International Journal of Physics
ISSN (Print): 2333-4568 ISSN (Online): 2333-4576 Website: Editor-in-chief: B.D. Indu
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International Journal of Physics. 2014, 2(6), 264-266
DOI: 10.12691/ijp-2-6-9
Open AccessArticle

Carl Sagan’s Conjecture of a Message in π

Arne Bergstrom1,

1B&E Scientific Ltd, Seaford BN25 4PA, United Kingdom

Pub. Date: November 23, 2014

Cite this paper:
Arne Bergstrom. Carl Sagan’s Conjecture of a Message in π. International Journal of Physics. 2014; 2(6):264-266. doi: 10.12691/ijp-2-6-9


In his novel Contact, the astrophysicist Carl Sagan hypothesized an alien message to be buried somewhere deep inside the numerical representation of the transcendental number π. The present article looks for markers that might possibly support such a hypothesis, and surprisingly finds a sequence of seven successive zeros (actually seven successive nines rounded off) at a depth of 3256 digits into the representation of 2π in the special case of base ten. Finding such a sequence of zeros within the first 1000 digits has a probability of 1 in 10000. No such occurrences happen even remotely for 2π at any base other than ten, nor even remotely in corresponding representations of other common transcendental numbers, such as e, which appear in physical applications. In π, this occurrence thus also remarkably appears at a depth that is a multiple of the same power of two as bits in a computer byte, which thus makes it even more enigmatic. Still, these effects are most probably just numerical coincidences without physical relevance.

transcendental number pi integer bases markers anthropic occurrence

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