Subject: Re: LISP - 2 exponent 0 = 1 From: Erik Naggum <firstname.lastname@example.org> Date: 18 Sep 2002 00:58:33 +0000 Newsgroups: comp.lang.lisp Message-ID: <email@example.com> * Brad Miller | Math is a formal system No. Math is being able to see patterns and think in terms of abstractions that focus on the patterns and discard everything else. The result is a massive formal system that has grown in size and complexity with tremendous speed over the past 400 years or so. But mathematics starts with looking at a box of a dozen apples and see the number 12, at a crate of a dozen boxes and see the number 12, at a truck that holds a dozen crates and see the number 12, and then realize that there are 144 boxes and 1728 apples without ever counting to more than 12 because you worked this out by putting three matches each in three matchboxes, and then you repeated this thrice and put the three sets of three matchboxes aside and noticed that you had used up 27 matches and 9 matchboxes. Mathematics is watching something move at 1 foot per second and noticing that after 5 seconds, it had traveled 5 feet, then watching something accelerate at 1 foot per second per second and noticing that after 5 seconds, its speed was 5 feet per second and that it had traveled 12.5 feet and that in both cases the distance traveled was the area under the graph of its speed. Mathematics is noticing that two marbles can be laid out in two patterns, three marbles laid out in three times the two patterns of the two marbles and reason that the number of patterns is the product of all the whole numbers from 1 to the number of marbles. Mathematics is watching a yardstick rotate around one end to describe an area that is half as large as its circumference and that the relationship to the length of the yardstick is a constant that is present in circumferences, areas, and volumes of all things circular. If you think mathematics is only the formal system that describes these discoveries, you have missed out on all the exciting discoveries. | and you should be good with reasoning over formal systems. You should be good at finding the relevant and ignoring the irrelevant aspects of things that are vastly different, yet still similar in some ways. -- Erik Naggum, Oslo, Norway Act from reason, and failure makes you rethink and study harder. Act from faith, and failure makes you blame someone and push harder.