Most of these entries are Private.

S A J J M [A] M F J 2009

April 20th - (CJ Invents new math) The Existence Paradox of Irreducibly Infinite Processes

music   _-Cortexelation-intro-4.mp3

Hypothesis: The problem of determining if irreducibly infinite processes exist-- is itself an irreducibly infinite process.



Wtf am I talking about?

So Godel incompleteness; any formal axiomatic system will either have true things it cannot prove, or will have paradoxes. BUT ask me this Godel: what about a formal system with an infinite number of axioms? Could that work? Could a theoretical system like this be complete? How infinite would it need to be?

I wonder if an unparadoxical mathematical system could exist only if it started with an infinite number of true assumptions. Is this trivial, or are there deeper things to consider here?

The trick in his proof is reducing everything into Godel numbers, but what about infinitely long Godel numbers?

What kind of uncomputability do you get when you run the halting program on itself, when (when it calls itself) its own filename is infinitely long? (never even gets a chance to be a paradox:/)

But back to infinite godel numbers. For instance, PI, a transcendental number, can be reduced to a generalized continued fraction, or computer algorithm, which could both be expressed in finite godel numbers.
http://en.wikipedia.org/wiki/Pi#Pi_and_continued_fraction

  1. Can all infinitely long Godel numbers be reduced to finite Godel numbers ?

  2. I.e. Can all infinite processes be reduced to a set of finite instructions for building them?

  3. OR do there exist infinite processes which cannot be reduced to finite instructions?

  4. Does something like this exist: Infinite processes which reduce to infinite instructions for building infinite instructions for building infinite instructions for building infinite instructions....etc?

  5. If something like that DID exist, would it be impossible to think of it? (thoughts themselves are finite, and so would any reasoning which could approach the existence of one)


My hypothesis: If an irreducible infinite process like this were to exist, not only would computing it be a task for a hypercomputer... but FINDING one in the first place may be a task for a hypercomputer.
(I would love to prove this.)
And if not, then we discover a level of uncomputability above hypercomputers, which is just as cool.

What if we looked to nature for one instead? (((potential idea: What if the search for unifying physical laws is one of these irreducible infinite processes--- Assume all constituents and forces of matter and energy can be broken down further and further, infinitely. A human civilization on a quest to find the unifying physical laws would never find them, but perpetually approach them. This is like a hypertask. You could reduce this hypertask into the finite rules of "humans-> go figure out the universe". But the very existence of humans in the first place is a result of these infinitely compounded laws. You can't create the humans without the laws. You can't create the humans (which never figure out the laws) without figuring out the laws. ??? ))) Would any potential candidate have some absurd amount of self-reference in it?

Or what if we could leverage unsolved problems in mathematics. Connect this to things which may not be able to be proven/cannot be proved or disproved? Like, what if it turns out that we can say something like "IF its impossible to prove if P=NP, then irreducible infinite processes exist".

Okay, so now, IF we assume irreducible infinitely long Godel numbers exist.... what does that say about his proof, his theorem, and of mathematics? What are the implications? Does this still fit nicely with his proof? If so, what does that mean. If not, why and (how) is this a significant idea? Either way, let's rework metamathematics xD

I wonder if this could be proved or disproved. or even more exciting: if it can be proved that it cannot be proved/disproved .. then its like wtf.. or if it can't be proved/disproved whether it can't be proved/disproved whether it can't be proved/disproved whether it can't be proved/disproved whether it can't be proved/disproved... and so in an INFINITE CHAIN!! do such things exist? (is this an extension of the same problem of irreducibly infinite processes? LOL the (dis)proof of itself requires itself)

Tell me what you think, and where/if I slipped in my reasoning. Basically I think it all comes down to:

Hypothesis: The problem of determining if irreducibly infinite processes exist-- is itself an irreducibly infinite process.



I lack the knowledge/ability to formalize these things all fancy academic like. If anyone wants to publish a paper with me, please express your enthusiasm. Or feel free to pirate my ideas and claim them as your own. Just as long as you throw in a :| somewhere in there; some sort of allusion to your inspirators, so that we can feel invisibly powerful.

emperorcj 04/20/10 12:57 am

okay so like, what is finite here? the description of a iip is finite. so that means we can go up to god and be like "God. This is what an Iip is. I need you to look through everything that exists and find me something that matches this criteria, and then start performing it". God then takes these finite instructions, and undergoes his task of looking through EVERYTHING that exists. If after infinitely long, he does not find an Iip, then Iips don't exist, or even God cannot find one. If he finds an Iip and starts performing it, its existence is negated, because the originating instructions were finite. Therefore Iips don't exist.

emperorcj 04/20/10 01:10 am

does "No one will ever find an x" imply "x doesn't exist" ??

resistentialism 04/20/10 02:02 am

The next obvious step is to make an ambigram of your absurdist math theory
:P

emperorcj 04/20/10 02:52 am


LO7

resistentialism 04/20/10 08:55 pm

Okay, now it's legit.

emperorcj 04/21/10 09:28 am

ltwas a pleasure to follow you on a wit's impulse ^^

emperorcj 04/21/10 01:58 pm

Ambigrammars, is that what they call us? (it evenn looks really legit, all latin like akil uitel lla 'ti6al hllear skool wava) ¿sn llec what teyt 'srewwerbiqwV

April 19th - Crab cannon

music   crab canon

Not mineI learned to play Bach on the piano. Two hands and everything! I was most impressed with myself. The whole time I was trying to be aware of my own learning process. Each hand was like a different hemisphere, orchestrating together two different worlds. I could really feel the story the notes played. Which is beautiful, because before, having listened to the canon endless times, I didn't see the story. I think the mechanical way of playing music loses something. The sounds of amateur pianists flowing together newly learnt music, harmonically justifying miskeys, synaptogenesis happening right before your very ears.

