I've cracked it. Hopefully I will eventually be able to generalize the technique.
The Monty Hall problem is not a problem in the direct sense. To work out the probabilities mathematically is pretty trivial. You can even draw all the chains of possible events and just count the outcomes.
The problem is that it starkly highlights a serious logical deficiency in most human brains.
The general solution used is thus;
We have three doors. We know one of them is a goat. Therefore, there's a 50% chance that one of the closed doors is a car.
As far as it goes, this is true. However, since it gets the wrong answer, it must be throwing out some relevant information.
Instead, examine the case of choosing to switch. If the above analysis were true, it should net the same probability as choosing to stay.
This is what happens;
Choosing a door eliminates it. Monty Hall then eliminates a goat. The chance the first elimination eliminated a car is 1/3. The chance Monty eliminates a car is 0. Therefore, the remaining door has a 2/3 chance of being a car.
Now I've worked out what I should have done in the first place, I can work backwards to see how I should have thought to do that in the first place, and thus plug this troubling logical hole.
August 10, 2008 update :
Here's a link to something I watched. I successfully re-analyzed the problem successfully, and so I declare this self-patch a success.
Wednesday, May 7, 2008
On the Pathetic Dearth of Philosophers
I've been puzzled lately about how I know so much about historical philosophy.
The few times I've tried to pick up a philosophy text, I've been unable to wring any value from them. All the discernible ideas - tucked carefully between bloated archaicisms and fluff - are obvious - right or wrong. (Usually wrong.)
Today I figured it out. People are very fond of repeating the ideas of other people as if they were their own. Through osmosis, I have apparently absorbed nearly every influential idea. As it turns out, this is basically the entire corpus of the so called major philosophers. It's easy - I read the writing of a bunch of people who like to think they are smart, (notice, I don't care if they are smart or not) and found the distilled ideas, ready to absorb.
I now know why I found philosophy so easy to self-teach. It's everywhere. Realizing this, I was struck by how profoundly weak the philosophical community is. Our society should be inundated with serious thought, much as we are inundated with the media in which these distilled droplets are embedded.
For the interested, I was reading this guy rant on about 'evidence' and 'testability' and realized that he thinks he knows these things because he reasoned them through, or found them useful, instead of because that's what he was taught to believe. It's a faithful reproduction and useful if you haven't seen Empiricism spelled out before. I realized this would work as a transmission of every idea. As a result, there is no need to actually read philosophy to be a good philosopher. You just need to read.
The few times I've tried to pick up a philosophy text, I've been unable to wring any value from them. All the discernible ideas - tucked carefully between bloated archaicisms and fluff - are obvious - right or wrong. (Usually wrong.)
Today I figured it out. People are very fond of repeating the ideas of other people as if they were their own. Through osmosis, I have apparently absorbed nearly every influential idea. As it turns out, this is basically the entire corpus of the so called major philosophers. It's easy - I read the writing of a bunch of people who like to think they are smart, (notice, I don't care if they are smart or not) and found the distilled ideas, ready to absorb.
I now know why I found philosophy so easy to self-teach. It's everywhere. Realizing this, I was struck by how profoundly weak the philosophical community is. Our society should be inundated with serious thought, much as we are inundated with the media in which these distilled droplets are embedded.
For the interested, I was reading this guy rant on about 'evidence' and 'testability' and realized that he thinks he knows these things because he reasoned them through, or found them useful, instead of because that's what he was taught to believe. It's a faithful reproduction and useful if you haven't seen Empiricism spelled out before. I realized this would work as a transmission of every idea. As a result, there is no need to actually read philosophy to be a good philosopher. You just need to read.
Wednesday, April 23, 2008
Consciousness is Not Physical: The Mind Node
My last post contained the unavoidable fact that consciousness isn't physical. If I'm not making sense you can read about the problem again and again. Now I'm going to talk a bit about what it might be in the positive sense. But first, a little bit of the completely different.
I often read articles with novel ideas not mainly for the ideas, but for the techniques used to formulate them. I really like stealing new thinking techniques. As a courtesy for anyone like me...
The idea below has an unusual property. It supports my ideas a little too well - as if I had come up with it first, and then formulated the theory it's supposed to illustrate. It looks like a classic case of confirmation bias.
However, this is temporally impossible. In fact, I came up with the mind node immediately after I proved that consciousness isn't physical.
So quickly, in fact, that I don't remember how I came up with it. (Reviewing some of my notes, I realize I was thinking the first part up up a second time, to refine the concept. During this I must have suddenly realized how it would work.) I recognize certain pre-existing elements, but I was so deeply enmeshed in thought that I don't remember what I was thinking.
By contrast, when I finally proved that consciousness isn't physical, I was meditating on the exact difference between a machine and a mind - what feature, exactly, the machine lacked. You can see the how my approach organically led to the structure of the proof.
I've noticed that I'm not unique in this process. Many very good ideas, such as the mind node, come about in a state a mental 'flow' which seems to inhibit self-awareness to the point that memory formation is...not inhibited...more like irrelevant to the process. Memory becomes unimportant. You don't set out to do this on purpose. It just sort of...happens with you.
In this case, though again I don't know how, I realized that an earlier proposal that I'd read that tried to use quantum randomness to create free will could be modified, using the fact that information processing is represented arbitrarily, (a primer on encoding) to produce a system that is both causal and acausal at once. A system that expresses true randomness and infinity through finite components.
(Sorry, I didn't save the proposal I'm working from. I'd link it otherwise.)
I call it a mind node. I'm going to describe the overview and then going into all the details.
This is a diagram of an abstract mind node.
It has two basic components, the randomness generator, here depicted as a pentagon of five possible quantum states, and an interpreter.
Technically a mind also requires memory, though the interpreter ends up being a kind of memory.
The mind node functions in cycles. First, the pentagon is measured, leading to a random state. This information is fed into the interpreter, which interprets it. The interpretation changes the interpreter itself for the next cycle, and biases the five possible states of the pentagram.
The equation is an example of a particular possible start-point for the interpreter; x-q are the five possible states of the pentagon, C is a constant. The vector (x,y,z,p,q) describes the probability that the pentagon will collapse into each of the five states; f_r() is an abstract recursive function - the part of the equation which describes how the total equation changes each cycle.
Setting f_r() to zero, this example is essentially a rotator. If the pentagon collapses to x, then there's an 80%+C chance that the next state will be y. Because of the inherent randomness, this rotator will jump around approximately once a cycle, 20% of the time.
The math for this, assuming I haven't made a mistake, is exactly the math of a completely unpredictable system, it is the physical expression of true randomness. The state of even this simple rotator becomes progressively less certain with each cycle. The math is exactly the opposite of normal probability - the chance of the node being at any particular state at a particular time is determined by the product of all previous states, instead of being completely independent of the past.
If we then take f_r() to be not zero, the process compounds - the interpretation, and how the interpretation changes itself, depend on all the previous random actions of the pentagon.
Such a system can literally encode anything. It has a domain of five states and a range of infinity.
The infinite range is crucial, as we'll see.
A mind node attached to any computational network, such as by reading off the bias vector before it's sent to the pentagon, will effectively make the entire network completely unpredictable. Consciousness is infectious :-)
True randomness should be physically impossible. Consider a set up where an electron in a one-slit experiment has a target, a one metre square plate, which it can hit anywhere. Assume there's no restrictions on the probability of the electron - it's actually free.
At first, the measured average of the electron will move all over the place. Each new point will take the average in new directions. However, even if the electron decides (it's free, it can) it wants to pull the average in a circle, after a large number of impacts the average will settle down to be the center of the plate, requiring more and more off-centre impacts to move it. Despite the apparent freedom of the electron, we can predict it to some degree.
True randomness requires that the electron have an infinite canvas. In this case, even though the average of all impacts will exist at every point in time, there's nothing stopping the electron from moving it drastically. For example, let's say that the average is, in (x,y) terms, at (0,3). Let's say this is an average of 100 separate impacts. So, even if there were 100 more impacts at (0,9) the average would only move to (0,6). However, the electron can always hit, just once, at (0,1 009 100). The average is now (0,1 010 000/101) = (0, 10 000). This fact scales. No matter how many impacts there are, the electron can overwhelm all of them at any time. It is actually completely unpredictable.
Because this is a delicate point, I'm now going to say the same thing from another perspective.
Some people like to imagine that quantum randomness, called stochasticity, would allow free will to escape the trap of physicalist determinism. This is untrue. Quantum events are unpredictable, but not completely so. A large number of events will form an average. This is what stochastic means. This average is uniquely determined by the system. True randomness, by contrast, is completely unpredictable.
While yes, any particular event is unpredictable, they eventually have to flesh out an average. A very definite average that can be calculated in advance. Said another way, being enslaved to Newtonian determinism isn't worse than being enslaved to slightly unpredictable randomness.
So stochastic behavior has an average, a distribution, and all that jazz. All very concrete. But what if the average moved? What if the average itself was somewhat random?
We wouldn't even notice. The new level 2 randomness would have an average, which would simply combine with the first average to produce a single distribution with a single centre.
(And indeed in the case of a one-slit experiment, it wouldn't make any sense. This second average would somehow have to operate on a timescale different than the electron impacts. For example, electrons hitting every second would have to be affected by a process occurring every 1.5 seconds.)
