Ancient mesopotamian science
Here we examine the development of astronomy, math, and science in ancient Mesopotamian science.
Akkadian era – 3000 – 2000 BCE.
Sumerian city-state kings fought over land from 3000 to 2000 B.C.
Sargon of Akkad was powerful leader, creator of worldʼs first empire – took over northern and southern Mesopotamia around 2350 B.C. – empire—many different peoples, lands controlled by one ruler (emperor) The Akkadian Empire
Sargonʼs empire was called the Akkadian Empire. This included the Fertile Crescent—lands from Mediterranean Sea to Persian Gulf
Known for rich soil, water, and good farming
Sargonʼs conquests spread Akkadian ideas, culture, writing system. Empires encourage trade and may bring peace to their peoples. Peoples of several cultures share ideas, technology, customs.
Babylonian mathematics
As early as 2000 BCE, Babylonians used pre-calculated tables to assist with arithmetic such as:
This became useful for their early astronomy.
Babylonians developed advanced forms of geometry, some of which was used in astronomy.
Info above comes from Houghton Mifflin Historical-Social Science: World History: Ancient Civilizations: Eduplace Social studies review: LS_6_04_01. This historical overview is brief, and by necessity, highly simplified.
Metallurgy
Chemistry connections
http://www.anvilfire.com/21centbs/stories/rsmith/mesopotamia_1.htm
“[People in ancient mesopotamia] made substantial advances in crafting higher quality bronze tools and weapons. It took trade to relatively distant places – because tin ore caches are sparse – to create tin-alloy bronze. This was the standard to aim for in the ancient world – and also prevented metal-smiths from developing limps and dying of gradual arsenic poisoning. (not joking)”
Babylonian era
First Babylonian dynasty – Amorite Dynasty, 1894–1595 BCE
Early Iron Age – Native Rule, Second Dynasty of Isin, 1155–1026 BCE
Assyrian rule, 911–619 BCE
Let’s look at this same area. in its larger geographical context:
This empire was very similar to the Akkadians. 1792-1749 BCE.
King Hammurabi of Babylon is a major figure.
• Akkadian Empire lasted about 200 years
• Amorites invaded Sumer about 2000 B.C., chose Babylon as capital
• Hammurabi—powerful Amorite king who ruled from 1792 to 1750 B.C.
– extended empire across Mesopotamia, Fertile Crescent
– appointed governors, tax collectors, judges to control lands
– watched over agriculture, trade, construction
Babylonians recognize that astronomical phenomena are periodic (e.g. the annual cycle of the Earth-Sun system)
The motion of the moon, and tides, are more examples of periodic phenomenon
Although they did not know the physical reasons why such patterns existed, they discovered the mathematical periodicity of both lunar and solar eclipses.
Centuries of Babylonian observations of celestial phenomena are recorded in the series of cuneiform tablets known as the Enûma Anu Enlil
Astronomical studies of the planet Venus
Writing of the “Mul Apin” clay tablets, catalogs of stars and constellations, heliacal rising dates of stars, constellations and planets
Babylonian cosmology
They developed a view of the universe in which our Earth was essentially flat, with several layers of heavens above, and several layers of underworlds below.
This diagram roughly shows their view of the universe – but note that this image is not meant to be geocentric. They didn’t imply that our world is the center of the universe; this was just what the universe was imagined to be like, locally.
The idea that our Earth is literally the center of the entire universe (geocentrism) didn’t develop until the later Greek era, circa the time of Aristotle.
“A six-level universe consisting of three heavens and three earths:
two heavens above the sky, the heaven of the stars, the earth, the underground of the Apsu, and the underworld of the dead.
The Earth was created by the god Marduk as a raft floating on fresh water (Apsu), surrounded by a vastly larger body of salt water (Tiamat).
The gods were divided into two pantheons, one occupying the heavens and the other in the underworld. ”
– History of cosmology, from Astronomy 123: Galaxies and the Expanding Universe
Assyrian empire 850 – 609 BCE
• Assyrian Empire replaced Babylonian Empire
• Located in hilly northern Mesopotamia
– built powerful horse and chariot army to protect lands
– soldiers were the only ones in the area to use iron swords, spear tips
– used battering rams, ladders, tunnels to get past city walls
• Assyrians were cruel to defeated peoples
• Enemies who surrendered were allowed to choose a leader.
Enemies who resisted were taken captive, and killed or enslaved.
• Enemy leaders were killed, cities burned
• Captured peoples were sent into exile
• Assyrian Empire fell in 609 B.C.
