Lyle,

That "a neuron either fires or does not fire" is a very, _very_ simplistic assumption. Single cells are highly complex computing devices, with a diversity in function and shape hardly found in any other type of cell. We are still far from understanding all mechanisms underlying single cell working, let alone small circuits or regions of the brain. Our knowledge may at best be statistic, if any.

The point, in my opinion, is to pin down the concepts that we are talking about. When you talk about a computer working "like a human brain", what is it exactly that this computer would do like the brain? Logic reasoning? Pattern recognition? Ageing? Metabolism? Communicating information with neurotransmitters?

If we talk about function, it is true that many functions can be mimicked algorithmically. But the question now is: is consciousness a function? And, back to the original question: can it be mathematically modelled?

I would like to remind here of the limits discovered by Gödel, Russel, Turing and all others about what can be algorithmically computed or not. So, while I am not claiming that brain functions cannot be implemented in a computer, I do claim that algorithmic computation (and mind the word "algorithmic") does have limits.

Cheers,

Fernando

I would say the answer is Yes. One attempt is the recent work by Phil Maguire, Philippe Moser, Rebecca Maguire and Virgil Griffith. You can find their article under the title "Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory" on arXiv.

Here is the link.

http://arxiv.org/abs/1405.0126v1

Thanks Konrad Burnik .. it is indeed a very interesting article,(need to study in depth).. interesting too that authors are from diverse fields..,it would appear then

that for practical purposes consciousness can be defined as infinite integrable lossless sensor fusion..so closer to DSP..(welcome gentle comments/views on this..)

Cheers

In this talk, Donald Hoffman presents a theory which he calls (interface theory) and eventually he presents a mathematical definition of conciousness and link it to physics of particles.

https://www.youtube.com/watch?v=dqDP34a-epI

Thanks Vahid Bastani.... it is an amazing lecture..given by Donald Hoffman

Cheers

The Maguire paper and the Hoffman lecture are interesting but I am not sure either of them has much to do with the maths of consciousness in brains.

The Maguire paper I think falls foul of some false assumptions. They suggest that integrating information should not be loss-making because that would affect memory. However, the representations in memory are different from the conscious representations we get when we retrieve those memories - I guess fairly similar to material 'saved to disc' and material being worked on in RAM or whatever. Moreover, we know that all neural signals diverge and converge so to avoid loss all you need is to send the same data to various different 'gates' at the same time. If you send 10,000 signals out through axons that divide to 10,000 branches each then you can supply 10,000 cells each with 10,000 signals and get 10,000 outputs - so no loss needed. Such divergent and convergent signalling is not what a Turing machine does so this is not 'computable' but we knew that from the anatomy. Also the authors talk in terms of data in strings and compression of such data. It is unlikely that the brain uses strings at all for data at the conscious level - if it does at all it is probably only at the interfaces with the outside world and even then it is doubtful whether these are really strings.

Underlying all this is the problem that Tononi's definitio of integrated information is peculiarly elusive. Integration ought to mean coming together and co-contributing to some event. Tononi sort of indicates this but then allows this to be distributed over several events. We end up with an idea that the information 'has been through a process of integration' but the trouble is that having been through it is now in lots of separate places again, so not together. I think Tononi is right to indicate that we want the information underpinning consciousness to function as a combinatorial relation between many elements - so you get vastly more options for content. However, as I understand it the only non-arbitrary pattern of signals that could relate in this way in situ physically is the pattern input into an individual dendritic tree. As soon as you have more than one neuron included there is no reason not to include all of them and also if you allow signals in sequence over time there is no reason not to include a lifetime of signals in one experience. It doesn't work - except for individual cells, which to my mind is the answer anyway.

I think Hoffman is right to equate consciousness to the dynamic relations of the world, so that physics is just consciousness going about its business (as in Leibniz). The problem I have with his maths is that it does not seem to bear any relation to experience itself other than in simple physical dynamic terms so his finding that the equation for experience is the same as for physics seems to me a self -fulfilling one. I also worry that he considers relations in terms of two body interactions, or three, four etc. My understanding of basic physics is that it is not like that except in the sense that under very artificial conditions it can be made almost like that. Normally an individual mode of excitation interacts with the whole universe, as represented by a field of potentials to which the mode is coupled. So Hoffman's diagrams have no ontological basis. There are no simple closed loops of interaction - each interaction always spills over to everywhere. So I think is model of introspection is totally implausible, for instance. Nevertheless I do like the general approach and at least he makes experience what it probably has to be - the effect of an input of signals to something (he says maybe 0 or 1). At least he makes experience an input. Tononi sort of does half the time and then pulls away the carpet and says it is not an input to anything specific - at least that is my reading.