What if we had an infinite series of averages, all of them moving? No single average would ever settle down. Each successive average makes the system more and more unpredictable - it widens the range. An infinite series of average is the limit of this behavior - it would have zero predictability.
Naturally, like all infinities, this shouldn't be physically possible. With anything that's not a mind node, it is impossible. The requirement of an infinite canvas is impossible to overcome.
I'm going to analyze the mind node again in the light of the series of averages.
Assume the mind node is initialized to be neutral - each state has a 20% chance of being measured. I'm setting f_r() as zero for now. Average level 1.
Run it once. Now, there's a 20% chance for each state to have an 80% chance of being measured.
Run it twice. There's a 20% chance for each state to have an 80% chance of having 80% chance of being measured.
Again, exactly the opposite of normal probability - each event depends completely on all previous events.
It looks exactly like what a completely true random event would look like. After each event, an average can be calculated - but it keeps changing. After an infinite number of runs, it would even reach the limit of having zero probability of being anything. Presumably, there is a quantum of probability. As such, only a finite number of runs would be required for the mind node to have less than a single probability quantum for each of the possible states.
Einstein taught us that two things that appear the same have to be the same. Things are defined by their interactions, which can be exactly described by math. The math for this is exactly the same as that for a spontaneous, true random event. Thus, it is a spontaneous, true random generator.
Combine this with a nonzero f_r() and the mind node can produce arbitrary sequences of bits. It can literally do any mathematically possible calculation, give any output.
Note that, while the math of a mind node exactly describes true randomness, at any moment in time it's completely causal. In short, a mind node breaks and upholds causality at the same time.
This is exactly what is required for interfacing with a separate physics. It must obey all the laws of the first physics, yet require outside influence to determine its behavior.
Further, a mind node would display all the behavior expected of a conscious entity. Moods, random deviations from expected patterns, favored behaviors (as the randomness settles on a particular region for a while) creativity as the interpreter explores new spaces, and so on.
Hopefully at this point, dear reader, you understand how and why a mind node works. Now I'll describe what it means. Also, as promised, I will discuss the consequences of nonphysical consciousness.
Discussion
First, as I mentioned before, since consciousness isn't physical there's no problem of Free Will. The brain is bypassing physical determinism. Nevertheless, it does not disprove Determinism. Rather, it means you can believe whatever makes you happy - there is no definitive evidence either way.
This discussion really annoys me, actually. The concepts aren't even physically valid and yet people insist on pouring on and on about the issue. [rant] It doesn't matter! There's no physical consequences! Not to justice, nor morals, nor feelings! It's a completely pointless discussion and I've proved not once but twice that you can't ever get anywhere in it![/rant]
Second, it means that evolution is even more impressive than we thought. Personifying it, it means that evolution takes advantage of not only every feature of physical law but actually transcends physical law, bringing something more into our universe.
Most impressively, it means I've solved the hard problem of consciousness. As a bonus, I've also solved the easy problem.
Fourth, it means that the difference between objectivity and subjectivity really is a profound qualitative difference. Literally, it means that objectivity is the realm of physics, while subjectivity is the realm of something I glibly call mentics, after the adjective mental.
Fifth, the proof does suddenly allow the idea of God, intention-manifestion, souls, reincarnation, ESP, etc... Nevertheless, it certainly does not provide any evidence for these ideas, and indeed a proper description of the subjective realm may simply re-prove that they're impossible. Indeed, since the subjective realm is almost certainly subject to self-consistency, we can rule out such objectionable things as the biblical God. Miracles are still impossible. Contradictions still don't exist. If they did, contact between the subjective realm and the objective realm could easily destroy the objective realm. Completely annihilate it, actually.
There's also some new, interesting questions. When you sleep, are you unconscious because you sleep or do you sleep because you're unconscious? The various answers have some profound consequences.
The mind node is equally fascinating.
I've already mentioned how even one of them would display moods and preferences.
It also handily explains why AI is so hard to do. A 'true' AI would be conscious, which is impossible without at least one mind node, and probably requires millions.
The state of any circuit computationally attached to a mind node would, as a whole, be a true random system. This has some fascinating possibilities.
For instance, it can explain why you can feel someone looking at you. Your mind nodes (you probably have something like a billion of them) and theirs become computationally linked. By seeing someone, their output is linked to your input, and you become single system, to a degree. Because it's all subjective, you can feel that click as it happens.
Similarly, it falls right in line with the fact that cutting the corpus callosum results in two people inhabiting a single skull. It's two sets of nodes that are no longer linked, which leads to two separate consciousnesses.
But, while I've established that a mind node is a hole in the law of causality, (which is identical to the fact that the universe is mathematically describable) the question remains, how does it restore causal closure?
Obviously, it somehow downloads information from the subjective realm. Similarly, it must somehow upload to the subjective material.
There's only one upload method possible in the mind node. It has to upload using the interpreter's feedback to the pentagon. This inevitably means that the particles themselves are conscious. It means that the electron in the pentagram can feel its probability distribution, and can further choose to collapse to any of them.
This is why consciousness isn't really a problem for physics. In reality, every particle in the universe is self-aware. Quantum randomness is consciousness, and it's both the upload and download method. It is the conduit through which consciousness affects energy and vice versa. Score one for Buddhism, I guess.
In fact, rather than being a problem, particle consciousness elegantly solves both the problem of decoherence and the problem of qualia at the same time.
Penultimately, the mind node illustrates why we need a physical brain to be conscious. The mind node does something very specific; it links the self-aware particle's output to a system of memory. Without that memory, the moment-to-moment existence of the conscious spark would be lost. Apparently, the subjective realm has no useful analogue to information storage and retrieval, and needs to employ physical structures. Similarly, freedom is impossible in the objective realm; it requires the influence of the subjective. In short, evolution has some strong reasons to evolve consciousness, and to ramp it up to the levels seen in human beings. Further, that consciousness depends so heavily on the state of the brain is not evidence for the physicality of consciousness. It's exactly what I would expect.
Ultimately, though, is the question of what an actual mind node looks like. I'm going to put that off and talk about the weather.
Climate is almost a mind node. It has an interpreter, the weather at present, and every single particle is a pentagon. The interpreter changes based on itself and on how the particles react to the forces of the present. However! The particles don't properly respond to the forces of the interpreter. Their state depends mostly on the ambient temperature. Similarly, with such a large number of interactions, the particles rarely reset to a superposition that can randomly decohere. Finally, there's no actual memory. The weather is incapable of recall.
Evolution is also almost a mind node. It has DNA strings, which randomly change, and are affected by previous states, and an interpreter (DNA polymerase plus physics) which nominally depends on the DNA itself. It even has memory in the form of the organisms which arise. However, the interpretation of the codons almost never changes. The thoughts of a consciousness using DNA as the pentagon would never change - the incoming information is constant. Also, the memory is not very robust. Storing memories would consist of the state of a species, and thus would corrupt very rapidly compared to the cycling frequency. (Our perception of a moment is almost certainly a result of our own mind nodes' cycling frequency.)
So near-mind nodes are prevalent in nature. They pop up often enough that it's somewhat strange that there aren't more actual mind nodes. Still, it's easy enough to build one in a lab.
We've been measuring quantum randomness for a while. Set any convenient system up, and then link it to a field programmable gate array (FPGA) which can program itself. Such a system will be a mind node and should display behavior reminiscent of consciousness, such as moods.
However, the initial condition of the FPGA interpreter are very important. There are lots of self-modifying equations that eventually settle out, especially since the number of equations that a normal FPGA can represent are limited by its logic gate count.
There's four classes of possible equations. First, equations that settle down to a constant equation. Second, periodic equations. Third, completely random equations. Fourth and most interesting, equations that display order but not consistent order. You can see these in cellular automata, and exactly the same kind of thing will occur in a mind node. Only class 4 initial interpreters will create useful consciousness.
Similarly, because of the random nature of the pentagon, even the most well-chosen equation will likely end up either chaotic or broken.
In fact, this is probably what happens if you stay up too late. As your sensory mind nodes accumulate garbage, the interpreter (which determines what you actually sense, remember) starts getting out of hand. In a brain, it will start co-opting more and more neurons, growing like a fungus. It's behavior will become more chaotic and self-referential rather than accepting outside input well. It will damage memory formation. In short, you stop being able to think and start being able to hallucinate.
So sleep is necessary probably because the mind nodes in your consciousness modules need to be reset every once in a while. So why do you dream? Test runs. Having reset the interpreter, it needs to be tested and tweaked a bit. With a poorly defined interpreter, the sensation it creates will be somewhat random. Once the diagnostic/reset is complete, you stop dreaming.
But what, exactly, is a mind node in the brain?
The brain is immune privileged, (which means it doesn't have the full range of features) just like the gonads and uterus are. They also share the feature of dealing with nonstandard DNA strings, which are usually attacked aggressively.
As I brought up before, DNA changes randomly when copied. What if the brain used low-fidelity copying to perform the pentagon function? We already suspect DNA fragments are being used as memory in the brain. This could be because they're actually past computations - run them through the proper interpreter and you think the thought again. The interpreters, of course, are neuronal pathways. Because of the massive parallelism in the brain, each neuron can be part of several interpreters at once, and because the brain's connections are completely plastic but depend on previous firing patterns, we have exactly a mind node. Incidentally, yes the mutation rate in different parts of DNA is different, and can presumably be tuned.
In short, having invented a mind node which breaks causality in exactly the way necessary from my proof that consciousness isn't physical, I found all the necessary components for the mind node in the brain.