Here is the first recording of the first time I played it all the way through. Nailed it on the first shot! Something about the self-consciousness made it flow out. Something about my awesomeness lingers crab-canon.mp3

Freewrite which appeared on Ann's computer a bit later


I LEARNED A song bY JS BACH TODAY On THE PiANO
i don't even really play piano, it was amazing, i felt so awesome
like, two hands, two parts
crab canon
lmao
i learned it in an hour
or at least, half of it, sort of
its like, a totally symmetrical piece
where the first half is the second half in reverse
and then your hands switch parts
and LMAO when you print out the music score in MIDI form, it looks just like a crab
clever bach
but yeah, i recorded myself after i basically learned it, and like, to my astonishment i pulled it off perfectly
on the first try lmao
something about the self-consciousness
and like, listening to it, it sounds beautiful
like, with all the delicate hesitations
i realized what piano is all about, and playing with emotion
the goal isn't to sound mechanical, like a computer
the real humanness comes in playing a piece you don't have confidence in playing
and you're in the moment, trying to pull it off,
and how you work around what comes out
in the moment, strange looped with yourself
and its beautiful, if you start playing something dissonant, you can always relieve the tension into something harmonious
like, if you just start playing chaotically, you can then reason your way into harmony
like, starting with a handful of random legos, and then putting them together into a shape
and the most beautifulest sounding music sounds like that
ppl making music up on the spot, because its the realest humanity
its like the musician makes up a lie (chaotic dissonance), and then justifies his way around it into truth (the harmony which relieves tension)
like, the musician plays something he didn't intend to play
it just came out
it just happens like that, because we're not mechanical
and then, the musician takes that spontaneity, and runs it with it, into new structure and harmony
and pretends he meant to do it all along
(this strongly resembles the geometry of creativity)
the difference between the unintentional dissonance, and the correction
IS the emotional content
the reasoning the musician uses, is a total capture of who the musician is, and what he feels at this moment
and one should often play like he has no idea what he's going to play
just like
free writes
and turns out jokes
you just jump into it, and justify and piece it together on the spot
kind of ilke romance
it really is music
jump in without knowing where you'll swim to
improvise along the way
dance with chaos
justify the noise
twist all loose threads into beautiful harmonies
dangling your legs over the void
with the confidence that should the cliff on which you sit crumble to pieces, sending you tumbling into the darkness, you'll be able to turn around and grab onto a tree
and climb back up to higher heights
music is beautiful
and its interesting how guitarists think vs pianists
guitar, its more about numerical geometry, and rhythm, and the amount of emotion you can pack into a single note
piano its more about harmonic/key based-geometry, and accompanying yourself (two hands), and the emotion you put into sets of notes
being a geometric thinker.. i rather like to read the MIDI piano rolls when learning piano
although i'm jealous of those who can sight read sheet music
because, there's a lot of emotion going on in those notes, on the sheet music page itself
like, groups of notes, and the key, and the sharps and naturals
its like, social
the notes are social entities
and you apply the part of your brain that deals with social-things to it
where as the MIDI piano roll.. its all about geometry
and shape
guitar tablature? hmm, maybe a little bit of both, and more about numerology and number math
tabs i'm most comfortable using, sometimes ill try to play piano like that
but when you get into the habit of translating from one to another, you lose the sort of, direct learning, that you really want
its like, learning a new language in terms of what it means in english
instead of how the language relates to itself
instead of how the language directly connects to meaning in reality


April 17th - ambigramwer6iqwe

music   dillinger escape plan - option paralysis

Check out this remix of The Universal Declaration of Awesomeness by Adam James Davis and Cactu. Eerie synths. Machine-elfish. Lmao. I freaking love you guys.


(also check out this fucking awesome ambigram i made)


April 6th - spreading music like toast / from my head to the coast

Hey everybody. I'm alive. Exploring New Zealand. Camping in the wilderness alone. Met heaps of cool people here. Rock climbing. Teaching campers to throat sing. Writing poetry. Cooking pizza. Explaining that my name is a self-referencing acronym of infinite recursion. Meditating into the fire. Playing hot potatoe. Thro...wing raves in my tent (set the torch to strobe/layer the chantbeat). Thinking about what it would be like to go jupiter diving. Long discussions on the mind, augmented reality, simulated brains, godel's incompleteness proof, the singularity, and my quest to build an artificial musician with computational creativity. Caving pitch black caves. Bouldering risky boulders. Gazing the blue blue horizon from high heights. Beauty and so much beauty. As long as my supply of green tea still holds, I shall be able to maintain a healthy insanity. I miss you all. *imaginates* Love as.

Where I am


S A J J M [A] M F J 2009