Benoît Mandelbrot obituary
|
|
- Moris Oliver Fleming
- 6 years ago
- Views:
Transcription
1 Benoît Mandelbrot obituary Mathematician whose fractal geometry helps us find patterns in the irregularities of the natural world Nigel Lesmoir-Gordon guardian.co.uk, Sunday 17 October BST larger smaller A computer generated fractal image. 'Why is geometry often described as cold and dry? asked Mandelbrot. One reason lies in its inability to describe the shape of a cloud, a mountain or a tree. Photograph: Stocktrek/Corbis Benoît Mandelbrot, who has died of pancreatic cancer aged 85, enjoyed the rare distinction of having his name applied to a feature of mathematics that has become part of everyday life the Mandelbrot set. Both a French and an American citizen, though born in Poland, he had a visionary, maverick approach, harnessing computer power to develop a geometry that mirrors the complexity of the natural world, with applications in many practical fields. At the start of his groundbreaking work, The Fractal Geometry of Nature, he asks: "Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree." The approach that he pioneered helps us to describe nature as we actually see it, and so expand our way of thinking. The world we live in is not naturally smooth-edged and regularly shaped like the 1 sur 6 18/10/10 14:21
2 familiar cones, circles, spheres and straight lines of Euclid's geometry: it is rough-edged, wrinkled, crinkled and irregular. "Fractals" was the name he applied to irregular mathematical shapes similar to those in nature, with structures that are self-similar over many scales, the same pattern being repeated over and over. Fractal geometry offers a systematic way of approaching phenomena that look more elaborate the more they are magnified, and the images it generates are themselves a source of great fascination. Mandelbrot always had a highly developed visual sense: as a boy, he saw chess games in geometrical rather than logical terms, and shared his father's passion for maps. Photograph: Nigel Lesmoir-Gordon Mandelbrot first visualised the set on 1 March 1980 at IBM's Thomas J Watson Research Centre at Yorktown Heights, upstate New York. However, the seeds of this discovery were sown in Paris in 1925, when the mathematicians Gaston Julia, a student of Henri Poincaré, and Pierre Fatou published a paper exploring the world of complex numbers combinations of the usual real numbers, 1, -1 and so on, with imaginary numbers such as the square root of -1, which Gottfried Wilhelm Leibniz had labelled "that amphibian between being and not being". The results of their endeavours eventually became known as Julia sets, though Julia himself never saw them represented graphically. It was Mandelbrot's uncle Szolem who initially directed him to the work of Julia and Fatou on what are termed self-similarity and iterated functions. In my documentary The Colours of Infinity, shown on Channel 4 in 1995, Mandelbrot told me how he set about developing his approach: '"For me the first step with any difficult mathematical problem was to programme it, and see what it looked like. We started programming Julia sets of all kinds. It was extraordinarily great fun! And in particular, at one point, we became interested in the Julia set of the simplest possible transformation: Z goes to Z squared plus C [where C is a constant number. So Z times Z plus C, and then the outcome of that becomes a new Z while C stays the same, to give new Z times new Z plus C, and so on]. I 2 sur 6 18/10/10 14:21
3 made many pictures of it. The first ones were very rough. But the very rough pictures were not the answer. Each rough picture asked a question. So I made another picture, another picture. And after a few weeks we had this very strong, overwhelming impression that this was a kind of big bear we had encountered." In his view, the most important implication of this work was that very simple formulas could yield very complicated results: "What is science? We have all this mess around us. Things are totally incomprehensible. And then eventually we find simple laws, simple formulas. In a way, a very simple formula, Newton's Law, which is just also a few symbols, can by hard work explain the motion of the planets around the sun and many, many other things to the 50th decimal. It's marvellous: a very simple formula explains all these very complicated things." Mandelbrot, born into a Lithuanian-Jewish family living in Warsaw, showed an early love for geometry and excelled at chess: he later admitted that he did not think the game through logically, but geometrically. Maps were another inspiration. His father was crazy about them, and the house was full of them. In 1936, the rise of nazism in Germany persuaded his family to leave for Paris, and eventually Lyon, in the south of France. A year of studying mathematics there after he left high school brought home to Mandelbrot his extraordinary visual ability. At the end of the second world war he returned to Paris for college entrance examinations, which he passed with distinction, winning a place at the École Normale and then moving on to the École Polytechnique. From there he went on to the California Institute of Technology, Pasadena, to study turbulence and gain a master's in aeronautics. After obtaining a doctorate in mathematics (1952) in Paris, he returned to the US, this time to the Institute for Advanced Study at Princeton University, New Jersey. There he came across the idea of the Hausdorff-Besicovitch dimension the revelation that there were phenomena that existed outside one-dimensional space, but in somewhat less than two dimensions. Mandelbrot took up the concept on the spot: it provided an all-purpose tool and was a special example of his eventual notion of fractal dimension. 3 sur 6 18/10/10 14:21
