How to think like a quantum monadologist

by Mitchell_Porter8 min read15th Oct 2009268 comments


Personal Blog

Half the responses to my last article focused on the subject of consciousness, understandably so. Back when LW was still part of OB, I stated my views in more detail (e.g. here, here, here, and here); and I also think it's just obvious, once you allow yourself to notice, that the physics we have does not even contain the everyday phenomenon of color, so something has to change. However, it also seems that people won't change their minds until a concrete alternative to physics-as-usual and de facto property dualism actually comes along. Therefore, I have set out to explain how to think like a quantum monadologist, which is what I will call myself.

Fortunately, this new outlook agrees with the existing outlook far more than it disagrees. For example, even though I'm a quantum monadologist, I'm still seeking to identify the self and its experiences with some part of the physical brain. And I'm not seeking to add big new annexes to the physical formalism that we have, just in order to house the mind; though I may feel the need to impose a certain structure on that formalism, for ontological reasons, and that may or may not have empirical consequences in the macro-quantum realm.

So what are the distinctive novelties of this other approach to the problem? There is an ontological hypothesis, that conscious states are states of a single physical entity, which we may call the self. There is a preferred version of the quantum formalism, in which the world is described by quantum jumps between spacelike tensor products of abstract quantum states (more on this below). The self is represented by one of the tensor factors appearing in these products. There is an inversion of attitude with respect to the mathematical formalism; we do not say that the self is actually a vector in a Hilbert space, we say that the nature of the self is as revealed by phenomenology, and the mathematics is just a way of describing its structure and dynamics. Finally, it is implied that significant quantum effects are functionally relevant to cognition, though so far this tells us nothing about where or how.

Quantum Jumps Between Tensor Products?

For this audience, I think it's best that I start by explaining the quantum formalism I propose, even though the formalism has been chosen solely to match the ontology. I will assume familiarity with the basics of quantum mechanics, including superposition, entanglement, and the fact that we only ever see one outcome, even though the wavefunction describes many.

Suppose we have three qubits, allegedly in a state like |011> + |101> + |110>. In a many-worlds interpretation, we suppose that all three components are equally real. In a one-world interpretation, we normally assume that reality is just one of the three, e.g. |011>, which can be expanded as |0> x |1> x |1>: the first qubit is actually in the 0 state, the second and third qubits in the 1 state.

However, we may, with just as much mathematical validity, express the original state as {|01>+|10>}|1> + |110>. If we look at that first term, how many things are present in it? If the defining property of a thing is that it has a state of its own, then we only have two things, and not three, because two of our qubits are entangled and don't have independent states. It is logically possible to have a one-world interpretation according to which there are two things actually there - one with quite a few degrees of freedom, in the state |01>+|10>, and the other in the much simpler state |1> (and with |110> being unreal, an artefact of the Schrodinger formalism, as must be all the unreal "branches" and "worlds" according to any single-world interpretation).

And there you have it. This is, in its essence, the quantum formalism or quantum interpretation I want to use, as a neo-monadologist. At any time, the universe consists of a number of entities whose formal states inhabit Hilbert spaces of various dimension (thus |01>+|10> comes from a four-dimensional Hilbert space, while |1> comes from a two-dimensional Hilbert space), and the true dynamics consists of repeatedly jumping from one such set of entity-states to another set of entity-states. Models like this exist in the physics literature (see especially Figure 1; you may think of the points as qubits, and the ovals around them as indicating potential entanglement). For those who think in terms of "collapse interpretations", this may be regarded as a "partial collapse theory" in which most things, at any given time, are completely disentangled; actually realized entanglements are relatively local and transient. However, from the monadological perspective, we want to get away from the idea of entanglement, somewhat. We don't want to think of this as a world in which there are two entangled qubits and one un-entangled qubit, but rather a world in which there is one monad with four degrees of freedom, and another monad with two degrees of freedom. (The degrees of freedom correspond to the number of complex amplitudes required to specify the quantum state.)

The Actual Ontology of the Self and Its Relationship to the Formalism

I've said that the self, the entity which you are and which is experiencing what you experience, is to be formally represented by one of these tensor factors; like |01>+|10>, though much much bigger. But I've also said that this is still just formalism; I'm not saying that the actual state of the self consists of a vector in a Hilbert space or a big set of complex numbers. So what is the actual state of the self, and how does it relate to the mathematics?

The actual nature of the self I take to be at least partly revealed by phenomenology. You are, when awake, experiencing sensations; and you are experiencing them as something - there is a conceptual element to experience. Thoughts and emotions also, I think, conform somewhat to this dual description; there is an aspect of veridical awareness, and an aspect of conceptual projection. If we adopt Husserl's quasi-Cartesian method of investigating consciousness - neither believing in that which is not definitely there, nor outright rejecting any of the stream of suppositions which make up the conceptual side of experience - we find that a specific consciousness, whatever else may be true about it, is partly characterized by this stream of double-sided states: on one side, the "data", the "raw sensations" and even "raw thoughts"; on the other side, the "interpretation", all the things which are posited to be true about the data.

Husserl says all this much better than I do, and says much more as well, and he has a precise technical vocabulary in which to say it. As phenomenology, what I just wrote is crude and elementary. But I do want to point out one thing, which is that there is a phenomenology of thought and not just a phenomenology of sensation. Because sensations are so noticeable, philosophers of consciousness generally accept that they are there, and that a description of consciousness must include sensations; but there is a tendency (not universal) to regard thought, cognition, as unconscious. I see this as just footdragging on the part of materialist philosophers who have at length been compelled to admit that colors, et cetera, are there, somewhere; if you were setting out to describe your experience without ontological prejudice, of course you would say something about what you think and not just what you sense, and you would say that you have at least partial awareness of what you're thinking.

But this poses a minor ontological challenge. So long as the ontology of consciousness is restricted to sensation, you can get away with saying that the contents of consciousness consist of a visual sensory field in a certain state, an auditory sensory field in another state, and so on through all the senses, and then all of these integrated in a unitary spatiotemporal meta-perception. A thought, however, is a rather different thing; it is something like a consciously apprehended conceptual structure. There are at least two ontological challenges here: what is a "conceptual structure", and how does it unite with raw sensory data to produce an interpreted experience, such as an experience of seeing an apple? The philosophers who limit consciousness to raw sensation alone don't face these problems; they can describe concepts and thinking in a purely computational and unconscious fashion. However, in reality there clearly is such a thing as conceptual phenomenology (or else we wouldn't talk about beliefs and thoughts and awareness of them), and the actual ontology of the self must reflect this.

