Exploding Dots and Base Ten: Unraveling the Fascination
Delve into the realm of Exploding Dots, where the magic of base ten captivates us. Explore wild machines, count on one hand, uncover codes, and ponder different cultural numeral systems. Why is 10 so appealing in counting and arithmetic? Discover the mysteries behind English names for numbers and other numerical wonders.
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Presentation Transcript
ADVENTURES IN EXPLODING DOTS: Exploration 2 WILD MACHINES A focus on base ten and why we humans are drawn to it.
Recall the ? ? Machine Recall that a 1 2machine is just a row of boxes extending as far to the left as we please. One places dots in this machine always in the rightmost box and the exciting part is that: Whenever there are two dots in a box, they explode and disappear KAPOW! to be replaced by one dot, one box to the left. KABOOM!
Recall the ? ? Machine For example, putting six dots into the box either all at once or one at a time eventually leads to the 1 2machine code 110.
Recall the ? ? Machine Hours of fun can be had working out the 1 2machine codes for numbers. Last time we performed a mind reading trick with these codes.
Counting on One Hand Count to 31 on one hand! Challenge: Count to 1023 using two hands!
The ? ? Machine In a 1 3 machine, three dots explode and disappear KAZIPP! to become one dot, one place to the left. Find the 1 3 machine codes for the numbers 1, 2, 3, 4, 5, 6, and 13!
The ? ?? Machine Here s a 1 10 machine. Let s be extra crazy and put in 273 dots in it. What is the 1 10 machine code for the number 273?
Other Cultures Many cultures on Earth used a base ten system. Why do we humans think that 10 is a good number to use in matters of counting and arithmetic? Some cultures used base twenty. Why 20? How does the Gettysburg Address by Abraham Lincoln begin? How do you say 87 in French? Some cultures used base twelve. Why 12? Martians happen to have three fingers on each of two hands. What base do you think they would say is natural and right to use?
English Names for Numbers English names for numbers reflect base 10, base 12, and base 20!
Web App Here s a web app that allows you to play with all the machines. https://www.explodingdots.org/station/OpenMachinesInsighto
Another Mind Reading Trick Here s another mind reading trick. It is based on the following six groups of numbers. Arisu is thinking of a number between 1 and 26, and says his number appears in groups A, C, and F. The mind reader correctly identifies his number as 22. Suzzy says her number appears in groups B and E. The mind reader correctly declares it to be 11. What do you think the mind reader is doing to identify numbers? There is an Exploding Dots machine behind-the-scenes here. Which one? Write out codes for the numbers 1 through 26 in this machine and see if you can explain the trick.
Another Mind Reading Trick Can you devise an interesting mind reading trick based on a 1 4 machine?
