fractal dimension of cities and cancers; using orders of magnitude to detect bullshit; free will and quantum economics; and the mathematics of cooperation in a networked world on the brink of a No Future collapse.

For more on Tom, you can follow him on Twitter, read the Technoccult interview with him or listen to this interview on the Acme Science podcast Strongly Connected Components.

EsoZone Portland 2011 will take place over the course of November 18th and 19th. It will include a few pre-scheduled presentations, workshops and performances along with ample free space for ad-hoc “unconference” sessions in the style of BarCamp or Bird of a Feather.

Watch this space for more announcements.

How Tibetan Singing Bowls Work

How Tibetan Singing Bowls Work

Ceremonial Tibetan “singing bowls” are beginning to give up their secrets.

The water-filled bowls, when rubbed with a leather-wrapped mallet, exhibit a lively dance of water droplets as they emit a haunting sound.

Now slow-motion video has unveiled just what occurs in the bowls; droplets can actually bounce on the water’s surface.

A report in the journal Nonlinearity mathematically analyses the effect and could shed light on other fluid processes, such as fuel injection.

BBC: Tibetan singing bowls give up their chaotic secrets

(via Edward Borasky)

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