A crude way to proceed here, which I introduce more as a suggestion than as the answer, is to distinguish between presence and interpretation as aspects of consciousness. It's almost just terminology; but it's terminology constructed to resemble the reality. So, we say there is a self, whatever that is; everything "raw" is "present" to that self; and everything with a conceptual element is some raw presence that is being "interpreted". And since interpretations are themselves processes occurring within the self, logically they are themselves potentially present to it; and their presence may itself be conceptually interpreted. Thus we have the possibility of iteratively more complex "higher-order thoughts", thoughts about thoughts.

Enough with the poetics for a moment. Is there a natural formalism for talking about such an entity? It would seem to require a conjunction of qualitative continua and sentential structure. For example, a standard way of talking about the raw visual field specifies hue, saturation, and intensity at every point in that field. But we also want to be able to say that a particular substructure within that field is being "seen as a square" or even "seen as an apple". We might build up these complex concepts square or apple combinatorially from a set of primitive concepts; and then we need a further notation to say that raw sensory structure X is currently being experienced as a Y. I emphasize again that I am not talking about the computation whereby input X is processed or categorized as a Y, but the conscious experience of interpreting sensation X as an object Y. It can be a slippery idea to hold onto, but I maintain that the situation is analogous to how it was with sensation. You can't say that a particular shade of red is really some colorless physical entity; you have to turn it around and say that the entity in your theory, which hitherto you only knew formally and mathematically, is actually a shade of red. And similarly, we are going to have to say that certain states and certain transitions of state, which we only knew formally and computationally, are actually conceptually interpreted perceptions, reflectively driven thought processes, and so forth.

Returning to the second part of the question with which we started - how does the actual ontology of the self relate to the quantum mathematics - I have supposed that there is a mapping (maybe not 1-to-1, we may be overlooking other aspects of the self) from states of the self to descriptions of those states in a hybrid qualitative/sentential formalism. The implication is that there is a further mapping from this intermediate formalism into the quantum formalism of Hilbert spaces. This isn't actually so amazing. One way to do it is to have a separate basis state for each state in the intermediate formalism - so the basis states are formally labelled by the qualitative/sentential structures - and to also postulate that superpositions of these basis states never actually show up (as we would be unable to interpret them as states of consciousness). But there may be more subtle ways to do it which take advantage of more of the structure of Hilbert space.

What About Unconscious Matter? 

If I continue to use this terminology of "monads" to describe the entities whose quantum states, tensored together, form the formal state of the universe from moment to moment, then my basic supposition is that conscious minds, e.g. as known from within to adult humans, correspond to monads with very many degrees of freedom, and that these are causally surrounded by (and interact with) many lesser monads in simpler, unconscious states. I'm not saying that complexity causes consciousness, but rather that conscious states, on account of having a minimum internal structure of a certain complexity, cannot be found in (say) a two-qubit monad, and that these simple monads make up the vast majority of them in nature.

In fact, this might be an apt moment to say something about the relationship between these "monads" and the elementary particles in terms of which physics is normally described. I think of this in terms of string theory; not to be dogmatic about it, but it just concretely illustrates a way of thinking. There is a formulation of string theory in which everything is made up of entangled "D0-branes". An individual D0-brane, as I understand it, has just one scalar internal degree of freedom. A particular spatial geometry can be formed by a quantum condensate of D0-branes, and particles in that geometry are themselves individual D0-branes or are lesser condensates (e.g. a string would be, I suppose, a 1-dimensional D0-brane condensate). Living matter is made up of electrons and quarks; but these are themselves just D0-brane composites. So here we have the answer. The D0-branes are the fundamental degrees of freedom - the qubits of nature, so to speak - and their entanglements and disentanglements define the boundaries of the monads.

Abrupt Conclusion

This is obviously more of a research program than a theory. About a dozen separate instances of handwaving need to be turned into concrete propositions before it has produced an actual theory. The section on how to talk about the actual nature of consciousness without implicitly falling back into the habit of treating the formalism as the reality may seem especially slippery and mystical; but in the end I think it's just another problem we have to face and solve. However, the point of this article is not to carry out the research program, but just to suggest what I'm actually on about. It will be interesting to see how much sense people are able to extract from it.

P.S. I will get around to responding to comments from the previous article soon.


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I may feel the need to impose a certain structure on that formalism, for ontological reasons, and that may or may not have empirical consequences in the macro-quantum realm.

This sentence pretty much guaranteed that the entire article would be vague, riddled with empty jargon, unfocused, and uninformative. It was right. Not saying you don't have a point; I'm saying this article is not clear enough for me to begin to determine if you have a point or not.

I very much suspect it's woo, but in any case it's written for a wrong audience. Mixing physics and thought raises red flags. Downvoted.

-1Nubulous12yThis site is full of people interested in implementing intelligence (and even themselves) on a new substrate .... but they're not going to be interested in the relationship between physics and thought ?

Articles should be legible to the audience. You can't just throw in a position written in terms that require special knowledge not possessed by the readers. It may be interesting, but then the goal should be exposition, showing importance and encouraging study.

It's great when thought is considered mechanistically, in terms of physics. It's also instructive to build ontology around knowability. There is a path across levels of abstraction between physics and intuition, and arguably a shorter path between intuition and logic. But mixing precision of physics with vague intuitive concepts such as "consciousness" at the same level is a no-no, an umbrella fallacy with supernatural a prominent example.

4mormon212y"Articles should be legible to the audience. You can't just throw in a position written in terms that require special knowledge not possessed by the readers. It may be interesting, but then the goal should be exposition, showing importance and encouraging study." I both agree with and disagree with this statement. I agree that a post should be written for the audience. I disagree in that I think people here spend a lot of time talking about QM and if they do not have the knowledge to understand this post then they should not be talking about QM. The other issue is I think this post may be too muddled to really require special knowledge before the author clarifies the post. General Post Question The one big thing that confuses me is the title do you actually mean Quantum Monadology? If so are you claiming some use of the formal term monad, or some definition of your own? I don't see this post as following from some real definition of monads as seen in scientific literature. General Post Comment I think to be blunt this post is a bit muddled with ideas from all over the place put into one big pot and the result is not very enlightening. If you haven't already I suggest you lookup the precise definition of monad. I can't find it now but there was a paper a while back published on this topic of formalizing QM within the formal idea of monads.
4Vladimir_Nesov12yMaybe they shouldn't (but not because they can't understand [] this post).
-1Mitchell_Porter12yAs I've been saying, I mean pseudo-Leibnizian monads (pseudo because unlike Leibniz's, they can interact), not computer-science monads.
8Furcas12yWe're all interested in the 'relationship' between thought and reality, but I think it's unlikely that thought exists at the simple, fundamental level of reality that is studied by physicists.

