Sage: Goldbach's Comet

I ran across Goldbach's Comet while surfing the net. This seemed like a straightforward Sage problem, so I spent some time creating a Sage Interact. You can find the code on the Python/Sage page. Copy and paste the code into a Sage cell server such as the ones on the Sage Sandbox page and you're ready to experiment. The image above was created by going up to 100,000. Though I didn't time it, I'd estimate it as taking about 30-40 minutes. The code posted has changed the max value to 1,000--you'll have to experiment what setting runs best on your computer. The link Goldbach.pdf in the bottom left creates a PDF file of your graph to download.

Here are some stories that caught my eye:

  • The fallout from the election has snowflakes melting: ZeroHedge with a piece on Ohio State offering "safe spaces" for students to survive the Trump inauguration. And do you remember how I pointed out how Trump was getting large crowds while Clinton was being chased around in Florida? Leave it to the media to explain that they didn't really miss the signs, they just chose not to mention them. But--if you believe them-- this means that the statisticians were even more clueless and inept. PJmedia with a piece "Chuck Todd Admits Media Treated Hillary with Kid Gloves" where"...NBC’s Chuck Todd confessed that he and others in the mainstream news media played down just how despised Hillary Clinton was in the heartland due to the fear of appearing “sexist.” ...“Where I think political correctness got in the way of what we all knew as reporters and didn’t fully deliver was how hated the Clintons were in the heartland,” the “Meet the Press” host admitted Thursday to former Bush White House press secretary Ari Fleischer in a interview for the “1947” podcast. “And I think it was a fear of, ‘Oh, is it going to look like it’s sexist, anti-woman if we say that?’” he added, pointing out that on the hustings he saw numerous “Hillary for Prison” signs adorning the front yards of rural America. “I think we underplayed it a little bit out of political correctness fears,” Mr. Todd said. “No member of the press corps wants to look like they’re singling out a group and making a group feel bad, right, whatever that [group] is. “If we sort of were straight-up honest and blunt about hey do we understand the level of hatred that’s out there and you know, all the Hillary for Prison signs that are out there, we certainly would have at least made the viewer know, hey, you know, she’s not well-liked in some places in this country in ways that’s times 10 when it comes to Trump,” he said." Refreshing honesty in reporting---once it's too late to do you any good. They aren't called presstitutes for nothing.
  • Anonymous with 10 lies you were taught in high school.
  • RT reports "Scientists add letters to DNA alphabet to create ‘semisynthetic’ life"
  • Tolerant snowflakes, ZeroHedge reports, "The NYU College Republicans likely had no idea what they were setting themselves up for when they invited Vice Media co-founder Gavin McInnes to speak on their campus.  Two years ago such an event almost certainly would have gone completely unnoticed but for the the couple of hundred students in attendance.  But in today's post-Trumpian world, every appearance of a conservative personality is taken by intolerant Leftists as just another opportunity to destroy public/private property, incite violence and shout catchy slogans incorporating the word "Nazi." According to Reuters, McInnes' speech was cut short when protesters rushed into the room where he was speaking and began interrupting him.  The protesters subsequently scuffled with police officers and McInnes supporters outside the university's student center in New York City, where he was invited to speak by NYU College Republicans."" And check out the screaming woman, claiming to be a profession, with a tirade of profanity. Because free speech only matters to these goons when it is speech they agree with.
  • Where else than California for a 1.5 billion dollar budget error. "...we, as taxpayers, generally rely on our expensive budget office employees to at least present annual budgets that reflect sound mathematics and accounting principles.  Unfortunately, that seems to be too much to ask of the math-challenged administration of California Governor Jerry Brown which decided to double count certain cost savings and simply "forgot" to incorporate other expenses altogether....Embarrassingly, when asked about the "mistakes" that resulted in a $1.6 billion budget deficit, the Chief Deputy Director of Brown's Department of Finance could offer no other explanation than that the "math was wrong" while another spokesman admitted, “There’s no other way to describe this other than a straight up error in accounting, which we deeply regret."" Don't hold your breath waiting for accountability even though that would get you fired at your job. Is a tax increase coming?
  • Intellihub with the statistic of the day, "Here is a staggering statistic from the National Alliance on Mental Illness (NAMI): “More than 25 percent of college students have been diagnosed or treated by a professional for a mental health condition within the past year.Let that sink in. 25 percent. Colleges are basically clinics. Psychiatric centers. Colleges have been taken over. A soft coup has occurred, out of view.You want to know where all this victim-oriented “I’m triggered” and “I need a safe space” comes from? You just found it. It’s a short step from being diagnosed with a mental disorder to adopting the role of being super-sensitive to “triggers.” You could call it a self-fulfilling prophecy. “If I have a mental disorder, then I’m a victim, and then what people say and do around me is going disturb me…and I’ll prove it.”
  • HeatStreet with a piece on "bias response teams" which notes, "....“Bias Response Teams” are creeping onto university campuses across the country. This was the conclusion of the first national survey of Bias Response Teams done by the Foundation for Individual Rights in Education (FIRE). The report identified 232 public and private American colleges and universities that had bias response teams on their campuses in 2016, affecting around 2.8 million students. BRTs encourage students to formally report on other students and faculty members whenever they perceive that someone’s speech is “biased,” which threatens free speech. Most universities receive a variety of complaints from students, including students who encounter “offensive” yet legally protected speech, but rather than responding to these incidents fairly if there’s an actual threat, campuses with Bias Response Teams conduct an investigation and if the “respondent” is found “guilty”, invite them for a “hearing”. Examples of Bias Response Teams exercising their power include a student humor publication at the University of California, San Diego (UCSD) that lost its funding after making fun of “safe spaces” on campus. They got their funding pulled after people filed bias incident reports, one openly calling the university to “stop funding”. At Ohio State University, students had to attend a “mandatory floor meeting about triggering events” after a group of students was reported for sharing memes comparing Hillary Clinton to Adolf Hitler. Students who dressed up as the “Three Blind Mice” for Halloween at the University of Wisconsin at Platteville were also reported, as the complainant felt the costumes could be interpreted as making of fun of disabilities."
  • Can a cone roll uphill? Yes!
  • Unz Review with an interesting educational story: "No Thug Left Behind"
  • Alphago was playing incognito over the internet and destroying the competition, "...AlphaGo took a clandestine route to toppling the worl'd top ranking players. Starting on December 29th, 2016, a newcomer used the account names Magister and Master on the Tygem and FoxGo servers and caused quite a stir among players and observers alike. Master defeated a long list of top Go players including Korea’s Park Jung-hwan, rated No. 3 in the world, Japan’s Iyama Yuta (No. 5) and China's Ke Jie who has held the No. 1 spot since mid 2014....Master won successive 51 games before his 52nd rival, Chen Yaoye (No.13), went offline, forcing the game to be recorded as a tie and by January 4th had clocked up 60 wins, that single draw and no losses....the user registered as "Master" provided his real identity - AlphaGo's Doctor Huang, a member of the Google DeepMind team - on foxwq.com.While Ke Jie still has his No. 1 ranking AlphaGo is already No. 2 and it seems doubtful that any human will ever beat it again. This is something that Ke Jie is finding hard to accept. Ali Jabarin, a professional Go player, who came across Ke soon after one of his defeats by the AI reported: "He [was] a bit shocked... just repeating 'it's too strong.'"". Now GBTimes reports AlphaGo will play the worlds top human in April. "The match between Ke Jie and AlphaGo will take place in Wuzhen, China’s eastern province of Zhejiang. If Ke loses the best-of-three match, China, Japan and South Korea may each form a team and challenge AlphaGo."

