Chapter 6
The Sciences, Technology, and Mathematics
The checklists covering the Sciences, Technology, and Mathematics are drawn from the physical and natural world and represent some of the facts that the well-rounded intellectual should know.
As you read through the checklists, give yourself one point for correctly identifying all the elements in a checklist or for correctly answering the question posed. At the end of the section you’ll have the opportunity to rate how intellectual you are on these subjects.
WHOSE CONTRIBUTION IS THIS
Match the scientist to the contribution.
| A.Werner Heisenberg | 1. Radioactivity |
| B. Marie Curie | 2. Discovery of the electron |
| C. Joseph J. Thomson | 3. Continental drift |
| D. Dmitri Mendeleev | 4. Periodic table of elements |
| E. Alfred Wegener | 5. Quantum theory |
ANSWER: A, 5; B, 1; C, 2; D, 4; E, 3
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I’LL TAKE ONE
Our early ancestors were more concerned with survival, so mathematics developed slowly. Are you aware of the following facts?
* Early societies used a counting system of “one, two, many”
* Any quantity larger than two was referred to as “many”
* Humans were counting objects 35,000 years ago
* A baboon fibula is the oldest counting artifact
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WANT TO TRADE
Commerce propelled the use of numbers. Did you know the following?
* Early Middle Eastern traders used small clay shards as counting tokens
* Counting boards superseded the token system
* Counting boards had different sections for 1s, 10s, and 100s
* Sumerians developed the abacus around 2700 b.c.
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THE EARLY DAYS
Our knowledge of our place in the universe is constantly increasing. Did you know the following?
* Scientists estimate that the earth is 4.6 billion years old
* The earliest human activity appeared about 2.7 million years ago
* Homo erectus, a hominid dating to 1.8 million years ago, migrated to Europe
* Homo erectus lived in a number of sites but probably died out
* Neanderthals may have descended from Homo erectus
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MODERNS COME OF AGE
Were you aware of the following facts about our ancestors?
* Our species, Homo sapiens, evolved from Homo erectus
* This change occurred in Africa about 150,000 years ago
* Homo sapiens reached full biological maturity about 50,000 years ago
* These early humans used language and music
* They migrated out of Africa about 70,000 years ago
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PLACES TO GO
Did you know these facts about early human life?
* Modern humans spread to Eurasia and Oceania by 40,000 years ago
* They reached the Americas by at least 14,500 years ago
* It is believed that they may have coexisted but eventually displaced other species
* Neanderthals became extinct about 30,000 years ago
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SETTLING DOWN
Civilization took a while to catch on, but it quickly became popular. Did you know the following?
* Until about 10,000 years ago, most humans were hunter-gatherers
* Small nomadic groups lived without permanent domiciles
* Agriculture, the domestication of animals, and metal tools led to permanent settlements
* This Neolithic Revolution—with food surpluses—encouraged trade and cooperation
* As a result, more complex and larger societies were created
POINTS
HAND ME THAT RULER
A means to measure length and weight was needed for building. How many of these facts were you aware of?
* People have had measuring standards for at least 5,000 years
* Ancient Egyptians measured property after Nile floods
* Pyramid construction required sophisticated calculations
* Egyptians used a decimal, or base 10, system of counting
* Egyptians had symbols for numbers up to one million
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THERE ARE THREE SIDES TO EVERY STORY
Pythagoras (ca . 580–500 B.C.) developed the most famous theory in geometry, the Pythagorean theorem . Did you know these other facts about him?
* Pythagoras founded a school of philosophy
* The Pythagoreans believed the physical world was explained by mathematical principles
* Pythagoras showed the mathematical basis for musical pitch and harmony
* Socrates and Plato were influenced by his mathematical world view
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EVOLVING IDEAS
Charles Darwin’s work on evolution is familiar, but did you know the following facts?
