"...for parents, the transition has been hard"

I feel like I'm beating a dead horse, especially since Math-Frolic really isn't an education blog… except that this isn't a DEAD horse; it's very much alive and kicking, and I see no near-term end to it... another piece, from NY Times, on why current-day parents have so much trouble with Common Core:

http://tinyurl.com/ms2pq38

a couple of sentences that capture the essence:

"Even supporters of the Common Core say changes are being pushed too quickly. Rushing to institute a new math curriculum does not make sense if you are 'planning to get the job done in a rational way,' said Phil Daro, one of three principal writers of the Common Core math standards.
"Tensions over the Common Core have been heightened because the standards are tied to new standardized tests being introduced in many states. Teachers are fretting that their performance ratings will increasingly depend on how their students perform on these tests."

and further on:

“ 'Imagine, if you will, if the state government came down to Detroit and said in six weeks you have to be 100 percent metric,' said Jonathan Marceau, a fourth-grade teacher in Shelby Township, Mich…"

or this from a parent: “They say this is rigorous because it teaches them higher thinking. But it just looks tedious.”

It's nice to know that parents are so passionately interested in their children's education… it's less clear whether that passion can lead from disagreement and controversy, to resolution and progress???

ADDENDUM (7/2/14): Dr. Keith Devlin has now responded to this NY Times piece here:
http://devlinsangle.blogspot.com/2014/07/the-power-of-dots.html

Algebra, Euler, and i

Sunday thought....

"In the eighteenth century, mathematicians realized that to solve equations no numbers are needed beyond the imaginaries, a result so important it is known as the Fundamental Theorem of Algebra. Every equation written with complex numbers will always produce a solution with complex numbers. The door that Rafael Bombelli walked through to investigate the square roots of negative numbers revealed a solitary room. But what a room it was! The squeamishness mathematicians once had with imaginary numbers has been replaced by joy. The concept of i is now considered a very natural and efficient extension of the number system. For the price of a solitary symbol, mathematicians gained an elegantly self-contained abstract universe. Bargain.

"Imaginary numbers are protagonists of two of the most famous examples of mathematical beauty. One is a picture and one is an equation, known as Euler's identity, which in 2003 was sprayed on the side of an SUV in an ecoterrorist attack on a Los Angeles car dealership. The nature of the graffiti led to the arrest of a physics PhD student at Caltech. 'Everyone should know Euler's [identity],' he explained to the judge. He was correct, but one should nevertheless refrain from daubing it on cars."

-- Alex Bellos in "The Grapes of Math"

(my look at Bellos' latest book is now up at MathTango)

Diversion

A diversion from Math-Frolic fare today… I've long admired Cathy O'Neil's penchant for addressing all manner of subjects over at her Mathbabe blog, especially her vigilant watch over our corporate/financial overlords (so blame Cathy if you don't like the following diatribe ;-))
In a slightly similar vein, I can't help being a bit skeptical over two recent lovely videos that have gone more-or-less viral. I love these videos as much as everyone else… but would frankly love them more if they came from a government agency or a non-profit, rather than from corporate entities.  Corporate America has itself to blame for my cynicism in wondering about the motives/sincerity behind these offerings from Verizon and Procter & Gamble. It would be nice to imagine that some company CEO woke up one day, and said to himself, 'I want to do something on behalf of my daughter and all her peers, and dammit I've got the money and the position to do it.'  But it seems just as likely (or moreso?) that a marketing or "Mad Man" whizkid approached some corporate officers saying 'hey, we just thought of a great way to burnish your image with 50+% of the population' (or in the case of "Always," virtually 100% of their customers) -- I mean how many marketing tests, focus groups, surveys, research-hours, psychologist-consultants, and Big Data number-crunchers were employed before the below videos ever went live?

I grew up in the 1950s when companies were presumed honest and trustworthy until proven otherwise.  Starting somewhere 'round-about the 1980s that began to change, until by today, due to my own experiences and those of friends, I feel required to operate on the assumption that businesses are dishonest and deceitful unless proven otherwise. I'm not even sure that truly honest, ethical businessmen have much chance of long term success in today's America. It's a distressing thing to go through life, or even through a single day, constrained to distrusting each sales and business person one encounters (...but it's more distressing to be continually ripped-off).

Anyway, if somehow you've missed either of these recent vids take a gander… the sentiments are lovely and ought be passed along far-and-wide… I just wish I didn't feel the compunction to question motives.
Further, I wonder if we've reached a state in this nation, where only corporate entities have the $$$, the creativity, the mass reach and resources, to produce and distribute such important messages… I hope not:






...In the event you prefer some mathy reading for the weekend I have a Friday potpourri list up over at MathTango.

