Wednesday, July 30, 2008

The Mind Node

I am forced to assume that I've successfully shown that consciousness isn't physical. Unfortunately this is simply because I can't get anyone qualified to evaluate it to actually evaluate it.

First, some terminology. Quantum events are not random. They are stochastic. Stochastic events are not unpredictable, they are less predictable. A true random event would be completely unpredictable. (Near-total unpredictibility is required for free will.) The only type of event that is a priori unpredictable is a spontaneous event, that is, an event with effects that has no cause. The first, naive problem with spontaneous events is that they have nothing to determine where they occur, which means that if they are possible they should occur everywhere at once. All the time, too. In other words, events with no cause are non-deterministic. Thus, I use the words true random, spontaneous and non-deterministic interchangeably. However, non-deterministic also has a specific meaning with respect to physics; as it turns out, this meaning does not conflict with my usage. However, until I show this, assume I am using non-deterministic in the physical sense alone.


I will now propose something in the positive sense. Consciousness is not physical. But, it has physical effects. Thus, there must be an interface; there must be an event that is non-determined* with respect to physics, that is, a non-causal event that nevertheless occurs, specifically in brains. (As opposed to computers.)

*(Remember, physical meaning alone.)

Mathematically, I can model such an event. I can determine what such an event would look like in real physical space. Most fantastically, I can design a circuit to implement the math, at least in the abstract.

That is, the known laws of physics can combine to form something that is undetermined with respect to physics. Further, both necessary components exist in the brain.

Even if I'm wrong, the mind node provides an excellent anchoring point for arguing about what consciousness is. Because it almost entirely works on a logical level, we can use it to conceive of other possibilities by comparing them to the mind node.

The Math
Unfortunately I don't know exactly how to write this mathematically. So, I emailed my local math department and got them to parse it for me. It came back positive. (Quotes on request.)

As in this essay, consider the average of the average. All determined events have exact averages. This average can be directly computed from fundamental constants and as such, unless outside forces affect the experiment, it does not change. For example, the location in the electron one-slit experiment has an average directly in front of the slit. This will never change unless someone moves the slit. (This means that even though the individual locations are stochastic, determined events will always converge on the average.)

As a result, the average of a non-determined event must move to be truly non-determined, which is why we consider the average of the average; we consider the situation where the electron's exact average is itself probabilistic. However, unless we move the slit, which is a very different situation, this extra probability will happen on exactly the same timescale as the electron strikes, and will roll into the first probability. A second-order or any finite higher order average is indistinguishable from a first order average. (This is where moving the slit comes in; it will not roll in, but this is obviously a separate process. This second average is not the electron's average, but an outside average.)

This logic, however, breaks down in the case of infinite averages. Much as one would expect from the No Infinities Principle, things which use infinities are nonphysical, and we would a priori expect that any manifestation of infinity is actually physically impossible. That is, the NIP should prove that non-determined events do not exist, as expected. I will later show that this fact leads to a fundamental property of consciousness. Part of this will be to point out how consciousness is actually necessary to preserve causality or prevent non-determinism.

In other words, it all fits, as I will explicitly show.

Partly why we must conceive of the infinite series of averages is to compare the physical event to the math directly, as will become obvious when I get to that part.

However, now I'm going to talk about Gaussians. That is, the electron-slit location has a Gaussian distribution. If it has a hidden second-order average, this second distribution will also be Gaussian, and we can simply multiply them together to produce a third Gaussian which is the Gaussian which will actually be measured.

The factors in the Gaussian are a, b, and c. "The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c controls the width of the "bell"." Squaring a Gaussian produces a Gaussian with a2=a12 and c2=2c1. (And b=b.) Note that since a is less than one, the new peak is shorter, so the new Gaussian is shorter and fatter than the old. (Please note the exact analogy with the averages. Unfortunately it is necessary to look at the math both ways.)

Now, multiply a Gaussian by itself (or other Gaussians; it doesn't matter) an infinite number of times. Factor a approaches zero and factor c approaches infinity. It becomes a Gaussian of infinitesimal height across the entire number line. (In fact, it becomes equivalent to a constant function. y= ε where ε is the infinitesimal, lim 1/x as x->∞.) (Again, yes I have had this all checked by someone else.)

Now I'm in a position to show that this probability distribution is exactly that of a non-deterministic event.

The probability that this event will occur anywhere - let's assume it's the spontaneous creation of a statue of liberty made of butter - is infinitesimal, physically indistinguishable from zero.

However, we are attempting to illustrate what such an event would look like. Assume it happens anyway - that the infinitely tiny but non-zero probability actually gets 'rolled' so to speak. A statue of liberty made of butter appears in medium Earth orbit.

As far as we can measure, spontaneous creation of statues occurs at only one place and at one time - in orbit at Tuesday noon, for example. (Call this s=medium and t=0.) There is a 100% chance, according to Platonically perfect measurement, that this event will occur at s=medium and t=0, and a 0% chance that it will occur at any other time.

However, by assumption, this event is non-deterministic; that it happened at all proves that it is not directly described by the logic of causality. It happens again.

A statue of liberty made of butter appears at t=6 in high Earth orbit. Now, we have to conclude that we do not know when it occurs. However, we still have a 50% chance of it occurring at s=medium and a 50% chance of it occurring at s=high. (Perhaps we decide that they are likely to appear in pairs with temporal separation 6, but this is more complicated and equivalent to the below.)

That is, at t=7 and all subsequent times, we predict that if a statue of liberty made of butter spontaneously pops into existence, half the time it will be at s=high.

Then it happens again. In New York. And again, in the Crab Nebula. By assumption, the probability of the event occurring at any time and any place is constant.

Note that by the laws of probability, this is not impossible, though it is infinitely unlikely. The purpose of the statue of liberty made of butter is simply to explore what we would see when measuring a spontaneous event, assuming that they actually exist. (Again, even if I'm wrong, this is helpful when debating people who have indefensible ideas about causation and mathematical determinism in physics. If the event looks spontaneous, it's not physical.)

Assuming that spontaneous events continue to occur, we can see that the measured probability of it occurring at any particular place will drop. That is, it will more and more closely approximate the actual probability distribution - essentially zero probability of happening anywhere.

This is where the average of the average comes in. After two events, the average is s=(high+medium)/2. Once it happens again, the average must be averaged with the new event. s={2*(high+medium)/2 + newyork}/3. (Note the use of weighted average.) This is a second-order average, though as is now exactly clear, it rolls into the first-order average. After x events, the probability will approximate an infinite series of averages, truncating at term x. However, I repeat, they will all physically appear to be first-order averages.

