Gaussís Children and Adamís Gold

 

The great mathematician 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 inauguration), 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 sergeants 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 sergeant 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 sergeantís 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 judgments 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 niece 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 by 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 weighs 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

 

 

This simplifies to

 

For gold the value of W is about 671569 oz/m3, and the price of gold in the 1890's was about $7.50/oz, so if we take N = 4% we have

 

 

According to the American definition, a quadrillion is 1015, whereas the British and German systems define it as 1024. 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 logarithms, he would presumably have taken exp[2000 ln(1.04)] = exp[78.44]. This equals A(10)B where

 

 

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 logarithms, 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.

 

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