Poetry should be italicized when it consists of mathematical variables, titles of books and periodicals, and emphasized words; there are probably other cases that I'm not recalling at the moment.
This being the fluorosphere, I have some hope that someone will take that as a challenge.
Cliff Royston @ 662: Note that the eigenvalue-based proof only shows that hierarchical tilings (using a particular dissection rule) must be non-periodic. The tiles themselves admit periodic tilings. So there is no aperiodicity to be found there.
The text of the spam is too good to lose:I have noticed many changes in your blog and they are like improvements for you.Who needs fortune cookies when we have blogspam?
As a somewhat socially inept person (whose self-image is even moreso) I would normally have absolutely nothing to say on this topic. I would probably have given up reading within the first ten comments, if I even made it to the cutline, on the grounds that this discussion is in some dialect that I've never been able to decipher. But by some accident of synchronicity, I've been examining my own behavior on ML, due to a suspicion that one of my recent comments was not terribly appropriate. So I decided to brave the incomprehensibility in hopes of understanding a little of what sort of posting is being deprecated here.
I've had two or three warnings from PNH in years past about the "huffy" tone I sometimes assume. I never really knew what he meant by that, except that the objectionable comments were ones in which I had to admit I wasn't thinking too thoroughly about what I was saying and how I was saying it. This topic, though, provides a description of an academic/authoritarian bully that is an embarrassingly good match for me when I'm being huffy. It has helped me understand both the insecurity that triggers the tone and the poisonous results of using it. Most importantly, it gives me a more explicit description of what kind of writing I need to guard myself against using. With this I have a chance at catching myself while I'm writing, rather than after I've posted.
So thanks, abi, for leading us to this discussion. Thanks, commenters, for the insights that have made it through my perceived-social-incompetence filters. And thanks to the whole fluorosphere for having put up with my occasionally semi-toxic writing pending the latest object lesson, which I sincerely intend to be the last of its kind. I look forward to repaying your patience.
I still don't find this stuff easy reading, but I guess learning stuff is hard.
Bruce Cohen @ 604:
Please disregard my response at #608. I certainly should have considered that the news was supposed to be surprising, and so counter to prevailing belief (at least, prevailing up to four years ago). In or out of context, though, I believe my response was arrogant and rude to you, and I deeply regret it. I once again resolve not to act that way in the future.
I've looked at the article (which is now up on the Saudi Aramco World site) and the Science article on which it is based, and I am quite astonished to see that some 12-15th century artisans apparently developed the concept of hierarchical tiling (as described in Wikipedia under "Aperiodic tiling").
As far as I can tell, these tiling methods actually do fall short of being aperiodic, in that there is no development of local adjacency constraints to enforce the hierarchical structure of the tiling. However, the use of hierarchical tiling is itself quite amazing. Thank you for bringing this to the fluorosphere.
This discussion led me to review the Wikipedia article on Penrose tiles, and I see that Penrose acknowledged Kepler's work on pentagonal tilings in Harmonices Mundi as the inspiration for his development of pentagonally-based tiles. Of course, Kepler's tilings were not aperiodic any more than the Moorish ones.
Perhaps one reason for Penrose's interest is the well-known result that a tiling with fivefold rotational symmetry about a point cannot be periodic. Thus if a set of tile shapes could enforce fivefold symmetry, the tiling would be aperiodic. While Penrose did find a way to ensure aperiodicity in pentagonally-based tiles, it is notable that his tiles do not enforce fivefold symmetry. In fact, only two out of the 2ℵ0 Penrose tilings possess fivefold symmetry.
Bruce Cohen @ 694:
I think you need to reread #595. The Moorish tilings based on kites and darts are not aperiodic. Kites and darts can be assembled to form periodic tilings. It is necessary to add constraints, as Penrose did, to get aperiodicity.
Bruce Cohen #516: On the question of Penrose tiles, non-periodic tilings are not difficult or new—you can make a non-periodic tiling from copies of a single triangle tile.* What has been developed since 1961 are aperiodic tilings, tilings of the plane with tile shapes that admit no periodic tiling. The first aperiodic tilings were due to Hao Wang using large numbers of tile shapes based on squares. Penrose was the first to demonstrate aperiodic tilings with only two shapes of tile.
Penrose used shapes based on rhombuses, kites, and darts with pentagonal symmetry, and these shapes appear in classical Moorish tilings. However, these shapes do not by themselves generate aperiodic tilings, because the tile shapes can be used to tile periodically. It is only the particular matching constraints introduced by Penrose that make the tiling aperiodic.
So the Moorish tilings are not the same as "Penrose, or quasi-crystal tesselations"†any more than a tiling by squares is a Wang tiling. Aperiodic tilings from a finite set of tile shapes were not demonstrated before Wang in 1961. The interest in aperiodic tilings is implied, though, as early as Hilbert's eighteenth problem from the last year of the nineteenth century.
*For instance, an isosceles right triangle can be used to tile the plane periodically as squares bisected along a diagonal. A subset of the squares may be modified to use the other diagonal, producing a non-periodic tiling.
†Though a large amount of confusion between the two is available on the net. The nature of Penrose's discovery is subtle and prone to misinterpretation, particularly if one concentrates on diagrams that do not emphasize the aperiodicity constraints.
Lenny Bailes @36: Your link gets me to a Google groups "topic not found" page for rec.arts.sf.fandom. Tinyurl considered harmful.
Zillions of hits today on "tell me right I wrote the following sentence" and "give true I wrote the following sentence". Someone is ESL-bombing the internets.
I suspect the payload is in the header URL. Though what "Members/Thinning" is supposed to represent is anyone's guess. Hair club for morons?
Serge @545 The wikipedia article says that Peter/Pierre/Petra/Petros/πετÏος is a translation of the apostle's Aramaic name Kephas or Cephas, all meaning "stone" or "rock".
55: Verily it is said, "Who picks by the nit will be picked by the nit."
I have it from reliable sources that Fitzgerald did not write "Bernice boobs her hair."
My apologies for any confusion.
It's worth noting that linguistic reanalysis, also called an eggcorn, mondegreen, or pullet surprise, was also discussed in Open Thread 37.
I'm still fond of the second-level reanalysis "a dog y dog world".
Terry Karney at 209: I suppose you put the cap on to prevent criticism of the resulting photography?
Fragano@391... I'm trying to imagine how someone could confuse Louis Antoine Juchereau de St. Denis with Christopher Columbus, or otherwise what the significance of 1714 might be.
Harriet@10.. Those links should be The Witching Hour, In the Company of Science, and She is the very model of a Singularitarian. You can also get there by way of the "Next" link on the previous pages.
Fragano@632: It's amazing what a homophone can do to two clichés, too. I ran into a mention of someone going "behind the veil of tears" a while back.
Clifton Royston @496: Thanks for pointing out the gem of that page. It's certainly harder to skim that sort of discussion.
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