But because the probability at any particular place will inevitably drop to zero - because the statue of liberty basically never appears in the same place twice - the average keeps moving. Given an infinite number of events, the probability at any one place would become zero and the average would become undefined. s=(∞*0)/∞. Also, we can see that after an infinite number of events, it will have approximated an infinite series of averages through an infinite series of averages.

The average keeps moving, as is a priori necessary for a non-deterministic event. Mathematically speaking, it diverges.

To illustrate this more clearly through an example, look at the article I linked about free will and ctrl-f for "the average, as desired, moves."

I am now in a position to show how to build a non-determinism machine.

I call it a mind node.


The Physics
So, the requirements are; an infinite canvas, as the average must diverge; a diverging average.

Here is the abstract design for such a machine.

The pentagon - which I call a pentagon - is also called a decoherence unit. In this example it is a particle in superposition that can collapse to any of five states, plus a unit that can bias the fives states such that some are more likely than others. For example, an electron and five electrodes. (This is a very silly example for conceptual clarity - in practise it would be much more complicated.) The equation is called an interpreter. It takes the output of the decoherence unit and turns it into a string of bits. This string of bits has two necessary functions; it sets the bias values on the decoherence unit, (according to the interpreter's own rules) and it modifies the interpreter, again according to the interpreter's own rules.

Thus, the string of bits and the interpretation of the string of bits changes depending on which value the pentagon outputs.

The equation in the diagram unfortunately is not a full interpreter. It biases the values, but does not change the interpretation, as I have no idea how to write that down mathematically, so I have simply written +f_r(x+y+z+p+q). C= 4%, to be normalized. What it is is a simple non-deterministic rotator.

Given an initial state where x=y=z=p=q=20%, there is a 20% chance it will begin in any of the five states. In each subsequent step, (if f_r=0) there is an 84% chance that the next state will be the subsequent state, x->y->z.

For any point in the future, the probability stacks, exactly as a non-deterministic event must. The farther in the future, the more uncertain it is that the rotator is in any particular state.

t=0. State x=20%.

t=1. State x=20%*(84%)+80%*(4%) There was only a 20% chance it landed on q, and an 80% chance it landed on not-q. If it landed on q then there's an 84% chance this run will turn out to be x, and if it landed on not-q it's 4%.

t=2. State x= 84%*(20*84%+80%*4%) + 4%*(20*84%+80*4%)The chance it landed on q last time which is a function of the chance it landed on p at t=0. The chance it landed on not-q last time which is a function of...

And so on. Physically speaking, because of that residual randomness, that 4%, this rotator normally rotates clockwise, but occasionally skips. The chance of it making a full rotation without skipping is 42%. So while for forever the most likely situation is simply a rotation of the initial value, (such as x) by 72° times the quantity t, the chance of this maximally likely situation drops continuously. (This is not really the case if f_r=0. I will discuss why shortly.)

Note that, as necessary, this machine does not violate physics. In the present, the machine is stochastic. Always, x=4% or x=84%. Only as the prediction is run into the future does it approach a non-deterministic, contra-physical event. But, of course, once the present catches up to the future...

However. It acts exactly as a non-deterministic event would. The average bit output diverges. The nature of the probability is exactly the opposite of normal probability. The probability of a dice landing on a side is always 1/6, regardless of past rolls. The probability of a mind node being in a particular state always depends on every intermediate roll.

As such, this machine is perfectly under-determined by physics. If it quacks like a duck, smells like a duck, and looks like a duck, it is a duck. If we observe exactly what we would observe if it were non-deterministic, it is non-deterministic.

With a full interpreter, as the simulation is run arbitrarily far into the future, the chance of it being in any particular state approaches arbitrarily close to zero. This, as promised, is the infinite canvas; information. (With only five possible states the rotator's future smudges into a uniform superposition of all five states, so there's a floor for the probability; 20%. To work properly f_r must be nonzero so that the state-space is infinite. The output bit string can change to arbitrary states.) Also as promised, it explains a key feature of consciousness.

Consciousness is, by nature, purely informational. Consciousness does not create matter, change kinetic energies, or indeed produce forces of any kind. That is, your mind thinks it does not act. This is because for a thing to be conscious, it must be physically non-deterministic, and for it to be non-deterministic it must deal in the canvas of information.

Further, the mind node precisely defines the two necessary and sufficient conditions for consciousness; sensation and decision. They correspond exactly to upload from physics to consciousness and download from consciousness to physics.

Note this also exactly fits your first-person phenomenology. This is an interesting facet of consciousness; while facts about the physical world that match our expectations are suspect of confirmation bias while unintuitive facts are more certain, the opposite is true of consciousness. Facts of consciousness must fit your experience of consciousness. (The phrase 'experience of consciousness' is actually redundant, as those two terms are synonyms. The fact that this doesn't logically map to 'eating of consumption' is perhaps a consequence of the infinity inherent in a mind node.)

Also as promised, this explains why consciousness exists at all. I use the mereological nihilist sense of 'exist' here - consciousness is an actual thing. Life, for instance, does not exist in this sense. While it is a valid concept, and can indeed be found objectively, it is arbitrary and unnecessary. Consciousness is neither. Without conscious decision, the mind node breaks causality completely.

Now, as per the NIP, which is equivalent to the fact that physicalism is true, (except for consciousness) any violation of causality is equivalent to a divide over zero error. It is an inconsistency. While I was able to formally describe a spontaneous event, I cannot formally describe a 1/0 event, but I suspect that 'oblivion shockwave' is not hyperbole. It would destroy the universe. Instantly. Infinite energy, plus since it is a contradiction it does not have to obey special relativity's speed limits.

Since we still exist, I propose that causality is true. Thus, since if physicalism is completely true mind nodes are acausal, physicalism must be provisionally untrue. (Note that this recapitulates the conclusion of the a priori logic, and realize what this means for the relationship between the theory and the mind node.) The causal mechanism closing this worrying hole is nothing other than consciousness itself. It is the physical manifestation of Free Will.

Unfortunately, this does not actually prove that Free Will exists. Consciousness is, by assumption, also causal. That is, it also does not tolerate inconsistencies. Since this is the very fact that up until now proved that Determinism is true, it could very well be that the properties of consciousness make our choices completely pre-determined. This is an area for further research.