Trump. Because statistics isn't math

Let me just start this touchy subject by saying I didn't vote in the election, which was the winning choice this election cycle, because I didn't like any candidate. George Carlin says it best. That said, the coverage of the election and more importantly the polls were obviously biased/rigged/wrong, pick the word you like best. And given the absolute shock by soooooo many people, I have to revisit the truth, as I mentioned just last post, that statistics of polling isn't math. That showed that not only do the +/- percent errors not mean what you think, but trained hacks statisticians can have exactly the same data and come up with several different answer. That's not how it's done in math. Previously we saw the BS field of statistics make a major error with respect to Brexit, when virtually everybody got it wrong. Trillions of market cap were wiped off the financial markets. That great job was followed up with the recent US election. Once again statisticians were wrong-- BADLY wrong --with over a trillion in losses for the week. Check out Goldseek's summary of polling data before the election. TheWrap also has plethora of pre-election predictions for electoral college, percentage chance of winning, and percentage to win by: L.A. Times: Clinton 352, Trump 186, Moody’s Analytics: Clinton 332, Trump 206, Rothenberg & Gonzales: Clinton 323, Trump 197, Sabato: Clinton 322, Trump 216, FiveThirtyEight: Clinton 302, Trump 235, Associated Press: Clinton 274, Trump 190, New York Times Clinton 85 percent chance of winning, Hypermind: Clinton 74 percent chance of winning, PredictWise: Clinton 89 percent chance of winning, Reuters/Ipsos States of the Nation: Clinton 90 percent chance of winning, ABC News Political Analyst Matthew Dowd: Clinton 95 percent chance of winning, Bloomberg: Clinton +3, CBS News: Clinton +4, Fox News: Clinton +4,Reuters: Clinton +3, ABC/Washington Post: Clinton +4, Monmouth: Clinton +6, Economist/YouGov: Clinton +4, Rasmussem: Clinton +2, NBC News: Clinton +6.

Those numbers were backed by strident rhetoric regarding the impending, decisive victory of  Clinton. NYPost on the pundits who got it so wrong, including: "Deadspin columnist and GQ correspondent Drew Magary went so far as to publish a scathing piece about the Republican candidate on Sunday — titledDonald Trump Is Going To Get His Ass Kicked On Tuesday.”" TheNewser mentions "Princeton ace Sam Wang, who in mid-October tweeted, "It is totally over. If Trump wins more than 240 electoral votes, I will eat a bug."" . Let's hope he is a man of his word and does it. But don't hold your breath. Even some of the margins of victory were way off: The Telegraph reports "In Iowa, the result was over six percentage points more in favour of Trump than the final polling average. In Ohio - the key bellwether state that has sided with the winning candidate in every presidential election since 1964 - the average polling was five points out....Non-college educated white people make up 41.2 per cent of Indiana's population, for example. The polling gap here was 8.6 percentage points - with the polls giving an average 10.7 point lead to Trump, compared to the actual 19.3 point lead he managed...Wisconsin...was a huge 7.4 percentage point gap between the polls and the result here: the average polling on Real Clear Politics before the vote had Clinton winning by 6.5 percentage points, when in fact Trump claimed the state by 0.9 points."

Which led TheWrap to ask how is it possible to be so wrong? While statisticians are confident of their pre-election prediction, once their wrong, they have no trouble coming up with a excuse reason as to why. From the link "Another theory is that many Trump supporters were simply ashamed to admit that they were going to vote for the GOP nominee and lied to pollsters. Trump is one of the most polarizing figures in American history and many voters wouldn’t even admit it to a complete stranger looking to conduct a poll.". That was a Brexit excuse, too. And yet they were still so sure of their prediction, rather than reduce their percentage of winning to reflect the possible problem. Maybe next time? Some claim the results are lies. Maybe some, but with trillions of dollars of investment capital being lost through Brexit and the US election, there is a lot of "smart money" that should have known better. When you mess things up that badly in math, you look through your work, find the error and fix the problem. In statistics, you find an excuse, or better yet multiple excuses as to why you're wrong and do it again. With each reason you hear ask yourself "then how can they be so sure?".

Of course, some will state "nobody saw it coming". But that's true only if you watch MSM. Check out the Keiser Report, for example where at the 9:35 mark they mention Chris Whalen and Jim Rickards. Chris Whalen is interviewed there. Jim Rickards had a more guarded prediction here. But nobody was more vocal than Andy Hoffman. And, oh yeah, he predicted Brexit, too. But these guy aren't pollsters. Curious, There's a lesson in there somewhere.

