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7-A.2. Organic Chemistry and the Beginning of Biology ..................................... 1927-B. Thermodynamics ............................................................................................. 194

7-B.1. Statistical Mechanics and Thermal Energy ............................................... 1957-B.2. Temperature and Heat.............................................................................. 196

7-C. Electricity and Magnetism ............................................................................... 2007-C.1. Electrostatics ............................................................................................ 2007-C.2. Magnetism ................................................................................................ 2027-C.3. Electromagnetism ..................................................................................... 2047-C.4. Electromagnetic Radiation ........................................................................ 207

7-D. Relativity ......................................................................................................... 2097-D.1. Special Relativity ...................................................................................... 2117-D.2. General Relativity ..................................................................................... 212

7-E. Quantum Mechanics and Atomic Physics ....................................................... 2137-E.1. Atomic Structure ....................................................................................... 2157-E.2. The Uncertainty Principle and Still More Atomic Physics ......................... 216

7-F. Nuclear Physics ............................................................................................... 2197-F.1. Isotopes .................................................................................................... 2197-F.2. High-Energy Physics ................................................................................ 222

7-G. Odds and Ends ............................................................................................... 2227-G.1. Radiation Damage in Biological Systems ................................................. 2237-G.2. Our Changing Universe ............................................................................ 2247-G.3. The Changing Earth ................................................................................. 2287-G.4. Biology: the Study of Life .......................................................................... 2297-G.5. It All Hangs Together ............................................................................... 231

7-H. Back to Natural Philosophy ............................................................................. 2317-H.1. Revolutions ............................................................................................... 2327-H.2. Science Has Limits ................................................................................... 234

7-I. Summary: Modeling Physical Science ............................................................. 234EXERCISES: (Chapter 7) Natural Science Overview ......................................... 237

CHAPTER 8 SCIENCE, TECHNOLOGY, AND SOCIETY ..................................... 239

Vocabulary ........................................................................................................... 239Expectations ........................................................................................................ 2418-A . The Nature of Physical Science Revisited ..................................................... 241

8-A.1. Philosophical Foundations and Methodology ........................................... 241


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8-A.2. Typical Difficulties ..................................................................................... 2448-B. Technology and Economics ............................................................................ 248

8-B.1. An Economic Framework .......................................................................... 2488-B.2. Education, the Ultimate Economy ............................................................. 251

8-C. Case Studies: Science and Society ................................................................ 2528-C.1. NMR (MRI) and Medical Technology ....................................................... 2528-C.2. Medical Pharmacology ............................................................................. 2538-C.3. Environmental Studies ............................................................................. 2548-C.4. Nuclear Energy ......................................................................................... 2568-C.5. Science and Society Exercises ................................................................ 260

8-D. Science Literacy Revisited .............................................................................. 2608-D.1. A General Review .................................................................................... 2608-D.2. Learning a New Topic .............................................................................. 2618-D.3. Science is no big deal; its only bunch of theories! ................................... 264

8-E. Summary ......................................................................................................... 265EXERCISES: (Chapter 8) Science Technology and Society .............................. 267


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i Version 4: Last updated: 1/18/2013, copyright Pearson, for personal use only, not for reproduction.

PrefaceThis approach to science education is based on the assumption that different students have a

wide variety of talents, needs, and interests. Students in non-technical areas need a more basicunderstanding of science than do science and engineering majors. It is not crucial for such students to

learn how to dophysics, but it is necessary for them to learn how physics works. The math and physicscoverage in this course emphasizes language, philosophical issues and the big ideas in science. Weattempt to expand the students science vocabulary and knowledge of fundamental concepts, and todevelop an ability to read equations. One important goal is to teach the student how to acquire new skillsthat involve technical understanding.

An understanding of the scientific method is stressed. The student will find a significantemphasis on cultural, philosophical, and social issues that relate to the process of modern science. Thismaterial does not require the student to learn physics in breadth and depth; it does not emphasize solvingphysics problems. The task is to become acquainted with some widely useful basic concepts and to dosome physics, while emphasizing an understanding of how physics evolved, how it works, what it doesreliably and precisely, and finally what it cannot do. The student needs to learn how to distinguish areasof knowledge that are well understood from those that are not.

I hope that the student will acquire a concrete sense that physical science plays a real role inevery day life; and that an appreciation will be acquired for the idea that the student can understand thebasic workings of the universe. The student is expected to discover why scientists and engineers findthese topics to be stimulating and exciting. Most of all, students may recognize that science need not beintimidating, that sometimes it can even be fun and friendly in spite of the fact that it is demanding.

Instructors will find that there is room for variation in the emphasis placed on different topics.This text is meant to be compatible with other books having technical, philosophical, historical, social, orpolitical themes.

The need for science literacy in the worlds citizenry will play a crucial role in the coming crisesof population growth, resource renewal, energy sources, and pollution control. No one, not even an

exceptional scientist, can stay abreast of developments in the variety of technical fields we face as the 21stcentury continues. But we can all share an understanding of the basic ideas about how science works.Scientists and non-scientists can learn to communicate with each other, and all can contribute to thecreation of a better global community. I hope this book will contribute to that end.

John W. White

Summer 2004

Since John White first wrote this Preface, the need for science literacy has only grown. One of thechallenges facing University students is access to the equivalent of a art appreciation course for sciencewhere the emphasis is on developing the skills required to read and evaluate science as opposed to doingscience. We have coined the phrase science spectator to capture the essence of this activity. Too manytextbooks focus on the doing of science at an amateur level (versus professional level science). This is

important and is the next step after this textbook.

Michael Dennin

John W. White

Summer 2011


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Acknowledgments

The authors appreciate the support and encouragement of Eileen Vergino leader of the science

education program at the Lawrence Livermore National Laboratory (LLNL), Brian Holmes of the PhysicsDepartment at San Jose State University (SJSU), and most particularly Jean Beard of the science educationprogram at SJSU. Thanks also to John Fletcher, Willy Moss, and Doug Clarke of LLNL, Bill Davies ofCalifornia High School, and Ken Meidl, Richard Anderson, and Mary Roslaniec of Modesto JuniorCollege (MJC). The authors also thank Henry Sobel (UC Irvine) for putting us in contact with each other.Without his connections, this collaboration would not have occurred. Finally, thanks are due to JudyEckart for her excellent work converting a crude manuscript into a textbook, and improving it along theway!\ As is always true, any errors are the responsibility of the authors.

This class began at LLNL in the 1980s. The students taking the course were talented technicalwriting editors supporting research and development done by lab engineers and scientists. Since then,the course has been taught several times at LLNL, SJSU, MJC and UC Irvine as a developing project. A

considerable thanks is due the many students who participated in these classes. In addition, there weremany faculty and staff members at all of these institutions who provided valuable constructive criticism.

Any scientific work or educational text is influenced by and owes a significant debt to previouswork. This book is no different. A wide variety of physical science texts have been influential includingPhysics for Poets by March, Conceptual Physics by Hewitt, Lectures on Physics by Feynman, andScience Mattersby Hazen and Trefil, plus many more standard books (such as the classic physics textby Resnick and Halliday). A debt is also due Holton for his Introduction to Concepts and Theories inPhysical Scienceas well as his writings on historical and philosophical accounts of science. There aremany other publications in this area that have been useful for this book, particularly The Structure ofScientific Revolutionsby Kuhn.

Instructors and students will observe that a whole new approach to physics instruction has beenopened up with this text, and it offers significant advantages. They will also note that the book is in anembryonic state of development that has significant disadvantages. You are invited to communicate yourconstructive criticisms and recommendations that may lead to the improvement of future editions.


