News roundup, and binary Cantor orthogonality

[Posted on august 15, 2017.]

Summer news:

• the extremely sad news that Maryam Mirzakhani died at only 40 ; a memorial took place at Harvard two days ago, and probably others will follow at Stanford and elsewhere
• Sir Michael Atiyah seems to be claiming another big result, but did not post it to the arXiv this time
• John Urschel retired from his pro american football career to concentrate on his PhD at MIT
• Bonn Computer Science Chair Norbert Blum claims a proof of
• MSRI is booked until the summer of 2020 already with lots of attractive programs
• several more prizes for Hugo Duminil-Copin
• Jérôme Germoni has a wide-audience paper (in french) on how easy it is to get a nonsensical paper (generated with mathgen) accepted in a predatory journal
• there is a (french medieval? or earlier?) numeral system that I’d really like to see identified (I currently don’t have access to Ifrah’s encyclopedia, where it may well feature update: I have now checked it and interestingly couldn’t find it, but I found a small comment by S.Lamassé in a more recent book, although not a really convincing one, see my answer in the link. )

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Completely unrelatedly, here’s probably another useless idea from this blog’s host. Consider a sequence of binary numbers in such that the number of digits of is at least equal to for all . Then one can apply Cantor’s diagonal argument to extract a number that is uniquely defined (since a digit different from must be and vice versa) and different from all the . Call the resulting number the “binary Cantor orthogonal” of that sequence. Can it have any useful properties?

Let’s look at the following example: , the binary version of the inverse of the th prime. That is, we do:

 

then extract the diagonal of the decimal parts and invert it modulo 2. The resulting sequence is 0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0… Unfortunately, the OEIS doesn’t know this particular sequence, so there’s probably nothing noticeable here.

Jardin des Roses in Rennes (a small area of this marvel).

August 2017. Public domain