RockofStrength

This phenomenon is explained by many-worlds: The two photons have both polarization orientations in the multiverse. We are limited to a single instance of the multiverse, and any interaction whatsoever between the photons and our universe will force them into a single instance of polarization orientation, as this is all we can experience, being interacting beings ourselves.

Reality is really an immense interconnected binary tree, and we must always travel along a single path. It has the property that reconciling paths (paths that diverged but met up again with no interaction in our universe) will again be accessible to us.

As Galileo was prosecuted for supporting Copernicus' heliocentric theory (more specifically for championing reason over faith), the Church's default stance was that the planets moved around the sky 'as if' they orbited the Sun. We are in a similar position now with many-worlds vs. 'as if' many-worlds, based on experimental evidence such as the Mach-Zehnder interferometer results.

Musicnovatory.com presents quite a few interesting music theory concepts, though it is quite opaque and off-putting in parts. For example, they present a generative binary theory of rhythm, a 'tetrad' theory of chords (by fifths and 'metamorphoses'), and a whole array of binary open/close 'entities' (rhythm, harmony, and 'melolines' (the chord tones of the melody)).

The only new tip I received from the article (I'd pretty much heard the rest before) is to make the peak of your free throw's arc parallel to the top of the backboard.

What I'm really interested in is learning how to dunk...all I need is about 4 more inches to do it comfortably.

The good thing about patents is that they motivate the discovery of alternate approaches. The bad thing is that they stagnate inter-connective progress.

Patents have become a hideously bureaucratic market unto themselves, creating a kink in the hose leading to the fountain of progress, but the fountain attained its magisterial beauty partially as a result of the motivation to circumvent roadblocks.

I'm a big fan of that approach. Betterexplained.com uses the method.

A very interesting theory of storytelling is the Dramatica theory of story. http://storymind.com/dramatica/

I believe the movie Contact (any many others) were written with the Dramatica template.

This area was how I was introduced to the site (I was investigating Robert Mckee because of seeing the movie "Synecdoche New York"): http://www.dramatica.com/theory/articles/index.htm

Actually I've heard him say that it was a misunderstanding in multiple interviews, quite candidly.

Not necessarily; I usually don't use a score when I play. It would also be insightful to see the 1st person perspective of a jazz musician playing from a lead sheet, to see how his eyes jump between page and piano.

I have a tangential question: What's the state of technology that would allow one to see through the eyes of another? This would be useful for piano tutorials, etc. I think it could be done with a separate eye-tracking device and a camera located between the eyes.

This type of technology would be a nice novelty item to implement into a futuristic zombie story. For example, there could be a large battle between humans and zombies, and the humans are equipped with pulse-magnifying glasses, allowing them to identify friend vs. foe.

To turn small talk into a conversation, switch from objective facts to subjective opinions.

"There is an interesting paradox in teaching: the better you know a subject, the harder it is to talk to beginners. Experience means you have forgotten what tripped you up when you were a beginner."

This reminded me of how I always have to clearly explain to my beginner piano students that the higher the note on the staff, the further right on the piano it goes. It's very non-intuitive that up/down on the staff = right/left on the piano.

Simple explanation for Benford's Law: When numbers expand out into an additional digit through doublings, a "1" is always present, "2" is usually present, and so on down the line. The law is present in proportion to the degree that the sample set possesses logarithmic distribution.

The distribution doesn't have to be limited to doublings. The law also applies to triplings, quadruplings, halvings, etc. The key is logarithmic/exponential/geometric distribution. Try it for yourself on the calculator and see how rarely 9s come up as the first digit for every x^n.

A good real world example would be the distribution of frequencies of musical pitch in equal temperament. In this case, the exponential multiplier (x) for x^n is 21/12, or about 1.059. Here's (http://en.wikipedia.org/wiki/Piano_key_frequencies) a list of the frequencies; notice how the first digits have tons of ones and almost no nines.

Thirty of the top fifty players are South Korean, while only one is from the US.

Both pi and tau form infinite strings of prime numbers with their digits. See if you can get the first twelve!

This is my layman's understanding of Godel's incompleteness theorems: Any set of axioms powerful enough to decide all its theorems will always have inconsistencies in its theorems (e.g. "if true then false"). To be consistent, the set of axioms must be incomplete (some of its theorems are undecidable).

The following sentences have some of the 'flavor' of Godel's theorems:

"This sentence is false." →if true, then false.

"These are not words." →if true, then irreconcilable with its own truth.

Hofstadter cares a lot about form, and thinks it is intimately connected to function. I believe in the end of "I Am a Strange Loop" he said that he edits every single line of text so it fits evenly and aesthetically across the line. In other words, each line must stretch to the far right of the page, but the letters can't be stretched out/separated too much. This must be extremely tedious to accomplish.

I'm impressed that Madoff was smart enough to mimic Benford distribution in his monthly returns (that's what the article led me to infer).

I actually made an r/math post about Benford's Law that I thought was pretty interesting, although it didn't get much attention or many comments (admittedly bad signs). Any peer review (or su-peer-ior review) is appreciated.

Here's a snippet: "...generation of the geometric layout for Benford first digits is a similar process to creating a Sierpinski Triangle by drawing a triangle, and randomly plotting midpoint dots between vertices and sides recursively. In the Benford case the plotted dots are instead individual numbers, which share a geometric connection (e.g. two galaxies colliding will on average be a doubling, so galaxy size should possess Benford distribution)."

http://www.reddit.com/r/math/comments/gkj2i/benfords_law_exp...