L.A.Times Reporter Might Have Messed up the Math — Will the Ancient Astronomers Come to the Rescue?

WOW!

You won’t believe the revolutionary discoveries that modern astronomers have found, by carefully decoding old astronomical tablets written on tablets, in cuneiform, as long ago as 700 BC in modern-day Iraq!

You might not be surprised that a science reporter and various commentators reporting on the story – including myself – may have got the math wrong.

This is not just clickbait – the historical research was very dedicated and quite clever, and it shows that all the  years I’ve tried to to study and learn Arabic, astronomy, Babylonian, calculus, Chinese, French, geometry, Hebrew, Latin, mathematics, Russian, Spanish and Turkish might actually pay off one day, when I grow up! (*)

What’s the scoop?

In a nutshell: Researchers read and translated a bunch of ancient and more recent records of eclipses of the Sun and Moon, from cultures all over the world, over a period of 27 centuries. They compared those results  with what modern software and computers calculate they should be if you simply went backwards in time at a rate of precisely 24 hours per day. That meant studying lots of obscure records written in Chinese, Babylonian, Arabic, and Latin, as well as in modern languages.

The researchers were quite impressed at how accurate the Arab and Chinese records were, even though their instruments were much cruder than what we have today. (Obviously, no telescopes, no electric clocks, etc, etc…) The records from the Roman empire and early Mediaeval Europe, however, are apparently not nearly as good (200 BC – 600 AD) as the Chinese and Arab ones were.

cuneiform-astronomy

After the invention of the telescope a bit over 400 years ago, records became much richer. For example, observers could record the time, to the second (or even better), when a star would get blocked out by the Moon and then eventually re-appear on the other side.

(David Dunham , though retired, is an expert on this.)

Bottom line, according to the newspaper reporter: If it’s noon right now, and you could somehow go back in time precisely twenty-five centuries ago to exactly where you are standing or sitting, then everybody else back then (about 500 BC) would see the time as the equivalent of 7 PM, because the earth is turning on its axis ever so slightly slower today.

Revolutionary, I told you! Not joking, not exaggerating either!

But wait a second – how much would that be slowing down per year? The article doesn’t spell it out, but 7 hours is 420 minutes, or 60*420 = 25200 seconds,. If we divide that by about 2500 years, you get 10 seconds per year!

Wait a second, that doesn’t sound right at all! These days, if the earth really got slower at a uniform rate of 10 seconds per year, many of our cheap quartz watches and clocks are so accurate that we would actually notice the difference!

Let’s go back. The LATimes reporter, Deborah Netburn, wrote:  “the amount of time it takes for Earth to complete a single rotation on its axis has slowed by 1.8 milliseconds per day over the course of a century” – which is not very clear.

A commenter on LATimes website, named “It is me Here” wrote:

The time discrepancy described as “It may not sound significant, but over the course of 2½ millenniums, that time discrepancy adds up to about 7 hours” is not 7 hours. Over 2500 years it amounts to: 1.8 (milliseconds) x 365 (days per year) x 2,500 (years) = 1,642,500 milliseconds, that equals 1,642 seconds that equals 27.38 minutes, not 7 hours.

 

Did you get that, and do you agree? If not, let’s go back a little further, to the  abstract of the original study report which says:

New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century.

(my emphasis – gfb)

 

So, would we really be 7 hours slow if we went back?

Maybe, maybe not.

Let’s think about it differently:

Since 500 BC, it has been about 25 centuries. According to the study, every century the earth slows down by about 1.8 milliseconds, which isn’t very much. 25 * 18 milliseconds is 450 milliseconds, which is a bit less than half a second. So does that mean we have to add up all of those 1.8 milliseconds by 365 days

That’s not much at all.

(BTW, why does the earth get slower? One source of the slowing down is simply the friction of the ocean tides. If you’ve ever been to the ocean and paid attention, you know that the gravitational pull among the Sun, Earth and Moon raise and lower a WHOLE lot of water all over the world, twice a day. That takes a HUGE amount of energy and a lot of it is dissipated in friction, which slows things down. But there are others.)

But here is a different way of looking at it still, as a trapezoid: the left-hand parallel side is about one-half second shorter than 24 hours – the length of a day in during ancient Babylonian days. The right hand parallel side is exactly 24 hours long. In between, there are 2,500 elapsed years.

Let’s pretend that each of those years contains 365 days (let’s agree to ignore the effect of leap years for right now). If the shape were a rectangle, then that would mean that the earth had not slowed down at all, and if you went backwards in time from now by 2500 years it would be exactly the same date, same time.

slowing-of-length-of-day

Apparently, it’s not. The lost or extra time is the part I show in this next diagram:

slowing-of-length-of-day-2

 

That little pink section is a a long skinny triangle with its right hand end 1/2 second per day long, and the base is 2500 years long, or 912,500 days. The area of a triangle is 1/2 * base * height, and so we use 1/2 * 1/2 * 912,500 and get 228,125 seconds lost (the ‘days’ units cancel out), or about 3802 minutes, or 63 hours, 22 minutes, which is 2 days, 15 hours, and 22 minutes off.

