SCIENCE AND MATHEMATICS - A BRIEF

EARLY HISTORY*1. Cave paintings and apparently regular scratches on bone and reindeer horn - prehistoric humans were close observers of nature who carefully tracked the seasons and times of the year. This was done for hunting and agricultural purposes.

2. About 2500 B.C. - a sudden burst of activity in Great Britain and northwestern Europe - construction of large stone structures from that era, the most famous of which is Stonehenge on the Salisbury Plain in England, that are remarkable from a scientific point of view. The construction of this and related structures indicated a workingknowledge of geometry.

* Information taken from the World Book and Encyclopedia Brittanica

3. The ancient Greeks developed practical mathematical systems and divided the field of mathematics into arithmetic (the study of "multitude," or discrete quantity) and geometry (that of "magnitude," or continuous quantity). Both were considered to have originated in practical activities.This Greek tradition was much like the earlier traditions in Egypt and Mesopotamia. Indeed, it is likely that the Greeks borrowed from such older sources to some extent. Geometry, literally, "measurement of land," first arose in surveying practices among the ancient Egyptians, because the flooding of the Nile compelled them each year to redefine the boundaries of properties. Arithmetic probably originated with the commerce and trade of Phoenician merchants.

4. Alexandria - the Intellectual Capital of Western Civilization. Founded by Alexander the Great in 332 B.C. on the shores of the Mediterranean Sea in what is now Egypt. Its success was due largely to the line of rulers (Ptolemy I et al.) that followed for hundreds of years who melded Greek knowledge/culture with that of Egypt. For example, the Alexandrian Library was the largest and most famous of the ancient collection of papyrus scrolls - over 700,000 in 200 B. C.

5. What was distinctive of the Greeks' contribution tomathematics‑‑and what in effect made them the creators of"mathematics," as the term is usually understood‑‑was itsdevelopment as a theoretical discipline. Thus, the science of numbers was expanded beyond practical use on a day-by-day basis.

6. The Greeks also constructed a deductive system of geometry whichculminated in deep theorems, some of which are still an important part of mathematics. The Elements, composed by Euclid of Alexandria, around 300 BC, was a central contribution to theoretical geometry, but the transition from practical to theoretical mathematics had occurred much earlier, sometime in the 5th century BC and was initiated by persons like Pythagoras of Samos (late 6th century). Euclid used figures drawn on a page or envisioned in his imagination, and he often assumed details and relations read from the figure that were not explicitly stated - postulates (axioms). Euclidian geometry was used without question until the end of the 19th century -the late 1800s. Elements were translated into Arabic during the reign of Harun ar-Rashid (786 ‑809), and the first Latin version in a complete form was made from the Arabic by the English scholastic philosopher Adelard of Bath about 1120.

7. Astronomy - the combination of religion and astronomywas fundamental to the early history of science. It is found in Mesopotamia, Egypt, China (although to a much lesser extent than elsewhere), Central America, and India. The heavens, with the clearly discernible order and regularity of most heavenly bodies highlighted by extraordinary events such as comets and the particular motions of the planets, was an irresistible intellectual puzzle to early mankind. For example, one of the astronomical "laws" of the Middle Ages was that the appearance of comets presaged a great upheaval, as the Norman Conquest of Britain followed the comet of 1066.

8. Astronomy was to remain the queen of the sciences (welded solidly to theology) for the next 4,000 years.

9. Ptolemy (A.D. 100-165?)** - Astronomer/ Geographer who made astronomical observations in Alexandria about 150 A.D. A. Mathematike Syntaxis or Mathematical Composition: 1. The earth is round and the force of gravity is directed toward the center of the earth. 2. The earth is motionless (does not move) and lies at the center of the universe. 3. The sun, moon and planets move around the earth at variousspeeds. 4. The stars are brilliant spots of light in a concave dome that arched over everything. 5. The planets are much closer to the earth than the stars, but farther away than the moon. 6. This system of astronomy was accepted as authoritative throughout Europe until 1543.

