Welcome to the Sea of Echoes

I’ve been playing music seriously now for about four years and it still suprises me how every few months a new dimension opens in my perception. 

At first I was content to simply play the right notes in a chord to some kind of tempo.  After that came microtiming, timbre, attack, degree of legato, the level of stress in chords and intervals, anticipation and suprise in rhythmic phrases, the hemiola.  The list of musical features goes on and on.

Today I want to reflect on a the physical feeling one gets when hearing or producing sounds.  We all know that there are many notes to choose from and that there are overtones of each note at multiples of the fundamental frequency.  Recently I’ve started noticing that certain overtones seem to stimulate certain areas of the physical body, especially when sung, and that these areas might have emotional effects.

For example one day I was watching Rage Against the Machine at a concert and I was struck (literally) by a pounding feeling in my chest every time the kick drum went off.  It seemed that the sound of the kick drum was somehow linked to the resonant frequency of my chest cavity, and perhaps this is the function of the kick drum - so that when the kick fires it is playing not only the air at 30-60Hz, but also playing the chests and hearts of everyone in range.   Consider this then, that vibrations in this 30-60Hz band map to a physical space in the lungs or chest.

On the opposite end I was mixing some vocal tracks and noticed an unpleasant nasal quality to some vowels which could be removed by adding a band stop filter around 2kHz.   (Or by singing slightly differently).  So perhaps the nasal resonance is near this frequency and produces an attention-getting, but slightly annoying quality.  Think of Axel Rose singing “Sweet Child of Mine” - you’ll definitely notice him, but I dont think it would lull anyone to sleep.

It is possible to think of the human vocal tract as a vibrating string with low tones low in the torso and higher tones in the throat or head.  Higher pitches require higher levels of tension to produce and probably result in higher tension in the listener.  I wonder if we could show some other physiologial effects by considering vibrations at different frequencies.

Here’s a rough map of frequency to body position:

• C3 (131Hz) - deep chest
• C4 (262Hz) - middle of the throat
• F#4 - this is the natural tension-free note for my voice
• C5 (524Hz) - back of nasal passages
• C6 (1.04kHz) - top of the nose

Questions:

• What is the natural frequency of the chest cavity or heart?
• If the deep chest sounds stop at 100Hz or so, what areas of the body are stimulated by deep bass (30Hz)?

Ok - this kind of stuff is really boring to most people, but I’m just writing it down because I’m going to forget it.

During server migratation, symbolic links stopped working.  The solution here was to set the open_basedir in php, which can be done in the vhosts.conf file.  It seems that the path name needs to be enclosed in double quotes to work.

Two hours gone for this stupid problem!@#(*$&)@#($*!!!

Really interesting panel on social games:

Social Games for Social Platforms: Unleashing Viral Fun Jeremy Liew (Lightspeed Venture Patners), Mark Pincus (Zynga Game Networks), Shervin Pishevar (Social Gaming Network), Michael Lazerow (Buddy Media), John Hwang (Tripmonger)

• Games are Hit Driven
• Some games can be financially successful at 20k users
• In-game purchases
• Virality is not the only way to grow
• Look at SGN links
• Look at games

(more…)

I’m building an isolation booth for drums in my garage.

Drums are loud.  In terms of decibels, John could probably play at 120dB easily.  Comfortable speech levels outside are at about 70dB, so we need about 50dB of attenuation between the drums and the outside.

Here’s a plot of the attenuation we have, with no box, with the box itself, and with the box and the enclosing garage.

The box provides about 15dB of attenuation right now, though it is essentially transparent at 160Hz, 250Hz, and 500Hz.  It’s 8 feet long, so that’s a round trip time of 16msec or so.  We’d expect a resonance around 60Hz.  Or this could be the self-resonance of the walls or window.  Clearly we need some damping to improve this.

The garage doesn’t block anything below 100Hz, but it’s good for 10-15dB above that.

Need another 15 db overall to get to our target of 50dB of attenuation.  I’m thinking a second layer of ply with some kind of damping or absorbtion will be necessary.  Might be best to experiment with curtains or light duty acoustic tiles and then decide if we need the extra plywood.

