Hi there! Welcome to my home-made page!
Anything you might stumble upon here could be taken very serious! So here's the disclaimer: You're entering a Jesus-free zone, infested with subliminal pathways of communication. This is your chance to back out and I personally advise you to do so if you are the sort of person that happens to be emotionally attached to certain traditional, dogmatic or conventional thought patterns. This page is intended for people who take full responsibility for their own behavior and have an open but critical mind with respect to ideas or concepts of any nature.
Basically I'm probably much like you (an idiot?), and although that's not much of an introduction, I think I'll leave it with that (except for a picture of me at the end of this page, along with my email address).
This page is dedicated to some of my favorite musicians/artists (the way figments of their more illusive material unravel themselves, in my moderately distorted, manipulative, perverted, paranoid, frustrated and heavily obsessed brain). There's a couple of pictures that are relatively authentic, but most of the material contained herein has been tampered with.
My motivation (or motto, if you will) comes together in the equation life = art and to you I may be nothing but an obnoxious piece of pot-puffing hippie-dirt, but despite of that, I demand recognition of the fact, that I'm (not, just) another animal... (or something like that... this part still needs some editing).
Any old way... I've had it with ignorance and intolerance, so I've joined the united mutations (i.e. I think for myself) and I'm ready to take off to another dimension any time (now where'd I leave that damn spaceship?!)... which reminds me of notifying you of irregular and unannounced mutilations to the very page you're staring at. Gee... what else is new?
In the near future, this homepage is probably also going to serve as a basis for clearly representing my point of view on various issues that I like to philosophize about (I'm sort of a newsgroupie), such as the nature of my existence and other irrelevant issues. I also like to program (any declarative language will do), so you can expect to find some sections on programming here in the near future just as well. Currently I'm thinking about ways for a computer to learn chess from practice (without the application of neural nets). Basically this problem boils down to finding an efficient way of encoding elements from the powerset (all subsets of a given set) of valid states... ideas/suggestions are welcome. Also, I'd like to develop a powerful GUI to my favorite language Prolog that treats pieces of code as molecule-shaped structures that can easily be evaluated, manipulated and constructed.
My philosophical rantings can be found mostly on sci.logic and comp.ai.philosophy but on occasion I also tend to post to rec.drugs.cannabis, comp.lang.prolog, nl.wetenschap and nl.politiek.
LOGIC
I've been fascinated with logic ever since I followed a rigorous course on propositional logic. I have written programs in both Gofer and Prolog to analyse and evaluate logical formulae. Now that I have a clear understanding of propositional logic, I've come to the conclusion that logic is equivalent to set theory as a basic means for comprehension (sets and concepts may be identified) and stems from primitive cognitive faculties like discrimination and identification. Hence logic can be used to analyse and comprehend itself and naturally it's intimately related to generic features of information processing like synthetic vs analytic, differentiation vs integration, serial vs parallel, etc...
I've noticed that a lot of people were unable to understand my illustrations on logic and this was to be expected since I didn't provide any explanation whatsoever. I've attempted to give a visual demonstration of 'truth-functional' logic in the next picture and I hope this clarifies my obscure notation. In this case a proposition is understood as a function consuming a bitstring as input and producing a bit as output (a bit is a bitstring of length 1). An interpretation is understood as a function consuming a variable and producing a value (in other words, the assignment of a value to a variable). On the left side bitstrings (a.k.a. combinations) are listed vertically and on the right side all possible functions assigning bits to bitstrings (combinations of combinations) are listed horizontally. So all bitstrings represent interpretations and a bitstring represents a proposition if, and only if, its length is a power of 2.
Alternatively (since the picture relating variables to propositions can be understood as a definition for logical operations), the 16 logical operations mapping two bits to a bit can be defined on combinations of bits:
This (how the aforementioned operations map a combination of bits to a bit) implies how the operations map a combination of bitstrings of length 2 to a bitstring of length 2 and likewise how they map a combination of bitstrings of length 4 to a bitstring of length 4:
The following animation shows a correspondence between numbers in Pascal's Triangle and a summation of unit squares. Notice how it relates a subsection of the circumference to the surface area it 'includes'.