Gotta agree with Psychohistorian and Nesov: this post is woo. Admittedly it's pretty hard to imagine how a classical computation can give rise to consciousness, but I don't see how quantum mechanics helps you. Please pinpoint the exact step in the reasoning where your monads actually require the quantum special sauce, rather than some massively complex Tinkertoys.


Why would you try to approach consciousness this way, as opposed to through neuroscience? Neuroscience has been making some real progress lately; what is it that you think this approach could add?

I can't help but notice that the "self-monad" looks a lot like a "soul" in a thin, crispy quantum shell. What are the differences? Are there differences? Dressing it up this way allows you to do math with the monad. Does that math tell you anything? Especially, can any testable prediction come out of this?

You describe how to think like a quantum monadologist. If you answer these questions, I'll be able to decide if thinking like a quantum monadologist is worth attempting.

3Mitchell_Porter12yThis is not in opposition to neuroscience. It implicitly calls for attention to quantum effects in the brain, and not just electrical and chemical signaling; and then there's the step where you explain the formal ontology of physics (used to describe the state of the monad) in terms of the ontology revealed by phenomenology, rather than vice versa. But that is all in addition. The root of it all is that you take phenomenology seriously, and you don't think it can be reduced to the physics we have, and you take that seriously enough to look for ways to revise the physics, both ontologically and mathematically. The majority of commenters here appear to be content with the theory of consciousness they have, or at least with the prospects for reduction of consciousness to existing physics. I am not, and we are therefore going over some of the familiar disputations in comments, but I really didn't write this to present the case against ordinary physicalism one more time. Chalmers does that, many others have done that. Some people get it and some people don't. This article is a sketch (and only a sketch) of a new alternative - a new starting point, rather than an argument against the old one. If you don't feel the need for a new starting point, you may not be interested. Is the self-monad like a soul? Yes and no, just as the brain is like and unlike a soul according to classic mind-brain identity theory. A monad is a "single substance", but here it is not a different sort of substance. A simple monad should be able to evolve into a complex one, or vice versa, given the right boundary conditions. There is also no radical independence of it from the body; it's a condensate of entangled electrons (or whatever) that forms as the brain develops, nothing more. As a quantum state, you might be able to transfer it into a new environment by a process resembling quantum teleportation; that's about as close to the traditional detachability of the soul as I can get in this theory

Actually, let me make a more general comment. This article seems to be aimed almost entirely at those who already agree that physics is going to have to change to account for qualia. I don't know if there's anyone but you here who accepts that, though. Your aim seems to be to show that a physics that could account for qualia in the way you want it to is possible, but I think the bit you needed to argue first was that it was necessary.

In particular, I'm really surprised that my Google searches haven't turned up anything by you setting out what problems yo... (read more)

4Mitchell_Porter12yNot quite. It is an experiment in seeing whether the people who insist that there is no problem may be moved by seeing a concrete alternative, rather than being told that their existing account of color, etc, is inadequate. (See first paragraph, last sentences.) No success so far. What do I think of Dennett? It is a while since I read him. But while of course I disagree with him, I think he is a superior exponent of the true consequences of standard physicalism. I have accused most physicalists of being stealth dualists, who posit an association between, say, color and some computational or other physical property, but call it an identity. Dennett simply says, there is no subjective color (which he calls "figment") and no unity of consciousness ("the Cartesian theater"). These are just intersubjective figures of speech, etc. And he's quite right: subjective color and the unity of consciousness do not exist in standard physics. But they do actually exist, which is why I've posited a monadic physics. A conscious monad is a Cartesian theater, a place where the components of conscious experience are genuinely simultaneously present, and among those components are color sensations. Responding to your other question - heterophenomenology is where you agree that other people's phenomenological reports must be explained, but you feel no commitment to the ontologies implied by taking the reports literally. In principle, I have no problem with that. People can be wrong. But I disagree with Dennett's specific eliminations, and especially want to show that they are not necessitated by physical ontology, because physical ontology can be different.
5Cyan12yThe point of my earlier comment about touching a hot plate (ETA: link [] ) was that once you know that your brain is capable of that kind of fiddling, you ought to be convinced of the essential unreliability of all subjective experiences up to and including unity of consciousness. Like the temporal order of events during a burn, unity of consciousness may not be what it subjectively appears to be, so you don't get to take it as a premise.
1cousin_it12ySo Mitchell's perception of colors as fundamental irreducible qualia could be a similar illusion. Intriguing possibility!
1Mitchell_Porter12yIt's not just an intriguing possibility, it's really the only counterargument anyone has, given that no-one has actually produced a way to make color out of noncolor.
1SilasBarta12yIn the sense that I think you mean, yes, you are correct: there exists at least one phenomenon that science has not explained in terms of reducing it to more fundamental phenomena. Now, Mitchell_Porter: do you want me to go over why that shortcoming is an insufficient reason to play "monad of the gaps", or do you think you can connect the dots yourself? In any case, I already showed you the research program that can attack this problem from a reductionist standpoint and what a solution would look like [].
2Mitchell_Porter12yThat research program reduces experience to computation. And in a brain that means atoms moving around. I have seen this position asserted in two forms. Color is atoms moving around in a certain way; or color is "how it feels" for atoms to move around in a certain way. The first is the sort of identity which I have been rejecting as outlandish - color is not motion, let alone collective motion. The second possibly introduces a whole new sort of property to the physicalist vocabulary, "how X feels" where X is some physical event or condition. Where we go from here depends on how this property of feeling-like relates to the purely physical properties making up X. If "how X feels" is just another way of saying "X is the case", then we are back to the first approach. If feeling-like is a new and different sort of property, then we have property dualism - unless feeling-like is itself physically reduced, e.g. to another order of computation, in which case we are back to the first approach after all. There is a gap and I'm putting a monad in it, yes; the monad is the place where consciousness actually happens. But we shouldn't overstate the difference between our views. In ordinary physical terms, this monad is supposed to be a big bunch of entangled biomolecules, nothing more; it's only when we go beyond making predictions, to asking what physical things actually are, that I insist upon this inversion of the usual approach, whereby (in effect) the physical state of the monad is going to be explained as an abstracted description of its actual, conscious state, rather than the other way around. When I say "physics contains no color" or "color can't be reduced to physics", I'm talking about the physical ontology you get if you take the physical formalism literally. That ontology contains no color. But I'm not saying that actual color exists in some extra realm outside of physics; the expectation is that it will be there in a slightly modified physics (a monadologized
-1jimrandomh12yColor is a property that objects, light, and experiences may have, not something that can exist independently, so "make color out of noncolor" is incoherent.
-1wedrifid12yNo, but give me an imperfect self-replicator and a few billion years and I may well be able to produce a creature that perceives, experiences and describes colour in much the same way that Mitchell Porter does. Monads, midichlorians and phlogiston just aren't required to explain the phenomena that can be seen in the universe.
0whowhowho8ywhich proves exactly nothing about whether or how it is being done physically. They aren't required to expalin the phenomena that have been explained. As to the phenomena that have not been explained...
0RobinZ12yI'm sorry, where was that comment? I can't find it now.
1SilasBarta12yIt was in another discussion [] : The Friendly singularity one. (I looked at Cyan's user page.)
0RobinZ12yAh, I missed that one.
0Cyan12yIt should have occurred to me to link it. Sorry about that!
0RobinZ12yThanks - it's not a huge deal, I just wanted to read the whole convo.
3Paul Crowley12ySo, given that you accept heterophenomenology, you are proposing a huge, epoch-making change to the way we approach physics solely in order to account for certain utterances people make. I don't think it's enough to say that you think Dennett's eliminations aren't necessary; I think you are going to have to show some pretty big problems with accounting for these utterances while sticking with standard physics if you're to get our attention on this one.
0whowhowho8yHe is probably trying to account for certain experiences he has. if you have never experienced any colours or other quaiia, you are unusual.
0Paul Crowley8yLook up heterophenomenology [].
0whowhowho8yI know what it means. it is not clear that Mitchell_Porter has "adopted" heterophenomeonlogy as an exclusive means of epistemic access to the mind. Indeed, the fact that he has a problem with qualia is evidence that he has not.

