I don't really understand this "Entropy Is All About Arrangements" takeaway. A fair coin has higher entropy than a biased one. What are the "arrangements" in this case?
The coins don't have entropy, the sequences they produce do (in information theory sense, this is not about physics).
For a long sequence (say 1000), the former will produce close to 500 heads and 500 tails. The latter, assuming one heads are three times as probable as tails, will produce around 750 heads and 250 tails. There are many more different sequences of the first kind.
I'm referring to the entropy of the Bernoulli distribution. If the coin is fair, the entropy is 1 bit... if the coin isn't fair, then the entropy of the distribution is less than 1 bit. I'm having trouble reconciling the information theory way of thinking about entropy as a function of a distribution, with how physicists tend to think of entropy of arrangements.
There is a relationship between the distribution of x_i and the sequences generated from that distribution x_1, x_2, ..., x_n. If the coin isn't fair there are less arrangements possible. If the coin has two heads there is only one possible sequence.
I always read comments about how Twitter is not profitable. Any ideas as to how much of their revenue comes from ads vs. businesses paying for API usage?
That's a broad question without one single answer.
In my experience, getting approved to use the API is substantially easier with Facebook than Twitter. Twitter will reject for bullshit reasons, and send you a "there can be no appeal" message. The only way around it is to kick up enough of a fuss with prominent people to get a manual reconsideration.
Once you're in, though, you can pretty much do anything a Twitter user can do. Facebook heavily limits what data you can get - you basically can't get any info about the user's personal profile/feed, or info about a user's friends. Twitter makes all that readily available.
On the other hand, analytics.twitter.com has no API (and hasn't for years), whereas Facebook makes all sorts of analytics info available on Pages.
One thing conspicuously missing is getting all of the replies to a given tweet. This makes it difficult to build anything resembling an alternative Twitter UI (such as existed the the hayday of more open Twitter APIs) using the official API.
For a long time my whole life was in a textfile called 'phone numbers.txt'. It had started as a list of phone numbers of my friends (I didn't have a cell phone myself; dumb phones existed but I didn't want one) and grew into a huge repository of information.
For a while now I've been using pieces of paper which I file in numerus currens style and keep inside shoeboxes. Many tend to be thicker "fiche de la police"-type cardboard so the whole thing stays up even if there are also many loose folded-in-half A4 sheets. OTOH I've almost lost notes in the laundry and still rescued them with the hair dryer.
It's also hard to represent equations and diagrams in most note-takers. Interfaces, as the etymology suggests, really get in your way! The one drawback is to find oneself occasionally without paper. But again in a pinch even business cards and receipts (you can photocopy the termal paper at home later) are possible hacks.
(Numerus currens is like paper nosql: when you file a new note, first you quickly browse through your archives for similar topics, otherwise you number it max_N+1. If there's something similar with number 110, you might number 110/A, 110/B, 110/C; if something that belongs with 110/B comes, it's filed as 110/B/1... but you can never shake the whole thing out and lose the order, so I wouldn't recommend this system to people with large dogs or small children.)
"Essays on Cellular Automata" by Arthur Burks is a good starting point. Then there's the proceedings of the conference, "International Conference on Cellular Automata for Research and Industry".
Start by going to a good library and checking out the proceedings of the Artificial Life (ALIFE) conference. Read the papers and start following the references.
In addition to the more directly related stuff others have mentioned it's also relevant and interesting to dive into Complex Adaptive Systems literature if you have the inclination, for the classic order-from-chaos essays and discussions of emergent properties and so on.
