Theory

some dazkarieh this time. i love this song, they have a new album out.

in the previous series we saw how information can be stored and processed by physical entities without any elaborate structure. we also saw how the speed at which it is both processed and stored has increased as life became more complex. today, i will summarize again the whole series from the beginning, including our formulation for minds.

1. reality R is a set of N discrete things repeated M times
2. the distribution of these things is non-random (i.e., it has patterns)
3. this distribution is not static, it can change thanks to free energy, leading to specific distributions that can be exceptionally complex (e.g., minds)
4. the development of complexity comes simply from random fluctuations and non random possibilities for existence (e.g., anti matter particles still form, but they are annihilated by reality (see 2.), hence the evolutionary trait present in all layers of reality)
5. these specific arrangements versus the general ones can be quantified using arbitrary boundaries, they are arbitrary because there are no boundaries in reality
6. minds represent a specific subset of R, whose distribution is non random, which is a subjective representation of the whole reality. this means minds can be conceived depending on the boundary: draw one around a planet, an animal, a cell, an atom, and you can define its observations and its thoughts
7. complex minds made of neurons represent not only observations themselves, but their structure allows for thoughts to generate hypothetical observations, i.e., by virtue of their hierarchical structure, they can generalize patterns so much that impossible distributions can exist as thoughts. this means that even fantasy is real, because it exists physically as a distribution of things (in this case for example, the electrical signals and wiring of the person with the idea).

note that it is not said whether all of the constituents of reality are observable by us, human beings, i.e., of the N things reality is made of, i make no claim on how many, and what type, are they made of. this means that if someone wants to use this model to justify spirituality, they can do so, all they have to do is say there is a “spirit particle”. and though i accept it, as i said before, the quest is for the simplest generative space with minimum distortion versus reality, and the more symbols are added that do not improve fitting, but instead distort it, the worse. but in essence, this is an objective formulation of a subjectivist model. it sounds completely ridiculous, but that’s exactly what it is. it harmonizes both subjectivity and objectivity in a way in which both are complementary, not opposing views.

regarding the minds as generative spaces, i will provide a simplistic formulation on how to look at complex brains and see them at work, and will provide predictions and tests that can be done to verify this model.

as we saw first, we are dealing with a limited and discrete set of symbols to work with. i postulate that brains create multi-dimensional spaces on which they project their sensory signals (sensory signals are not observations, they are interpretations, thoughts done over classification of input). the best way to imagine this is to imagine a two dimensional brain (two neuron brain). one of its neurons can classify red, and another can classify green. if we shine red, the red neuron lights up. if we shine green, the green neuron lights up. but if we shine yellow, both light up. now, each neuron “knows” only one color, but combined they can represent colors that alone they couldn’t represent. this is typical of many dimensional systems. two lines, one dimensional, once put perpendicular to each other can now represent all points in a plane, even though each one of them has only one dimension, together they’ve expanded “each other’s” representation of reality. red could not see yellow without green, and vice versa.

this means, and this is mostly, as i said, a very broad generalization i am making, that a single neuron is a base vector of that multi-dimensional space. so these two color neurons can represent yellow because when combined together they create a base vector for a 2 dimensional space versus two 1 dimensional spaces. obviously this view is a bit influenced by neural networks (which actually estimate an n-dimensional polygon and hyperplanes). but i take a simpler approach: i’m thinking just in terms of axis, projections and expansions.

each neuron is a base vector, and together they create the “brain” (a base matrix). the imaginable space of a “brain” is, therefore, the space expanded from these base vectors. note that it might be that not all neurons are independent of each other, that would be expectable, so this actually overestimates the capacity of this system. the main point is that i’m saying we are dealing with generative complexity, not actual complexity: the ideas that flow are consequence of the possibilities of representation, and this representation is a consequence of a reducible set of base “structures”.

i will develop on this soon, with more concise definitions, and discuss this whole block of ideas in terms of their predictable consequences in understanding the interaction of living things.

a “repasseado”, one of the many portuguese folk dances. this one is particularly fun to dance to. playing is one of the last makers of mirandese pipes, master célio pires.

