Some uplifting thoughts !

Jonathan Swift describes the flying island of Laputa in Gulliver's travels in the following way- " The flying or floating island is exactly circular, its diameter 7837 yards, or about four miles and a half, and consequently contains ten thousand acres. It is three hundred yards thick...But the greatest curiosity, upon which the fate of the island depends, is a loadstone of a prodigious size, in shape resembling a weaver's shuttle. It is in length six yards, and in the thickest part at least three yards over...By means of this loadstone, the island is made to rise and fall, and move from one place to another...But it must be observed, that this island cannot move beyond the extent of the dominions below, nor can it rise above the height of four miles."

Was Swift foreseeing a day when objects could be levitated by the use of technology? One can draw some parallels to our current technology that uses a very advanced version of the crude loadstone. Magnetic levitation has become a reality in the recent past, being put to use for transport at very high speeds. Below, we offer a few hints based on the information provided by Swift to see if it is possible today to levitate a island like Laputa based on our current technology.

Steps:
1) Calculate the magnetic field strength necessary to keep the island afloat?
When magnetic force balances the island against gravity we can equate the total magnetic energy to the gravitational potential energy .

where B represents the magnetic field strength in a volume V, m is the mass of the island ( assume the density of Laputa to be same as of Earth), g is the acceleration due to gravity and h is the height to which the island is levitated.
In comaparision the magnetic field strength of the Earth is typically 0.5 Gauss.


Suppose we want to levitate a house with a giant balloon (like in the movie Up), what would be the size of the balloon required? We can use the following expression


where rho is the density of gas, V is the volume of the balloon and m is the mass of the house. Compare with the volume of the largest gas balloon launched which is about 60 million cubic feet.

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Numerology:

The Euler-Mascheroni constant is the limiting difference between the harmonic series and natural logarithm. It is denoted by the greek letter gamma.


There is a prime number version of the Euler-Mascheroni constant known as the Meissel Mertens constant which is the difference between harmonic series and natural logarithm of natural logarithm.


where p is a prime number less than or equal to n.
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Image courtesy:
1. http://www.wisdomportal.com/Levitation/LevitationLiterature.html
2. http://www.popbytes.com/archive/film/reviews/