And it's not like it was difficult to see some problems: Kaine canceling a Sarasota, Florida rally after only 30 people (about half of which were press) showed up at his West Palm Beach rally. Meanwhile Trump had a different experience: "Republican presidential nominee Donald Trump held a massive rally Tuesday evening at an airplane hangar in Melbourne, Florida to a massive crowd of about 10,000 supporters-while an equal number were turned away when the fire marshal declared the event at capacity....Neal interviewed the last person in line allowed in, Rachel Padrick-Miller. She had been in since 2 p.m. When the fire marshal cut off the line she said ‘thousands were trying to break through the line…jumping the barricades.". And Clinton? "The New York Times features a photo of Hillary Clinton being welcomed to an early voting site in Pompano Beach, Florida on Sunday…
Surrounded by screaming TRUMP supporters!
". Not to mention people chanting "Lock her up!". And see the 11:33 mark of the Keiser Report link above where they witnessed so much more Trump support in North Carolina that they couldn't reconcile with what the pollsters were predicting guessing.  This attendance deficit was in lots of states which witnessed packed Trump events versus a few hundred Clinton supporters. Statistical hacks saw nothing wrong with there models despite the fact that these are the people more likely to go out and vote [See Reuters story below]. They were also aware of Wikileaks and the other umpteen excuses and yet they still were sure of a Clinton win. Now they will "fix" the models. But don't expect the predictions to get any better 10 years from now--statistics isn't math.

Here are some stories that caught my eye:

  • The World Chess Championship has begun. Magnus Carlsen, the champion, takes on Sergey Kajarkin. The official site is here, but I'd recommend Chessbomb for following the games (unless you're willing to pay up for coverage).
  • The best chess is being played between the computers. Komodo has already been dethroned. This year, Stockfish battles Houdini for the 9th TCEC Superfinal. Follow it here.
  • Sott.net reports "Professors across the nation are cancelling classes Wednesday to help students deal with their emotional distress as they come to grips with the "shocking" election of Donald Trump. ". Poor, poor snowflake.
  • The Atlantic has a more in depth look of the various excuses reasons why pollsters were so wrong.
  • TruePundit on Newseek's election goof: "The partisan hacks at Newsweek are recalling 125,000 copies of its Hillary Clinton “Madam President” issue. The brutal mistake, printing and shipping the issues to wholesalers and retailers weeks before the election, is estimated to cost Newsweek a loss of approximately $500,000. But Newsweek is not new to making lousy management and fiscal decisions. Newsweek claimed it made a Donald Trump edition too although it never shipped it or produced a verified copy of it. Now Newsweek says it will print and ship the Trump edition and hope to break even on the misadventure."
  • ZeroHedge on fudged polls: "The problem, said Cliff Young, president of Ipsos Public Affairs US, the polling partner of Reuters, came down to the models the pollsters used to predict who would vote - the so-called likely voters. The models almost universally miscalculated how turnout was distributed among different demographic groups, Young said. And turnout was lower than expected, a result that generally favors Republican candidates. Ultimately, missing that shift in the state polls tripped up the predictions. It also highlights how the otherwise empirical process of polling rests on a subjective foundation. Each pollster must make a decision about turnout. Their decisions are informed by historical voting patterns. But the actual turnout in each state is unknowable before election day."

 

Polling: statistics isn't really math

I've said it before: statistics isn't really math. It's an application of math like engineering,  mathematical economics, mathematical finance, predicting the weather, etc that uses math to claim respectability. Sure, theoretical statistics is math--akin to analysis--but actually applying statistics to numerous problems when there is no certainty that underlying assumptions (such as the data being random) are true is just wrong. In a previous post, "Statistics Isn't Really Math" I looked at some of the problems with statistics. In particular, I cited the post at AMSTAT News, (The Membership Magazine of the American Statistical Association) saying  "Statistics, however, is not a subfield of mathematics. Like economics and physics, statistics uses mathematics in essential ways, “but has origins, subject matter, foundational questions, and standards that are distinct from those of mathematics” (Moore, 1988, p. 3). David Moore, statistics educator and former president of the American Statistical Association, gives the following four compelling reasons why statistics is a separate discipline from mathematics:

  • Statistics does not originate within mathematics
  • The aims and foundational controversies of statistics are unrelated to those of mathematics
  • The standards of excellence in statistics differ from those of mathematics
  • Statistics does not participate in the inter-relationships among subfields that characterize contemporary mathematics

Statistics exists because of the need for other disciplines to examine and explain variation in their data."

That's a nice, clean authoritative explanation by statisticians as to why statistics isn't really math.

I followed that post up later with "Brexit: because statistics isn't really math" when virtually all the hacks statisticians made a horrendous call on Brexit. The bad prediction wiped out trillions in market cap when the vote went against what almost every public poll believed would happen.

Now with the US election coming up, I figure I should highlight a couple of new pieces that caught my attention. The first is a link that was brought to my attention by a reader, courtesy of the NY Times: "When you hear the margin of error is plus or minus 3 percent, think 7 instead". Now margin of error is a key term in polling statistics; except, according to this article, prepare to have your knowledge challenged: "In a new paper with Andrew Gelman and Houshmand Shirani-Mehr, we examined 4,221 late-campaign polls — every public poll we could find — for 608 state-level presidential, Senate and governor’s races between 1998 and 2014. Comparing those polls’ results with actual electoral results, we find the historical margin of error is plus or minus six to seven percentage points. (Yes, that’s an error range of 12 to 14 points, not the typically reported 6 or 7.)". Yes, throw out everything you learned about confidence intervals. But wait, it gets worse. A link off of that article takes you to here, an article entitled: "We Gave Four Good Pollsters the Same Raw Data. They Had Four Different Results" which is about just what the title indicates. Four pollsters were given exactly the same set of polling data and 4 different predictions. This is NOT what you'd get in a math course. The reason?: "Polling results rely as much on the judgments of pollsters as on the science of survey methodology. Two good pollsters, both looking at the same underlying data, could come up with two very different results.How so? Because pollsters make a series of decisions when designing their survey, from determining likely voters to adjusting their respondents to match the demographics of the electorate. These decisions are hard. They usually take place behind the scenes, and they can make a huge difference....Pollsters usually make statistical adjustments to make sure that their sample represents the population – in this case, voters in Florida. They usually do so by giving more weight to respondents from underrepresented groups.". Got that? Pollsters tamper with adjust the data as they feel like.

In fact, ZeroHedge has this post where polls contradict the margin error of others, and another post looking at the methodology behind a recent Washington Post poll: "Of course, like many of the recent polls from the likes of Reuters, ABC and The Washington Post, something curious emerges when you look just beneath the surface of the headline 12-point lead."METHODOLOGY – This ABC News poll was conducted by landline and cellular telephone Oct. 20-22, 2016, in English and Spanish, among a random national sample of 874 likely voters. Results have a margin of sampling error of 3.5 points, including the design effect. Partisan divisions are 36-27-31 percent, Democrats - Republicans - Independents."As we've pointed out numerous times in the past, in response to Reuters' efforts to "tweak" their polls, per the The Pew Research Center, at least since 1992, democrats have never enjoyed a 9-point registration gap despite the folks at ABC and The Washington Post somehow convincing themselves it was a reasonable margin."