The next animation demonstrates that the principle generalizes to higher dimensions (in this case the third, a summation of unit cubes). Although it may not seem evident from the animation at first, here a subsection of the surface is related to the volume it 'contains'. The first animation corresponds with {(1,0), (2,1), (3,3), (4,6), (5,10), ..} while this one corresponds with {(1,0), (3,1), (6,4), (10,10), (15,20), ..}.
Below you will find a hypercube (cube in 4 or more dimensions) illustrating valid implications (except transitive and reflexive implications) among all unique logical propositions in terms of 2 logical variables {X, Y}. The uniqueness of these 16 propositions means that no logical equivalence relationships hold among them (except reflexive ones). This graph pretty much sums up my current understanding of propositional logic and its relationship to sets. An alternative interpretation for vertices (points) are elements from the powerset of a set of cardinality 4 where edges (arrows) become subset relationships among these sets.
The ratio between incoming and outgoing arrows of a proposition is a measure of logical strength and reveals Pascal's Triangle. The triangle of Pascal is intimately related to both logic and sets and provides an interesting connection between natural (or even rational) numbers and logic. There is a link on Pascal's Triangle for more detailed information.
By the way, don't forget to check out the link featuring an animated stereoscopic hypercube!
The operations Not, And and Or are known as negation, conjunction and disjunction. Not is unary (consumes one input) while And and Or are binary operations (consuming two inputs). Constants (a.k.a. values) can be seen as 0-ary operations (consuming nothing). Note that N-ary operations are embedded among M-ary operations for nonnegative integers {N, M} such that (0 less than or equal to N) and (N less than or equal to M). Below is a picture of a set-theoretic interpretation of the hypercube. The 4 elements represent all possible assignments of values to 2 variables (interpretations; conjunctions of literals, where a literal is a potentially negated variable) while the 16 sets represent all possible assignments of values to these 4 elements (propositions; disjunctions of interpretations). An empty disjunction denotes False and the formalism which expresses propositions as disjunctions of (conjunctions of literals) is known as disjunctive normal form (DNF). Dually, propositions can be expressed in conjunctive normal form as conjunctions of (disjunctions of literals). An empty conjunction is interpreted as True. So, for instance, {{}, {Y}, {X,Y}} represents (((Not X) And (Not Y)) Or ((Not X) And Y) Or (X And Y)) in DNF.
The Venn-diagram above shows how colors are to be interpreted in the set-theoretic hypercube. The left circle denotes X and the right circle denotes Y. Every color represents one of the four cases and a proposition is a subset of this set of four cases. Note that a case can be seen as a subset of the set of two variables {X,Y}. So the powerset operation goes from variables to cases and subsequently from cases to propositions.
Another set-theoretic version which demonstrates recursive aspects as well.
The picture below was used to create a regular hypercube, it also demonstrates spatial proportions.
Here is a 'visual problem' concerning combinations and permutations.
In a similar vein, I've made the following graphic of a kind of visual analysis of the 'I Ching'.
You may recognize the following image from a webpage featuring a bizarre theory regarding the I Ching by Terence McKenna.
I find it fascinating to ponder how logic relates to such visual patterns, similar to those found in the oriental game Go.
I've also created an interactive graphic, that illustrates how the 24 possible permutations of 4 objects {A,B,C,D} are embedded among the 64 possible combinations of 6 bits (where 6 is the third triangular number). In general, permutations of N objects are embedded among combinations of the (N-1)th triangular number of bits, e.g. the 120 possible permutations of 5 objects are embedded among the 1024 possible combinations of 10 bits (10 is the fourth triangular number). The triangular numbers (1, 3, 6, 10, 15, ...) can be found in Pascal's Triangle.
You can click anywhere in the list of 64 combinations and the edges of the tetrahedron will be updated accordingly. For every edge XY between vertices X and Y, the edge (or arrow) has two possible associated color transitions that distinguish between the statements (X precedes Y) and (Y precedes X). A loop, depicted by a circle in one of the 4 faces of the tetrahedron, indicates a contradiction between the statements (X precedes Y), (Y precedes Z) and (Z precedes X) for face XYZ associated with vertices X, Y and Z. If there are no such contradictions, the 6 statements associated with the 6 edges in the tetrahedron characterize a particular permutation of the 4 objects. So for instance, the first permutation ABCD is characterized by the 6 consistent statements (A precedes B), (A precedes C), (A precedes D), (B precedes C), (B precedes D) and (C precedes D).
