The New Pythagoreans: The Secret Society of Modern Math

Donald Duck in Mathmagic Land

When I was a child, I remember seeing a Disney short about mathematics called Donald in Mathmagic Land. In it, I learned about the Pythagoreans, a secret math society from Ancient Greece who believed that all the universe consisted of countable numbers.

Pythagorus, the founder of the society, never published any mathematical work. Or at least, nothing survives that can be attributed to him. Pythagorus started the group after discovering that musical harmony at its root was a ratio of whole numbers. Pythagorus wondered if all orderings of the universe were in truth ratios of countable numbers (what today we would call rational numbers) and formed his society with the task of unlocking these secrets.

The story is that Pythagorus was passing a blacksmith when he heard what sounded like musical notes each time the blacksmith hammered on his anvil.  Pythagorus stopped in to investigate and discovered that that the blacksmith had three anvils of different sizes.  One anvil was 1/2 the size of the largest and the smallest was 2/3 the size of the largest.  

Modern Mathematics: A New Secret Society

On the surface, mathematics seems to be in the open. After all, it's required study in both high school and college. But, deeper down, if you think about it, it is a secret society.

On the surface, mathematics is about problem solving. You are given a formula, then a word problem, and then you must use the formula to solve the world problem. The goal of mathematics seems to be to challenge your problem solving skills and logic.

The way that mathematics is taught, it is perhaps very surprising to learn that the problem solving aspect has little or no interest to the professional mathematician. Indeed, the basic mathematics of school: algebra, geometry, trigonometry, and calculus, are for the most part, completely ignored. They are after all well established and not in need of expansion.

The technique of interest to the mathematician is the mathematical proof. While on the surface, math seems to be about intellectual development and problem solving, it is for the practitioner, a search for underlying patterns and harmonies. Mathematics, the way it is studied by mathematicians, is really about beauty and truth. While it may appear to be about engineering and accounting, mathematics really has more in common with art and science.

Math Papers: A secret code

It is as if all math papers are encoded in unfathomable mathematical terminology. According to the Disney documentary, each Pythagoreans need to show the symbol of the pentagram in order to gain admittance to Pythagorean gathering. In todays, mathematics, to gauge the underyling logic requires far more substantial knowledge.

The reason that the Pythagoreans chose the pentagram is for me very interesting. The ratio of the sides of the pentragram represent the golden ratio. The details of this ratio can be found here.

Professional mathematicians today seem to feel little or no obligation to share their knowledge with the uninitiated. Indeed, it seems to me that the true wonders of mathematics, today, are only communicated to other mathematicians. If you are not a member of the Modern Pythagoreans, then you are not invited to share in their wisdom and their insights.

There is a coterie of brave souls who try to translate mathematics for the general reader. They try to write on topics that will appeal to the general reader and share some of the amazing ideas which has been part of the last two hundred years of mathematics. Unfortunately, because of the math drillings in school, they have a difficult market. Few people are open to hearing about math voluntarily.

Facebook takes and stores data, numbers from your iPhone

People using the iPhone Facebook app could unknowingly be sharing their number, their friend's numbers and their friend's friend's numbers thanks to a syncing feature. 

Facebook's "Contact Sync" feature synchronises your friends' Facebook profile pictures with the contacts in your phone, but instead of keeping them safely on your handset it imports all the names and phone numbers you have on your phone, uploads them to Facebook's Phonebook app and lets you and your mates view everyone's details. It's taking data from your handset.

As The Guardian's Charles Arthur points out: "The implications are huge, and extremely worrying. All it takes is for someone's Facebook account to be hacked (perhaps via their phone being stolen) and lots of personal details are revealed."

According to The Guardian, a bloke called Kurt von Moos wrote up his privacy concerns this year. He says that there are a number of reasons to be concerned.

Firstly, Facebook doesn't warn users that they are uploading their phone's address book to Facebook.

As Facebook doesn't sync contact numbers or email addresses to phones, most users wrongly assume that Facebook Contact Sync only syncs user pictures. In reality though, they are flashing your address book, without your consent.

Facebook says you can remove your mobile contacts, but it's not clear that that will remove your mobile if someone else uploads it.

On the Facebook Phonebook page it says: "If you would like to remove your mobile contacts from Facebook, you need to disable the feature on your mobile phone and visit this page."

However, when we had a go, the page said "Please try again later". 

Tendulkar beats Swann to top cricket award

Graeme Swann was today beaten by Sachin Tendulkar to the International Cricket Council Cricketer of the Year prize.