– defeated by combined forces of the Medes and Chaldeans
– victors burned the Assyrian capital city of Nineveh
Science
Astronomers of their day discovered a repeating 18-year Saros cycle of lunar eclipses
(data for this GIF is from http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros101.html)
Chaldean Empire/Neo-Babylonian empire 625 – 539 BCE
• Chaldeans ruled much of former Assyrian Empire
– sometimes called New Babylonians because Babylon was capital
• Chaldean empire peaked from 605 to 562 B.C. under Nebuchadnezzar II
– took Mediterranean trading cities, drove Egyptians out of Syria
• Nebuchadnezzar seized Jerusalem when the Hebrews rebelled in 598 B.C.
– destroyed the Jewish people’s Temple in Jerusalem, and held many captive in Babylon for about 50 years. (Many Jews returned to their homeland under Cyrus the Great.)
At the height of their wealth and power, the Chaldeans:
• Nebuchadnezzar built Babylonʼs Ishtar Gate, Tower of Babel ziggurat
• Built the Hanging Gardens of Babylon, one of Seven Wonders of the World
– an artificial mountain covered with trees, plants
The Empire Fades
• Weak rulers followed Nebuchadnezzar II
• Internal conflicts over religion divided Chaldean people
– made it easy for Cyrus The Great, King of Persia to conquer land
Post-Chaldean Babylonians
Jesse Emspak, in the Smithsonian, “Babylonians Were Using Geometry Centuries Earlier Than Thought” 1/28/16
As one of the brightest objects in the night sky, the planet Jupiter has been a source of fascination since the dawn of astronomy.
Now a cuneiform tablet dating to between 350 and 50 B.C. shows that Babylonians not only tracked Jupiter, they were taking the first steps from geometry toward calculus to figure out the distance it moved across the sky.
Obliquity of the Nine Planets http://solarviews.com/eng/solarsys.htm
Mathieu Ossendrijver of Humboldt University in Berlin found the tablet while combing through the collections at the British Museum.
The written record gives instructions for estimating the area under a curve by finding the area of trapezoids drawn underneath.
Using those calculations, the tablet shows how to find the distance Jupiter has traveled in a given interval of time.
The distance travelled by Jupiter after 60 days, 10º45′,
computed as the area of the trapezoid whose top left corner is Jupiter’s velocity over the course of the first day, in distance per day, and its top right corner is Jupiter’s velocity on the 60th day.
In a second calculation, the trapezoid is divided into two smaller ones,
with equal area to find the time in which Jupiter covers half this distance.
Photo credit: Trustees of the British Museum/Mathieu Ossendrijver
http://www.space.com/31765-ancient-babylonians-tracked-jupiter-with-math.html
Until now, this kind of use of trapezoids wasn’t known to exist before the 14th century.
“What they are doing is applying it to astronomy in a totally new way,” Ossendrijver says. “The trapezoid figure is not in real space and doesn’t describe a field or a garden, it describes an object in mathematical space—velocity against time.”
Scholars already knew that Babylonians could find the area of a trapezoid, and that they were quite familiar with the motions of planets and the moon. Previous records show that they used basic arithmetic—addition, subtraction, multiplication and division—to track these celestial bodies.
By 400 B.C. Babylonian astronomers had worked out a coordinate system using the ecliptic, the region of the sky the sun and planets move through, Ossendrijver says. They even invented the use of degrees as 360 fractions of a circle based on their sexagesimal, or base 60, counting system. What wasn’t clear was whether the Babylonians had a concept of objects in abstract mathematical space.
The trapezoid method involves learning the rate at which Jupiter moves and then plotting the planet’s speed against a set number of days on an x-y graph. The result should be a curve on the graph. Figuring out the area of trapezoids under this curve gives a reasonable approximation of how many degrees the planet has moved in a given period.
Babylonians Were Using Geometry Centuries Earlier Than Thought, Smithsonian Magazine
External references
https://en.wikipedia.org/wiki/Babylonian_astronomy
Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Understandings about the Nature of Science: Science knowledge has a history that includes the refinement of, and changes to, theories, ideas, and beliefs over time.
Science Is a Human Endeavor: Scientific knowledge is a result of human endeavor,
imagination, and creativity. Individuals and teams from many nations and cultures have contributed to science and to advances in engineering.
