Chaos Iguana - Music from Maths (the logistic map in the chaotic regime)

This is what the logistic map sounds like in the chaotic regime.
Well, after you map the continuous outcomes to the chromatic scale.

A little ditty I dreamed up while I was Mr. Botak  (Guess I still am, Botak means bald in Bahasa Indonesia) for the occasion of the inauguration of a dynamical professor.

Also a tribute to a great monologue by Speed Levitch in Waking Life and a great poem by Lorca

"It looks random, but it is not"

(Edward Lorenz in the Essence of Chaos described deterministic chaos and similar phenomena as "Things that look random, but are not")

天

The connectome: Into the brain and beyond

As you may know, I am not a fan of contemporary neuroscience that attributes to the brain the central processor function that you may encounter in a computer.

Of course, it must be there for a reason and it is probably not just there to cool blood as Aristotle believed

As you may also know, I am currently studying the brain (again) using a complex network approach. The video below is a very impressive talk I came across on TED. Although I would go much further and be more radical about what it is that is connected, or rather nested this talk very elegantly gives an insight in the overwhelming complexity that is involved. Yes, much more complex than a machine that obeys the algorithmic laws of computation.

http://youtu.be/HA7GwKXfJB0

http://www.ted.com/talks/sebastian_seung.html

Just ignore the technology fallacy at the end (i.e. if we wait for bigger, better, fancier technology, we'll know everything...). Where are the robots?

day 11: Origins #1 - Lost Archetypes, Fading Shamans and Unfinished Labyrinths

[caption id="attachment_332" align="alignnone" width="427" caption="Masters of the Labyrinth - Lyrics"][/caption]

Apparently this was too much for slow connections in combination with slow iDisk servers, so I split it in two.

Part #1

A long time ago in a Netherlands far, far away...
Before I knew anything about things that look random but are not
Before I knew anything about branes, brains and automatons
Before I knew about Musashi, Lao Tse, Gödel, Escher and Bach
Before I knew about structure and systems

I wrote Confessions of a Demi-God, a song lyric

Well... “wrote” is not really the correct tense here, maybe “started to write” is better.
I didn’t write it as one piece, not in one go, but it was always meant to be a trilogy in three stages:

Confessions of a Demi-God stage one: Random Order
Confessions of a Demi-God stage two: Sentient Chaos
Confusions of a Semi-God stage free: The Lost Archetype

Always a part of it and appearing as a piece of prose was All in a Day’s Dream: An epilogical prologue

Over the years it emerged from high-school scribblings between homework assignments into an epic that has been (partially) set to music three times now by different musicians...

The 92/94 - Lost Archetype - version
The 97/99 - Fading Shaman - version
The 01/03 - Unsolved Labyrinth - version

Over the course of the years lyrics have been added, removed, changed and reintroduced again.

The 92/94 - Lost Archetype - version

The second stage was actually performed and recorded first chronologically, in the period of 1992-1994. Back then we changed our high-school band name from Nightcrowd to Scrythe (yeah, I know), as we changed our musical direction and dropped some personnel. We made a demo tape on a 4-track recorder (yes youngsters, that’s what people did in the old days)! Incidentally, Hank Heijink the owner of the 4-track, whom I didn’t know very well at the time, was the brother of the girlfriend of our drummer Marco, became my colleague at the Radboud University many years later as he got his PhD in cognitive (music) psychology @ the Music, Mind Machine Lab, after his masters degree in computer science and after he finished the Brabant Conservatory in Classical Guitar, only to continue after his PhD to get a degree in Lute and Theorbo at the famous Royal Conservatory in The Hague. Apparently he’s also writing iPhone apps now, in NY. I just knew his reputation as an extremely talented drummer and percussionist in 1992.

Oh, how people can change...

But I digress, back to the trilogy that never was:

Here is a part of the booklet (click the image to download the entire thing). All in a day’s dream is already there as prose to fill the booklet. In the last column it says: Not included but definitely part of the story... Those songs did not exist as music back then.