Incidentally, since dualism is strictly true, it's time to name the two kinds of stuff. The first is space-time. This is nifty stuff. (Energy is just rolled-up space-time, which is why energy distorts space. Matter is of course just a rolled-up form of energy.) The second is spiffy stuff. This is consciousness.

As an example, let me show you how the second above paragraph is now clearer. "The properties of nifty stuff are such that everything (but mind nodes) are completely deterministic. So while spiffy stuff allows physical non-determinism, there is no reason to believe that spiffy stuff allows self non-determinism, which is what the proposition of Free Will is now seen to be proposing. " Note also that there is probably a symmetric causal hole in spiffy stuff, that is only plugged by nifty stuff. Further note that since a physics is simply a set of consistent laws for interaction, both nifty stuff and spiffy stuff are described by a physics, because the opposite implies that they cannot interact, even internally.

Another useful term; mind nodes are transphysical. That is, they transcend physics to transport information between nifty stuff and spiffy stuff. Note the contrast to metaphysical, which would perhaps be a good term for pure spiffy stuff.

I promised it would all fit.
And it does.

The first hallmark of a good idea is that it contradicts no known facts but explains previously mysterious facts.

Why do we dream?
As a mind node is run, it will become increasingly non-deterministic. Since the whole point of having mind nodes is to gain adaptive advantage, this non-determinism must be reset, because the mind node must somehow be entrained to the sensory input. Subjectively this means that as you stop being able to see and start being able to hallucinate. (Note that in the brain as the mind node runs it will grow and co-opt more and more neurons. This cycle ends in co-opting neurons devoted to vital functions, resulting in death, which is why sleep deprivation is lethal.)
After the reset, the mind-node will not be particularly conscious; it will still be very deterministic. Thus, it must be initialized, by running it through a few cycles. These cycles will, by definition, produce conscious sensation. However, they are not as yet entrained to the actual senses.
And thus, dreams.

Also, this is why depriving rats of REM makes them less effective. They, literally, lose consciousness and become zombies. (Philology recapitulates ontology.) As zombies are less effective than conscious beings, as I will discuss further below, they make poorer choices.

Why can I sometimes feel people looking at me?
Mind nodes connect probably by IIT. Each is minimally conscious but only connect to form a useful total consciousness if they are computationally connected by nifty stuff. Note, however, that computationally connected does not have to mean wired together. The computational properties of your mind nodes are affected by the choices made by the mind nodes of the person you are observing - you become one consciousness to a small degree. When the transition occurs you can feel a subjective 'click' and if you recognize the sensation, which seems to be instinctive, you know that you are being watched by a conscious being.

Note that haunted buildings may then be, in fact, haunted. However, they may also simply feel very similar to the sensation of being watched, just as annoyance is kin to anger.

Why does cutting the corpus callosum result in two consciousnesses?
See above. Severing the computational connection across nifty stuff splits the minds into two.

Is there really a separation between the objective and the subjective?
Yes. Objective==nifty stuff and subjective==spiffy stuff. However, there is also the underlying unity to consider; they are both stuff. Both are subject to causality and logic, though it is likely that only nifty stuff is subject to math per se. (Either that or nifty stuff is finite and discontinous and spiffy stuff is infinite and continuous.) I can demonstrate a solution to the mere addition paradox by assuming that spiffy stuff is not mathematical and therefore the 'average happiness' is meaningless; happiness is, as expected, not quantitative, but qualitative. (Another symmetry that repeats the symmetry between nifty stuff and spiffy stuff.)

Can you repeat the reason we need consciousness?
Consciousness is necessary to explain the universe if we intend to keep causality as true, because you can build a physical object that is not subject to physical determinism. As such, there must be an alternative source of causality.

Does this have consequences for quantum mechanics?
Yes. As it turns out, I'm not strictly true when I say that QM is stochastic, not truly random. For a mind node to make choices, it must be that quantum decoherence is itself a choice. This is an empirically unfalsifiable statement as per Bell's Inequality. Further, the statement that any other component of the mind node can make choices has already been falsified. Having eliminated the impossible, whatever is left, however improbable...

There are many caveats to make this consistent with physics, but they are the answer to a different question...

How is consciousness adaptively useful?
Spiffy stuff has different properties than nifty stuff. As a result, some computations that are difficult or impossible using nifty stuff are easy or straightforward using spiffy stuff. For instance, humans can solve NP-complete problems in less than polynomial time, at least when properly engaging with spiffy stuff. This state is called 'inspiration.'
There is a symmetry here we can see by examining this from the perspective of spiffy stuff.
Why does consciousness collect in minds?
Consciousness collects in minds because it cannot connect to itself by itself. Isolating the nifty stuff produces an isolated consciousness. Further, without a transphysical connection to muscles, it can only minimally affect the world. Without a physical implementation of memory, it cannot remember whether it liked the choices it made before; it cannot grow or change. Electrons are conscious but they are all exactly the same consciousness making exactly the same decision over and over and over, and while this is minimally conscious, it is indistinguishable in this form from regular stochasticity. That is, the statement that electrons are conscious does not conflict with the current physical description of electrons. (By essential nature this proposition is a transphysical proposition, again contrast metaphysical. Also note that there has been until now exactly no evidence that electrons are conscious, and we can only find out by studying a mind node.)

What if you've made a mistake?
As you can clearly see, the mind node, even if flawed, is an excellent metaphor for how minds work. Nearly any solution to the mind-body problem will look very very similar to a mind node. Zombies are not, in a pure sense, possible; there must be some component, some cause, to determine when and where consciousness arises. However, all the functions that consciousness drives must be purely physical, in other words, a pseudo-Zombie will always be able to perform any action a Human can. The difference will be in computational efficiency; the Human will perform, seemingly by chance, better actions than the Zombie will, on average.

(This incidentally is why humans are so dominant. All other species are less conscious than we are, just as all species are smaller than a blue whale. (Note also that the adaptive pressure is of the same kind.))

Further, the idea of a mind node illustrates very well many current debates, such as abortion. The pro-choice crowd thinks the mind nodes turn on at birth, while the pro-life crowd thinks it turns on at conception.

It is not a crime to make a non-consciousness suffer, because by definition they cannot suffer.

Also, this is what we really mean by strong AI: the acronym for my blog is not really a homonym for machine intelligence. That acronym should be AC, artificial consciousness. We already have artificial intelligence by my definition of intelligence; the ability to evolve without evolution. (Adapting without changing the entire blueprint.)