Massachusetts History and Social Science Curriculum Framework
Mesopotamia: Site of several ancient river civilizations circa 3500–1200 BCE
7.10 Describe the important achievements of Mesopotamian civilization.
Next Generation Science Standards
HS-ESS1 Earth’s Place in the Universe
Construct an explanation based on valid and reliable evidence obtained from a variety of sources (including students’ own investigations, theories, simulations, peer review) and the assumption that theories and laws that describe the natural world operate today as they did in the past and will continue to do so in the future. (HS-ESS1-2)
Apply scientific reasoning to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. (HS-ESS1-6)
Engaging in Argument from Evidence: Use appropriate and sufficient evidence and scientific reasoning to defend and critique claims and explanations about the natural and designed world(s). Arguments may also come from current scientific or historical episodes in science.
Connections to Nature of Science:
Science Models, Laws, Mechanisms, and Theories Explain Natural Phenomena.
A scientific theory is a substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment, and the science community validates each theory before it is accepted. If new evidence is discovered that the theory does not accommodate, then the theory is generally modified in light of this new evidence. (HS-ESS1-2),(HS-ESS1-6)
Graphing data that means something
Goals
1. How to graph data
2. How to identify trends (linear data)
3. How to identify more complex trends (simple harmonic motion)
4. Discover that data doesn’t always tell you about a physical phenomenon: Most of the time we need to know what phenomenon we’re analyzing, before the data can be understood at all.
Use the lesson ““Data has no meaning without a physical interpretation”
Actual student data
Learning standards
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Dimension 1: Scientific and Engineering Practices.
Practice 4: Analyzing and Interpreting Data.
“Once collected, data must be presented in a form that can reveal any patterns and relationships and that allows results to be communicated to others. Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evidence.”
Surface tension
Surface tension
New section: to be written
MythBusters: Buried Alive & Falling off of a bridge 10/2003
(1) If a person is falling off a bridge, can they save themselves by throwing a hammer ahead of them to break the surface tension of the water prior to their own impact?
How can cliff divers survive their dives?
http://physics.stackexchange.com/questions/9059/jumping-into-water
Dimensional analysis
(Also called the factor-label method)
Dimensional analysis is a super useful technique used for many different reasons:
scaling up recipes to much larger quantities
Converting English-to-metric units (or vice-versa)
Physics problems, e.g. involving speed and distance
Chemistry problems (how much product is made from how much starting materials?)
Dimensional analysis is just a a trick in which we use conversions factors to get from the info we have, to the answer we need.
Sometimes we need to string several conversion factors together to get the answer that we need.
What is a conversion factor?
Two things that are exactly equivalent
We can always write 2 equivalent things as a fraction
The fraction can be written with either term on top, or bottom:
Conversion factor for money
Conversion factor for distance
Example: How do we convert inches to cm?
Convert days to seconds
Worksheet: Dimensional analysis worksheet: By JenniferBarankovi
External links
Fun with Dimensional analysis, Eric Lee, RN
____________
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
Science and Engineering Practices: 5. Using Mathematics and Computational Thinking:
Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m 3, acre-feet, etc.).
NSTA: The efficiency and effectiveness of the metric system has long been evident to scientists, engineers, and educators. Because the metric system is used in all industrial nations except the United States, it is the position of the National Science Teachers Association that the International System of Units (SI) and its language be incorporated as an integral part of the education of children at all levels of their schooling.
objects in motion
Kinematics is the study of objects in motion. It allow us to study displacement, velocity, time and acceleration. Check out our introductory lesson on this study of motion here:
https://kaiserscience.wordpress.com/physics/kinematics/
The Thirty Million Word Gap
The full article is available here: The Early Catastrophe: The 30 Million word gap by age 3. and at http://www.aft.org/periodical/american-educator/spring-2003
Betty Hart and Todd Risley entered the homes of 42 families from various socio-economic backgrounds to assess the ways in which daily exchanges between a parent and child shape language and vocabulary development. Their findings showed marked disparities between the sheer number of words spoken as well as the types of messages conveyed.
After four years these differences in parent-child interactions produced significant discrepancies in not only children’s knowledge, but also their skills and experiences with children from high-income families being exposed to 30 million more words than children from families on welfare.
Follow-up studies showed that these differences in language and interaction experiences have lasting effects on a child’s performance later in life.
The Early Catastrophe
Betty Hart & Todd R. Risley
Mission:
Betty Hart and Todd Risley were at the forefront of educational research during the 1960’s War on Poverty. Frustrated after seeing the effects of their high quality early intervention program aimed at language skill expansion prove unsuccessful in the long-term, they decided to shift their focus. If the proper measures were being taken in the classroom, the only logical conclusion was to take a deeper look at the home.
What difference does home-life make in a child’s ability to communicate? Why are the alarming vocabulary gaps between high school students from low and high income environments seemingly foreshadowed by their performance in preschool? Hart and Risley believed that the home housed some of these answers.
