Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

September 8, 2011

Math and Physics on Google+

Posted by John Baez

I’ve started using Google+ to share fun tidbits of information about math and physics — the kind of stuff I used to put near the start of each issue of This Week’s Finds. It’s quick and easy.

There are lots of cool people on Google+, sharing all sorts of information. It’s become one of my main sources of news.

Currently Google+ works by invitation only. If I know you and like you, I’ll be glad to send you an invitation. (Please only ask if we’ve had some pleasant encounters in cyberspace, and not many unpleasant ones.)

And if you want, I can also add you to my “Mathematicians”, “Physicists” or “Azimuth” circles. If I do that — and only if I do that — you’ll see certain more technical items that I don’t want to inflict on the uninterested masses.

Here are some samples of the stuff I’m talking about…

Here are three that I broadcast to the world at large:

Fool’s icosahedron

No crystal in nature can be shaped like a regular dodecahedron or a regular icosahedron. (Quasicrystals are another matter.) But crystals of iron pyrite can form various kinds of approximate regular dodecahedra. They pull off this stunt by approximating the golden ratio by a ratio of consecutive Fibonacci numbers.

It’s also possible for iron pyrite to form a “pseudo-icosahedron”. But it’s rare. Johan Kjellman pointed out this nice example to me… a bit too late. Maybe I could have bought it for 50 dollars!

Stewart Dickson’s 3d version of the Pythagorean pentagram

To get a Pythagorean pentagram, you take a pentagram and keep drawing lines through points that are already present, as shown in this picture drawn by James Dolan:

It’s packed with pentagrams that are related by various powers of the golden ratio. In the 3d version, Stewart Dickson starts with a stellated dodecahedron!

For more on the Pythagorean pentagram try this.

Zipf’s law for dolphins

Zipf’s law says that the frequency of appearance of a word is inversely proportional to its rank when you list words by frequency. For example, the 6th most common word will show up about 1/6 as often as the most common one. Why? It’s very controversial, but some argue that Zipf’s law arises from trying to maximize the rate of information transmission.

Now scientists have done a similar analysis of dolphin whistles. It’s tricky, since we don’t know what a dolphin “word” is, or even if they have words! But based on some assumptions, the scientists get Zipf’s law.

For squirrel monkeys, they instead get an exponent of -0.6. “You can combine the calls any way you want and you won’t get a -1 slope.” They believes this “suboptimal” power law reflects the animals’ limited social behavior.

David Brin originally shared this post:

An interesting and fair discussion of the possibility that dolphins have a sort of language and a sort of “intelligence.” As a sort-of dolphinish guy, I actually have subtle and complex beliefs about this. The folks I know who’ve worked with high cetaceans all tell me their impression: that the creatures seem to “wish they were smarter.” Subjective, but poignant and telling. (I’ll discuss dolphin “uplift” in EXISTENCE.)

For more on Zipf’s law, entropy and dolphins, see:

Posted at September 8, 2011 4:55 AM UTC

TrackBack URL for this Entry:

12 Comments & 0 Trackbacks

Re: Math and Physics on Google+

This invitation business may only work if you have a gmail account. David Roberts is testing this out: I sent him an invitation one hour ago, to a non-gmail address, and he hasn’t gotten it yet.

Posted by: John Baez on September 8, 2011 12:30 PM | Permalink | Reply to this

Re: Math and Physics on Google+

Another way is, when inviting someone, you can instead “share this link with a group of people” to invite any number of people.

In theory, click on that link, and you can get a free Google+ account…

Posted by: Alex Nelson on September 9, 2011 3:11 AM | Permalink | Reply to this

Re: Math and Physics on Google+

And when the invite did come through, it was to the alternative gmail address I gave John. Just one data point, though.

Posted by: David Roberts on September 10, 2011 12:46 AM | Permalink | Reply to this

Re: Math and Physics on Google+

Something that makes me unhappy about Google+ is that there is no way to filter incoming posts other than by the circle that the poster belongs to. For instance, if I add someone to my “Friends” circle because I want to share personal thoughts with them, then everything they share with me appears in my “Friends” stream, even if what they post is primarily about, say, math. We figured this out back when we invented email, folks: the groups of people that I create in my address book to send messages to are separate from the mailboxes and filters that I use to organize my incoming email.

Posted by: Mike Shulman on September 8, 2011 10:06 PM | Permalink | Reply to this

Re: Math and Physics on Google+

Since people at Google know a thing or two about software, I figure they’ll keep tweaking and optimizing Google+ until most people are happy. I’m happy already because all of a sudden I get to listen and talk to lots of interesting people, in a way that’s a lot easier than firing off emails or roaming from blog to blog.

