Note: I found this of interest only because I do not understand a word of it! lol I read it in a science magazine.
h2.
Physical Reasoning: Baking Cookies Problem
Characterize the following:
When baking cookies, after you prepare the cookie dough, you lightly spread flour over a large flat surface; then roll out the dough on the surface with a rolling pin; then cut out cookie shapes with a cookie cutter; then put the separated cookies separately onto a cookie sheet and bake.
What happens if: You do not flour the surface? You use too much flour? You do not roll out the dough, but cut the cookies from the original mass? You roll out the dough but don't cut it? You cut the dough but don't separate the pieces?
What happens if the surface is covered with sand? Or covered with sandpaper? If the rolling pin has bumps? or cavities? or is square? If the cookie cutter does not fit within the dough? What happens if you use the rolling pin just in the middle of the dough and leave the edges alone? If, rather than roll, you pick up the rolling pin and press it down into the dough in various spots? Ordinarily the cutting part of the cookie cutter is a thin vertical wall above a simple closed curve in the plane; suppose it is not thin? or not vertical? or not closed? or a multiple curve? If the cuts with the cutter overlap one another?
Does the dough end up thinner or thicker if you exert more force on the rolling pin? If you roll it out more times? If you roll the pin faster or slower? Do you get more or fewer cookies if the dough is rolled thinner? If a larger cookie cutter is used? If there is more dough? If the cuts with the cutter are spread further apart?
What is the point of placing waxed paper on the surface? What happens if the above procedure is tried with a recipe for drop cookies? bar cookies? refrigerator cookies?
h2. some people have their own language:
statement notation terminology
___________________________________________________________
p and q p /\ q "conjunction"
p or q p \/ q "disjunction"
p implies q p => q "conditional"
negate p ~p "negation"
p if and only if q p <=> q "if and only if"
either p or q (not both) p _\/ q "exclusive or"
Notation: Let S and T be sets. Assume that S is contained in a set X.
statement notation terminology
___________________________________________________________
set of elmts in S and T S intersect T "intersection"
set of elmts in S or T S union T "union"
set of elmts in S or T (not both) S Delta T "symmetric difference"
elmts in X not in S S^c "complement of S in X"
S is a subset of T S subset T "subset"
Logic/set theory analogs:
set theory logic
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sets statements
union or
intersection and
subset implies
symmetric difference exclusive or
equal if and only if
Venn diagrams truth tables
Erno Rubik, the creator of the cube, became an overly rich man from his ingenious creation, but remained-as a colleague remembered him: "a bit sour". Tibor Laczi, a business associate, said when he first met him, "When Rubik first walked into the room I felt like giving him some money. He looked like a beggar. He was terribly dressed, and he had a cheap Hungarian cigarette hanging out of his mouth. But I knew I had a genius on my hands."
After Rubik's success having returned from a conference in the Unites States, Laczi said, "It was his first trip to the West, and he didn't ask me to take him anywhere after the press conference. Most Hungarians that come here want to look at shops or buy jewelry or visit a bar. Rubik went back to his hotel. He was always that way, even after the money started.
He never liked to be away from his family for long or spend money on himself. The only thing he did was start smoking better cigarettes. There was no drinking, no excitement--he just went back to his hotel room to read. He was always in another world. I really do like Rubik, but I can't imagine having a real friendship with him.
He doesn't enjoy talking."