If one more point is added in the center of the tetrahedron, it can be used to visualize how the 120 possible permutations of 5 objects {A,B,C,D,E} are embedded among the 1024 possible combinations of 10 bits (where 10 is the fourth triangular number). I've created another interactive graphic which illustrates this, but it's a lot larger in size (64 MB for t5.html vs 2.5 MB for tetra.html), so it's probably not a good idea to have a look at it unless you have a fast computer and a fast internet connection. It takes a while for it to load completely, so please be patient.
If 'visual thought' seems a bit vague, follow the link on algebraic factoring or diagrammatics.
For more about logic, combinations (Pascal's Triangle), permutations, trees, information, interpretation and communication one might like to visit dejalogic at dejanews.
Alas! Dejalogic is gone... and mental hygiene, my logic group at yahoo has mysteriously disappeared. I will try to upload some of the graphics that have been available at those sites to my gallery at www.fotopic.net.
MUSIC
This could very well be my favorite album... Trout Mask Replica (released in '69).
It contains monumental ways of expression (in comprehensible terms: It really fascinates me to go through the weird textual imagery, surrounded by various landscapes of sound and rhythm) and subject matter that reflects the adventurous nature of this altogether...
Don van Vliet (a.k.a. Captain Beefheart) had worked on a couple of albums by the time this double-EP (TMR) appeared.
One of them (his debut: Safe as Milk) is pictured on the left. It was John Lennons favorite album.
The last album by CB and his MB came out in '82 and he's devoted to painting ever since, as far as I know. Below you can find a picture of a transformed Magic band in the 80's and an oil painting by Don van Vliet.
Here's a couple of pictures of the Velvet Underground. Along with several other bands/artists (like Pink Floyd, Jimi Hendrix, Cream, Bob Marley, the Doors, Roxy Music, etc... ) their work constitutes the best part of my absurd investment in (relatively expensive) disc-shaped pieces of plastic that contain nothing but a piece of perforated foil (maybe that's not the most impressive part of Compact Disc technology)!
Note that I donot think that music produced nowadays (or fairly recently) is in any way degenerate (unless we're talking disco, although I used to like... what was his name again?) compared to the music I've simply picked from a pop-encyclopedia (scanning for words like "influential" and "original"). An uncle of mine deserves credit for initially stimulating my interest in (besides computers) popular music. I started with the Doors and bought an album of VU because it was featured in both the movie "the Doors" that appeared at that time, and the soundtrack of that movie, containing the song "Heroin". I bought their debut album (with Nico), and it didn't take long to get addicted to it along with my interest in "the Doors".
TMR was produced by someone who had a great impact on the way I look at (my) ideas, his name is Frank Zappa.
Below you find the cover of the first double-EP ever produced ('65); the debut of Frank Zappa and the Mothers. Maybe they called themselves that way because they cared (for an absurd/provoking name)?
WHAT IS "FREAKING OUT"? [a few paragraphs quoted from the 'FREAK OUT!' cdsleeve]
On a personal level, Freaking Out is a process whereby an individual casts off outmoded and restricting standards of thinking, dress, and social etiquette in order to express CREATIVELY his relationship to his immediate environment and the social structure as a whole. Less perceptive individuals have referred to us who have chosen this way of thinking and FEELING as "Freaks", hence the term: Freaking Out.
On a collective level, when any number of "Freaks" gather and express themselves creatively through music or dance, for example, it is generally referred to as a FREAK OUT. The participants, already emancipated from our national social slavery, dressed in their most inspired apparel, realize as a group whatever potential they possess for free expression.
We would like to encourage everyone who HEARS this music to join us... become a member of The United Mutations... FREAK OUT!