England spinner Swann was edged out by India legend Tendulkar for the top gong at the ICC Awards in Bangalore.

But there was good news for Swann's team-mate Steven Finn, with the fast-bowler named Emerging Player of the Year.

Swann, 31, was short-listed along with Tendulkar, India batsman Virender Sehwag and South Africa's Hashim Amla.

ICC officials were left red-faced in August when they initially excluded Nottinghamshire off-spinner Swann from their long-list of contenders, despite him taking 49 wickets in Tests and 28 in one-day internationals during the qualification period.

An outcry followed and the ICC quickly added Swann to the list, describing his omission as "an oversight".

Swann had been hoping to follow in the footsteps of recently-retired team-mate Andrew Flintoff, who shared the Sir Garfield Sobers Trophy with Jacques Kallis in 2005.

Middlesex's Finn, meanwhile, beat off competition from Pakistan's Umar Akmal, Sri Lanka's Angelo Matthews and Australia's Tim Paine to land the emerging player prize.

The 6ft 8in fast bowler, 21, played in six Test matches during the voting period, taking 27 wickets at an average of 21.85.

Receiving his award from legendary West Indies bowler Joel Garner, Finn said: "It's a great honour to win this, an award I wasn't expecting and I'm very pleased and honoured to be playing Test match cricket for my country.

"I've enjoyed the last few months representing my country and I hope it continues.

"Next up is the Ashes and I think we're well prepared to win the series - we've got a settled side ready to go for this winter."

Swann had the consolation of being named in the Test Team of the Year along with James Anderson, while Paul Collingwood and Stuart Broad were selected in the One-Day International Team of the Year.

Tendulkar also claimed the inaugural LG People's Choice Award, with England captain Andrew Strauss among those to miss out.

Tendulkar said: "I'm really excited to have won two awards and this last season for the entire team has been really special.

"To win both of these awards tonight, Cricketer of the Year and the LG People's Choice Award, is special and it's the game's way of appreciating someone's performance.

"It feels great to have two trophies in front of me and I am feeling very proud and happy."

During the voting period, the 37-year-old from Mumbai played in 10 Tests, making 1,064 runs, including six centuries, at an average of 81.84.

Tendulkar also played in 17 ODI matches in the time period, smashing his way to 914 runs at an average 65.28 in a period, including a record-breaking double-century against South Africa in Gwalior.

Tendulkar lost out to Sehwag and South Africa's AB de Villiers in the Test Player of the Year and ODI Player of the Year categories, respectively.

England's Katherine Brunt, meanwhile, was beaten by Australia all-rounder Shelley Nitschke to the Women's Cricketer of the Year prize.

But former captain Rachael Heyhoe Flint made history by becoming the first female inducted into the ICC Cricket Hall of Fame.

Japan issues Europe travel alert, joining US

Taipei, Taiwan

• A daily summary of global reports on security issues.

Japan on Monday issued a travel alert for visitors to Europe, reflecting widening concerns over terror strikes in Europe by militants trained in Pakistan, some of them possibly European citizens.

Tokyo's alert followed a similar one from the United States on Sunday, which drew support from the United Kingdom and France. The UK raised its terror warning to "high" for its nationals in France and Germany after the US announcement. But Germany has said it sees no danger of imminent terror attacks, and German intelligence is skeptical of the warnings, reportsAgence-France Presse today.

Japan's alert, issued by its Foreign Ministry, "made no mention of a specific country, but advised its citizens to be cautious when using public transport and visiting popular tourist sites," according to The Guardian. "An official at the ministry said that the highly unusual warning was not prompted by any specific intelligence but by the previous British and American alerts."

A Japanese official also told the Associated Press it was very unusual for Tokyo to issue such an alert, a sign of how seriously the threat is being taken by governments the world over.

Neither Japanese nationals nor Japan itself have have been major targets of Al Qaeda terrorism. The attack in August on a Japanese oil tanker was said to be the first Al Qaeda attack on a Japanese target – and though an Al Qaeda-linked group claimed responsibility, the veracity of that claim is still in question. In 2004, a French citizen with alleged Al Qaeda connections was arrested by Japanese police, according to a report at that time from the Associated Press, although French authorities said claims were "exaggerated" that the suspect was trying to start an Al Qaeda cell in Japan.