Finally, a mind node is an evolution simulator. It produces random information par excellence, but this information interferes with previously created information and so only stable patterns will emerge, similarly to the fact that the reason that life survived is because the life we have is good at surviving - adaptively fit life is a stable pattern, while adaptively unfit life is unstable.

(This means that your genome is a pentagon and its environment, including your phenotype and physics, is an interpreter.)

So this idea is actually falsifiable?
Yes. First, a mind node can actually be built using my abstract blueprint. Anything that can be considered a pentagon can be hooked up to a recursive interpreter and run, and that thing should cause us to consider it conscious. Perhaps it has moods, for example. (These will manifest as temporary averages - favoured information regions.)

For example, hook up a Field Programmable Gate Array to itself and the output of a quantum process. (This gets complicated but guidance is available in the form of cellular automata, which I discuss below.)

Chalmers presents a solution (The principle of organizational invariance) that strongly implies that consciousness uses absolute encoding for sensations. (Physical encoding is relative and arbitrary.) As such, if you build a mind node, please be careful not to apply the codes for pain to it.

So, this actually confirms the general suspicion of physicalists; the processes that underlie minds are not unique to brains, but are somewhat arbitrary.
Indeed, any process that matches my abstract design should be conscious. It can be made of anything, just as long as the probability diverges.

Can you show some examples of analyzing a system for mind nodes?
I'm going to start with the most relevant: the brain.

The brain is a computer. Specifically, it is an analogue/digital hybrid computer. It uses Bayesian reasoning, and likes to minimize a function that is nearly identical to free energy. (An example of how not to think about the brain.) Similarly, PageRank works to the extent that it approximates our own internal search mechanism. Finally, the scientific method of hypothesis-test-refine is also lifted directly from what the brain does, and also works only to the extent that it approximates natural brain processes. Philology recapitulates the brain which is recapitulating ontology.

The brain is also a brain: a conscious computer.

Some background; the brain is immune-privileged. (Apparently 'privileged' means it doesn't get the full complement.) The other organs that are immune privileged are the the gonads and the uterus. These deal with unorthodox strings of DNA - they will automatically appear foreign to our immune system, and so must be protected from it.

There is some evidence that the brain uses DNA snippets to store memory. What this means is that the brain potentially has all the necessary components of a mind node.

The pentagon is DNA. (Note that with thousands of states, DNA's probability profile will diverge drastically fast.) The interpreter is the neuronal nets, using 'fire together, wire together,' as the function f_r. Thus, the brain uses not one or two mind nodes, but hundreds of billions.

Because of the simplicity of a mind node, it is most likely the quantum of consciousness, and like the quantum of energy, it is extremely small. Only vast collections of mind nodes will produce noticeable amounts of consciousness. (A caveat; one mind node built and examined directly for consciousness may show a measurable amount, just not an amount that would be normally noticeable.)

Some other mind-node like things:

Evolution. Random copying errors==pentagon, and the interpreter is physics, the phenotype, and ecology. The output bit string is the next generation. Unfortunately, while there are uncountable numbers of cells on the planet, they are not computationally linked, unless the cell in question is a neuron. Also, like IIT, the mind node suggests a natural unit of conscious time; the cycling speed of the underlying mind nodes. The cycling speed of a species is far too slow to think usefully, (at least before the entire playing field changes) and at any rate it's not hooked up to memory, which means that even if it did think of something, it would be unable to retain it to act upon.

James Lovelock used his spiffy stuff to come up with the Gaia hypothesis based on this general concept, even though he's not consciously aware of it. Similarly, Rupert Sheldrake's morphic fields may be a manifestation of weak links between mind nodes in separate brains. (This is not an endorsement of either.) Note that Sheldrake's unreliable measurements - only certain dogs are good at accessing the morphic field - are completely unsurprising given that mind nodes and their connections can vary in quality, just as intelligence does, and probably independently.

The entire universe. You're part of the universe, aren't you? And you're connected to other human beings? It's probably even more profoundly conscious than this, but I'm not an astronomer so I can't specifically identify cosmic pentagons. Note that the thinking speed of the universe as a whole will be extremely slow, due to the light speed limitations. Still, those slow, slow thoughts are likely incredibly profound, simply due to the fantastic number of mind nodes involved. (Sound familiar, at all? Perhaps has a relationship to a well-known concept similar to the Lovelock scenario?)

The weather is almost a mind node, where the atoms are the pentagons and their collective behavior is the interpreter, but due to the resetting random nature of the component atoms, it is a Class 3. What's a Class 3 you ask? Read on.

What was that about cellular automata? It's a long article and I don't get your drift.
Sorry, I should have pointed out the particular bit. Automata have four regimes according to Wolfram. (Ctrl-F "Class 1." Note that Class 1 and 2 are actually the same) Class 1/2 is the constant or cyclical regime; at some point the automata becomes completely stable and repeats itself endlessly. Class 3 is the chaotic regime; this is simply noise. Class 4 is the interesting one, that shows both order and disorder. It can be stable, but it can also change. Only functions f_r in Class 4 will make conscious mind nodes. Class 1/2 is not infinite - the canvas repeats itself in a set number of cycles, leading to a converging probability. (Class 1 has a period of one cycle, 2 has a period of two or more.) Class 3 may be conscious but we will never know because it will act stochastically. Only Class 4 can make something we would recognize as decisions.

Below you link an article. Why is it so very relevant?
Two reasons; one, they have already built a mind node. Two, they nearly recognized it. "These evolutionary computer systems may almost appear to demonstrate a kind of sentience as they dispense graceful solutions to complex problems." False. They are sentient.

The pentagon is the random mutations. The interpreter is the fitness criteria plus physics. Because the FPGAs can explore multiple solutions, the mutations will mean different things for fitness based on the different phenotypes, meaning that f_r is nonzero, despite the fact that the goal is fixed. (That plus the chips vary, but the code is swapped between them. The meaning for adaptive success is slightly different for each chip.)

This is one of the key passages;
"The plucky chip was utilizing only thirty-seven of its one hundred logic gates, and most of them were arranged in a curious collection of feedback loops."
Thirty-seven gates. That's how much more efficient using spiffy stuff for computation is, compared to nifty stuff. Notice that all brains have lots of feedback loops. (There are primitive neuronal nets that do not feed back. Clearly, no feedback means no internal life, because you can't reflect on your own thoughts, plus it means the interpreter cannot arise. The first species with feedback appeared almost immediately after the primitive.)