Experimental Method:
Hart and Risley recruited 42 families to participate in the study including 13 high-income families, 10 families of middle socio-economic status, 13 of low socio-economic status, and 6 families who were on welfare. Monthly hour-long observations of each family were conducted from the time the child was seven months until age three. Gender and race were also balanced within the sample.
Results:
The results of the study were more severe than the researchers anticipated. Observers found that 86 percent to 98 percent of the words used by each child by the age of three were derived from their parents’ vocabularies.
Furthermore, not only were the words they used nearly identical, but also the average number of words utilized, the duration of their conversations, and the speech patterns were all strikingly similar to those of their caregivers.
After establishing these patterns of learning through imitation, the researchers next analyzed the content of each conversation to garner a better understanding of each child’s experience. They found that the sheer number of words heard varied greatly along socio-economic lines. On average, children from families on welfare were provided half as much experience as children from working class families, and less than a third of the experience given to children from high-income families.
In other words, children from families on welfare heard about 616 words per hour, while those from working class families heard around 1,251 words per hour, and those from professional families heard roughly 2,153 words per hour. Thus, children being raised in middle to high income class homes had far more language exposure to draw from.
In addition to looking at the number of words exchanged, the researchers also looked at what was being said within these conversations. What they found was that higher-income families provided their children with far more words of praise compared to children from low-income families. Conversely, children from low-income families were found to endure far more instances of negative reinforcement compared to their peers from higher-income families.
Children from families with professional backgrounds experienced a ratio of six encouragements for every discouragement. For children from working-class families this ratio was two encouragements to one discouragement. Finally, children from families on welfare received on average two discouragements for every encouragement. Therefore, children from families on welfare seemed to experience more negative vocabulary than children from professional and working-class families.
The authors conclude:
We learned from the longitudinal data that the problem of skill differences among children at the time of school entry is bigger. more intractable. and more important than we had thought. So much is happening to children during their first three years at home, at a time when they are especially malleable and uniquely dependent on the family for virtually all their experience. that by age 3, an intervention must address not just a lack of knowledge or skill, but an entire general approach to experience…
…Estimating, as we did, the magnitude of the differences in children’s cumulative experience before the age of 3 gives an indication of how big the problem is. Estimating the hours of intervention needed to equalize children’s early experience makes clear the enormity of the effort that would be required to change children’s lives. And the longer the effort is put off, the less possible the change becomes. We see why our brief, intense efforts during the War on Poverty did not succeed. But we also see the risk to our nation and its children that makes intervention more urgent than ever.
_______________________________________
A summary from “The Early Catastrophe: The 30 Million Word Gap by Age 3” by University of Kansas researchers Betty Hart and Todd R. Risley. (2003). American Educator. Spring: 4-9, which was excerpted with permission from B. Hart and T.R. Risley (1995). Meaningful Differences in the Everyday Experiences of Young American Children. Baltimore, MD: Brookes Publishing.
Parallel universes in quantum mechanics
Intro
New quantum mechanics theory says parallel universes exist and interact, 4 Nov, 2014
To the average person, quantum mechanics is the convoluted, science fiction-y branch of physics. A radical new theory plays into that, proposing that parallel universes exist and interact with each other ‒ and that scientists may be able to test for them.
Prof. Howard Wiseman, a physicist at Griffith University in Brisbane, Australia, along with his collaborators Dr. Michael Hall, also of Griffith University, and University of California, Davis mathematician Dr. Dirk-Andre Deckert, published their new “many interacting worlds” (MIW) theory in the journal Physical Review X.
They posited that other universes are real, exist in vast numbers and exert influence on each other.
“The idea of parallel universes in quantum mechanics has been around since 1957,” Wiseman said in a statement. “In the well-known ‘Many-Worlds Interpretation’, each universe branches into a bunch of new universes every time a quantum measurement is made. All possibilities are therefore realised – in some universes the dinosaur-killing asteroid missed Earth. In others, Australia was colonised by the Portuguese.”
“But critics question the reality of these other universes, since they do not influence our universe at all,” he added. “On this score, our “Many Interacting Worlds” approach is completely different, as its name implies.”
There are three main points to the MIW theory, according to the Griffith statement.
First, that the universe we live in is just one of an unknown “gigantic” number of worlds, some of which are “almost identical to ours,” but most are “very different.”
Second, all of the worlds are “equally real,” existing continuously through time with precisely defined properties.