I never tried Myspace and Facebook, so perhaps this is old hat to most people… but Google+ is developing a different sort of ethos, and I suspect one that suits me better.

I’m hoping Google+ will make it easier to develop the Azimuth Project into the highly interdisciplinary thing it needs to become.

Posted by: John Baez on September 9, 2011 3:01 AM | Permalink | Reply to this

Re: Math and Physics on Google+

You can put people in multiple circles. So, for example, you could choose to have a set of outgoing circles and a set of incoming circles, and put people in the appropriate ones. Then use the outgoing circles for your posts and the incoming circles for reading others’ posts. (So far I haven’t bothered much with circles, but I thought I’d point out that what you want is possible.)

My annoyance is that I can’t filter someone’s stream based on my interests. For example, people have to ask John to be put into his circles if they want to see various topics. It would make more sense for John to just send out public posts with various tags, and let people filter them based on the tags they are interested in. The current method just doesn’t scale.

Posted by: Dan Christensen on September 9, 2011 4:11 PM | Permalink | Reply to this

Re: Math and Physics on Google+

Dan, I think that what I want and what you want are really the same; I just expressed myself poorly. The problem with “incoming circles” is that whatever John posts will appear in all circles that he happens to be in, with no distinction based on what sort of post it is.

I figure they’ll keep tweaking and optimizing Google+ until most people are happy

That would be nice. Unfortunately, some of their recent tweaking of their applications like Gmail and Calendar has made me less happy. But perhaps I am not in “most people”.

And now I will stop complaining about Google and let us get back to doing productive things. (-:

Posted by: Mike Shulman on September 10, 2011 5:18 PM | Permalink | Reply to this

Re: Math and Physics on Google+

Actually, I got a Google+ invitation not sent to a Gmail account several weeks ago.

Something that makes me unhappy about Google+ is the realname policy. You cannot hide your public profile completely, it will always show your real name. This does not worry me as much the fact that every single comment you ever make has your real name next to it, making it easy to compile a list of all the things you ever said.

I hope this post isn’t too off-topic. Controlling one’s online appearance is more important to some people than to others. The reason does not have to be fear of oppression and total surveillance, which may seem irrational to some, but may just be not wanting to have very cool posts on some hobby or minor interest to dominate Google’s search results while you’re trying to build a professional career or a business. It seems to me that by choosing Google+ instead of some other venue, such as a blog, one chooses not to talk to people who feel differently about always using their full real name, and one will never know what they would have contributed.

Posted by: anonymous coward on September 8, 2011 11:59 PM | Permalink | Reply to this

Re: Math and Physics on Google+

For what it’s worth, I talk to people a lot both here and on my blog Azimuth. These blogs allow anonymous and pseudonymous comments.

Posted by: John Baez on September 9, 2011 5:12 AM | Permalink | Reply to this

Re: Math and Physics on Google+

Thanks for doing this all these years. No one should expect you to do this in any other way than that which suits you best, sorry if my previous post sounded like I do.

Posted by: anonymous coward on September 9, 2011 4:03 PM | Permalink | Reply to this

Re: Math and Physics on Google+

in re:

Interesting piece on our local NPR yesterday about how Google ? and others are tracking all our data and
then searching and sending us stuff based on their algorithms assumptions about what we want to see!

Posted by: jim stasheff on September 9, 2011 12:51 PM | Permalink | Reply to this

Re: Math and Physics on Google+

As someone who thinks carefully about online postings, and who used to use a “consistent pseudonym”, I can say that I’m not worried about government surveillance. This is for a combination of two reasons: firstly if a government wants to do that they have the resources to do this using non-online sources. But there’s a second non-obvious consideration: sometimes governmental (including police, council, government contracts, etc) background checks are required for various things, and again these can find out various things you wish they didn’t know, whether using online or non-online sources. However, the people who do this are trained and will know how likely it is you’ll find, eg, a drunken escapade in a random individuals past, and in particular they are able to put what they discover in a reasonable context. My worry about putting unguarded stuff online because everyone has access, the people who are doing searches on you may put weights on the various things about you they find out which aren’t “contextually reasonable”. Combine this with the fact that they may not tell you what they’ve found that they believe is problematic (particularly since “officially” people like job interviewers aren’t allowed to do this in places like the UK) and there’s a potential for ill effects which you can never rectify.

Posted by: davetweed on September 9, 2011 6:37 PM | Permalink | Reply to this

Post a New Comment