Some questions that will probably reveal some of my ignorance but should help clear things up for everyone if answered.

You are saying that there is some monad in my head and that monad is me? No?

Living matter is made up of electrons and quarks; but these are themselves just D0-brane composites. So here we have the answer. The D0-branes are the fundamental degrees of freedom - the qubits of nature, so to speak - and their entanglements and disentanglements define the boundaries of the monads.

Does this mean the entire human brain could be a "monad&q... (read more)

1Mitchell_Porter12yYes. I think a concrete example of a quantum-monadological hypothesis is in order. The best-known quantum-mind theories revolve around microtubules, so let's start there. Orthodox cognitive neuroscience revolves around synapses and action potentials. But let's suppose Stuart Hameroff is right and microtubules are relevant as well, and are not just structural molecules. Maybe there are quantum-entangled mobile electrons in the shell of the microtubule, they feel the action potential, and they affect the binding of microtubule-associated proteins, i.e. let's suppose they are causally relevant to neuronal information processing, as they had better be if they are going to be the locus of consciousness. So, some subpopulation of microtubules, in some subpopulation of neurons, contains a big set of entangled electrons - and that is the monad that is you. Although I have described it as a "set of entangled electrons", it is to be regarded as elementary because entangled objects no longer have independent individual states - they are more like aspects of a bigger thing (at least under the interpretation of quantum theory I'm using). Mathematically, it has a large number of degrees of freedom, and I suppose that in reality, those degrees of freedom are busy being your conscious thoughts, perceptions, and so forth. Does that make things clearer? I certainly know about David Chalmers's work and I generally agree with it. I just think we need to go even further and say, not just that "raw sensory qualities" aren't present in physics as normally conceived, but that they are bound together in consciousness in a way which suggests an underlying ontological unity beyond that possessed by a collection of spatial parts.
5Jack12yThanks, that is quite a bit clearer. How would a quantum-monadological hypothesis make sense of split-brain cases? Surely the slicing of a corpus callosum can't divide a monad.
5SilasBarta12yWhoa, how do you get to make the jump to the degrees of freedom being my conscious thoughts? Whenever anyone else does that, you call it a deficient ontology, denying reality of experience, vaguing out, etc. But you're doing the exact same thing! You have no standing on which to object to someone saying, "The brain state consistent with a certain wavelength of EM radiation hitting my eyes is my conscious experience of blue."
4Mitchell_Porter12yI plead guilty to talking in a way which is ambiguous about the relationship between the actual thing and its mathematical description. I am frankly not sure what the right way to do so is. My objection to the similar identity statements that people produce is that they can't explain how the identity could be true, and will even define away the phenomenon they are supposed to be explaining.

Again I ask, does this theory make any testable predictions and if so what?

2SilasBarta12yNow, now, I'd like to tear into the methodological flaws in monadology as much as anyone here, but Mitchell_Porter clearly said: It would be unreasonable not to think about any idea until it's at the theory stage, else you'd never get there.
3billswift12yYou need to be thinking about tests at all levels of development. The actual creation of the hypotheses should have in mind tests which could test them. A scientific theory has already been tested. Or are you using "theory" like the creationist whack-jobs who are always saying "Evolution is only a theory".
2SilasBarta12yHeh, no I'm not one of those people -- except when trolling forums, of course ;-) And I already explained [] why, even if Mitchell_Porter answered the hard problems, it still wouldn't vindicate his ontology. That counts as giving it a pre-theory "test". But at the very least, PlaidX shouldn't be calling Mitchell_Porter's ideas a "theory" or expecting an experiment yet. Though I agree it's fair to ask, e.g. "what would cause you to give up this whole monadology project?" And there it is indeed troubling, since Mitchell_Porter seems to decree, right from the beginning, that conscious experience is different in a fundamental way from the "mere" operation of quarks that prohibits any new discovery from showing that the two are not different.
1billswift12yI misinterpreted your comment, entirely my misreading, though your last sentence is rather confusingly structured. In fact, my first three sentences basically just repeat what you wrote in different words. But I disagree about when you should be thinking about experiments - you should be thinking about how to test your ideas from the very beginning, from the time they first come together well enough that you can put it into words. Hal Clement's next to last novel, "Half Life", has some interesting points to make about social interactions around science, especially about hypothesis testing. One rule the characters live by is to never present a hypothesis without also presenting either an alternative explanation or a means to test you idea.
5SilasBarta12yWell, then I think we do have a disagreement. I think that sometimes it is necessary to grope in the epistemic dark without such constraints before you can put together a coherent understanding that can answer such questions. However, it looks like Mitchell_Porter has been at this for eight years [] and this post is all he has to show for it. I would definitely agree that counts as Doing It Wrong.
3PlaidX12yI don't think it's essential that everything be testable, it's just that it would help me understand what he's trying to say. I can't even tell if he's actually saying something about the way the universe works, or just relabeling things.
1Mitchell_Porter12yThe major prediction is that mesoscopic quantum effects are functionally relevant in conscious cognition. Beyond that, there's also the prediction that the neural correlate of consciousness is one large quantum-entangled subsystem of the brain. But the crucial threshold, yet to be crossed, is simply for there to be such a thing as "quantum-computational neuroscience". If no-one ever sees an empirical need for that, then theories like this will go nowhere.

the physics we have does not even contain the everyday phenomenon of color.

