Day 08, MAT115

• You have an assignment due today.

• I hope that you've had a chance to read Location, Location, Location (p. 35) in our text.

• You have a new reading assignment for next time (available from the assignment page). It's an on-line reading.

Question of the Day: What is this table, and how does it work?

• Babylon, then (source)
• Babylon, today

• the Babylonians and place value?
• the purpose of the table?
• the Babylonian's missing number(s)?

How would the Babylonians write these numbers:

1. 3600
2. 573
3. 14001

1. How cumbersome are the Roman numerals! How would you write your own birth year?
2. "biology is deeply embedded" in number systems (10 "digits" in our system; tallies of 5; 5 and 10 in Roman numerals; 10 in Babylonian; 5 and 20 for the Mayans)
3. Babylonians based their system on
4. We need no new symbol for 10 in our arabic numerals: we use only the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -- and place value (hence the name of the chapter: "location, location, location").
5. Place value suddenly makes arithmetic possible. "Just master a few facts", our author says.

   My own musing: it's interesting that we seem to be abdicating our arithmetic to machines. Many educated people can't do arithmetic anymore....

6. The unsung hero is the digit 0 -- a symbol for nothing! (The Babylonians can't distinguish the numbers 1 from 60, without some additional context.)
7. Binary, or base 2 math: a place-value system with just two symbols, 0 and 1. Perfect for computers....
8. Cornell built the first telegraph line (Baltimore to Washington, D.C.): 1844. I know that the telegraph displaced the pony express, which only ran for one year, at the beginning of the Civil War (1860-1861).

This system is based on only two symbols, with a position, or place value. (Dit is "dot"; Dah is "dash".) Notice that in graphic above, you can see how long it will take to key a particular letter or number by its length.

How do you say "SOS" in Morse code?

How do you tap it out?

"If the duration of a dot is taken to be one unit then that of a dash is three units. The space between the components of one character is one unit, between characters is three units and between words seven units. To indicate that a mistake has been made and for the receiver to delete the last word, send di-di-di-di-di-di-di-dit (eight dots)." (source)

Look at right, for the pattern in the digits of our number system. Isn't 0 out of order? Everyone's got a problem with zero! (Except the Mayans....)

Maybe this table makes the pattern a little clearer (I'll put the number zero on both ends). Think of 1 as a dot, 0 as a dash. Then: