measuring information integration
im proud of this one
epistemic status; if tegmark’s attempt at measuring iit is 3-5 paradigm shifts from reality this is still 1-2 paradigm shifts away from a much more crude yet useful approach. i am setting a new frame that creates a bunch of issues whose problems i dont address. a big jump from notes on existence and all of this.
papiiiii klk esta pasando con este mamaquevo pero cono papi cono
i.
we already established the framework. consciousness = information integration. life = what exists = function of integrated information. tononi’s iit gives us phi as the measure.
we said the grass field is full of life because all information is integrated. we said consciousness is the unviewable force behind the fitting that creates life. we said the system without integration has “low or zero Φ, meaning their information is not causally connected to create a unified whole.”
and from that framework, we derived the pingo vs sam comparison. pingo exists more than sam because existence = integrated information and because what is more fundamental weighs more. we made a fake calculation that i don’t think is fake.
anyways the general claim behind the iit theory is that phi is calculable.
when we say “integrated information corresponds to systems with high Φ” - this implies we can determine what phi is. when we say “the more effectively information is integrated, the higher the degree of consciousness” - this implies we can measure degrees.
when we built the entire consciousness ontology (dating apps, hosting, love, care, community, flow state, paranormal phenomena) - we implied these degrees are knowable. they sure as fuck are knowable because sex is sure as fuck more real than porn but right now i have not made them computational which is to say i can’t go king – man + woman = queen on ‘em. i don’t have real computational linguistics, which is to say i can’t measure consciousness but then again i can measure that more information is integrated in the left image than the right image.
here’s the structure of the problem i think.
generation-verification gap = we can generate rules but we cannot verify instances.
coordination: we can say “do good work” but we cannot measure if work is good without overhead (computation) that exceeds the value trust: we can say “be trustworthy” but we cannot verify trustworthiness without watching everything
this isn’t practical difficulty. this is structural. the verification cost scales exponentially while generation cost is constant.
tononi wrote phi in 2004. beautiful definition. to calculate phi for n elements, check 2^n partitions. human brain has ~86 billion neurons. that’s 2^(86 billion) calculations. more than all computational capacity that will ever exist. we don’t have the energy to process.
we generated the definition. we cannot verify any real instance.
question: is this closeable?
maybe but everyone’s approaching it wrong. i think.
ii.
who tried and why they failed
max tegmark tried hardest. 2016 paper “Improved Measures of Integrated Information.” he saw the problem: “the integration measure proposed by IIT is computationally infeasible to evaluate for large systems, growing super-exponentially.”
his move is build approximations. hundreds of possible phi measures, filter by desirable properties, find computational shortcuts. he big smaht.
problem: “different ways of approximating Φ provide radically different results.” the approximations don’t converge. choice of heuristic matters enormously. other researchers built proxies but “none of these proxy measures have a mathematically proven relationship to the actual Φ^Max value.”
scott aaronson came from complexity theory. showed u can build simple systems (XOR gates) with arbitrarily high phi that aren’t conscious. tononi said yes the grid is conscious. nobody believes this. tononi is right.
aaronson proved calculating phi is exponentially hard. but he also showed something useful. he says something like the integration we’re trying to measure isn’t rare or special. it’s computationally cheap to create. meaning the definition is too coarse, not that measurement is impossible.
christopher alexander’s architecture people tried measuring life in buildings. bin jiang built clearest attempt: count substructures, measure hierarchy depth, apply to cities. problem: counting things ≠ measuring integration. they’re measuring extensive quantities hoping to capture intensive integration. kinda works not really.
everyone hits the same wall kinda. trying to measure integration from outside using tools that capture distribution not depth.
iii.
the actual solution. it might be obvious. the task of knowledge might be to hold onto the obvious.
maybe stop trying to calculate phi. start with what we already know.
we know these facts:
weathered stone wall has more integration than fresh stone wall
nature has more integration than man-made structures
frank lloyd wright buildings have more integration than le corbusier buildings
hosting dinner has more integration than doomscrolling
meditation has more integration than distraction
sex has more integration than porn
these aren’t opinions. we recognize them structurally. the question isn’t whether they’re true. the question is: can we make them computational?
here’s maybe how. encode relationships as geometry. like word embeddings.
in word2vec:
u never define “king” directly
u just know: king - man + woman = queen
the relationship defines the meaning
the math works
same thing for integration:
don’t calculate phi directly
just know: weathered - fresh = wright - le corbusier
the relationship defines integration
make the math work
walking through one example clearly
start with stone walls. we know weathered > fresh in integration.