* As a young man, Darwin studied medicine and the ministry
* All 1,250 copies of the first edition On the Origin of Species were sold in one day
* From his reading, Darwin acquired the concept of “deep time”
* In Origin, Darwin estimated the earth’s age at 306 million years
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A SEA VOYAGE
Darwin’s five-year voyage on the HMS Beagle was formative, but did you realize the following?
* Darwin was invited to sail on the HMS Beagle as company for Captain Robert FitzRoy
* The survey ship’s mission was to chart coastal waters for the navy
* Captain FitzRoy hoped to find evidence for the biblical theory of creation
* Darwin and the captain’s different viewpoints caused much friction
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BACK HOME
Darwin did not develop his theories during the voyage of the Beagle. Did you know the following?
* This adventure would last him a lifetime—he never left England again
* He acquired specimens and fossils sufficient for his further work
* He discovered a new species of dolphin
* He developed a new theory that coral atolls require a million years to form
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THE LONG ROAD TO PUBLICATION
Origin (1859) had a lengthy gestation period. Were you aware of these facts?
* It wasn’t until six years after the Beagle voyage that Darwin started work on Origin
* He worked on his notes for two years and then stopped
* He spent eight years writing a work about barnacles
* Vestiges of the Natural History of Creation was published in 1844
* Written anonymously, the book suggest humans were descended from lesser primates
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COMPETITION
It’s possible that Darwin might never have published Origin. Did you know the following?
* A young naturalist, Alfred Russel Wallace, contacted Darwin in 1858
* Independently, Wallace had developed a theory of natural selection like Darwin’s
* Darwin compromised and they presented a joint summary at the Linnaean Society
* The next year, Darwin published Origin and the theory became known as his alone
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AN UPHILL STRUGGLE
Origin was not greeted with acclaim by the scientific community. Did you know the following?
* Darwin’s theory on the process of evolution required more time than the accepted age of the earth allowed
* There was no fossil evidence to support the transitional forms his theory required
* There were many who did not believe that complicated organs developed in stages
* Even Darwin himself thought the idea “absurd”
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THE NEXT BIG THING
It wasn’t until he published The Descent of Man that Darwin expressed his beliefs on human lineage. Are you aware of the following?
* The Descent of Man, and Selection in Relation to Sex was published in 1871
* The human/ape lineage theory was not supported by contemporary fossil evidence
* Darwin presented the view that sexual selection was responsible for animal features
* Darwin maintained that despite their differences, all humans are one species
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A PROLIFIC AUTHOR
Despite deteriorating health, Darwin published many books . Which of the following was not one of Darwin’s works?
A. The Voyage of the Beagle (1839)
B. The Expression of the Emotions in Man and Animals (1872)
C. The Effects of Cross and Self Fertilization in the Vegetable Kingdom (1876)
D. The Formation of Vegetable Mould through the Action of Worms (1881)
E. The Consequences of Mollusk Deposition on Hardwood (1882)
ANSWER: E
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MISCONCEPTIONS
Did you know these facts about Darwin?
* Evolution as a concept was in use for decades by the time of Darwin
* Darwin theorized how organisms pass along survival advantages
* Darwin did not use the phrase “survival of the fittest”
* He didn’t use the term “evolution” until the sixth edition of Origin
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OF GEEKS AND GREEKS
The ancient Greeks made significant advances in mathematics. Did you know the following?
* The Greeks were using a numbering system, geometry, and proofs by 600 b.c.
* Euclid (ca. 300 b.c.) is known as the father of geometry
* Euclid’s Elements collected everything known about geometry
* Elements was a successful textbook—it was used for 2,000 years
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BABBLE ON
The Babylonians (today’s Turkey and Syria) were using mathematics 4,500 years ago. Did you know the following?
* Clay tablets were used for calculations
* One cuneiform symbol was used for the number 1 and another for 10
* The position of digits was significant
* Babylonians used a base-60 system instead of our base-10 system
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AND THE GLORY
How many kingdoms are there in the scientific classification system, and do you know them all?