In 2008, Al Qaeda's number two, Ayman al-Zawahri, implied in taped responses to questions from Japan's Kyodo News service that Japan was an Al Qaeda target because of its alliance with the US and its assistance to the invasion of Iraq. Japan had sent a 600-member non-combat contingent to Iraq to help the country's reconstruction, and also helped fly equipment between Kuwait and Iraq.

"Why did the Japanese start the aggression on us within the alliance of the Americans?" Zawahri said, according to Kyodo News. "Our Islamic faith incites us to resist the despots and tyrants, even if they were the most powerful force on Earth so will Japan learn a lesson from this?"

The US alert, published Sunday, warns US citizens to the "potential for terrorist attacks in Europe" targeting "official and private interests" including "public transportation systems and other tourist infrastructure."

"US citizens should take every precaution to be aware of their surroundings and to adopt appropriate safety measures to protect themselves when traveling," according to the State Department alert, which is less severe than an official "travel warning."

The New York Times, in a Sunday report, quotes terrorism expert Bruce Hoffman complaining about the vagueness of the alert.

“Usually they’re at least country-specific,” Dr. Hoffman said. “This one is an entire continent. I’m not sure what it says, beyond the fact that the world’s a dangerous place, and we already knew that.”

But the Times also quoted an anonymous US counterterrorism official saying the threat of attacks on Europe was credible, but that not enough details were known yet about the plot to issue more specific advisories.

The German intelligence community is skeptical of warnings about imminent attacks on Europe. German daily Der Spiegel reports today that one main source of the intelligence that has worried US officials is Ahmad Sidiqi, a German jihadist currently in US custody in Afghanistan and being questioned by "special units of the CIA and the American military."

His statements apparently alarmed Sidiqi's American interrogators. Still, it remains unclear whether the reports can be considered reliable or whether Sidiqi's claims are the typical Al Qaeda brew, consisting of one-third truth, one-third lies and one-third omission. Although the CIA is taking Sidiqi seriously, German authorities are more reserved in their analysis.

A German diplomat met with Sidiqi on Sunday, and German intelligence officials are preparing to travel to Afghanistan to question Sidiqi themselves, Der Spiegel reports.

In France, the daily Le Monde reports today that the French public deemed labor strikes a more pressing problem than terrorism, according to a France Info-20 Minutes poll. But 79 percent of the French public did say terrorism was a "serious" or "very serious" threat, the poll found.

Meanwhile, American tourists interviewed by the Associated Press in Paris on Monday said the alert had not disrupted their travel plans. And NBA teams in Europe for pre-season exhibition games will continue their tours as scheduled, the Associated Press also reported.

Meg Whitman’s Illegal Housekeeper Threatens Race For California Governor

Further proof that the personal is political: Today’s second debate between California gubernatorial rivals Meg Whitman and Jerry Brown was dominated by a scandal over Whitman’s former illegal immigrant housekeeper.

Channeling the Zoe Baird-Kimba Wood controversies–each withdrew her name from consideration for attorney general during the Clinton administration for hiring illegal immigrants as domestic help–Brown was on the offensive as to how Whitman, the GOP candidate, had an illegal immigrant housekeeper on the payroll for nine years and, according to her, didn’t know it.

“Don’t run for governor if you can’t stand up on your own two feet and say, ‘Hey I made a mistake,”‘ Brown said at the forum at California State University, Fresno, which was hosted by Spanish-language network Univision and the first California gubernatorial debate broadcast in Spanish. ”You have blamed her, blamed me, blamed the left, blamed the unions. But you don’t take accountability.”

Whitman told reporters after the debate that the controversy over Nicky Diaz Santillan, who the former CEO of eBay says confessed to being an illegal immigrant last year and was subsequently fired, is just a distraction to her race for governor.

Immigration is a high-profile issue in California, with 2.6 million illegal immigrants in the state and the home of one-quarter of the nation’s total illegal immigrant population.

“The real tragedy here is Nicky,” said Whitman in the debate with Brown, the Democrat state Attorney General who served two terms as governor of California from 1975-83. “After Nov. 2, no one’s going to be watching out for Nicky Diaz. And Jerry, you know you should be ashamed, you and your surrogates … put her deportation at risk. You put it out there and you should be ashamed for sacrificing Nicky Diaz on the altar of your political ambitions.”

Don’t break out the Kleenex just yet: Gloria Allred, a supporter of Democratic candidates, is the housekeeper’s (unpaid?) attorney–one and the same lawyer who represented Tiger Woods’ reputed mistress Rachel Uchitel to the tune of at least a $1 million settlement last year. Allred said Whitman caused Diaz Santillan to “feel exploited, disrespected, humiliated and emotionally and financially abused,” and is filing a claim for unpaid wages and mileage reimbursement.