** - not a Greek ruler in the Ptolemy dynasty

BACKGROUND The Rise of Modern Critical Science1. The Ptolemaic Geocentric System had been in place for almost 1,400 years.2. Nicolaus Copernicus set out to modernize the astronomical apparatus by which the Church made such important calculations as the proper dates for Easter and other religious festivals. In 1543, as he lay on his deathbed, he finished reading the proofs of his great work which proposed a Heliocentric System. He died just as it was published. His De revolutionibus orbium coelestium libri VI ("Six Books Concerning the Revolutions of the Heavenly Orbs") was the opening shot in a scientific revolution whose consequences proved greater than those of any other intellectual event in the history of mankind.

3. HELIOCENTRIC SYSTEM - OUTCOMES/CONCLUSIONS A. The apparent back‑and‑forth movements of the planets, which had required considerable ingenuity to accommodate within the Ptolemaic system, could be accounted for just in terms of the Earth's own orbital motion added to or subtracted from the motions of the planets. B. Variation in planetary brightness was also explained by this combination of motions [See Galileo and the Phases of Venus]C. The fact that Mercury and Venus were never found opposite the Sun in the sky was explained by placing their orbits closer to the Sun than that of the Earth. [M = 1, V = 2 , E = 3] Indeed, Copernicus was able to place the planets in order of their distances from the Sun by considering their speeds and thus to construct a “solar” system of planets, something that had eluded Ptolemy.

IMPACT ON CONVENTIONAL THOUGHT1. Why should the Earth circle the Sun?2. How was it possible for the Earth itself to revolve on its axis once in 24 hours without hurling all objects, including humans, off its surface? 3. If the Earth revolved around the Sun, then the apparent positions of the fixed stars should shift as the Earth moves in its orbit. Copernicus and his contemporaries could detect no such shift (called stellar parallax), and there were only two interpretations possible to explain this failure. Either the Earth was at the center, in which case no parallax was to be expected, or the stars were so far away that the parallax was too small to be detected. Copernicus chose the latter and accepted an enormous cosmos consisting mostly of empty space. God, it had been assumed, did nothing in vain, so for what purposes might he have created a universe in which the Earth and mankind were lost in immense space?

4. The heliocentric system was a grim intellectual prospect and not one that recommended itself to most 16th‑century philosophers andscientists. 5. Copernicus' grand idea remained on the periphery of scientific and astronomical thought. All astronomers were aware of it, some measured their own views against it, but only a small handful eagerly accepted it.

THE WORK CONTINUES 1. Tycho Brahe (“Bruh”) measured stellar and planetary positions more accurately than anyone before him using a compass and sextant. However, he insisted that the Earth was motionless. Copernicus did persuade Brahe to move the center of revolution of all other planets to the Sun. 2. Perhaps the most serious critical blows struck were those delivered by Galileo after the invention of the telescope. He could literally see what no human had ever seen before and beganobserving the universe. In quick succession, he announced that there were mountains on the Moon, satellites (“moons”) circling Jupiter, and spots on the Sun. Moreover, the Milky Way was composed of countless stars whose existence no one had suspected until Galileo saw them. Also, Venus exhibited phases that by inductive reasoning (the process of drawing general conclusions from particular instances) could not be explained by a geocentric system. This evidence struck at the very roots of the scientific system the world had known.

3. At the same time Galileo was searching the heavens with his telescope and reaching these revolutionary conclusions, in Germany Johannes Kepler was searching them with his mathematical mind. Brahe’s precise observations and measurements permitted Kepler to discover that Mars (and, by analogy, all the other planets) did not revolve in a circle at all, but in an ELLIPSE, with the Sun atone focus. Elliptical patterns of movement tied all the planets together in grand Copernican harmony. Kepler then derived 3 laws to describe planetary movement.