Color is determined by the wavelength of light. If you meant the experience of seeing color, it's still very much a neuroscience problem - we are nowhere near reducing the brain to the pure physics level.

Well, yes, based on his previous writings, that's what he meant. While it's not completely solved, it's not as mysterious as Mitchell_Porter makes it out to be:

We know why light departs from objects with the EM wave frequency that it does. We know what EM waves are well enough to generate them in other contexts consistent with our observations of light on objects. We know that detection of EM radiation at certain frequencies creates a physical response in the retina. Information about that response is passed to the brain through the optic nerve.

Based on this previous comment, Mitchell_Porter would consider even these last steps mysterious:

We can quantify certain things about subjective color; and we can describe certain physical realities which are somehow correlated with color. Thus 450-nm wavelength light "is" a type of blue light. But I submit that it makes no sense to say that when you see a particular shade of blue, you are "seeing a length"; or that blue itself "is a length". That might do as a poetic description of the physics behind the perception, but as an ontological statement, it simply substitutes the correlated geometric property fo

... (read more)
7Psychohistorian12yExactly. Blue-ness is a property of the retina and brain, not of the light. The light just has a wavelength.
-3Mitchell_Porter12yWhich property? Under the usual assumptions, the particles composing the retina and the brain are exactly the same sort of particles composing the rest of the world. At what point in the piling up of colorless particles and forces does an actual shade of blue magically spring into existence?
5Vladimir_Nesov12yDirectly related: Angry Atoms [].
1SilasBarta12yThanks for the pointer. Another underrated pre-LW post.
2Psychohistorian12yI have no idea. I don't pretend to deserve a Nobel prize. But I am reasonably sure that the colorless particles and forces we need to look at to figure that out reside in the brain, not in EM radiation of a specific wavelength. I'm also pretty sure that however the experience of seeing blue springs into existence, no magic is involved.
0SilasBarta12yThat's it? That's all it took to make you start hiding behind the Sorites paradox? That was easy.

In this discussion of whether color experience can be reduced to the physics we have, let us return to the beginning and at least try to agree on why we disagree.

Before I knew about science, I lived in a world which included colored objects. Subjectively I still do. But I have also learned a theory of the world according to which it is made entirely of particles and fields. For the purposes of discussion, we can say that according to this theory, the world consists of particles and fields in a changing spatial configuration. (If quantum mechanics comes up... (read more)