Diaz Santillan alleges Whitman knew she an illegal worker but overlooked it until her run for governor. ”‘Don’t ask don’t tell’ may have become, ‘Oh my God she will tell if I continue to employ her,’” said Allred.

First reaction is that Whitman, one of just 14 female billionaires in the world who earned their fortunes, rather than inherited them, probably wasn’t paying too much attention to her housekeeper’s immigration status. And the Whitman campaign has provided Diaz Santillan’s immigration, IRS and Social Security information from 2000 that she says was a legal resident.

Then again, at today’s press conference Whitman told reporters, “For the 10 years, nine years she worked for me, she called me Meg and I called her Nicky.” Pretty chummy/gullible/hypocritical for someone who is campaigning for a crackdown on employers.

There is no doubt that some California residents–let’s say 25%–are unbothered, even cheered, by her hiring Diaz Santillan in the first place. And we can talk about the double standard in regard to working women politicians who have to answer to questions about domestic help when their male counterparts don’t.  Although, in defense of males politicos, there are many more questions about their “help” in the bedroom vs. the kitchen and laundry room.

Or we can stick to the facts, the law and voters’ right to full transparency.Did she or didn’t she know…or did she or didn’t she want to know? Californians deserve answers.

Upshot: Whitman profited by hiring Diaz Santillan. Brown gained political points by calling out Diaz Santillan. Allred is sure to gain buzz and clients from the case.

What do you think? Leave your comments below and let’s see how the story pans out.

Pakistan win 4th one day by 38 runs from England

Pakistan win 4th one day by 38 runs from England

پاکستان کی طرف سے عمر گُل ایک بار پھر کامیاب ترین بالر رہے۔ انہوں نے بتیس رنز دے کر چار کھلاڑیوں کو آؤٹ کیا۔ عمر گُل نے اوول میں کھیلے گئے تیسرے ایک روزہ میچ میں انگلینڈ کے چھ کھلاڑیوں کو آؤٹ کر کے پاکستان کی جیت کو یقینی بنایا تھا۔

دیگر پاکستانی بالروں نے بھی انہیں اچھی مدد فراہم کی۔ شعیب اختر نے تین جبکہ سعید اجمل نے دو کھلاڑیوں کو آؤٹ کیا۔

انگلینڈ کے اوپنرز نے ایک عمدہ آغاز فراہم کیا تھا اور ایک سو تیرہ رنز کی پارٹنر شپ بنائی تھی لیکن بعد میں آنے والے کھلاڑی اس شاندار آغاز سے فائدہ نہ اٹھا سکے۔

انگیلنڈ کی آؤٹ ہونے والے پہلے کھلاڑی ایس ایم ڈیویز 49 رنز بنا کر سعید اجمل کی گیند پر بولڈ ہوئے۔ ان کے بعد آنے والے کھلاڑی جوناتھن ٹراٹ چار رنز بنا کر آفریدی کی گیند پر بولڈ ہوئے۔

اس کے فوراً بعد شعیب اختر کی گیند پر فواد عالم نے سٹراس کا ایک عمدہ کیچ لیا۔ سٹراس نے آٹھ چوکوں کی مدد سے اڑسٹھ رنز بنائے۔

پال کولنگووڈ کو چار کے انفرادی سکور پر عمر گل نے بولڈ کیا۔

اس سے قبل عبدالرزاق نے پاکستان کی اننگز کے آخری اوورز میں جارہانہ بیٹنگ کرتے ہوئے آٹھ چوکوں اور ایک چھکے کی مدد سے صرف بیس گیندوں پر چوالیس رنز بنائے۔ رزاق نے اننگز کے پچاسویں اوور میں ٹم بریسنن کو لگاتار پانچ چوکے لگا کر اکیس رنز سکور کیے۔

پاکستان کی جانب سے محمد حفیظ سب سے زیادہ چونسٹھ رنز بنا کر گریم سوان کی گیند پر ٹراٹ کے ہاتھوں کیچ آوٹ ہوئے۔

گریم سوان نے چار وکٹیں حاصل کیں۔ انہوں نے محمد حفیظ کے علاوہ فواد عالم (29)، اسد شفیق (11) اور محمد یوسف (3) کو آؤٹ کیا۔