4 Fractals have structures that are self-similar over many scales, the same pattern being repeated over and over. Photograph: Nigel Lesmoir-Gordon His interest in computers was immediate, and his use of the new resource grew rapidly. He returned to France, married Aliette Kagan and became a professor at the University of Lille and then at the Centre National de la Recherche Scientifique in Paris. His academic future looked assured. But he felt uncomfortable in that environment, and in 1958 he spent the summer at IBM as a faculty visitor. The company asked him to work on eliminating the apparently random noise in signal transmissions between computer terminals. The errors were not in fact completely random they tended to come in bunches. Mandelbrot observed that the degree of bunching remained constant whether he plotted them by the month, the week or by the day. This was another step towards his fractal revelation. During the 1960s Mandelbrot's quest led him to study galaxy clusters, applying his ideas on scaling to the structure of the universe itself. He scoured through forgotten and obscure journals. He found the clue he was looking for in the work of the mathematician and meteorologist Lewis Fry Richardson: he took a photocopy, and when he returned to consult the volume further, found it had gone to be pulped. Nonetheless, he knew he had struck a rich seam. Richardson loved asking questions others considered worthless, and one of his papers, Does the Wind Possess a Velocity? anticipated later work by Edward Lorenz and other founders of Chaos Theory. One of Richardson's great insights was a model of turbulence as a collection of ever-smaller eddies. Mandelbrot was struck too by Richardson's 1961 observations on the lengths of coastlines, and published a paper called How Long is the Coast of Britain? This apparently simple question of geography reveals, on close inspection, some of the 4 sur 6 18/10/10 14:21
5 essential features of fractal geometry. At IBM in 1973 Mandelbrot developed an algorithm using a very basic, makeshift computer, a typewriter with a minute memory, to generate pictures that imitated natural landforms. While the ideas behind fractals, iteration and self-similarity are ancient, it took the coining of the term "fractal geometry" in 1975 and the publication of The Fractal Geometry of Nature in French in the same year to give the quest an identity. As Mandelbrot put it, "to have a name is to be" and the field exploded. He had bolstered his own presence by adding a middle initial that stood for no particular name, and Benoît B Mandelbrot became a fixture at IBM, with visiting professorships at Harvard and MIT, the Massachusetts Institute of Technology. He started teaching at Yale in 1987, becoming a full professor there in His many awards included the Wolf prize for physics in Fractal geometry is now being used in work with marine organisms, vegetative ecosystems, earthquake data, the behaviour of density-dependent populations, percolation and aggregation in oil research, and in the formation of lightning. Lightning resembles the diffusion patterns left by water as it permeates soft rock such as sandstone: computer simulations of this effect look exactly like the real thing. Fractals hold a promise for building better roads, for video compression and even for designing ships that are less likely to capsize. The geometry is already being successfully applied in medical imaging, and the forms generated by the discipline are a source of pleasure in their own right, adding to our aesthetic awareness as we observe fractals everywhere in nature. Their beauty and power are displayed in the just-published book The Colours of Infinity, updating the account given in the film. In the course of making that and a further film with Mandelbrot Clouds Are Not Spheres (2000, now a DVD) I became aware of his great kindness and generosity. At the end of Clouds Are Not Spheres he reflects: "My search has brought me to many of the most fundamental issues of science. Some I improved upon, but certainly left very wide open and mysterious. This had been my hope as a young man and has filled my whole life. I feel extremely fortunate." He is survived by Aliette and his two sons, Laurent and Didier. Benoît Mandelbrot, mathematician, born 20 November 1924; died 14 October 2010 guardian.co.uk Guardian News and Media Limited sur 6 18/10/10 14:21
6 6 sur 6 18/10/10 14:21
MISSOURI S FRAMEWORK FOR CURRICULAR DEVELOPMENT IN MATH TOPIC I: PROBLEM SOLVING
Prentice Hall Mathematics:,, 2004 Missouri s Framework for Curricular Development in Mathematics (Grades 9-12) TOPIC I: PROBLEM SOLVING 1. Problem-solving strategies such as organizing data, drawing a
More informationRaindrop Plotter. Joyce Ma. June 2005
Raindrop Plotter Joyce Ma June 2005 Keywords: < formative environmental rain, outside > 1 PURPOSE To gauge Outdoor Exploratorium: Formative Evaluation Raindrop Plotter Joyce Ma June 2005 What visitors
More informationWhat is Dialectical Materialism?