My suggestion for the maths of consciousness is that it is the relation between about 10,000 on or off post synaptic potentials (as an EM field) to a mode of excitation (probably acoustic) in the membrane of the dendritic tree of a neuron. The maths will depend on the number of degrees of freedom of input (10,000), the dynamic parameters of the classical waveform of the acoustic mode, and the way the two interact - which might in simple analogy be like the way the placing of the fingers interacts with the sound made by a French horn. You then have the maths of a complex wave based 'computational event' in the broad rather than Turing sense. People are already working on this in great detail, although they probably do not think they are working on experience!

This is definitely venturing in Kurzweilian territory. The ramifications of a model for human consciousness is staggering. Physicist James Gates' theoretical findings suggest that there is a fundamental algorithm encoded in the fabric of reality. Describing the universe in terms of equations seems to be the most logical perspective .

In my opinion , no.

Mathematics cannot mimic consciousnesses, as consciousnesses is purely meta-physical. It interfaces with the brain and that is how our brain perceives a form of human like consciousnesses.

However if the brain is deprived of oxygen rich blood enough, then the 'soul' leaves the physical body, it can still see, hear and whatever else that is going on in usually the resuscitation / recovery room of hospitals, until either the brain dies in which case it simply goes elsewhere, but if the patient recovers, then provided that the patient recovers AND has had ( an out of body experience), gives a full account of their experiences. The research was/ is being carried out by Southampton Hospital in the UK.

Thanks to

Jonathan Edwards, Konrad Burnik ,Vahid Bastani, Toheeb Adeyinka Owolabi,

Bernard Mcgarry for so much overwhelming knowledge and insights .

It is indeed inspiring to digest these comments..I hope after due

diligence I can share my humble..response as a lay person in this..

field. much indebted to all.

Cheers

This may possible but difficult because needed large no of equations

Thanks Mukesh Kumar for your valuable view..

I am reminded of Niels Bohr .. quote.. The opposite of a Truth maybe another profound Truth.. unquote..

Cheers

Dear Bernard,

I would agree that mathematics cannot mimic consciousness in the sense that all we can do is model mathematically the dynamic processes that underlie experience. But that is all we can really be wanting. And it would make sense if, for instance, the number of degrees of freedom of the dynamics was reflected in those of the experience in some sense. To have an experience of five roses it seems likely that the dynamics involved have to be complex enough to cope with both discriminating roses from bluebells and encoding 'fiveness' rather than fourness in some way.

I would be sceptical about souls moving about. I have had one of these experiences as a child having nitrous oxide for tooth extraction, but I do not believe my soul was out of my body. After all if you tilt your head back and look straight ahead you will probably have the distinct feeling that 'you' or your soul is behind your eyes - roughly in the corpus callosum (not way off to the right and to the left). If you now tilt your head forward you will still feel you are behind your eyes - somewhere in you pharynx. Getting your 'soul' to jump around is easy. Tony Marcel has shown that our sense of occupying our bodies is very easily tricked. ANd I believe out of body experiences have now been manufactured by extracranial magnetic stimulation. So I don't think we need to postulate souls actually going anywhere, any more than postulating that the houses in the street you played in as a child are now half the size they used to be.

What I think may be salutory, is to consider that we have lots of souls. We more or less have to have at least one on the right and one on the left, since Descartes's pineal is not the place. And if we allow two, why not two million souls? Very few people can handle that idea, but there is absolutely no reason why not. And if we want to have a mathematical model we need to get that right.

Dear Jonathan,

Thanks for your response which has provided valuable guidance on the limits and data extraction of what we are trying to achieve using the frameworks and use of mathematical structures in such a way as to emulate possibly the ‘outcomes’ of the brain being influenced by ‘human like’ consciousness. The data from such ‘outcomes’ may potentially be a major step within the field of AI, which let’s face it has lacked ‘momentum’ for many years now. I agree about the dynamics and degrees of freedom of movement’s processes necessary to extract and use such data.