[caption id="attachment_334" align="alignnone" width="720" caption="Masters of the Labyrinth Booklet"][/caption]

Now about Hank’s 4-track, we did not have anything else. Just some cheap mics. The noise you hear (especially in the beginning as I play the harmonics with delay, is also because of the effects unit I had at the time for my guitar: a cheap Zoom that the entire band called zoem (hum). The distortion was of course worse than the delay as you can hear. So we used all four tracks to record the music, then down-mixed some tracks to create room for vocals... we just didn’t have a vocalist.

So I did it, in a room the mother of our bassplayer (and my neighbour) Bjorn used to cut people’s hair in. With a mic that didn’t even have a detachable cable, or an XLR plug. I don’t even remember if I had headphones....

[audio: 05 Scrythe - side b - 05 - Confessions.mp3]

Yeah it sounds terrible and so do I, but the music is still pretty ahead of its time :)

Bjorn came up with the the term Lost Archetype by the way. In a phone conversation about band names I had suggested Lost Horizon and Ancient Archetype, a simple contraction did the trick. He is the best bass player I know, I mean listen to the bass slap breaks in this song, we were 18 for God’s sake. I have NO idea how to do that. He lives in LA now.

The Lyrics to stage two at the time were as follows, maybe you should read them as the music plays:

Confessions of a Demi-God
Stage: Two

-- Sentient Chaos --

So I was wrong to believe in the absence of structure,
But I never claimed to be a soulless one,
I found that chaos speaks to us through order,
Controlling the flow of reality itself.
Precognition?
Indeed!

This is the evil playground,
Where we witness the creation of our own damnation.
This is the factory of lies,
We built in the city where truth was born.

Oh no!
Not again,
Not now.
Recounting my years in captivity,
Twenty-one and some,
A raid of ego to bind the last to the least,
The anguish arrives!
Here it comes!
HERE I GO!

The really funny funny, strange, weird -I don’t know- thing about this text is that it makes a LOT of sense to me now. I can’t imagine what I meant by it back then when I was 21. That’s actually the age I first started drinking beer. Well... there you go

The 97/99 - Fading Shaman - version

Then some years later (1997/1998) and some personnel changes later we did some proper recordings, this time of stage one and we asked my brother to sing (he added some cool lines too!). Below are the lyrics, read them as you listen. The three song demo (on CD this time!) was called “All in a Day’s Dream” and of course again featured All in a day’s dream as prose in the booklet.

About a year after the release, I met the people of Entheon in Nijmegen who translated and published Terence McKenna’s “Food of the Gods” in Dutch. We cooperated for a certain underground movement, on some stuff... that... well... eh... is not for this blog right now.

Anyway... When the translator read All in a day’s dream and Confessions stage one, she said: “Wow can I send this to Terrence? He’ll love it!” ... uhh ... hey well who am I to refuse such a great mind? Well, it turned out he had just been diagnosed with brain cancer, or glioblastoma multiforme. I am not sure he actually read it, because this thing is so aggressive he died a few months later. Since then, the subtitle in my mind has been:

For Novelty, whenever I may find her. Well, perhaps in two years :)

Ok, so here it is, in honour of a great shaman:

All in a Day's Dream
An Epilogical Prologue

The Master of the Labyrinth sighed as he knelt beside me. I saw his eyes focus on my naked brain and I guessed he was examining it for abnormalities. He then spoke to me:

"Foolish young creature, your quest continues. I will share with you the Truths you must pursue, for they are One and they are All. First, analyse the manifestations of Order, then delve for the powers of Chaos. When you are still in possession of your life after having done these things, you must begin the search for the Lost Archetype. Be everywhere, investigate nowhere."

And of all the voices I had ever heard, from the roaring of the pit-demons to the angelic high whispers of the air-spirits, this voice was the softest, the deepest and the most frightening one. Then he took a piece of my brain and as he slowly merged with the dark surroundings he said:

"You won't be needing this."

----

Confessions of a Demi-God
Stage: One

-- Random Order --

I - RES EXTENSA

Overt and blurred
The race for time begins (now!)
Naked and hurt
I breathe life!