1. Law of Ellipses - The orbits of planets are ellipses with the sun at one focus. [An ellipse always has 2 foci and a circle has 1; see illustration on page 17- Drawing an Ellipse]

2. Law of Equal Areas - A line (radius vector) joining a planet tothe sun sweeps out equal areas in equal intervals of time.

3. Harmonic Law. The ratio of the square of a planet’s orbital period to the cube of its mean orbital radius is a constant valuefor all planets in the solar system.

A. T 2 = Orbital period (time)

------------------------------------ = A Constant Value R3 = Distance from the sun

Earth = 2.97

B. T1 2 = T2

2

------------------------------

R1 3 = R2

3

Mercury = 2.97 (closest to the sun)Pluto = 2.96 (farthest from the sun)

THE REVOLUTION CONTINUES 1. The views of the Catholic Church implemented via the Inquisition had a chilling effect on the development of science in Italy and the surrounding Mediterranean countries. 2. Other countries caught up in the Reformation Movement were more hospitable/less severe so the intellectual center of science moved north from Italy. 3. Kepler’s Laws were known by most astronomers by the mid-1600s but the force(s) which caused the motion of the planets was unknown. Kepler had suggested that magnetism from the sun might be the universal force that moved the planets. 4. Isaac Newton supplied the explanation of the system's structure and stability in the form of the Law of Universal Gravitation: There exists between every two bodies in the universe a force of attraction which is directly proportional to their masses and inversely proportional to the square of the distance between them.

HISTORICAL BACKGROUND - THE DEVELOPMENT OF CHEMISTRY** 1. By his observations and scientific methodology, Isaac Newton had developed a method of inferring laws from close observation of phenomena and then deducing forces from these laws.

2. One of the major advances in chemistry in the 18th century was the discovery of the role of air, and of gases generally, in chemical reactions.

3. By extensive and careful use of the chemical balance, Joseph Black showed that an “air” with specific properties could combine with solid substances like quicklime (Calcium oxide - CaO) and could be recovered from them. This discovery served to focus attention on the properties of"air," which was soon found to be a generic, not a specific, name.

** Information taken from the Encyclopedia Brittanica

4. Chemists then discovered a number of specific gases and investigated their various properties: some were flammable, others put out flames; some killed animals, others made them lively.

5. The Newton of chemistry was Antoine-Laurent Lavoisier. In a series of careful experiments using precise gravimetric methods,Lavoisier untangled combustion reactions to show that, in contradiction to established theory, which held that a body gave off the principle of inflammation (called phlogiston) when it burned, combustion actually involves the combination of bodies with a gas that Lavoisier named oxygen. Lavoisier insisted that only when materials were analyzed as totheir constituent substances was it possible to classify them and their attributes logically and consistently and that this was the central concern of the “new” chemistry. Thus, the chemical revolution was as much a revolution in method as in conception because gravimetric methods made possible precise analysis.

6. The submicroscopic world of material atoms became similarly comprehensible in the 19th century. An atom is generally defined as smallest unit into which matter can be divided without the release of electrically charged particles. It also is the smallest unit of matter that has the characteristic properties of a chemical element (Democritus-indivisible quality of matter). As such, the atom is the basic building block of chemistry. 7. John Dalton made a fundamental assumption that atomic species differ from one another solely in their weights:When atoms combine to form a particular compound, they always combine in the same ratio by weight. (Law of Definite Proportions)8. Elements were eventually arranged according to their atomic weights and their reactions. The result was the Periodic Table, devised by Dmitry Mendeleyev, which implied that some kind of subatomic structure underlay elemental qualities.

CHEMICAL ELEMENT - A substance that cannot be broken down chemically into simpler substances - a substance that contains only one kind of atom.

NAMES AND SYMBOLS OF ELEMENTS - Some names come from Greek or Latin words and other elements are named in honor of a person or place.