Regarding the ‘souls’ topic, yes it is really a different dimension, and not applicable to the above modelling system. I sometimes think about the ‘mystery’ of human consciousnesses and how it evades our attempts to locate it’s interfacing with the human brain, which so far seems impossible, thus the concept of the consciousnesses being possibly meta-physical, and if this is the case then it’s not currently possible to ‘tap into’ this source…well as far as we know, maybe the ‘super powers’ are attempting it!! I have no doubt that the human mind can be ‘tricked’ into all sorts of illusions and distortions, but I observed in a recent documentary (possibly Horizon), possible physical evidence of a ‘soul’ leaving the body of a patient in a temporary unconsciousness state, it levitated high enough above a strategically placed shelf which contained objects that could not be viewed from where the patient was being treated, then when the patient became consciousness again, he was able to describe in accurate detail every object that was present on that shelf, as well as the other peripheral information of the conversations that took place when he was unconsciousness. This is what the documentary conveyed, as to its authenticity, I took it at ‘face value’.

http://www.youtube.com/watch?v=i77K4tft0b8 this link is a neuroscientist’s experience during a coma.

Bernard McGarry

I do think we need an operational definition of consciousness, do we equate consciousness with self-awareness? I wonder if a vastly complex and intuitive system of algorithms can mimic what constitutes as consciousness in this paradigm. If a computer-modeled facsimile of consciousness can "act" self-aware it may be indistinguishable from the human consciousness. I think that before we have a model for consciousness we can expect to have intuitive AI that can mimic aspects of human consciousness.

Dear Ramon,

Some interesting points there. But note that Hoffman does not reduce consciousness to physics; if anything he reduces physics to consciousness, much as Leibniz did, and I think rightly so. Yet this is not really a reduction so much as a recognition that all physics is about the dynamic patterns that determine changes in experience - as Descartes would have agreed. I am not sure that the old idea that you cannot reduce chemistry to physics holds any more since chemistry is now entirely quantum theory and its ramifications. Similarly for biology, now that we know protein structure down to the electron orbital level. And metaphysics is very definitely science - it is just the discussion of deeper level issues for which there is no current direct empirical test. Relativity and QM arose from metaphysical premises, as did conservation of energy, etc etc. I believe.

My reservation about Hoffman's theory is that the broad thrust is not new - it is mainstream in neuropsychology - and the dynamics are unrelated to neurobiological structures in an interesting way. Hopefully I can say more later but I am short of time now.

Dear Bernard,

I tend think of consciousness just as 'being influenced'. Consciousness is not some other force that influences on top of influences as we try to describe in physics. I also have reservations about saying that consciousness would be the brain being influenced. The brain is too much of an aggregate. Whatever is a soul, is something influenced in some very small portion of brain.

I don't think any of this has much relevance to AI, which is artificial intelligence, not artificial consciousness. I see no reason why a machine should not be far more intelligent than us but have nothing within it with any consciousness like ours. I think AI lacks momentum because it was a muddled idea in the first place.

I don't think consciousness really evades attempts to locate it as an interface. It is just hard to pin down the precise spot becasue of ascertainment problems. It would not, as I say, be an interface with the brain, but with something smaller and dynamically indivisible. I don't have a mystery about consciousness because I think Leibniz explains exactly what it is and now that we have neuroscience, more or less where to locate it. LIke Hoffman, I think it is just 'physical influence' but I think he has gone off on the wrong track with his physics. There is nothing impossible about locating the interface. The problem is just that people have very fixed beliefs - like that they only have one consciousness in their head, when they might have lots. If neuroscientists were prepared to be scientists and argue from facts to discriminate between theories within the framework of physics we might already have a detailed solution, but they are people, and people stick to intuitions.

I am not sure what you mean by meta-physical - that term to me just means relating to deeper levels of physics that are hard to get at directly with experiments. Maybe you mean supernatural? If so, I don't think there is any useful discussion to be had to be honest.

I wouldn't take too seriously someone's account of seeing things on a shelf they could not have seen from a bed. When one is in this sort of altered state under anaesthesia all sorts of things go out of the window, including the reliability of one's impressions of what might cause what. If you are a biologist you will know that even observations in research labs that are supposed to be under strictly controlled conditions are really all over the place with taints from beliefs. I am amazed at some of the conclusions I drew from experiments I did 30 years ago in my enthusiasm for a particular theory. The odd chap saying he saw something on a shelf is not worth putting in to this debate I think.