* Plantae
* Animalia
* Fungi
* Protista
* Archaea
* Bacteria
ANSWER: There are six kingdoms
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COMBINED POINTS
LOOK CLOSELY
What are the differences among these types of mono-cellular animals?
* Bacteria are single-celled prokaryotic organisms
* Archaeans are similar to bacteria, but they have different genes and enzymes than bacteria
* Protista are more like animals, but have characteristics of plants and fungi
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A SURPRISING FIND
When were microbes first discovered?
Microbes were discovered by Anton van Leeuwenhoek using a microscope of his own design in __________________
ANSWER: 1675
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IT’S ALL RELATIVE
Match these animals with their closest relatives.
| A. Manatee | 1. Raccoons |
| B. Tapir | 2. Elephants |
| C. Panda bear | 3. Horses and rhinoceroses |
ANSWER: A, 2; B, 3; C, 1
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A BETTER WAY OF THINKING
British geologist Charles Lyell (1797–1875) had a profound influence on Darwin. Did you know this about him?
* Some geologists of his time believed the Earth was shaped by cataclysmic events
* Catastrophism allowed for biblical happenings like Noah’s flood
* Lyell was a uniformitarianist
* Uniformitarianism held that the Earth changed slowly over long spans of time
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NOT PERFECT
Lyell and the uniformitarians, despite the soundness of their ideas, were incorrect about many geological concepts. Were you aware of the following?
* Lyell did not think that glaciers were responsible for change
* Lyell refused to accept the idea of ice ages
* He believed that animals had existed relatively unchanged since the beginning of time
* He did not believe that animal species could become extinct
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THE BASICS
Despite his scientific shortsightedness on some topics, Lyell’s work was important to Darwin. Did you know the following?
* Lyell first published his Principles of Geology in 1830
* Darwin had a first edition of Principles with him on the Beagle voyage
* The book, which saw twelve editions printed, influenced geologic thinking for a century
* Not until the tenth edition of Principles did Lyell endorse evolution
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WHO’S WHO
Can you match the famous mathematician with his contribution?
| 1. Al-Khwarizmi | A. Wrote Conics |
| 2. Apollonius | B. Wrote Arithmetica |
| 3. Descartes | C. Developed algebra |
| 4. Diophantus | D. Founded spherical trigonometry |
| 5. Menelaus | E. Founded analytic geometry |
ANSWER: 1, C; 2, A; 3, E; 4, B; 5, D
POINTS
OFF BASE
Different counting systems, other than our base-10 system, have influenced us to this day. Did you know the following?
*The base-60 system is why we have 60 seconds in a minute and 60 minutes in an hour
* The base-20 system is heard in French numbers: quatre-vingt means
“four-twenty”
*The base-20 system was found in the former British monetary system
* The base-12 system can be found in our measurement of hours in a day and months in a year
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TRULY NOBLE
What are the noble gases?
* Helium
* Neon
* Argon
* Krypton
* Xenon
* Radon
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COMBINED POINTS
HOW ABOUT STATE OF MIND
Can you name the states of matter?
* Gas
* Liquid
* Solid
* Plasma
POINTS
WHEN WAS THAT
In which year was the transistor invented?
a. 1940
b. 1956
c. 1962
d. 1984
ANSWER: B, 1956, by John Bardeen
POINTS
A VISIONARY
The history of computers dates, improbably, to the nineteenth century. Are you acquainted with the following facts?
* English mathematician Charles Babbage (1791–1871) is considered “father of the computer”
* Babbage conceived of a machine to reduce errors in contemporary calculations
* He started work on a prototype “difference engine” in the 1820s
* He received ample funding but completed only a fragment of the project
* The steam-powered machine would have weighed 15 tons and required 25,000 parts
* A working model of his updated design was built in 1990
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AN ENGINEERING PROBLEM
Babbage was undaunted despite his inability to complete the difference engine. Did you know the following about his later efforts?