after the previous definitions, we can move on to bigger structures easily, since the principle is the same. a brain is included in the previous definitions, but it is different in a very important aspect: its feedback loop for thought is done by both reality and its own internal processes: brains (and complex living things) can do work on themselves effectively changing their own information. this has the advantage of not taking hundreds of trials and errors through evolution to produce meaningful responses to environmental pressures. note that DNA can actually act on itself by making proteins that inhibit or change its own structure. overall, this process is more like a spaghetti of loops mixing internal structure and work and external structure and work. the difference i’m focusing on is both how long it takes to cause information to change (the thought ‘clock’), and how much information can be stored (the ‘capacity’). the boundary of “internal” and “external” is artificial, and can be drawn arbitrarily. i tend to prefer a boundary between the part that does work and the part that just provides energy for the work. the first is all things in “motion”, the latter is just the fabric in which they stand.

now, we saw previously that it is not sufficient to account for the information represented, it is also necessary to account for the information reading machine, e.g., knowing a DNA sequence is meaningless without the appropriate cell machinery to process it and an environment that triggers its responses. this additional information should be assumed included in everything i describe as “information”. as i said, it is not sufficient to know the words, it is necessary to know what the words mean. since we generalized the definition of mind and thought, a cell + DNA is actually a small mind with very simple thoughts. its non-random response to the environment signals some sense of understanding of the real world: too hot, too cold, too moist, too dry, stressed, peaceful, all these chemical signals that bathe it are interpreted and processed according to some internal representation of reality. this representation is the chemical structure of the cell itself in its whole: it must include all the parts necessary for the accurate observation and change of reality’s constituents.

the same holds true for a brain of any kind with a big difference. a cell might go through reproduction to change its DNA, but a brain (a brain is a mind made of connected cells we call neurons) can do so on the fly by rewiring itself. a brain, thanks to the capacities of its neurons, can change its observations and its actions easily without necessarily going through the reproductive process (the actions are changed thanks to its relative power over its supporting systems). this allows for it to be a contained self-reorganizing system. but what defines the fitness of this organization is, obviously, reality. the brains that are better at reorganizing themselves to fit an optimal response to reality are favored, and the ones that don’t, aren’t. so it’s plausible to expect that brains are good at observing reality efficiently, otherwise they wouldn’t survive. more on this later.

this representation of information (which we analyzed previously) is quantifiable, like every other before it. but now we have to deal with a self-modifying observation, instead of a passive one (like our planet analogy). a planet has no choice on what information it will store: it is just a consequence of its surroundings. but a mind, through self-modification, can create a subset of information from all the information it gets. both are subjective observers (their observation is a subset of reality), yet the brain can take that subset and change it. this change, sometimes called reflection or learning, can exist in simple and elaborate brains. we like to think that only humans reflect on what they are doing, but i argue that reflection and learning are a consequence of active self-modification.

the reality observed by brains is distorted not only by its location (like the location of a planet), but also by its structural responses and modifications. this means that brains are worse than passive observers at representing reality. this might seem counter intuitive, but as we said before, we may be able to imagine other planets, but this is a long way away from what a dweller of that planet would observe. even a pebble on its surface will know more about the history of the planet than all our telescopes combined. this should be a humbling perspective above all. we must understand that our observations as consequence of our brains are distorted both by being exposed to a limited subset of data and a filtered, biased alteration of the said data. the wrinkles of our skin, the spots and wounds are a much better catalog of what happens to us than our interpretations of what happened to us.