But Enough About American Education…

 It can get tiring to read the constant debate, tirades, criticism of American math education, and so in a misery-loves-company sort of way, it was almost refreshing to read this piece on the travails (even "death spiral") the Australian math education system is going through:

http://www.smh.com.au/national/education/the-paradox-of-australian-mathematics-education-20140620-3ahwz.html

"There is a famous and fascinating paradox of movie-making: the French are funny, sex is funny and comedy is funny, but somehow French sex comedies are never funny. Which brings us to the topic of Australian maths education."

How's that for a lead line! Much of the discussion sounds familiar… except perhaps even harsher!
With this toward the end:

"The simple truth is, the major stumbling block for mathematics education in Australia is that teachers, qualified or not, don't learn enough mathematics and they don't learn it well enough. Discussion of anything else is pointless until that problem is resolved. And the second simple truth is that education faculties are so divorced from the study of mathematics, so lacking in understanding and appreciation of mathematics, they can play no meaningful role in fixing the problem except by getting out of the way."

And then from Canada there's this posting of a math teacher:
http://www.joebower.org/2014/06/im-teacher-i-never-saw-this-coming.html

Wow... it's almost enough to make one feel like we in America must, by comparison, be doing something right (...I said, almost).

Rewarding Math, Generating Excitement

The big news of the morning is the awarding of the new "Breakthrough" mathematics prizes  ('most lucrative ever established') to five recipients:

http://www.theguardian.com/science/2014/jun/23/britons-win-3m-breakthrough-mathematics-prize

While the award is intended to "celebrate scientists and generate excitement" for science/math fields, another mathematician notes that most mathematicians can no longer even understand the "technical, esoteric stuff" that many of their colleagues do.

Scientific American piece on the award focuses on Terry Tao, one of the winners, who says I "hope we can live up to the prize" ($3 million):
http://www.scientificamerican.com/article/with-awards-like-the-breakthrough-prize-who-needs-a-nobel/

Article notes that it is hoped that the prizes'  "lavish payouts and star treatment will turn the winning researchers into household names and inspire future generations to pursue math and science as prestigious careers."
For what it's worth this year's inaugural math winners range from 36 to 56 years of age.

The NY Times coverage here:
http://tinyurl.com/mbdlfam  (possible paywall)

Deadline for making nominations for next year's prize is around the corner on June 30.
In addition to mathematics, there are also "Breakthrough" awards for physics and the life sciences.

Even if the general goal of household-name status and public comprehension of the math achievements is never attained, still love the sentiment of drawing press attention to accomplished mathematicians (...now, most of you can go back to watching the World Cup ;-)).

ADDENDUM:  these awards have opened some debate over the efficacy of such news-grabbing, high $$$ prizes to a select few (versus, perhaps, more, smaller, awards to a greater number of deserving recipients). Anyway, here's Columbia's Peter Woit's somewhat middle-of-the-road-take on the issue:

http://www.math.columbia.edu/~woit/wordpress/?p=6972

Proofs As Artifacts...

Sunday Meditation (to wrap your brain around)…

"Like any other mathematician, Euclid took a good deal for granted that he never noticed.  In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means.
"Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn.
"These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."
-- David Berlinski (from "The King of Infinite Space")

Evangelizing For Math... Devlin and Ellenberg

Keith Devlin, being his usual succinct, persuasive, insightful self, in a new transcribed interview on what mathematics is and the use of digital games for math education (so many good points, and if you skim through, be sure to read his very last response):
http://blogs.kqed.org/mindshift/2014/06/digital-games-and-the-future-of-math-class-a-conversation-with-keith-devlin/

And in a similar vein, still more from Jordan Ellenberg on mathematical thinking (including a new podcast from "Inquiring Minds" with Chris Mooney):
http://tinyurl.com/ojtsykp

Meanwhile, over at MathTango additional link-reads to fill your weekend:
http://mathtango.blogspot.com/2014/06/friday-wrap-up.html

Math… Performing vs. Learning

Stanford's Jo Boaler defends Common Core in this recent 20-min. YouTube video:

Hurry, Read This Post!

Month after month, after month, after month… I get the same "Hurry! Limited Time Only" offer from a certain phone company. Either they have a different conception of "time" than I do, or, perhaps they are actually dealing with an asymptotic limit???
In any event, I think this falls under the consumer hashtag, #IsItAnyWonderIHaveTroubleBelievingYou

Yanofsky on "7th Avenue Project"

My favorite book of 2013 (and one of my favorites EVER!), though not strictly a math book, was Noson Yanofsky's "The Outer Limits of Reason." Yesterday, the author was interviewed on the "7th Avenue Project" (a great radio series, I've just learned of). Try to set aside an hour for a listen:

https://soundcloud.com/7th-avenue-project/noson-yanofsky-radio-interview-the-outer-limits-of-reason
[You may wish to check their archives for past episodes as well.]

I hope you've read Dr. Yanofsky's book, but if not, this podcast will give the flavor of what he discusses therein.