What is Dialectical Materialism? There is an interesting aphorism from Taoism: That which is known is not the truth. This is an important observation. It is true because any description of reality is fixed
More information110 september 2017 reader s digest
110 september 2017 reader s digest My Most Unforgettable Teacher The story of an extraordinary mentor who left a life-changing impression By Maitreesh Ghatak Illustration By keshav kapil I first met Pinaki-da
More informationMcDougal Littell High School Math Program. correlated to. Oregon Mathematics Grade-Level Standards
Math Program correlated to Grade-Level ( in regular (non-capitalized) font are eligible for inclusion on Oregon Statewide Assessment) CCG: NUMBERS - Understand numbers, ways of representing numbers, relationships
More informationProfessor Manovich, welcome to the Thought Project. Thank you so much. I love your project name. I can come back any time.
Hi, this is Tanya Domi. Welcome to the Thought Project, recorded at the Graduate Center of the City University of New York, fostering groundbreaking research and scholarship in the arts, social sciences,
More informationSophie Germain
Sophie Germain 1776-1831 HISTORICAL CONNECTIONS IN MATHEMATICS 83 2012 AIMS Education Foundation SOPHIE GERMAIN MATHEMATICS IN A MAN S WORLD Biographical Information: Sophie Germain (zhair-man) was a French
More information6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 21
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 21 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare
More informationGeorgia Quality Core Curriculum
correlated to the Grade 8 Georgia Quality Core Curriculum McDougal Littell 3/2000 Objective (Cite Numbers) M.8.1 Component Strand/Course Content Standard All Strands: Problem Solving; Algebra; Computation
More informationI decided to take a class about you, your life, and your history because I thought it
MIT Student Dear Mr. Galileo, I decided to take a class about you, your life, and your history because I thought it might be interesting. Admittedly, I didn t really know what I was getting myself into.
More informationADAIR COUNTY SCHOOL DISTRICT GRADE 03 REPORT CARD Page 1 of 5
ADAIR COUNTY SCHOOL DISTRICT GRADE 03 REPORT CARD 2013-2014 Page 1 of 5 Student: School: Teacher: ATTENDANCE 1ST 9 2ND 9 Days Present Days Absent Periods Tardy Academic Performance Level for Standards-Based
More informationConferences. Journals. Job Opening
November 2015 November 2015-2016 ASE Sixth North American Conference: June 2016 -Third International Conference of the Polish Society for the Psychology of Religion and Spirituality: Psychology, Culture,
More informationThe Problem of Evil and Pain. 3. The Explanation of Leibniz: The Best of All Possible Worlds
The Problem of Evil and Pain 3. The Explanation of Leibniz: The Best of All Possible Worlds Opening Prayer Almighty and everlasting God, you made the universe with all its marvelous order, its atoms, worlds,
More information6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 3
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 3 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare
More informationThe Development of Knowledge and Claims of Truth in the Autobiography In Code. When preparing her project to enter the Esat Young Scientist
Katie Morrison 3/18/11 TEAC 949 The Development of Knowledge and Claims of Truth in the Autobiography In Code Sarah Flannery had the rare experience in this era of producing new mathematical research at
More informationExtract How to have a Happy Life Ed Calyan 2016 (from Gyerek, 2010)
Extract How to have a Happy Life Ed Calyan 2016 (from Gyerek, 2010) 2.ii Universe Precept 14: How Life forms into existence explains the Big Bang The reality is that religion for generations may have been
More informationGrade 6 correlated to Illinois Learning Standards for Mathematics
STATE Goal 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions. A. Demonstrate
More informationcorrelated to the Massachussetts Learning Standards for Geometry C14
correlated to the Massachussetts Learning Standards for Geometry C14 12/2003 2004 McDougal Littell Geometry 2004 correlated to the Massachussetts Learning Standards for Geometry Note: The parentheses at
More informationPersonalize these Powerful Affirmation Templates and Become a BOSS CHICK
Disclaimer Copyright 2013 by Kathleen Johnson All Rights Reserved Published by Quist Media The information contained in this publication and all associated information without limitations to brand associated
More informationThe Problem of Evil and Pain 3. The Explanation of Leibniz: The Best of All Possible Worlds
The Problem of Evil and Pain 3. The Explanation of Leibniz: The Best of All Possible Worlds Leon Bonnat Job 1880 The Problem of Evil and Pain 1: Introduction to the Problem of Evil and Pain 2: The Explanation
More informationFlatland. Assignment: There are 3 parts to this assignment. Each part will be weighted for your final grade.