now, there is something very interesting about brains made of neurons, which in my opinion is quite surprising but makes perfect sense. it is impossible to represent reality in a few billion neurons accurately. but, as we saw in our information analysis of abstraction, it is possible to represent increasing quantities of information by creating abstractions. an abstraction is no more than a subset of common information extracted from a large data set. like in my earliest examples, consider that we have the data set {a,b,a,b,a,b}. we can abstract it by saying it is 3 times {a,b}. note that this is not the same as knowing the entire set: it is merely creating an internal observation that has minimal distortion versus the real thing, saving resources, assuming its elements are interchangeable. it is possible, therefore, to represent billions of tons of steel as a mix of a concept of quantity and a concept of steel. note that you won’t be able to point out atom number x in the bulk of steel (therefore your data will not be fully accurate), yet you have a general sense of what it’s made of. this process of pattern recognition and abstraction makes brains naturally scientific. i’m going to get in trouble because of this one i know it. but in this lies a physical flaw in what is abstraction: all the elements of the set abstracted as the same category are considered to be interchangeable and the same, i.e., and iron atom can be swapped by another one with no trouble. while this might turn out to be true for some cases (like chemical elements), it is completely false for other cases (like people). yet our brains are capable of extrapolating data with equal power regardless of the category used. this is not because our brains have elaborate internal representations of both iron atoms and people. it is because the neurons themselves make no distinction between a pattern that is a person and a pattern that is iron. the fact that we can generalize does not come from richness of observation and understanding, instead, comes from a deep lack of understanding of things. this understanding of the differences between things in reality is something that is fine tuned by our interaction with it. to a young child, a puppet is just as alive as a human being: its brain generalized both as living. it is only after much training and learning that these two can be split between a dead puppet and a living being. and what makes the split is the child’s understanding that a puppet can’t move on its own. but the reason why the puppet can’t move on its own comes from the outside world: reality, through the laws of physics, provides that information permanently in every observation. its brain will then, if it’s not deceiving itself, correct its observations to generate a better observation of reality. i hope this is clear because this is essential to understand what will come next.

why is it naturally scientific (actually, i should say naturally philosophic)? let’s go through the process of a mind growing. the mind starts with mind M as it inherited from its ancestors (DNA, cells, etc). this mind M has both observations and actions (as i said before, they are both physical things). if M is faced with a new pattern p and observes and acts on it adequately, then M will prevail. if not, either M corrects itself into a fitter M’ or it will perish. this requires that M is permanently observing reality and testing its internal representation against reality. this is similar to the scientific method: bad ideas are discarded because they don’t work, but whether they work or not is verified by reality. i already provided a definition of the scientific method previously, but now it should become clearer. brains calculate a generative space through abstraction: 3 times {a,b} is a generative space because it can “create” via work a set bigger than itself. abstraction allows us to change the 3 into 4 or 5 and imagine new {a,b} worlds that don’t exist. this is a natural consequence of abstraction. the algorithm used to create the perfect fitting between the abstractions of reality and the observations of reality is the scientific method. its error is the measurement of scientific progress. let’s do a simple example to clarify.

consider miniverse R = {a,b,a,b,a,c}. two competing abstractions exist in minds M1 and M2. M1 = 3 times {a,b} and M2 = 3 times {a}, 2 times {b}, 1 time {c}. which is the one that fits the data best? we generate the extrapolated reality of each, RM1 = {a,b,a,b,a,b} and RM2 = {a,a,a,b,b,c}, and compare them with reality R. we can see that the first mind miscalculated one observation (b instead of c), so it has an error of ~17%. the second calculated all observations correctly. the best choice is, therefore, M2. my formulation of the scientific method is the search for the optimal abstraction whose generated observation space fits reality with 0 error. it is impossible, but an interesting goal. any animal whose understanding of reality is fitter than another will have an advantage over others, and therefore, will thrive. being scientific is no more than being very good at following our survival instinct.

the main point i’m getting at is, however, not how reality as a feedback is key to understanding minds, but actually, how minds themselves represent reality as generative spaces instead of static observations. as we saw above this makes sense if our observation resources are limited to a small quantity of data. it is easier to store the generative space of reality and generate it than to store reality itself. much like my example. but there is a problem. if you accepted my premise that brains store mostly generative spaces instead of real observations, then this means brains can generate realities that do not exist. the existence of brains creates extrapolated realities that do not fit reality. for example, i can imagine an extrapolated crocoduck from my abstractions of living beings, ducks and crocodiles. but this generated observation, when tested, is proven to be false as an existing animal. my abstractions of living beings, ducks and crocodiles are good scientific evidence tested by reality, yet i can generate equally easily completely invalid ones. how can we tell them apart? as i said, for survival reasons, animals with a good sense of “real” should survive better than animals without it. but if survival is out of the picture, then there is no way of stopping fantasy (non-scientific knowledge) from becoming the center actor of a brain’s activity. this hints at the subject of the coming posts. note that even a false idea resides in reality, so it is real only as far as the molecules sustaining its concepts are real. once extrapolated and tested and proved false, it should remain as a hypothetical tale and a proof of the insufficiency of generative spaces.