Third, quantum phenomena arise from “a universal force of repulsion between ‘nearby’ (i.e. similar) worlds, which tends to make them more dissimilar.”
“All quantum effects arise from, and only from, the interaction between worlds,“ the physicists explained in their abstract.
Hall said the radical new theory may even create the extraordinary possibility of testing for the existence of other worlds.
“The beauty of our approach is that if there is just one world our theory reduces to Newtonian mechanics, while if there is a gigantic number of worlds it reproduces quantum mechanics,” he said in the statement. “In between it predicts something new that is neither Newton’s theory nor quantum theory. We also believe that, in providing a new mental picture of quantum effects, it will be useful in planning experiments to test and exploit quantum phenomena.”
image from “Parallel Universes”, Max Tegmark, Scientific American, May 2003
American theoretical physicist Richard Feynman once noted: “I think I can safely say that nobody understands quantum mechanics.” And the MIW group admits that their theory is a bit out there.
“Any explanation of quantum phenomena is going to be weird, and standard quantum mechanics does not really offer any explanation at all ‒ it just makes predictions for laboratory experiments,” Wiseman told the Huffington Post in an email.“Our new explanation… is that there are ordinary [non-quantum] parallel worlds which interact in a particular and subtle way.”
Motherboard asked if the theory suggests that humans might someday be able to interact with other universes.
“It’s not part of our theory,” Wiseman replied. “But the idea of [human] interactions with other universes is no longer pure fantasy.”
Others in the quantum mechanics field ranged from skepticism to excitement, Huffington Post reported, noting there is no consensus on whether “many interacting worlds” exist or interact.
“There are some who are completely happy with their own interpretations of QM, and we are unlikely to change their minds,”Wiseman said in his email. “But I think there are many who are not happy with any of the current interpretations, and it is those who will probably be most interested in ours. I hope some will be interested enough to start working on it soon, because there are so many questions to answer.”
https://www.rt.com/usa/202255-many-interacting-worlds-quantum-mechanics/
Learning Standards
AP Physics Curriculum Framework
Essential Knowledge 1.D.1: Objects classically thought of as particles can exhibit properties of waves.
a. This wavelike behavior of particles has been observed, e.g., in a double-slit experiment using elementary particles.
b. The classical models of objects do not describe their wave nature. These models break down when observing objects in small dimensions.
Learning Objective 1.D.1.1:
The student is able to explain why classical mechanics cannot describe all properties of objects by articulating the reasons that classical mechanics must be refined and an alternative explanation developed when classical particles display wave properties.
Essential Knowledge 1.D.2: Certain phenomena classically thought of as waves can exhibit properties of particles.
a. The classical models of waves do not describe the nature of a photon.
b. Momentum and energy of a photon can be related to its frequency and wavelength.
Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.
A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)
Electromagnetic radiation can be modeled as a wave of changing electric and magnetic fields or as particles called photons. The wave model is useful for explaining many features of electromagnetic radiation, and the particle model explains other features. Quantum theory relates the two models…. Knowledge of quantum physics enabled the development of semiconductors, computer chips, and lasers, all of which are now essential components of modern imaging, communications, and information technologies
The Writing Revolution
The Atlantic, October 2012
By Peg Tyre
in 2009, when Monica DiBella entered New Dorp, a notorious public high school on Staten Island, her academic future was cloudy. Monica had struggled to read in early childhood, and had repeated first grade. During her elementary-school years, she got more than 100 hours of tutoring, but by fourth grade, she’d fallen behind her classmates again. In the years that followed, Monica became comfortable with math and learned to read passably well, but never seemed able to express her thoughts in writing. During her freshman year at New Dorp, a ’70s-style brick behemoth near a grimy beach, her history teacher asked her to write an essay on Alexander the Great. At a loss, she jotted down her opinion of the Macedonian ruler: “I think Alexander the Great was one of the best military leaders.” An essay? “Basically, that wasn’t going to happen,” she says, sweeping her blunt-cut brown hair from her brown eyes. “It was like, well, I got a sentence down. What now?” Monica’s mother, Santa, looked over her daughter’s answer—six simple sentences, one of which didn’t make sense—with a mixture of fear and frustration. Even a coherent, well-turned paragraph seemed beyond her daughter’s ability. An essay? “It just didn’t seem like something Monica could ever do.”
