I joined Google+ on July 10, and put my activity there on a hiatus today.
There were some big positives for me there — notably the ease of sharing links with people, the way I quickly built up a collection of contacts (many of whom I knew before, many of whom I didn't) with posts that interested me on art, mathematics, and politics, and the level of immediate feedback I got from the +1s and comments on my posts that was much stronger than I've been getting on LiveJournal. For me it hit a happy medium between LJ (where I mostly feel I have to say something substantive to make a post) and twitter (which I follow but where the 140-character-per-post limitation seems too limiting for me to post). I ended up posting a bit more than one post per day, mostly external links with a sentence or two of description, compared to my rate here which is close to one a week.
One negative for me is that, like LJ's friends, G+'s circles conflate too many unrelated concepts: they describe the sets of people whose posts you want to read, they describe the sets of people who can read your posts (so far both like LJ) but they are also used by some people to filter different subsets of their posts to the people they think might be interested in that subset (something I think they work very badly for, because the audience should be choosing which topics they are interested in, not having that choice made for them by the person making the post). When sharing a link, Google automatically chooses the text to describe the link and doesn't let you edit it, and you can only have one nicely-formatted link in a post. And when a post on Google+ gets shared by someone else, the discussion thread gets split up into two places, neither of which is conveniently linked to the other.
But those are all minor. I could list equally many negatives about LJ. The big reason I stopped using G+ is because of the nymwars. Google has started insisting that everything posted there be traceable back to your real physical identity, and (in order to make this enforceable) that the only people who can participate are those who have conventional Western-style first-last names. I find this unacceptable, repressive, totalitarian, and I don't want to contribute to it. I'm happy enough to participate under my own real name (despite a couple of incidents where acting as an admin on Wikipedia under my real name has led to people harrassing the real-life administrators at my workplace) but I feel strongly that there are many good reasons to be pseudonymous, that pseudonymity has been an important part of our culture, that disallowing it is also stifling free speech, and that it doesn't even work as a way of preventing trolls and spammers (because the trolls and spammers are happy to use real looking names).
Anyway, since Google doesn't make my posts there easy to search, and I'm not entirely happy about them being kept only on a service whose philosophy I disagree so strongly with, here's a brief timeline of my posts there.
7/10. The most obvious thing to do with my new Google+ account seemed to be to link it with some of my other existing online activity. I began with a cross-post of my LJ post on a James Turrell installation at the De Young Museum in San Francisco.
7/10. Cross-post of my LJ post on some of the accepted papers at FOCS.
7/11. Another thing I set out to do on my new Google+ account was to publicize some of the technical articles on Wikipedia that I'd been recently working on improving, among an audience I thought might find those articles interesting. I started with Theil–Sen estimator, a method from robust statistics for fitting lines to points in the plane. This set me on a pattern of posting much more often to G+ than I was posting to LJ, and of making much shorter posts with a few sentences of description followed by a link.
7/12. Implicit graph on Wikipedia.
7/13. Curtis–Hedlund–Lyndon theorem on Wikipedia, a topological characterization of cellular automata.
7/15. De Bruijn–Erdős theorem on Wikipedia, about coloring infinite graphs, with a very helpful comment from set theorist Andres Caicedo.
7/17. Impact factor engineering (link to a blog post by Peter Cameron).
7/18. Crosspost of my LJ post on conference acceptance rates.
7/18. A plug for dermophoto's urban abstractions.
7/19. Crosspost of my LJ post on my county fair photos.
7/19. Crosspost of my LJ post on nine new JGAA papers (and new material requirements for journal papers).
7/20. Factor-critical graph on Wikipedia. In the discussion, Jean-Marie Madiot makes the amusing observation that, because friendship graphs are factor-critical, killing any of your friends would allow all the survivors to form happy couples.
7/21. Hajós construction on Wikipedia, a way of automatically generating k-chromatic graphs. With some discussion about whether it can be made to generate all and only the k-critical graphs (probably not).
7/25. A Wired story about photos of windblown sand patterns. I didn't say so in the post, but when I made it I was thinking about a similar photo that Jan Kratochvíl had included for my benefit in his SoCG 2011 talk.
7/26. Link to some 3d-printed jewelry leading to a discussion on artists who use 3d printing technology.
7/27. Link to some flat-origami tessellation patterns.
7/27. Link to another post on Google+ concerning integrating MathJax with Google+.
7/28. Reshare of a post by one of my contacts linking to a story on endemic plagiarism among computer security textbook writers. This is a case where I think Google+'s "circle" model is broken: the original Google+ post was set to "extended circles" meaning that only people within two steps of the original poster could see it. To respect that, I set my post to be visible only within my circles. But really, there's nothing in this that couldn't be public. So my choices were: strip off my contact's name and avoid giving proper credit for finding the link, fail to strip it off but make the post public, violating their privacy, or self-censor. I took the safe self-censorship route but now I'm not sure that was the right choice.
7/28. A brief description of the Kruppa–Demazure theorem (on reconstructing five-point scenes from two perspective views) in the context of a new Wikipedia article on Michel Demazure. Some time after that I got Demazure onto the front page of Wikipedia, briefly, in their "Do You Know?" section, with a sentence that included something about his pseudonymous participation in Bourbaki.
7/29. More on pseudonyms: a link to one of Skud's posts observing that even well-connected former Google people are having difficulty getting any level of non-robotic assistance getting their accounts straightened out after the banhammer comes down. In my post and the ensuing discussion I hinted that this issue might cause me to leave G+ but agreed to give the G+ administrators time to clarify their position.
7/31. Cross-post of my LJ post on toughness.
8/3. In an attempt to continue boosting the signal about pseudonyms, I linked to the My Name Is Me project and denise/rahaeli/synecdochic's explanation of why Dreamwidth deliberately allows pseudonyms.
8/7. Link to Uli Westphal's mutatoes, a photo gallery of colorful and misshapen vegetables.
8/8. Link to Can't Decide? Undecide!, an article by Chaim Goodman-Strauss on undecidability.
8/8. The final straw: Google makes it clear that their no-pseudonym policy is firm. I link to a couple more pro-pseudonym pieces and declare a hiatus until pseudonymic people are treated as first class participants.
A first answer. I'll need some time to read all this stuff, thank you for the links. I will keep following you here.
The 120-cell video is nice, and a bit too much fast. The video link to the spacefilling curves has to be ik2CZqsAw28 instead of ik2CZqsAw2.
In the Home page for 'spacefilling curves and applications' why are they using a Sierpinski spacefilling curve instead of a Hilbert one?
I fixed the video link; thanks for catching that. As for why Sierpinski — I guess you'd have to ask them. The Hilbert curve or the Z-order curve would have been my choice.
The Hilbert curve business is cool; how would the skeleton of such a thing look? what would be the complexity of it for a given approximation level?
For a curve that can resolve details at a scale of \( \epsilon \) (assuming the bounding box has unit length) the number of features in the curve is \( O(1/\epsilon^2). \) More importantly, like the Z-order curve but only a little more complicatedly, it is possible to sort a set of points into their positions along the curve by looking only at the bits of their binary representations, so you don't have to build the whole curve first, just apply your favorite sorting algorithm with a custom comparison method.