so far, these seemingly elaborate concepts have been given without any apparent goal. from here on i will begin to build on these concepts and analyze bigger and bigger systems. it’s been very boring, but this sets up the foundation on which i will work, so that ambiguity is removed.

some asturian gaita again, this time a pipe band

on part 1 we first discussed the broad definition of observation and mind. today we’ll continue to more complex structures. to summarize, the first observations are the physical patterns due to reality’s laws of nature (the mindless observers of reality), and the first minds are the ones that change their physical structure by using the laws of nature as the feedback loop for their structure.

as we identify more and more complex structures, the pattern is the same: represented information and replicated information through work on itself/others. this work can be done by consequences of the structure itself. for example, a cell whose work is basically chemical and thermodynamical with no “brain” controlling it (we’ll define this soon). we can say that the reason why these regulation processes that allow this to happen exist are the consequence of an evolutionary thought that led there. note that this definition of “thought” is simpler than usual: it is the processing of information through work. it makes no distinction if this processing is done using forces outside of the system (laws of nature for example) or internal forces (the biased expression of internal energy of the system). so a cell thinks through evolution and this allows it to adapt.

as these structures develop growing internal information (quantifiable as the total information of its constituents, which is the information of the arranged molecules), they can interact with similar, work capable, structures. i’m not adding a definition, but merely identifying another feedback that can happen: not only laws of nature apply, but also other things can do work to change information in other things. the chemical communication between cells is an excellent example of this and has incredible effects. if the work loop can be done with “faster” laws, i.e., if information can be processed faster than through evolutionary time, then thoughts can occur more frequently and evolution can move faster. this is evident in single cell organisms that react to their environment and that leave chemical cues to their partners. sexual reproduction is another good example of the first multiple agent thinking. sex is effectively a non-conservative transformation of information: we feed a and b in, and we get a part of a and a part of b mixed in an unpredictable way. this is another type of information processing.

in general, and layer blindly (this is very important), i will therefore give the following definitions:

• an observation is a non-random arrangement of a subset of basic elements of reality (as a written description of a sunset is to the random arrangement of the letters it was written with);
• a thought is a transformation of information from one state to another (this information can be internal or external and transform it into internal and external information, in any order);
• a mind is anything capable of producing work that creates thoughts and/or observations

or, in mathematics just to annoy everyone again, let reality R be the set of all existing elements (does it include itself? not going there, this is an axiom, remember?).

• observation: such that , where indicates the elements of O and I is information (that arrangement is less likely than many random ones of its elements);
• thought: , a function t that takes internal observations O and reality R (note that O is inside R, making the distinction unnecessary, but used for clarity), and generates a new arrangement of O and R, O’ R’ (note that this kind of definition is applicable to almost any physical system that does a work cycle);
• mind: the set , where O is the observation and f is its thought function.

now, this is a bit idiotic again. i am using an abstraction to define O and R as separate things, but it should be obvious that one is a partial copy of another. there is only R, and O is in it. the only apparently special thing is the f, that is hard to understand why it is there. we can both say it is part of R or of some other kind of medium outside R. in my case, i prefer to say these f s are just R ‘s constituents interacting and affecting one another with their own properties. this, obviously, could be a lengthy discussion, so i’ll leave it there. O and f are subsets of R.

now that we formalized thoughts, minds and observation as simpler things, we can understand them in a broader sense. i will tackle bigger and bigger structures in the next parts.

more portuguese gaita. as promised a long time ago, we will begin exploring the implications of this information model in minds. we will start with simple, brainless, minds. note that this means that my definition of mind is a bit broader than usual.

previously we saw how structure is a property of the arrangement of things. this structure can be quantified using information theory, which actually measures a quantity similar to entropy. we will avoid adding wholes to our parts, since after what i explained previously, that would create issues with infinite information quantities. the information of a whole is the information of its parts. we will consider this as the base principle from now on.