Frank Zappa is the leader and musical director of the Mothers. His performances in person are rare. His personality is so repellent that it's best he stay away... for the sake of impressionable young minds who might not be prepared to cope with him. When he does show up he performs on the guitar. Sometimes he sings. Sometimes he talks to the audience. Sometimes there is trouble.
This is the cover of their third album that appeared in '68.
Unfortunately Zappa died of cancer (1940 - 1993) during the period I first heard about his music and started listening to it, leaving behind a massive collection of interesting music, ranging from classical to popular. I wish I could've seen him performing in person.
MP3s
Since a while I've been collecting mp3s... mostly music but some audiobooks as well.
LINKS
Info on various psychoactive substances.
More info on psychoactive substances.
Beefheart related info.
More Beefheart related info.
Zappa related info.
Java applet for visualizing a 4D cube
Ever seen a 4D cube in the third dimension?
a page that explains Pascal's Triangle
Ask Dr.Math FAQ
a page that explains algebraic factoring
A great example of thought in visual terms.
a visual proof of the Pythagoras Theorem
Another great example of thought in visual terms. Click the Behold! link at the top left of the Diagrammatics page to view the proof. If anyone out there knows about similar examples on the WWW, I'd be very grateful if you can mail me the URL.
Since a while I regularly import and export my internet bookmarks to save them online at www.mybookmarks.com.
That's me messing around with a laser. For more visual stuff, check out my digital graphics and pictures at fotopic and flickr.
I hope the pictures I've used in this page are not too big, and in a few days I'll set up this page more decently. Duh...
This page has been available since (4-28-'97) 16:30h
Name: Niek Sprakel
Address: IBB 117 IV, 3582 XP UTRECHT
I can be reached at the following address:
You'd have to contact me on MSN first, since I have to add addresses to my contact list in order to circumvent the spam protection.
Alternatively, you can use ICQ. My number is 151232944 (old number 8247756).
Here is another picture, for people who like flashy colors...
Favorite fortune cookies!
SAGITTARIUS (Nov 22 - Dec 21) You are optimistic and enthusiastic. You have a reckless tendency to rely on luck since you lack talent. The majority of Sagittarians are drunks or dope fiends or both. People laugh at you a great deal.
Experience is that marvelous thing that enables you to recognize a mistake when you make it again. -- F. P. Jones
Experience is what you get when you were expecting something else.
We may hope that machines will eventually compete with men in all purely intellectual fields. But which are the best ones to start with? Many people think that a very abstract activity, like the playing of chess, would be best. It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English. -- Alan M. Turing
If God had intended for Men to Smoke, He would have set them on Fire.
It's not an optical illusion, it just looks like one. -- Phil White
God did not create the world in seven days; he screwed around for six days and then pulled an all-nighter.
It has been said that man is a rational animal. All my life I have been searching for evidence which could support this. -- Bertrand Russell
"Text processing has made it possible to right-justify any idea, even one which cannot be justified on any other grounds." -- J. Finnegan, USC.
Which is worse: ignorance or indifference? Who knows? Who cares?
Rhode's Law: When any principle, law, tenet, probability, happening, circumstance, or result can in no way be directly, indirectly, empirically, or circuitously proven, derived, implied, inferred, induced, deducted, estimated, or scientifically guessed, it will always for the purpose of convenience, expediency, political advantage, material gain, or personal comfort, or any combination of the above, or none of the above, be unilaterally and unequivocally assumed, proclaimed, and adhered to as absolute truth to be undeniably, universally, immutably, and infinitely so, until such time as it becomes advantageous to assume otherwise, maybe.
A master was explaining the nature of Tao to one of his novices.
"The Tao is embodied in all software -- regardless of how insignificant," said the master.
"Is Tao in a hand-held calculator?" asked the novice.
"It is," came the reply.
"Is the Tao in a video game?" continued the novice.
"It is even in a video game," said the master.
"And is the Tao in the DOS for a personal computer?"
The master coughed and shifted his position slightly. "The lesson is over for today," he said.
-- "The Tao of Programming"
Do not believe in miracles -- rely on them.
An idea is not responsible for the people who believe in it.
Jazz ain't dead... it just smells funny. -- F. Zappa