For decades, no one at New Dorp seemed to know how to help low-performing students like Monica, and unfortunately, this troubled population made up most of the school, which caters primarily to students from poor and working-class families. In 2006, 82 percent of freshmen entered the school reading below grade level. Students routinely scored poorly on the English and history Regents exams, a New York State graduation requirement: the essay questions were just too difficult. Many would simply write a sentence or two and shut the test booklet. In the spring of 2007, when administrators calculated graduation rates, they found that four out of 10 students who had started New Dorp as freshmen had dropped out, making it one of the 2,000 or so lowest-performing high schools in the nation. City officials, who had been closing comprehensive high schools all over New York and opening smaller, specialized ones in their stead, signaled that New Dorp was in the crosshairs.
And so the school’s principal, Deirdre DeAngelis, began a detailed investigation into why, ultimately, New Dorp’s students were failing. By 2008, she and her faculty had come to a singular answer: bad writing. Students’ inability to translate thoughts into coherent, well-argued sentences, paragraphs, and essays was severely impeding intellectual growth in many subjects. Consistently, one of the largest differences between failing and successful students was that only the latter could express their thoughts on the page.
If nothing else, DeAngelis and her teachers decided, beginning in the fall of 2009, New Dorp students would learn to write well. “When they told me about the writing program,” Monica says, “well, I was skeptical.” With disarming candor, sharp-edged humor, and a shy smile, Monica occupies the middle ground between child and adult—she can be both naive and knowing. “On the other hand, it wasn’t like I had a choice. I go to high school. I figured I’d give it a try.”
New Dorp’s Writing Revolution, which placed an intense focus, across nearly every academic subject, on teaching the skills that underlie good analytical writing, was a dramatic departure from what most American students—especially low performers—are taught in high school. The program challenged long-held assumptions about the students and bitterly divided the staff. It also yielded extraordinary results. By the time they were sophomores, the students who had begun receiving the writing instruction as freshmen were already scoring higher on exams than any previous New Dorp class. Pass rates for the English Regents, for example, bounced from 67 percent in June 2009 to 89 percent in 2011; for the global-history exam, pass rates rose from 64 to 75 percent. The school reduced its Regents-repeater classes—cram courses designed to help struggling students collect a graduation requirement—from five classes of 35 students to two classes of 20 students.
…[Why were the students previously failing?]
…. New Dorp students were simply not smart enough to write at the high-school level. You just had to listen to the way the students talked, one teacher pointed out—they rarely communicated in full sentences, much less expressed complex thoughts… Scharff, a lecturer at Baruch College, a part of the City University of New York, kept pushing, asking: “What skills that lead to good writing did struggling students lack?” …
Maybe the struggling students just couldn’t read, suggested one teacher.
A few teachers administered informal diagnostic tests the following week and reported back. The students who couldn’t write well seemed capable, at the very least, of decoding simple sentences. A history teacher got more granular. He pointed out that the students’ sentences were short and disjointed. What words, Scharff asked, did kids who wrote solid paragraphs use that the poor writers didn’t? Good essay writers, the history teacher noted, used coordinating conjunctions to link and expand on simple ideas—words like for, and, nor, but, or, yet, and so. Another teacher devised a quick quiz that required students to use those conjunctions. To the astonishment of the staff, she reported that a sizable group of students could not use those simple words effectively. The harder they looked, the teachers began to realize, the harder it was to determine whether the students were smart or not—the tools they had to express their thoughts were so limited that such a judgment was nearly impossible.
The exploration continued. One teacher noted that the best-written paragraphs contained complex sentences that relied on dependent clauses like although and despite, which signal a shifting idea within the same sentence. Curious, Fran Simmons devised a little test of her own. She asked her freshman English students to read Of Mice and Men and, using information from the novel, answer the following prompt in a single sentence:
“Although George …”
She was looking for a sentence like: Although George worked very hard, he could not attain the American Dream.
Some of Simmons’s students wrote a solid sentence, but many were stumped. More than a few wrote the following: “Although George and Lenny were friends.”
A lightbulb, says Simmons, went on in her head. These 14- and 15-year-olds didn’t know how to use some basic parts of speech. With such grammatical gaps, it was a wonder they learned as much as they did. “Yes, they could read simple sentences,” but works like the Gettysburg Address were beyond them—not because they were too lazy to look up words they didn’t know, but because “they were missing a crucial understanding of how language works. They didn’t understand that the key information in a sentence doesn’t always come at the beginning of that sentence.”
Some teachers wanted to know how this could happen. “We spent a lot of time wondering how our students had been taught,” said English teacher Stevie D’Arbanville. “How could they get passed along and end up in high school without understanding how to use the word although?”