we discussed how complexity can be quantified, but we didn’t discuss how it can be created. this stretches back to some of my early posts. through work (in the physical sense), we can increase the structure of things, provided that this work is fed by some external energy source. gravity for example, during transitory astronomical stages (like the accretion period of planet formation), clumps these things together into more specific arrangements of things. it is arguable whether this is the first case of work or if it is just a property of reality. but in practice, besides clumping things together, it increases the information of a given region in space, versus every other. for example, in the volume of the solar system, information is present in high density areas (planets, sun) and low to no density (empty space). some excellent questions pop up, such as dark matter and so on. all principles are consistent if instead of using matter, we use some other, lower level, organization quantity. for the sake of the argument, it is irrelevant whether dark matter exists or not (but not for the absolute quantities of information).

we can hardly call gravity a mind, or our planet a mind, but it is an example of structured matter that tends to become more and more structured, and by analyzing its structure, we can know factors of the external reality. for example, if a planet could think (which it can’t), it could tell that its heavier bits were more to its center, and that its lighter bits were more to its edge. this implies that there is something that causes these differences, and that the planet actually represents information about its reality. i.e., the matter of the planet is affected by external things (e.g., gravity, electromagnetism), and this causes its shape to change, representing the consequence of these external forces. this means that a planet is a crude, but subjective, observer of its reality. why subjective? because different sections of space have different elements, and planets cannot observe (incorporate) elements that do not exist within its gravitational pull. now, it does not process it, i.e., doesn’t do work on its own structure (e.g., a planet doesn’t suddenly turn all its iron and nickel into hydrogen out of free will), yet the reality around it has consequences on it and these define its own information, versus a random arrangement. so arranged matter is a mindless observer of reality, in the sense that it only collects information about reality (the information collected is its own particular arrangement), but does not act on it (does not do work cycles to change this information).

for example, three things emerge from elements a and b, aa, ab and bb. we know that ab, thanks to the electrical force, will be able to remain together. we also know that aa and bb can’t stay together for long in their environment for the same reason. this means that in the next nearest moment, it is more likely to find the arrangement ab than aa or bb. reality has shaped the structure of these things by virtue of its own laws, and by consequence, ab not only exists, but any other group doesn’t. this narrowed (or structured) the things themselves into a more specific arrangement. it also means that ab has in it an observation of the laws of reality around it, it is a mindless observer of reality.

this brings us to the simplest, and the first, mindful observers of reality. the difference between a mindless observer and a mindful observer is that the latter can do work to change its structure or its environment’s, versus being passively changed by reality. i will start with self-replicating molecules. a self-replicating molecule has both a particular structure and the structure that causes it, thanks to external reality, to replicate. i.e., it is an observer (collects information from reality in the form of its particular constituents and their positions), and it is an agent (by being immersed in an environment it is capable of affecting its structure and the structure of things around it). this implies that its actions have a prior knowledge of reality and how to affect it. by simply copying itself and making mistakes, a molecule will optimize its structure versus its environment for the simple fact that the ones that don’t optimize their structure versus their environment won’t be able to copy themselves. these primitive minds don’t think, thinking is the act of processing internal and external information into different internal and external information. in this case, the thinking is done by the laws of nature. this might seem confusing, but let’s see an example.

two things, c and d, are immersed in reality and made of a and b. thing c, thanks to its molecular structure, can, through the physical interactions occurring around it, take its two constituents from the environment and cause them to turn into another c. thing d cannot. start with a “bath” of many a s and b s, and one c and one d. as a s and b s bump into each other and into c and d, whenever c, a and b are together, another c is formed. no such thing happens with d. whenever c is formed, an a and a b are consumed. so our soup of letters soon will have many c s and only one d. if there is any chance of d breaking down into a s and b s (dying), it will again be more likely for it to become a c than a d. what we see here is the laws of nature doing the work that represents the thought. this simple thought is no more than the information required to process information flowing from reality and back: a and b come together close to c, another c emerges. this implies that c not only has information (a and b), but also changes information around it (causes other a s and b s to turn into c s). since it is not capable of doing this on its own, the thoughts are carried by the forces of nature. but this simple thought could be written as “if a and b are close to me they will become c”, and it occurs whenever a b touch a c and turn it into c. i separate knowledge (internal information) and thought (work done on information) from each other because a self replication might not need all its information to do work. for example, it may be that only b causes c to appear, but since a is required to make a c even though it doesn’t contribute to its replication, it gets copied too, i.e., b does all the work, but needs an a to make a c.