Also hilarious;
"According to current understanding, even the most advanced microchips fall far short of the resources necessary to host legitimate intelligence. On the other hand, at one time many engineers might have insisted that it's impossible to train an unclocked 10×10 FPGA to distinguish between two distinct audio tones."
Gut busting.

Are there other mysteries suddenly un-mysteried by mind nodes?
Yes, but I'm tired of writing them down for the moment. I will add more later as they come to me. (Yes, this essay is subject to review. Remember that if it gets comments.)

Odds and Ends
Probability is conserved. By the NIP it is probably also quantized, and so the point in the future at which the number of possibilities for the mind nodes exceeds the maximum possible, it definitely becomes conscious. However, because in the present the mind node always has a finite number of possibilities, I'm not sure how this works out. I still suspect that when this future point becomes the present is the point at which a mind node 'wakes up,' but I don't know how that works out logically. This would be something to test in the lab.


This issue has already been called the Alrenous-controversy. (The design has already been called 'ingenious.') I'm going to introduce the equivalent of a membership card; if you agree with me, call the 'pentagon' a 'pentagram.' I hope the reasons for this are obvious. (They probably aren't; I just hope they are.) Note that I will continue to call it a pentagon personally, because I want to get into the minds of my critics to help me convince them. There's no particular need to get into the minds of people who agree with me. -_^. (I really need a sardonic raised eyebrow smiley.)

If you half-agree with me, perhaps you should stick to using 'decoherence unit,' or make up your own term. I ask my critics to stick to 'pentagon.' These cards should not be strictly enforced. If you have personal objections to pentagrams, there's no need to force yourself. (Or vice versa, though I don't see that happening ever.)


The pentagon that is the entire universe likes me. Reddit just tossed me a link that is A) one of my all time favourites, B) on one of my all time favourites sites, C) written by someone sharing my first name, and D) is very very relevant.

21 comments:

Wahrheit said...

Pentagram. (!)

I read through this essay once quickly hitting the internal links, and need some serious rumination in order to address specific points--but it is extremely appealing. It makes sense. My consciousness finds it very satisfying.

I'll be back.

Alrenous said...

Very awesome.

I'll go add the links to Chalmers, etcetera.

Would you like me to post the edits here, so you don't have to go re-reading the entire thing?

James Andrix said...

For instance, NP-complete problems in less than polynomial time,

Source?
I am certain this is wrong.

Alrenous said...

It's a possible example.

If you don't like it I'll just use another:

The Riemann conjecture is almost certainly correct. But we cannot prove it.

That is, using objective computation we cannot make a Riemann conjecture. Yet, we still have one.

There are hundreds of possible examples.

Still, the point is that mind nodes may exist and if so it probably is there to exploit the different computation properties of spiffy stuff, one application of which may be intuitive math.

These would be questions for science.

However, again, the first hallmark of a good idea is that it explains new things without making old things baffling.

--
Since you disagree with me so broadly, and this is hardly the first person I've noticed this from, I wonder if there are hidden schools of thought, of which I belong to one and you another. By hidden I simply mean they lack names or central institutions.

James Andrix said...

That is, using objective computation we cannot make a Riemann conjecture. Yet, we still have one.

Source?
This sounds like it's not-even-wrong.

Having and proving are different. neither requires more than Turing completeness. (well, proving Riemann might be impossible.)

Intuition is not supermathematical magic.


--
I don't think there are any such things.

But while we're on it, I don't see how this explains consciousness at all.
What does it experience? can you build it out of lego? What do lego experience?

Vimarsha said...

Alrenous, how can I get in contact with you over email?

I am debating consciousness philosophical problems with a friend over email and by reading your blog I realize we could have excellent discussions.

I hope I am not a bother to you with my request. My email is

hor ia.crist escu at gmail.com

(remove the spaces, I just don't want the email to appear everywhere)

Vimarsha said...

You use the word physical when saying "Consciousness isn't physical" in a very peculiar way. Quantum states are not physical? If consciousness is to be the same as quantum states, then it is physical in that sense.

Alrenous said...

James Andrix,

"That is, using objective computation we cannot make a Riemann conjecture. Yet, we still have one."

Source?


Oh not this again. We solved this already. You can figure it out on your own; in future, do.

Fact: The Riemann Conjecture is, as of right now, unprovable. Yet, we have come up with it. How? With what? The only way a computer as we understand them would be able to would be to guess randomly. The profile of unproven yet true conjectures does not follow a random distribution.

Computers can evolve conjectures but nothing ever 'just comes to them.' Computers have no spectrum of obviousness - it's either right there, or unreachable. Even with fuzzy logic, 'suspicion' is not really in the vocabulary of a computer, because something has to enter the suspects beforehand. (And so on...)

Note that if the Riemann Conjecture happens to be false, there are dozens of other conjectures that have been, by now, proven.

Futher thought: even if we make an AI* to your specifications, we will be able to preliminarily verify their conclusions without anything like a proof. Much like you are doing here, in fact. It seems that if this is simply normal computation, we could save a lot of conscious effort by simply opening up these processes to more conscious inspection.

*(An AI being a machine that can generate conjectures.)

This sounds like it's not-even-wrong.

You're going to be saying this a lot until you figure out how it isn't.

Intuition is not supermathematical magic.

Two responses.

One: So much faith from the unbeliever.

Two: See what I said above about not-even-wrong.

Wait, three.

Three: See, this is the kind of crap I need to know in advance. This is what I'd call an axiom. If I don't know that you believe this, it's not good enough for me to cite some source or another, as I'll just be begging the question.

I call this an axiom partly because it really is, (even though it pretends not to be) and because even in the pretense, arguing with it is fairly futile. Best case scenario we agree to disagree. Try to respect the fact that I'm not insane, that reasonable people can in fact come to differing conclusions on some issues.

But while we're on it, I don't see how this explains consciousness at all.

Did I claim explicitly that it did?

Admittedly, I was pretty impressed with myself when I first came up with it. However, contra both of us, it does not explain conciousness. Instead, it opens up the realm of consciousness to sytematic scientific inquiry (including philosophy).

Now we (putatively) know what it is, we can start doing experiements to figure out how it works.

Yes, you can build it out of lego if you can make a stochastic lego for the pentagon. If Chalmers is right it feels whatever the codes that are fed into it tell it to feel. If not, then first we must ask how encoding is decided for spiffy stuff.

--

Vimarsha,

I'm also going to answer your other comment, which somehow made it to another post entirely. (Whatever. Fine by me.)