Dear Toheeb,

The problem with algorithms is that brains work in a way that bears no resemblance to an algorithm. There is no particular point in a logical sequence where 'one is' in the brain at any one time. Vast numbers of integrations with outputs are going on at the smae time with divergence and convergence between them mediating competition that cuts across discrete time frames of the sort you have in an algorithm. No doubt you could get a computer to achieve a better result than a human but it would be achieved in a totally different way and I see no reason to think there would be anything in it that was influenced in the complex way something would need to be to get a complex experience like ours. I thin kit is a false quest.

Dear Ramon,

A few more thoughts. I agree with your caution about how Hoffman derives his magically similar equations. I don't mind him using all sorts of forms of thought to come to a theory - I think Karl Popper said in one of his essays that he had no intention of laying down a 'scientific method'. Any sort of thought can be useful in science as long as it relates to testing an idea, either by internal consistency or by observation.

Where I think Hoffman is right, and with respect, young Lyle is dead wrong, is to see consciousness as an interface. It really is the little man viewing the screen - as long as one takes Dennett's point that he is not doing it **optically** and thereby 'repeating entire the talents it is rung in to explain'. An interface without a receiver inside the brain, or several, is not an interface - the analogy is empty. If there are signals, something has to get the signals and that is not a brain because they are inside the brain, at a finer level of grain. Arnold Trehub puts the signals at his retinoid system. I think it is the step after Arnold's retinoid cells, but we are not so far apart. The interface must be an input and inputs are in dendrites and the maths of dendrites are being sorted out as we write by people like Michael Hausser and his group. Interestingly, if the 'particles' with the input here are Bose modes with spin zero, as they pretty much have to be, then Hoffman's equations would collapse into something looking much more like standard classical wave equations without little i. That to me is the nitty gritty of 'mathematical modelling of consciousness'. It is being done but the people doing it just call it post synaptic integration and write papers in Science or whatever.

Dear Lyle,

I have sympathy for your spirited defense of intuitive materialism. I would have said much the same 30 years ago. But there is a problem. Physical science describes dynamic interactions that operate locally. It does not deal with ‘emergent properties from several other brain functions’. I agree that consciousness is an ambiguous and perhaps rather useless concept, but then it is not an emergent property, which is equally useless.

I think the mistake is to think that consciousness is a property of a system called a brain. As the Extended Mind people have pointed out, this is a totally arbitrary choice of a cluster of events. One can consider a much smaller system within the brain or a much larger system involving the outside world. The idea that somehow there is a system that has consciousness that is limited by the skin is the anthropomorphism. Similarly for the thermostat – an entirely arbitrary system. Physics has no place for that.

If we have an illusion of being conscious there still has to be some local physical basis for the point of view of having the illusion. You can’t make that ‘the brain’ or ‘the thermostat’. We are not actually interested in input–output relations – that was David Chalmers mistake. We are just interested in input (the having of the illusion) and how you get to it. So, since you cannot get computers to model the input events in nerve cells because all inputs in computers are a pair of 0 or 1 options, I cannot see that computers can help us. We are interested in interfaces because all causal relations in physics are interfaces and, as I think is agreed, consciousness is just the acting out of physics, or vice versa – no extra sauce needed. The input interface in a thermostat is the action of heat on an expansile structure. We need something similar for our illusion of consciousness.

Dennett is interesting. He correctly points out that there is no one SINGLE place in a brain where things come together. (Descartes’s idea was not absurd, it just turned out to be wrong.) So he suggests that experience is based on multiple drafts at specific points all over the brain. He is quite happy that there are specific local events involved. I think he is dead right in suggesting that there are many of them. But then he bottles out of his own physics base. He does not want anything to ‘experience’ these drafts, probably because he cannot quite see how you can have multiple experiences, although there is no problem with this. So he just makes them ‘drafts’. But that is no good in causal terms if nothing is informed of these drafts. In a computer simulation there is no point in printing a detailed draft on to a Turing tape that is never then read. So he says experience is just the illusion you get from all these drafts – but nobody gets the illusion. It cannot work. He has the right idea in one sense – it is not a ‘person’ that gets the colour red, anymore than a thermostat gets the heat, it is something more local. It is not a computer that gets 0 or 1 but a gate.

What Dennett seems to miss is that there are millions of places where vast numbers of signals come together as inputs in brains – in dendritic trees. These are presumably where the ‘drafts’ would be delivered. In computers integration occurs by a piecemeal serial process using a stack or ‘Turing tape’ but the brain has no need to bother since it integrates lots of signals at one go in complex time sensitive ways. You might be able to simulate the logical input-output structure with a computer but you would not be simulating the inputs.