4rhollerith_dot_com12yThis will probably be my last reply to Mitchell on consciousness or ontology. It is now very highly probable that my differences with Mitchell in this thread stem from differences over epistemology. Specifically, Mitchell considers it epistemologically satisfactory to adhere to his current position until provided with strong evidence or strong argument against it. The best summary of that position in a few sentences is probably the following passage written by Mitchell less than 36 hours ago to be found in the parent of this comment: My position is that what Mitchell considers outlandish is a perfectly normal and perfectly satisfactory hypothesis. None of Mitchell's indictments of the hypothesis strike me as actual handicaps in a proper contest among hypotheses (i.e., in a proper epistemological process). If you want a summary in a few sentences of my position (which is the standard position round here) on how hypotheses should be judged, see the first paragraph of something I wrote less than 48 hours ago []. I would gladly elaborate on it and how it applies to Mitchell's concerns if anyone is interested. Alternatively, the interested reader could just wait for the top-level submission promised by jimrandomh in a sister to this comment.
1Mitchell_Porter12yThe only way I can see to impose a quantitative framework upon this disagreement is to construct a Bayesian belief network encompassing all the key propositions in both your argument and my argument, and then we try to find where your probabilistic dependencies are different to mine. But I wonder if that's even necessary. Here's my reasoning: * Colors exist. * Colors would not exist in a universe consisting solely of colorless particles in motion through colorless space. (In a nutshell: you can't get color from noncolor.) * Therefore, this is not such a universe. Your reasoning is something like: * We explained everything else in terms of colorless particles, etc, so far. * Therefore we'll do it this time too. To come around to your view, I have to deny my second premise. I see three ways you can try to make me do that. First, you can show me a specific way to get color from noncolor - but no-one has shown me that. Second, you can use historical analogy to argue that my intuition is wrong. But in my most recent comment to RobinZ [] I explained why consciousness is different. Third, you can appeal to consensus: everyone else here thinks we can get color from noncolor somehow. But that consensus can be explained psychologically, culturally and historically. Like I said, we can set about the laborious task of formalizing all this. But do we need to?
2rhollerith_dot_com12yI am going to ignore the parts of Mitchell's comment where Mitchell repeats points I already responded to, which leaves us with one point: I do not know what you mean by a Bayesian belief network about an argument. I humbly suggest that when you wrote that sentence, you were confused about how a quantitative framework (as you call) or a formal epistemological treatment (as I would call it) would go. Please allow me to give the miminum amount of exposition necessary for present purposes. Although it is a clear improvement over what Mitchell wrote, there might be mistakes in the following exposition because I came to "technical epistemology" after the age of 40 and life circumstances have prevented me from giving it the study it deserves. If Eliezer, Anna Salamon or Steve Rayhawk takes exception to anything I say below, then believe them, not what I say below. In the gospel according to Jaynes, Pearl, Solomonoff, etc, there is one Bayesian belief network out of all the possible Bayesian belief networks that is the accurate model of reality. If we knew which one it was, we would be able to use it to answer any question about any cause-and-effect relationship that is in principle answerable -- or so it seems to me according to my untutored understanding. Parenthetically, in Causality Pearl opines that systems of equations similar to the structural equation models pioneered by the econometricians are probably a better representation than Bayesian belief networks. Hutter and Schmidhuber I think use Turing machines instead of Bayesian belief networks. Needless to say, if you have a formal model of reality in one representation (Bayesian belief network, say), it is a fairly easy mathematical exercise to put it into a different representation. So, there is one "objectively true" model of reality, but I do not know which one it is. Consequently, what I have as my model of reality is a distribution over models -- er, to be precise, a distribution over candidates for the On
3wedrifid12yIf I have The True Belief Network then I don't need to predict cause-and-effect relationships. I just know the full state of the timeless universe. I mean to ask, why is a belief network constrained to representing physical laws and not physical state? After all, my current network has a bit of both...
0rhollerith_dot_com12yI did not say it is constrained to represent physical laws, wedrifid. Could it be that you believe that my use of "cause-and-effect relationship" implies that constraint? If so, I'm not conceding the implication.
0wedrifid12yI'm not asking you to concede anything. I'm trying to explore your meaning. What would you (or, for that matter, the experts you cite) say is the One True Model? I can imagine various types of mathematical abstractions but aren't sure which kind you are referring to.
2rhollerith_dot_com12yThe casual reader might be saying to himself, "There goes Hollerith with another long comment about what he is calling formal epistemology. Why doesn't he have the manners to refrain from injecting a long thread on an unrelated topic into Mitchell's article on monads, consciousness, etc?" Well, two replies to that. First, I say formal epistemology is not unrelated. Mitchell has been writing for many years around these parts on how consciousness presents a problem for standard physics. He has even solicited donations to support him in researching the matter further, saying that it is dangerous to have a singularity without having done that research. So, one of the ways formal epistemology enters naturally into this comment section is that I humbly sumbit that anyone engaged in such a project that Mitchell is engaged in should have as part of his technical background an education in formal epistemology. It leads to crisper thinking, and given how many resources Mitchell is devoting to the project, his dedicating some of those resources to learning formal epistemology is probably a good use of his time (and, oh, by the way, I'm not going to pay anymore attention to his writings on consciousness, ontology, etc, till he does). Second, now that it has become plain that my mention of formal epistemology might lead to a long thread of conversation, I will indeed move the conversation to this place []. It might move back to Less Wrong in the form of a top-level article by me with a title something like Why most people here should probably learn technical epistemology, a.k.a., the math of rationality. This prospective article would cover no ground that Eliezer has not already covered, but when it is important to publicize some point, then it often wins to have more than one voice making that point.
2Mitchell_Porter12yIt would be possible for a person to maintain that only the natural numbers exist, and that there is nothing else. They could point to all the things which can be described using natural numbers; and if you insisted that some particular thing was not actually a natural number, but merely had a relationship to the numbers, they would keep returning their focus to the numerical part of the description of everything, and handwave away every other aspect as not really real, or as itself just being another number. In the discussion of whether color can be reduced to the motions of particles in space, I feel myself to be in a comparable situation. The discussion of color as such repeatedly turns into a discussion of particles in the light source or particles in the brain... Perhaps someone out there has conducted the subjective experiment of attending to actual color for a moment, and asking themselves afresh whether this thing could "really" be just particles in motion. The first thing to ask yourself is whether this alleged identity derives any impetus at all from the intrinsic nature of particles in motion. If somehow you knew nothing of color experiences or of neuropsychology, would you have any reason to think, in contemplating any assortment of particles circulating in space, that "color" or "the experience of color" was there? I think not. The motivation for the identity comes entirely from the belief that the world in general has already been explained by a physics of this form, and so color (and everything else about consciousness) must, somehow, also reduce to particles in motion. There is nothing in the intrinsic nature of color or the intrinsic nature of particles in motion to make you think that it is even possible for one to be the other. That is the sort of argument that you have to resort to with someone who thinks that color is particles, or that everything is a number. You have to draw their attention to their actual experience, and make them qu
0Mitchell_Porter12yBut can this formal epistemology be the whole of epistemology? What is your formal epistemic basis for thinking that something exists, or that you have experienced blueness, or that 1+1=2?
0wedrifid12yI look forward to that.
1Mitchell_Porter12yWhat I called a BBN (it may be a generalization of the standard concept) is a belief system schema constructed to be capable of representing your reasoning and my reasoning. Nodes are propositions and arrows are inferential steps. The schema must contain a node for every proposition that I use and every proposition that you use, and similarly must contain an arrow for every inferential step appearing in the argument of either person. Once we have that diagram, our two arguments may then be represented as each flowing through a portion of it. We arrive at opposite truth values for a common terminal proposition, so the arguments are in contradiction. To resolve the contradiction or at least identify its cause, we move upstream and try to identify where initial conditions differ. This process will most likely require one to state opinions regarding certain implicit premises, used by the other person, which did not even play a role in one's own argument, as well as to express differing opinions about the arrows, i.e., about the implications of one proposition for the truth of another. One of us may regard the truth of B as independent of the truth of A, whereas the other would say that if A is true, then B is definitely false - or probably false. It is merely a formal process meant to guarantee that the sources of disagreement are mutually understood, something which should happen anyway if the disagreement has developed in a lucid and orderly fashion.
1Alicorn12yI'm concerned that you want to dive down an explanatory hole with no bottom. Suppose we say: okay, the particles are colored; or space is colored; or otherwise, beneath the objects we perceive to be colored, there are colors. Won't you want those colors explained too?
0Mitchell_Porter12yWhen I emphasize that the building blocks of physical ontology have no color, I'm not saying that everything would be solved if only they did. But if you start out without color, and your only way to make bigger things is through spatial and causal aggregation, color will not appear by itself - that is the message.
4Alicorn12yCertain properties can be described counterfactually - does that help? For instance, "fragility" can be a property of an object that never in fact breaks, as long as it would have been disposed to break under a greater proportion of conditions than many comparable objects. An object is a certain color if it is disposed to reflect light of one wavelength as light of a certain wavelength, which may be different from the original. An object can have this property even if it spends its lifetime in the dark.
2Mitchell_Porter12yThe physical property to which you refer is deemed color only because it can induce an experience of color. And the experience of color can occur without that specific external stimulus. So the true nature of color must be sought within the brain.
7jimrandomh12yHere is the confusion underlying this whole mess. There are three types of things which color can apply to: objects, light, and experiences. These are related causally: blue objects cause blue light which causes blue experiences; and evidentially: a blue experience is evidence that there was blue light, which is evidence that there was a blue object. However, color as it applies to objects, light, and experiences are three separate entities with different reductions. We use them interchangeably because the causal and evidential relationships allow them to substitute for eachother in almost all contexts. If you start with one of blue objects, light, or experience clearly defined, then you can use that definition plus the causal/evidential relationships to define the other two. The natural way to define them is to define all three only in relation to eachother - ie, refer only to the entire structure, and depend on the ability to compare the color of reference objects/light/experiences to keep the definition stable. Fortunately, some discoveries from physics have enabled a simple physical description of blue light. Blue light is any light made predominately of photons with a wavelength close to 470nm. Based off that definition, a blue object is one that reflects or produces blue light, and a blue experience is one involving some particular set of neurons which I identify by their causal relationship to blue light. But stimulating these neurons without using light still makes a blue experience, and I could in principle identify those neurons some other way - for example, if I were to discover that protein X is found only in blue-experience neurons, then I could define a blue experience as an experience involving neurons containing protein X, and then define blue light and objects based on that. There are some other strange entities which can have color because of causal relations, too. For example, the number 255 (#0000FF) is blue because it causes blue photons to be
3RobinZ12yI don't think you understand the nature of the exercise. Let me return to the example of temperature. Temperature exists. I say this without qualm - I am an engineer working on thermal issues in electronic packaging, dealing with temperature is my profession. However, temperature is nowhere described in the most current theories of particle physics. Instead, we find that in certain special cases, we can relate certain properties of the distribution of particles to a summarizing parameter in different locations in space, and that if we analyze the behavior of the particles in time this implies certain patterns in the development of the field corresponding to our parameter. These patterns are identical to those observed regarding temperature distributions, and indeed predict in great detail the physics of temperature - even explaining when these physics 'break down'. We therefore conclude that we have discovered a reductive explanation of temperature. The exact same story may be told about semiconductors, about conductors, about electricity and magnetism, about weather, about chemistry, about sound, and about light. We find a phenomenon associated with certain conditions, and we can relate the nature of that phenomenon to the underlying physics. We further prove this relation constitutes the innate nature of the phenomenon by examining edge cases - very thin conductors, chemistry in extreme conditions, light passing through a fine grating - and observing that the higher-level physics (of electrical conduction, of chemistry, of optics) break down just in the way which the lower level physics predicts. We haven't finished the job of reducing subjective phenomena to their fundamental physics, but what we've accomplished so far looks like what we observed in all the previous cases: the normal patterns break down in edge cases (e.g. brain damage) and the science of the underlying phenomenon predicts certain aspects of the phenomenon in very, very special cases (e.g. au
-2Mitchell_Porter12yI had thought you were someone else, thus the wrongly gendered pronouns, but I know who you are now. The world can be divided into what goes on in the consciousness of some individual (e.g. yourself), and everything else, some very small part of which will play a role in causing the experience of that individual. Until this point, all naturalistic reductions have consisted of replacing one theory about everything-else with another theory about everything-else, or in otherwise adjusting the overall theory. Since everything-else is known (if you can call it that) only indirectly, by means of its effects on the consciousness of that individual, we have been free to suppose anything about it (that it consists of atoms in the void, that it consists of pure space-time geometry, that it consists of registers in the universal Turing machine), so long as its predicted causal outputs match up with appearances. But when the time comes to account for appearances themselves, this absolute freedom to hypothesize no longer applies. There must be some fidelity to the appearance of appearances (to use an awkward phrase) in your theory of what they are. I am quite happy to assert that there is no color in a colorless physics because the range of things you can get out of such a physics is so straightforward to describe. Everything reduces to causal interactions among localized quantitative properties, and so the possible higher-order entities are those you can build out of quantity, space, and causality. It's thoroughly unmysterious. What is mysterious is to suggest that you will get colored objects spontaneously showing up as well, like the ghost of Mickey Mouse hovering above the equations. None of this is meant to suggest that neuroscience will cease to make progress in producing a causal, analytical and physical account of human consciousness. On the contrary, that progress is going to highlight ever more strongly the ontological mismatch between appearance and physical t
3RobinZ12yDon't sweat it -- I honestly don't care in the slightest. I will have to agree with rhollerith_dot_com here -- you are treating as absurd a thesis we consider ordinary. And I think it's actually worse than that: you are treating as absurd a theory which you explicitly state you would not treat as absurd in any other context. That's not just strange -- that's downright reckless. Now, you would be justified in being this reckless if you had a substantial amount of evidence to support your idea. We accept quantum mechanics, which is downright strange relative to the Middle-World [] of our day-to-day experience, but we accept it because it's been proven sixteen ways to next Sunday. But in support of your thesis that human consciousness must be analyzed differently to every other phenomenon in the universe, you have ... the naive sensation of indivisibility in the subjective experience of color. That's not evidence. That's the phenomenon that needs explaining. And given all the myriad ways in which consciousness fails -- all the errors it makes in analyzing the physical world -- there is no sense in which subjective sensation can ever be a fitting element in a fundamental Theory Of Everything the way you seem to be proposing.
1SilasBarta12yHeh, I was kind of scratching my head at it though. "Wait, did I miss something about Robin Z?"
1RobinZ12yOnly the degree of my indifference to pronouns!
-2Mitchell_Porter12yBut I did explain why. We have some direct knowledge of consciousness. We have no direct knowledge of what's outside it. Therefore we are not as free to theorize about what consciousness really is; we must at least acknowledge what is there. That includes color, and so theories of nature which don't include color are ultimately untenable, even if they can have interim value as heuristic partial theories. And by the way, indivisibility of color is not the problem. It is the failure to actually produce color by piling up lots of noncolor.
3RobinZ12ySo far as I can determine, you have not understood anything I or any other physicalist has said. I cannot see any value in spending any further time on this discussion.
1RobinZ12yA small note (no need to respond): my account as constructed so far is consistent with what Silas has proposed, a proposal I am inclined to accept. A second small note (again, no need to respond): the analogy to the videogame was not an analogy to the visual output of the console as seen on the television, but to the internal representation within the program. So far as I can ascertain, the distinction is probably moot with regards to your reply.
1jimrandomh12yThe confusion in this debate has nothing to do with color or experience; it's about how ontologies and definitions are (or should be) structured. Rather than try to give an incomplete explanation here, I'll write a top-level post to cover the topic properly (probably in about a week)