I often read articles with novel ideas not mainly for the ideas, but for the techniques used to formulate them. I really like stealing new thinking techniques. As a courtesy for anyone like me...
The idea below has an unusual property. It supports my ideas a little too well - as if I had come up with it first, and then formulated the theory it's supposed to illustrate. It looks like a classic case of confirmation bias.
However, this is temporally impossible. In fact, I came up with the mind node immediately after I proved that consciousness isn't physical.
So quickly, in fact, that I don't remember how I came up with it. (Reviewing some of my notes, I realize I was thinking the first part up up a second time, to refine the concept. During this I must have suddenly realized how it would work.) I recognize certain pre-existing elements, but I was so deeply enmeshed in thought that I don't remember what I was thinking.
By contrast, when I finally proved that consciousness isn't physical, I was meditating on the exact difference between a machine and a mind - what feature, exactly, the machine lacked. You can see the how my approach organically led to the structure of the proof.
I've noticed that I'm not unique in this process. Many very good ideas, such as the mind node, come about in a state a mental 'flow' which seems to inhibit self-awareness to the point that memory formation is...not inhibited...more like irrelevant to the process. Memory becomes unimportant. You don't set out to do this on purpose. It just sort of...happens with you.
In this case, though again I don't know how, I realized that an earlier proposal that I'd read that tried to use quantum randomness to create free will could be modified, using the fact that information processing is represented arbitrarily, (a primer on encoding) to produce a system that is both causal and acausal at once. A system that expresses true randomness and infinity through finite components.
(Sorry, I didn't save the proposal I'm working from. I'd link it otherwise.)
I call it a mind node. I'm going to describe the overview and then going into all the details.
It has two basic components, the randomness generator, here depicted as a pentagon of five possible quantum states, and an interpreter.
Technically a mind also requires memory, though the interpreter ends up being a kind of memory.
The mind node functions in cycles. First, the pentagon is measured, leading to a random state. This information is fed into the interpreter, which interprets it. The interpretation changes the interpreter itself for the next cycle, and biases the five possible states of the pentagram.
The equation is an example of a particular possible start-point for the interpreter; x-q are the five possible states of the pentagon, C is a constant. The vector (x,y,z,p,q) describes the probability that the pentagon will collapse into each of the five states; f_r() is an abstract recursive function - the part of the equation which describes how the total equation changes each cycle.
Setting f_r() to zero, this example is essentially a rotator. If the pentagon collapses to x, then there's an 80%+C chance that the next state will be y. Because of the inherent randomness, this rotator will jump around approximately once a cycle, 20% of the time.
The math for this, assuming I haven't made a mistake, is exactly the math of a completely unpredictable system, it is the physical expression of true randomness. The state of even this simple rotator becomes progressively less certain with each cycle. The math is exactly the opposite of normal probability - the chance of the node being at any particular state at a particular time is determined by the product of all previous states, instead of being completely independent of the past.
If we then take f_r() to be not zero, the process compounds - the interpretation, and how the interpretation changes itself, depend on all the previous random actions of the pentagon.
Such a system can literally encode anything. It has a domain of five states and a range of infinity.
The infinite range is crucial, as we'll see.
A mind node attached to any computational network, such as by reading off the bias vector before it's sent to the pentagon, will effectively make the entire network completely unpredictable. Consciousness is infectious :-)
True randomness should be physically impossible. Consider a set up where an electron in a one-slit experiment has a target, a one metre square plate, which it can hit anywhere. Assume there's no restrictions on the probability of the electron - it's actually free.
At first, the measured average of the electron will move all over the place. Each new point will take the average in new directions. However, even if the electron decides (it's free, it can) it wants to pull the average in a circle, after a large number of impacts the average will settle down to be the center of the plate, requiring more and more off-centre impacts to move it. Despite the apparent freedom of the electron, we can predict it to some degree.
True randomness requires that the electron have an infinite canvas. In this case, even though the average of all impacts will exist at every point in time, there's nothing stopping the electron from moving it drastically. For example, let's say that the average is, in (x,y) terms, at (0,3). Let's say this is an average of 100 separate impacts. So, even if there were 100 more impacts at (0,9) the average would only move to (0,6). However, the electron can always hit, just once, at (0,1 009 100). The average is now (0,1 010 000/101) = (0, 10 000). This fact scales. No matter how many impacts there are, the electron can overwhelm all of them at any time. It is actually completely unpredictable.
Because this is a delicate point, I'm now going to say the same thing from another perspective.
Some people like to imagine that quantum randomness, called stochasticity, would allow free will to escape the trap of physicalist determinism. This is untrue. Quantum events are unpredictable, but not completely so. A large number of events will form an average. This is what stochastic means. This average is uniquely determined by the system. True randomness, by contrast, is completely unpredictable.
While yes, any particular event is unpredictable, they eventually have to flesh out an average. A very definite average that can be calculated in advance. Said another way, being enslaved to Newtonian determinism isn't worse than being enslaved to slightly unpredictable randomness.
So stochastic behavior has an average, a distribution, and all that jazz. All very concrete. But what if the average moved? What if the average itself was somewhat random?
We wouldn't even notice. The new level 2 randomness would have an average, which would simply combine with the first average to produce a single distribution with a single centre.
(And indeed in the case of a one-slit experiment, it wouldn't make any sense. This second average would somehow have to operate on a timescale different than the electron impacts. For example, electrons hitting every second would have to be affected by a process occurring every 1.5 seconds.)
What if we had an infinite series of averages, all of them moving? No single average would ever settle down. Each successive average makes the system more and more unpredictable - it widens the range. An infinite series of average is the limit of this behavior - it would have zero predictability.
Naturally, like all infinities, this shouldn't be physically possible. With anything that's not a mind node, it is impossible. The requirement of an infinite canvas is impossible to overcome.
I'm going to analyze the mind node again in the light of the series of averages.
Assume the mind node is initialized to be neutral - each state has a 20% chance of being measured. I'm setting f_r() as zero for now. Average level 1.
Run it once. Now, there's a 20% chance for each state to have an 80% chance of being measured.
Run it twice. There's a 20% chance for each state to have an 80% chance of having 80% chance of being measured.
Again, exactly the opposite of normal probability - each event depends completely on all previous events.
It looks exactly like what a completely true random event would look like. After each event, an average can be calculated - but it keeps changing. After an infinite number of runs, it would even reach the limit of having zero probability of being anything. Presumably, there is a quantum of probability. As such, only a finite number of runs would be required for the mind node to have less than a single probability quantum for each of the possible states.
Einstein taught us that two things that appear the same have to be the same. Things are defined by their interactions, which can be exactly described by math. The math for this is exactly the same as that for a spontaneous, true random event. Thus, it is a spontaneous, true random generator.
Combine this with a nonzero f_r() and the mind node can produce arbitrary sequences of bits. It can literally do any mathematically possible calculation, give any output.
Note that, while the math of a mind node exactly describes true randomness, at any moment in time it's completely causal. In short, a mind node breaks and upholds causality at the same time.
This is exactly what is required for interfacing with a separate physics. It must obey all the laws of the first physics, yet require outside influence to determine its behavior.
Further, a mind node would display all the behavior expected of a conscious entity. Moods, random deviations from expected patterns, favored behaviors (as the randomness settles on a particular region for a while) creativity as the interpreter explores new spaces, and so on.
Hopefully at this point, dear reader, you understand how and why a mind node works. Now I'll describe what it means. Also, as promised, I will discuss the consequences of nonphysical consciousness.
Discussion
First, as I mentioned before, since consciousness isn't physical there's no problem of Free Will. The brain is bypassing physical determinism. Nevertheless, it does not disprove Determinism. Rather, it means you can believe whatever makes you happy - there is no definitive evidence either way.
This discussion really annoys me, actually. The concepts aren't even physically valid and yet people insist on pouring on and on about the issue. [rant] It doesn't matter! There's no physical consequences! Not to justice, nor morals, nor feelings! It's a completely pointless discussion and I've proved not once but twice that you can't ever get anywhere in it![/rant]
Second, it means that evolution is even more impressive than we thought. Personifying it, it means that evolution takes advantage of not only every feature of physical law but actually transcends physical law, bringing something more into our universe.
Most impressively, it means I've solved the hard problem of consciousness. As a bonus, I've also solved the easy problem.
Fourth, it means that the difference between objectivity and subjectivity really is a profound qualitative difference. Literally, it means that objectivity is the realm of physics, while subjectivity is the realm of something I glibly call mentics, after the adjective mental.
Fifth, the proof does suddenly allow the idea of God, intention-manifestion, souls, reincarnation, ESP, etc... Nevertheless, it certainly does not provide any evidence for these ideas, and indeed a proper description of the subjective realm may simply re-prove that they're impossible. Indeed, since the subjective realm is almost certainly subject to self-consistency, we can rule out such objectionable things as the biblical God. Miracles are still impossible. Contradictions still don't exist. If they did, contact between the subjective realm and the objective realm could easily destroy the objective realm. Completely annihilate it, actually.
There's also some new, interesting questions. When you sleep, are you unconscious because you sleep or do you sleep because you're unconscious? The various answers have some profound consequences.
The mind node is equally fascinating.
I've already mentioned how even one of them would display moods and preferences.
It also handily explains why AI is so hard to do. A 'true' AI would be conscious, which is impossible without at least one mind node, and probably requires millions.
