Wednesday, July 1, 2015

Pluto

Here is a diagram of what imagery we can expect in the next two weeks from the New Horizons Pluto probe:

And if you want to see the new images as they come in, the best place to go is here:

Pluto has very bright and dark regions on it. Does it have a giant mountain range running all the way around the equator? Giant impact basins? We will know soon.


Sunday, May 24, 2015

evil, evil, evil, evil dogs



Things that are the same in high dimensions

I have a set of high-dimensional vectors. These vectors are distributed as a gaussian surrounding zero in all the dimensions. I choose two of those vectors, perform an operation on them, and search for the nearest neighbors among the set using Euclidean distance. The following operations all tend to return the same neighbors:

The sum
The average
n * the sum, where n is large enough (something like 0.25 to infinity)
The vector product (I think that's what it's called)
The element-wise maximum
The element-wise minimum
The sum of the element-wise sign function (e > 0 : +1, e < 0 : -1)

All of these basically give me something that is approximately a 50/50 mixture of the elements of the two vectors. Each of the elements of the result vector will resemble an element of one of the two input vectors. The multiplier n can be as large as you like because after a certain point, it's just saying "whatever is furthest out along that direction."

If you think of a simpler version of the same situation, it is easier to see what is happening.  Let all the coefficients be +1 or 0, still distributed as a half-gaussian. Then you can think of the values that happen to be +1 as "words" which "define" the vector. The result of any of the above operations will give you a definition that includes words from the definitions of both the inputs, and no others.

I think I could prove this mathematically, but maybe someone knows of a proof already I could use as a reference?

Friday, April 10, 2015

New planet candidates


The following three planets look like really good possibilities for life. In general, with a radius larger than Earth, one hopes for a temperature lower than Earth's, expecting a thicker atmophere. All three have suns that are close to the same temperature as our own, but the first two are smaller than our sun (.8 x) and the third is larger (1.2 x).
None of these have been announced on the news because they like to wait for confirmation.

These are different from earlier reports because they are orbiting yellow stars, like the sun, rather than orange or red stars (which are smaller and cooler).

Source.
Name
Year in Earth days
Radius in Earths
Temperature relative to Earth's
KOI 7016.01
385
1.2
35 C lower
KOI 7235.01
299
1.2
18 C lower
KOI 7179.01
407
1.2
17 C higher



















EDIT: On July 23, NASA announced that KOI7016.01 was confirmed. It's new name is Kepler 452-b. As of that date it was the most Earthlike planet found so far. The new radius is 1.6 and the new estimated temperature is higher than Earth.

Uninvited

I imagine everyone's favorite music comes from when they first begin to discover it on their own. Growing up, I listened to whatever eclectic variety the rest of my large family brought home-- Andrew Lloyd Webber, Holst, Simon and Garfunkel, Bon Jovi, Enya, Roy Orbison, Pachabel, John Williams. (One of my favorites at a very young age was the William Tell Overture. I loved how it built to an exciting crescendo, and then gave one satisfying ending after another. I would run and jump and leap off the furniture to the galloping orchestra.) But I never owned a CD of my own until I went away to college. I was driving for the first time, and would change the radio station to whatever I liked as I drove.
What was becoming popular in those days, the mid-90s, was what was called Alternative music. It was the alternative, I guess, to the rest of popular rock music. My impression was that the radio stations were called alternative first, and the music they happened to play picked up the tag from them. I liked it because it was a little bit richer-- the melodies did more complex things, the lyrics were more thoughtful, the voices cracked with pain, as if the singers were just barely holding it together. (And it was coming from the left-- there's nothing like being dropped into a hyper-conservative place like BYU to make you realize that your own opinions are rather more liberal on things like feminism, environmentalism, and the roles of government.)
When I tried to share the music with my family, they were unimpressed. Where I heard suppressed anger and pain, they heard mostly whining and swearing and drugs. And I guess I liked that, too: it was transgressive, a little shocking.
Alanis Morissette was at the center of the genre. The songs from Jagged Little Pill-- "You Oughtta Know," "Hand in my Pocket," "Ironic," "You Learn"-- were all among the most popular. I liked them, but I don't know that I would have picked her as a particular favorite. And then came "Uninvited."
The song was written for the soundtrack of City of Angels. (a good romantic movie in its own right, if far less rich than the black-and-white European film Wings of Desire it was based on.) Although some of the lyrics make sense in the context of the movie, I didn't see it until it came to the dollar theater (where it had been edited, as was the custom in Provo) and by then I had already imagined what the song might be about-- a picture that fits the lyrics better than the movie does.
The song starts minimally, with four notes played over and over. Then Alanis's voice comes in, carefully controlled, precise, beautiful and cold. The words she uses-- "unfortunate slight," "worthy," "deliberate"-- they aren't the pop radio sound of "love me, baby, yeah, yeah." It's precisely the way a royal would speak. Whenever I hear this song, I imagine her sitting on a throne, a little like this, though surely wearing black instead of white:
It's capturing a single instant in time. A man has just entered the court, someone mysterious and handsome and powerful in his own right. We never see him-- he's the listener, addressed in second person throughout the song-- but we see her reaction to him. She's flattered by his fascination. He, like her, is a ruler, a shepherd meeting a shepherd. There's a mystery here, for both of them. She calls herself an uncharted territory, he's an uninvited stranger. What she's feeling is an a attraction to the dangerous unknown that he embodies, and she knows he feels the same about her.
But what kind of royal court could this be? There are electric guitars in the background. The singer, Alanis herself, is inescapably part of the modern city world. What I imagine is the urban fantasy of Charles DeLint, where hiding behind the everyday reality of life in the city, there are supernatural courts of powerful and secret people. 
The lyrics spell this all out, but it's backed up at the same time by an incredible synthesis of modern and classical styles. Everything about the music is calculated to produce a feeling of uncomfortable, building, dangerous excitement. The minor key, established in the first repeated measure, grows repeatedly richer and wilder. Strings come in at unexpected moments, bending the notes to a new, even more unsettling harmony. The stoic squirms. The instruments come in a few at a time, building and building, blending perfectly the electric guitar and the symphony in a wild dance, and then, suddenly-- back to the first four notes themselves, and her ever-so-carefully chosen words of dangerous politeness: "I don't think you unworthy / I need a moment to deliberate." Again, in a rush, it all comes back, building to an even more frenzied peak before ending with a single, dying guitar chord.