Silent, unstirred
The virgin universe cries
Forced to compel
Infinity!

II - RES COGITANS

Systems within systems
So relieved to have reached the shores of reason
The burning dreams I left behind
A testimony of my treason
Wild guesses, my new vessels
Across the planes of panic
Beware of the two-faced trespassers
Their touch will leave you frantic

The attempted blend with reality
Left me blind to the light of relativity
Crippled, in a way, I seek my refuge
To keep me from collapsing in insanity

Systems within systems
While I release the firm hold
And dive into a free-fall
Of distance through cold

Overt and blurred
The race for time begins (now!)
Naked and hurt
I breathe life!

Silent, unstirred
The virgin universe cries
Forced to compel
Infinity!

III - UNITAS MULTIPLEX

Crystalline dreams
Lost in my world
Blessed and deceived
Losing the race!
Violent minds
Reach for my land
Intangible leash
Can’t be set free!

Somewhere between stimulus and response

IV - SOMEWHERE BEYOND STIMULUS AND RESPONSE

Tempt me all you like
There is just one way
Out of this apocalypse
Strife drowns my pride
Self preservation
Must delete itself
Prison deep within
Guarded by hauntings
Who appear to be
Mere fragments of me

"Lie not", they tell me
And with lies they hold me

Forget
Reject
Relay
The will to crave

<As far as I can remember the underlined words were added by my brother>

I used to have a website called Purple Brain Recordings whose index page looked like this:

[caption id="attachment_324" align="alignnone" width="380" caption="Purple Brain Recordings"][/caption]

L.A.P stood for Lost Archetype Productions

day 10: She’s Back!

[caption id="attachment_311" align="alignnone" width="300" caption="She's back!"][/caption]

What is so butter about these flies anyway?


Follow the link by clicking the picture, wait for the applet to load and hit the start button on the page. Now the applet window pops up. Fill in the applet as shown (just the dX0 box), hit Reset and then Start, speed it up by moving the slider.

This is the butterfly attractor of the Lorenz system for two different initial conditions. The amount by which the initial conditions differ is in this case 0.0001, what you filled in at dX0, but you can make it even smaller: 0.0000000001

[caption id="attachment_312" align="alignnone" width="407" caption="Lorenz attractor applet"][/caption]

After a while the trajectories start to diverge. At some point both trajectories predict the complete opposite atmospheric conditions. Each coordinate (x,y,z) corresponds to a state of the atmosphere and hence the weather. Imagine that the left wing represents predominantly sunny weather, the right wing could be a nasty hurricane and this difference is “caused” by the very small difference in initial conditions at dX0. It could represent a sneezing butterfly, so small. At least the speech was a storm in glass of water at the other side of the globe.

Must have been my Grog.

It’s apparently a difficult question, about the flying butter.

Chaos is much easier.

Huhuh... He said: “that which gapes wide open, is vast and empty”

Gaaaaaaaaaape...


doh!

Gape-Gaap-Looks random, but probably is not...

day 6: Rainy Reflections (three of them)

[caption id="attachment_297" align="alignnone" width="216" caption="I {heart} Noëlla"][/caption]

Rainy weather is always good for reflection

(i) I think “heavy downpour” is now my favourite English collocation. It easily surpasses the much acclaimed “cellar door” in phonaesthetics and I am certain everyone agrees it beats “beautiful phonaesthetics” in spellaesthetics. As far as I know the word or concept of spellaesthetics does not exist. For me it is really strange there is no antonym to the “the claim or study of the inherent pleasantness or beauty (euphony) or unpleasantness (cacophony) of the sound of certain words and sentences.” Apparently there is eugraphy and cacography. They refer however to aesthetics of handwriting or funny misspellings or to semantics or images, since eugraphy may be used as an antonym to pornography. NOT to the aesthetics of the arrangement of the letters. The form, or “picture” of the letter string. To call it a painting would be too much I agree and conjures up images of calligraphy which is not what I mean: No matter what font, or which handwriting, there is a certain beauty in some letter sequences. Not just in digraphs (like ae, eu, ou,ei) and tripgraphs (like eau, sch,ieu). Beyond that. The beauty of “heavy downpour” for me lies in the following:

(a) The sequence “wnp”, which is not a trigraph, but a trigram with a low frequency of occurrence

(b) The fact that the second and the second-to-last sound are represented by a digraph: “ea” and “ou”

(c) Two letters protrude above the baseline, two below: “h-d”, “y-p”

(d) These letters are in fact each others diagonal reflection: “h-y” and “d-p”. There is a third: “u-n”

(e) o = o

(f) vy ≈ w

(g) I don’t like the r, except that “h____ _____our” is probably the reason I associate a long period of time with the downpour

(h) It’s a kind of feeling of symmetry that, if you look very carefully, still isn’t really there.

(ii) I think Feynman has swapped places with Bohr and Einstein as my favourite awe-inspiring physicist. I’m reading QED - the strange theory of light and matter. In which he explains the most successful theory about the workings of the universe ever to be produced by human minds, by talking about the reflection of light. In just 152 pages, no equations, your mum would understand it too. In Quantum Electro Dynamics (now Quantum Field Theory) the predictions of the theory and the results of measurements are in accordance down to the 8th decimal place! That’s why 20 countries invested 6 billion euros to build the Large Hadron Collider in eight years. That’s how certain they are in all the uncertainty. Apparently Feynman was also a proponent of spelling reform of English, a sensible man in all areas.

But that’s not why I think he’s awe-inspiring. Also not because he: “... was regarded as an eccentric and free spirit. He studied Maya hieroglyphs, was a prankster, juggler, safecracker, bongo drum player, painter, and even developed his own pickup artist method he tested in bars.” Nope. That’s standard for awe-inspiring people. 

This is why: He explained and understood the universe through pictures. He brought back a visual form or conceptualisation of the constituents of the world around us: The Feynman Diagram. In this case a conceptualisation of gluon radiation. I think its beautiful too. I won’t bother you with the details, because... I don’t know the details. If you can make a picture of it, it does not necessarily mean it is has become easier.

What I do know and understand is that some of the things he helped discover are so universal that they will need to be introduced into psychology at some point in time. One is he path integral and another (and more important one) the least action principle on which it is based and, of course (gauge) symmetries. I will come back to that at some point later this year.

 
(iii) I think I do not have a favourite awe-inspiring mathematician yet. Not that one needs to. The obvious candidate, Benoît Mandelbrot is actually much more. I am (also) reading Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise and R/S. It is not like anything I have ever read before. The first line reads: “This books subject matter is nontraditional and its style and organisation are unconventional” It is a collection of papers and new texts and comments and observations, exploring the concept of self-affinity, another very important notion for psychology.

There is a pattern here. Mandelbrot is also someone who likes to represent and conceptualise things with pictures. In fact, he claims that all mathematics stem from geometry. This picture here is the ‘fundamental phase diagram’ for a symmetric three-interval generator. Of course he generalized this to a grid free functions (i.e. all-intervals). This time I do know the details, but I still won’t bother you with them. Just that I think he deserves the Nobel prize for this.

What actually struck me in the book are the passages on being an outsider and maverick in science. About maniacs, who will take an idea and proclaim it ubiquitous and universal. About deniers of whom there are many and about bashers who will do anything to keep things as they are. He calls himself a ferocious moderate and gives a very striking example of what happens to me almost daily (3.3 and 3.4): 


























He also calls himself a philosopher. Something which has been held against me several times last year by empirically oriented colleagues. Interestingly my view of philosophy is the same as his: “I'm certainly a philosopher—how do you say?—entranced with unifying ideas. However, I don't only study books; I study nature. Also art of the past, for the purpose of finding artifacts that I could embrace.”

Reflect on that!

Where were you this morning at 5 AM?

Well officer....

I was writing a pre-proposal for research funding, because the deadline was today and planning is on one of those pages in my dictionary which was accidentally removed by brute force.