The state of any circuit computationally attached to a mind node would, as a whole, be a true random system. This has some fascinating possibilities.
For instance, it can explain why you can feel someone looking at you. Your mind nodes (you probably have something like a billion of them) and theirs become computationally linked. By seeing someone, their output is linked to your input, and you become single system, to a degree. Because it's all subjective, you can feel that click as it happens.
Similarly, it falls right in line with the fact that cutting the corpus callosum results in two people inhabiting a single skull. It's two sets of nodes that are no longer linked, which leads to two separate consciousnesses.
But, while I've established that a mind node is a hole in the law of causality, (which is identical to the fact that the universe is mathematically describable) the question remains, how does it restore causal closure?
Obviously, it somehow downloads information from the subjective realm. Similarly, it must somehow upload to the subjective material.
There's only one upload method possible in the mind node. It has to upload using the interpreter's feedback to the pentagon. This inevitably means that the particles themselves are conscious. It means that the electron in the pentagram can feel its probability distribution, and can further choose to collapse to any of them.
This is why consciousness isn't really a problem for physics. In reality, every particle in the universe is self-aware. Quantum randomness is consciousness, and it's both the upload and download method. It is the conduit through which consciousness affects energy and vice versa. Score one for Buddhism, I guess.
In fact, rather than being a problem, particle consciousness elegantly solves both the problem of decoherence and the problem of qualia at the same time.
Penultimately, the mind node illustrates why we need a physical brain to be conscious. The mind node does something very specific; it links the self-aware particle's output to a system of memory. Without that memory, the moment-to-moment existence of the conscious spark would be lost. Apparently, the subjective realm has no useful analogue to information storage and retrieval, and needs to employ physical structures. Similarly, freedom is impossible in the objective realm; it requires the influence of the subjective. In short, evolution has some strong reasons to evolve consciousness, and to ramp it up to the levels seen in human beings. Further, that consciousness depends so heavily on the state of the brain is not evidence for the physicality of consciousness. It's exactly what I would expect.
Ultimately, though, is the question of what an actual mind node looks like. I'm going to put that off and talk about the weather.
Climate is almost a mind node. It has an interpreter, the weather at present, and every single particle is a pentagon. The interpreter changes based on itself and on how the particles react to the forces of the present. However! The particles don't properly respond to the forces of the interpreter. Their state depends mostly on the ambient temperature. Similarly, with such a large number of interactions, the particles rarely reset to a superposition that can randomly decohere. Finally, there's no actual memory. The weather is incapable of recall.
Evolution is also almost a mind node. It has DNA strings, which randomly change, and are affected by previous states, and an interpreter (DNA polymerase plus physics) which nominally depends on the DNA itself. It even has memory in the form of the organisms which arise. However, the interpretation of the codons almost never changes. The thoughts of a consciousness using DNA as the pentagon would never change - the incoming information is constant. Also, the memory is not very robust. Storing memories would consist of the state of a species, and thus would corrupt very rapidly compared to the cycling frequency. (Our perception of a moment is almost certainly a result of our own mind nodes' cycling frequency.)
So near-mind nodes are prevalent in nature. They pop up often enough that it's somewhat strange that there aren't more actual mind nodes. Still, it's easy enough to build one in a lab.
We've been measuring quantum randomness for a while. Set any convenient system up, and then link it to a field programmable gate array (FPGA) which can program itself. Such a system will be a mind node and should display behavior reminiscent of consciousness, such as moods.
However, the initial condition of the FPGA interpreter are very important. There are lots of self-modifying equations that eventually settle out, especially since the number of equations that a normal FPGA can represent are limited by its logic gate count.
There's four classes of possible equations. First, equations that settle down to a constant equation. Second, periodic equations. Third, completely random equations. Fourth and most interesting, equations that display order but not consistent order. You can see these in cellular automata, and exactly the same kind of thing will occur in a mind node. Only class 4 initial interpreters will create useful consciousness.
Similarly, because of the random nature of the pentagon, even the most well-chosen equation will likely end up either chaotic or broken.
In fact, this is probably what happens if you stay up too late. As your sensory mind nodes accumulate garbage, the interpreter (which determines what you actually sense, remember) starts getting out of hand. In a brain, it will start co-opting more and more neurons, growing like a fungus. It's behavior will become more chaotic and self-referential rather than accepting outside input well. It will damage memory formation. In short, you stop being able to think and start being able to hallucinate.
So sleep is necessary probably because the mind nodes in your consciousness modules need to be reset every once in a while. So why do you dream? Test runs. Having reset the interpreter, it needs to be tested and tweaked a bit. With a poorly defined interpreter, the sensation it creates will be somewhat random. Once the diagnostic/reset is complete, you stop dreaming.
But what, exactly, is a mind node in the brain?
The brain is immune privileged, (which means it doesn't have the full range of features) just like the gonads and uterus are. They also share the feature of dealing with nonstandard DNA strings, which are usually attacked aggressively.
As I brought up before, DNA changes randomly when copied. What if the brain used low-fidelity copying to perform the pentagon function? We already suspect DNA fragments are being used as memory in the brain. This could be because they're actually past computations - run them through the proper interpreter and you think the thought again. The interpreters, of course, are neuronal pathways. Because of the massive parallelism in the brain, each neuron can be part of several interpreters at once, and because the brain's connections are completely plastic but depend on previous firing patterns, we have exactly a mind node. Incidentally, yes the mutation rate in different parts of DNA is different, and can presumably be tuned.
In short, having invented a mind node which breaks causality in exactly the way necessary from my proof that consciousness isn't physical, I found all the necessary components for the mind node in the brain.
Tuesday, April 22, 2008
Consciousness is not Physical: Primitive Version
What is consciousness?
Are you conscious? Did you evolve?
With the available evidence, we can now prove that consciousness isn't physical.
(Abstract: Consciousness isn't necessary to describe the physical world. Consciousness is necessary to fully describe a human being. Thus, consciousness must not be physical. Even if consciousness isn't necessary to fully describe a human being, it exists. Thus, consciousness must not be physical.)
I shall now go through the entire chain of logical possibilities. Any time I reach a possibility that proves physics isn't causally closed, then I will say so. At the end of the essay, I will have shown that every twig of the possibility tree terminates in causally open physics.
That is, while we can't yet say exactly why consciousness isn't physical, we can rule out the fact that it isn't. This is why I state this idea as a negation; I cannot describe consciousness. I can only determine a few things it is not.
I need a catchphrase so I can put it here. Something less lame than 'phear the logicz!' Let's begin.
First, let's assume you answered 'No, I'm not conscious. I do not experience qualia. Consciousness does not exist and the question is meaningless.' This is logically incoherent. I'm conscious. I can't be confused about my experience; it can't be some illusion; my experience of experience is consciousness itself. I think, therefore, I am.
So, are you conscious? You're welcome to answer no, but I'm taking all your stuff. If you're not conscious then you cannot suffer.
Next, did you evolve? If you didn't evolve, then this essay is moot anyway - we know that there's something beyond physics. If humans did not evolve, then biology is not causally closed under physics.
If you evolved and you are conscious, then consciousness is either free or confers some specific fitness advantage.
If consciousness is free, then that means it has no physical overhead. It appears spontaneously. It either has no physical effects in which case it is purely nonphysical, or it has physical effects and your brain is not causally closed under physics. (There would also be no constraints on the occurrence of consciousness.)
However, consciousness is not free. First, it requires specialized brain structures, and second consciousness has the property of 'choice' or 'decision' which allows you to, among other things, kill yourself.
Thus consciousness must confer a selective advantage that outweighs the costs. However, it is physically impossible.
First let me note that I'm distinguishing thoughts from actions; information processing from rearrangements of energy.
The relevant action, reproduction, is entirely physical, as are all the relevant prerequisites. However, all of these actions could be carried out without experiencing them. We could program, hard-script, a robot to do so without much trouble. (If computers are conscious then consciousness is free.)
Let me digress, considering some physical action that cannot be performed by a robot. What is preventing it? Are their hands not simply patterns of atoms, just as ours are? If we were to find a test of consciousness it would mean we have literally discovered magic. If there is an action robots cannot perform, then physics is not causally closed under physics.
Similarly, things like 'creativity' which are strings of fully physical actions, cannot be unique to consciousness. It would mean that there's literally an incantation that you can do to prove you're conscious. Which step exactly would a robot be unable to mimic and why? How would it know to fail if you hard-code it to mimic the action?
Further, the relevant thoughts are similarly constrained. There is no calculation that can be performed by a brain that cannot be performed by a computer. To posit such a calculation would require it to be not a calculation - it would require it to be non-mathematical and thus consciousness would perform nonphysical calculations.
As such, a robot can perform all the relevant physical actions of reproduction. Because computers have a much easier time staying consistent, it would likely perform the actions and calculations at a much higher efficiency than a human would.
Thus, a computer is fully capable of emulating human action, in the physical world, without consciousness. There is no physical action or thought that consciousness is a prerequisite for.
What if all this is true, but consciousness is physical but just somehow does it better than a computer? That, sure, you don't have to experience it, but experience makes it more effective? That would literally mean consciousness is a magic ingredient. Two otherwise identical computers compete, one experiencing its calculations, one not, and the conscious one wins. Consciousness would affect the physical world without actually being a part of it, contradicting the premise.