Finally, there is this somewhat humorous post "Here's The 30 Seconds After The Last Debate That CNN Would Rather You Didn't See" where CNN polling has a 52% to 39% win for Clinton in the 3rd debate "So when the CNN focus group was asked "did this debate help anyone make up their mind or possibly change their vote", the results did not turn out how Goebbels they expected...

  • 5 Clinton
  • 10 Trump
  • 0 3rd Party
  • 6 Undecided

A much, much different result than there poll. Polling data is not the same coin flip data and the situation is even worse with respect to the integrity of the data---Stanford University called attention to Election Fraud here. By now it should be even more obvious that statistics isn't really math: the margin of error doesn't mean what it should and qualified statisticians with exactly the same data come up with different answers.

Here are some events that caught my eye lately.

  • Poor Nigel Short can't really catch a break. After getting into trouble with PC police for his comments on women which got twisted and blown way out of proportion, he had a 6 game match with Hou Yifan, the highest rated woman chess player in the world. The match was actually less close than the score would indicate with Short winning the match after 5 games in which he was never really in trouble--before losing badly in the final game. Was it a gift?--after all, he'd won the match, the last game wouldn't be rated, and it would be good gesture. Whatever the reason for the one game in which Short played badly, he got punished yet again. Chess.com has a report which states, "Well, Short had secured match victory after the fifth game, and later that day, he discovered that according to official regulations the last game should not be rated. Paragraph 6.5 of the FIDE Rating Regulations says:"Where a match is over a specific number of games, those played after one player has won shall not be rated." Short had an email discussion with tournament director Loek van Wely late Friday night. Van Wely wasn't immediately convinced. In fact, two years ago, when Anish Giri had won his match before the last game with Alexey Shirov, that sixth game was rated." So Short showed clear dominance throughout the first 5 games, never being in any danger, knew the last game wasn't going to be rated before it was played and "finished" the match with a bad loss, only to find the game WAS rated, which violated FIDE rules. Now he's not happy. And check out the footnote like reference to Short winning the match at Chessbase. Had he lost there would have been a BIG story on woman beats man in grudge match.
  • American Thinker with a piece on  precious snowflakes scared of Halloween: "College offers round-the-clock counseling for students 'troubled' by Halloween costumes"
  • EAGNews on the high school principle who told a student to remove his headphones in school, and  "When the student refused, Tossman attempted to remove the headphones, which allegedly sent Penzo into a rage. “ … (T)he 18-year-old student cold-cocked the principal,” according to the news site. “Penzo continued to pounce on Tossman, socking him several times in the face, causing swelling and lacerations around both the principal’s eyes.”A prepared statement released by the school contends “The NYPD immediately responded” and took Penzo into custody.""
  • FiveThirtyEight reports "A new study shows that first-grade teachers consistently rate girls’ math ability below boys’ — even when they have the same achievement level and learning style. The study out today in the journal AERA Open from researchers at New York University and the University of Illinois at Urbana-Champaign seems to represent a setback for gender equity in math. A widely reported 2008 study found that girls score as well as boys do on standardized state math tests. But the latest study suggests that early in their math education, many girls run into a teacher who perceives them as being worse at the subject than they are — which could discourage some of them from heading down a path that could lead to a career in math, science or engineering.". This is surprising to me because I have the impression that most math teachers at that level are women. Unfortunately I don't have the data to back that up. Is anyone aware of the data for this?
  • A powerful image of education winds up in a story on Sott.net.  Take a look at the school in Afghanistan halfway down the page. I've got to believe that some teachers would find that useful in their class.
  • Geekwire with a piece "Meet the minds behind Axiomatic: An art project based in theoretical mathematics"
  • Carlsen versus Nakamura in a blitz match today. Chess.com tells you how to watch it online.

Irrational Numbers with Patterns

img_20160919_163743715I'm not really posting anymore but I had to make an exception. The bad quality picture above is from a student's math class and the worksheet says: "Decimals that never end and have no pattern, think MUMBO JUMBO NUMBERS" in describing irrational numbers. Some context: the student had prealgebra last year where they learned that rational numbers were numbers that can be written as an integer divided by a nonzero integer and that irrational numbers were real numbers that weren't rational. More importantly, the student had learned the decimal characterization of rational and irrational numbers: rational numbers are terminating or nonrepeating and irrational numbers are nonterminating and nonrepeating.

So when the student, now in algebra, went through the beginning of the school year review of the real number system with this worksheet you have to cringe. First, the algebra class has learned the important definitions for rational and irrational numbers, so why not review those terms? That SHOULD be the goal. Second, the characterization of irrational numbers as "have no pattern" is wrong and she uses pi as an the only example to back up her claim. The teacher has given the class a worksheet with wrong information and doesn't know it. Welcome to a quality public school.

So let's give some quick examples to of irrational numbers which have decimals that never end BUT have a pattern.

.123456789101112131415......

Yes, ... is ambiguous, so let's describe the pattern. Just count the positive integers and put them together after the decimal. Understanding the pattern you know the next digits are ....161718192021..... and you can calculate whatever place after the decimal you want if you need to because there is a pattern. Here's another example:

.101101110111101111101111110.....

The pattern is to have separate one "1" from two "1"s from three "1"s from...using a 0. Under that pattern, you know the next digits are 11111110111111110..... and so on. Both of these decimal numbers are nonterminating and nonrepeating. You can't shouldn't make up your own math, especially when it's wrong. It causes unnecessary confusion.