I also think it's just obvious, once you allow yourself to notice, that the physics we have does not even contain the everyday phenomenon of color, so something has to change.

You feel comfortable with throwing about hilbert spaces, monodologies, d0-branes and tensor products but not comfortable with a physics which represents colour in terms of the interaction between photons of various wavelengths, a few types of receptors in the eyes and a brain. Mind boggling.

About a dozen separate instances of handwaving need to be turned into concrete propositio

... (read more)
-2whowhowho8yRepresenting isn't explaining.
-3Mitchell_Porter12yThe formal revisions to physics that I propose do not in themselves reintroduce color (or any other aspect of consciousness) into the real. But they are meant to make it possible, and the key move is to identify the thing that is conscious with a sharply defined entity in the physics, the monad. At present, computational neuroscience revolves around coarse-grained computational states of physical aggregates whose boundaries are vague from a fundamental perspective. (Under exactly what conditions does a wandering electron count as part of a neuron that it's passing through? Etc. And yet conscious states are supposed to be identified with computational states of neurons.) Once you have sharp boundaries, you still have to deal with the formal mismatch between physical properties and phenomenal properties, but I think that's doable. But if you can't even be precise about whether there's a conscious entity there, and how many of them there are, then you cannot even get started.
2wedrifid12yWould a rose smell more sweet if you were defined as a fundamental entity in physics?
4Mitchell_Porter12yAt least it could have a smell.

