Building 4d Polytopes

Building 4d Polytopes

That is a group where the generators have relations of the form: \((ab)^{m_{ab}}\), as above: $$(RG)^4 = (GB)^3 = (RB)^2$$ The generators must also be their own inverse: $$R^2 = B^2 = G^2$$ Since the generators are their own inverses, they can be associated with reflections. Here is a demo (use the ‘step’ button to fill the table):

Let us look at the various cosets you get when you use Todd-Coxeter on the symmetry groups for the regular polytopes, using different subsets of the generators to specify a subgroup:

An interesting structure emerges here: looking at the cosets for the subgroups generated by leaving out one of the generators, the number of cosets matches the number of vertices, edges, or faces! Given the generator relations, we know the angles between the reflector planes: If there is a relation on the form: \((RB)^{N}\), the angle between the reflection planes R and B must be \( \pi / N \) – which again corresponds to a rotation of \( 2\pi / N \) degrees.

Source: syntopia.github.io

When this eBook store closes, your books disappear too

When this eBook store closes, your books disappear too

Image copyright
Getty Images

Image caption

When you buy an eBook, you typically don’t actually end up owning the book at all

There’s bad news for users of Microsoft’s eBook store: the company is closing it down, and, with it, any books brought through the service will no longer be readable. This is how we’ve been led to this curious situation, where Microsoft’s eBook customers – however few – will see their book collection vanish, just because company executives have decided it’s no longer worth keeping the store running. Books sold on most eBook stores (but not all) come loaded with digital rights management software – DRM – which makes sure the copy you are accessing has been bought and paid for properly.

Source: www.bbc.co.uk

Fantastic Mr. Fox

Fantastic Mr. Fox

On Saturday February 19, 2005, a day after the Hunting Act came into force, I was standing beside a man named Aubrey Thomas looking over a wall at some of the 14,000 acres of land that form the Englefield estate in Berkshire, fifty miles west of London. Aubrey and his friend stood by while the terrier-men, the farmhands and village men with dogs who accompanied the hunt, dug down for an hour to trap the fox. For this, the first day of the rest of their lives—when they had, theoretically, stopped being vilified ‘antis’ and started being respectable ‘monitors’, collecting evidence of illegal fox hunting—Aubrey had chosen their hunts carefully.

Source: granta.com

540M Facebook Records Exposed

540M Facebook Records Exposed

The two batches of user records were collected and exposed from two third-party companies, according to researchers at security firm UpGuard, who found the data. It’s the latest data lapse involving the social media giant since the Cambridge Analytica scandal in 2018, which saw more than 87 million Facebook user records scraped without consent by the U.K.-based political data firm. UpGuard found a batch of scraped Facebook profiles involving 48 million records in 2018 from LocalBlox, a data firm that scrapes data from social media profiles.

Source: techcrunch.com

Vladimir Nabokov, Literary Refugee

Vladimir Nabokov, Literary Refugee

Officially the couple were stateless, having been issued Nansen passports, a document that in Nabokov’s view essentially identified its holder as “a criminal on parole.” While France was unhappy about the influx of foreigners — it had been less welcoming to foreigners than Berlin — Nabokov managed to secure a work visa. “I have sound reasons to believe that I shall be able to make good in America,” Nabokov assured the American Committee for Christian Refugees.

Source: www.nytimes.com

Usain Bolt’s Split Times and the Power of Calculus

Usain Bolt’s Split Times and the Power of Calculus

The following graph shows the elapsed times at which Bolt crossed 10 meters, 20 meters, 30 meters, and so on, up to the 9.69 seconds it took him to cross the finish line at the 100-meter mark. It indicates that Bolt reached a top speed of around 12.3 meters per second (27.5 miles per hour) at about the three-quarter point in the race. In Usain Bolt’s speed data, the wiggles took a smooth trend and made it look as bushy as a pipe cleaner.

Source: www.quantamagazine.org

The future of undersea Internet cables: Are big tech companies forming a cartel?

The future of undersea Internet cables: Are big tech companies forming a cartel?

Other reasons for new cables include connecting some remote parts of the world that are still reliant on satellites and providing more options to economies that have only one or two cables, because any damage to these cables can cause massive disruptions. The content providers are currently only deploying their cables on major routes, mostly trans-Atlantic and trans-Pacific, to link data centres. Think of the undersea cable network as the new economic trade routes and the commodity in transit as data — arguably the most important commodity of the Information Age.

Source: blog.apnic.net

JavaScript at the Edge

JavaScript at the Edge

Write, run, and test Edge Applications with the open source Fly runtime . Deploy your app to our infrastructure and we’ll route your users to the nearest datacenter. Our application servers connect them to your JavaScript environment in under 1ms.

Source: fly.io

Git9: Git Reimagined for the Plan 9 OS

Git9: Git Reimagined for the Plan 9 OS

Tracking is
done with empty files under implemented in Plan 9 flavor C, and provides tools for writing
repository contents, and a file system for read-only access, which
will mirror the current state of the with `mk install`. The implementation is mixed c and rc,
so after installing you need to union /rc/bin/git and $objtype/bin/git`
yourself: ‘bind -a /rc/bin/git /bin/git’ will usage examples:

git/clone subdir/name
git/add foo.c
diff bar.c are presented as directories with the file containing the author name
hash: A file containing the commit hash
parent: A file containing the commit parents, one per line. msg: A file containing the log message for that commit
tree: A directory containing a view of the repository.

Source: bitbucket.org

Google’s brand-new AI ethics board is already falling apart

Google’s brand-new AI ethics board is already falling apart

Of the eight people listed in Google’s initial announcement, one (privacy researcher Alessandro Acquisti) has announced on Twitter that he won’t serve, and two others are the subject of petitions calling for their removal — Kay Coles James, president of the conservative Heritage Foundation think tank, and Dyan Gibbens, CEO of drone company Trumbull Unmanned. Nearly half the board has resigned or is under fire

Google announced their AI ethics board last week, saying the board would “consider some of Google’s most complex challenges that arise under our AI Principles, like facial recognition and fairness in machine learning, providing diverse perspectives to inform our work.” These critics see the unpaid positions as another sign that Google isn’t taking the AI ethics board very seriously, and that the company doesn’t expect members to spend much time on it, either.

Source: www.vox.com