Bring Back the 80's!

A number called Bob

I was reading slashdot and came across this article / book review about a number called "omega" by it's author.

It's some number that's so big that it can't be talked about, or some such. I think that sounds silly, since talking about it defeats the purpose.

But it reminded me of a math puzzle I invented in College, which is more pedestrian and less of a catch 22.

Imagine the smallest integer that has never been directly expressed by an equation (such as 10^100^100 = google-plex) or written out or refered to explicitly even by a computer. That's a much more timid feat than "irreductability" or whatever the article mentioned, as the number in question probably *can* be easily expressed, even written out in decimal form.. it just never has had the honor so far.

Of course finding such a number and writing it out, or refering to it with an equation would be futile, as you would ruin it by definition, but all I am interested in is.. how many digits would such a number have?

So I got tired of saying "such a number" all the time, and decided that the number must exist and I'd name it. I call it Bob. Furthermore, the number of digits Bob has would be called Lbob. The goal of the puzzle is to determine the exact value for Lbob; or as exact as you can.

One thing I have been able to determine is that Lbob itself almost certainly has 2 digits (eg, LLbob = 2) and I've made some reasonable guesses at upper and lower bounds for Lbob. I'll let you lot weigh in with your thoughts on the subject.

Finally, I figure that if I can't get the government to fund my Lbob research, I might seek corporate sponsership with Enzyte.

Posted by jesse at June 15, 2004 10:50 PM