Homework 1

Reminder: You can (and are encouraged to) discuss problems with your classmates. Then write down the answers by yourself.

1. Find a quotation that includes a definition of mathematics (for instance, one from the first week slides or one that you found) and explain what you think it means. Discuss whether it agrees or not with your own defintion of mathematics.
2. Say there is pile of pencils on a table. You are given a (small) number and you have to grab this number of pencils without actually couning. What is the maximun number of pencils that will work for you? (Ralph Waldo Emerson wrote about Thoreau "From a box containing a bushel or more of loose pencils, he could take up with his hands fast enough just a dozen pencils at every grasp.”) Do not overthink this question, it is as easy as it sounds. Keep in mind that there is only one Thoreau, The point is to think about the maximum number of objects one can count in one sight; later we will relate this number to certain number symbols.
3. Days and years are both units of time. A year about 365 1/4 days long, in other words the ratio between a year and a day is about 365.4. How people originally were able determine how many days there are in a year? Discuss whether a calendar is needed by each of the following societies (of about fifty family each) and whose main economical activity is
   1. hunting, fishing, and gathering vegetable food.
   2. following a migrating reindeer herd
   3. tending a herd of domestic animals
   4. planting and tending crops.
4. Why counting was necessary for each of the societies listed in Problem 3.? List at least two reasons. Unleash your creativity.
5. 1. Create a hypothesis as to the meaning of the scratches on the Ishango bone or why they might have been made. Be creative. The only requirement is that your hypothesis matches the pattern exhibited in the bone.
   2. Discuss whether your hypothesis fits with what we know of math history at that point.