If there is no structure in the brain specifically relating to consciousness, why has Stanilas Dehaene just published a book saying that he knows more or less exactly where signals that we report as conscious occur – forward towards frontal lobes, cingulate, precuneus etc.? The only problem, again, is that Dehaene does not think of these in terms of what they are inputs to. They are only ‘signals’ if they input into something.

There is, I admit, a curious difficulty here. If I report that ‘I’ have a sense of red, on my analysis this report as actually referring to millions of senses of red within my brain. This raises tricky issues about the role of cause in reference and problems with de re and de dicto interpretations. It may be true to say that the only ‘real referent’ of my report is the barrage of signals output from upstream cells that are destined to arrive, via myriad branchings, at the cells that have the sense. But it is still the case that they only act as referent because they are going to arrive somewhere. If you cut these axons there is no sense of red reported. Thus Dehaene is probably right to try to pin down the supplying signals as what will be in consciousness but ‘being in consciousness’ entails their arriving together at cells further on.

I don’t think there is anything very new age about any of this. It is rather close to Descartes. The physics needed is at the Andrew Huxley’s level of waves with classical behaviour, although I think this is underpinned by a modern field theory solid state analysis with quantised modes, as required. If we want a theory to fit with physical science we want physical science, not ‘emergent properties of computational systems’ and other such hand-waving. Pretty old age stuff really – you get to it once you are past 55!

Lyle,

That "a neuron either fires or does not fire" is a very, _very_ simplistic assumption. Single cells are highly complex computing devices, with a diversity in function and shape hardly found in any other type of cell. We are still far from understanding all mechanisms underlying single cell working, let alone small circuits or regions of the brain. Our knowledge may at best be statistic, if any.

The point, in my opinion, is to pin down the concepts that we are talking about. When you talk about a computer working "like a human brain", what is it exactly that this computer would do like the brain? Logic reasoning? Pattern recognition? Ageing? Metabolism? Communicating information with neurotransmitters?

If we talk about function, it is true that many functions can be mimicked algorithmically. But the question now is: is consciousness a function? And, back to the original question: can it be mathematically modelled?

I would like to remind here of the limits discovered by Gödel, Russel, Turing and all others about what can be algorithmically computed or not. So, while I am not claiming that brain functions cannot be implemented in a computer, I do claim that algorithmic computation (and mind the word "algorithmic") does have limits.

Cheers,

Fernando

I listened to the Hoffman lecture. I have a few doubts:

1- One of the axioms of the model was that the world constitutes of conscious agents. But the speaker did not clarify as to the whether he means that the world constitutes of only conscious agents or conscious + unconscious agents. In the examples, he talked about interaction of conscious agents only without taking unconscious agents into consideration.

If one of the axioms of Hoffman's model is: The world constitutes of conscious agents only, then I believe this axiom is wrong.

2- The speaker says that the conscious agent asymptotics and the wave function of free particles are equivalent. However, they are similar but not equivalent (time: 30:00 of the video).

I think I have successfully mathematically create the model consciousness. See my paper "The Mathematic Model of Consciousness " in my web.

This is my mathematical model of consciousness.

Lyle,

I agree that many fine details of the nervous system can be abstracted away through mean-field modelling, but I don't agree with the simplification of a neuron being something like a point-process. There are neurons that display subthreshold oscillations, there are tonic spiking neuron, there are bursting and there are chaotic neurons. You may say that all of those are different instances of a {0, 1}-process, but you may as well reduce human language to a {talking, not-talking}-process, and that would be too much of a simplification.

The nervous system has to operate in a physical world, and it has to be attuned to its physical properties. At some level, there are functions which we may consider computable, but there are others that are not computable. One of the most astonishing functions of the nervous system is that of telling time. Many neurons code information as the frequency of their spikes. So, to tell the whole story, information would not be binary, but continuous over the range of possible frequencies. Now, to decode frequency you need to be able to somehow count spikes and measure the time length of the spike sequence. Time is not computable, it is a physical property. You can then compute as much as you want with the decoded information, but coding and decoding takes place in another aspect of reality, in a non-computable one.

Further mechanisms that include time are coincidence detection or STDP learning. You can write an algorithm that simulates that, and you can simulate time in a computer as well. But you cannot compute (in the Church-Turing sense) "real" time unless you rely on physical processes. Take a cessium clock, take a piezoelectric quartz clock, build an oscillator with resistors and capacities, and you will still not be computing time in the algorithmic sense.

