The squaw of the hippopotamus is older than we thought

[vaskidmark]

http://www.cnn.com/2010/WORLD/meast/12/17/old.babylonian.math/index.html?hpt=C2

Over 1,000 years before Pythagoras was calculating the length of a hypotenuse, sophisticated scribes in Mesopotamia were working with the same theory to calculate the area of their farmland.

Working on clay tablets, students would "write" out their math problems in cuneiform script, a method that involved making wedge-shaped impressions in the clay with a blunt reed.

These tablets bear evidence of practical as well as more advanced theoretical math and show just how sophisticated the ancient Babylonians were with numbers -- more than a millennium before Pythagoras and Euclid were doing the same in ancient Greece.

"They are the most sophisticated mathematics from anywhere in the world at that time," said Alexander Jones, a Professor of the History of the Exact Sciences in Antiquity at New York University.

And worse yet, there were geeks even back then:

For non-mathematicians, these tablets are a fascinating document of life in Mesopotamia. Most of the problems displayed are grounded in the everyday needs of ancient Babylonians.

But some tablets show the students engaging in what Jones calls "recreational math" -- math for math's sake.

"The only point of learning to do this kind of thing is really as a mental exercise, as a way of showing how smart you are," he said.

About the only thing I am having difficulty with is:

According to Melville, teachers can continue to learn a thing or two about the way math was taught in Mesopotamia.

"You look at the way they set up their sequences of problems and it's all very carefully graduated, from simple problems to more complicated problems," he said.

"As a teacher of mathematics, it's very interesting to see how they organized their material," he continued. "There's still interesting things to learn from cutting-edge pedagogy 4,000 years ago."

I just don't have the faith necessary to believe that teachers will take note and follow up on learning anything new.  Even in mathematics.

stay safe.

[HankB]

I just don't have the faith necessary to believe that teachers will take note and follow up on learning anything new.  Even in mathematics.

The teaching of mathematic was quite poor when I was in college. Once past calculus, the mathematics courses for science majors covering differential equations, tensor analysis, etc., were called Applied Mathematics 1,  Applied Mathematics 2, etc.

The mathematics professors who taught these courses had NO concept of actual applications, nor did they take kindly to students who had the temerity to inquire about possible applications.

[230RN]

Very interesting that their manipulations were apparently all verbal, with no "manipulation" symbols. I wonder how they handled the concept of zero and fractional (or decimal or octal or whatever) parts of unity.  And maybe negative "numbers."

It all seems to reinforce the notion (not a theory) that much thinking can be done with pure concepts, sans the symbology that we use for communicating these concepts.  That is, if we are looking for a red box one's Christmas gift came in, we do not go around looking for a "red box that's so wide and so long," we just go look for a conception of the red box.  It is only when we want to communicate what we are looking for, that is, "a red box that's so wide and so long" that we have to verbalize the concept itself.

Similarly, it looks as if they could "think" directly in terms of the quantities involved without actually manipulating symbols and numbers and mathematical operations to come up with an answer. 

Sorta like the triangle-with-squares erected along each side of the triangle to illustrate the hippopotamus relationship.  We can "see" the concept directly, without actually counting the squares in each box.

I remember in high school a teacher asked me to prove a sin-cos-tan identity on the blackboard and I "visualized," or "conceptualized" the answer in my head before I stepped to the blackboard and formally wrote out the steps for the proof.  Sorta like that.

Anyhow, that's the way it "looks" from this side of my baby blue eyeballs.  And the words above are merely a poor attempt to symbolize that notion.

Terry, 230RN

[Nick1911]

Hrm. I like that, Terry.

[griz]

I just don't have the faith necessary to believe that teachers will take note and follow up on learning anything new.  Even in mathematics.

Have faith.  Teachers have been looking for the way to teach correctly ever since they forgot how.  They just needed a 4000 year old refresher course to jump start there teaching skills.  The wait is over, everybody be smart now.

[230RN]

Well, I recall reading that in the good ole one-room schoolhouses, where all the grades were intermixed, the older kids would actually teach stuff to the younger kids --thereby learning the aforementioned stuff intimately well themselves.

