Conference rusure::math

>    Alpha is a 64 bit machine.  (2^64) - 1 is 18,446,744,073,709,551,615.
>    Can someone provide the units to "read" this number?
    
We call it  18 trillion, 446 billiard, 744 billion, 73 milliard, 709 million,
	   551 thousand and 615.

	Power		Dutch		Enlish/American
	-----------------------------------------------
	10^0		one		one
	10^3		thousand	thousand
	10^6		million		million
	10^9		milliard	billion
	10^12		billion		?   \
	10^15		billiard	?    \
	10^18		trillion	?     \
	10^21		trilliard	?      \
	10^24		quadrillion	?       > Can someone fill this in?
	10^27		quadrilliard	?      /
	10^30		? pentillion	?     /
	10^33		? pentilliard	?    /
	10^36		? sextillion	?   /
	etcetera ... (basic counting in Latin/Greek)

RE: .1

    The British have traditionally used the European system -- but there
    has been a move towards following the American sytem of late.  The
    traditional British scheme does not generally use "milliard" but mostly
    refers to 1000 millions.  The American system is basically a
    superimposition of a simple base one-thousand numeration scheme on top
    of the base ten scheme.  The European system uses base one-million
    instead.  The powers of 1000 in the American system go:

	1000^1 = a thousand
	1000^2 = a thousand thousand = a million
	1000^3 = a thousand million = a billion
	1000^4 = a thousand billion = a trillion
	1000^5 = a thousand trillion = a quadrillion
	1000^6 = a thousand quadrillion = a quintillion (sometimes a
	    pentillion but that is improperlly formed from a Greek rather
	    than a Latin root).
	1000^7 = a thousand quintillion = a sextillion
	1000^8 = a thousand sextillion = a septillion
	1000^9 = a thousand septillion = an octillion
	1000^10 = a thousand octillion = a nonillion
	1000^11 = a thousand nonillion = a decillion

    And so on, tacking on Latin cardinals' combining forms as needed.

				Topher

In VAX LISP V3.0-A,

Lisp> (format t "~R" (1- (expt 2 64)))
eighteen quintillion, four hundred and forty-six quadrillion, seven hundred and
forty-four trillion, seventy-three billion, seven hundred and nine million, five
 hundred and fifty-one thousand, six hundred and fifteen
NIL
Lisp>

    Man, Is'nt LISP powefull !

    Why did LISP stop format when the number got larger?
    
    /nasser
    ps. i think the congress need a LISP to help them figure how to say our
    budget deficit :-)
    
    -----------------------------------------------------------------------
    the break down happens at (expt 2 220)
    
    (format t "~R" (1- (expt 2 220)))
    ; Starting full GC ...
    ; ... Full GC finished
    1684996666696914987166688442938726917102321526408785780068975640575
    NIL
    
    
    (format t "~R" (1- (expt 2 219)))
    eight hundred and forty-two vigintillion, four hundred and ninety-eight
    novemdecillion, three hundred and thirty-three octodecillion, three 
    hundred andforty-eight septendecillion, four hundred and fifty-seven 
    sexdecillion, fourhundred and ninety-three quindecillion, five hundred 
    and eighty-threequattuordecillion, three hundred and forty-four 
    tredecillion, two hundred and twenty-oneduodecillion, four hundred and 
    sixty-nine undecillion, three hundred andsixty-three decilli
    on, four hundred and fifty-eight nonillion, five hundred and fifty-one
    octillion, one hundred and sixty septillion, seven hundred and sixty-three
    sextillion, two hundred and four quintillion, three hundred and ninety-two
    quadrillion, eighthundred and ninety trillion, thirty-four billion, four 
    hundred andeighty-seven million, eight hundred and twenty thousand, 
    two hundred and eighty-seven
    NIL
    
    

That's weird...the way I remembered it working, it used to
use "times ten to the sixty-sixth" for the next block after
"vigintillion".  I suppose someone complained about that and
it was changed.

Dan

    Thanks for the answer, and for using lisp to provide it.

    So, can LISP output in Dutch?