Again, this is not to say that there is a divine separation between brain and machines, nor to say that computers will never be able to perform as the brain. I won't go that far. But to me, the original question remains open: where does consciuosness lie? Is it a computable function, only dependent on abstract, enumerable information? is it a non-computable process, more intricately related to physical processes? does anything matching the term "consciousness" exist at all, or is it only a human subjective perception, as itching or love or the sense of self?

Cheers,

Fernando

@ Fernando Herrero Carrónprocess

" Is it (consciousness) a computable function, only dependent on abstract, enumerable information? is it a non-computable process,?"

My anwer:

I once thought that consciuosness is computable, so computation function is just the consciousness. But now I think that there should be non-digital process, which might not be computable by Turing machine. So we might divid consciuosness into two parts: (1) computable, which are about symbolic (languages);(2) continuous, infinite, so uncomputable,like perception or feeling, which are acompanied with less symbolic.

That's an interesting question, Ramón, one that has been around for centuries, I'm afraid. For my part, I will take a "Dirac delta" approach to the subject. As with a Dirac delta, you can talk about it, you may define its mathematical behaviour, but noone has ever seen one. Freely quoting Wittgenstein: "about that about which one cannot speak, better remain silent".

To me, consciousness is the background silence underlying all phenomena. Ever noticed that annoying noise that our fridges make _only_ the moment it shuts down? It is quite remarkable to me that we can detect the ceasing of phenomena. We somehow imply that consciousness is a "some thing", but to me consciousness is a "knowing" that is still there even after stimulating phenomena have ceased.

I know this is a subjective description of the experience, rather than an objective, instrumental study. So, Ramón, together with your question, let me put forth another one: is consciousness objective or subjective? And then, is it possible to model subjective phenomena? Should we reformulate the original question as: can we model the biological processes underlying consciousness?

Cheers,

Fernando

@Ramon Quintana

Perhaps, Gödel incompleteness not only for machine, but also for human. So if there is a discrimination between human consciousness and machine's function similiar with consciousness, it is not concerned with Godel.

Lyle is indeed trying hard to wave the 0 and 1 flag but I see this as completely beside the point. Conscious is not a thing – that would indeed be a naïve idea. Nor is it a black box input-output function that can be simulated. As Fernando says, when puzzle over consciousness we are interested in is the ‘knowing’ aspect – which must be an input. For X to know it must be influenced by the world – i.e. it must have an input from the world. Nothing else makes sense. There is a fashion for denying that anything ‘receives’ the contents of consciousness but if nothing has an input what on earth is the point of a computer model of input-output. We don’t even have an input. There is some very Imperial tailoring going on.

The sites of inputs in brains are dendritic trees and the causal relations in dendritic trees that appear to mediate these inputs are between tens or hundreds of post synaptic potentials out of a potential 10-50,000 input ports and a propagating wave causing downstream ion channel opening. The PSPs are not just 0 or 1 because they can be negative or positive or null and of varying strength (unlike action potentials).

The output from the cell is thus irrelevant, because we are interested in input. But even the output is not 0 or 1. It is now clear from the complex hierarchy of synchronisations of latent periods in cell banks that for at least some cells what matters is how soon they fire, not whether they fire. There is competition for salience and since action potentials are of fixed amplitude it is almost certain that this competition is temporal. So the ‘value’ of an output depends on whether or not it fires before any other cell. It is contingent on all other outputs. It only has to be the first output to be in the winning team. That depends both on how good all the other teams are and on the teammates. I am unaware of any Turing type algorithm that works like that. The rate coding issue is also relevant although this may turn out just to be a way of increasing the statistical likelihood of hitting the downstream cell at exactly the right time to win out.

In relation to the further discussion I don’t think brains are either analogue or digital. Analogue tends to mean a signal encoded in one degree of freedom temporally. Inputs in brains (rather than peripheral sense organs) have many degrees of freedom. Moreover, as they are used to extract invariances they cannot use the isomorphism normally associated with the analogue concept. In fact, the signals tend to be discrete. But again, the input-output relations bear no relation to that in a binary logic gate.