Consciousness physically does nothing. Consciousness confers a selection advantage. Your brain is causally open under physics.
This isn't easy, let's recap.
Physics is best described as a consistent set of rules for the interaction of energy. Without such a set, interaction is in fact impossible, because contradictions do not exist.
Therefore, I propose that there is an orthogonal physics that uniquely defines the physical output of consciousness. I could call it the physics2 of vacuum2. (I won't.) This system must have a similar set of rules, though not necessarily mathematical ones. Also, if it is to not violate causality, (which you'll note I used to discover it) the system must be incapable of violating any physical law.
The system presumably has a similar causal hole. The system mutually closes causality with the physical vacuum.
This is the set of rules that allows us to be conscious - to experience the world. It is the plane of the mind. Unfortunately, that's nearly everything I know about it.
Most likely it allows free will, but it is possible that it simply confirms determinism. [rant]So please, quit debating it. You have no idea. The concepts of free will and determinism aren't even consistent concepts. Believe whatever the hell you want and tell anyone who argues with you to stuff it.[/rant]
So, in physics, what's the hole? There's only one hole in physics that I know of. It's been rigorously proven, too. Quantum randomness is true stochastic behavior. There's no physical way to predict what any particular particle will do, ever.
Technically speaking, a second set of rules could easily interface at this level, without violating any law or indeed being detectable at all, except through logic.
But for now I'm done with the firm certainty of deductive logic. This tree has grown up and borne delicious philosophical fruit. In my next essay I'll discuss some of my minor hobbies, the consequences of this fruit, and develop some of the ways consciousness may be implemented in the brain.
Are you conscious? Did you evolve?
With the available evidence, we can now prove that consciousness isn't physical.
(Abstract: Consciousness isn't necessary to describe the physical world. Consciousness is necessary to fully describe a human being. Thus, consciousness must not be physical. Even if consciousness isn't necessary to fully describe a human being, it exists. Thus, consciousness must not be physical.)
I shall now go through the entire chain of logical possibilities. Any time I reach a possibility that proves physics isn't causally closed, then I will say so. At the end of the essay, I will have shown that every twig of the possibility tree terminates in causally open physics.
That is, while we can't yet say exactly why consciousness isn't physical, we can rule out the fact that it isn't. This is why I state this idea as a negation; I cannot describe consciousness. I can only determine a few things it is not.
I need a catchphrase so I can put it here. Something less lame than 'phear the logicz!' Let's begin.
First, let's assume you answered 'No, I'm not conscious. I do not experience qualia. Consciousness does not exist and the question is meaningless.' This is logically incoherent. I'm conscious. I can't be confused about my experience; it can't be some illusion; my experience of experience is consciousness itself. I think, therefore, I am.
So, are you conscious? You're welcome to answer no, but I'm taking all your stuff. If you're not conscious then you cannot suffer.
Next, did you evolve? If you didn't evolve, then this essay is moot anyway - we know that there's something beyond physics. If humans did not evolve, then biology is not causally closed under physics.
If you evolved and you are conscious, then consciousness is either free or confers some specific fitness advantage.
If consciousness is free, then that means it has no physical overhead. It appears spontaneously. It either has no physical effects in which case it is purely nonphysical, or it has physical effects and your brain is not causally closed under physics. (There would also be no constraints on the occurrence of consciousness.)
However, consciousness is not free. First, it requires specialized brain structures, and second consciousness has the property of 'choice' or 'decision' which allows you to, among other things, kill yourself.
Thus consciousness must confer a selective advantage that outweighs the costs. However, it is physically impossible.
First let me note that I'm distinguishing thoughts from actions; information processing from rearrangements of energy.
The relevant action, reproduction, is entirely physical, as are all the relevant prerequisites. However, all of these actions could be carried out without experiencing them. We could program, hard-script, a robot to do so without much trouble. (If computers are conscious then consciousness is free.)
Let me digress, considering some physical action that cannot be performed by a robot. What is preventing it? Are their hands not simply patterns of atoms, just as ours are? If we were to find a test of consciousness it would mean we have literally discovered magic. If there is an action robots cannot perform, then physics is not causally closed under physics.
Similarly, things like 'creativity' which are strings of fully physical actions, cannot be unique to consciousness. It would mean that there's literally an incantation that you can do to prove you're conscious. Which step exactly would a robot be unable to mimic and why? How would it know to fail if you hard-code it to mimic the action?
Further, the relevant thoughts are similarly constrained. There is no calculation that can be performed by a brain that cannot be performed by a computer. To posit such a calculation would require it to be not a calculation - it would require it to be non-mathematical and thus consciousness would perform nonphysical calculations.
As such, a robot can perform all the relevant physical actions of reproduction. Because computers have a much easier time staying consistent, it would likely perform the actions and calculations at a much higher efficiency than a human would.
Thus, a computer is fully capable of emulating human action, in the physical world, without consciousness. There is no physical action or thought that consciousness is a prerequisite for.
What if all this is true, but consciousness is physical but just somehow does it better than a computer? That, sure, you don't have to experience it, but experience makes it more effective? That would literally mean consciousness is a magic ingredient. Two otherwise identical computers compete, one experiencing its calculations, one not, and the conscious one wins. Consciousness would affect the physical world without actually being a part of it, contradicting the premise.
Consciousness physically does nothing. Consciousness confers a selection advantage. Your brain is causally open under physics.
This isn't easy, let's recap.
- You evolved.
- You are conscious.
- Consciousness costs resources.
- There is no action you must experience to perform.
- There is no action you could perform better by experiencing it.
- There is no computation you must experience to perform.
- Ergo, consciousness cannot physically do anything.
- Consciousness confers a selective advantage.
- Ergo, consciousness isn't physical.
- Your brain is causally open under physics.
- Ergo, the universe is causally open under physics.
Physics is best described as a consistent set of rules for the interaction of energy. Without such a set, interaction is in fact impossible, because contradictions do not exist.
Therefore, I propose that there is an orthogonal physics that uniquely defines the physical output of consciousness. I could call it the physics2 of vacuum2. (I won't.) This system must have a similar set of rules, though not necessarily mathematical ones. Also, if it is to not violate causality, (which you'll note I used to discover it) the system must be incapable of violating any physical law.
The system presumably has a similar causal hole. The system mutually closes causality with the physical vacuum.
This is the set of rules that allows us to be conscious - to experience the world. It is the plane of the mind. Unfortunately, that's nearly everything I know about it.
Most likely it allows free will, but it is possible that it simply confirms determinism. [rant]So please, quit debating it. You have no idea. The concepts of free will and determinism aren't even consistent concepts. Believe whatever the hell you want and tell anyone who argues with you to stuff it.[/rant]
So, in physics, what's the hole? There's only one hole in physics that I know of. It's been rigorously proven, too. Quantum randomness is true stochastic behavior. There's no physical way to predict what any particular particle will do, ever.
Technically speaking, a second set of rules could easily interface at this level, without violating any law or indeed being detectable at all, except through logic.
But for now I'm done with the firm certainty of deductive logic. This tree has grown up and borne delicious philosophical fruit. In my next essay I'll discuss some of my minor hobbies, the consequences of this fruit, and develop some of the ways consciousness may be implemented in the brain.
Thursday, March 13, 2008
Karl Popper; Analysis; He's Anarchist!
Got a bit about Karl Popper. Found out it supports Philosophical Descent and The First Step.
Small problem though; Popper was very impressed with deduction.
There's a thing called 'the problem of induction' if you weren't aware.
Popper's ideas about deduction are unimpressive to me because I seem to have solved the problem. Deduction, you see, is a special case of induction. To say "Popper stresses that we ascertain whether one theory is better than another by deductively testing both theories, rather than by induction." is complete nonsense. It's like saying you're hammering with a hammer, not a tool. Programming with Lisp, rather than a language.
Notably, Popper is one the few philosophers that I don't hate...so far. It goes recursive because not hating a philosopher is so refreshing, leading to greater enjoyment of his work, leading to more relief, and so on.
Also, Popper rejects the empiricist doctrine that empirical observations are, or can be, infallible, in view of the fact that they are themselves theory-laden.
This needs to be corrected to "observations are infallible, but our application of them to theory is most certainly fallible. " The reality is that, as I've mentioned before, to distrust your senses is to be insane. As such every single observation ever is infallible, even schizophrenic hallucinations. However, the simplistic way everyone applies these data to theory is flawed, to say the least. The hallucination is indeed data - but of what? Well, first it means they're hallucinating, which can be verified with whatever senses aren't involved in the hallucination, or at the very least by a separation in time. Therefore, the most meaningful way to apply this data is to a theory of how the schizophrenic's brain is working. They hallucinate a girl on a busy street, but she isn't hit, passersby are unhorrified, etc... Thus, they can safely conclude that their visual system has an interesting bug, and [safely conclude that they (cannot safely conclude that objects in their visual field exist, without some independent corroboration.)]
Regardless of how 'faulty' our senses may be for some particular purpose they cannot help but provide a wealth of valuable information.
One of the reasons I like Popper is that he's capable of saying things I haven't thought of.
"But if this is true, Popper argues, then, paradoxical as it may sound, the more improbable a theory is the better it is scientifically, because the probability and informative content of a theory vary inversely - the higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false."
Learning is so awesome!
On the other hand,
"Popper, then, is an historical indeterminist, insofar as he holds that history does not evolve in accordance with intrinsic laws or principles, that in the absence of such laws and principles unconditional prediction in the social sciences is an impossibility, and that there is no such thing as historical necessity."