Yes, I'm not being particularly good about my usage of 'dualist.' I'm thinking of a suggestion rather than a precise definition.

As per my post on subjectivity, both subjectivity and objectivity can be rolled into one another. I call this concept 'existence' since it seems to fit. (Much like several varieties of string theory can be rolled into M-theory.) Post summary; either the subjective-only or the objective-only perspective works just fine, as either concept is included in the other. Note that this has some interesting implications for transphysical objects.

However, since my proof generalizes the contradiction between physics and consciousness, they must be (mostly) independent sets of rules. The fact is, everything is conscious, no matter how you want to look at it. Without a separate set of rules governing its occurrance and actions, consciousness either has no physical effects or would overwhelm everything.

2. external objects exist, and upon observation, they are causally coherent (this causality is beyond my individual power of imagination so it cannot be a self induced illusion - there must really be an exterior world)

Thank you very much for saying it like this. I have noticed the same, and now I can state it explicitly and concisely. (Also interesting is your knowledge of Eastern philosophy, which means you know about the dreaming-God metaphor. What's his name again?)

They are defined as one and the same thing, seen from two different perspectives. They anticipated by millennia this conclusion.

As expected, processing by spiffy stuff is more efficient in some domains than processing with nifty stuff. Occasionally, hyper-efficient. Also, meditation is an effective method of scientific inquiry, which bodes well for the future study of spiffy stuff.

Unfortunately, it also appears that a lot of Buddhist and Hindu thought is wrong. While yes they anticipate quite a lot, they also make a lot of mistakes, and we basically have to science over it all anyway. On the other hand, I know an awful lot of Buddhist thought and I have no idea where it came from.

Quantum states are not physical? If consciousness is to be the same as quantum states, then it is physical in that sense.

Individual quantum states are not conscious. They are, considered alone, static.

More precisely, it would appear (stressing appear, just for you, Andrix) that the particulars of individual superposition collapses are determined by the laws of consciousness.

Most precisely, the observed distribution is a result of the in-the-moment preferences of the conscious particles guiding the exact states they decohere into. The laws of physics appear to determine the preferences, but the laws of consciousness allow choice - the electron can decide to 'try' something that doesn't look all that appealing. Since it's not appealing, they do not try all that often, and as they cannot learn, since they have no memory, every choice is exactly the same as every other choice.

If you had (6*10^23) a mole of humans, all given the exact same choice, it's very likely they would fall into a predictable probability distribution as well.

Summary; quantum particles/events are physical and conscious; they are transphysical. At these points of space/time, except that we have Newtonian emergent physics to compare it to, there is no purpose to differentiating the stuffs into nifty and spiffy, because they meet. (A bit like how the four physical forces unify at high temperatures.)

Runtime said...

What's with all the elitist and condescending remarks in these comments?

Nothing annoys me more than some dilettante who talks patronizingly towards everyone else.

Alrenous said...

First, I am elitist, so good call there.

Second, if you don't like it, you're welcome to not come.

Third, if you want to come anyway, simply saying what I'm doing is not helpful - I would like to become less annoying, but I kind of need to know exactly what I'm doing wrong so I can stop.

Fourth, I'm not a dilettante, so bad call there.

It's been mentioned before that I sound patronizing. Since I don't feel patronizing, I have no idea why this is.

James Andrix said...

It might have something to do with that post about me.

Oh not this again. We solved this already. You can figure it out on your own; in future, do.

We have solved nothing. I asked for a source to support your claims, I can look up Riemann and NP, but what I learn there does not support the gobblydegook you are putting out.

Fact: The Riemann Conjecture is, as of right now, unprovable. Yet, we have come up with it. How?

By the fact that proving a conjecture and finding it are two entirely different things. Which I stated before, and you ignored. That fact is what makes you not-even wrong.

The computational requirements to prove something, if it is provable, bear little to no connection to the computational requirements to find it.
IIRC, Godel had a statement which he proved was unprovable, but it was not horrendously difficult to construct.
Indeed we can talk about statements that are true but impossible to prove, but there is no similar notion of a conjecture which cannot be expressed.
What would that even mean?
It's fairly trivial to write a program that will output all possible conjectures in a given language, and in finite time it will output all conjectures under a finite length. (possibly including some true but uinprovable ones.) Granted this will be exponential time relative to the lengths of the outputted conjectures, but at the lengths of conjectures we're talking about that hardly matters.

::Intuition is not supermathematical magic.

One: So much faith from the unbeliever.
Two: See what I said above about not-even-wrong.
Three: See, this is the kind of crap I need to know in advance. This is what I'd call an axiom.

It is not faith, it is not wrong, and above all, it is not an axiom.

It is a conclusion based on the evidence. We simply do not do anything remotely like anything math says we can't do. if you think we do, then you misunderstand the math.

I'm not saying 'math says it's impossible therefor we must not be doing it' I'm saying there is nothing that we actually in fact do that is at all beyond what we should be expected to be able to do. Nothing that a Turing machine can't do in principle.

Pretending that intuition is something a turing machine can't do, and then pretending that the things that we know one can't do are things that we can do by intuition, does not help you.

The mind node is a non-solution in search of a problem.

Alrenous said...

We have solved nothing. I asked for a source to support your claims, I can look up Riemann and NP, but what I learn there does not support the gobblydegook you are putting out.

My problem here is that I'm expecting too much. First, some background.

The Myers-Briggs test does not compare favorably to the experimental correlations as compared to the Big Five, discovered by analysing linguistics. (This makes sense, because it has too much symmetry: there are exactly 16 types arranged in very neat geometrical relationships.) However, it seems to be a good illustration. A painting rather than a model.

I test as INTP. That N is intuitive, which means I'm a big-picture person, and I often don't know exactly what details I'm even noticing.

In this case, the problem has nothing to do with the details of Riemann. The problem is how Andrix responds to my arguments.

As you can see, Andrix completely missed the point. This is not his fault; he's probably S, which stands for sensing, which means he deals in the details that make up the picture. My expectation that he can dilettante to intuitive is an expectation too much.

Unfortunately this is also an example of the kind of event that played out in the comments on my post on academia. When I start slinging insults, they treat me better. Last time I got Andrix to solve the problem - again that N means I have difficulty naming it - it was by slinging insults.

I just don't want to do that again. So, basically I'm waiting to see if Andrix will accidentally figure this out on his own.

The computational requirements to prove something, if it is provable, bear little to no connection to the computational requirements to find it.