Math As Monasticism, Math As Dynamite

Sunday morning with Jordan...

"Outsiders sometimes have an impression that mathematics consists of applying more and more powerful tools to dig deeper and deeper into the unknown, like tunnelers blasting through the rock with ever more powerful explosives. And that's one way to do it. But Grothendieck, who remade much of pure mathematics in his own image in the 1960s and '70s, had a different view: 'The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration… the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it… yet it finally surrounds the resistant substance.'
"The unknown is a stone in the sea, which obstructs our progress. We can try to pack dynamite in the crevices of rock, detonate it, and repeat until the rock breaks apart, as Buffon did with his complicated computations in calculus. Or you can take a more contemplative approach, allowing your level of understanding gradually and gently to rise, until after a time what appeared as an obstacle is overtopped by the calm water, and is gone.
"Mathematics as currently practiced is a delicate interplay between monastic contemplation and blowing stuff up with dynamite."
-- Jordan Ellenberg in "How Not To Be Wrong"

[...my review of Ellenberg's fine book is now up at MathTango.]

Happy Birthday Grigori (wherever you are)

hmmm… I'm not sure I ever thought of reclusive, brilliant mathematician Grigori Perelman (whose birthday it is today) as "adorable"… but somebody does:

http://xinvogue.blogspot.com/2014/06/mathematics-being-this-romantic-thing.html

[If you wish to watch the video with English subtitles, click on the cc/captions button.]

Pomegranate-Blueberry Juice... NOT!

What follows is one person's opinion….:

Today, a guest post from Albert Einstein… or, well, at least that percentage of me that is a match for Einstein… which is to say a LOT more than the percentage of Coca-Cola's "Pomegranate-Blueberry" juice product that actually contains any pomegranate or blueberry juice...

I wouldn't normally even cover this story, except it deals with something that has ticked me off for a long while… and, hey, there is some simple math involved (tooooo simple perhaps for the minds of corporate America, unencumbered by conscience):
http://www.latimes.com/business/la-fi-court-fruit-drinks-20140422-story.html 

http://tinyurl.com/m3o7r5q  (possible paywall)

In a rare-these-days, unanimous decision, the U.S. Supreme Court has (from NY Times) "allowed a false advertising suit against a Coca-Cola juice blend to move forward, saying the company’s practices 'allegedly mislead and trick consumers, all to the injury of competitors"...
Well, of course, truth-be-told, there's NO "allegedly" about it; this is what major corporations have been actively doing for decades. The story continues: "The blend, sold under Coca-Cola’s Minute Maid brand, is made almost entirely from apple and grape juice. But it is called 'Pomegranate Blueberry,' followed in smaller type by the phrase 'Flavored Blend of 5 Juices.'" A better label might read: "99% NON Pomegranate or Blueberry Juice," or, just as truthfully, "99% NON-Dom Pérignon."

Of course Coke doesn't have a logical, ethical, or honest leg to stand on, though that won't stop high-paid lawyers employing warped reasoning, perhaps for years to come, to argue they are 1 centimeter on this side of an imagined legal line. And the dishonorable marketers who concoct these "truth-in-labeling" blasphemies will intone that 'ohh, everybody does it.'

Yes, this practice isn't just common, it's the norm... fooling the public, with wordplay, into thinking they are getting a healthier, or simply different, product than the one they are wasting $$$ on.** Over the years there have been several scandals involving misbranded fruit juices that contained NO actual juice whatsoever, just water, fructose, coloring, and artificial flavors… often with the major companies involved, claiming that well, 'gee whiz, we had no idea our suppliers were deceiving us with adulturated or fake product… we're shocked, SHOCKED, we tell you'… rrrrrrrrrrrrrrrrrright!

So yeah, I'm peeved that something loudly proclaiming itself on the grocer shelf as Pomegranate Juice can have 1% or less pomegranate juice… hell, I'm peeved it can have only 70% pomegranate juice… but that is the way of corporate America… always squeezing a few more unearned pennies out of the customers viewed as sheep.

And this is just one isolated item brought to attention… how many other products does Coca-Cola et.al. flagrantly deceive customers on??? For now, the operative consumer stance is essentially "caveat emptor"… i.e., DON'T assume anything a company tells you, means what it appears to mean… and ALWAYS read the small print. (Interestingly, POM Wonderful, the company that brought suit against Coke, is battling its own lawsuits against ITS advertising claims.)

Here is some of the "truth-in-labeling" legalese that applies, though it is weak in addressing font styles and sizes:
http://www.law.cornell.edu/cfr/text/21/102.33

Speaking of the 99% figure, and the overpaid shysters, er, I mean, lawyers who argue this case on Coke's behalf, I can only recall Steven Wright's quip, "99% of lawyers give the rest a bad name."

