Years ago, I read a very entertaining science fiction series by Frederik Pohl known as the Heechee saga. The main plot of the series is that humans find alien spacecraft that allow them to travel to distant worlds. In their travels, the human explorers come across alien technology that they eventually come to understand and use.
In the second book of the series, Beyond the Blue Event Horizon, humans aboard an alien vessel are introduced to Gosh Numbers. As explained to the character Wan in the story by one of the “Dead Men”:
“Gosh numbers are numbers which represent more than one
quantity, so that when you perceive the coincidence you say, ‘Gosh.’ Some
gosh numbers are trivial. Some are perhaps of transcendental importance.
Some religious persons count gosh numbers as a proof of the existence of
The Dead Man goes on to give several examples of Gosh Numbers:
“Oh, well,” said the Dead Man gloomily, “all right. Point-five degrees
is the angular diameter of both the sun and the Moon as seen from Earth.
Gosh! How strange that they should be the same, but also how useful,
because it is partly because of this coincidence that Earth has eclipses.
Minus-forty degrees is the temperature which is the same in both
Fahrenheit and Celsius scales. Gosh. Two thousand twenty-five is the sum
of the cubes of the integers, one cubed plus two cubed plus three cubed
and so on up to nine cubed, all added together. It is also the square of
their sum. Gosh. Ten to the thirty-ninth is a measure of the weakness of
the gravitational force as compared with the electromagnetic. It is also
the age of the universe expressed as a dimensionless number. It is also
the square root of the number of particles in the observable universe,
that is, that part of the universe relative to Earth in which Hubble’s
constant is less than point-five. Also-well, never mind, but gosh! Gosh,
gosh, gosh. On these goshes P. A. M. Dirac constructed his Large Numbers
Hypothesis, from which he deduced that the force of gravity must be
weakening as the age of the universe increased. Now, there is a gosh for
“You left out one thirty-seven,” the boy accused.
The Dead Man cackled. “Good for you, Wan! I wanted to see if you were
listening. One thirty-seven is Eddington’s fine structure constant, of
course, and turns up over and over in nuclear physics. But it is more than
that. Suppose you take the inverse, that is one over one thirty-seven, and
express it as a decimal. The first three digits are Double Ought Seven,
James Bond’s identification as a killer. There is the lethality of the
universe for you! The first eight digits are Clarke’s Palindrome, point oh
seven two nine nine two seven oh. There is its symmetry. Deadly, and
two-faced, that is the fine structure constant! Or,” he mused, “perhaps I
should say, there is its inverse. Which would imply that the universe
itself is the inverse of that? Namely kind and uneven?”
Gosh – isn’t that cool?! It is a very good series by the way, and I recommend it if you are into sci-fi. Anyway, I am adding the category “Gosh Numbers” to Math Tricks, and will periodically post numbers that are interesting in various ways.
Well, that was a rather lengthy introduction, so I will not delay any further the first Gosh Number:
1729 is the least number expressible as the sum of 2 cubes in two different ways:
1729 = 123 + 13 = 103 + 93
1729 is also the 3rd Carmichael number
1729 is also a centered cube number, a dodecagonal number, a 24-gonal and 84-gonal number. The creators of the television cartoon Futurama thought so much of 1729 that they included it within the show on several occasions.
In fact, 1729 has more “Goshness” to it – can you name some? Are you aware of any other interesting numbers? Please be sure to share them in the comment section at the end of this post!