This is not what I'm talking about.

What you seem to be saying is;

"To write down a postulate is very different than to be able to prove it."

What I'm trying to say is;

"We know a bunch of postulates are true. (We make mistakes sometimes, which doens't detract from my point.) How?"

For third parties: Again, I don't see how this is so difficult to see. Perhaps it is, of course, I might not know. I Accept my Ignorance.

However, if you want to interpret it that way, you can. If that's your agenda.

The same results could be achieved by assuming I'm a kind of person that I'm not, a kind I'm sure you're familiar with. This assumption is not falsified by the rest of the comment.

This, that you can spin a statement into stupidity, is true of most writing. I don't make a particular effort to block it first because it's so common that I can safely expect that everyone who wanted to can learn to read the author's intent instead of the alternatives. Everyone who doesn't want to probably isn't reachable anyway. Second, because it's bloody difficult to erase possible spins from writing. It's just not worth it.

It is not faith, it is not wrong,

(Laughter)

Okay..okay...yeah...oh wait

(Laughter)

I didn't say it was wrong. I said it was faith. You made that connection all by yourself. All I did was suggest that it wasn't based on evidence.

The reason this is funny is because if I wanted to, I could use tendencies like this to lead you around by the nose. You would believe about me whatever it is I want you to believe about me. I wouldn't have to lie either - I could call this 'misleading around by the nose.'

(Incidentally this is a real problem for me. As you can see here, I do it by accident. I actually have to be very vigilant to stop myself from manipulating people like this.)

We simply do not do anything remotely like anything math says we can't do.

Note for future reference that the statement 'intuition is not supermathematical magic' is a very different statement than the one above.

You need to add at least, 'because nothing is supermathematical' or else simply say outright what you did above.

'Intuition is not supermathematical magic' is the kind of statement that usually leads into 'instead, X is.' Just by convention.

Regardless, see below, as the response is the same.

I'm saying there is nothing that we actually in fact do that is at all beyond what we should be expected to be able to do.

Yes, you effectively communicated that. You can just read it again, especially the part about 'figure out how it isn't'

Consider that humans may in fact not have thought of everything. The appearance of pure math is not the fact, nor the proof, of pure math.

While it may seem to be 'evidence based' it is no longer vulnerable to evidence.

For instance, see below.

The mind node is a non-solution in search of a problem.

No, that's a completely different argument. We're talking about intuition here...or, I guess, were talking about it.

The mind node is primarily a problem, not a solution. Specifically, it is a non-determinism machine.

For third parties:

This, incidentally, is a good example of Andrix doing things that make me say, "Oh not this again."

If you know what it's called, do let me know.


A final note. Why am I putting notes to third parties in this comment? Technically, aren't I signalling Andrix not to read them, yet simultaneously putting them in a comment meant for him?

The first thing is that I would be thinking them anyway. It's very difficult to correct problems in thinking by telepathy, so I write it down.

The next is that if Andrix wants to know what kind of impression he's actually leaving, it's right there. If he wants to have a normal conversation - where I pretend I'm not thinking all this, as per the conventions - he can do that too. This way he at least has the option, rather than me trying to decide for him.

Third is that I do often get random third parties reading my threads, which I know because people like Runtime randomly show up. I want to leave them notes, and I have to put them somewhere, and here follows logically for those third parties.

Finally, this all serves as auditing material for me as a philosopher. The more candid things I write, the more easily you can audit my thinking and figure out what kind of errors I'm prone to make, so that if you do adopt some of my philosophy, there's less danger of adopting mistakes as well.

Even if you don't adopt, you can use the error data to make repairs and form your own theories.

Runtime said...

I want to apologize for my insulting remarks, all I was saying before is that you could use a softer tone in these comments.

I came here through a blog post on the Brood Crumb.

Alrenous said...

Comment edit hack:

But...but... I am elitist. It's not an insult.

Your apology is accepted.

I have to admit it makes me suspicious, because your actual data was valid. I do come off badly, often.

And if you could give me some criticisms with meat, I would appreciate it.

Be warned that I'll probably argue with you. I expect you to be able to defend your criticisms. Something Myers and Briggs noticed about INTP is that we're intellectual chameleons - our arguments don't map straightforwardly to our beliefs, so I may argue even when I agree.


Thanks for the link. It had at least one interesting thing on it, plus I like knowing how stuff works.

James Andrix said...

"We know a bunch of postulates are true. (We make mistakes sometimes, which doens't detract from my point.) How?"

For third parties: Again, I don't see how this is so difficult to see.


Probably because you said:
Fact: The Riemann Conjecture is, as of right now, unprovable. Yet, we have come up with it. How?

Sorry for again shooting down the arguments you actually made, instead of the ones in your head. I guess I'm not big-picture enough.

But that doesn't matter because you're still making the same non-point that I rebutted but you're confusing something else for proving, namely 'knowing'.

You assert as a fact that we 'know Riemann is true, without a proof. What does this 'know' mean? It doesn't mean 'proven'. More people know the Pythagorean theorem than know the proofs. Let some kid check it a thousand times and they'll believe it, but they won't have a proof.

When you heard of the four color problem did you intuit that it was correct? or did you play with sketched out maps trying to find a counterexample? When you gave up and accepted it, did that give you proof?

How hard would it be to write a program that tests a given postulate in a variety of ways and if it passes, declares the postulate to be probably true?

Where is the magic?

I didn't say it was wrong. I said it was faith. You made that connection all by yourself. All I did was suggest that it wasn't based on evidence.

Re-read the backlog. My not-faith, not-wrong, not-axiom was in response to your one-two-three.

Not based on evidence? You seem to be having trouble showing any evidence that intuition is super mathematical magic. I think you have the burden of proof here.

You need to add at least, 'because nothing is supermathematical' or else simply say outright what you did above.

Odd, because I don't take that as an axiom. I could accept an NP-oracle if we had one. It just so happens that there is no evidence for one, and I have no indication that one is possible with our physics.


'Intuition is not supermathematical magic' is the kind of statement that usually leads into 'instead, X is.' Just by convention.

Heh, so I either accept your model of intuition, propose some other super mathematical magic, or you you say I'm taking it's impossibility as an axiom. Nice.

Yes, you effectively communicated that. You can just read it again, especially the part about 'figure out how it isn't'

So you're asking me to just change my state of mind until I agree with you, and then you talk about being evidence based? The baptists tell me I need to read the bible with faith, wanting to believe.