…The Hochman Program, as it is sometimes called, would not be unfamiliar to nuns who taught in Catholic schools circa 1950. Children do not have to “catch” a single thing. They are explicitly taught how to turn ideas into simple sentences, and how to construct complex sentences from simple ones by supplying the answer to three prompts—but, because, and so. They are instructed on how to use appositive clauses to vary the way their sentences begin. Later on, they are taught how to recognize sentence fragments, how to pull the main idea from a paragraph, and how to form a main idea on their own. It is, at least initially, a rigid, unswerving formula. “I prefer recipe,” Hochman says, “but formula? Yes! Okay!”
…Within months, Hochman became a frequent visitor to Staten Island. Under her supervision, the teachers at New Dorp began revamping their curriculum. By fall 2009, nearly every instructional hour except for math class was dedicated to teaching essay writing along with a particular subject. So in chemistry class in the winter of 2010, Monica DiBella’s lesson on the properties of hydrogen and oxygen was followed by a worksheet that required her to describe the elements with subordinating clauses—for instance, she had to begin one sentence with the word although.
Although … “hydrogen is explosive and oxygen supports combustion,” Monica wrote, “a compound of them puts out fires.”
Unless … “hydrogen and oxygen form a compound, they are explosive and dangerous.”
If … This was a hard one. Finally, she figured out a way to finish the sentence. If … “hydrogen and oxygen form a compound, they lose their original properties of being explosive and supporting combustion.”
As her understanding of the parts of speech grew, Monica’s reading comprehension improved dramatically. “Before, I could read, sure. But it was like a sea of words,” she says. “The more writing instruction I got, the more I understood which words were important.”
Classroom discussion became an opportunity to push Monica and her classmates to listen to each other, think more carefully, and speak more precisely, in ways they could then echo in persuasive writing.
PEG TYRE is the director of strategy at the Edwin Gould Foundation and the author of The Good School: How Smart Parents Get Their Kids the Education They Deserve.
http://www.theatlantic.com/magazine/archive/2012/10/the-writing-revolution/309090/
Van Gogh’s Starry Night
Physicist Werner Heisenberg said, “When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.” As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks.
Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work.
The unexpected math behind Van Gogh’s “Starry Night”
https://www.youtube.com/watch?v=PMerSm2ToFY
Natalya St. Clair, Educator
Avi Ofer , Animator
Addison Anderson, Script Editor
http://ed.ted.com/lessons/the-unexpected-math-behind-van-gogh-s-starry-night-natalya-st-clair
The new Hi-Fi debate and the science of sound
Music today is listened to almost exclusively through digital compression. The most common digital compression format is called MP3 (MPEG-2 Audio Layer III.) A competing digital compression format is FLAC (Free Lossless Audio Codec.)
Many audio enthusiasts believe that FLAC provides significantly more accurate sound reproduction, which can be heard by listeners. Most audio enthusiasts, however, hold that more is not always better, and that the FLAC format does not produce any audible benefits for listeners. PONO is a highly publicized FLAC-based digital music player, a high-tech MP3 player of sorts, that promises significantly better music reproduction.
Both FLAC proponents and skeptics use math and physics based arguments to explain their position. Here’s a brief overview, with links to articles that have more detail.
Our physics article on sound :
Sources of sound
The physics of sound.
On Cnet, Stephen Shankland writes about the science of sound, in the latest generation of audio devices:
Pono Music’s roaring success on Kickstarter, raising $4.3 million so far, shows that thousands of people believe better audio quality is worth paying for. The company — backed by star musician Neil Young and selling a $400 digital audio player along with accompanying music — promises people will hear a difference between Pono Music and ordinary music that’s “surprising and dramatic.” The company’s promise is based in part on music files that can contain more data than not only conventional MP3 files, but also compact discs.
… Just as some skeptics think 4K TVs is wasted on human eyes, which mostly can’t perceive an image quality improvement over mainstream HD 1080p under normal viewing conditions, others think CD audio technology that’s now more than three decades old is actually very well matched to human hearing abilities. For playback, they’re fine with two key aspects of CD audio encoding: its 16-bit dynamic range, which means audio is measured with a precision of 65,536 levels, and its 44.1kHz “sampling” frequency that means those levels are measured 44,100 times each second.
“From a scientific point of view, there’s no need to go beyond,” said Bernhard Grill, leader of Fraunhofer Institute’s audio and multimedia division and one of the creators of the MP3 and AAC audio compression formats. “It’s always nice to have higher numbers on the box, and 24 bits sounds better than 16 bits. But practically, I think people should much more worry about speakers and room acoustics.”