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Dedication

For students and teachers everywhere who have struggled to learn and/or teach physical scienceand its significance. We hope you will find this text user friendly. May it help to illuminate one ofmankinds most impressive, most exciting, and most useful accomplishments.

Foreword

This approach to science education is long overdue.

Jean Beard, Leader

Science Education Program

San Jose State UniversitySan Jose, California

About the Authors

Michael Dennin is a PhD physicist who is currently a professor at the University of California,Irvine, in the Department of Physics and Astronomy. His research focuses on complex systems ranging

from foams to biological structures. He is especially interested in the mechanical response of thesesystems and emergent behavior that is due to the interactions in the system. A classic question asked inhis research is whether or not foam is a solid or liquid! He has been involved in teaching at all levels fromcourses for non-scientists, to introductory physics for biologists, to upper-division quantum mechanics, tograduate physics courses. His interest in teaching has been recognized with a number of awards,including the Cottrell Scholar Award from the Research Corporation and the UC Irvine Academic SenateDistinguished Faculty Award for Teaching (the highest teaching award at UC Irvine). One of his currentinterests is maximizing the impact of online technologies in teaching. He has been seen in popular sciencetelevision shows, such as Star-Wars Tech, Spiderman-Tech, and Ancient Aliens. One of his mainhobbies is coaching his kids in soccer and softball an experience which motivates much of his teachingphilosophy and his excitement with creating science spectators!

John White is a retired PhD physicist who served on the technical staff of the Lawrence LivermoreNational Laboratory for over thirty-five years. During that time, he worked on a broad range of physical

science topics at LLNL. Most of these projects supported national security programs. He also has

extensive experience in a wide variety of science education activities. He served on the laboratorys

continuing education committee for several years, and he served as a mentor for many ne lab employees.

As a hobby, he pursues applications of physics to sports, particularly baseball and softball.


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IntroductionJust as college engineering and science majors take courses in art or music appreciation,

this book offers a science appreciation option to liberal arts majors and students in other non-technical fields. We hope it provides a meaningful alternative to traditional physics courses

offered to these students. Our view is that the world can loosely be divided into professionals,amateurs, and spectators. The traditional physics courses offered to students are really aimed atamateur scientists. An excellent goal, but most people are best suited to be spectators. Hopefully,they will be well trained and critical spectators! But, too many individuals have found traditionalscience courses frustrating, preventing them from being the type of engaged spectator of sciencethat society really needs. This book is addressed primarily to those students. The reader shouldbe forewarned that many topics are repeated; occasionally this is done for emphasis because thetopic is important, sometimes to develop the topic further, and sometimes to place the topic in adifferent context.

The first two chapters present a variety of ways of looking at science (particularly theidea of science literacy). Another central theme here is the scientific process and its philosophicalbasis. A historical perspective is given of the impact of science on culture and the impact ofculture on science. Physical concepts and models are discussed, as is the all-important and oftenmisunderstood scientific community.

Chapter 3 and 4 emphasize the quantitative nature of science, and the key role ofnumbers in science. This is important in order to understand ideas related to the accuracy,precision, and the reliability of science and technology. This chapter may appear to be out oforder to some teachers, but it is placed early because mathematics and numbers are thefundamental language of science. One would not consider going to a foreign country withoutsome access to the language a phrase book or online translator! This chapter provides thestudents with the critical mathematics phrase book. For many students (and teachers), this will bevery different than the traditional view of mathematics, where it is being taught to be usedinstead of our focus on teaching how to read mathematics.

The next three chapters focus on minimal science content that every spectator needs.Consider it the basic rule book for the sport of science! Chapter 5 covers the birth of modernscience via the study of motion. This is the most traditional chapter in the book, and it providesan elementary case study example of how physics is done with a focus on how science makesquantitative predictions. Chapter 6 focuses on the most fundamental concepts in science thatprovide the necessary vocabulary for a science spectator and our broadly applicable across manydisciplines. Chapter 7 covers a breadth of science topics: chemistry, biology, earth science,astronomy, and applied science (engineering). The purpose is not to provide expertise in theseareas, but to provide students with a window into the exciting world of science. From thisexperience, the hope is that they will continue their career as spectators, and explore some ofthese topics in more detail. Perhaps, they might elect to move on to amateur status! Chapters 9and 10, which are optional, cover specific mathematical and scientific topics, respectively, at a

more sophisticated level.Chapter 8 explores the interaction of science and society. It is obvious that every citizen

of the world needs to be aware of their effect, technology in everyday affairs. As a practicalmatter, everyone needs to learn new things and acquire new skills as they go through life, andmost of these experiences involve some science and technology.

A summary of essential concepts is provided at the end of the book; students might wantto read this overview of core ideas and goals as they begin the course and then revisit these pagesas they progress through the course.


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Chapter 1: Introduction

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CHAPTER 1 INTRODUCTION TO SCIENCE LITERACY

Why be an informed science spectator.

Science and technology play a major role in modern everyday life. These technical topics interact

heavily with our economy, medicine, entertainment, politics, arts, and religion. Every individual

needs to be conversant with the general workings of science; most of all, everyone needs to be

able to learn about the technical topics that touch our lives. In an analogy to sports, every

individual is capable of, and needs to become, an active and informed science spectator to be a

truly engaged citizen of the 21st

century.

Expectations

After completing this chapter, the successful student will understand the overall goals ofthe textbook and the larger context in which this textbook is placed. This will include

understanding the general historical and social context of the modern process of science, anddeveloping a definition of science literacy. The successful student will develop proficiency withthe following concepts:

1) Science is fundamentally about quantitative predictions.

2) Science is a collective activity based on common paradigms.

3) Science has its roots in most human cultures and is the result of interactions betweenthose cultures.

4) Science is an extremely powerful activity in the areas for which it applies.


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1-A. The Role and Meaning of Science Literacy

Science literacy enables students whose talents and interests lie in other areas to gain anappreciation of topics that will touch and enrich their lives in many ways. Science literacyenables us to make informed decisions when faced with a new technology or scientific report,and it implies the ability to acquire at least a modest competency that will help us maximize ourexperience of any new technology. Finally, it provides focus and a strong foundation whenscientific questions intersect political, social, and economic issues.

On the personal level, the need for science literacy is most apparent in the context of medicalstudies and general questions of health. Our knowledge of the human physiology and biology ingeneral is one of the most rapidly changing areas of scientific study. For example, as late as the1980s, medical recommendations regarding cholesterol focused only on your total cholesterollevel. Then, it was reported that there was good and bad cholesterol. Because your goodcholesterol was beneficial, it was bad for it to be too low! Suddenly, everything was more complexand people where taking supplements to increase good cholesterol. As of the writing of thistextbook, there are studies looking at how high your good cholesterol should really be, andhow it help you.

Given this apparent constant change in our understanding of the health benefits and risks ofcholesterol, how do you, an average citizen, respond to each new medical result? Do you needto go back to medical school? Do you blindly trust your doctor and every new report? How longshould something be held to be true before you trust it?

As an example of a social, political, and economic issue, one of the biggest questions of the late20th and early 21st century is climate change. This is an incredibly complicated issue involving awide range of science: measurement of temperatures, CO2 levels in the ocean, solar activity,differences between average behavior and fluctuations, just to name a few. One would hope thatscience could provide a clear answer. But, anyone paying attention to the mainstream mediaduring this period is struck by how there appears to be two sides to this issue. Even in the face

of an apparent scientific consensus that climate change is occurring and is at least in part theresult of human activity, there are repeated statements by highly prominent scientists thatclimate change as a result of human activity is not happening. How are we to interpret thisapparent conflict? Are these apparent two sides a construction of the media, or is the sciencereally uncertain? Is there no way to make an informed decision, so do we trust the side that bestmatches our own views, or are there tools and skills we can develop to sort through thiscomplicated problem?