Cathy O'Neil ("Mathbabe") wrote a bit ago that she was boycotting Amazon; I'd like to broaden that out to a boycott of Coca-Cola, or any other company so disrespectful of the paying public. [I know, for some the phrase, "tilting at windmills" will come to mind, but for myself, I won't be purchasing any of these brands for the near-future.]


** ADDENDUM: one of the Coke lackeys lawyers opened mouth wide and inserted foot when she claimed that American consumers were intelligent enough to recognize the difference between a juice and a juice blend… to which Justice Anthony Kennedy aptly responded (bringing courtroom laughter), "Don't make me feel bad, because I thought this was pomegranate juice." 

Sunday Thoughts…

From Freeman Dyson in  "The Scientist As Rebel":

"Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.
"It is a curious paradox that several of the greatest and most creative spirits in science, after achieving important discoveries by following their unfettered imaginations, were in their later years obsessed with reductionist philosophy and as a result became sterile. Hilbert was a prime example of this paradox. Einstein was another…

"Science in its everyday practice is much closer to art than to philosophy. When I look at Gödel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral… The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Gödel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalization into unexplored territory."

Yo America, Does This Sound Familiar…

 Australia has a problem with math education:

"Mathematics is in a death spiral in Australian schools."  That's just the first sentence in this story on the "maths crisis" in Australia (h/t to Egan Chernoff):

http://www.afr.com/p/national/education/australia_maths_crisis_I3P1MZ7bcKJKqiyOSnGDVM

...much of this will sound familiar to readers of American math, STEM, and gender woes.

Mathematicians, Employment, and NSA… Ohh My

hmmm... working for NSA??? Nothing too new in this controversy (Keith Devlin and some other mathematicians have been raising it for awhile now), but it's a tad unusual to see Forbes magazine covering it:

http://tinyurl.com/o2qermv

As one mathematician wrote: "Any relationship with an organization whose activity is so harmful for the fabric of human society is unhealthy. For the sake of integrity, the AMS should shun all contacts with the NSA.”

or as Keith Devlin, wrote: “I think mathematicians should refuse to work for the NSA until they both follow the US Constitution and demonstrate responsible use of mathematical tools. The latter is something they clearly failed to do by engineering weaknesses into mathematical crypto systems, which mathematicians know to be a very dangerous thing to do. I think it is very regrettable that the current NSA leadership has broken the immense goodwill that most of us in the mathematical community once had toward them.”

[Some of Dr. Devlin's views are contained in this interview I did with him a year ago:
http://mathtango.blogspot.com/2013/06/keith-devlin-as-you-may-not-have-heard.html ]

Oh, and by the way, a similar debate is occurring in Britain as well -- see this new post from "n-Category Cafe":
http://golem.ph.utexas.edu/category/2014/06/should_mathematicians_cooperat_2.html 

which was preceded by these two posts (by same author):
http://golem.ph.utexas.edu/category/2014/04/should_mathematicians_cooperat_1.html#more 
http://golem.ph.utexas.edu/category/2014/03/should_mathematicians_cooperat.html

Let Z1 be Z-Squared + C...

Why am I re-running, yet again, Jonathan Coulton's tribute to Benoit B. Mandelbrot...? Because I suddenly realized that this week marked the 4-year anniversary for Math-Frolic being around, which means 4 years of fun for me -- at the moment don't have time for a new post, though, so will just fill in with this favorite rollicking bit from 4 years ago:



lyrics:

Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set and the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born

His disdain for pure mathematics and his unique geometrical insights
Left him well equipped to face those demons down
He saw that infinite complexity could be described by simple rules
He used his giant brain to turn the game around
And he looked below the storm and saw a vision in his head
A bulbous pointy form
He picked his pencil up and he wrote his secret down

Take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set

Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way

Mandelbrot's in heaven, at least he will be when he's dead
Right now he's still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home

Just take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C and so on
If the series of Z's should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandelbrot Set you're a Rorschach Test on fire
You're a day-glo pterodactyl
You're a heart-shaped box of springs and wire
You're one badass f**king fractal
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
And you're just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Go on change the world in a tiny way
Come on change the world in a tiny way

Chaitin on the Seduction of Mathematics

I didn't have any Sunday reflection picked out for today, but then Joselle Kehoe posted something that makes for a good one:

http://mathrising.com/?p=1160

It's about Gregory Chaitin reflecting on Ramanujan, Cantor, Euler, and mathematics as a seductress!

a couple of provocative lines:

From Chaitin:

"I believe mathematics is based only on emotion and inspiration and it’s totally irrational and we don’t know where it comes from especially in cases where it’s an obsession."

 and from Joselle:

"...maybe the right way to think about the universe is that the universe is a computation  – computing its future state from its current state.  One can think of everything as a computation – understanding, the physical universe, DNA, as well as current technology."