Blogtrek

Out of range

Numbers are getting out of their range. That is, numbers are wandering into the next higher range. The ranges are defined on my Hamlet page. What numbers not getting out of range means is that budgets can be billions of dollars but not googols. Here are some examples of why numbers don't get out of their ranges, one for each range boundary:

1. A committee of 1,500 can't get the job done.

2. If you sue for $30 trillion, you will never collect.

3. A googol or more years is preposterous - that's more years than there are elementary particles.

4. Disk drives are getting too big - the numbers of their possible states are inconceivable.

5. Logicians try too hard to define huge ordinal numbers and hence finite numbers. They can never exceed W, defined as the largest number that we will ever be able to define (notation due to Rudy Rucker).

Recently, however, numbers are getting out of their range. I mentioned earlier that my home disk drive should have a literary number of possible values, as the sequence of characters can be or could be a literary work. But my current disk drive is 80GB, putting the total number of configurations in the inconceivable range instead. Now I hear that 9/11 families are suing rich Saudi families for $1 trillion. This is 100 trillion pennies and so comes close to being a scientific (a quadrillion or above) number instead of a statistical number (between a thousand and a quadrillion). Can they ever get that much?

There's a good reason why in our common life we almost never have numbers much greater than one quadrillion: 1,000,000,000,000,000. The total worth of the world is probably about $10-50 trillion, or in the early quadrillions of pennies. Objects that we meet in our lives, such as cars, buildings, hula hoops, gold necklaces, space shuttles and so forth, have to have a net worth less than that of the entire world, and to measure worth, we need at least a penny, which is coming close to being worthless nowadays. The worth of all these objects must therefore be less than a quadrillion of units we can perceive. This is why we see trillion a lot in our everyday lives, but not a quadrillion.

Numbers rarely get out of their ranges. I will never be able to use all of my disk drive, and the 9/11 families will never be able to collect all that money.