The claim of this textbook is that the answer to the above situations, and reports in general, is thatyou do not need an advanced science degree to make sense of these situations but you do needto develop some basic skills of science literacy. The development of these skills is sufficientlydifferent from the skills of doing science that it takes a specific type of training to develop theseskills, and that is the fundamental goal of this textbook. By the time you finish this book, youwill hopefully be able to answer two questions in relation to any scientific claim or report:

1) Is the question being asked actually a scientific question, and if so, was it addressedusing the scientific process?

2) What level of reliability can I assign to the claims or report?


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Having answered these two questions, you can then determine what, if any, impact the reportwill have on decisions you face regarding practical issues like, what foods should I eat, or howmuch should I worry about my carbon footprint?

A skeptic might argue that you cannot understand science and judge scientific claims withoutdoing a significant amount of science, i.e. taking real science courses. And yet, many science

students take courses in music appreciation, but few ever play an instrument or compose anopera as a result of these courses. (They may do it with other training, but that is a differentissue.) Many engineering students take courses in art appreciation, but they are not expected toturn out fine sculptures as homework. In other words, such courses do not emphasize thatstudents do the topic; rather, students learn about the topic and what the experts do. The successfulstudent leaves such a course with a reasonable ability to judge art or music, and if the course istruly successful, they become a fan of art and music, with a lifelong interest in their new foundpassion!

This book brings the same idea and experience to science with two main goals. The first goal is toprovide you, the reader, with a sense of how and why scientists do what they do. This mightloosely be called the science appreciation part. The second, and more important goal, is to provide

you, the reader, with the ability to judge scientific claims that you encounter in your daily life.What does it mean when a test has a 10% chance of being a false positive? How can yourecognize when you have enough information to make a decision or when you really need toseek expert help with the decision! This is what we mean in the textbook by a critical sciencespectator. Hopefully, this book will serve to excite you enough about science, or at least specificaspects, for you to follow up with either conceptual science books or to probe specific topics inmore detail. Perhaps you will develop such a passion for science from this experience; you mighteven major or minor in a science!

Science Literacy

scientificp

rincipless

cie

ntifi

cprocess

Figure: A schematic representation of the three key elements of science literacy thetools needed to evaluate scientific claims. These are: understand the scientificprocess, understanding the scientific language (mathematics) and understanding keyscientific content.


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The approach in this book focuses on three key elements of scientific literacy. One can think of

them as the three legs of a stool you are trying to stand on! These elements are: understanding the

process of science; understanding the role of mathematics; and having a familiarity with what we

will call the fundamental principles of science. We start with an in depth look at the process of

science both as practiced by individuals (or small groups) and the larger community (Chapters 1

and 2). This sets the stage for understanding the role of mathematics in the sciences (Chapters 3

and 4) and fundamental principles of science (Chapters 5 7). Finally, Chapter 8 puts it all

together.

It is worth briefly commenting on what this book is not. This is not a philosophy or history ofscience book, though it will touch on aspects of these topics. It will not provide you with detailedcoverage of scientific topics. Because the successful student needs to develop a broad vocabularyand awareness of many scientific concepts while striving for science literacy, this textbookincludes a review of many topics. But, a fully comprehensive vocabulary and conceptualfamiliarity are not possible, even for a professional scientist.

Though we have stated that this is not a philosophy of science book, before going any further, we

do need a definition of science to use throughout the book. If we were to focus on the shortest

possible definition of modern science it would be: a highly reliable process for making

quantitative predictions with a known level of accuracy. It is the interaction between the three

legs of the stool process, mathematics, and content that makes science such a reliable

predictive tool. Therefore, we will use this definition as our yardstick for evaluating scientific

claims. Essentially, the question we will is ask is whether or not a given claim effectively uses the

three legs of our stool to achieve predictive power. By following this well-defined program for

evaluating scientific claims, the reader will then become an active spectator of science, without

the stereotypical fear of science so often encountered in contemporary society.

After all, watching a professional athlete perform does not intimidate us into forgoing our ownparticipation in the sport, and more importantly from forgoing our pleasure of being a spectator

of sport! We may still play golf or shoot hoops for pleasure, and we certainly will watch,comment on, and discuss in endless detail, professional sports of all types. We may notappreciate art as well as Rubens, but we can appreciate it at a meaningful level. Likewise, weshould be willing to become scientifically literate even though our level of proficiency will notmatch that of the professionals. We should develop a skill level that allows us to appreciate theimpact of research being done in science and technologyand this level of proficiency is easier toachieve than many may believe.

1-B. Key Elements of Modern Science

We have defined science as the ability to reliably make quantitative predictions with a knownlevel of accuracy. Given that predictive power has been a goal of humanity essentially for our

entire history, what are the elements of modern science that makes it such a powerful approachto quantitative prediction? In this section, we provide a brief highlight of the relevant elements ofmodern science. We will follow this with the briefest of historical overviews of four areas ofhuman exploration in order to provide a context for how modern science uses all of theseelements. We will close this chapter with a discussion of how technology and science interact, asthis is an important distinction when evaluating science. Finally, in Chapter 2, we provide a morein depth discussion of the central elements of modern science.

Modern science has been divided into topics.


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In your early years in school, you take science as a course. But, as you progress to high schooland beyond, you rapidly become exposed to the divisions in science. First, we experience thebroad division into biology, chemistry, and physics. As we progress, the list only grows:astronomy, biological physics, biochemistry, geology, earth science, organic chemistry,microbiology, geophysics, nanophysics, etc. What is surprising is how some of the topics are arefinement of a broader subject, such as the division of chemistry into organic and inorganic

chemistry. Other topics are the combination of previously distinct topics, such as the bringingtogether of physics and chemistry in earth science.

Just as our experience with science starts with generic science classes, the separate divisions thatexist today did not always exist. Instead, we had the more generic idea of natural philosophy, ornatural science. However, as our understanding of the world increased, we developed morespecialized tools for studying the wide-range of natural phenomenon. It is this specialization oftools and techniques that was a fundamental driving force behind the development of separatefields. Likewise, the continued merging and division of fields is generally driven by the tools andconcepts needed as new areas of exploration are undertaken. For example, the study of biologyrequires an understanding of the chemical basis of life, and chemistry depends on the physics ofatoms and their interactions with each other. This has lead to fields with names like biochemistry

and biological physics.

It is wise to assume that separating branches of knowledge is somewhat artificial, particularly inscience. Also, as our quantitative tools continue to expand and improve, we will see a broadeningof what we consider to be science. However, in this book, we give more attention to physics than

to the other sciences. For our purposes, physics is the study of the fundamental properties of

material objects, their internal structure, and the interactions (such as forces) between different

material objects. Four of the reasons we focus on physics are:

Historical: Physics was the first of the sciences (except, perhaps,

for astronomy) to clearly define itself within the broader subject of

natural philosophy.

Mathematical: Physics was the first of the sciences to develop

quantitative means for conducting its work and expressing its results

and provides an excellent forum for demonstrating how mathematics is

used in science.

Operational: Physics was the discipline that matured the scientific method of

comparing theory and experiment.

Fundamental: Physics provides an essential foundation for understanding other

sciences. Branches of physics (quantum mechanics, statistical

mechanics, etc.) provide the basis for chemistry. Likewise, physics and

chemistry provide the basis for biology.

But, perhaps the most important is the reason illustrated by the figure of the science spectrum.