Here are some stories that caught my eye recently:

  • From the Daily Mail, "Meet the boy geniuses who developed a math theorem that calculates problems faster than a COMPUTER - despite still being in high school"
  • Russian chess announces the passing of chess trainer Mark Dvoretsky. As someone fortunate enough to have attended some of his training sessions, I appreciate just what a tragic loss this is for chess.
  • Poor Chicago teachers! Well, not poor exactly. ZeroHedge reports they are ready to strike yet again. "Chicago teachers have a 13% raise (over four years) offer on the table, but that is not enough. They set a strike date of October 11 because the city wants the union to contribute more than 2% for their underfunded pensions, among the worst funded pensions in the nation. The Chicago public school system is bankrupt. Its bonds are deep in junk status....an affiliate of the American Federation of Teachers, is gearing up for a strike. It would be the union’s second in four years, despite the fact that the median salary for a teacher in Chicago is $78,169. When you add another $27,564 for various benefits, the total compensation for a teacher – good, bad or middling – becomes almost $106K per annum. (Please keep in mind teachers work 180 days a year, while employees in other professions typically work for 240 to 250 days.) In retirement, the average Chicago teacher receives a hefty $50,000 a year.
  • Truthdig with a sobering look at the status of adjunct teachers. With the hurdles to teach at public high school too onerous they are the working poor.
  • Sott.net with a well covered story on a Michigan student who, "...noticed nasty discolored water coming from the sink in her school, so she took a picture and shared it with social media. Hazel Juco was hoping that she could raise awareness about the potentially dangerous issue, and perhaps get the problem fixed. Unfortunately, the school was not impressed with the student's whistleblowing and actually suspended her for violating the school's policy of taking photos in the bathroom."
  • Propublica on "Education Department Terminates Agency That Allowed Predatory For-profit Colleges to Thrive"
  • Daily Mail with a viral image. You can't trust your senses.
  • Remember the poor Yale professor who was screamed at by hysterical brats? The Federalist has more video of what led up to the incident. "Altogether, the footage is nearly 25 minutes long — during which Nicholas manages to keep his cool in an attempt to rationally discuss his wife’s email with a cluster of impassioned students. The scene is chaotic — students verbally attack Nicholas, demanding he apologize for his wife’s “racist” comments. Ultimately, he does not decry the content of Erika’s email, but he emphatically and repeatedly apologizes for any pain her words caused....Based on this footage, it’s clear the students at Yale were incapable of having a rational discussion with another individual who dared to push back against their hasty accusations of racism. Despite what others have tried to claim, it’s plain as day many of those students who loudly disrupted the campus with their protest really were crybabies that threw tizzies over an email about Halloween costumes."
  • Lew Rockwell with a nice video on the value of a college degree.
  • American Thinker has some thoughts on reforming higher education: "We need to increase by 40% over the next ten years the number of people with college degrees, a state official once lectured us. Sitting in the audience, I thought, we know how to give people degrees. We no longer know how to give them a college education...."
  • Quartz with a piece on "Seven Rhode Island universities, including Brown and Rhode Island College, will move to open-license textbooks in a bid to save students $5 million over the next five years, the governor announced Tuesday"
  • The Federalist spotlights just how worthless a PhD in education is in reporting on  a PhD candidate who claims "Science Is Sexist Because It’s Not Subjective". "Throughout her dissertation, Parson assumes and asserts that women and minorities are uniquely challenged by the idea that science can provide objective information about the natural world. This is an unfair assumption, she says, because the concept of objectivity is too hard for women and minorities to understand."

 

Odds and Ends: Aug 30, 2016

Just a quick post. As I'm no longer teaching I won't be working on the website as much.

Here are a few stories that caught my eye since the last update. A lot of links for you science teachers:

  • RT with an entertaining video from a finalist in the Best Illusion of the Year Contest 2016. Science teachers, take note!
  • Listverse has "10 Reasons Academic Journals Are Filled With Junk Science". Number 9 is a good one, related to bogus journals: "A pair of computer scientists, frustrated with unwanted spam from a pay-for-publication journal, submitted a joke article. It was 10 pages of the same seven words repeated over and over: “Get me off your f—king mailing list.”"
  • Reason adds its voice on junk science, "Sarewitz cites several examples of bad science that I reported in my February article "Broken Science." These include a major biotech company's finding in 2012 that only six out of 53 landmark published preclinical cancer studies could be replicated. Researchers at a leading pharmaceutical company reported that they could not replicate 43 of the 67 published preclinical studies that the company had been relying on to develop cancer and cardiovascular treatments and diagnostics. In 2015, only about a third of 100 psychological studies published in three leading psychology journals could be adequately replicated.....Sarewitz also notes that 1,000 peer-reviewed and published breast cancer research studies turned out to be using a skin cancer cell line instead. Furthermore, when amyotrophic lateral sclerosis researchers tested more than 100 potential drugs reported to slow disease progression in mouse models, none were found to be beneficial when tested on the same mouse strains. A 2016 article suggested that fMRI brain imaging studies suffered from a 70 percent false positive rate. Sarewitz also notes that decades of nutritional dogma about the alleged health dangers of salt, fats, and red meat appears to be wrong."
  • Signs of the Times with "Madam Marie Curie's research papers still radioactive 100+ years later".
  • Signs of the Times again with a piece on "The first computer programmer was a woman - Ada Lovelace"
  • Salon with an article: "The State College of Florida recently scrapped tenure for incoming faculty. New professors at this public university will be hired on the basis of annual contracts that the school can decline to renew at any time."
  • Reason on generation obnoxious: ""We have spoken. We are speaking. Pay attention." Nothing captures the attitude of the modern college activist as perfectly as this statement, made by Yale University students petitioning the English department for changes to the curriculum (they wanted to read fewer white male poets).It's the constant refrain of the far-left social justice student: Our minds are made up. The time for discussion is over. We aren't here to be educated. We are here to educate you."
  • Huffington Post on the US winning the math olympiads for the 2nd year in a row.

Sagetex and Graph Theory

SageTexPaley

I've added some information to the Graph Theory, Sage, LaTeX page. For more complicated graphs, typesetting the placement of each individual vertex is too time consuming. Sage can help us out. Some of the important commands are located here. Many of the named graphs are posted here. SageTeX lets you use the power of Sage in both creating the graph and calculating the various parameters you want. You can find more details posted on that page along with working code to get you started.

