Adam's Gold

Carl Friedrich Gauss had two sons and a daughter by his second wife 
(Minna).  The oldest of these was Eugene, born in 1811.  It seems that
Eugene was the most intellectually gifted of all Gauss's children, 
but despite this (or because of it?) relations between them were very
poor.  According to one of Eugene's sons (Charles Henry)

  Grandfather did not want any of his sons to attempt mathematics,
  for he said he did not think any of them would surpass him and 
  he did not want the name lowered.  Probably he felt the same in 
  a measure of any other line of scientific study.

Whatever the reason, Carl was determined for Eugene to study law, but
the boy disliked the subject, and spent much of his time at school 
gambling and drinking.  He fell into debt, and was forced to ask for 
his father's help, but Carl refused.  As Eugene's son Charles Henry 
later told it

  This decided Father, and without bidding the family good-bye
  or making any preparations for his journey, he left home, 
  purposing to come to America.  Grandfather [CF Gauss] learning
  of it, followed him and urged him to return, at the same time 
  telling him he had brought his trunk and if he was determined 
  to seek his fortune in the New World, he would furnish him 
  with funds for the journey.

It was certainly thoughtful of Gauss to bring along the lad's trunk
(presumably packed with his belongings), just in case he was unable 
to persuade Eugene to stay.  William Henry went on to say that his 
father and grandfather "parted on good terms", but most scholars have 
reached a different conclusion.  Eugene's departure occurred in 1831,
the same year in which Gauss' wife Minna finally passed away after a 
prolonged illness.  In November of that year Gauss wrote to a friend

  What depresses me so much is the relation to the good-for-
  nothing in America who has brought shame on my name.

When the "good-for-nothing" Eugene arrived in Philadelphia with no 
money and no prospects, he enlisted in the United States army, and 
was sent off to the furthest outpost of civilization at that time, 
the recently constructed Fort Snelling, in what is now the state of
Minnesota.  The fort had recently been commanded by Zachary Taylor,
who later became the US president (only to die in office just 18
months after his inaguration), and among the officers at the fort 
was Jefferson Davis, later the first (and last) president of the 
Confederate States of America.  (Interestingly, one of Taylor's
daughters married Davis, but she lived for only three months after
the wedding.)

Once while Eugene was stationed at Fort Snelling an officer found
him drawing with chalk on the barracks floor, surrounded by a few
of the other enlisted men.  Earlier in the day one of the drill
sergants had instructed the men on how to "march obliquely" by
making diagonal steps of a prescribed length (say, 20 inches).  To
specify the required angle, the sergant said the foot should be 
placed a certain distance (say 18 inches) forward and a certain
distance (say 9 inches) to the right.  Eugene was explaining to the
men by means of a Pythagorean triangle drawn on the barracks floor
that the sergant's instructions were inconsistent, because the 
hypotenuse of a right triangle with sides of 18 and 9 inches is 
20.1246 inches, not 20 inches.

At some point the commanders learned that Eugene Gauss spoke French 
fluently, and began using him as a translator when dealing with the
French travelers that passed through the area.  Eventually he was 
put in charge of the post library.  After his discharge from the 
army, he worked for the American Fur Company in the territories 
now occupied by the mid-western states of Wisconsin, Illinois, and 
Missouri.  It is said that he learned to speak the language of the
Souix Indians fluently.  (Apparently he had inherited his father's 
facility for languages.)

It was also during this time that Eugene evidently encountered a
Frenchman named Nicollet.  (Residents of modern Minneapolis are
familiar with Nicollet Avenue and Nicollet Island.)  Joseph Nicolas
Nicollet (1786-1843) had been a mathematical prodigy as well as
a noted astronomer, but financial problems forced him to leave
France in 1832.  He went to America and led several expeditions
to explore the territories of what is now Minnesota and the Dakotas.
Eugene mentioned having met Nicollet in a letter to his father 
[C. F. Gauss], who wrote back (in 1845) saying he knew of Nicollet's
early work, and judged it to be "not without merit" (uncommonly high 
praise from Gauss).  Interestingly, the elder Gauss had also heard 
that Nicollet had published a "clownish" article in an American 
newspaper "about truly absurd discoveries which he alleged Herschell
had made at the Cape of Good Hope".  This is clearly a reference to
the famous "Moon Hoax" published in the New York Sun in 1836.  The
hoax consisted of a series of increasingly outlandish articles 
claiming that the famous astronomer Sir John Herschell (1792-1871,
son of William Herschell, the discoverer of Uranus) while in South
Africa had constructed the world's most powerful telescope, and had 
sighted a variety of living creatures on the Moon.  Eventually one 
of the newspaper's employees admitted to having perpetrated the hoax,
but modern accounts often speculate that the articles themselves were
written by Nicollet.  Gauss' letter shows that this suspicion was 
widespread even in 1845.

Eventually Eugene settled in St. Charles, Missouri, and went into
business for himself.  He announced to his sister and father in a
letter his intent to marry a woman named Henrietta Fawcett, and in
reply (the same letter discussing Nicollet) the elder Gauss commented
that, since he could not form any judgements of the girl from 
personal knowledge,

  I willingly submit to the confidence that your age and your 
  experience will protect you against such disappointment as 
  indeed thoughtless and inexperienced youths fall prey to.

