Science Forums 2

[Turtle]

___Hello again. See here on the ground I have filled in the box lids, added a label to the third row, & as promised, listed some squares & some of their transforms under K. Now I scratched a table in the cave floor with a stick rather than use boxes again for the squares; see that it is only a change in abstraction. Before I ask you to fill in the rest of the squares table for K(n), (I see some of you already have), I want to point out some things about my original first three rows of boxes.
___No matter to what degree or extreme of abstraction, we are really talking about quantity, i.e. how much of something. It's just a matter of efficiency to use the symbols; we simply can't carry all those rocks! As long as you see how my abstraction, the K function, truly represents some qualities of count, we can do away with the rocks. Moreover, because the K function truly represents the same quality of count as the modulo function, we can for the time being set it aside as well.
___I mentioned efficiency & in this venue, the K function is far more efficent than the modulus. Take this number:333,435,686,792,008,566,344,780,128. Now quickly, with pencil & paper, tell me what is the value of that number modulo 9? .......... Times up: it's 4. You see, I needed just 20 sec to sum those digits. I didn't use paper or pencil. Right then; off you go on your own then again until next time.