Flatland PAP Geometry 3 rd Six-Weeks Project Objective: Explore the use of geometry in literature and in theology. Important Note!! Although the Dover edition subtitles this book A Romance of Many Dimensions,
More informationWhat describes the market? What underpins the structure
40 What describes the market? What underpins the structure of financial trading? Do we accept wholesale the intuitions of Brownian motion, the normal distribution, the continuous nature of prices, the
More informationTo my most precious YOU DESERVE TO KNOW WHO YOU REALLY ARE. The Planet Earth Guide, August 2016.
To my most precious YOU DESERVE TO KNOW WHO YOU REALLY ARE The Planet Earth Guide, August 2016. Title The Planet Earth Guide Author Neymon Abundance Editing Irena Jeremic Graphic design Neymon Abundance
More information1 Introduction. Cambridge University Press Epistemic Game Theory: Reasoning and Choice Andrés Perea Excerpt More information
1 Introduction One thing I learned from Pop was to try to think as people around you think. And on that basis, anything s possible. Al Pacino alias Michael Corleone in The Godfather Part II What is this
More informationSOME FUN, THIRTY-FIVE YEARS AGO
Chapter 37 SOME FUN, THIRTY-FIVE YEARS AGO THOMAS C. SCHELLING * Department of Economics and School of Public Affairs, University of Maryland, USA Contents Abstract 1640 Keywords 1640 References 1644 *
More informationDBQ FOCUS: The Scientific Revolution
NAME: DATE: CLASS: DBQ FOCUS: The Scientific Revolution Document-Based Question Format Directions: The following question is based on the accompanying Documents (The documents have been edited for the
More informationrenew: Skills for Leading New and Renewing Progressive Churches Hartford Seminary
renew: Skills for Leading New and Renewing Progressive Churches AM-612: Breaking the Rules Growing a Mainline Church Hartford Seminary Instructor: Rev. Michael Piazza Phone: 888.249.8244 E-mail: mike@progressiverenewal.org
More informationThe following content is provided under a Creative Commons license. Your support
MITOCW Lecture 15 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a
More informationORDINAL GENESIS 1:1/JOHN 1:1 TRIANGLE (Part 1)
ORDINAL GENESIS 1:1/JOHN 1:1 TRIANGLE (Part 1) ORDINAL GENESIS 1:1/JOHN 1:1 TRIANGLE (Part 1) By Leo Tavares Several researchers have pointed out how the STANDARD numerical values of Genesis 1:1/John 1:1
More informationEDIFIED TAKING CARE OF THE MIND
GOAL EDIFIED TAKING CARE OF THE MIND LIFE NIGHT OVERVIEW The goal of Edified is to encourage teens to build up their minds in order to better know themselves and God. KEY CONCEPTS Our intellect is a gift
More informationBase Camp Spirit Building
Base Camp We are going on a journey or an adventure together - Map Journey of discovering how to engage the spiritual realms Discovering the realms within us, around us and the heavenly realms There are
More informationOn the epistemological status of mathematical objects in Plato s philosophical system
On the epistemological status of mathematical objects in Plato s philosophical system Floris T. van Vugt University College Utrecht University, The Netherlands October 22, 2003 Abstract The main question
More informationNew Calculations of Space-Time Dimensions of the Visible Universe
Australian Journal of Basic and Applied Sciences, 5(6): 931-935, 2011 ISSN 1991-8178 New Calculations of Space-Time Dimensions of the Visible Universe 1,2,3 M. Al-Seady, 4 A. Al-Hossain 1 Jazan University
More informationPETER WALKED ON WATER WITH JESUS
PETER WALKED ON WATER WITH JESUS LIFE POINT: People can follow Jesus example and teachings. LEADER BIBLE STUDY PEOPLE LEVEL OF BIBLICAL LEARNING People can take deliberate actions to grow in Christlikeness.