* Babbage started work on a more complex machine called an “analytical engine”
* The analytical engine was not a single machine but a series of designs
* It could be programmed using punched cards—a technique used until the 1970s
* Ada Lovelace (1815–1852) wrote the first computer program for the machine
* The analytical engine could operate on numbers with up to fifty decimal places
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A HOT TOPIC
Other scientists were working in the field of computing in the late 1800s. Did you know the following?
* American scientist Herman Hollerith built the first electromechanical “tabulator”
* The machine was put to use by the U.S. Census Bureau in 1890
* The success of his design inspired him to form the Tabulating Machine Company in 1896
* By 1924, the company was called International Business Machines (IBM)
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EUROPEAN DEVELOPMENTS
Are you aware of early computer developments in Germany?
* In 1936, German scientist Konrad Zuse built the first programmable binary computer
* Notably, he adopted the binary system of converting numbers to zeroes and ones
* This system is also called “digital computing”
* His machine was controlled by perforated strips of discarded movie film
* The machine was destroyed in an air raid on Berlin in 1943
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ANOTHER QUIP
The Incas had no written language and a huge empire to administer. Did you know the following?
* A quipo was a cord of cotton with additional knotted cords attached
* The quipo was used to record and transmit information
* The number of knots, their position, size, and color were significant
* A quipo with 1,800 cords has been discovered
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QUOTABLE
Who is quoted as saying about Sir Isaac Newton: “Nature to him was an open book, whose letters he could read without effort?”
1. Bertrand Russell
2. Stephen Hawking
3. Albert Einstein
4. J. Robert Oppenheimer
ANSWER: 3
POINTS
SIR ISAAC
Sir Isaac Newton left an indelible impression on the fields of science and mathematics . Were you aware of the following?
* He built the first practical reflecting telescope
* His Principia (1687) is among the most influential books in the history of science
* The Principia explains the behavior of celestial bodies and the law of gravitation
* He competes with Gottfried Wilhelm Leibniz for credit of having developed infinitesimal calculus
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TURING’S WORK
How many of the following facts about English mathematician Alan Turing are you familiar with?
* Turing (1912–1954) published a computer theory in 1937
* His paper can be considered as the foundation of computer science
* He formalized the concepts of algorithm and computation
* During World War II, he worked for Britain’s code-breaking center on German ciphers
* His techniques were fundamental in breaking the German Enigma codes
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WAR EFFORTS
Codebreaking was critical to the Allied war efforts in the 1940s. Are you aware of the following?
* English engineer Thomas Flowers also worked on the British code-breaking efforts
* In 1943 he built Colossus, the world’s first programmable digital electronic computer
* Ten Colossus machines were built to perform the data crunching decryption duties
* All the computers were destroyed in 1945 to maintain secrecy
* Their existence only became generally known in the 1970s
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ADDING IT ALL UP
Military requirements prompted the creation of another historical technological development. Are you familiar with these facts?
* The Electronic Numerical Integrator and Computer was contracted by the Army in 1943
* ENIAC was designed to compute firing and bombing tables for the military
* It went into use in 1946 and was in continuous operation until 1955
* ENIAC consisted of thirty units, had 18,000 vacuum tubes, and weighed thirty tons
* It was used later to make calculations used in designing the hydrogen bomb
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ADDING TO THE BOTTOM LINE
It took further developments before the use of computers could expand. Were you aware of the following?
* The transistor was invented in 1947 at AT&T Bell Labs
* Replacing vacuum tubes with transistors made computers faster and smaller
* IBM became the primary supplier of mainframe computers to business
* From the 1960s on, mainframes took over the processing of computing tasks
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MUCH ADO
A famous problem in mathematics, finally solved in 1995, was Fermat’s Last Theorem. Do you know these facts:
* The theorem: xn + yn = zn has no integer solutions for n > 2 and x, y, and z are positive
* Fermat first proposed this problem in 1637
* He wrote the problem in the margin of his Arithmetica
* He claimed he had a proof, but it wouldn’t fit
* Countless mathematicians attempted to solve the problem for 358 years
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HE SHOULD KNOW
According to Johannes Kepler, what are the two “treasures of geometry”?