Even though physics is stereotyped as the hardest science to master, this is generally connected

to the fact that it is the most quantitative. What people really struggle with is learning the

mathematics required. In reality, physics tends to study the conceptually simplest questions in

terms of the amount of stuff involved and their interactions. For example, physics commonly

studies the interactions of only two particles! In contrast, the study of cellular systems in biology

or the interactions between people in economics or politics is highly complex and extremely


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difficult to study quantitatively. Because our focus is the quantitative predictions science is

capable of, we will focus more time on physics, then chemistry, then biology, etc., following the

level of quantitative power each of these disciplines have. However, it is important to keep in

mind that our quantitative ability is constantly improving, and the boundaries in this chart are

always changing.

Scientific Spectrum

1 2 10 100 1000 106 1023

VERY QUANTITATIVE LEASTQUANTITATIVE

Physics ChemistryNano-science

Physics(again)

Biology

Social sciences

MOST COMPLICATEDLEASTCOMPLICATED LEAST COMPLICATED

VERY QUANTITATIVE

amount of stuff:

(psychology, economics, politics, etc.)

Figure: A chart relating the number of objects involved in the problem (from

single particles to the typical number of particles in matter) and thecorresponding difficulty of the problem. Notice the surprising feature that the

most complicated problem are the hardest to be quantitative about, and tend toinvolve 10s to millions of particles exactly the regime of social sciences!

Science is a human activity (frequently spiritual).

Because science is a human activity, it is worth considering the motivations of scientists. In

generally, scientists are driven by a search for truth (or beauty) that is often motivated by

curiosity. Of course, the motivations of individual scientists are as many and varied as the

motivations of most people, but curiosity seems to play a special role. The stereotype of the

unfeeling, logical scientist (think Spock and Data from the Star Trek series) is surprisingly untrue.

The best scientists are generally very passionate about their studies and anyone witnesses a

scientific conference for the first time will probably be amazed at the level of emotion and

excitement.

The pursuit of science is based on a particular philosophical stance.

It is not possible in this textbook to explore the philosophy of science in detail, and there is a lot

of room for argument and discussion about what science really is and how scientists actually

pursue science. But, despite these caveats, there is a general philosophical attitude that underlies

the practice of modern science: the universe is regular, knowable, andpredictable. Keep in mind that

the central element of our definition of science is the ability to make quantitative predictions. This

would not even be possible if the universe was not regular, knowable, and predictable! We will


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expand briefly on these assumptions regarding the universe here, and then we will explore their

implications and how they are put into practice in Chapter 2.

a. The laws that govern the behavior of things in the universe are discoverable (via the senses)

in a quantitatively measurable way. Einstein said it this way: the most incomprehensible

thing about the Universe is that it is comprehensible. It is the ability to put numbers onmeasurements (being quantitative) that allows for the second aspect of discoveries; they

are repeatable.

The discoveries of science are repeatable both by the person doing the experiments and by

others. If an experimenter repeats the same experiment in the same way, the result should

not change. This is often referred to as reproducible. If someone else does the same

experiment in the same way, the result should be the same. This is often referred to as

replicable. This allows scientists to check their own work and the work of others in a

fashion that leads to organized skepticism (a concept discussed in detail later).

Consider, for example, the following theory proposed by a believer in astrology: the planetMars emits undetectable rays that influence the behavior of people on Earth. This theory

proposes the existence of something that cannot be observed quantitatively (undetectable

rays), and thus it cannot be discovered. There is no way to reproducibly test such a

theory or for other scientists to verify it by replication, and therefore it is not scientific.

Another astrologer might present the theory that Mars influences humans through its

gravitational pull. This, at least, is a theory that can be tested by measurements. It happens

that the force of gravity exerted on your body by Mars is much smaller than the

gravitational force exerted on you by a number of other objects, such as nearby buildings

and cars. So it is likely that such objects will influence you gravitationally much more than

Mars will. This kind of quantitative comparison is at the heart of scientific analysis.

b. The laws of science are uniform: they are the same everywhere in the universe. This means

that different laws do not apply, for example, on the earth and on the moon. In contrast,

many Greek philosophers did not believe that the laws of nature were uniform; their

theories of motion were different for objects on the earth and objects in the heavens. Indeed,

they believed that objects on the earth and objects in the heavens were made of different

substancesthat objects on the earth consisted of combinations of earth, air, fire, and water,

whereas objects in the sky were made of another element, called quintessence. This word is

still used today to denote something extraordinary and special. The story is told of Isaac

Newton observing a falling apple and asking himself whether the moon also felt the pull of

gravity. This demonstrates his insight that the laws of the universe were uniform, so the

same laws should apply to the apple and the moon. It is this assumption about the nature of

reality that allows us to study the far reaches of the universe today.

c. The laws of science are invariant: they do not change in time. That is, the laws we discover

now have always applied in the past, and will always apply in the future. For example,

light from some distant objects may have traveled for billions of years before reaching us.


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But scientists have no trouble interpreting what kinds of atoms emitted that light, because

they are confident that the laws governing the emission of light by atoms have not changed

in billions of years. The idea that the laws of physics are uniform and invariant is a

philosophical position (a matter of belief) that

scientists use. Experience has reinforced this

view many times. Laws that apply on one partof the earth do predict behavior on other parts

of the earth (and on the moon, and on distant

stars, etc.) We also look back in time (fossils,

signals from distant stars, etc.) and we get more

reinforcement that the laws are invariant. Still,

we have not checked the laws of nature in all

places for all times, so these two assumptions

about the universe remain an active area of

enquiry. It is not unreasonable when anomalies

appear to be discovered to ask if they are dueto a violation of the invariance of the laws of

nature in either space or time.

d. The laws of science are simple. Part of

this simplicity rests in the invariance and

uniformity of the laws of science. But an

important aspect of science is the belief that

even complex phenomena have simple

explanations, and that the complexity of the

world arises not from the complexity of the

laws of science, but rather from the interaction

of many simple laws. Einstein, in an

illuminating remark, suggested that a theory

should be made as simple as needed, but no simpler. This is deeply connected with the

use of models and hypotheses in science. Models can take the form of verbal, visual, and

mathematical descriptions of a set of behavior, and their importance is generally tied to their

ability to make successful predictions. When we refer to the laws of science as simple, we

really mean that the models we use to describe natural phenomena are simple. This idea is

facing interesting challenges as scientific ideas are applied to biological and social systems.

It remains an open question as to whether or not these systems can truly be explained in

terms of simple models that exhibit complexity, or if the models themselves must beinherently complex.

e. The laws of science are objective, rather than subjective: the validity of science does not

depend on the voice of authority, that is, who is doing the science. The results of science

should be the same no matter which scientist is studying them. The only recognized

authority is the behavior of nature (particularly in carefully measured experiments). Science

is also objective in the following sense: the laws are believed to have a reality that is

PHILOSOPHICAL ASIDE:

Skepticism is often listed as a key

element of science. But skepticism is a

subtle and challenging practice that

requires a level of maturity to be

efficient. Too much skepticism and we

are never able to trust the results of

others without reproducing them

ourselves an extremely expensive and

nearly impossible task. Too little

skepticism and we believe almost

everything (without questioning) that we

are told by authorities. Too often, this

leads to either believing unreliable

authorities, or faced with a choice

between two apparent authorities, with

no mechanisms between deciding

between them. It is interesting to note

that the general process of growing up

tends to take us from too little skepticism

(children believe most things grown-ups

say), to too much skepticism

(adolescents tend to challenge

everything grown-ups say), to hopefully

an appropriate level of skepticism as

adults! Part of developing into a true

science spectator is deepening yourunderstanding of the role of skepticism.