This expression of confidence must have been gratifying to Eugene,
as was the senior Gauss' hope that Henrietta's (presumed) good 
qualities would "well balance the absence of material endowments",
i.e., she was not from a wealthy family.  Gauss remarked that "your
two brothers have also chosen life companions without fortunes".
Incidentally, one of those brothers, Wilhelm, also quarreled with
his father and left Germany for America, in 1837, but not before 
marrying a neice of the astronomer Friedrich Wilhelm Bessel.  Bessel
and C. F. Gauss had once been friends, but they had a falling out
in 1832, and thereafter were not on very cordial terms, so the
union of their families was not exactly welcome to Gauss.  Like
Eugene, Wilhelm settled in Missouri, ironically near the town of
New Brunswick (the namesake of Brunswick, Germany, the Gauss' home
town).  

Eugene had four sons, including the previously mentioned Charles 
Henry.  Wilhelm also had four sons, and a daughter.  Most of these
grandchildren of C. F. Gauss made their homes in either Missouri 
or Colorado, but subsequent generations have spread out to many 
locations across the United States.  As Buhler says in his biography
of C. F. Gauss, "In Germany, not many direct descendants of Gauss 
have survived, but the family seems to be flourishing in the United
States".  Charles Henry Gauss had a daughter named Lois Gauss, who 
had a daughter named Lois Simmons, who had a daughter named Susan 
Chambless.  It was Susan who translated some letters written C. F. 
Gauss, his children, and his grandchildren, from her family 
collection and made them available on the internet.

Although C. F. Gauss may have mellowed on his "American" sons during
his old age, he seems to have never completely forgiven their youthful
transgressions.  In his last will and testament, written in 1854 (a
year before his death), Gauss was apportioning his possessions,
making note of the circumstances that justified each bequest, and 
he made a special provision for his first-born son Joseph

  If he so desires, my oldest son may choose as a special souvenir
  up to 30 volumes of my books. [In pencil:] for whose education
  many very significant costs did not occur as in the case of 
  his brothers.

Apparently Gauss was still holding his two younger sons to account 
for the expenses they had incurred by irresponsible behavior during
their school days.

Eugene, the once unruly student (who wore a scar from a duel in his
student days), gave up drinking and found religion in later life, 
and was remembered by all as a good Christian and family man.  In
his old age he went blind, but retained his mental faculties.  His
son Charles Henry recalled that when Eugene was over 80 he mentally 
calculated, over a period of several days,

   ...the amount to which one dollar would grow if compounded
   annually at the rate of 4% interest from the time of Adam 
   to the present, assuming this to be six thousand years. This
   if in gold would make a cubic mass so large that it would 
   require light four quadrillions of years to pass along one
   side of it. This is so startling as to be almost beyond belief.

Now and then Eugene asked his son Theodore to write down some
intermediate results, but otherwise the entire computation was
performed in his head.  This certainly shows that, like his father,
Eugene had a remarkable facility for numerical calculation, and a
remarkable memory, enabling him to recall long strings of numbers
for days.  Charles Henry stated that he did not think Eugene had
ever studied calculus, and did not use logarithms.  It would be
interesting to know exactly how Eugene carried out this calculation.
Unfortunately, there is some ambiguity in trying to reconstruct
Eugene's calculation, because another of Eugene's sons, Robert, 
remembered the interest rate as 6% rather than 4%.  Also, we don't
know for sure what price of gold Eugene assumed.  Even the term
"quadrillion" has multiple distinct meanings, depending on whether
we assume the American or the British and German definition.  

Still, we can roughly estimate the result.  Beginning with 1 dollar, 
and increasing it by N% per year (cumulative), the value after 6000
years is (1 + N/100)^6000 dollars.  We then need to multiply this
by the number of cubic meters of gold per dollar, using a price of
gold in the 1890s.  If gold weights W ounces per cubic meter, and
costs P dollars per ounce, then the volume per dollar is 1/(WP).
The edge of a cube with this volume is the cube root of this number,
and the time required for light to traverse this edge is this
number divided by c (the speed of light).  Therefore, the time is

                   1   / 1             6000  \ 1/3
            T  =  --- ( --- (1 + N/100)       )
                   c   \ WP                  /

This simplifies to

                      1   (1 + N/100)^2000 
               T  =  ---  -----------------
                      c      (WP)^(1/3)

For gold the value of W is about 671569 oz/m^3, and the price of
gold in the 1890's was (I think) about $7.50/oz, so if we take N=4%
we have
             T = 2.26E+23 seconds = 7.18E+15 years

According to the American definition, a quadrillion is 1E+15, whereas
the British and German systems define it as 1E+24.  The answer quoted
by Charles Henry is four quadrillion years, which is pretty close
if we use the American definition.  If the price of gold assumed by 
Eugene was $4.25, then we would get the same result.  

As to how he computed his answer, notice that if he had used logrithms,
he would presumably have taken exp(2000*ln(1.04)) = exp(78.44).  This 
equals A*10^B where

                    78.44  =  ln(A) + B ln(10)

Knowing that ln(10) is about 2.3, and that B is an integer, we find
B = 34 and so A = 1.16.  However, Charles Henry tells us that he
doesn't think Eugene used logrithms, so the question is, how did 
Eugene compute (1.04)^2000 ?  (On the other hand, we might question
whether it's credible that the son of C. F. Gauss, after attending
school into the college level in Germany, was unacquainted with
logarithms.)