* The Pythagorean theorem (a2 + b2 = c2)
* The golden ratio (a+b/b = a/b ≡ ϕ)
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LANDMARKS IN MATHEMATICS
Match the mathematicians with their works:
| A. Descartes | 1. Harmonices Mundi |
| B. Fibonacci | 2. La Géométrie |
| C. Plato | 3. Liber Abaci |
| D. Kepler | 4. Timaeus |
ANSWER: A, 2; B, 3; C, 4; D,1
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THE BETTER PART OF VALOR
Discrete mathematics studies noncontinuous events. Can you name four areas of discrete mathematics?
* Computing—the binary language of computers is discrete
* Probability—from the simple coin toss to meteorology
* Graph theory—examines networks and paths
* Logic—the study of true/false relationships
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IT’S OBVIOUS
What is the difference between a eukaryote and a prokaryote?
* Eukaryotes have a defined nucleus and as well as other organelles such as Golgi apparatus
* Prokaryotes are cells without a nucleus or other organelles
* Prokaryotes don’t have internal membranes
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AT THE BEGINNING
Where can you find one of the earliest forms of life?
* In the Marble Bar area of Australia
* Fossilized remains of cyanobacteria called stromatolites are more than 3 billion years old
* Their living descendents are estimated to be several thousand years old
* They can be found in the Hamelin Pool Marine Nature Reserve in the Sharks Bay area of Australia
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ISLAND LIFE
Which of these are not volcanic islands?
A. The Hawaiian Islands
B. Line Islands
C. Lesser Antilles
D. Madagascar
ANSWER: D
POINTS
STAND BACK
Which of these volcanoes is not active?
A. Mount Vesuvius
B. Mount Kilauea
C. Mount St. Helens
D. The Hohentwiel
ANSWER: D
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COMBINED POINTS
IN THE BEGINNING
The ubiquitous Internet, like many good ideas, had humble origins. Did you know the following?
* The Internet’s first incarnation was called ARPANET
* The U.S. Department of Defense proposed the ARPANET research project in 1967
* The project was designed to facilitate communication between two computers
* UCLA and Stanford were the two nodes of this network, which went live in 1969
* E-mail was added in 1972 and quickly became its main service
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NOW YOU SEE IT …
Can you name the eight different electromagnetic spectrums?
* Radio
* Microwave
* Infrared
* Visible
* Ultraviolet
* X-rays
* Gamma rays
* High energy gamma rays
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WAVES OF MANY LENGTHS
What are the different types of wavelength?
* Microwave
* Shortwave
* Medium wave
* Long wave
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COMBINED POINTS
LOOKS WINDY
Did you know these facts about El Niño and La Niña?
* El Nino/La Nina are part of a weather pattern
* This weather pattern occurs in the Pacific Ocean roughly every 4–5 years
* It is characterized by a warming or cooling of the surface ocean temperature
* El Niño happens when the ocean gets warmer
* La Niña occurs when the ocean gets cooler
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WE’RE NOT ALONE
What is the most numerous type of animal on Earth?
A. Insects
B. Mites
C. Nematodes
ANSWER: C
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WISH YOU WERE HERE
How many of these natural oddities have you seen?
* La Brea Tar Pits
* The Great Salt Lake
* The Dead Sea
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COMBINED POINTS
SCORING YOURSELF: SCIENCE, TECHNOLOGY, AND MATHEMATICS
Based on your responses to the checklists in the preceding section, use the rating system below to determine how you stand as an intellectual in science, technology, and mathematics.
0–11: A scientist may have frightened you at a young age.
12–28: You probably struggled with the sciences in school.
29–43: Your scientific knowledge should enable you to read and understand many technical articles.
44–60: At MIT they speak of you in hushed tones.