I mention this to illustrate a common truth; there are so many different ways history could logically arrange itself that there must be some logically nontrivial historical necessities. On the other hand, due to the chaotic nature, these will almost certainly be inaccessible to science and philosophy. In any case, the evidence suggests that there aren't enough to be useful in particular, even if you could use ESP to find them.
Later,
"At a very general level, Popper argues that historicism and holism have their origins in what he terms 'one of the oldest dreams of mankind - the dream of prophecy, the idea that we can know what the future has in store for us, and that we can profit from such knowledge by adjusting our policy to it."
So, we predict the future with certainty so that we can change the future? Uhhh...about that....
I don't actually know whether prophecy is a longtime human longing or not, but it doesn't actually matter. I'm treating this idea a bit like the schizophrenic does their visuals; the explicit or base knowledge is of no consequence. Instead, the higher meanings dominate.
I like fantasy books, especially the ones with prophecy. This prediction accords with my experience. But why? The way prophecy in fantasy works is that the world is somehow predetermined to follow an ironclad pattern, usually through sheer force on the part of the source of prophecy. But, if indeed the entire world (is prophesied or can be prophesied are logically identical for this analysis) then prophecy is useless. The information of the prophecy either cannot be acted upon, or else the prophecy takes into account its own effects, leading to an infinite regression that most likely does not converge.
On the other hand, if some of the world is free to decide, then prophecy basically can't work, because it would have to shield the prophetic events from any and all feedback, which in practice is an impossible task. I'm going to neglect completely trivial prophecies like the ones we can make ourselves. "I'm going to finish writing this post. I'm even going to edit it and add links and stuff like that." These prophecies are dependent on free will, basically. I'm not sure how to clearly demonstrate this, but it's true anyway.
On the other hand, what is science but the first successful attempt at prophecy? I prophecize that if I drop an object in the vicinity of the Earth, it will accelerate at 9.8m/s/s in the approximate direction of Earth's center of gravity. Woot! I'm a prophet!
Notably, I'm equivocating quite a bit here, but I think that's okay because hominid brains are good at parsing crap like that.
Popper clearly wanted to be anarchist; he wanted piecemeal evolutionary solutions to social problems, he just thought for some reason that the state can accomplish instead of impede this. It's not his fault - while it's logically necessary that states be hypocritical, the arguments are extensive and emotionally charged - not the easiest thing to get your head around, unless you're already predisposed to the emotional charge.
It's not the first time I've run across a thinker who wants to be an anarchist but rejects anarchist solutions. In fact, it seems to me that if you gathered everyone together in the town square and made them vote for what they actually want, we'd all end up anarchist. Even people who explicitly state that they don't believe in anarchy.
Small problem though; Popper was very impressed with deduction.
There's a thing called 'the problem of induction' if you weren't aware.
Popper's ideas about deduction are unimpressive to me because I seem to have solved the problem. Deduction, you see, is a special case of induction. To say "Popper stresses that we ascertain whether one theory is better than another by deductively testing both theories, rather than by induction." is complete nonsense. It's like saying you're hammering with a hammer, not a tool. Programming with Lisp, rather than a language.
Notably, Popper is one the few philosophers that I don't hate...so far. It goes recursive because not hating a philosopher is so refreshing, leading to greater enjoyment of his work, leading to more relief, and so on.
Also, Popper rejects the empiricist doctrine that empirical observations are, or can be, infallible, in view of the fact that they are themselves theory-laden.
This needs to be corrected to "observations are infallible, but our application of them to theory is most certainly fallible. " The reality is that, as I've mentioned before, to distrust your senses is to be insane. As such every single observation ever is infallible, even schizophrenic hallucinations. However, the simplistic way everyone applies these data to theory is flawed, to say the least. The hallucination is indeed data - but of what? Well, first it means they're hallucinating, which can be verified with whatever senses aren't involved in the hallucination, or at the very least by a separation in time. Therefore, the most meaningful way to apply this data is to a theory of how the schizophrenic's brain is working. They hallucinate a girl on a busy street, but she isn't hit, passersby are unhorrified, etc... Thus, they can safely conclude that their visual system has an interesting bug, and [safely conclude that they (cannot safely conclude that objects in their visual field exist, without some independent corroboration.)]
Regardless of how 'faulty' our senses may be for some particular purpose they cannot help but provide a wealth of valuable information.
One of the reasons I like Popper is that he's capable of saying things I haven't thought of.
"But if this is true, Popper argues, then, paradoxical as it may sound, the more improbable a theory is the better it is scientifically, because the probability and informative content of a theory vary inversely - the higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false."
Learning is so awesome!
On the other hand,
"Popper, then, is an historical indeterminist, insofar as he holds that history does not evolve in accordance with intrinsic laws or principles, that in the absence of such laws and principles unconditional prediction in the social sciences is an impossibility, and that there is no such thing as historical necessity."
I mention this to illustrate a common truth; there are so many different ways history could logically arrange itself that there must be some logically nontrivial historical necessities. On the other hand, due to the chaotic nature, these will almost certainly be inaccessible to science and philosophy. In any case, the evidence suggests that there aren't enough to be useful in particular, even if you could use ESP to find them.
Later,
"At a very general level, Popper argues that historicism and holism have their origins in what he terms 'one of the oldest dreams of mankind - the dream of prophecy, the idea that we can know what the future has in store for us, and that we can profit from such knowledge by adjusting our policy to it."
So, we predict the future with certainty so that we can change the future? Uhhh...about that....
I don't actually know whether prophecy is a longtime human longing or not, but it doesn't actually matter. I'm treating this idea a bit like the schizophrenic does their visuals; the explicit or base knowledge is of no consequence. Instead, the higher meanings dominate.
I like fantasy books, especially the ones with prophecy. This prediction accords with my experience. But why? The way prophecy in fantasy works is that the world is somehow predetermined to follow an ironclad pattern, usually through sheer force on the part of the source of prophecy. But, if indeed the entire world (is prophesied or can be prophesied are logically identical for this analysis) then prophecy is useless. The information of the prophecy either cannot be acted upon, or else the prophecy takes into account its own effects, leading to an infinite regression that most likely does not converge.
On the other hand, if some of the world is free to decide, then prophecy basically can't work, because it would have to shield the prophetic events from any and all feedback, which in practice is an impossible task. I'm going to neglect completely trivial prophecies like the ones we can make ourselves. "I'm going to finish writing this post. I'm even going to edit it and add links and stuff like that." These prophecies are dependent on free will, basically. I'm not sure how to clearly demonstrate this, but it's true anyway.
On the other hand, what is science but the first successful attempt at prophecy? I prophecize that if I drop an object in the vicinity of the Earth, it will accelerate at 9.8m/s/s in the approximate direction of Earth's center of gravity. Woot! I'm a prophet!
Notably, I'm equivocating quite a bit here, but I think that's okay because hominid brains are good at parsing crap like that.
Popper clearly wanted to be anarchist; he wanted piecemeal evolutionary solutions to social problems, he just thought for some reason that the state can accomplish instead of impede this. It's not his fault - while it's logically necessary that states be hypocritical, the arguments are extensive and emotionally charged - not the easiest thing to get your head around, unless you're already predisposed to the emotional charge.
It's not the first time I've run across a thinker who wants to be an anarchist but rejects anarchist solutions. In fact, it seems to me that if you gathered everyone together in the town square and made them vote for what they actually want, we'd all end up anarchist. Even people who explicitly state that they don't believe in anarchy.
Tuesday, March 11, 2008
Skimming the Blog
If you're skimming my archives and have the urge to read something you're not obviously interested by, in case one of my tangents is interesting, it's better just to ask me about it. I'll have a quick look and summarize all the tangents, and you can pick the ones you like.
Wednesday, February 6, 2008
No Infinities Principle: Proof
- Physics can be described mathematically,
- Therefore every phenomenon corresponds to an equation.
- Equations with infinities in them are not meaningful
- No variable can ever be infinite.
QED
So yeah. That's how bad modern physicists are at thinking. The proof really is that short.
Remember, they already use this principle. They simply don't recognize its full implications.
For example, as I said before, space and time are considered to be infinite by some, and this is socially accepted.
Nevertheless it is not mathematically acceptable. If space is infinite, then consider the very simple equation of constant motion in a straight line.
x=Ct That is, every second, the particle goes C meters further away from the origin.
So at t=9, the particle is at 9C. Simple.
Because space is relative, we can redefine the origin.
x - 12=Ct.
So at t=0, the particle is already at x=12.
Because space is infinite, we can redefine the origin to be infinity.
So at t=0, the equation reads
∞-∞=0
The problem is that ∞ - ∞ is undefined.
To show this mathematically, consider t!=0.
x-∞=3
x=∞ +3
Infinity + 3 is infinity
x=∞
Ergo, the particle hasn't moved. This is inconsistent. If we take any infinity to be physically meaningful, any equation with the infinite constant becomes meaningless.
The physical interpretation of this is that if space is infinite, then a particle can't ever reach a local area through finite movements. Ergo, it doesn't actually exist.
Therefore, either space is not infinite, which means the universe must have some sort of edge, or it is infinite but all the infinite space doesn't exist.
These statements are exactly equivalent under physics.