I don’t think consciousness can emerge in wet circuits because ‘circuits’ do not have inputs. Only individual integrating units (cells) have inputs. In fact there are no specific ‘circuits’ in brains – everything connects to everything. The content of experience must depend on null signals as well as active ones so you cannot equate it just to ‘active circuits’. It must be encoded in a pattern of null and active inputs to some integrating unit. I think the experiences we discuss here belong to individual dendritic trees, which may be wet in a sense but at the appropriate level of condensed matter physics wetness is probably rather irrelevant. I suspect electromechanical coupling is crucial and that could easily be done dry.

As a last comment, it seems that we often solve non-computable problems. Roger Penrose wrote an entire book on the implications of this. His favourite example was his solution to complex tiling problems that showed that a particular set of tiles could tile an infinite surface but never in a repeating fashion. He claimed that the problem was non-computable and I rather doubt he was wrong about that.

One simple point in relation to Narasim's original question is that there need be nothing counterintuitive about the sub atomic world for inanimate objects to sense the external world. How could they obey the laws of physics as applied to their specific environment if they did not sense it, i.e. be influenced by it, - in operational terms. How could there be a time dependent Schrodinger equation? All we need be bothered with here is operational terms. We can take a purely behaviourist approach to 'our experience' - the operational knowing that allows us to talk about it if we are inclined to. The talking may be an output, but what we are interested in is what gets the input in the form we talk about?

Ramón:

Ok, I implicitely took the analogue/binary dichotomy to be the continuous/discrete dichotomy. Thanks for the pointer to another thread, I will search for it.

Though it is a little over my head (and certainly far outside of my field of research), An individual by the name of Bachir Boumaaza Nicknamed "Athene") has released a series of YouTube documentaries discussion and providing his (and many others) theories regarding consciousness, neuroscience, quantum physics, and so on. Of this series, one was called "Athene's Theory of Everything", in which he presents consciousness in the equation of "C=hf", in the linked video, it is explained (around the 6:30 mark) that:

"[. . .] As De Broglie's equations apply to all matter, we can fundamentally establish that C equals hf, where C stands for consciousness, h for the constant of plank and f for frequency.

C is responsible for what as the now, a quantized or minimum unit of an interaction. The sum of all moments C uptil the current moment shapes our concept of life. This is not a philosophical or theoretical statement but an inherent consequence of all matter and energy being quantized. The formula shows how life and death are abstract constructions of C. [. . .]"

It goes on and elaborates. I have to admit that I have not sat and fully internalized or absorbed Bachir's ideas in these presentations, they have provided some groundwork for my own directions of research and are at the least thought provoking.

http://youtu.be/dbh5l0b2-0o

Dear Luke,

I fear that C=hf is a complete nonsense. This is the sort of thing Lyle is rightly contemptuous of I think. Consciousness has to be a causal interaction for us to even begin to talk about it. Frequency is not a causal interaction.

Dear Lyle,

We need to be precise here. (Receptors are not inputs but sites of input.) The question is what are receptor inputs inputs to? We loosely talk of inputs to the brain but we have no precise definition of the extent of a 'brain' and when it comes down to detail they are not really inputs to brains. 99% of inputs to receptors never influence the frontal lobes or any of the motor areas. Those that influence the frontal lobes and motor areas may influence arms and legs and cups of tea and grass under our feet and so are inputs to ... the universe really. This is why William James said that it made no sense for a brain to experience. You cannot lump together separate causal relations in this way. We are not talking of brains being conscious in this sense. We are looking for specific individual causal relations, the inputs to which appear to be what our talk of 'what I experience' is about. As Stanislas Dehaene argues, on the basis of a large body of consistent evidence, these causal relations occur well forward in the brain in association with certain very specific patterns of cell activity that do not occur with subliminal inputs. The problem with Dehaene's account is that he does not ask where the relevant inputs are, only where the preceding outputs are, because he is caught up in the fashion for denying that conscious content is input to anything (which seems absurd since he judges its presence by verbal accounts which would need to be based on some input to generate a verbal output).

