The Cosmic Microwave Billboard

It's a good day for arXiv.

The irrational number π [17] occurs throughout physics, in anything related to rotations, waves, vibrations or phases. It occurs explicitly in Coulomb’s law, Kepler’s third law, Einstein’s field equations, the Fourier transform, the normalization of a Gaussian, the reduced Planck constant, etc. And perhaps most astonishingly, if you divide the circumference of a circle by its diameter, you get exactly π!

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Despite the fact that the power spectrum of the CMB anisotropies carries around 2000 σ worth of information [23], the apparently 2–3 σ significance of the Cold Spot is fantastically important. A quick glance at Fig. 1(a) shows just how prominent this feature is on the sky. Although not the large blue region near the centre [24], and not actually the coldest place on the CMB sky [25], the chances of finding a cold region of exactly this size and shape in Gaussian random skies is quite small. And the chances of finding such a spot in precisely this direction is almost vanishingly small.

In the digits of π there is an analogous feature, which might be called a ‘hot spot’, since it involves a cluster of the number ‘9’. Specifically, ‘9’ occurs six times concurrently after the 762nd digit of π, as shown in Fig. 1(b). This is sometimes called the ‘Feynman point’ [26], and appears fantastically earlier in the digits of π than one would expect for such a repeated run... It has also been pointed out [27] that the digits of 2π contain seven consecutive 9s at about the same position as the six 9s in π. This is of course even less likely to occur by chance.

It was pointed out by the WMAP team [4] that one can find Stephen Hawking’s initials in the CMB sky, as shown in Fig. 7(a). These same features, clearly being two roman characters in roughly the same size, font and orientation, are also present in the Planck data. We are not aware of any systematic search for all combinations of letters, with arbitrary position, font, size and orientation. But presumably such a search would turn up many other interesting examples of writing on the ‘cosmic billboard’.

As a final remark, we add this utilitarian view – if the AAAs mean that the CMB information is somehow already encoded in π, then perhaps in future we can avoid all the fuss and bother of building real CMB experiments, minimising systematic effects while operating them, painstakingly analysing the data, and debating the statistical interpretation of the results – and instead simply look more carefully at the digits of π, or in any other random string of digits [44].
http://arxiv.org/abs/1603.09703