Mozilla weighs in on why Facebook's side of the story doesn't hold water: blog.mozilla.org/en/mozilla/ne

Facebook shuts down the personal accounts of university researchers studying how Facebook violates its users' privacy in targeting political ads, citing as an excuse to do so...its agreements with the FTC over its violations of user privacy. bloomberg.com/news/articles/20, via news.ycombinator.com/item?id=2

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Topology is witchcraft

Relevant for ongoing sports events: Rankings in all-play-all competitions (like group play stages of many Olympic games) typically use total numbers of points for wins. It's simple, so audiences understand it. But really you might want to do something more complicated, like finding a ranking having the minimum number of upsets. The good news is that point score approximates the minimum-upset ranking: cse.buffalo.edu/faculty/atri/p

Trying to watch Olympics replays on Roku / NBC Sports is an exercise in frustration. (1) up to 14 unskippable ads in a row; (2) trying to fast-foward over breaks in sports action gets into a broken mode showing the same ads over and over while the underlying fast-foward goes on with disabled controls; (3) rewinding to content you missed while uncontrollably fast-fowarding gets back into ad overload mode. Who designed this unusable app and why do they think this will bring me back for more?

A new paper by Asperó and Schindler (annals.math.princeton.edu/2021) argues that principles of maximal forcing, unified in their paper, provide natural models for set theory in which many natural questions that are independent of ZF have clear answers. For instance, in these models, there are $$\aleph_2$$ real numbers, not $$\aleph_1$$.

I got to this via a popularized treatment in Quanta (quantamagazine.org/how-many-nu), but I think the introduction of the paper is quite readable. (The rest is not.)

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Bulles multicolores à la surface du café...

Scott Aaronson takes a break from quantum supremacy to tell us about busy beavers: scottaaronson.com/blog/?p=5661

These are Turing Machines that take as long as possible to do stuff. "As long as possible" is an explosively-quickly growing function of the number of states, but the gist of the post is that the "do stuff" part can be defined in various ways, some of which make the explosion happen earlier than others.

You remember that simple fruit pictogram equation with the ridiculously complicated answer? David Roberts has another one in the same style for which we don't even know the answer. thehighergeometer.wordpress.co

Solid Objects: 16th-Century Geometric and Perspective Drawings from the Herzog August Bibliothek in Wolfenbüttel, publicdomainreview.org/collect, via news.ycombinator.com/item?id=2

Imperfect comb construction reveals the architectural abilities of honeybees: doi.org/10.1073/pnas.210360511, via arstechnica.com/science/2021/0

How do bees cope with making hexagonal honeycombs when some kinds of cells have different sizes and some patches of honeycomb don't align when they come close to first meeting up? Answer appears to be: they see the problems coming and accommodate them gradually by intermediate variations in size and degree of cells.

A dead mathematician co-authored a paper after appearing in a dream: boingboing.net/2021/07/20/a-pe

The paper is "Higher Algebraic $$K$$-Theory of Schemes and of Derived Categories" by Robert Wayne Thomason and Thomas Trobaugh (2007), doi.org/10.1007/978-0-8176-457, ams.org/mathscinet-getitem?mr=

It appears to have been quite an influential one; the MR review calls it a landmark, and it has over 1000 citations on Google Scholar.

Hamming cube of primes: cp4space.hatsya.com/2021/07/20

Make an infinite graph whose vertices are the binary representations of prime numbers and whose edges represent flipping a single bit of this representation. (For instance, 2 and 3 are neighbors.) Surprisingly, it is not connected! 2131099 has no neighbors.

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A paper almost a decade in the making, now in the Notices of the American Mathematical Society. In 2012, Marco Paoletti asked me a question about rolling acrobatic apparatus. Answering this led to new designs, one of which was fabricated by Lee Brasuell and is now being performed with.
ams.org/journals/notices/20210

If you modify the sieve of Eratosthenes so that each generated number $$p$$ knocks out the numbers $$pn+2$$ instead of the usual $$pn$$, you get the prime-like sequence 2, 3, 7, 13, 19, 25, 31, 39, 43, 49, 55, 61, 69, ... (oeis.org/A076974).

Although many non-primes are in this sequence, and many primes are not, Bill McEachen has observed that with one exception the larger prime in every twin prime pair is part of this sequence! The proof is not difficult; see the OEIS link for spoilers.

My 5-year-old Macbook Pro decided yesterday to start shutting down the screen if you open it too wide. Seems likely to be a physical problem; time to replace it, I guess. New hardware should be nice but I had been holding off on several versions of OS updates and I'm not looking forward to the disruption in my software setup caused by the move.

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Building a trivalent graph of harmonic relations among major and minor triads.

Two more new Wikipedia Good Articles:

Cairo pentagonal tiling (en.wikipedia.org/wiki/Cairo_pe), a tiling of the plane by congruent but irregular pentagons, formed by overlaying two hexagonal tilings. It appears in street pavings, crystal structures, and the art of M. C. Escher.

Halin graphs (en.wikipedia.org/wiki/Halin_gr), the planar graphs formed from trees by connecting their leaves into a cycle. Studied by Kirkman long before Halin and significant in graph algorithms because of their low treewidth.

The editorial board of ACM Trans. Computation Theory has some explaining to do for publishing a cranky-looking P=NP paper, "A Polynomial Time Algorithm for 3SAT" by Lizhi Du, doi.org/10.1145/3460950 after a suspiciously brief review.

Yoshimura Crush Patterns: blogs.ams.org/beyondreviews/20

See also en.wikipedia.org/wiki/Yoshimur, which repeats Robert Lang's observation that these patterns can be seen on Mona Lisa's sleeves.

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