Ergo, the universe isn't infinite. It has an edge. Well...it can also wrap around in the manner of a video game world, or indeed the Earth's surface.
The proof for every other relative physical variable follows similarly.
And, out of curiosity, do you think absolute variables can be infinite? Infinite charge? Infinite mass? Infinite density? Infinite force?
Incidentally, this inevitably means that infinitesimals also cannot exist.
Because of this, I can NIP string theory right here.
- No infinities or 1/∞ exist.
- Strings are one dimentional.
- One of their physical properties, such as width, is infinitesimal.
- Strings do not exist.
Now that's sad. Pathetic and tragic. Twenty years of string theory and the proof that it was mostly a waste is four lines long.
Four lines.
Similarly, we know for a fact that particles are not point particles.
A point particle has infinitesimal length, width, and depth, and therefore doesn't exist. But, particles do exist. Ergo they are not point-like.
Now, I can hear one objection. What equation uses the width or whatever of a particle?
Luckily, there is a separate proof. Given these two proofs are consistent, I use Axiom Two, say self-consistency is sufficient evidence for truth.
Here it is.
Assume our world has three dimensions of space, just as it appears to.
Assume a two-dimensional object exists. A plane, much like the thinnest piece of paper ever.
Now, according to cartoons, if you view it from the front, you'll be able to see it. However, if you view it from the side it will disappear.
We can verify that from the side, it disappears. Without width, it will not impede the flow of information from one side to the other.
But this leads to a contradiction! If the object does not exist from one angle, then it cannot exist from ANY angle! This is the principle of relativity.
To check this, ask; 'as a three-dimensional object passes through the plane, what part of the object will the plane intersect?' None. The intersection will have a volume of zero.
Look at this another way. If you stick your finger into the edge of the plane, it won't exist. It forms no barrier to entry. What happens if you now move your finger sideways? Well, it still can't form a barrier! That's relativity.
As such, true zero-dimension particles cannot exist. Therefore, they must have at least infinitesimal volume. But they cannot have infinitesimal volume, by the NIP.
As such they must have a regular amount of volume. And indeed the uncertainty principle ensures that the exact position of the 'point' particle can never be known. It always has some spatial extent.
Similarly, two colliding electrons cannot ever actually touch and produce infinite force. Either there must be a limit on their velocity to prevent them from exceeding their limited ability to produce force, OR when their maximum repulsion force is exceeded, their interaction will change them into some non-electron.
Or, you know, something completely surprising.
NIP has at least one surprising consequence. Nothing is continuous, at least physically. Everything must be quantized. Space, time, energy, everything. This is because the definition of continuity is that infinitesimal changes are allowed. However, infinitesimal changes are physically meaningless, and therefore continuity is physically meaningless. Physically meaningless things do not exist.
Also of interest is that NIP is equivalent to causality because it's equivalent to the fact that we can describe physics mathematically.
Consider any physical variable. It can vary, and it can only vary in quantum jumps. If the universe can be described mathematically, then these jumps will follow a formula. Each jump will be directly dependent on the position reached by the previous jump.
This is causality. Each cause has a unique set of effects. I say set because there is some leeway in the quantum jumps, but these are described by fixed averages, so you can't really say that causality is weakened by randomness.
(There is just one tiny problem. Particles are actually conscious. We can tell because we have brains. More on this later.)
On a human note, would you like to know how I discovered the NIP? I was considering fundamental particles one day, and how quarks are more fundamental than protons. I was wondering if it were logically possible for quarks to be made up of yet more fundamental particles.
After all, we've already gone from atoms to protons to quarks. Could we keep going? Yes, we could keep going, in principle. However, we cannot keep going indefinitely. Eventually, there must be a most fundamental particle. Otherwise it's turtles all the way down. Infinite regression.
(Note that this isn't just logically repugnant, it also violates Godel's Incompleteness Theorem. An infinite regression, if true, would technically be able to prove its own consistency. For any particle you wanted to prove was consistent, you could go one level deeper and use those particles as proof.
Because you can make the level arbitrary, this proves it for all levels. (Infinity is weird.) Godel proved that any such theorem can only prove itself by being inconsistent, and thus false.)
Because you can make the level arbitrary, this proves it for all levels. (Infinity is weird.) Godel proved that any such theorem can only prove itself by being inconsistent, and thus false.)
In short, Zeno was right, in a sense. However, he wasn't applying his theory in the right domain.
Also, he didn't know space and time are quantized, and so at some point the arrow will be touching the soldier, and one Planck-time (approx 1/10^43 s) after that, it must be at least one Planck-length (approx 1/10^35 m) inside the soldier.
Mathematically you can do continuous calculations. However, physically, you cannot.
I just found out about Compton wavelengths. These are minimum uncertainties in particle locations. These cutoffs satisfy the NIP.
Also, reading about de Broglie wavelengths, I just realized that the wavelength of a person is smaller than the Planck-length. This is why people never display, say, quantum tunneling behavior, not even really really rarely. The wavelength of a person isn't really really close to zero, it's actually indistinguishable from zero.
Notice again that physics has already discovered many of the predictions of the NIP, and yet has somehow failed to discover the NIP itself. I really do find this boggling.
So yeah. Take that, government-funded physics. Accept your ignorance lest I have to do it for you.
Friday, February 1, 2008
The Stock Market and Government Intervention
Inspired by an article on the new recession.
The stock market is not, as this and every other article treats it, the economy. It's not even like the economy. The economy is a heart - it drives the entire body. The stock market, by contrast, is the spot on my wrist that I can use to take my pulse. In fact, exactly like that.
Because of this fact, when the government tries to 'inject liquidity' into the stock market, it's exactly like injecting blood into my wrist, from another part of my body...as a strategy for increasing my blood pressure.
Naturally, this is, compared to its objectives, unfathomably harmful.
The economy is about the exchange of objects to accumulate value.
Notably, there is no objective way to define value. It's totally subjective, but it does exist. Because it's subjective, it doesn't have to be conserved, which leads to the real difference between the wealthy and the poor. While it's true that wealthy people generally have more objects than the poor, the real difference is because the wealthy have more things they value, and these things happen to be objects. They have taken advantage of the nonconservative nature of value by trading things they value less for things they value more, reciprocally. Wealthy people simply do this more effectively.
Notice that these trades do not, in themselves, significantly change the physical world. A camper is traded for some dollars which are traded for some building materials, say. Now, the dollars, camper, and two-by-fours are in a different place, and could easily be moved back, but suddenly the total wealth and value of the arrangement has greatly increased.
(This is, naturally, one reason government redistribution never works. There's no way for the government to determine who really values what, which means it will inevitably destroy wealth on a disastrous scale, compared to anything it tries to do.)
(The only way (we know of) to determine what people really value is to put it up for auction on the free market. Government is simply the manifestation of the idea that people want the wrong things. )
(Also, don't forget that ownership isn't physical in any sense either.)
It's these trades that actually increase wealth. Production is quite separate. Production is merely motivated by the future possibility of these trades; without that production would halt.
This is the basic truth of a recession. The expectation of future trades diminishes, and so production declines, ensuring that through normal wear and tear, wealth declines, and everyone feels the pinch.
What does this have to do with the stock market? In a healthy society, nothing you'd ever need to worry about. Why not?
Because the stock market does not trade in anything of real value. No one values stock in and of themselves, but only as a means to obtain new things they do value.
Similarly, dollars are not true wealth. The only real value to dollars is that they facilitate trade, they are never an end, a value, unto themselves, unlike campers and two-by-fours. Also unlike similarly intangible but truly valued things like communication or the various types of security, or a feeling of well-being from a massage or similar service.
Stock is, actually, very like the banknotes that, way back, actually preceded fiat currency, back when banknotes were in fact notes from the bank. Both are, in a very real sense, merely currency.
Currencies all take their entire value from the fact someone will agree to trade that currency for something of real value.
So, the stock market is a big currency exchange. This gets a bit complicated and subtle, so I'm glossing over some things. Regardless, like all currency exchanges, a stock market cannot truly create or destroy wealth. Every dollar 'lost' to a portfolio is merely gained by another portfolio.
And, like all currency exchanges, it can tell you something about the conditions affecting the underlying real values backing the currencies. It cannot, or rather should not, affect those underlying values.
It doesn't matter what happens to your money. If you value huge, delicious steaks, the only reason you value your dollar is because it represents, to you, huge, delicious steaks. The association cannot run in reverse.
As such, the stock market can tell you stuff about the issuing entities - the corporations. (A word that just means 'reification of legal arrangement,' in this case reifying through a corpus - pretending that the legal arrangement is a body, a person.) It cannot, however, work in reverse. Indeed, if I own a factory that makes huge, delicious steaks, does that factory care what its stock price is? Do the buyers of my steaks? My workers?
That would be hilarious actually.
"Crap! I bought this steaks, but the corporation's stock price crashed yesterday and now it tastes terrible. Ugh."
"Urgh! Cheap stock steak! Gross! I hate it when that happens."
The stock market is the pulse of the market - not its heart.
In short, the Great Depression wasn't caused by a stock price collapse. That's preposterous. The stock price collapse was caused by the Great Depression.
There is, of course, one problem with this analysis. It's pretty clear that our economy is affected by what happens in the stock market. Why is this?
Basically, because of the government.
Through various, generally unrelated intentional corruptions, government regulation is now supporting a situation where the actions of America's Wall Street account for, I'm not making this up, half of all American economic activity. The situation is similar in all wealthy countries.