پاکستان کے کپتان آفریدی نے جارحانہ انداز میں بیٹنگ کرتے ہوئے تین چوکوں اور دو چھکوں کی مدد سے بائیس گیندوں پر 37 رنز بنائے۔ ٹِم بریسنن کی گیند پر سٹراس نے ان کا کیچ لیا۔ عمر اکمل اکیس رنز بنا کر کیچ آؤٹ ہوئے۔

پاکستان کی پہلی وکٹ باسٹھ کے مجموعی سکور پر گری جب کامران اکمل کیچ آؤٹ ہوئے۔ کامران اکمل نے بتیس گیندوں پر چار چوکوں اور ایک چھکے کی مدد سے اٹھائیس رنز بنائے اور سٹورٹ براڈ کی گیند پر سٹراس کے ہاتھوں کیچ آوٹ ہوئے۔

انگلینڈ کے سپنر گریم سوان نے اپنے پہلے ہی اوور میں اسد شفیق کو بولڈ کردیا۔ اسد شفیق صرف گیارہ رنز بنا کر آوٹ ہوئے۔ سوان نے اپنے اگلے ہی اوور میں محمد یوسف کو بھی آؤٹ کر دیا۔ محمد یوسف نے صرف تین رنز بنائے۔

9/11 memorial ceremony at ground zero simple, poignant

New York

Thousands of victim’s family members, friends, and onlookers gathered on a cold, windy morning to commemorate the ninth anniversary of the September 11 terrorist attacks in New York City.

A simple raised platform fronted the rising skeleton of the Freedom Tower – the World Trade Center Memorial. Family members of some of the 2,752 World Trade Center attack victims alternated with workers engaged in the rebuilding effort as they read the names of those who had died. The simple, poignant ceremony was punctuated by four moments of silence, noting the exact times that planes struck the twin towers, and when those towers fell.

For Charlie Jaffe, a teacher who lost his brother-in-law Lonny Stone that day, nine years has done little to heal the sudden, senseless loss.

IN PICTURES: Revisiting Ground Zero

“My wife still cries every year. She used to cry two months before, now it is two weeks before. Maybe now we don’t anticipate the dread with as much trepidation as we did,” Mr. Jaffe says. Still, he takes some comfort in the small joys the passage of time brings. A friend of his brother-in-law had fathered twin baby girls who later attended Jaffe’s school. “It’s the only solidarity I can really feel.”

A few major political figures – Vice President Joe Biden, New York City Mayor Michael Bloomberg, and former mayor Rudy Giuliani – shared the stage with victim’s families, but their comments were short, confined to the recitation of poetry.

Politics, however, were not entirely absent, as family members spoke to the media about ongoing controversies regarding the proposed Islamic center and mosque near the ground zero site, and the furor over a Florida pastor’s threats to burn the Quran. Protests and counter-protests for Park51, the name of the controversial community center, were expected to grow during the day.

Among the earliest visitors to the memorial site was Tavis Moonan, who sat high on a stone wall, alone, by 7 o’clock in the morning. “I feel connected … I certainly remember where I was when it happened,” Mr. Moonan says. “I’m fairly liberal but at the same time I’m patriotic. What it has given us has not all been good, but we are definitely united.”

“I don’t know that there is going to be forgiveness for the individuals involved and for the motive for the event,” he says. “There will be forgiveness for the faith, but the mosque debate certainly hasn’t helped.”

Kathy Usher, whose son works as a New York firefighter, was at ground zero to remember, and to wish for a brighter future. “We just want peace in this world,” Ms. Usher says. “Rebuilding is not just about rebuilding ground zero, but about rebuilding the human spirit…. We can never forget, but we have to build.”

Carl Clark made his pilgrimage to the site early, to mourn while the plaza was still empty. Mr. Clark, who works in finance, says many friends and colleagues of his perished on September 11, fundamentally altering his world.

“This has become the central holiday of the year for me,” Clark says. “Like any traumatic experience, you relive it, and you almost become … entrenched in it, in the reliving.” He is happy that the memorial tower is rising, quickly, after years of false starts. The site has become “an emptiness I can’t deal with…. I grew up with the twin towers.”

It took over three hours to read the names of the victims as the day grew warmer, and family members cried and clutched each other throughout. Some carried pictures or flowers. One woman wore a shirt asking “Who was Johnny?”

“Johnny was a twinkle in the eye,” the shirt read. “He was a trekkie from the beginning, a little geeky at times, and a deadhead to the end.”

In the afternoon, after the ceremony ended, protests over the controversial mosque would grow. But for the time being, all was silent, save the names of those who were lost.