Anyway.
Since chances are slim I will be invited to send in a full proposal (because my #@XX%&@ is not finished yet) there will probably be about three people who will ever read it. So, for the effort, I'll post it here as well :)

Here's a part of my alibi (including spelling errors and general awkwardness :) ):

On the origins of the discrete contents of the mind

How and why do we translate our continuous external environment into an internal environment, which consists of matters predominantly discrete, bounded and categorical? Even our actions in the external world can be described as discrete movements or movement patterns. These discrete contents of our internal world are often the objects of study in Psychology. Examples are speech-sound categories extracted from a continuous acoustic signal, the individual words they are compiled into and the categorical semantic information the word conveys. Colour labels attributed to specific ranges of a continuous distribution of electromagnetic radiation are another example. Attitudes towards a minority population and gender stereotypes may be viewed as the outcomes of a categorization process as well. Many streams of information from different sources need to be combined and evaluated to designate a category label like “us” or “them” or “Masculine” or “Feminine”. It is evident that the process of transforming the continuous flow of information from different sources into distinct categories requires a mechanism operating across different spatial and temporal scales. It is also evident that an answer to the question might benefit from an interdisciplinary approach.

Stored and static or emergent and dynamic?

The dominant theory used for the scientific description of the discrete cognitive world is one in which cognitive processes may be understood as algorithmic operations on abstract symbol-like mental representations of stored information. The mental representation of a speech sound would consist of information about the range of frequencies that would trigger the activation of the representation if they were to be detected.

Many objections can and have been made against this machine-metaphor of cognition. One objection is that it is not clear how these discrete representations are created from the continuous stream of perceptual information. It often appears psychologists assume the external world to be as discrete and sequential as the representations and the algorithms. Moreover, many categorical boundaries and algorithms are assumed present at birth and thus coded in our genes. More important is the fact that abstract mental representations of categories are static. Their boundaries should be at certain critical values of a feature variable. Several studies have shown however that perception of category boundaries on a continuum of an acoustic parameter is subject to well-known nonlinear phenomena as hysteresis. This means that the boundary between the categories is not perceived at one critical value, but changes to other values dependant on the direction the continuum is sequentially traversed. [1,2]. These results were successfully modelled by a potential model describing the categorisation performance: The speech sound categories were conceived of as the discrete attractor states whose relative strength was influenced by the value of the continuous acoustic parameter, but also by previously perceived trials.

If we generalize this dynamic account of categorical speech perception to the broader question of the apparent discreteness of the contents of mind, we may arrive at the following conjectures:

1. The apparent discrete nature of the contents of the mind can be understood as the emergence of discrete attractor states at the macro-level of cognition from the continuous interactions between system components at the micro-levels.

2. The emergence of a discrete attractor state occurs as a consequence of the strength and the nature of the coupling between system components at the micro-levels

3. As the system self-organises its way through an ever changing landscape of attractor states this may appear as a sequential succession of discrete cognitive content. The changes are however driven by the continuous interactions of processes at the micro-levels.

4. The coupling of two previously independent systems will create discrete attractor states in a shared phase space depending on the strength and nature of the coupling

It is the main goal of this project to investigate whether these conjectures are universally applicable to all phenomena characterised by discretization of a continuous variable. A sub goal is to evaluate whether it can serve as a plausible alternative ontology to the machine-metaphor. Plausible in this case would mean not only by scientific standards like empirical support and evidence from simulation studies but also relating to the strong intuitive validity of the machine metaphor.

 

Electric Sheep

Recently installed the Electric Sheep screensaver on my mac.



The concept, created by Scott Draves, is quite interesting...
The "Sheep" are so called Fractal Flames,  generated by a genetic algorithm. They take some time to render and by installing the Electric Sheep screensaver your computer will help render new sheep while it is asleep... it will indeed dream of electric sheep.

The cool thing is that the sheep will evolve based on popularity ratings (you can press the up or down arrow key to rate), they will mate and mix and you can create your own and add them to the gene pool.



On the sheepserver you can watch the lineage and the genome of the sheep  (Currently flock 244).