THE PERIODIC TABLE - Arranges the elements in horizontal rows,called periods, on the basis of their ATOMIC NUMBER (# of protons): Example: Cobalt (Atomic Number) 27 [ 2 ] (Symbol) CO [ 8 ] (Atomic Weight) 58.9332 [15] [ 2 ] [ = number of electrons in each orbital, beginning at top with the orbital closest to the nucleus]

PERIODIC TABLE - Continued

Each VERTICAL COLUMN in the Periodic Table makes up a related group of elements - the elements behave somewhat alike informing compounds because of the similarity of the structures ofthe atoms, particularly the number of electrons in the outer orbitals.

As chemists discovered new elements, they also learned that certain elements behaved in a similar way and the fact that elements with similar properties occur at regular intervals is known as thePERIODIC LAW.

This concept was first articulated by Dimitri Mendeleev in 1869 who stated that “ The properties of the elements are periodic functions of their atomic weights (protons + neutrons).”

Dr. Linus Pauling and the Nature of the Chemical Bond* [see http://www.paulingexhibit.org/bio/index.html]

1. 1945 a friend described sickle cell anemia. Using his knowledge ofchemistry, Pauling thought it might be caused by a defect in the redblood cell's hemoglobin. In 1948, he and his colleague, Dr. Harvey Itanoconfirmed sickle cell anemia was caused by a genetic abnormality inthe hemoglobin molecule. Pauling called this a molecular disease. Thisidea is currently the focus of human genome research.2. On November 3, 1954, Linus Pauling was preparing to address agroup of students at Cornell University (1937 Baker Lecture Series*) when news arrived that he had been selected for the Nobel Prize in Chemistry. Pauling was given the award for his work on the Chemical Bond; this is the only time the Nobel Committee has selected an individual for a body of work instead of a discovery that occurred that year. With his passport in limbo, it was unclear ifPauling would be able to travel to Sweden to receive the award. He received his passport two weeks before the award.

3. Pauling's early political talks explained nuclear fission. More and more,he started expressing the need for international treaties and the use ofinternational law to settle disputes instead of war. During the McCarthy era, many scientists who had taken an anti-nuclear stand avoided thecontroversy and were putting their efforts back into science. Paulingmaintained his stance and was investigated by the Senate committee.With continual questioning about who had influenced him, Pauling madethe statement, "Nobody tells me what to think, except Mrs. Pauling.”4. Pauling lost funding grants from the NIH and the NSF. When he askedthe NIH why he had been denied his grants, he was told to reapply under the name of his associates. The grant was reinstated and even increased.5. In 1958 Pauling wrote No More War! which discussed the threat ofnuclear war and testing. He and Ava Helen, with the support ofstudents, circulated then submitted an anti-nuclear petition to theUnited Nations, which included the signatures of over 11,000 scientistsfrom 49 countries.

6. In 1962 Pauling protested in front of the White House. That evening, he dined with President and Mrs. Kennedy. Mrs. Kennedy shared this anecdote, "When Caroline saw you out there she asked, 'What has Daddy done wrong now?'”7. On October 10th, 1963 President Kennedy and representatives from Great Britain and the Soviet Union signed the partial nuclear testban treaty that Ava Helen and Linus had championed. On that same day, the Nobel Committee announced that Pauling had won the Nobel Peace Prize for his efforts. In the Nobel Presentation speech, Gunnar Jahn, chairman of the Nobel Committee, presented Pauling with the award stating, "since 1946 (Linus Carl Pauling) has campaigned ceaselessly, not only against the testing of nuclear weapons, not only against the spread of these armaments, not only against their very use, but against all warfare as means of solving international conflicts."8. The CalTech Chemistry Department did not hold a celebration forPauling, but the Department of Biology did. Pauling felt this departmentwas more sympathetic because they better appreciated the damage done by radioactive “fallout” (nuclear radiation).

9. Pauling felt the university neither understood, nor supported, his peace activism. He left CalTech. In 1963 he joined the staff of the Center for the Study of Democratic Institutions; this allowed him to divide his interests between chemistry and world peace. 10. Pauling advocated taking megadoses of Vitamin C on a daily basis - a controversial idea that is still being researched. He died in 1994 at the age of 93.