Alanis Morissette never again wrote anything similar. I've looked for other music like this; Orchestral Metal has the guitars and the violins, but ruins it by filling it with angry men yelling at me. The group Evanescence managed to capture the feeling, occasionally, but never manages to get it all in the same song, and inevitably goes to a repeated chorus, which "Uninvited" never stoops to. Part of the power of the song is its uniqueness, its sense of otherworldly origins.

Monday, April 6, 2015

word2vec, Babel-17, Galileo, Adamic, and the displacer beast from Adventure Time

I came across (in a book of esssays by Italo Calvino) the following passage from Galileo's Dialogue Concerning the Two Chief World Systems:

"I have a little book which is considerably shorter than Aristotle and Ovid, which contains all sciences, and which with just a little study can allow others to form a perfect idea of it. The book is the alphabet, and there is no doubt that the person who knows how to put together and juxtapose this or that vowel with those other consonants, will get the most accurate responses to to all doubts and he will derive lessons pertaining to all the sciences and the arts. In exactly the same way the painter can choose from different primary colours set separately on his palette and by juxtaposing a little of one colour with a little of another can depict men, plants, buildings, birds, fishes; in short, he can represent all visible objects even though there are no eyes, feathers, scales, leaves or stones on the palette. In fact it is essential that none of the things to be represented, or even any part of them, should actually be there amongst the colours, if one wants to use them to depict all manner of things, because if there were on the palette, say, feathers, these could only be used to depict birds or plumage."

This immediately reminded me of word2vec (which is on my mind constantly these days). You can think of word2vec as a bilingual dictionary. The other language is a strange one: every word has exactly 300 letters. The difference is that in that language, words which have similar spellings are similar in meaning. The remarkable thing is what an enormous amount of knowledge about the world is wrapped up in the spelling of these words. Just as one can guess at the meaning of tele-phone by the meanings of its Greek roots, or at the meaning of a Chinese word by the meaning of its characters, so to in this language the meaning of a word can be learned from the characters it is written with. The consonance, assonance, and rhyme between parts of the name, and the relationships between the letters, encode "approximate knowledge of many things."

There are two important differences, however. The first is that each of the letters, by itself, has an incomprehensible meaning. This is similar to what Galileo was saying about letters and colors of paint. If you have a pigment that is "feathers" you can only draw birds or fancy hats. But these letters let you express whatever you want, by not carrying a meaning by themselves, only by their juxtaposition.

The second is the sheer enormous amount of knowledge contained in the structure of the spellings. The capital of every country or state, the parts of machines, the attributes of movie characters, the celebration of holidays, all are contained in the spelling of the words. It resembles Babel-17 in that once you learn the true names of things, you know all the facts about those things. It is the language the world is written in. And yet at the same time it is profoundly dependent on our culture.

Wednesday, April 1, 2015