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Interesting properties of the entropy function

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Update 2017-07-03: Corrected equation for associative definition, thank you /u/Syrak. This may not be the first time someone recognized this, but I have recently discovered some interesting and useful properties of the entropy function and now share them. First a definition: Entropy  —  H(p 1 , p 2 , ..., p n )  —  is a function that quantifies surprise in selecting an object from a set where the probability of selecting each object is given: {p 1 , p 2 , ..., p n }. This has utility in communications, information theory and other fields of math. H b (p 1 , p 2 , ..., p n ) = Σ(i..n)-p i log b (p i ) where b is normally 2, to express entropy in bits. Other definitions of H() use expected values and random variables. As an analog to the definition above, I will discuss entropy of a set of frequencies. p i  = f i  / Σ f i. Entropy defined without bits: A definition that doesn't use bits is: H(p 1 , p 2 , ..., p n ) = Π(i.....
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Nontechnical: What is ERC-721?

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Read time: 6 minutes. This post explains how ERC-721 works and does not require any prior knowledge of Ethereum or blockchain. 简体中文 -->  http://www.sfgroup.hk/news_post/通俗易懂的告诉你什么是erc-721/  （奇点财经翻译） How does your phone connect to a web server? Most of your time on computers/phones/technology is spent with a web browser accessing a web page. Most of the screens you see out in the world that display information are usually using a web page to show it, but they just hide the URL bar. The flight arrivals screen -- it's just a web page Think for a minute about how this ubiquitous technology works. You.  You are very busy and you are trying to access some information, maybe cat videos or sports scores or your family members' feedback on a photo you posted of your kid.  Your phone , or whatever other device is in your hand, that acts on your behalf. The web server decides how it wants to reply to your request. Technology people, the ones that ma...
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I Was Kidnapped in Manila and Lived to Tell About it

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Other potential titles: The US Embassy Doesn't Want You Know About This Kidnapping in Manila Scopolamine / Devil's Breath Trip Report It started Easter weekend This story starts at Noon Tuesday April 18th, 2017 on Makati Avenue. I just finished a meeting with the Philippines Board of Investments to discuss how my company can expand our business in Manila. (Also saw the QBO Innovation Hub , it was awesome.) I had plenty of time to kill and some emails to catch up on, so it's time for some brain food! I walked right to the hottest part of town, Makati Ave. and Jupiter Ave. , surely there will be something good to eat. And then suddenly, The Guy approaches me, I'm marked. Hey, I know you are you staying at the Jazz Residences? Jazz is about a 12 minute walk to here, and I did not walk towards Makati Ave. from that direction since I just came from the meeting. I'm always guarded with information and paying attention to stuff like that. There's abo...
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