Here are some stories that caught my eye over the last week:

  • WTVR.com, CBS 6, reports "The mother of a Virginia middle school student said she was angry, frustrated, and mad after her son was handcuffed, suspended from school, and charged with stealing a 65-cent carton of milk from the cafeteria. As it turned out, Shamise Turk's son Ryan was on the school's free lunch program and the milk -- was free.....Police said the larceny charge was because Ryan tried to "conceal" the milk, a claim Ryan's mother denied. The school spokesperson said Ryan was suspended for theft, being disrespectful and using his cell phone in school."
  • Money.CNN says, "For years, America's college campuses swelled with more and more students. But enrollment peaked in 2010 at just over 21 million students. Attendance has dropped every year since....The two types of colleges with the biggest declines in enrollment are: community colleges and for-profit universities. Those schools draw heavily from low-income and minority households."
  • Reason.com checks in with today's most whiny generation at Oberlin, which was highlighted in a recent The New Yorker issue. "...activist students not only wanted to abolish all grades below a 'C,' they also thought faculty members should proactively offer them alternatives to taking a written, in-class midterm exam." The New Yorker had a longer piece which went into more detail "For years, a campus café and performance space called the Cat in the Cream had a music-themed mural, painted by an alumnus, that celebrated multiculturalism: it featured a turbanned snake charmer, a black man playing a saxophone, and so on. Students recently raised concerns that the mural was exoticizing. “We ended up putting drywall over it, and painting over that,” Robert Bonfiglio, who had been the chair of the Student Union Board, told me. “They were saying, ‘Students are being harmed. Just do something now.’ ” But if individuals’ feelings were grounds to efface art work, he reasoned, every piece of art at Oberlin would be in constant danger of being covered up, or worse—a practice with uncomfortable antecedents. “The fear in class isn’t getting something wrong but having your voice rejected,” he said. “People are so amazed that other people could have a different opinion from them that they don’t want to hear it.”...Copeland has taught at Oberlin since the nineteen-seventies. He was puzzled by many things about today’s students—“They do not make eye contact! They do not look into your motherfucking eyes!”—but what galled him most was their apparent eagerness to go over their professors’ heads. In the late fall of 2014, during rehearsals for a play he was coördinating, he spoke sharply to a student: a misfire not of language, he says, but of tone. The student ran out of the room. Copeland says that he wanted to smooth ruffled feathers and keep the production on track, so he agreed to meet with the student and his department chair. At the meeting, the student asked that he leave the room, and she and the department head spoke alone for about half an hour.Later, the dean of arts and sciences asked to meet with him. He reported complaints that Copeland had created “a hostile and unsafe learning environment,” and that he had “verbally berated” a student—but said that it must be kept confidential which student or incidents were concerned. Then the dean asked Copeland to sign a document acknowledging that a complaint had been lodged against him....He gave the dean a list of students he thought could confirm that he hadn’t “berated” anyone. He says the list was brushed aside: “They said, ‘What matters is that the student felt unsafe.’ ” Then he was told that, because gender could have been a factor, the issue was being investigated as a possible Title IX violation. That inquiry was later dropped; by then, Copeland had hired a lawyer. In September, 2015, the original inquiry was still going on, and Copeland said that the dean told him that if he wouldn’t meet without his lawyer he would be brought before the Professional Conduct Review Committee. Copeland and his lawyer welcomed that idea: the committee process would bring some daylight. They never heard back."
  • Science Daily with a piece on titled "40-year math mystery and four generations of figuring" which "So, what is the Kelmans-Seymour Conjecture, anyway? Its name comes from Paul Seymour from Princeton University, who came up with the notion in 1977. Then another mathematician named Alexander Kelmans, arrived at the same conjecture in 1979. And though the Georgia Tech proof fills some 120 pages of math reasoning, the conjecture itself is only one short sentence: If a graph G is 5-connected and non-planar, then G has a TK5."
  • Oregonlive reports "Portland Superintendent Carole Smith apologized Friday for allowing students and teachers at two schools to continue to drink tainted water after tests showed unsafe levels of lead...At Rose City Park, that meant students were free to drink lead-laced water for eight school days after district officials knew about the toxic results."
  • ZeroHedge reports "Federal investigators revealed another blow to Detroit Public Schools this week. Meet Carolyn StarkeyDarden - the system’s former grant-development director - who has just been charged on suspicion of obtaining nearly $1.3 million by lying about children’s tutoring services....Carolyn Starkey Darden set up a company and allegedly ran a scheme between 2005 and 2012 in which she submitted fake invoices for tutoring services that were never provided to students, according to charges filed by the U.S. Attorney’s Office in Michigan’s Eastern District." This is so typical of the public school system where huge amounts of money can be easily skimmed by the corrupt. Because it's almost never about the kids.
  • RT on the 8 year old who brought a loaded gun to class. "It is unclear to whom the gun belonged and what made the boy bring it to school. The NYPD said there were no arrests made so far. Authorities believe that the boy might have had a dispute with another child, and they suspect his teenage brother had something to do with this incident, WABC reported....This is the sixth time authorities in New York confiscated a firearm inside a city school since March. In one case, a 14-year-old boy brought a loaded 9-millimeter gun to Middle School 61. "
  • The Third Shakmir tournament is underway with chess superstars Caruana, Kajarkin, Radjabov, Hou Yifan and more. The games can be followed live here.

Sage Interact: Generate Discrete Data

DiscreteData

In an earlier post I designed a Sage Interact to generate data for continuous distributions. This week I've added a Sage Interact to generate data for discrete distributions. A screenshot of the Interact is shown above. To use the Sage Interact, copy the code posted on the Python/Sage page and paste it into any Sage Cell Server. Press "Evaluate" to start the interact. Pick the distribution you want to generate data for, adjust the parameters and the Interact will create your data as well as calculate standard statistics for the data. This is a quick way to generate examples for quizzes, tests, and lessons.

Here are some stories that caught my eye in the last week:

