Conference rusure::math

million, billion, trillion, quadrillion, quintillion, sextillion,
septillion, octillion, nonillion, decillion.  I've forgotten what
comes next.

    undecillion, duodecillion, tredecillion, quattuordecillion,
    quindecillion, sexdecillion, septendecillion, octodecillion,
    novemdecillion, vigintillion 
    
    centillion
    
    
    				-- edp

    Re .2:
    
>    undecillion, duodecillion, tredecillion, quattuordecillion,
>    quindecillion, sexdecillion, septendecillion, octodecillion,
>    novemdecillion, vigintillion 

    googol
    
>    centillion
    
    googolplex
    

    --  Barry   ;^)

BTW, the (10? 12?) theatre complex in Perth Amboy, NJ visible on the east
side of the Garden State Parkway just south of the Raritan River bridge is
popularly known as the Googolplex by at least one group of NJ hackers.

An example of proper usage:

"
X: Let's go see Star Trek IV.
Y: OK; where's it playing?
X: It must be showing at the Googolplex, let's go there.
"

Told to me by Michael J. Aramini.
				/AHM

I seem to remember there is also ANOTHER system of naming large numbers, which
is different than the American system. I think the difference is that new names
are given every SIX additional decimal zeros (rather than every THREE).

Anyhow, the common name for 10^9 over here is "milliard".

Nitsan.

> Anyhow, the common name for 10^9 over here is "milliard".
    
    Does that make 10^12 a "billiard"?

      John :-)

No, 10**15 should be a billiard. 10**12 is a billion (unless you are a Yank,
in which case it is a trillion)

The two systems are a bit confusing to non-Yanks. I always thought, and will
continue to believe, that the English system makes more sense. Unfortunately
here in Oz we tend to go the other way...

   Name             English              American

million              10**6                10**6
billion              10**12               10**9
trillion             10**18               10**12
...                  ...                  ...
<prefix>illion       10**(6*prefix)       10**(3*(prefix+1))

where <prefix> is the Latin/Greek prefix value (m for mono-, bi-, tri-, etc.)

10**9 is a milliard in most of Europe, but in England I'm pretty sure it's
just a thousand million. The upshot of all of this is that large numbers
should just be expressed as their log, or in scientific notation. There's
not much use for a googol and beyond, as it is generally agreed (except
maybe by creationists :-) that the number of elementary particles in the
universe is about 10**80.

= Giles =

Re:    "No need for numbers beyond gooplex since only 10**80 particles
	in universe"


Yeah, but, if we're talking about how many ways those particles can
arrange themselves, or how many different objects (partitions of the
particles) are possible, and then more if varying over time, etc.
then, yes, we still need large numbers.

/Eric

    So what's the biggest number we need?
    
    (Assuming a fixed lifetime for the universe).

      John

	10**200 ?

	I have used 200 digit primes in a crypto system.

Assuming there are several ways to name/describe every number in English (for
example: 21 is "twenty one" or "the integer that follows twenty" or "three
times seven" etc.), then there is a limit to the amount of numbers one can
describe with K words (we have a final set of words!).

So take the largest number that can be described with twelve words, plus one.
This number ofcourse cannot be described with twelve words, or can it? I just
did it! it's "the-largest-number-that-can-be-described-with-twelve-words-plus-
-one". You may count the words in its description...

How do you solve this contradiction?

>Assuming there are several ways to name/describe every number in English (for
>example: 21 is "twenty one" or "the integer that follows twenty" or "three
>times seven" etc.), then there is a limit to the amount of numbers one can
>describe with K words (we have a final set of words!).
>
>So take the largest number that can be described with twelve words, plus one.
>This number ofcourse cannot be described with twelve words, or can it? I just
>did it! it's "the-largest-number-that-can-be-described-with-twelve-words-plus-
>-one". You may count the words in its description...

Alternatively, what about "the smallest number NOT nameable in fewer than 
nineteen syllables"? This is even stronger, as it is not impacted by our 
ability to create new words out of old ones, as is common in German.

In either case, these are examples of [Bertrand] Russell's Paradox, which 
he resolved (at least to his own satisfaction) by his "theory of types",
which limits the number of ways in which a statement can be 
self-referential and still be said to be meaningful. Douglas Hofstadter's 
book, "Godel, Escher, Bach" deals with self-reference a lot.

    re .3
    	Isaac Asimov has pointed out (in Adding a Dimension) that the
    proper name for 10^100 is ten duotrigintillion (American system).
    
    re .7
    	Other noters have pointed out that extremely large numbers are
    still needed beyond that which comes up in physics, some good examples
    are probability (number of shuffles of a Canasta deck far exceeds
    10^100), DNA is believed to have 10^2,400,000 variations, and finally
    in mathematical proofs there are numbers such as the one discovered
    by a South African mathematician (Skewes) 10^10^10^34.

     The VAX LISP built-in number speller agrees with .3; it
     spells successive powers of 1000 as:

          thousand
          million
          billion
          trillion
          quadrillion
          quintillion
          sextillion
          septillion
          octillion
          nonillion
          decillion
          undecillion
          duodecillion
          tredecillion
          quattuordecillion
          quindecillion
          sexdecillion
          septendecillion
          octodecillion
          novemdecillion
          vigintillion

     Above that it reverts back to digits.

     Dan

     
    
      The number "googol" is 10 to the hundreadth power, or 1 followed
    by 100 zeros.
                                        Len.

    A slghtly bigger number is googolplex, which is ten to the power
    googol.

    even bigger:
    
    
    		Gigagoogolplex.

    How many RA82s (~1216000 user blocks available) would it take to store
    the binary expansion of googolplex factorial?
    
    (Extra credit) Assuming 100% efficiency converting the sun's energy
    into electricity, how much of the sun's energy would we need to power
    that many disk drives?
    
    Lots of other questions are possible, like what volume would that many
    disks occupy (solar system size?  galaxy size?), how many light-years
    of cabling would be required?  How much time would a backup take?  Etc.
    
      John

If I recall correctly, Eddington estimated the number of protons in the 
universe at 10^237, so even googol^3 is well beyond the range of anything 
physically realizable. Goolplex is a reasonable unit for measuring ways in 
which the physical universe can be permuted, but there is not enough room 
to write such numbers down.

	I thought the estimate on the number protons in the universe
	was about 10^80.

	Dan

    You forget -- the universe has expanded since then :-)
    
    Besides, since when does pure mathematics confine itself to the limits
    of the physical universe?  Shall we prove FLT only for numbers worth
    bothering about?