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independent of any observers. This point has some philosophical difficulties, some of which

are at the heart of a famous questions:

If no one observed a tree as it fell in a forest, would it make any sound?

Considered as an issue in science, this question is tricky because the methods of sciencedepend on observation, but the question asks what happens when there is no observer.

There are two possible answers. One is that the question is meaningless: sound is

something you observe, and so the question is really asking Could sound be observed

when there is no observer? A second answer might reflect a scientists faith in the objective

nature of science, that sound has an objective reality independent of any observer. So the

second answer is Yes, the tree would make a sound. All observed trees make sound when

they fall, and the behavior of falling trees is not affected by the presence or absence of any

observers.

Quantum mechanics, a branch of physics suited to the description of small objects such as

atoms and electrons, raises important issues about the independence of reality on the

observer. According to quantum mechanics, experimenters cannot measure properties of

small objects without interfering with and changing those properties. In other words, the

experiment itself changes what is being measured. This represents one of the most active

areas of thought for the philosophy of science, and a continued area of research into the

proper interpretation of our current theories of quantum mechanics.

Science can be a useful tool.

The results of science can often be used to solve problems. Engineering and technology areexamples of areas that rely on the applications of science. In general, there are two kinds of

science. Pure science probes how things are in the universe, without reference to possibleapplications; applied science uses the results of pure science or initiates its own research to solveparticular problems. Congress voted not to build the Superconducting Super Collider, amultibillion-dollar machine to be built in Texas to investigate the structure of elementaryparticles such as protons. This project was an example of pure science wherein the extension ofknowledge was the only goal. Much of the debate centered on the absence of useful applicationsfor this research.

Doing science only to solve problems (or, in industrial laboratories, to improve next quartersbottom line) may be too short-sighted, because useful advances frequently appear fromunexpected sources. The U.S. project to land astronauts on the moon provided one particularlyinteresting and unexpected advance. The amount of knowledge gained about the moon was

actually rather small, and could have been obtained more cheaply with unmanned probes. Butthis project was pivotal in developing the spin-off technology of integrated circuits, which isnow the basis of the modern computer industry and the information explosion. There aremany such instances in the history of science and technology that led to valuable spin-offs.

Science is an international community of people. Scientists are motivated by their interests inscience, but also the fulfillment they can get from being part of a community: love, security, fame,and service. Effective science can be enhanced when scientists work, not in isolation, but as partof a larger scientific community sharing a common language, goals, interests, and methods. A


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scientific advance might be slowed if it requires changes in the views of the entire scientificcommunity, but most often the scientific community acts to further scientific progress. Weobserve that science is also a human activity!

Science is embodied in many institutions. One finds formal science practiced withinuniversities, societies, laboratories, and agencies. This structure has developed over time,

becoming especially elaborate since World War II, which saw for the first time large-scalegovernmental intervention in the affairs of science through the control implied by sizablefunding. These institutions sponsor forums that facilitate communications and the practice oforganized skepticism: for example, journals and conventions.

Science is a method or process. One usually learns the scientific method at some point inschool. Generally, this is presented as a very formulaic and rigid process. Though the scientificmethod will be a point of emphasis in this text, we will focus on the more fluid nature of thisprocess as it is carried out in practice.

The crucial elements of the process of modern scienceare:

1. The scientific method.2. The use of quantitative methods.

3. The institution of organized skepticism.

These items will be the focus of Chapter 2.

Science is constrained in two very important ways.

1. Science is constrained to the study of topics that can be studied by human senses (andtools enhancing the human senses). Unambiguous measurements can be made about thebehavior of such topics, particularly by employing carefully defined operations. Thus,art, literature, poetry, religion, justice, and traditional philosophy, etc. are not areas ofscience.

2. Topics within scientific areas are quantitatively limited due to many conditions:instrument restrictions, measurement fluctuations, human error, chaotic systems,

Heisenbergs Uncertainty Principle, etc. Within science, quantitative limitations can never

be fully overcome, but the proper practice of science always provides a measure of theselimitations.

1-C. Historical Examples of Elements of Modern Science

One of the fun aspects of developing an appreciation of sports, art, or music is to develop a senseof the history of the activity and its pursuit in a wide-range of cultures. This is equally true ofscience. With science, there is the added benefit of providing insight into the unique combination

of elements that make up modern science both its strengths and its limitations. The followingsection is a very brief survey of interesting developments in the human understanding of thenatural world. There is no way this short introduction can do justice to the history and breadth

of cultural experience, but the examples are selected to provide the reader with a better sense of

perspective on the elements that we identified as central to the modern scientific endeavor.


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As we explore different points and history and culture, one develops a sense that in addition to

the elements of science identified in Sec. 1-B, the following four cultural conditions are necessary

for the expression of all the elements of science as we understand it:

1. The existence of economic surplus with a mature technology base.

2. Encouragement of individual enterprise in open competition.

3. An outlook in which craft (manual arts and technique) and thought (academic

theory) were coupled.

4. Diverse resources (skills, talents, ideas, materials, etc.) and a tolerant intellectual

climate in which community leaders did not feel threatened by diversity and the

possibility of change.

It is worth paying attention to how these conditions contribute to different approaches tounderstanding the natural world.

1-C.1 Astronomy

With the focus of science being observation, it is no surprise that astronomy was the first science.It emerged from humanitys sense of wonder about the night sky in an era when the sky wasclear and bright. Everyone was aware of the stars in that age without electric lights and smog.Speculation about the heavenly bodies and their movements was routine for all people in ancienttimes; and these speculations gave rise to religion, mythology, astrology and astronomy. Oneelement of science that is present in all of these forms of the study of stars is the goal of makingpredictions. Even if we now question the reliability of many of the methods ancient people used tomake predictions based on the stars (astrology), it is interesting to explore the human desire forpredictive power right from the earliest times.

The drive for predictive power is not

surprising when we recognize theimportance of developing a reliable calendarand its use for agricultural reasons. Thecalendar is important not just for reckoningtime (When should I pull out my springwardrobe?), but also for predicting eventsthat happen annually. In ancient Egypt, forexample, astronomy was used to predict theflooding of the Nile. This marks an earlystep in agricultural engineering. In climatesfar from the equator, calendars areimportant for selecting planting seasons thatdepend on warmth and/or sunshine.

Figure 1: Image of Night sky


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Figure 2: Current model of the solar system showing the order of the planets around the sun.

One feature of astronomy is the wide range of written records from cultures throughout theworld, from Babylonian star catalogues (1200 BC), to the Vedanga Jyotisha in India, to the starcatalogue of Gan De in China (4th century BC), to the Mayan use of cycles of astronomical objects

including Pleiades to develop their calendars. Going beyond the written record is the deepconnection to astronomy in ancient cultures that is often inferred from the structures thesecivilizations have left behind. Though we cannot always be sure of their purpose, many ancientstructures, ranging from Stonehenge in England to the pyramids of ancient Egypt, appear to haveclear connections with astronomical measurements. Given the intense human effort expended onastronomy, it is interesting to highlight a fundamental question that only appears to have beenresolved in the 1400s do objects orbit the Earth (geocentric view) or do we orbit the sun(heliocentric view)?

