Interludes
Rules, Proofs, and the Magic of Mathematics
David Socher gives university students some toys with which they discover the Pythagorean Theorem.
> Make those toys and give them to individuals who are not thinking about the theorem... describe how they find the theorem.
During the Renaissance in Europe, the study of religion and natural science were one in the same. Natural philosophers sought to understand God's granduer throught studying nature and theology was a framework within which naturalists interpreted their observations. In The Assayist, Galileo took the position that the natural sciences were different from religion; and wheras religious texts were the language of theology, mathematics was the language of the sciences. In the centuries since, science and religion have been understood as human endeavors that seek to answer different questions.
> In the 20th century, a number of disputes in which the seperation of religion and science were debated in public forums (the Scopes Trial in 1925 is a famous example). Late in the 20th century, evolutionary scientist Stephen Jay Gould proposed the non-overlapping magisteria (NOMA) as a resolution to the social debates over continuing debates of this nature. NOMA was the subject of much of Gould's writing for general audiences. Do you think NOMA is a reasonable approach to avoiding potentially devisive public debates?
Crease points out that the image of Isaac Newton being hit on the head with an apple and "discovering" gravity as a result is probably just myth.
> Look over some sceince materials for children... (web sites
Crease provides examples of how equations have been used in literature and other non-mathematical contexts to illustrate points, including creating comedy.
> Create equations for similar effects: make political points... create humor... make emotional appeals; consider topics of immediate relevance and those that are timeless.
Perpetual motion machines commonly capture the imagination of the public despite being impossible (meaning their existence violates accepted scientific laws). Of course, other "impossible" things (e.g. space flight) are now common.
> Report on one of the following: an impossibility that has boondoggled the public; an impossibility that has become common; an impossibility in science fiction that you think will become common.
Overcoming Anosogosia or Restoring the Vitality of Humanities
Crease suggests that some historians have ignored the controbutions scientists have made to solving problems of social importance.
> Review the discoveries for which Nobel prizes in the sciences were awarded over the last 30 years. Do you conclude these problems had social relevance or not?
Science has a strange relationship with crazy ideas: as scientists we demand "extrordinary evidence" for "extraordinary claims," and we reject the nul hypothesis only when we are 95% sure of our conclusion, but ours is a history full of revolutionary ideas that were "crazy."
> What is a crazy idea you have? What would happen if it were either true or accepted?
Crease points to others who have suggested science is in need of critics to help the general public interpret and understand scientific discovering and the meaning of those discoveries on their lives. Critics are portrayed as playing an important role in educating the general public rather than the scientific community.
> What scientific discoveries are important in your community at this time?
The Double Consciousness of Scientists
Scientists are humans who are affected by all of the factors that affect other humans in their judgements of information, beliefs about priorities, and demeanor in interpersonal relationships.
> Richard Feynman was a20th century physicist. In a video called "The Pleasure of Finding Things Out" (there is a collection of essays with the same title that included an essay with the same title), Feynman comments on how these fators affected him as a scientist.
One of the difficulties in comprehending the Heisenberg Uncertaintity Principle is the "semi-abstractness" of the idea. Whereas classic mechanics deals with physical objects or idealized concepts (like frictionless planes), Heisenberg conceptualized phenonema that are neither of these and that our inability to conceptualize these phenonema interfere with our ability to understand them.
> Some thinkers (typically thinkers whe are identified as psychologists or educational theorists) propose metaphors as a tool that help humans build concepts of unfamiliar ideas. (The reasoning is that metaphors help us build copnnections between what we know and what we do not know.) Use a metaphors to build connections to explain something.
The equations presented in the book were not defined in isolation. The scientists were working in rich milieu of sociocultural influences, and the equations affected the evolution of the sociocultural context that came later. Crease tells the story of describing the book to an "old scientist" who concluded the equations are tirvia.
> Are these equations "great" as the title of the book suggests or "trivia" as the old scientist suggests?