Are those number accurate to 15 decimal places or 16:)

it's amazing that it's pretty easy to imagine numbers that are greater than all of the little-itty-bitty things that actually exist.

You've a better imagination than I:). The other day I was playing with Othello, and worked out that on an 8x8 board there are 3^63 possible positions. My first thought was that if I could represent each board position using 128-bits, I might be able to compile a complete compendium of all possible board positions--till I did the math!

3^63 = 1.144561273^10 = 1_144_561_273_430_837_400_000_000_000_000

But just how much storage would that require? Assuming 16 -bytes per board, if I packed them onto 73MB CD's with no overhead for the file system, then it would take

59_810_339_179_409_363_000_000 cd's.

A lot for sure. More than exist, or ever probably will, but it's still just a number. So I tried to take this a litte further, and the best I could come up with was that, assuming there are a nice round 6 billion people on the Earth, then it would require every person on Earth to have 1662 CD's, for every other person on the Earth, to be able to hold all those board permuations.

Now, I'm not entirely sure that all the math in there is correct, it could be out by a magnitude or two, but it was sufficiently accurate to convince me to try a different approach:)

I got in the habit of trying to visualise such numbers very early on. My last year of Junior school, age 11 (I've no idea how that translates into US style grades), we were learning about Napier's Bones, logarithms and stuff, and the teacher told us the old riddle about 1 grain of rice on the first square of a chess board and 2 on the second etc. He then had us weight 1 ounce of rice each and count the grains, and average the counts. Then we calculated the total number of grains, and from that the weight, and from that the volume, and discovered that it would fill the school hall that had a 20 ft high ceiling and was capable of seating 500 kids.

Needless to say, I never forgot the experiment, nor the power of the visualisation, but trying to wrap my brain around just how much larger 10^83 is that 10^30 I cannot even begin to see a way:)