Though it is entirely embedded in our culture now that the Earth orbits the sun, the obviousexperimental evidence is that the sun moves around the Earth. Just look up in the sky and askyourself if you feel the Earth moving! In contemporary society, this conflict between a geocentricand heliocentric world view that is generally portrayed as the ultimate science versus religion

debate, and yet a closer evaluation of the historical development suggests that this is really ascience versus science debate! Essentially, the views of astronomy in place in Europe of themiddle ages were due to over 2000 years of Greek influence on astronomy. According to Greekthought, the earth was at rest and at the center of the universe. Objects in the heavens wereperfect, and so their motions around the earth were eternal and perfect. Therefore their motionswere circular, since the circle is a perfect shape, suitable for eternal motion without a beginningor an end. In this explanation of the natural world, we see applications of model building and theuse of a mathematical framework. However, the underlying assumptions were based on a modelthat heavenly objects were perfect, and this influenced the response to observations. Forexample, the planets have, in fact, irregular motions through the sky that the Greeks hadmeasured. But, instead of abandoning the notion that objects in the heavens move in circularpaths, the Greeks supposed that the planets moved on spheres that pivoted on other spheres.

This lead to models with reasonable predictive power, but that grew increasingly more complexas measurements of planetary motions grew more accurate, especially with the invention and useof telescopes.

THOUGHT EXERCISE: Imagine that you are assigned the task of justifying to someone thatthe Earth orbits around the sun. How would you justify this model of the Earths


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motion?

So, how did the accepted model of the solar system change from an earth-centered to a sun-centered view? One way to get a sense of the process, skipping many of the details, is to considerthe contributions of three people involved in this process: Johannes Kepler, Galileo Galilei, and

Isaac Newton.

Johannes Kepler(15711630) showed that the motions of the planets around the sun canbe described by simple mathematical patterns (elliptical orbits). The match of theory and datawas precise enough to be persuasive. It had the advantage over existing scientific models of beingsignificantly simpler than sets of circular orbits, one of our key principles of modern science. But,it departed from the major assumptions of the time heavenly objects move in circles. Kepler didnot have a good model orprinciple to justify the use of ellipses beyond its simplicity and predictivepower. This is probably one reason Kepler delayed publication of his results in order to avoidpolitical problems with the authorities of the time that relied on the results of Greek science,especially the ideas of Artistotle.

Galileo Galilei(15641642) is perhaps most important for showing that experiments are akey to testing the validity of scientific theories. For example, he is famous for making precise

measurements of balls rolling down an inclined plane to investigate the physics of falling bodiesunder the influence of gravity. This is connected to the geocentric-heliocentric debate because hiscareful studies of how gravity affects the motions of objects provided the first steps inoverthrowing the foundations of Aristotelian models of the world that were used to justify thegeocentric model (see Sec. 1.C-4). Additionally, Galileo (and others) observations of the sun andplanets with telescopes provided clear evidence that they were not perfect which providedadditional evidence that the premise used to justify the geocentric model may not be correct.

Ironically, Galileo doubted the elliptical trajectories found by Kepler. Galileo could notlet go of circular orbits. This prevented him from making further advances. Even a genius likeGalileo who was able to discard some of the Aristotelian influence was unable to discard others.

We all have difficulty changing our thought patterns and beliefs!

Isaac Newton(16421727) showed that the laws of gravity and motion were simple anduniversal, applying equally well on earth and in the heavens: two of our key principles listedearlier. This provided the final piece for the heliocentric model an explanation of theelliptical orbits based on Newtons model of gravity and motion (generally referred to asNewtons Laws). This is what we ultimately mean by a model that is used to make predictions.Interestingly, with Newtons understanding of gravity, we realize that the sun and Earth orbiteach other, but with the point they orbit about inside the sun! So, though we generally say thatthe Earth orbits the sun, in a sense, the sun orbits the Earth as well!

At its heart, the geocentric versus heliocentric debate provides an important example of how to

approach the interaction between models and experimental data in the scientific effort. In this case,people had had a model of the universe that had worked for centuries, and was able tosuccessfully predict the motion of planets and stars. This model had a strong philosophical basis.So, in the face of such an extremely successful model, what did it take to overthrow it? Notice,experimental data was not sufficient. Initially, as the data improved, the response was to refine(change, or improve) the model while preserving what was felt to be the key elements: circularorbits. Only when a model with superior predictive power and simplicity was shown to besuccessful Newtons Laws was the old model finally abandoned. This process is repeated overand over in the history of science and is one of the reasons that it is so much fun and such a


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challenge! It helps that the modern view of science tends not to hold individuals as ultimateauthorities. This can help in the approach to competing models, but we still run into problems asa society when science intersects withpolitical and economic authorities. We will explore this issuein more detail in Chapter 2.

The example of the geo- versus helio-centric view of the solar system helps shed light on the

complications of the interaction between science and social authorities. We start by consideringthe question, if the heliocentric view was fundamentally a challenge to prevailing scientific ideas,why do we look back on this as a science vs. religion issue? First, many of the scientists at thetime were members of the clergy. Second, the Church controlled many of avenues of academiccommunication such as publication of books and even the educational institutions. Finally, manyclergy believed that their theology was dependent on the philosophy Aristotle being correct.Ironically, we often view this debate as the first case of the blind acceptance of the Bible versusscientific experiment, when a better description is probably blind acceptance of Aristotle as ascientific authority versus scientific experiment! Therefore, there was a double problem of conflictamongst scientists and conflict between scientists and political or social authority. What is anexample of this in contemporary times?

Consider the history of climate science in the late 20th

and early 21st

century. A prevailingphilosophical view was that the climate was sufficiently complex and robust that one could notimagine human activity truly impacting the global climate. And yet, many scientists were findingthat their studies suggested just such a situation. This placed them in the position of challengersto a status quo scientific view. However, this has not been the main challenge for climate science.The real issue has been the fact that the basis of a significant portion of the first-world life style istechnologies that are implicated in climate change. This places the science in conflict withdominate political and economic structures. Therefore, from a sociological point of view, we cansee many parallels between the debates over models of the solar system and debates over the roleof human activity in climate change! And if we are lucky, perhaps we can learn some lessons?

1-C.2 Materials Science

Another set of ancient sciences are any of the variations of what we now call chemistry and

materials science. Fundamentally, these two sciences are about manipulating materials in the

natural world to create new materials or compounds with specific properties. Hence, in the area

of metallurgy we have the movement from the stone to the bronze to the iron ages in history as

humans learned to manipulate metals in complex fashions. The earliest chemistry is arguably

cooking, including the development of bread and beer! As society became more complex, we see

the foundations of modern chemistry in various approaches to medicine and alchemy. As we

explore this area of human activity, a theme we will consider is the differing role of models versus

what we might callpure experiments in technology and science.

As with astronomy, we find examples across all cultures. Some rather dramatic examples are the

development of fireworks (gunpowder) by the Chinese, the famous metal used in Samaraiswords of the Japanese (an excellent example of materials science), and the creative use of wood

and other material in bows across all cultures, for example the Huns used a combination of wood

and bone to great effect. In fact, the entire history of weapons for hunting and warfare is an

example of the science of materials at work. To gain an advantage, the goal of weapons makers is

to predictably produce materials with specific properties of strength, elasticity, durability, and

sharpness.


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But human efforts in chemistry and materials science went beyond weapons development and

produced a vast store of knowledge with respect to modifying and utilizing stone, wood,

ceramics, and metals. Just think of how much of our knowledge of ancient cultures comes from

the surviving materials that had been used in cooking, agriculture, construction, and for leisure

activities including art and music. For example, just recall the common image of the archeologist

carefully cleaning pottery shards is ubiquitous in our culture!

THOUGHT EXERCISE: Make a list of famous objects that are examples of interesting usesof materials from ancient cultures. Try to think of at least one object from eachcontinent!

One of the most fascinating parts of the development of materials and chemistry is how late in

the process we understood what matter really was!