More informationPRESS RELEASE. REACH OUT AND TOUCH THE SOURCE OF ALL LIFE? New Experiential Cinema Genre Allows Viewers to Experience the Divine
PRESS RELEASE Contact: Caroline Cory Telephone: 561.536.6446 Email: iamtheuniversemovie@gmail.com FOR IMMEDIATE RELEASE REACH OUT AND TOUCH THE SOURCE OF ALL LIFE? New Experiential Cinema Genre Allows
More informationA Defense of the Urantia Book s Earth-Moon Evolution Philip Calabrese
A Defense of the Urantia Book s Earth-Moon Evolution Philip Calabrese In Volume 11, Number 3, May/June 2004 and in earlier publications of Innerface International, along side many good examples of the
More informationCurriculum Guide for Pre-Algebra
Unit 1: Variable, Expressions, & Integers 2 Weeks PA: 1, 2, 3, 9 Where did Math originate? Why is Math possible? What should we expect as we use Math? How should we use Math? What is the purpose of using
More informationThe Universe Prismic Lens
The Universe Prismic Lens How does this starglyph assist one? What is its purpose? First I will begin by explaining that a starglyph is a term that I coined in 1998. At that time I realized some of the
More informationMITOCW ocw f08-rec10_300k
MITOCW ocw-18-085-f08-rec10_300k The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free.
More informationThe Intimate Connection Between Physics and Theology HUI-YIING CHANG
The Intimate Connection Between and HUI-YIING CHANG Abstract: Knowledge of physics is an indispensable tool in interpreting the Bible. The fundamental physical principles reflect the nature of God s Kingdom
More informationProbability Foundations for Electrical Engineers Prof. Krishna Jagannathan Department of Electrical Engineering Indian Institute of Technology, Madras
Probability Foundations for Electrical Engineers Prof. Krishna Jagannathan Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 1 Introduction Welcome, this is Probability
More informationUnder the command of algorithms
Under the command of algorithms One of the greatest thinkers of modern mathematics believes that bad math education keeps knowledge away from people and makes them vulnerable to dangerous innovations.
More informationI Found You. Chapter 1. To Begin? Assumptions are peculiar things. Everybody has them, but very rarely does anyone want
Chapter 1 To Begin? Assumptions Assumptions are peculiar things. Everybody has them, but very rarely does anyone want to talk about them. I am not going to pretend that I have no assumptions coming into
More informationMini-Unit #2. Enlightenment
1 Mini-Unit #2 Enlightenment (new ideas) Assessment: Determine which 2 Enlightenment thinkers had the most impact on the rights of people. Defend your choices with specific evidence from the background
More informationWelcome back to WHAP! Monday, January 29, 2018
Welcome back to WHAP! Monday, January 29, 2018 Turn your PERIOD 4 MAPS into the tray! We are studying the Scientific Revolution today. Be ready to take some notes. -> Choose an identity for tomorrow s
More informationGodfrey Harold Hardy (February 7, 1877 December 1, 1947) is noted almost as much for his charm
GODFREY HAROLD HARDY Godfrey Harold Hardy (February 7, 1877 December 1, 1947) is noted almost as much for his charm and colorful eccentricities as for the power of his remarkable mind. He is sort of a
More informationFaculty of Philosophy. Double Degree with Philosophy
Faculty of Philosophy Double Degree with Philosophy 2018-2019 Welcome The Faculty of Philosophy offers highly motivated students the challenge to explore questions beyond the borders of their own discipline
More information6 February Dr. Cindy Ausec
6 February 2014 Dr. Cindy Ausec Recognize his Major Works Comprehend his Major Contributions Course of Positive Philosophy Comprehend the two general goals of this work Define Positivism or Positive Philosophy
More informationAl-Sijistani s and Maimonides s Double Negation Theology Explained by Constructive Logic
International Mathematical Forum, Vol. 10, 2015, no. 12, 587-593 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.5652 Al-Sijistani s and Maimonides s Double Negation Theology Explained
More informationIn Alexandria mathematicians first began to develop algebra independent from geometry.
The Rise of Algebra In response to social unrest caused by the Roman occupation of Greek territories, the ancient Greek mathematical tradition consolidated in Egypt, home of the Library of Alexandria.