And even this wouldn't be a problem. It doesn't matter if Wall Street accounted for 90% of the economy, it still can't break logical truths. The currencies are valuable because they can be traded. For steaks.
However, the basic support government is providing, without which Wall Street would have to contract drastically, is risk protection. Some institutions have been perceived as too big to fail. There's an actual policy named after it.
Since the people in these institutions aren't dumb, and higher risks generate higher payoffs, this has naturally lead to a drastically blase attitude to high risk. After all, if an investment fails, the government is going to bail them out. They can't lose.
I suspect this is due to a basically voodoo association between the stock market and the economy. The stock market suffers when the economy tanks. It's hard to see the economy, but easy to see the stock market. Therefore, the association gets made between recessions and stock market failures.
As a result, lobbyists can successfully convince lawmakers to prop up the stock market as a method of controlling the economy.
Is my little sub-theory true? Is this voodoo? Well, the opposite is surely false. The Americans are right now pumping vast sums of 'liquidity' into their stock market...but the economy is still tanking.
But wasn't the tanking economy due to the subprime thing? Isn't that simply an extention of the stock market? Yes! So how, according to my theory, did it affect the real economy?
Ask yourself: "Where does the money for these 'liquidity injections' come from?"
The simple answer is, "From the money-printer."
But value cannot be created out of nowhere. Despite being subjective, and nonconservative, it still exists. As I've repeated already, money is valuable only in relation to real values.
Creating more money only causes...drumroll...inflation. Or, for those who read the John Law piece, debasement. The philosopher's stone of taxation.
And this is how the stock market affects the real economy in diseased societies, like ours.
All these 'liquidity injections' represent massive tax levies at the expense of anyone who has a positive asset balance. And while the dollars aren't value themselves, they do represent someone of value that has been previously traded. It's value waiting to be realized, except now it's being realized at Wall Street, by investment bankers, instead of by the person who actually created the value.
Naturally, their store of excess value depleting, these people start sending signals that they won't be engaging in future trades. Which causes stock prices to fall, in addition to various other financial instruments. Which means the bad investments are going to get worse. Which means there will be more 'liquidity injections.' Which means there will be more debasement. Which means these people will start sending signals that...
When I said unfathomably harmful, I meant it. As said in Hazlitt's Economics in One Lesson, we never see all the things we would have made with the destroyed wealth. We only get to see the protected wealth on Wall Street. Cuz you know, that's where it's needed most.
Because, obviously, government has only our interests at heart. It is our mommy, after all. Or we own the thing, or something like that? We vote, right? This is a democracy, right? Yeah, something like that.
In short, another day, another reason to be an anarchist.
The stock market is not, as this and every other article treats it, the economy. It's not even like the economy. The economy is a heart - it drives the entire body. The stock market, by contrast, is the spot on my wrist that I can use to take my pulse. In fact, exactly like that.
Because of this fact, when the government tries to 'inject liquidity' into the stock market, it's exactly like injecting blood into my wrist, from another part of my body...as a strategy for increasing my blood pressure.
Naturally, this is, compared to its objectives, unfathomably harmful.
The economy is about the exchange of objects to accumulate value.
Notably, there is no objective way to define value. It's totally subjective, but it does exist. Because it's subjective, it doesn't have to be conserved, which leads to the real difference between the wealthy and the poor. While it's true that wealthy people generally have more objects than the poor, the real difference is because the wealthy have more things they value, and these things happen to be objects. They have taken advantage of the nonconservative nature of value by trading things they value less for things they value more, reciprocally. Wealthy people simply do this more effectively.
Notice that these trades do not, in themselves, significantly change the physical world. A camper is traded for some dollars which are traded for some building materials, say. Now, the dollars, camper, and two-by-fours are in a different place, and could easily be moved back, but suddenly the total wealth and value of the arrangement has greatly increased.
(This is, naturally, one reason government redistribution never works. There's no way for the government to determine who really values what, which means it will inevitably destroy wealth on a disastrous scale, compared to anything it tries to do.)
(The only way (we know of) to determine what people really value is to put it up for auction on the free market. Government is simply the manifestation of the idea that people want the wrong things. )
(Also, don't forget that ownership isn't physical in any sense either.)
It's these trades that actually increase wealth. Production is quite separate. Production is merely motivated by the future possibility of these trades; without that production would halt.
This is the basic truth of a recession. The expectation of future trades diminishes, and so production declines, ensuring that through normal wear and tear, wealth declines, and everyone feels the pinch.
What does this have to do with the stock market? In a healthy society, nothing you'd ever need to worry about. Why not?
Because the stock market does not trade in anything of real value. No one values stock in and of themselves, but only as a means to obtain new things they do value.
Similarly, dollars are not true wealth. The only real value to dollars is that they facilitate trade, they are never an end, a value, unto themselves, unlike campers and two-by-fours. Also unlike similarly intangible but truly valued things like communication or the various types of security, or a feeling of well-being from a massage or similar service.
Stock is, actually, very like the banknotes that, way back, actually preceded fiat currency, back when banknotes were in fact notes from the bank. Both are, in a very real sense, merely currency.
Currencies all take their entire value from the fact someone will agree to trade that currency for something of real value.
So, the stock market is a big currency exchange. This gets a bit complicated and subtle, so I'm glossing over some things. Regardless, like all currency exchanges, a stock market cannot truly create or destroy wealth. Every dollar 'lost' to a portfolio is merely gained by another portfolio.
And, like all currency exchanges, it can tell you something about the conditions affecting the underlying real values backing the currencies. It cannot, or rather should not, affect those underlying values.
It doesn't matter what happens to your money. If you value huge, delicious steaks, the only reason you value your dollar is because it represents, to you, huge, delicious steaks. The association cannot run in reverse.
As such, the stock market can tell you stuff about the issuing entities - the corporations. (A word that just means 'reification of legal arrangement,' in this case reifying through a corpus - pretending that the legal arrangement is a body, a person.) It cannot, however, work in reverse. Indeed, if I own a factory that makes huge, delicious steaks, does that factory care what its stock price is? Do the buyers of my steaks? My workers?
That would be hilarious actually.
"Crap! I bought this steaks, but the corporation's stock price crashed yesterday and now it tastes terrible. Ugh."
"Urgh! Cheap stock steak! Gross! I hate it when that happens."
The stock market is the pulse of the market - not its heart.
In short, the Great Depression wasn't caused by a stock price collapse. That's preposterous. The stock price collapse was caused by the Great Depression.
There is, of course, one problem with this analysis. It's pretty clear that our economy is affected by what happens in the stock market. Why is this?
Basically, because of the government.
Through various, generally unrelated intentional corruptions, government regulation is now supporting a situation where the actions of America's Wall Street account for, I'm not making this up, half of all American economic activity. The situation is similar in all wealthy countries.
And even this wouldn't be a problem. It doesn't matter if Wall Street accounted for 90% of the economy, it still can't break logical truths. The currencies are valuable because they can be traded. For steaks.
However, the basic support government is providing, without which Wall Street would have to contract drastically, is risk protection. Some institutions have been perceived as too big to fail. There's an actual policy named after it.
Since the people in these institutions aren't dumb, and higher risks generate higher payoffs, this has naturally lead to a drastically blase attitude to high risk. After all, if an investment fails, the government is going to bail them out. They can't lose.
I suspect this is due to a basically voodoo association between the stock market and the economy. The stock market suffers when the economy tanks. It's hard to see the economy, but easy to see the stock market. Therefore, the association gets made between recessions and stock market failures.
As a result, lobbyists can successfully convince lawmakers to prop up the stock market as a method of controlling the economy.
Is my little sub-theory true? Is this voodoo? Well, the opposite is surely false. The Americans are right now pumping vast sums of 'liquidity' into their stock market...but the economy is still tanking.
But wasn't the tanking economy due to the subprime thing? Isn't that simply an extention of the stock market? Yes! So how, according to my theory, did it affect the real economy?
Ask yourself: "Where does the money for these 'liquidity injections' come from?"
The simple answer is, "From the money-printer."
But value cannot be created out of nowhere. Despite being subjective, and nonconservative, it still exists. As I've repeated already, money is valuable only in relation to real values.
Creating more money only causes...drumroll...inflation. Or, for those who read the John Law piece, debasement. The philosopher's stone of taxation.
And this is how the stock market affects the real economy in diseased societies, like ours.
All these 'liquidity injections' represent massive tax levies at the expense of anyone who has a positive asset balance. And while the dollars aren't value themselves, they do represent someone of value that has been previously traded. It's value waiting to be realized, except now it's being realized at Wall Street, by investment bankers, instead of by the person who actually created the value.
Naturally, their store of excess value depleting, these people start sending signals that they won't be engaging in future trades. Which causes stock prices to fall, in addition to various other financial instruments. Which means the bad investments are going to get worse. Which means there will be more 'liquidity injections.' Which means there will be more debasement. Which means these people will start sending signals that...
When I said unfathomably harmful, I meant it. As said in Hazlitt's Economics in One Lesson, we never see all the things we would have made with the destroyed wealth. We only get to see the protected wealth on Wall Street. Cuz you know, that's where it's needed most.
Because, obviously, government has only our interests at heart. It is our mommy, after all. Or we own the thing, or something like that? We vote, right? This is a democracy, right? Yeah, something like that.
In short, another day, another reason to be an anarchist.
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