Not sure if I’m right or not, but would appreciate comments.

Here is one of the figures from the paper:

intercalation-revolution-of-earth

(*) Note that I don’t claim to be fluent in all of them. Far from it! Guess in which of the languages ones I can reed perdy guud and which ones I can at least stumble a conversation in?

 

Published in: on December 8, 2016 at 4:39 pm  Comments (4)  

A Cartoon Strip I Like – TeachingTed.Com

I just found out about this cartoonist from Diane Ravitch. He’s a good artist and has something to say about education and the world that teachers inhabit. You might like his work, too. Here are a couple of his strips:

cartoon-on-ed

 

cartoon-on-trump

 

cartoon slippery slope.png

What if Finnish Teachers Taught in the USA?

You have all heard that FInland does the best job in the world at getting high scores on tests like PISA without burdening their students or their teachers with extreme workloads. Finland does not have long hours of homework for elementary kids, and they don’t require the daily filing of rigidly formatted, complex lesson plans for teachers. Finnish teachers are selected from the very best of their university classes, and have enormous amount of control over what they do, which they plan with their peers.

So what if some of these Finnish teachers came and worked here in the US?

Now we know, thanks to an article in The Atlantic.

A couple of quotes, from three such teachers. One said,

“If you asked me now, my answer would be that most likely I would not continue in this career.”

Another:

While teaching in Finnish schools, she had plenty of leeway to plan with colleagues, select curricular materials for the principal to consider purchasing, and influence decisions about schedules and responsibilities.

Today, with 16 years of teaching in U.S. public schools under her belt, this ESL teacher feels that she lacks a career in teaching. She described it as a rote job where she follows a curriculum she didn’t develop herself, keeps a principal-dictated schedule, and sits in meetings where details aren’t debated.

And another:

“I teach six classes a day with a one 45-[minute] ‘planning’ period,” she said. “My classes are at three different proficiency levels, and I have four minutes between classes to prepare for the next class. At the same time, I am expected to stand in the hallways to monitor students as [they] transfer from class to class, and to check my email for last-minute updates and changes because of ongoing testing or other events.”

All of those tasks, and several others, wear her down: “I feel rushed, nothing gets done properly; there is very little joy, and no time for reflection or creative thinking (in order to create meaningful activities for students).”

Muja concluded her response with a quote from one of Pasi Sahlberg’s articles for The Washington Post, “What if Finland’s great teachers taught in U.S. schools?”

Sahlberg, an education scholar and the author of Finnish Lessons 2.0, answers the theoretical question in his article’s title, writing in part: “I argue that if there were any gains in student achievement they would be marginal. Why? Education policies in Indiana and many other states in the United States create a context for teaching that limits (Finnish) teachers to use their skills, wisdom and shared knowledge for the good of their students’ learning.”

More on Rigging Elections

Now, let us suppose that somehow the Hillary campaign actually managed to

(a) make sure that a rigged coin – supplied by them, not taken from somebody’s pocket – was used in each of the six coin toss cases

(b) figure out in advance which caucuses had to get those coins

(c) tell their person which side of the coin to choose in case a toin coss came up,

(d) none of the other folks noticed any of this skullduggery taking place right in front of their eyes — (by the way, you should watch this video of how this worked in practice)

THEN, yes, that weighted coin might help their odds, as you can see in this chart:

rigging-elections

I used the binomial theorem to figure this one out. Let me give a few examples: in the row that’s highlighted in green, the probability of heads and tails is both 50%, and as I indicated int he last post, the probability of getting ‘heads’ five times out of six is about 9.38%. However, if you could somehow figure out how to make a coin that came up ‘heads’ 60% of the time, then your chances of getting 5 heads would improve to 18.66%.

And if you could boost the unfairness of your coin to the point that it would come up heads 80% of the time then your chances of getting 5 ‘heads’ would be 39.37%. Still not a slam-dunk.

I only know of two ways to make a coin biased. One method is to carefully split two coins in half the hard way, and make a two-headed coin (or two-tailed) coin. Such coins are actually sold in magic shops.

The other method is to bend the coin slightly – I am told that the concave side will end up being on top more frequently (like a cup).

So, Hillary’s nasty minions would have had to either distribute a bunch of bent coins or two-headed coins, and nobody else would have had the brains or eyesight to notice, for this to have been rigged.

I don’t think so.

Super Scenario for Tonight’s Debate

Wonderful screenplay for an alternate-reality presidential debate, from Aaron Wiseman, who’s been a friend of my own kids for decades – they’be been to each others’ weddings, etc. I had no idea he could write like this. It’s fantastic, don’t you agree?
 