My fundamental problem with any quantum-based theory like this is that since quantum systems (as far as we can tell) can always be modeled computationally equivalent (but slower) classical systems, such theories necessarily end up hypothesizing the possibility of zombies: non-conscious entities that simulate conscious ones perfectly.

This is extremely unlikely, for several different reasons.

1Mitchell_Porter12yIn a monadology such as I propose you cannot have zombies in the classical sense, but you should be able to have unconscious simulations of consciousness. The zombie as described by Chalmers is implicitly proposed within the framework of property dualism: you have a causally closed physical world, and an epiphenomenal world of consciousness linked to the first by a psychophysical bridging law, and a zombie world results by subtracting consciousness from the picture. In his book The Conscious Mind he has a chapter on "the paradox of phenomenal judgment", which is that zombies - being behaviorally identical to their conscious counterparts - talk about consciousness and even philosophize about it, without having it. In my monadology, the conscious state is identical with the state of the monadic self, so it is causally efficacious and you cannot simply subtract it from the world while preserving the causal structure. There is also no paradox of phenomenal judgment, because phenomenal judgments - judgments about the experience you are having - are in fact caused by consciousness. However, there is no obvious barrier within monadology to the creation of a black-box simulation of consciousness whose interior mechanism is made up of many simple monads rather than a single complex conscious monad, and which is therefore not conscious itself.
3Nick_Tarleton12yIf the conscious monad's internal dynamics are uncomputable (even if its behavior is computable), and such a simulation must therefore have a radically different internal structure, perhaps not. But if such a simulation can be made which is structurally similar enough to the conscious monad, then it z-talks about consciousness for the same reason (at the appropriate level of abstraction) as the conscious monad, and the standard anti-zombie arguments return.
0Mitchell_Porter12y"At the appropriate level of abstraction" is pretty broad. Part of the reason that a conscious monad talks about seeing colors is because it does see colors, whereas its simulation (let us suppose) talks about seeing colors only because it contains computational tokens imitating the causal role that colors play in the conscious monad's internal transitions of state. I don't see any contradiction. How would you employ a standard anti-zombie argument here?

Mitchell, I enjoy your posts (though I usually disagree with your conclusions). But they are very long, so would you please consider putting in breaks so that they don't consume so much space on the New Articles page?

1Mitchell_Porter12yDone. Thanks (and thanks to Alicorn for assisting).

Why do you assume unconscious matter exists?

1Mitchell_Porter12yIt might be best to just be agnostic about the simpler monads, until the nature of the state space region between simple and complex states is much clearer. Given the monadic hypothesis, it is natural enough to wonder if the states of even the simplest monads have a psychological interpretation - maybe they are thinking some minimal thought or having some minimal perception. But I'm not going to assume that.

EDIT: ignore this, see my second comment for discussion

I find when I ask more generally about Consciousness Explained the answers I get don't help me as much as I would like, so permit me to ask a more specific question. What do you think about heterophenomenology?

(To people who have posted replies in this comments section - I have recently gone through and added a lot of up- and down-votes. If your rating has jumped by a significant number of points today, this may be a cause.)

Don't mind me. I just found "Less Wrong" recently, and I'm here to learn things. I say that this is a great post as it makes me think. I've yet to find the directions to this place to know if any "higher purpose" is idealized, or if conducting electricity into thought is its own reward.

I'm an artist, and believe that any two given individuals will not share an identical color perception. For that reason, I have argued in the past that color did not exist until the widespread use of the computer. Rather than debate teal, blue, or green, ... (read more)

7meanerelk12yBeing an artist has nothing to do with the accuracy of this belief. There are two problems here. First, irrational numbers are the ones that cannot be expressed as a fraction of integers. Transendentals are defined as numbers that are not algebraic. All transcendental numbers are irrational, but the converse does not hold. Second, pi is defined as the ratio of circumference to diameter, true. This would only be a contradiction if both the circumference and diameter could be integers at the same time, which is impossible. You are confused about what numbers actually are. Some classes of numbers are useful for certain tasks, but there is no sense in which one class is more 'real' than another. I recommend Mathematics, Queen & Servant of Science by Eric Temple Bell for a wonderful overview of mathematics. Chapter 2, "Mathematical Truth", is relevent to this discussion. Also, see Godel, Escher, Bach, Chapter 11: "Meaning and Form in Mathematics".
-1ellenjanuary12yFirst of all, thank you for your reply. Honestly, I'm here because I love this place. I guess one is required to figure out the rules as one commiserates, hmmm? ;) 1) I agree. Being an artist does not validate the belief, it is merely shorthand for the formation of the belief. 2) Thank you for the definition of transcendentals. I'm a passionate writer more than an accurate one. That shall improve, and is part of the reason why I am here. The contradiction formed in my mind due to "skipping a couple of steps" and concluding that "all infinities converge at infinity." I agree that there is no contradiction. 3) We're going to have to agree to disagree in this area. Previously I was told I was "confusing the referent for the symbol" when I sat on a thread and took all comers with the proclamation that "zero is not a number, it is a concept." Glory days in the mind of a mathematician. (Yes, we are strange. ;) ) Irrelevant. I fully intend to dedicate the next four years on discovering the reality of concepts, and I will be sure to look into what you have recommended. The bookstore on the corner had the last tome; if it is still there in two weeks, that baby is mine. Thanks. PS. In writing "thank you for the definition of transcendentals," it occurs to me that it sounds sarcastic. It is not. Previously, the stupid brain did not have a concise definition; and now it does. I fully intend to be polite, courteous, and respectful in all discussion on this blog. If I am not, please let me know. Thanks again. :)
2RobinZ12yI apologize for the belated reply, but did you sincerely believe this at the time at which you said it, and do you sincerely believe it now?
[-][anonymous]7y -4

"A conceptual framework is an analytical tool with several variations and contexts. It is used to make conceptual distinctions and organize ideas. Strong conceptual frameworks capture something real and do this in a way that is easy to remember and apply. For example, Isaiah Berlin used the metaphor of a “Fox” and a “Hedgehog” to make conceptual distinctions in how important philosophers and authors view the world.[1] Berlin describes hedgehogs as those who use a single idea or organizing principle to view the world (examples given include Dante, Pasc... (read more)