Building on previous work, the first periodic table of

elements was only published as late as 1869 by

Mendeleev! And it was only in the early 1900s,

culminating with work such as Einsteins explanation of

diffusion, that the atomic picture of matter was finally

universally accepted. Yet, despite what we would

classify as having an incorrect model of matter, humans

developed very useful rules for manipulating matter based

purely on careful experiments. In a sense, the history of

materials science and chemistry is one of using halfof the

modern scientific process quantitative experiments! To

illustrate the use of careful experiments, lets briefly

consider a famous branch of early materials science alchemy.

One of the most famous goals of alchemy was to turn base materials, such as lead, into

valuable materials, such as gold. This enterprise is often derided now, and viewed as magic or

pseudo-science. So, why were people like Isaac Newton so serious about pursuing alchemy? At

the heart of historical alchemy was a key element of modern science: the need for careful

measurements and tracking of the results. After all, if you wanted to be able to repeat a process for

turning lead into gold, you needed a careful record of how you achieved it!

If alchemy involved careful measurements, recording of experiments, and the goal or repeatable

results, why is it different from modern chemistry and science? Here we see the influence of the

role of models in modern science. Despite the simplified definition of science as the ability to make

quantitative predictions, modern science also views the development of the best model as an

end in itself. Alchemists were basically working from the Aristotelian view that matter was

composed of the four elements of fire, water, air, and earth, and not the modern understanding

of atoms and molecules. This was not really a barrier to careful experiments, but it was a barrier

to achieving their goals.

As we will see in later chapters, the structure of the nucleus determines the element (gold or lead),

and the combination of elements into different molecules involves the interactions of theirelectrons and the formation of chemical bonds. Alchemists only had access to manipulations of

Practical Aside: The idea of theopen sharing of knowledge is soimportant to contemporaryscience that many grantingagencies require a disseminationplan if they are going to fund aresearch project. This meansthat scientists have to explicitlydetermine how they will sharetheir results and provide accessto their data to otherresearchers!


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chemical bonds, and not the structure of the nucleus. Therefore, they could create new molecules

and compounds, but they could not change one element into another! From our perspective, if

they had access to the correct model of matter they would have understood that what they were

attempting was impossible with the techniques at their disposal! To transform the elementsthemselves requires nuclear physics, something we now achieve on a regular basis in nuclearreactors, and is one reason we trust our current model of matter.

In summary, on the one hand, the careful investigation of matter undertaken by many alchemistsprovided a solid foundation for modern chemistry. But, on the other hand, the limitations placedon their studies by the tools of the time prevented them from achieving one of their major goals the transformation of lead into goal. And, their model of matter did not help them understandthe limitations of their technology. And yet, it was the constant improvements in methods andtechnology that the alchemist pursued that eventually transformed into the disciplines that werecognize as chemistry and nuclear physics and allowed for the development of a better modelof matter.

Contemporary Example: Improvements in technology and measurements are one of the mostcommon ways science advances. For most of the late 20th century, there were two competingviews within cosmology (the study of the structure and evolution of the universe) as to thecurrent state of the universe: (1) it would expand forever, but at a slower and slower rate or (2) itwould eventual stop expanding and contract. However, as technology lead to better and bettermeasurements, since the 1990s, the prevailing view is that the universe is accelerating, i.e. it isexpanding faster and faster! This came as a complete surprise to the scientific community, and itis surprises like this that improved technology often provides. As with the development ofnuclear reactors finally allowing us to turn base metals into gold!

As we consider the impact of the culture on the practice of science, there is a final lesson to be

learned from the history of materials science and alchemy. Both of these endeavors tended to be

secretive in nature. Guilds and other societies were developed to maintain trade secrets. After

all, this is very much a case of knowledge equaling wealth and power. For example, if you finally

made the breakthrough that turned lead into gold, this achievement does not have significant

value if you let everyone know how to do it since one value of gold is the fact that it is relatively

rare! The idea of keeping knowledge secret for a select few is in contrast to the general goal of

modern science: shared knowledge.

As a general rule, reproducibility and an open exchange of ideas and results is critical for modern

science. In fact, it is so important that in Chapter 2, we call it organized skepticism and discuss it in

more detail. The act of sharing and evaluating others results is a significant part of the scientific

process that allows people to trust results that they cannot afford to reproduce themselves. But,even in the modern era there is the challenge of knowledge being wealth and power. This is

perhaps most obvious in the field of medicine and drug research. Here the costs of drug

development and the potential for making profit from it often causes tension with the concept of

shared and open exchange of ideas. This also provides challenges for evaluating the effectiveness

and value of new drugs, and for developing accurate testing methods.


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1-C.3 Architecture and Statics

Another ancient area of human activity that we will briefly consider is the realm of architecture. It

is clear that humans early on developed great skill at building massive structures. When one

considers massive construction projects, whether it is the Great Wall in China, the temples in

South America, the massive heads on Easter Island, or the pyramids of Egypt, there are a numberof obvious technological or engineering questions that immediately come to mind. How did they

transport and work with the massive stones often involved? How were they able to form relativeprecise shapes? What were the tools and processes used in their construction? As interesting asthese questions are, they go beyond the scope of this text. Instead, our focus will be how thehistory of construction ties into a key element of the development of modern science: theconnection between mathematics and scientific models, in this case, the understanding of statics.

Briefly, statics is the field of science that deals with whether or not physical objects in contact

with each other are stable, i.e. they are able to remain in a constant position. They are static! By

definition, the buildings, bridges, and monuments are all intended to be static, so an

understanding of statics is a key part of construction. As with many engineering efforts, one could

proceed purely on trial and error and keep a detailed record of what works withoutunderstanding the underlying scientific principles. But, the best engineers understand and/or

develop careful mathematical models that allow them to make accurate predictions regarding

their designs. This generally involves a mathematical model as part of the process.

What area of mathematics is most relevant to statics and the design of structures? The answer is

geometry. In this area, we see the constant back and forth between technology and science, with

mathematics providing important connections. The need to measure and create straight lines andaccurate angles provided great motivation for understanding the fundamentals of geometry. Theinsights provided by geometry into basic scientific issues of stability, such as the development ofthe arch, provided significant advances in construction. Therefore, it is no surprise, that anunderstanding of geometry was one of the first developments in mathematics. In fact, the

geometry most students study in high school, Euclidean geometry, is named after the Greekmathematician credited with formalizing the subject in 300 B.C. Euclid! Likewise, some of thefirst truly quantitative science on record is in the area of statics. For example, the Greek scientistArchimedes is famous for the development of a number of topics in statics, particularly theanalysis of levers and the concept of center of gravity.

The power of quantitative experiments: There is a famous story in which Archimedes measuresthe purity of the gold in the Kings crown with quantitative techniques. In this story, he goesrunning naked down the street yelling Eureka, meaning I have discovered it. While bathing,he realized that when an object is immersed in water, that object displaces a volume of waterequal to its own volume. (This was the start of the topic we call hydrostatics- a branch of statics..)This provided an easy way to measure the volume of the crown. If the crown was lighter than agold bar of the same volume, then the goldsmith must have diluted the gold in the crown. Sureenough, this is what had happened, and the goldsmith was executed.

As with the history of materials science, the history of architecture provides us with an importantlesson regarding the practice of science the need for careful records! For too many of the


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fascinating ancient structures we have no written record of the methods, tools, and designconcepts used to complete the project! Was it purely trial and error? How much science wasreally involved? It suggests that we carefully consider whether or not we are doing a sufficientjob are recording our methods, achievements, and understanding of the world. Especially as weenter the digital age, there are new challenges of data storage related not just to issues oflanguage and longevity, but readability and access to the medium. How many readers remember

what a floppy disk is and could retrieve the information stored on it?