Something strange was happening last time when we looked at the probability that two words occur together on the same page.  It appeared that even distantly related concepts appeared to have joint probabilities hundreds of times higher than chance.

To figure out what is going on I’ve compiled a list of how many pages come up on google doing a single word search for about 50,000 words.  Here are some significant entries:

and 5140000000
the 4790000000
reserved 4300000000
copyright 4200000000
home 3880000000
or 3700000000
not 3660000000
s 3520000000
are 3400000000
an 3280000000
that 3090000000
search 3090000000
page 3040000000
…
projectile 5450000
pert 5450000
partake 5450000
linguist 5450000
devolution 5450000
Reba 5450000
Grimaldi 5450000
sleepwear 5440000
…
mechanizer 585
fraternizer 575
acclaimer 557
entrammel 552
baulker 543
rumourmonger 520
homoeotherm 502
enfranchize 478
harmoniousnesses 340
humourer 279
vialful 278
arithmetise 250
non-sympathiser 115
shakeably 46

Amusingly, this web page will now have a 2% increase in the occurance of the word “shakeably” on the web.
Yesterday’s calculations were based on pages with the word ‘the’, though it seems like ‘and’ would have been a better choice to find more pages with English.

If letters make words, then words make thoughts.  One way to try to represent relationships between words is to look at how often they occur together on web pages.  We can get an estimate of this by looking at page counts in search engines.

Pages of English

First we need an idea how many pages contain English sentences.  A search for the term “a*” produces about 15 trillion, but many of these are pages which do not contain english sentences.  A search for the word “the” returns about 4.8 trillion, which is probably a better estimate of the number of pages containing english.  We may have missed quite a few, but we will be close. 

Is George Bush a Maniac?

Here’s a simple example using the words “George Bush” and “Maniac”.

• A google search for “George Bush the” returns 165 million pages.  This is a probability of about 3.4e-5.
• “maniac the” returns 2.75million, or a probability of 5.7e-7
• The joint probability if the two terms were independent is about 2e-11, which should produce about 94 pages.
• Instead we get 545k pages, which is 5.7e3 times more combined pages than what you would predict otherwise.

Something strange happens when I try to create a counter-example.  If I look for the relationship between ‘George Bush’ and a randomly chosen number like ‘193443′, I get the following:

•  Probability of a page containing ‘193443 the’: 2.2e-9 (15k pages)
• Expected number of joint pages: 0.52
• Actual number of pages: 52 pages
• Ratio of likelyhood: 101 more than chance

Although it is counter intuitive, it turns out that there are relationships between ‘George Bush’ and this particular number, even though the average person might not expect it.

Consider the following likelyhood ratios:

• cat-dog: 3561
• airplane-sasquatch: 10313
• copper-existentialism: 2898
• preponderance-evidence: 12887
• invisible-brick: 2360

What is going on here?  Clearly the likelyhood ratio is high for common phrases, but it is also high for things that seem rather unlikely such as ‘invisible brick’.  It’s actually really tough to come up with pages with low likelyhood ratios:

What is going on here?

The Machine That Ate the Planet 

I’ll be starting to work at Google next week and from what I can gather they are basically building a computer the size of a planet to store and process all human knowledge.  Actually with the addition of video to searches it might be closer to say that the computer will store all of human experience, but hey, one step at a time kids…

I’ve always been suprised that the best way Google can pay for it’s ginormous database is by selling ads.  There’s nothing wrong with ads, it’s just seems to me that there’s a progression from an index of keywords on web pages to a semantic representation of information.  If we could alter the representation of a page suitably, would we transition from a machine which is able to find pages to a machine which knows things about the world.

What is ‘Knowing’? 

Of course this raises all kinds of spooky questions about what it means to know things.  If I can type a question into google’s search bar and find a page that gives me the answer without too much trouble, then this might be as good operationally as a true AI.

For example, if I type the question ‘What is the diameter of the earth?’ I receive the following response as the first result:

What is the diameter of the earth?

The answer to the geography question - what is the diameter of the earth?

