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.)
- Keith Cooper, Dolphin studies could reveal secrets of extraterrestrial intelligence, Astrobiology Magazine, September 2, 2011.
For more on Zipf’s law, entropy and dolphins, see:
- Steve Nadis, Look who’s talking, 13 July 2003.
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.