    This may be more a matter of grammar than mathematics, but I remember
    being taught that the use of "and" in numbers is limited to where we
    put the decimal point. For example, "three hundred AND forty two
    dollars AND twenty six cents" is wrong; "three hundred forty two
    dollars AND twenty six cents" is right. So, if that's true, the answer
    should be:

    eighteen quintillion, four hundred forty-six quadrillion, seven hundred
    forty-four trillion, seventy-three billion, seven hundred nine million,
    five hundred fifty-one thousand, six hundred fifteen.

    Dwayne

    re .3
    
In VAX LISP V3.0-A,

Lisp> (format t "~R" (1- (expt 2 64)))
eighteen quintillion, four hundred and forty-six quadrillion, seven hundred and
forty-four trillion, seventy-three billion, seven hundred and nine million, five
hundred and fifty-one thousand, six hundred and fifteen
NIL
Lisp>
    
    LISP may know its math, but what it does not know is English (or is it
    Americanish that it does not know?)
    
    The correct answer is:
    
eighteen quintillion, four hundred forty-six quadrillion, seven hundred 
forty-four trillion, seventy-three billion, seven hundred nine million, five
hundred fifty-one thousand, six hundred fifteen
    
    Alex

re last 2 ("and") ...

Yes, that's been mentioned here before (420.17).  I didn't want
editing the answer in .3 by hand to make it look like the problem
in VAX LISP had been corrected.  The correct reading requested in
the base note is as in .9 and .10.

Dan

re .10
    
>    LISP may know its math, but what it does not know is English (or is it
>    Americanish that it does not know?)
    
    Americanish, I think. In English the "and" is normal usage.

    Interestingly enough this offers an opportunity to use intergers for
    money instead of floating point format.  As a signed number with an
    implied decimal point;
    
    	92,233,720,368,547,758.08
    
    represents a large enough value to deal with almost any amount likely
    to come up in the financial world.

    RE: -.1
    
    � represents a large enough value to deal with almost any amount likely
    � to come up in the financial world.
    
    Don't count on it.  :-)
    
    Old fogys like me remember being told that a 16-bit address space was
    plenty.  "Who would ever need more than 64K?"
    
    I would not be surprised if in 20 years the U.S. deficit exceeds the
    figure stated.

>    I would not be surprised if in 20 years the U.S. deficit exceeds the
>    figure stated.

    Even without the implied decimal point, 2^64 is almost exactly the rate at
    which Hungarian peng�es were exchanged for a single new �forint� in 1946.
    
      John

    re .13
    
>    Interestingly enough this offers an opportunity to use intergers for
>    money instead of floating point format.  As a signed number with an
>    implied decimal point;
    
>    	92,233,720,368,547,758.08
    
>    represents a large enough value to deal with almost any amount likely
>    to come up in the financial world.
    
    Integers with an implied decimal have been used as a rule in financial 
    application since "time immemorial" as far as electronic computing is
    concerned.
    
    Even the lowliest 16-bit PDP-11s in the seventies had business-oriented
    operating systems that allowed up to 18 decimal digit signed arithmetic
    specificially to represent $,$$$,$$$,$$$,$$$,$$$.�� which is only
    one digit short of the above.
    
    Alex

    
    Can someone compare 2^64 to some physical things like the
    number of ATOMS that compose the earth, etc. 
    
    Jon
    

    
     2^64 ~= 18 x 10^18  
    
    "close" earth numbers:
    
    Volumn = 1083 x 10^9  cubic meter
    moment of inertia = 8 x 10^44 gram square cm
    loss of heat of earth throug radiation into space = 2.4 x 10^22 
                                                              cal/100 years
    area of land = 149 x 10^6 km square
    mass of earth = 5.97 x 10^27 grams 
    
     physical constants:
     electron charge to mass ratio = 10^11  C/Kg
     Faraday constant = 10^7 C/Kmol
     Energy mass conversion = 10^16 J
     light year = 9.4 x 10 ^15 meters
    

    there are about 5.97x 10^58  electrons in earth body, assume as
    "average" 12 electrons per an atom, there are about 5 x 10^57 atoms.
    
    

    The number of electrons and protons in the universe, according to
    Sir Arthur Eddington, is about 10^79, or roughly 2^262.

If dark matter has electrons in it, the number of electrons in the universe
is probably much much higher
tom