this demonstrates the first working mind, using reality as the carrier of its thoughts. i’ll give a slightly more elaborate example, that i referred previously. a sunflower has in it the information required to make a sunflower, and its structure interacting with the environment cause it to replicate, we saw above how this works. genes and cells are like the above example, they use time as the extra dimension for their thought process. but it also has a solar-tracking feature that i want to use as an example. does the fact that a sunflower track the sun mean it “knows” where the sun is? according to my definition of minds, yes! the sunflower has: a) information about the world around it; b) does work according to that information working on itself accordingly and/or the world around it.

as an argument for a), consider an alien from a starless planet could use the sunflower as a way to know what a star is by simply analyzing the bit of its constituents that reacts to sunlight and makes it grow faster. the alien could induce that the plant was in an environment where sunlight existed, even though he never saw one. and though the alien might induce an incorrect description of the sun observed by the sunflower, he could do better than guessing.

as an argument for b), consider that the sunflower cells grow faster on the areas excited by the sun, making it turn. now, it turns because these areas grow faster when in sunlight, but the reason why they grow faster is because, by thinking using evolution, the plants that turned did better than the ones that didn’t. this thinking was done over many iterations of its structure until it reached this point, where the implicit understanding that the sun moves is can be induced from the explicit motion of the plant. if a plant didn’t understand the sun and its motion, it could not turn accordingly. now, it doesn’t fully understand the sun (neither do we), since it is still subject to, for example, being fooled by artificial human lights. but we have to understand that evolutionary thoughts take thousands of generations to reach conclusions. so it would be like learning how to read in english and then being given a transliterated japanese text and say “but they are the same letters”. the letters here are light, english is the sunlight, and japanese is the artificial light. since through evolutionary thought the sunflower only learned english, it won’t learn japanese instantly. but if given long enough, it might.

i know that observer planets and thinking plants and molecules sounds a bit exotic and silly. so i’ll finish for now. we are not dealing with elaborate thoughts. in fact, if you take the sunflower example, its thoughts would be something like “sun is here” “sun is there” “sun is nowhere”. not very elaborate thoughts, but they are proto-thoughts nevertheless, that themselves require some subjective internal representation of the world and action according to this interpretation. my opinion is that by broadening the definition of thought and mind, it might be easier to understand more complex structures. we’ll do that in the coming parts.

portuguese gaita again. today i’ll be continuing the subject of structure and quantification. this time, i will use our concept of thing directly in the calculation of structure.

we first saw that a thing of layer l , i.e., a thing is made of things. for each thing, its information (quantification of structure), is a function of the arrangement of its constituents, . note this is only true if there is no mutual information between the constituents. if there is, we can just conjure up a higher level “middle layer” that hides this mutual information as a single entity. this makes the structure of a thing of any layer quantifiable and independent of its constituents, only their quantity and arrangement. this means we do not need to know the information of constituents to know the information of a higher level system. this is a bit mind boggling, for sure, but this means our layers are irrelevant for the calculation of information, what matters is the quantity of sub-elements.

how is this relevant? this means that to properly quantify any structure, we can either quantify it in a single layer, just like the real world, or quantify it including explicitly all the information of the parts (as we, sentient beings, define them). if we choose to quantify and include the parts, we get . infinite recursion, just as we would expect from a seemingly fractal definition. what does this lead to? let’s calculate it using induction (philosophers start panicking!).

grouping,

we can now group this beast using sum and product operators. this will only disguise the big beast this is.

let’s hope nobody notices how big these numbers are. it’s obvious it is a divergent series and grows with N.

what this means is that we can expand or contract our “zoom” to define structure at any level and accounting for any layer whatsoever. we’ll need this in the future. for now, let’s let these concepts settle. when structure is quantified over a hierarchy as ours, the quantity always depends on the zoom chosen. this paradoxical result is well known from fractal mathematics. i guessed our structure was fractal, this is the proof. fractals are a consequence of abstraction. for nature, since she is abstraction-less, there is only one value for the structure of the universe: the value for the structure of the universe. nothing like ending a philosophical text with a tautology