I remember offering a couple of courses in real estate (nuthin' accredited, just through a "free school") and having to actually learn how actual amortization actually worked --along with a few other actual things.  Actual teaching is actually the best actual teacher.

But I still have trouble with the "times table."  Especially "7 times..."

For 7 X 6, I have to turn it around to "6 X 7."

Maybe I'm lysdexic about seven. (No offense to anyone, please.)

Dunno why.

Terry, 230RN

[Scout26]

But I still have trouble with the "times table."  Especially "7 times..."

For 7 X 6, I have to turn it around to "6 X 7."

Maybe I'm lysdexic about seven. (No offense to anyone, please.)

Dunno why.

Terry, 230RN

Me too.  Once I get to 6 x 7, 6 x 8, 7 x 8, I have to stop and think about it.  Nice to see that I'm not only one.   

[230RN]

Or 7.62 X 39.

I always stumble over that one and have to switch it around to 39 X 7.62.

I'm not signing this one so nobody will know who posted it.

[Physics]

Well, I recall reading that in the good ole one-room schoolhouses, where all the grades were intermixed, the older kids would actually teach stuff to the younger kids --thereby learning the aforementioned stuff intimately well themselves.

I remember offering a couple of courses in real estate (nuthin' accredited, just through a "free school") and having to actually learn how actual amortization actually worked --along with a few other actual things.  Actual teaching is actually the best actual teacher.

But I still have trouble with the "times table."  Especially "7 times..."

For 7 X 6, I have to turn it around to "6 X 7."

Maybe I'm lysdexic about seven. (No offense to anyone, please.)

Dunno why.

Terry, 230RN

Anyone who has actually taught will agree very heavily with this statement.  Nothing motivates you to learn a subject than knowing you will be open to questions on the subject.  It's such a great feeling to know your subject well enough that you can walk into class with nothing in your hands but a piece of chalk and lecture off the top of your head, and not have the students giving you the 100 meter stare.

Also, just so you know, there is a dyslexia for cure now.

[Gowen]

You should have seen the stuff that they were doing in Atlantis, as they were flying around in their hovercraft.  This is back before they ticked off God and he wasted them in the flood.  You can check this all out for yourself if you just ask Shirley Maclaine. 

[MechAg94]

Nothing really says that the people we think invented certain concepts actually invented them.  They are just the earliest or oldest records of those developments we have. 

[Tallpine]

While at my brand new in-laws* house, I read part of a book that said there were relatively accurate maps of Antartica possibly dating back to pre-Hellenian times ... 


* via my new son-in-law

[230RN]

^^, ^
So true.  Take a look at this:

http://en.wikipedia.org/wiki/Antikythera_mechanism

The mechanism has three main dials, one on the front, and two on the back. The front dial has two concentric scales. The outer ring is marked off with the days of the 365-day Egyptian calendar, or the Sothic year, based on the Sothic cycle. Inside this, there is a second dial marked with the Greek signs of the Zodiac and divided into degrees. The calendar dial can be moved to compensate for the effect of the extra quarter day in the solar year (there are 365.2422 days per year) by turning the scale backwards one day every four years. Note that the Julian calendar, the first calendar of the region to contain leap years, was not introduced until about 46 BC, up to a century after the device was said to have been built.

What's equally amazing here is when you think about the background science and technology necessary to build this device. 

Even assuming it was all done with hand tools on soft metal (bronze, brass, whatever), There had to be pre-existing  rather precise cutting tools (files, "hack saws," etc.) to build this thing.

And pre-existing arithmetic to calculate the gearing, which had to involve the concept of zero and fractional numbers.

And precise measuring devices.

Not to mention a bench vise to hold the parts while you worked on them.

How far back did all this antecedent technology go?

As the Wiki article says, "...its flawless manufacturing suggests that it may have had a number of undiscovered[10] predecessors during the Hellenistic Period."

There were also a couple of artifacts discovered elsewhere that looked similar to a modern electric battery... leading to the hypothesis that electrolytic plating of metals might have taken place in very ancient times.*

"There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy."  (Hamlet Act 1 Scene V)

Terry, 230RN

*Wouldn't it be funny if someday it were discovered that all the "solid gold" artifacts discovered in, say, King Tut's tomb, were actually just gold plated lead or something? :}