Scientific Method & Quantitative Reasoning

The Scientific Method Systematized by Francis Bacon, Descartes and Galileo in the 17th century Not the only way of knowing, but a very successful one A method to yield conclusions that are independent of the individual Conclusions are based on observation Turtle story (Bertrand Russell?)

Francis Bacon (1561-1626) Contemporary of Shakespeare, Elizabeth I, Kepler and Galilei Rejects Aristotelianism and Scholasticism Major Work: Novum Organum (1620) (“New Tools”, the old Organum was Aristotle’s)

Francis Bacon (1561-1626) Novum Organum Title: Allegory on the daring mind: A Ship passes through the “pillars of Hercules”, beyond old knowledge.

Rene Descartes – The Rationalist Described the method to do science, known for his mind-body dualism Major Works: Discourse (1637) [full title: Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences] Meditations on first Philosophy (1641) [6 Meditations: Of the Things that we may doubt; Of the Nature of the Human Mind; Of God: that He exists; Of Truth and Error; Of the Essence of Material Things; Of the Existence of Material Things; Of the Real Distinction between the Mind and the Body of Man] Rene Descartes (1596-1650)

Rene Descartes’ Discourse Describes the method to do science in a straightforward way (see below) Major points: Science must be based on correct reasoning (logic) Science must be formulated in mathematical language Starting line: “Good sense is the most evenly distributed thing in the world, for all people suppose themselves so well provided with it that even those who are the most difficult to satisfy in every other respect never seem to desire more than they have.”

A Classical Example Aristotle observes that during lunar eclipses the Earth’s shadow on the moon is curved He assumes it will be curved for all eclipses A hypothesis that explains this: the earth is a sphere A prediction of this theory is that the location of the stars in the sky should be different for observers at different latitudes This is confirmed by additional observations E.g. Canopus is visible in Egypt but not further north It is applied by Eratosthenes to determine the size of Earth In fact Aristotle used the difference in apparent position of Polaris from Egypt and Greece to make an estimate of the radius of the earth; (probably) got about twice the currently known value

Science: Kepler finally figures out Mars’ orbit See video

Quantitative Reasoning Amazingly powerful tool to understand the world around us Fundamentals: Area &Volume Scaling Algebraic statements

Scientific Literacy An important skill to have in an increasingly complex society As a voting citizen you should know what you are voting on As a consumer you should know (or be able to figure out) what you buy Makes life more interesting Nobody knows everything, but smart people can figure out fast if something is obviously wrong moving electric charges produce EM waves EM waves move charges (radio, TV)

Achieving Scientific Literacy (Arons Article) Two types of knowledge Declarative (Learned Facts, “book knowledge”) Operative (actually knowing how to solve problems) Trouble with GenEd courses Too much in too little time Getting a “feeling” for the subject doesn’t work Need to understand the underpinnings first (area, volume, scaling, energy, atoms,…)