While it may seem to be 'evidence based' it is no longer vulnerable to evidence.

Umm, yes it is. Present evidence that we're doing something unexpected. Such as proving unprovable theorems, or solving NP-complete problems in P time.

The mind node is primarily a problem, not a solution. Specifically, it is a non-determinism machine.

Well ok, then why is it relevant?
I mean, you delve into nifty stuff and spiffy stuff, why? What are you trying to explain?
or
Why do you care about this problem?

Last time I got Andrix to solve the problem - again that N means I have difficulty naming it - it was by slinging insults.

Funny, as I recall I had said you needed to clarify your definition a post or two prior. You insulted me for asking for clarity. Then you actually started to more clearly lay out the argument that was in your head, instead of the one you had written down previously.
Sadly, you're still patching the holes I predicted in my first post. (and the circularity keeps coming back.)

INTJ

Alrenous said...

Yes, of course you see it as an insult. Naturally. I do get so tired of coddling people, though. On my blog, you're just gonna have to deal with it.

Sorry for again shooting down the arguments you actually made, instead of the ones in your head.

Even if I accept that you did, this argument again avoids the argument that I actually made; that your style of argumentation seems to inherently avoid the point.

But that doesn't matter because you're still making the same non-point

Oh what was that I said? "You're going to be saying that a lot until..." Again, your comments about my biases would have more force if my predictions didn't keep coming true.

Present evidence that we're doing something unexpected.

Yes, I did that. See the prediction referenced above.

Why do you care about this problem?

You don't give a crap about why I care about this problem. I have a better question; why do you care about this problem?

Then you actually started to more clearly lay out the argument that was in your head, instead of the one you had written down previously.

Notice that this doesn't actually falsify my observation; that Andrix changed his behavior after I started slinging insults.

Of course, having realized this, we do note that the interpretation is clearly different, but that doesn't matter until we solve the underlying dispute about the data.

Alrenous said...

That 'J' means, again that I'm right.

According to the Myers-Briggs illustration, that means your intuition in introverted, while your sensing is extraverted.

This is the opposite of my situation.

James Andrix said...

::Present evidence that we're doing something unexpected.

Yes, I did that. See the prediction referenced above.


Oh ok, just so it's clear that you're not actually saying anything meaningful about math or physics. At first I thought you were, because you were making such specific statements, for instance "humans can solve NP-complete problems in less than polynomial time," which is of course completely false.

Now I realize that you just use 'mathy' and technical words like "prove", disconnected from their meaning.

When the supporting detail erodes away, you stay latched on to your big picture conclusion and just grab another supporting detail as if they are just for decoration. That is not logic.

I did not take detail orientation as an insult, I understand that different perspectives are valid. I took as arrogant that you leapt on my failure to see something you saw while ignoring my suggestion that your forest contains very few actual existent trees.

Alrenous said...

"humans can solve NP-complete problems in less than polynomial time," which is of course completely false.

Sorry, what's the source for this?

I did not take detail orientation as an insult,

Um.

I guess I'm not big-picture enough.

So yeah, about that.

Now I realize that you just use 'mathy' and technical words like "prove", disconnected from their meaning.

When the supporting detail erodes away,

Oh, you actually thought you were arguing about the mind node?

I thought you just took issue with collection of off-the-cuff predictions. I don't give a crap about them, but I assumed you did so I humored you.

Try attacking the actual meat of the article.

Well, learn to do so, and let me know when you're done.

When the supporting detail erodes away, you stay latched on to your big picture conclusion and just grab another supporting detail as if they are just for decoration. That is not logic.

Apparently it's better than your 'logic.'

Let me demonstrate.

A:
As you can see, Andrix completely missed the point. This is not his fault; he's probably S, which stands for sensing, which means he deals in the details that make up the picture. My expectation that he can dilettante to intuitive is an expectation too much.

J:
INTJ

A:
According to the Myers-Briggs illustration, that J means your intuition in introverted, while your sensing is extraverted.

This is the opposite of my situation.


While my exact detail - the S vs N thing - was wrong, the overall conclusion was right. Andrix lacks an extroverted intuition, and yes his sensing is extraverted. (And probably hasn't developed his introverted intuition, by the looks of it.)

So I guess I'm not 'logical' enough...to be wrong, that is.

So anyway, for people who aren't obsessed with proving me wrong...

This detail;

When the supporting detail erodes away, you stay latched on to your big picture conclusion and just grab another supporting detail

is interesting, because it's sort of true.

I very often have trouble assigning words to the ideas in my head.

For instance, I can almost always describe and predict simple mechanical systems, such as those I found in my first year physics assignments. I cannot (easily) actually write down the mathematics that describe them, except in general terms. (It oscillates in a distorted sine wave pattern roughly X amplitude phase phi. I will have no idea which coefficients, and will probably forget a constant somewhere.)

This flaw of mine extends also to philosophical subjects, where I find that what I've said and what I'm trying to get at are completely different - but until someone on the outside re-interprets what I've written, I'm oblivious to the difference.

What I've also found, which had to be done through extensive testing, is that I'm not wrong. (Actually, many people are like this - they know something, are right, but can't put it into words. Incidentally, by 'extensive' I mean 'at every opportunity for something like a decade.')

When I sense a truth, even when I write it down wrong, I'm always correct given the facts that I know.

So yeah, I latch onto my big picture. I know there's a truth around there somewhere.

For instance, I finally worked out the No Infinities Principle properly, I think.

Basically, there's a problem with infinite physical systems in that you can take infinite physical limits in them. However, the mathematics of the limit clearly make a mockery of relative space and time.

There may be specific pure-math restrictions on what limits are vaild that stop this, but crucially to my theory above, I'm not, nor have ever been, aware of them.

But yeah, I've written that down 'wrong' a bunch of times.

You should go look at my first proof that consciousness isn't physical if you want to see bad, bad logic. (You'll have to ask me for the link.)

Alrenous said...

For the interested, as opposed to the hostile;

Source?

Intuition is not supermathematical magic.

Actually... Check out the first and last paragraphs. (The others aren't too bad either, though I'm not sure they're true.)

Intuition regularly acts like supermathematical magic. You can watch actual mathies talking like this as well, which I can quote from the emails referenced in the article above.

Alrenous said...

Also, from here

Nonalgorithmic processing, for example, is put forward by Penrose (1989; 1994) because
of the role it might play in the process of conscious mathematical insight.


An honest-to-god citation, though I have no idea what, exactly it refers to. But good for Penrose.