More informationBlaise Pascal
Blaise Pascal 1623-1662 Blaise Pascal background and early life Born 1623, Clermont-Ferrand, France Mother died when he was 3 Father was a senior government administrator, which meant he was a minor member
More informationABSOLUTISM. The absolutist believes mathematics is:
FALLIBILISM ABSOLUTISM The absolutist believes mathematics is: universal objective certain discovered by mathematicians through intuition established by proof after discovery. Most mathematicians share
More informationAbsolutism. The absolutist believes mathematics is:
Fallibilism Absolutism The absolutist believes mathematics is: universal objective certain discovered by mathematicians through intuition established by proof after discovery. Most mathematicians share
More informationYou are Not a Beautiful and Unique Snowflake
Devin Howard You are Not a Beautiful and Unique Snowflake My project began last summer while at Shad Valley Calgary, a summer enrichment program for grades 11-12. It was there that I heard the phrase emergence
More informationProbability Distributions TEACHER NOTES MATH NSPIRED
Math Objectives Students will compare the distribution of a discrete sample space to distributions of randomly selected outcomes from that sample space. Students will identify the structure that emerges
More informationThoughts, Things, and Theories
Thoughts, Things, and Theories Abstract: We to critique the following question: can we have reasonable certainty that the terms in speculative or empirical theories correspond meaningfully to things in
More informationIntroduction to Statistical Hypothesis Testing Prof. Arun K Tangirala Department of Chemical Engineering Indian Institute of Technology, Madras
Introduction to Statistical Hypothesis Testing Prof. Arun K Tangirala Department of Chemical Engineering Indian Institute of Technology, Madras Lecture 09 Basics of Hypothesis Testing Hello friends, welcome
More informationUNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION. Address by Mr Federico Mayor
DG/95/9 Original: English/French UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION Address by Mr Federico Mayor Director-General of the United Nations Educational, Scientific and Cultural
More information9 Knowledge-Based Systems
9 Knowledge-Based Systems Throughout this book, we have insisted that intelligent behavior in people is often conditioned by knowledge. A person will say a certain something about the movie 2001 because
More informationjustified the use of motion in geometry, something that Aristotle would not have accepted, because he
Isaac Barrow English mathematician and divine Isaac Barrow (October, 1630 May 4, 1677), one of the most prominent 17 th century men of science, was a pioneer in the development of differential calculus.
More informationPrentice Hall World Geography: Building A Global Perspective 2003 Correlated to: Colorado Model Content Standards for Geography (Grade 9-12)
Prentice Hall World Geography: Building A Global Perspective 2003 : Colorado Model Content Standards for Geography (Grade 9-12) STANDARD 1: STUDENTS KNOW HOW TO USE AND CONSTRUCT MAPS, GLOBES, AND OTHER
More informationTHE OFFICIAL NEWSLETTER OF NARUVI HOSPITALS. Naruvi Print September 2018 Naruvi Hospitals all rights reserved.
THE OFFICIAL NEWSLETTER OF NARUVI HOSPITALS The whole difference between construction and creation is exactly this: that a thing constructed can only be loved after it is constructed; but a thing created
More informationMathematics as we know it has been created and used by
0465037704-01.qxd 8/23/00 9:52 AM Page 1 Introduction: Why Cognitive Science Matters to Mathematics Mathematics as we know it has been created and used by human beings: mathematicians, physicists, computer
More informationGrade 7 Math Connects Suggested Course Outline for Schooling at Home 132 lessons
Grade 7 Math Connects Suggested Course Outline for Schooling at Home 132 lessons I. Introduction: (1 day) Look at p. 1 in the textbook with your child and learn how to use the math book effectively. DO:
More informationNeurophilosophy and free will VI
Neurophilosophy and free will VI Introductory remarks Neurophilosophy is a programme that has been intensively studied for the last few decades. It strives towards a unified mind-brain theory in which
More informationSPEECH. Over the past year I have travelled to 16 Member States. I have learned a lot, and seen at first-hand how much nature means to people.
