## Gosh Numbers

September 18th, 2012 by Math Tricks | 2 Comments | Filed in Gosh Numbers

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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

God.”

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!”

“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

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.

GOSH!!

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!