1-C.4 Studies of motion: Aristotle versus modern science

The final issue we will consider is the study of motion. Understanding motion has a more subtlemotivation but obvious when you think about it. Once we start hunting by throwing spears atanimals, it is important to understand how things move if we want to increase our chance ofhitting the animal! Also, the study of motion is tied closely with the predictions of astronomy, asthese derive from understanding the motion of celestial objects. Therefore, you will see anoverlap with some of the ideas discussed in the section on astronomy. In this case, instead ofproviding a broad overview, we will provide a more detailed comparison of two models ofmotion: Aristotelian versus Newtonian. The reason for doing this here is three-fold:

(1) the Aristotelian model dominated the view of motion for much of human history

(2) for many people, the Aristotelian model is still their intuitive picture of motion

(3) Aristotle developed his model using many, but not all of the elements of modern science.Also, there is a reasonably continuous evolution from Aristotelian to a Newtonian world-view. So, it is an excellent historical example to show how science developed.

The central point of the following discussion is how intuition, observation, and logic can failwhen not combined with quantitative experiments. Also, this example illustrates the danger ofaccepting a philosophical view as the authoritative starting point, and requiring experimentalresults to be explained only in a particular context. We will start the discussion of Aristotelianversus Newtonian models of motion with some early experimental observations on motion.

1) If you push an object on a surface, it slidesfor some distance and then comes to rest.

2) If you release an object in the air, it falls tothe ground.

3) Different objects fall at different rates.Compare a feather versus a brick.

4) Objects in the sky (sun, moon, stars) are in

constant motion in a regular and predictablefashion.

How did Aristotle explain these four observations?

Step 1: He defined two types of motion.

ASIDE: Aristotles philosophical view

regarding ethics and religion attached high

value to moderation in behavior and an

acceptance of life as you found it. This

made Aristotle appealing to church

authorities in the Middle Ages. Thus

Aristotles ideas became institutionally

entrenched on a wide scale, and people

became afraid to challenge any of them.

Ironically, the Greeks themselves wouldhave found this situation unsatisfactory.

Their academic tradition was very skeptical

and argumentativeit just did not have a

significant element of quantitative

experimentation.


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Natural motion tends to restore objects to their natural position in the universe. At the

conclusion of natural motion, an object will be at rest where it belongs. Natural motion is not

caused by force, but it arises from the intrinsic nature of objects. The objects that display motion

are imbued with lifelike characteristics. They are said to strive to reach their natural state. For

example, a rocks natural place is on the ground at rest.

Arguments of this type conform to our experience. As a result they are intuitively appealing, particularly

when presented by a skillful orator. The same type of intuitive appeal continues in the following.

Violent motion, on the other hand, is motion that disrupts the natural order of things.

Violent motion is caused by forces. An example is the process of lifting a rock above its natural

location on the ground.

Step 2: He defined forces.

Forces are either a push or a pull. Mankind uses forces to achieve a measure of control over

activities that take place in the world. Animals also exert forces, as do the wind and other

inanimate objects.

Step 3: He had a model of the composition of the world in terms of four pure elements: earth,water, air, and fire.

All other substances were composed of combinations of these basic elements. There was anappropriate organization of these elements with earth (solids) at the lowest level, water next, airnext, and fire at the highest:

fire

air

waterearth

Step 4: Now one can put these pieces together to make qualitative and semi-quantitative predictions.

Prediction Example 1: If I lift a stone from the ground, the motion of the stone is violent, becauseI am moving the stone from where it belongs. I have to exert a force on the stone to cause thisviolent motion. When I release the stone, it will exhibit natural motion as it returns to the earth.This natural motion does not require a force. At the end of the natural motion of the stone, it willbe at rest on the earth, where it belongs. On the other hand, fire is even lighter than air, andsmoke from the fire rises just as naturally as the stone falls.


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Prediction Example 2: A cart moving along a road is in violent motion, since it is not at rest. Aforce is necessary to keep it moving. But when the force that causes the motion ceases, naturalmotion brings the cart to rest. No force is necessary to cause this natural motion; it arises fromthe nature of the cart.

Prediction Example 3: In this model, heavy objects fall faster than lighter objects. This prediction

arises from the model: when we lift a heavy object, we are doing greater violence to the universethan if we lift a lighter object. Consequently a heavy object, when allowed to fall, will return toits appropriate position sooner than the lighter object. This prediction seems to be supported byobservations of falling objects: a leaf, which is light, falls slower than a book, which is heavy.

General Feature 1: Note that natural motion was expected to be up or down. Smoke moves upbecause it is light; it could be viewed as mostly a mixture of fire and a small amount of othersubstances. The sun itself could be viewed as the ultimate fire (at a very great height). A forcewas required to make something move horizontally; thus all horizontal motions were violent.

General Feature 2: Celestial motions were a separate third category. They were not of the earth,but were part of the perfect motions associated with the heavens. The only perfect motion

possible was circular, so all heavenly objects had to move in circles, endlessly repeating theirperfect cycle. This was confirmed by observation, as long as one didnt look too closely, or aslong as one didnt take extended careful measurements!

FIGURE: This figure represents the celestial motion of the moon and stars.

As an intellectual accomplishment, Aristotles statements on Natural Philosophy wereexceptional. For their time, they provided a satisfactory framework for viewing the world on

many topics. Aristotle was very adroit at collecting information and classifying groups of relateditems. His most notable achievements were in biology, but he ranged over many fieldsintellectually with considerable success. The sheer volume of knowledge that he spanned wasawe-inspiring. So, at this point, a science spectator might be very happy. We have a model. Wehave predictions. We have observations that agree with predictions. We have a model that isfundamentally repeatable, invariant, simple, and reasonably objective. These were most of themain criteria for the modern process of science. What are we missing? Aristotles model does nothave truly quantitative predictions. It is the need for quantitative models that will motivate themathematics in Chapters 3 and 4.

Many of the predictions of the Aristotelian model were disproved by the experiments of Galileonear the beginning of the 17th century, and the general framework was effectively replaced by

the work of Newton. Many other scientists contributed to this work, and our contemporaryunderstanding of motion is referred to as classical mechanics. The subject is important enough thatwe devote Chapter 5 to this topic. However, it is worth highlighting the main elements here sothat one can see the contrast with the Aristotelian view. We will first consider the experiments ofGalileo and then the framework developed by Newton that built on Galileos (and others) work.

Experiment 1: The Aristotelian model predicted that object fell at a rate determined by theircomposition based on how much Earth, Air, Fire, and Water they contained. Galileodemonstrated quite clearly that objects with different masses fell at the same rate. His main work


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focused on objects rolling down inclined planes. However, he is perhaps most famous for thestory of dropping two different objects, with very different masses, from the leaning tower ofPisa. The most important fact was that Galileo was skeptical of Aristotles teachings, and hechallenged these ideas directly and quantitatively using the scientific method.

Experiment 2: Galileo used the telescope to explore the heavens, which under the Aristotelianmodel were supposed to be perfect in every way. The discovery that the surface of the moon wasmessy and that Jupiter had moons going around it just like Earth had was a real blow toAristotelian philosophy. Notice, this is actually a qualitative prediction in that it has more to dowith a description of objects than a quantitative prediction. But, it provided direct evidence againstkey assumptions in the Aristotelian model. So, even though quantitative results are important in

science, qualitative predictions do play a role. Since every model has assumptions built in, oftenthe role of qualitative experiments is to test the assumptions behind a model.

Galileos work had demonstrated the need for a new model of motion. We now summarize theele

chapter1-ver4

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