  • the74million.org has a surprising piece on "Connecticut’s Shame: In One of America’s Richest Counties, a High School Has Been Failing for 50 Years". The school is so bad there isn't really any way to get worse "Even to the jaded, Bassick’s achievement statistics are disturbing. Last year, only 15 percent of students tested proficient in language arts on the new Common Core-aligned state tests. The percentage of students who met that benchmark in math? Zero." Good thing they have certified teachers getting the most out of them.
  • Segregation--it wasn't that long ago. Actually, it's still going on. RT reports, "A northwest Mississippi school district has been ordered by a federal district court to "consolidate its secondary schools" that have long been separated along racial lines some six decades after the US Supreme Court ordered school desegregation.....This decision serves as a reminder to districts that delaying desegregation obligations is both unacceptable and unconstitutional,” said Principal Deputy Assistant Attorney General Vanita Gupta, head of the DOJ's Civil Rights Division. " In what way was the 50 year delay shown to be unacceptable?
  • Sputnik news notes that "A former elementary school paraprofessional in the Atlanta area must report to jail by 6:00 on Friday evening after being charged with reckless endangerment for hanging a five-year-old student by his belt from a classroom blackboard."
  • Reason.com closes the chapter on a teacher who used the N-word in class. "Andrea Quenette, the University of Kansas communications professor subjected to protests and a formal investigation after offending her liberal students, was cleared of wrongdoing. But she is still ultimately out of a job."
  • EAGnews with a horrific tale of student animal behavior that was impossible to imagine decades ago. "South Fort Myers High School officials believe as many as 25 boys had “inappropriate activity” with a 15-year-old female student inside of a bathroom on campus Tuesday. Students told NBC 2 the incident occurred in a girl’s bathroom after classes ended and involved the school’s football team." The NBC 2 link has a video and there's another link here with a little more depth, "While she would not pinpoint why the different students were on campus after hours, she said South Fort Myers students involved in extracurricular activities — athletics or otherwise — participate in a study hall from 1:47 to 2:30 p.m. This is roughly the time frame for when the bathroom activities took place, Chandler said." So about 45 minutes in which we have dozens of students unaccounted for and no adult apparently around the area to see or hear what was happening.
  • The Greeley Tribune on the decline of teachers in Colorado. "Since 2010, UNC has watched enrollment in its teacher preparation programs plummet from a high of nearly 4,000 in 2011 to just 2,900 last year. The state is expected to graduate only 2,000 next year, and it needs twice that amount, education officials say...There are states that are worse off than Colorado (Oklahoma, California). There are states that are doing better (Connecticut). But every state has seen its list of needs increase as the number of people pursuing teaching as a career has decreased." The school system is run by many people who aren't up to the challenge but there is little consequence for mismanagement and poor quality. Take the Connecticut situation above: what will be the consequence for poor performance? Will the school close for having 0% proficiency in math? How did the school get to a 0% proficiency rating with "professionals" running the school? Do teachers still get pay increases (above the rate of industry) for such an awful showing? Money will keep coming in from taxes, and the system will continue on. When there's no consequence for failure, expect more of it.

Graph Theory, Sage, and LaTeX page

Graph1

I've added another page to the website. It's still in the beginning stages but it will cover graph theory, $latex \LaTeX$ and Sage. You can find it here and it's listed on the sidebar or click here. From this documentation at the Sagemath website you can see the way Sage works with $latex \LaTeX$ to produce graphs. This method is quite different than what you'll find in the Altermundus tkz-berge package despite the fact that Sage uses that package. The information I just posted has to do with the creating a graph in the simplest and cleanest way. I opted for the 'Normal' representation of graphs to allow for a choice of labels inside or outside. A vertex is created as follows:

\Vertex[LabelOut,Lpos=270,L=$v_1$,x=0,y=0]{R1}

where R1 is what the vertex will be referred to by the program and the factors which determine the label are handled in the options:

LabelOut to put the vertex label outside the vertex. Lpos is the label position. It's the angle of rotation around the center of the vertex (0 is east of the vertex, 90 is north of the vertex, etc). L= will be the label, and x=, y= handle the placement of the vertex. Simple and efficient. You can read more on the new page where I've posted the code for two 'Normal' graphs, with labels out and with labels in.

Here are some stories that caught my eye this past week:

  • 11alive covers Tennessee phasing out Common Core. "Common Core standards ignited a political brawl last year when state lawmakers, who saw the standards as federal overreach, pushed to scrap them. In response to cries for state-specific standards, Gov. Bill Haslam authorized a review of the state's English and math standards."
  • St Louis Post Dispatch reports "Missouri became the latest state to adopt a new set of education benchmarks to replace the national Common Core standards, ditching the benchmarks Tuesday following conservative backlash.". Common Core is not so common anymore.
  • EAGnews has a piece on  Tennessee students "Parents and community leaders in Murfreesboro are fuming after police arrested numerous elementary students at school over a fight that occurred off campus several days prior....Several students at Hobgood Elementary School, ranging in age from about 6 to 13 years old, were then handcuffed and arrested, and hauled to a juvenile detention center before their parents were even notified, WKRN reports.....“Here’s the catch, the girls were just bystanders in the video. They were not fighting, they were not instigating it, they were just standing in the video. And there was actually no technical fight in the video,” he said. “But the claim and the accusation is that they didn’t stop the fight, so they should be arrested.”"
  • RT has a piece where the title says it all: "Teacher tackles pupil to the ground in ‘deeply disturbing’ classroom attack".  A violent, profanity laden assault that will hopefully lead to jail time.
  • But it's better overseas, right. Not all the time. RT has video footage of  "A teacher in China bore the brunt of a vicious classroom uprising after he tried to forcibly collect a student’s exam paper in a shocking case of school violence caught on camera."
  • Don't even think about messin' with Colorado schools. ABC news reports, "A suburban Denver school district is arming its security staff with military-style semiautomatic rifles in case of a school shooting or other violent attack, a move that appears unprecedented even as more schools arm employees in response to mass violence elsewhere."
  • Chalkbeat reports  "Facing widespread backlash after years of controversies and testing glitches, one of the world’s largest testing companies is taking an unusual approach to quieting critics: It’s opening its doors." The Washington Post covers some of the problems here.
  • The Altibox Norway Chess 2016 tournament has 4 rounds in  the books. Magnus in first but with Kramnik, Giri, and MVL lurking around the tournament is wide open. You can follow it here. Click on the "Live Streaming" button at the top of the page to follow it live.
  • There are just 2 rounds left in the US Chess Championship. You can watch it live here. Caruana leads for the championship section, and Abrahamyan for the women. Irina Krush doesn't control her fate anymore as she competes for another title.

Handouts: Integral Table

IntegralTable1

I've added a Table of Integrals, a PDF and the tex file that created it, to the Handouts page. This will let you customize the integrals to the ones most appropriate for your class.

