The test is open-everything with the sole limitation that you neither solicit nor give help while the exam is in progress.

1. Back in the day many scientists "believed in" phlogiston, the ether, and Élan vital. All turned out to not exist. Today physicists talk about dark matter and dark energy even though they admit not knowing exactly what these things are. How, though, are dark matter and dark energy different from the three proposed substances mentioned above? Why do we not speak of "belief in" or "faith in" dark matter and dark energy? What is different here?
2. Why do people say the speed of light is a constant, when we know light travels at different speeds through different media?
3. How might David Hume have phrased his principle of empiricism if he had known about relativity?
4. Why can't the frequency interpretation of probability serve as a counterargument to Hume's claim about induction?
5. Consider the following argument:

   Everything that has a beginning in time has a cause
         The Universe has a beginning in time
   ---------------------------------------------------
              The Universe has a cause
   

   This is a valid argument. Is it deductive or inductive? Can we conclude, therefore, that the Universe has a cause? Why or why not?
6. Express in logical notation: Juliet believes that Romeo believes that Juliet Believes that all Capulets might one day be rich or landless.
7. How does one prove a universal negative? That is, if you were asked to prove ∀x.~Px (for all x, Px is false), how would you do this? It would appear reasonable that trying to do this by examining every x in the universe and showing that P does not hold for x would take too long.
8. A test for a disease affecting 0.01% of the population is 95% accurate. You've just tested positive. What is the probability that you have the disease? Derive your solution using Bayes' Theorem. Solve the problem like a baus probability expert.
9. The character Pinocchio was said to have been punished so that his nose would grow after telling a lie. If he utters the statement "My nose will grow now (in response to this statement)" we have the Pinochio Paradox. Explain this very, very briefly. Now that you understand this paradox, you can create your own. The next time you pick up an old lamp and release a genie that is willing to grant you a wish, you can make a wish that will, well, it's um, like the Pinocchio paradox. What is the wish?
10. Given the grammar

    Sentence    →  NounPhrase VerbPhrase
    NounPhrase  →  Determinant? Adjective* Noun PrepPhrase*
    VerbPhrase  →  Verb
                |  Verb NounPhrase PrepPhrase*
                |  Verb Sentence
    PrepPhrase  →  Preposition NounPhrase
    

    show that the following two sentences "Teacher strikes idle kids" and "I saw the girl on the hill with the telescope" are both ambiguous. To show ambiguity, draw two parse trees for each sentence.

    In the grammar notation, ? means optional (zero or one), * means zero or more, and | means "or".

11. Consider the orbit defined by the generating rule x → x * x. What happens if the initial input to this rule is 1? What if the initial point is nudged ever, ever, so slightly to 1.000000000000001? Does this mean the system is chaotic? Why or why not?
12. Give an example of where a scientific understanding of a process or thing enhances the beauty or awe of that thing (other than those used by Feynman — the flower as an elegant system, and the universe as galaxies unfathomably far apart and not just points of light on a dome). What reasoning accounts for the fact that some nonscientifically literate people accuse scientists of not seeing beauty?
13. Several studies have shown that, for simple tasks that people can do, like pushing a left or right button, FMRI scanners can predict what decision a person is going to make several seconds prior to the person being consciously aware of that choice. To many, these studies invalidate (prove the illusory nature) of free will. But this does not follow. Why is free will still possible, even if these studies are proven 100% accurate? (Hint: think about why the results of these studies are not surprising.)
14. Is Severus Snape real?
    Is "Severus Snape" real?
    Is Snape Snape Se-ver-us SNAPE real?
15. So, thoughts are not words, it seems. And we know the difference between use and mention. Now here's your chance to be creative. Draw a picture of Wednesday. Note that I did not say "Wednesday." I don't want you to draw a picture of the the word "Wednesday"; rather, you need to draw a picture of Wednesday. Don't use any letters; the picture has to get across the concept of Wednesdayness to English and non-English speakers alike. You may assume they know what Wednesday (or среда or Onsdag or miércoles, etc.) is.
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    

    I have spent no more than 2 hours on this exam and did not solicit any answers:
    
    
    

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    Name                                              Date