SPEECH Ladies and Gentlemen, It is a great pleasure to welcome you here to the Square. The eyes of Europe are upon us, as we consider its most vital resource its nature. I am sure we will all be doing
More informationFallacies of the Warren Commission Solution
Fallacies of the Warren Commission Solution by Thomas Purvis from his unpublished work, There Is No Magic (published with special permission) Altered Evidence By utilizing the services of a Registered
More informationMedia and Lost History. Kanchan Luthra Assistant Prof. Ghanshyamdas Saraf College of Arts & Commerce, Mumbai
Media and Lost History Kanchan Luthra Assistant Prof. Ghanshyamdas Saraf College of Arts & Commerce, Mumbai kanchan.luthra@sarafcollege.org Abstract: History has actually become history. The society is
More information=EQUALS= Center for. A Club of Investigation and Discovery. Published by: autosocratic PRESS Copyright 2011 Michael Lee Round
1 2 =EQUALS= A Club of Investigation and Discovery Published by: autosocratic PRESS www.rationalsys.com Copyright 2011 Michael Lee Round All rights reserved. No part of this book may be reproduced or utilized
More informationAhimsa Center K-12 Teacher Institute Lesson
Title: Map of Gandhian Principles Lesson By: Mary Schriner Cleveland School, Oakland Unified School District Oakland, California Ahimsa Center K-12 Teacher Institute Lesson Grade Level/ Subject Areas:
More informationThe King Ascends Lesson Aim: To honor Jesus final words and to look forward to His return.
Leader s Guide: Ages 12-14 Kings & Kingdoms Part 1: The Life of Jesus Unit 4, Lesson 22 THE WORSHIP Who God Is: The King Who Rose THE WORD What He Has Done: Jesus ascended into heaven. Scripture Focus:
More informationGFS HISTORY Medium Term Plan Year 7 SPRING 1 Fertile question: When did Greenwich grow during the 19 th century?
GFS HISTORY Medium Term Plan Year 7 SPRING 1 Fertile question: When did Greenwich grow during the 19 th century? Second order concepts: Cause and consequence Change and continuity Substantive concepts:
More informationWhat is Dowsing? Who Can Dowse? How Can I Tell If I Am A Dowser? Which Device Shall I Start With?
All about Dowsing! What is Dowsing? Remember when your grandfather "witched" for water with a forked stick? That is dowsing! The basic dowsing tools have evolved into L-rods, pendulums, Y-rods, bobbers
More informationA Stroke of Genius: Striving for Greatness in All You Do
About the author: A Stroke of Genius: Striving for Greatness in All You Do by R. W. Hamming Dr. Richard Hamming is best known for the Hamming code, Hamming distance and the Hamming spectral window along
More informationThe Book of Nathan the Prophet Volume II
The Book of Nathan the Prophet Volume II This book is here now for many reasons. This code has been hidden and destroyed. I have made parts of this book obtainable through multiple forms of media. They
More informationJenna Cavelle Judith Lee Stronach Baccalaureate Prize Letter Home March-April
Jenna Cavelle Judith Lee Stronach Baccalaureate Prize Letter Home March-April 2013 1 Dear Stronach Committee & Supporters: March and April have brought many challenging though not insuperable tasks, which
More informationStructure and essence: The keys to integrating spirituality and science
Structure and essence: The keys to integrating spirituality and science Copyright c 2001 Paul P. Budnik Jr., All rights reserved Our technical capabilities are increasing at an enormous and unprecedented
More information6.080 / Great Ideas in Theoretical Computer Science Spring 2008
MIT OpenCourseWare http://ocw.mit.edu 6.080 / 6.089 Great Ideas in Theoretical Computer Science Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationTheory of knowledge prescribed titles
Theory of knowledge prescribed titles November 2009 and May 2010 Your theory of knowledge essay for examination must be submitted to your teacher for authentication. It must be written on one of the ten
More informationHow do the humanities anchor democracy?
How do the humanities anchor democracy? We may live in a STEM-focused world, but the humanities remain crucial in helping us understand one another. And that is key to sustaining our democracy, writes
More informationJonathan WENG. Exchange Programs:
Jonathan WENG JC: Raffles Institution Exchange Programs: -2012: Paris -2014: Rambouillet -2015: Lycée Janson de Sailly Tertiary Education: Considers a Scientific Preparatory Class at Lycée Henri IV (Paris)
More informationWhat Is Awana? The Role of the Game Director
What Is Awana? Welcome to one of the most exciting and rewarding leadership roles you can fill! Children and youth are the richest mission field in the world. Did you know that the probability of a person
More informationSpinoza and the Axiomatic Method. Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to
Haruyama 1 Justin Haruyama Bryan Smith HON 213 17 April 2008 Spinoza and the Axiomatic Method Ever since Euclid first laid out his geometry in the Elements, his axiomatic approach to geometry has been
More informationA MATHEMATICAL CHALLENGE
The date: December 12 The year: 1855 A MATHEMATICAL CHALLENGE The words of the Lord are pure words, as silver tried in a furnace of earth, purified seven times Thou shalt keep them, O Lord; thou shalt
More informationKey Stage: 1 Year Groups: Lesson Title of lesson Main points of content / Bible references for Christianity units
ASU Title: A Celebration of Christian Education Key Stage: 1 Year Groups: Length of unit: 6 lessons Lesson Title of lesson Main points of content / Bible references for Christianity units 1 INTRODUCTORY
More informationContent Area Variations of Academic Language
Academic Expressions for Interpreting in Language Arts 1. It really means because 2. The is a metaphor for 3. It wasn t literal; that s the author s way of describing how 4. The author was trying to teach
More informationThe Fallacy in Intelligent Design
The Fallacy in Intelligent Design by Lynn Andrew We experience what God has designed, but we do not know how he did it. The fallacy is that the meaning of intelligent design depends on our own experience.
