Friday, August 22, 2014
Heap, Zillion, and Bandwidth
Define the “Heap” as the first boring number; that is, the first number without features of any interest to you. Surely there must be a first such number, for you cannot be interested in every number, as there are infinitely many, and attention is finite.
But surely being the first boring number is interesting! Defining the Heap clearly would create paradox; for a number fitting any clear definition has at least one interesting property. The Heap is fuzzy; it’s where your mind slips a gear, so your mind can’t tell you where it is.
Now consider the “googol”, defined by young Milton Sirotta to be 10^100. He then defined the “googolplex” to be “10 ^ until your hand gets tired”. He and his mathematician uncle Edward Kasner decided to change that to 10^googol; but the original definition really is 10^Heap.
So define a Zillion as 10^Heap. But then Heap = 10^what? What to call the logarithm of a Heap? I propose the “Bandwidth”; meaning the number of digits needed to name every interesting number.
Zillion = 10^Heap.
Bandwidth = log Heap
A zillion is a number too big to accurately compute with, for it has too many digits to hold your interest; and the bandwidth is how many digits your system needs to process every number that interests you. A zillion is beyond the mind, the bandwidth is the size of the mind.
Thursday, August 21, 2014
Schlimbesserung and Cyber-Cascade
“Schlimbesserung” is a German word meaning an improvement that does not improve. Awhile back I experienced schlimbesserung and a cyber-cascade.
It started, as usual, with slow internet. We decided that the router was too small for our three computers, so we got a new one. Alas, Hannah’s machine couldn’t log on to it because it needed Windows 7 or up, and her hand-me-down computer had Windows XP, and couldn’t upgrade. So we needed a new CPU with a new operating system, to interface with the new router!
This was done, but alas, her new computer had new glitches. We called in a computer tech, who fixed up the glitches; but he also offered to upgrade our other two computers to…
… wait for it…
… Windows 8!
Well, my computer had been plagued by unblocked ads, as had Sherri’s, so we foolishly said yes. It took him hours, and us $100, to do the reinstall. After a rocky start I got my system going more or less as before. Ads are blocked, and it is stabler, but I lost the chess game. I let it go; that game was a time-sink. So now I have less of a computer, but a better one.
But poor Sherri lost all of her bookmarks.
This illustrates Hellerstein’s Cyber-Warning:
Installing new programming isn’t like a meal; it’s like surgery.