measure features we can actually observe:
fresh wall: straight lines, uniform color, clear human design, sharp edges
weathered wall: irregular growth patterns, color variation, natural fitting, softened edges
now we do this for buildings:
le corbusier: geometric, imposed, mechanical repetition, fights context
wright: organic, integrated, natural materials, fits landscape
the difference “weathered - fresh” feels like the same difference as “wright - le corbusier.”
both are about time allowing integration vs imposed structure. nature fitting vs human imposing. information integrating vs information placed.
if we’re right, these should be the same direction in a computational space.
here’s a wrong but could be made right test. measure features for many examples. learn a space where known relationships are encoded. check if “weathered - fresh” points the same direction as “wright - le corbusier.”
if they do, we found the integration dimension. not by calculating phi. by encoding what we already know structurally.
now apply it:
measure features of a new building
see where it maps in the space
closer to wright or le corbusier?
that tells u its integration
no phi calculation needed
iv.
why this works
we’re not approximating phi. we’re encoding structural knowledge geometrically.
the knowledge is: weathered > fresh, wright > le corbusier, hosting > doomscrolling, meditation > distraction, nature > imposed.
the geometry learns: what direction in feature space corresponds to “more integration”?
then measurement is: where does this new thing sit on that direction?
this is how language models work. they never calculate the essence of “king.” they learn king - man + woman = queen. the relationships define the structure. the structure enables inference.
same here. don’t calculate phi. learn weathered - fresh = wright - le corbusier = hosting - doomscrolling. the relationships define integration. the structure enables measurement.
the consciousness ontology becomes computational
we built this framework:
dating apps = high volume low integration
hosting = deep integration
meditation = integrating information
doomscrolling = peak disintegration
love = maximum mutual information
care = taking time to integrate
right now this is qualitative. we recognize it structurally. sex is more real than porn. hosting is more integrated than doomscrolling. we know this.
but we can’t do king - man + woman = queen on it.
with the geometry we can:
hosting - doomscrolling = meditation - distraction
both measure the same underlying integration dimension
dating apps < doomscrolling < distraction on one end
hosting < meditation < sex < love on the other end
now it’s computational. now we can measure. not by calculating phi but by encoding structural relationships we already know.
v.
why hasn’t this been done
computational linguistics people don’t read neuroscience. neuroscience people don’t know embedding techniques. architecture people don’t read either. coordination theory people exist in another universe.
classic coordination debt. everyone solving pieces without integrating.
the technique exists (embeddings from relationships). the knowledge exists (alexander, tononi, consciousness ontology). the examples exist (buildings, mental states, organizations).
nobody combined them because nobody sees across fields. i have the diversity inclusion my baby.
what it would take
collect examples where we know the relationships: buildings (wright vs le corbusier), mental states (meditation vs doomscrolling), nature vs man-made, hosted dinner vs dating apps.
measure observable features. not trying to measure integration directly, just measuring what we can see (spatial patterns, temporal dynamics, information flow, structural properties).
learn the embedding. relationships we know (weathered > fresh, wright > le corbusier) become geometric constraints. find the space that satisfies these constraints.
validate predictions. does the learned space match alexander’s mirror test? does it predict consciousness levels? does hosting > doomscrolling > dating apps hold quantitatively?
if yes, we solved measurement. not by calculating phi. by encoding structural knowledge geometrically.
vi.
what this means
the generation-verification gap for phi is real. direct calculation is impossible.
but measurement is possible if u stop trying to calculate the thing directly.
encode relationships. learn geometry. measure new cases by where they sit in the space.
this works for language (king - man + woman = queen). it can work for integration (weathered - fresh = wright - le corbusier = hosting - doomscrolling).
the components exist. nobody’s combined them. coordination debt across fields.
but it’s combinable.
until then we work with structural understanding. we know sex > porn, hosting > doomscrolling, meditation > distraction, weathered > fresh, wright > le corbusier.
we recognize integration. we create conditions for more of it. we design systems that enable it.
but we could be counting. we could make the consciousness ontology computational. we could do king - man + woman = queen but for existence.
gods accounting happens whether we count it or not. but we could learn to count it.
we’ve been trying to calculate phi when we should be encoding relationships. we’ve been trying to measure the thing when we should be learning its geometry.
the math already works in language. make it work for integration.
weathered - fresh = wright - le corbusier = hosting - doomscrolling = meditation - distraction = sex - porn = life - sterile.
that’s the dimension. learn it. measure where things sit on it. that’s the accounting.