More informationChildhood Biography Euler was born in Basel to Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter. He had two yo
Childhood Biography Euler was born in Basel to Paul Euler, a pastor of the Reformed Church, and Marguerite Brucker, a pastor's daughter. He had two younger sisters named Anna Maria and Maria Magdalena.
More informationBrabourne Church of England Primary School Religious Education Policy Statement July 2017
Brabourne Church of England Primary School Religious Education Policy Statement July 2017 'We show love and compassion for others by truly helping them, and not merely talking about it, John 3:18 Religious
More informationThe Nature of God. By David Butterworth 2/18/2018 Content is available under CC0
The Nature of God By David Butterworth 2/18/2018 Content is available under CC0 1 Overview The amorphous nature of the canvas the universe is projected upon points to a creator who's nature can be partially
More informationTouch the Future Knowledge & Insight by David Bohm, PhD.
The following was adapted from an informal talk given by professor Bohm in Santa Monica, California in 1981. Also included are several brief passages from two additional sources: Thought As A System -
More informationWHEN EVERYTHING CHANGES, CHANGE EVERYTHING: WORKBOOK AND STUDY GUIDE BY NEALE DONALD WALSCH
Read Online and Download Ebook WHEN EVERYTHING CHANGES, CHANGE EVERYTHING: WORKBOOK AND STUDY GUIDE BY NEALE DONALD WALSCH DOWNLOAD EBOOK : WHEN EVERYTHING CHANGES, CHANGE EVERYTHING: Click link bellow
More informationJerusalem in 2050 will be the capital of peace.
306947Narrative Text COMmon human UNITY Peace is a gift of men for themselves ELIE WIESEL One day, we were speaking with my eternal and illustrious friends about humanity I told them: - Jerusalem in 2050
More informationCultivating Your Light Body
Cultivating Your Light Body A Handbook Living in the Center of the Circle of the Heart Dr. Patrick MacManaway MB.ChB. Cultivating Your Light Body A Handbook Living in the Center of the Circle of the Heart
More informationMeaning of the Paradox
Meaning of the Paradox Part 1 of 2 Franklin Merrell-Wolff March 22, 1971 I propose at this time to take up a subject which may prove to be of profound interest, namely, what is the significance of the
More informationAn E-book by Lisa Michaels
An E-book by Lisa Michaels The Law of Attraction You Are A Magnet To every action there is an equal and opposite reaction. In universal terms, the law of attraction says like attracts like. What that means
More informationCogito Ergo Sum. "I think, therefore I am." René Descartes 1596 to Born La Haye (now Descartes),Touraine, France
Cogito Ergo Sum. "I think, René Descartes 1596 to 1650 therefore I am." Born La Haye (now Descartes),Touraine, France Abu Arrayhan Muhammad ibn Ahmad al-biruni 973-1048 Once a sage asked why scholars always
More informationAn Update on Resourcing Ministerial Education, and Increases in Vocations and Lay Ministries
GS Misc 1190 An Update on Resourcing Ministerial Education, and Increases in Vocations and Lay Ministries Key Points The number of ordinands entering training grew by 14% between 2016 and 2017, with a
More informationChapter 3. Truth, Life, Love. What is Truth and how can we approach the Truth?
Chapter 3 Truth, Life, Love What is Truth and how can we approach the Truth? I admit that this is a very difficult subject, very, very difficult. I will try to tell you as well as I can in simple words
More informationIntroduction Questions to Ask in Judging Whether A Really Causes B
1 Introduction We live in an age when the boundaries between science and science fiction are becoming increasingly blurred. It sometimes seems that nothing is too strange to be true. How can we decide
More information