Here are some stories that caught my eye over the last week:

  • Remember the big decline in SAT scores I posted not that long ago? The American Enterprise Institute has reported that a more comprehensive breakdown has been completed, "But the story was incomplete, because the College Board had embargoed the breakdown of scores by ethnicity until a few days ago. Now they can be published. Here are the 10-year changes in test scores by ethnicity:" Check out the chart of performance, in words, "The new text should point out that the white change was small, just an aggregate of 6 points. That black scores fell by an aggregate 14 points is troubling because their scores in 2006 were already lower than those of any other ethnic group. That the scores of Latinos and American Indians fell by 26 and 28 points is even more troubling. But how about those Asians! Their aggregate mean score rose by 54 points.". So it looks like the news isn't all bad. Whose the courageous soul who wants to explain the differences in perforamnace?
  • I mentioned here that one third of high school math teachers didn't have a degree in mathematics. That was based on 2007-2008 data. AllGov.com reports that with more updated data (2011-2012), "Almost half of high school students are learning history from a teacher without a degree in the subject.". A link on the page sends you to Humanities Indicators website which has data on other subjects, including math. There is a nice chart to help you make sense of the data. Math is roughly the same.
  • ScienceNews reports that Terry Tao has solved an old outstanding math problem that had a $500 bounty from the late Paul Erdos. The site only gives nonmembers the first few paragraphs of the article. Nature.com has the details and RJ Lipton's blog has more of the mathematics behind the story.
  • The Boston Globe reports "State education officials withheld MCAS math results from Boston’s English High School as they released statewide scores Thursday, citing irregularities that require examination....The score suppression came as a surprise to Boston school officials, who learned of it a short time before the state provided MCAS data to media outlets. Boston Superintendent Tommy Chang said the state did not tell him why the scores were withheld,...". Scores withheld for no reason? I hope that poor scores aren't the explanation.
  • The Daily Caller reports, "The state of New York looks to be the next state with plans to re-brand the Common Core by calling it something else but otherwise making virtually no substantive curriculum changes." I wonder how much tax money that will cost.
  • Business Insider does a follow up to the 100 million contribution to Newark schools made by Mark Zucherberg some 5 years ago, "One of the major miscommunications about how his money would be spent had to do with teacher contracts. Zuckerberg wanted to be able to create more flexibility in teacher contracts to reward high-performing teachers and be able to fire teachers with poor records of student achievement. But those types of protections are determined by New Jersey State law, and Zuckerberg couldn't simply come in and change the rules without going through the state legislature to make the changes......Zuckerberg envisioned the teacher contract reform to be a centerpiece of the reform and had intended for half of his $100 million donation to go to working on that cause.But instead, the opposite occurred. Chris Cerf, the New Jersey commissioner of education at the time, worked with the legislature and was able to negotiate some new accountability measures in teacher contracts. But the teachers' union only agreed upon those measures if the seniority protections remained intact.". I was recently pointed to a more thorough examination that I had missed by the NYTimes given here.  It's a veritable case study in how the layers of educational bureaucracy eat up most of the money--a fundamental reason (plus lack of accountability) that is the albatross around the neck of public education: "Their five-year plan gets off to a rocky start. Initial funds go to a bevy of consultants, most of them white, most of them well connected, some of whom are getting paid $1,000 a day...Moreover, it quickly becomes apparent that this is a top-down effort, with politicians and the well-to-do setting the agenda. When Booker sets up a local foundation to handle Zuckerberg’s gift, the seats on the board go only to donors of at least $5 million.....And Zuckerberg, a newcomer to philanthropy, seems frustrated by the inability to negotiate a union contract that would quickly raise the salaries of promising young teachers and pay substantial merit bonuses for high performers.....What ultimately derails this grand experiment is the unwillingness of the reformers to include parents and teachers in shaping the reforms.". Another piece from the NY Times says,"Almost half of Zuckerberg’s grant was spent (or committed) to help gain new labor contracts; out of the $200 million in his money and the matching grant, a full $21 million went to buying out unwanted teachers and other staff members, for instance. Yet Zuckerberg didn’t realize until too late that New Jersey state law — not teacher contracts — imposed the seniority system he was trying to get rid of....The district schools get $19,650 per pupil, but only $9,604 trickles down to the schools. Money that the charter school is spending on extra support is being soaked up by the bloated bureaucracy in the public school system. It is a devastating fact.".  Some excellent articles by the NY TImes. Mark Zuckerberg got an expensive lesson in how those managing the education of public school are enriching themselves first at the expense of the kids they oversee. It's difficult to reform public education  with such a huge structural obstacle to real change.
  • OregonLive informs us test scores are"Sky-high in writing, ultra low in math". And notice "Oregon and other states are mapping passing scores on their old exams to those new tests; Washington is the only other state that has completed the process.". That's a fancy way of saying that to compensate for more difficult tests, you lower passing scores--then schools can talk about tougher standards, even if they lower their performance. "Policymakers said they would determine which Smarter Balanced scores were equivalent to passing marks on the old state graduation exams and use those. Oregon's new graduation requirement in math is merely to score the lowest possible "Level 2" Smarter Balanced score, a basic skills level that is far from the "college-ready" performance standard agreed to by experts in 17 states, the state board decided.". The Bulletin explains, "What the board was doing was setting the closest match between Oregon’s old tests and the new exams. According to Oregon’s rules, the state can’t just bump up the standards for graduation without giving students some time to prepare. The rules say students have to be told by the end of eighth grade if they can expect to face tougher standards. That makes sense on some levels. But think about what it means. It means Oregon has not aimed at a high school diploma that means college ready in math or reading.". So when do newer standards come into effect?
  • The Seattle teachers' strike is over and NYC Educator is impressed by how well Seattle teachers gained.

Tikz-euclide: marking angles

MarkAnglesJust a few points of interest: I've added a little more information to the Points, lines, line segments, rays, and labels page. It explains the very basics of marking angles using the tikz-euclide.

Next, in a recent post I mentioned there has been a militarization of schools in Texas. Now there are reports that the same thing is happening in San Diego. NBC news San Diego reports that "A heavily armored vehicle is now a part of the San Diego Unified School District Police Department’s arsenal, though administrators say it will only be used for rescues.". And an article from the Daily Beast asks, "Why Does My Kids' Elementary School Need a Tank?". However you answer that question, the key piece from the article is:

"San Diego Unified School District is the second largest in California: in terms of geography, it’s about 22 miles long and 23 miles across. According to the FBI, the average school shooting lasts for 12 minutes, which is probably not enough time to get a crew assembled at the facility where the MRAP is stored, much less drive through miles of SoCal traffic. SDPD and Fire Rescue would probably be on the scene long before anyone remembered where they had left the keys to the MRAP. Even if the shooting were an atypically protracted event, or the MRAP just happened to be in the neighborhood, in the case of many campuses, the vehicle couldn’t get very close to the classrooms. In short, the critics argued, the chances that this machine could ever be useful were minimal."

Finally, there's a website: You're Getting Old! which could be useful in your class, especially if you work with rates/ratios/unit analysis. Just input a date and you'll page of information. Some statistics, such as shown below

GettingOldbut also key events in history and  milestones in that person's life.