Pono’s recordings will range from CD-quality 16-bit/44.1kHz to 24-bit/192kHz “ultra-high resolution.” To house the data, Pono follows in the footsteps of the digital audiophile industry by sticking with a file format called FLAC (Free Lossless Audio Codec) that compresses files for smaller sizes but not to the degree of alternatives including MP3 and AAC that throw away some of the original data. The company also is betting its success on a player with better electronics and a catalog of HD music designed to let listeners hear music true to its original sound in the recording studio.
…The idea is that more data allows a higher dynamic range — the span between the loudest and quietest passages of music — and comes closer to the detail of live, original sound….
A prominent part of the case against high-resolution audio is a 2007 study by E. Brad Meyer and David Moran of the Boston Audio Society – that concluded listeners couldn’t tell the difference between SACD and DVD-A music on the one hand and CD-quality versions of the same recordings on the other.
Results of a blind audio test. By E. Brad Meyer and David R. Moran
In that experiment’s 554 tests, listeners correctly identified when a SACD or DVD-A recording compared to a CD only 49.8 percent of the time — in other words, they didn’t do better than randomly guessing.…
Another high-profile non-believer is Christopher “Monty” Montgomery, an engineer who writes codec software for the Xiph.Org Foundation and who works for Firefox developer Mozilla. The most prominent part of his effort is a video arguing that CD quality sound is good enough. Montgomery’s video, illustrated with lucid demonstrations and backed by a blog post, persuasively debunks misconceptions such as the idea that encoding music digitally reduces it to a series of jagged stairsteps instead of the original smooth curves.
24/192 Music Downloads …and why they make no sense:
Video on 24/192 music downloads: D/A and A/D | Digital Show and Tell (Monty Montgomery @ xiph.org)
Montgomery and his allies have yet to persuade everyone on two points, including the idea that 16-bit resolution and 44.1kHz is sufficient.
“Monty is wrong. Twenty-four bits does matter — but for a very small sliver of the music business,” said Mark Waldrep, an audio engineer who’s founder and chief executive of AIX Records and iTrax.com and who focuses on high-resolution audio — including efforts of his own to debunk some claims. And of the sampling frequency he said, “I’d rather err on having those frequencies in the signal rather than assuming we don’t need them.”
But Grill thinks any purported benefit would be lost in the real world. “The limiting factor is the loudspeaker, the room acoustics, and the human ear,” he said.
From “The Digital Myth: Why Digital Audio Sounds Better Than You Think”
By Gordon Reid
Now, perhaps the greatest myth in digital audio relates to the misconception that digital signals are shaped like staircases, and that much of their ‘brittleness’ is a consequence of the steps. This is nonsense. Digital signals are not shaped like anything — they are sequences of numbers. Unfortunately, the type of representation in diagram 8 has led many people to confuse graphics with reality.
Let’s be clear. When the samples in a digital signal are converted back into an analogue signal, they pass through a device called a reconstruction filter. This is the process that makes the Sampling Theorem work in the real world. If there are enough samples and they are of sufficient resolution, the signal that emerges is not only smooth but virtually identical to the analogue signal from which the samples were originally derived. Of course, it’s possible to design a poor reconstruction filter that introduces unwanted changes and artifacts but, again, this is an engineering consideration, not a deficiency in the concept itself.
__
Source: Sound bite: Despite Pono’s promise, experts pan HD audio
Another great article on this topic
What is FLAC? The high-def MP3 explained. C|Net
Here is a detailed physics experiment showing an analysis of FLAC and MP3 audio files. The result is that there is no audible difference between any of these formats! Each is equally good. There are, however, significant problems in how iTunes engineers (and probably engineers from other companies) are choosing to compress original recordings. many times they make choices which negatively affect the music. However, those errors are independent of whether one ends up using MP3, FLAC or other formats.
Also see “There are no “stair steps” in digital audio ! What The Matrix can teach us about “resolution””
There are no “stair steps” in digital audio ! What The Matrix can teach us about “resolution”
Latest Posts
-
Is it feasible and safe to colonize Mars?
Over the last decade many people working in space exploration have become much more skeptical about the possibility of human colonization of Mars, at least…
-
Soil profile Lego lab
First let’s learn about soil and its layers – Soil profiles This image comes from Build a Layers of Soil Model by Sarah McClelland. Clicking…
-
Epithelial cell tissue box model
Students can build a realistic model of epithelial cells with a tissue box. Here’s an article on Skin – the integumentary System Using a tissue box…
-
Making a winter cat shelter for outdoor cats
New England winters are beautiful, but they can be awful for feral cats. We have a few cats in our home that we got from…
KaiserScience 
