Showing posts with label proof. Show all posts
Showing posts with label proof. Show all posts

Saturday, January 8, 2011

Knowledge, Belief, Proof, Love, & Commitment

Below are two pieces of dialogue between John Nash and his wife-to-be Alicia from the movie, "A Beautiful Mind." Use them as a jumping off point to reflect on the relationship among knowledge, belief, and proof (a.k.a. justification?).

Nash: Alicia, does our relationship warrant long-term commitment? I need some kind of proof, some kind of verifiable, empirical data.
Alicia: I'm sorry, just give me a moment to redefine my girlish notions of romance.

Alicia: How big is the universe?
Nash: Infinite.
Alicia: How do you know?
Nash: I know because all the data indicates it's infinite.
Alicia: But it hasn't been proven yet.
Nash: No.
Alicia: You haven't seen it.
Nash: No.
Alicia: How do you know for sure?
Nash: I don't, I just believe it.
Alicia: It's the same with love I guess.
Most of this last piece of dialogue can be viewed starting at the 52 second mark in the trailer at
http://www.imdb.com/video/screenplay/vi2279866649/

Monday, May 28, 2007

Dark Energy on Parade

Courtesy of Melanie Gibson...

Check out the cover story on today's Parade Magazine, titled "The Secrets of Dark Energy." Some time on Tuesday, the full text becomes available on Parade's website; clicking here will take you to it. (Yes, I will leave the blog open for comments thru the school's 3 p.m. Wednesday deadline for seniors to turn in work.)

Questions & issues to consider:

•Melanie specifically points out the following quote from the author of the article, Meg Urry:
What excites me personally is how the discovery of Dark Energy illustrates that science is not a set of beliefs that one constructs. Instead, scientists observe nature, then develop theories that describe their observations. Science is driven by nature itself, and nature gives us no choice. It is what it is.

This quote raises connections to several readings and discussion topics from this year:
A) How might the author of the reading, "Ten Things We Think We Know About Science," regard or respond to this quote? Would he say it is consistent with an accurate understanding of science, or another example of where science education falls short?
B) During the mathematics unit, we briefly touched on the question of whether mathematics are discovered or created. And for those who attended the lecture on Kurt Gödel's incompleteness theorem, the speaker raised this issue again, indicating Gödel's position on the issue. Use this quote as a springboard to compare and contrast the natures of science and mathematics to one another, particularly with respect to the philosophical question of discovered or created.
C) Dr. Urry's quote and the issue raised in B above become still more interesting when considered in light of the nature of the very close relationship between science and mathematics. Take a look back at the 3 articles we read as a jigsaw activity in class about that relationship (one article had the clever title, "Math has π on its face"), then comment on Dr. Urry's quote.

•The article is filled with knowledge claims about "dark energy" -- its impact on the universe, its place in science history, and its potential economic uses and impact. And yet, ironically, the caption to an accompanying picture of the author includes this quote, "Dark Energy makes up two-thirds of the universe -- and we don't know what it is." The article itself includes this paragraph:
But first, we have to figure out what exactly Dark Energy is. So far, we know only that it causes the expansion of the universe to speed up. We call it 'dark' because we don't directly see it. 'Dark' is code for 'we have absolutely no clue what it is!'
(Emphases in each quote added.) It seems rather ironic to have so many knowledge claims about something the author says we know so little about. What is your response to this irony? How do you reconcile these seemingly conflicting comments?

•Immediately after the quote that Melanie pointed out, Dr. Urry writes: "As new facts emerge, scientific theories can be proved wrong or in need of modification, but scientists cannot ignore them. Eventually the facts will lead to the right theory."
A) To reprise some questions I raised in an earlier post: What is a "fact?" We've spent a lot of time this year wrestling with the concepts of "knowledge," "truth," and "belief," but we've never discussed the term "fact." What do we mean by that term? What makes something a "fact?" How is a fact different from knowledge, truth, and belief? Or is it different from any one of those?
B) And as I asked about another quote above: How might the author of the reading, "Ten Things We Think We Know About Science," regard or respond to this quote? Would he say it is consistent with an accurate understanding of science, or another example of where science education falls short?

•Consider the knowledge claims contained in this quote from the article's concluding paragraph: "The answers are there, and I have no doubt that we will figure them out with the contributions of the smart young people now taking high school physics...." Consider and comment on the nature (psychological, epistemic) and intensity of the certainty expressed in that statement. What bases, what justifications do you think Dr. Urry might point to in support of her expressed certainty and knowledge claims?

Friday, April 6, 2007

Global Warming, Science, Fact, and Belief


Click here for a larger image of the comic strip.

Questions & issues that could be considered:

A) What is a "fact?" We've spent a lot of time this year wrestling with the concepts of "knowledge," "truth," and "belief," but we've never discussed the term "fact." What do we mean by that term? What makes something a "fact?" How is a fact different from knowledge, truth, and belief? Or is it different from any one of those?

B) On a related note: The first frame of the comic strip juxtaposes the concepts of "fact" and "belief." What do you make of that juxtaposition? (To see a definition, click on the word.) What is your reaction, or what thoughts does it prompt? Are the two concepts related to one another? If "yes," why and how? If "no," why not?

C) The punchline of the comic strip obviously turns on the play-on-words with the title of the Al Gore film, "An Inconvenient Truth." What are the two "inconvenient truths?" Why are they each inconvenient? If we accept the comic strip at face value, can both "inconvenient truths" be true? Why or why not?

D) Consider the ideas discussed in two of our science readings, "Science" (the reading about science as telling explanatory stories) and "Evaluating Scientific Claims." Share insights you gain by applying concepts from those readings to this comic strip.

E) Was this comic strip drawn in support of those who claim to know that global warming is real? Or was it drawn in support of those who claim to know that global warming is not real? How do you know? What is your basis for claiming to know that?

Thursday, March 22, 2007

"What Do You Believe Is True Even Though You Cannot Prove It?"

According to its website (www.edge.org), the purpose of the Edge Foundation is "to promote inquiry into and discussion of intellectual, philosophical, artistic, and literary issues, as well as to work for the intellectual and social achievement of society." (Obviously, it is not to be confused with "The Edge," the diversion on page 1 of The Oregonian's Living Section.) Each year for the past 10 years, Edge has posed "The Edge Annual Question" and published online the responses of acclaimed thinkers and scientists. The question for 2005 is a classic TOK question:

"WHAT DO YOU BELIEVE IS TRUE EVEN THOUGH YOU CANNOT PROVE IT?"
Great minds can sometimes guess the truth before they have either the evidence or arguments for it (Diderot called it having the "esprit de divination"). What do you believe is true even though you cannot prove it?
[See http://www.edge.org/q2005/q05_print.html for comments from the editor-publisher of Edge.org about the question and the published responses.]

Questions & issues to consider:

A) Keeping in mind our readings and discussions from the first part of the school year, what do you make of this question? Analyze it in terms of the concepts of knowledge, justification, truth, and belief. Is the Edge question a valid question?

B) As you think about it and analyze it, what thoughts and ideas does it spark about the relationships between those concepts (i.e. knowledge, justification, truth, and belief), as well as the concept of proof?

C) What does it mean to "prove" something? What is "proof," as it seems to be used here? What constitutes proof (and not just in a strictly mathematical sense)? How is the concept of proof related to the concepts of knowledge, justification, truth, and belief?

D) What does the question seem to imply about the nature of belief? the nature of truth? Why isn't the word "knowledge" used in the question?

[Please note that you are NOT being asked to answer Edge's question. Appropriate comments should focus on analyzing and commenting on the nature of the question and on the concepts that comprise it.]