“Best case scenario for tonight’s debates?
 
10-minutes in, we’re seeing the same bullshit.
 
Suddenly, all the house lights go down. The arena is awash in total darkness. Panic begins to set in when the lights flicker and momentarily reveal a cloaked figure in the rafters.
 
The lights flash again and the figure is gone. Suddenly, a crushing guitar riff fills the entire venue. A spotlight shines down on the arena floor. The figure from the rafters has magically moved with supernatural speed.
 
As the music builds, the cloak falls to the floor. IT’S JOE BIDEN! He’s wearing a crisp blue two button suit complete with arm tassels and full Warrior face paint.
 
As the music hits full crescendo, Joe takes off towards the stage at a full sprint! In one graceful move he slides onto the stage and hits Trump with a forearm to the dome.
 
The Great Pumpkin, takes the blow like it’s nothing. That doesn’t slow ole Joe and he hits the Cheeto Demon with a super kick to the face. B-Side Beelzebub just smiles.
 
Is he even human? How can he take so much punishment? Joe looks to the audience pleadingly.
 
As if to say, “I hit him with my best shot. How?” But then the carroty façade begins to falter and Trump’s knees buckle. His eyes roll into the back of his head and he begins to stagger around the stage.
 
Joe goes in for the finisher and hoists Trump into the air by his belt. As Trump begins to flail, Joe sends the would-be-dictator-tot crashing to the floor. A perfectly executed Gorilla Press.
 
Hillary walks up to Joe, her arms open in gratitude. But instead of matching her embracing, Joe grabs the mic from the former Secretary of State.
This wasn’t for you. Hill. A. Ry. Clin. Ton” Joe growls, “It was for America!”

“You will differentiate instruction for every student in exactly the same way, or else”

Or,

One of the many reasons I rejoice every day that I was able to retire!

 

Read what classroom observations have devolved to:

http://nyceducator.com/2016/10/you-will-differentiate-instruction-same.html

Math and Sex

You may not think that math and sex don’t mix, but I show here that they really do:

https://guysmathastro.wordpress.com/2016/09/01/sex-and-math-the-zero-to-two-percent-of-our-actual-lives-that-rules-our-lives/

Published in: on September 1, 2016 at 12:38 pm  Leave a Comment  
Tags: , ,

Bill Gates’ Billions Haven’t Panned Out in Third World Health Care Either

(From about a year ago – somehow this never made it into the blogosphere)

I just read that much of Bill Gates’ international health initiative has been about as much of a high-tech boondoggle and waste of effort as his education initiatives here in the US.

For example, in trying to solve the problem of human waste disposal (ie human poop and pee) in poor nations where people make $1-$5 per day, his researchers came up with high-tech commodes costing thousands of dollars and probably requiring lots of maintenance. Excuse me for stating the obvious, but nobody is going to pay five to twenty years’ annual income for an outhouse or toilet!

I’m not making this up. See http://mobile.nytimes.com/2013/11/19/opinion/bill-gates-cant-build-a-toilet.html?_r=1

By the way, my humorous profile picture is of a composting toilet I built up at the Hopewell observatory out of two plastic cat-litter containers (free), a toilet seat ($10?), a piece of wood and a few screws. You put in some wood chips or dead leaves after you are done. When it gets full, you dump it in a designated place. It doesn’t stink. I personally wouldn’t use the resulting compost to grow food, but there are parts of the world where such “night soul” is highly valued. (My solution is not original: here is one writeup http://weblife.org/humanure/chapter8_2.html )

Gates recently held a meeting in Seattle where he admitted most of his high tech initiatives on third world health had failed.

http://seattletimes.com/html/localnews/2025279289_grandchallengesxml.html

One of the initiatives involved cholera. Were they completely unaware that for at least 20 years a very cheap and simple way to rehydrate cholera victims and restore their electrolytes has been in use in many third world countries?

Published in: on February 16, 2016 at 12:39 pm  Leave a Comment  
Tags: , ,

Teacher Depression

“Mr. Fitz” is perhaps my favorite comic strip, even though he teaches English rather than math (as I did).

He discusses here (and draws strips about) the intense amount of stress that has come about for teachers since NCLB and RTTT pressures became way more than overwhelming.

Temps Who Have Never Taught are Grading Common Core Tests

Makoto Rich of the New York Times, Peter Greene of Curmudgacation, and Diane Ravitch all discuss the way that Pearson is running the scoring of the Common Core tests, employing temporary employees who have never taught, at $12-14 per hour, with of course no benefits.

If you’ve worked in a mass-chain fast-food joint, then you know what Pearson wants: mindless uniformity. Isn’t that what parents and kids really, really want from our public schools?

Here’s the link.

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