Published 9 August 2006
From Chris Brooking
Feedback might be a bit quick to dismiss the idea of fractional gods (Feedback, 22 July). The Hindu Brihadaranyaka Upanishad certainly considers the possibility of one-and-a-half gods:
Then Vidagdha, the son of Sakala, asked him: “How many gods are there, Yajnavalkya?
Yajnavalky said, “As many as are indicated in the Nivid of the Visvadevas – 300 and 3003.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Thirty-three.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Six.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Three.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“Two.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“One-and-a-half.”
“Very well,” said Sakalya. “How many gods exactly are there, Yajnavalkya?”
“One.”
“Very good,” said Sakalya, and he asked: “Which are those 303 and those 3003?”
Yajnavalkya said: “There are only 33 gods. These others are but manifestations of them.”
In Hinduism there are said to be 330,000,000 gods. Perhaps a really staunch atheist, who believes with 100 per cent conviction that there is no god, could count as a negative god (as opposed to the more common sceptical agnostics). How many such atheists are there? Well, if there were 330,000,000 of them, this would give us your “most likely” average of zero.
• Our spoof proof that the expected number of deities in our universe is zero (Feedback, 22 June) attracted many responses in addition to this one. Enough, possibly, to disprove Phil Adsley’s extension of precisely the same argument to life in general: “The number of life forms ranges from negative to positive infinity (leaving the philosophers to argue over negative life forms…) and therefore the expected number of life forms is zero.”
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Several readers, like Chris Brooking, challenged our assumption that the number of deities is whole – some, with Dai James, pointing out, “The Greek heroes were the result of couplings between gods and mortals, thus producing demi-gods.” Over many generations this would produce hemi-demi-gods and so forth – beings whose deicity was a fraction with any whole number on the top and a number on the bottom that is a power of two: 2, 4, 8, 16 and so on. Those fractions would be what mathematicians call rational numbers, leading James to conclude: “The deities would thus be rational – a considerable relief as there are obvious dangers associated with an irrational god.” He goes on to reach a startling conclusion: “Since no gods can be irrational, none of them can be transcendental.”
We thank readers who made a similar argument based on the Christian doctrine of the Trinity – but we’re not going there. Archie Campbell suggests that the true number is “an imaginary number with no real part” and Vilnis Vesma elaborates – whooshing over our mathematical head – that imaginarily numbered deities “would only interact with the real world if there were zero of them”.
Luther Blisset also challenges our identification of deities with integers. Should we not count them using either the unordered cardinal numbers (as in, “Daisy the cow, Ermintrude the cow”) or the ordinals (as in “best cow, second-best cow, third…”)? Theologians may argue over which we should use, but in either case the range is from zero to infinity and so, assuming our universe is typical, the expected number will be one-half infinity which is, er, infinite.
Which brings us to Stephen Scott’s observation that we pre-answered ourselves on this matter, when on 22 April we quoted Neil deGrasse Tyson, director of the Hayden Planetarium in New York, responding to a discussion of the number of universes: “We live in the middle of infinity? Did those words really just come out your mouth?”
Bradford, Yorkshire, UK
Issue no. 2564 published 12 August 2006
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