Friday, April 01, 2016

An unusual property of the integers

Source: Wikipedia
 How does one explain the age of Methuselah?

The meaning of Methuselah's age has engendered considerable speculation, but no widely accepted conclusions.

Interpretations of the Bible following Biblical literalism take Methuselah's 969 years to be 969 solar years. Some literalists suggest certain arguments for how this could be: early humans had a better diet, or a water vapor canopy protected the earth from radiation before the Flood.

Some believe that Methuselah's extreme age is the result of an ancient mistranslation that converted "months" to "years", producing a more credible 969 lunar months, or 78½ years, but the same calculation applied to Enoch would have him fathering Methuselah at the age of 5 using numbers from the Masoretic Text.

Such conundrums are unnecessary.

The reason is simple: Millenia ago, the integers were much closer together than they are now.

Not only does this explain the extreme age of Methuselah and others, the same logic can be used to solve other important riddles:

The age of the Earth

While scientists argue that physical evidence leads to the inevitable conclusion that the Universe is 13.7 billion years old, more or less, and the Earth itself is 4.54 billion years old, Biblical scholars and noted scientists such as Isaac Newton thought the Earth was created around 4000 BC. These are reconcilable if one assumes that, prior to the 6thday of Creation, the integers experienced something akin to the inflationary expansion of the early universe:
"The fact that O is between 0.1 and 1 today means that in the first second of the Big Bang it was precisely 1 to within 1 part in 10^{60}".

The value of π

Mathematicians argue that π possesses an infinite number of non-repeating decimals, 3.14159265358979...

[I use the mnemonic - attributed to Richard Tolman at Cal Tech -  "Yes, I need a drink, alcoholic of course, after the heavy sessions involving quantum mechanics" to remember π to 15 decmials as shown above.]

This could be interpreted as 3 plus a fraction that is small now and was smaller years ago - so small that in 1879 it was nearly legislated that the value of π was exactly 3.

The Easter Island statues 

It is well-known that the Rapa Nui people had erected large states, perhaps as large as 270 tons:
Moai are monolithic human figures carved by the Rapa Nui people on Easter Island in eastern Polynesia between the years 1250 and 1500 CE...
The production and transportation of the 887 statues are considered remarkable creative and physical feats.[5] The tallest moai erected, called Paro, was almost 10 metres (33 ft) high and weighed 82 tons; the heaviest erected was a shorter but squatter moai at Ahu Tongariki, weighing 86 tons; and one unfinished sculpture, if completed, would have been approximately 21 metres (69 ft) tall with a weight of about 270 tons.
Since the integers were much closer together 3600 years ago than they are today, the mass of such statues would have been much less, easily manipulated by the Rapa Nui, whose physical condition was surely improved by frequent canoeing over large expanses of open ocean [citation needed].

As one can see, there are an infinite number - surely a denumerable number - of similar problems easily resolved by applying the same reasoning.

I wish I could take credit for this, but I cannot. The inspired absurdity - the integers were once much closer together than they are today - is due to Peter Doan, now Associate Research Professor in the Hoffman groups at Northwestern.

Bravo, Signore Doan!

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