Could an AI do any better?

Still, it is tempting for me to believe that Google might be able to do better if it represented information with some kind of semantic network.  I.e. breaking pages down into paragraphs and sentences.  Semantic networks are sort of an old idea in AI, and are discredited now as far as I know.  But they make possible several interesting linguistic tricks like the generation of non-sense sentences.

Sentence #123901210312

We tend to represent our thoughts online in a written language like English.  The information density of English is pretty low - something like 1 bit per ASCII character.  So we know there is a lot of redundancy in english sentences.   But there is another kind of reduncancy.  The same thought can be repeated over and over.  For example, a search for the sentence:

“Albert Einstiein is a smart guy”

 produces two hits.   The sentence:

“George Bush is an asshole.”

produces 14,500 pages.  We might be able to draw inferences about beliefs based on how frequent certain sentences are used.

There are a couple of trillion web pages out there, say 10 to the 10th power.  If every web page could be analyzed into say, 100 sentences on average, that means that every sentence on the web could be given a number from 1e15.  That’s a measly 52 bit number to represent all the possible sentences on the internet.

 

Letters Make Words

You could also choose to build a semantic network around the notion of sentences in pages, or words in sentences.  To do some simple visualization experiments though it’s fun to ask google about simple character frequencies.

As of this morning, Google has about 8 trillion pages in the index that contain the word “a”.  You can actually do this query for all 26 single-letter “words” and you get a frequency diagram that looks like this.

 

 

 

The word “a” is the most common single letter word followed by “e” “i” “o” and curiously by “s”.

In true Martin Gardener fashion, you could do the same thing with two letters next and you get a little frequency chart like this:

 

The bright spots in the image correspond to words like “be”, “is”, “of”, etc, so this figure does say something about the english language.

 

Building a frequency table like this isn’t that enlightening and it gets progressively harder as the number of letters increase.  But it does provide some early clues about how we might build or visualize a semantic map.  Next time I’ll try to extend this idea with words.

 

During a recent trip to Lake Tahoe, I was eating dinner with five other friends when we stumbled on the problem of chosing one of us to eat the last salmon ravioli.  Someone suggested rock scissors paper, but the combined geekiness of me and my friends (Bill and Anne shown above, among others)overwhelmed us and we came up with a generalization of the game.

Say you have N players.  Each person picks a number between 0 and N and in rock-scissors-paper style in reveals their numbers by thrusting their hand into the middle of the circle on the count of three.  The number they selected is indicated by the number of fingers raised.

Players are eliminated anytime someone has chosen a number exactly one larger than them.  For example if I chose three and any other players selected four, then I would be eliminated.  The player who selected four would be eliminated if five had been chosen by someone else, but I would still be eliminated.  That is to say, of any collection of people who select a run of numbers, only the highest survive.

As you might expect in rock-scissors-paper fashion, 0 beats N.

Someone is guaranteed to survive because there are N+1 numbers and only N people.  You can choose to reduce N at this point if there is more than one survivor (which could happen if more than one person chooses the same number).  Sometimes, keeping N the same is the simplest, and it prolongs the game a little since two people can circle each other for a little while before one of them gets the kill.

We called this game fingle because it uses fingers and because all good things in this day and age seem to rhyme with Google.  :->

The floating blobs you see on this page are the result of me waiting time simulating celestial mechanics in javascript…

One of the first projects I worked on at Stanford was the handvox.  I had this idea for using hand gestures to control speech synthesis so you could “talk” on a busy train.  I used Stanfords Music 250A class to try this out.  The result was an accelerometer-based data glove that drove

Soldering the compoents took about two days, and adapting the code on the AVR Mini took about a day or two.  The AVR program sent OSCserial messages to a program running on my PC, which translated the serial port OSC into OSC over IP, which then drove a synthesis patch in PD.  The results of the synthesis were ok - I could modulate volume and pitch and switch from voiced to unvoiced sounds.  The data rate of the serial link was too slow with all the sensors I had and there were definite ergonomic and usability issues with the glove.  A better interface would be to have an inobtrusive camera mounted somewhere.