As James points out, in order to have a coherent account of experience we need to commit ourselves to what is an 'individual causal relation' or perhaps 'event' that is not an arbitrary merging of a group of causal relations each with its own input. Science has in general evaded this question, with the exception of Leibniz, who placed it at the very centre of his account of the world. In the computer world there is no such thing as 'a computer' anymore. Everything is causally linked up via the web. Any distinction between one collection of events and another is arbitrary. The same applies to brains. Two people in conversation have causal relations between them just as much as there are causal relations inside them. Why do they not have the same phenomenal experience? There must be domains in spacetime which delineate individual experiences for reasons of them hosting 'individual causal relations' in some way if we are to explain individual episodes of phenomenality. If we forget phenomenality it is true that a robot can 'chunk' together various causal relations according to arbitrarily programmed rules and in electronic speech say 'I saw five red roses'. However, we have every reason to think that the single bit serial processing involved in this would be orders of magnitude too slow for a brain to do what it does. Brains can only possibly work as fast as they do with such a slow signal integration rate if they work in parallel on inputs with many degrees of freedom. And they do that - in fact the degrees of freedom are bafflingly huge at about 10,000. So although there are many further layers to this (that you will find in an essay called Reality Meaning and Knowledge on my UCL homepage) it looks as if our accounts of rich inputs are indeed accounts of rich inputs, and we can match that up with the phenomenality too, so everyone is happy. Receptors generally only have one degree of freedom and are too early in the chain. The inputs up in the front of the brain that correlate with reported experience have about 10,000 degrees of freedom and are inputs to dendrites.

Jonathan Edwards, thank you for your reply. That right there does indeed pretty much kill the theory, at least in that iteration. And because I have spoken to Bachir (who constructed this theory) a few times, I've known him to not simply be full of hyperbole and nonsense, I feel that he might have been onto something interesting. Though his theories need refinement and perhaps reconstruction. However, as far as I can tell, he seems to have dropped most of his attention from this field...

In any case, I appreciate the response.

Dear Luke,

I agree that there may be some insight behind the C=hf equation but I suspect it is one that Feynman summarised by there being 'plenty of room at the bottom'. The richness of a causal interaction between a superposed mode and a field would depend on frequency. However, it would also depend on the domain of superposition and the nature of the coupling. One might also have to factor in a level of significant 'grain' for the field, perhaps corresponding to some biological parameter. If experience is a causal interation between mode and field, as I think it will prove to be then I would expect to end up with an equation a bit more like:

rC< kh x V/F(W)

Where rC is 'richness' or complexity of a conscious experience, kh is a constant in which h probably does play a role, W is the de Broglie wavelength of the mode, V its domain volume of superposition. The Function F(W) might be the cube of W but might under some circumstances be closer to just W. The < sign indicates that the richness would have a hypothetical maximum, constrained by grain factors. This equation could collapse into something like Bachir's if certain parameters were taken as unitary but I think you do need to include variables for both mode and field to describe a causal interaction.

A most excellent feedback sir, thank you. This was exactly the sort of response I was hoping for. This provides much food for thought, and I only wish that I could contribute an equally insightful idea in this field (as my work lies in another). This, at least I think, fills in some grey matter and direction for me, and hopefully others. Thank you.

I actually do not think there is an answer to that question even if we omit word "mathematical" from it, because please note, there are much simpler things, like randomness, that we cannot mathematically simulate.

The reason why I think so is the following. Is a fly conscious? Is a fish conscious? Is a cow conscious? Is a monkey conscious? Is a man conscious? I believe consciousness is not a yes-no thing. There is an infinite finesse around any arbitrary threshold at which we say: OK above this beings are conscious an below that they are not.

When my God fearing granma told me that no animal has "soul" but only Man, I immediately noted that this cannot be true. If you look to those unfortunate men who have serious brain deficiencies and operate at a very low level, or are vegetating in a hospital or are in coma, you can understand that some animals are much more "conscious" than some men, unless there is something Biblically axiomatic about Man.

Man exists for some hundreds of thousand years years and we only know so little by now. At best, we are probably 500.000 years away from having an answer to your question. But heads up, Sun will shine well for another billion or two years...

Dear Mario,

I quite agree about your comments on the graded nature of consciousness, but I don't see why this leads to pessimism about building quantitative (mathematical) models. In fact if consciousness was a yes no thing there would be no quantity to mathematically model - merely a quality.

So why do we think cats and even flies are conscious to a degree? It seems that we think these are aggregate physical dynamic structures that:

1. Have stable causal pathways for taking in information about the world, and filtering and collating and subjecting it to differential analysis in time and space to generate information in a new form that encodes in 'conceptual' form what is of most use in guiding strategic behavioural output (or something like that).

2. Some causal relation in which this 'distilled' information' is received as an input, and is received in some 'overt' 'phenomenal' sense that makes it what we call 'experience'.

3. A set of causal pathways that involve making use of stored potential chemical energy (usually ATP) to trigger mechanical actions and movement.

4. A connection path between 2 and 3 that allows for the input at 2 to influence the actions in 3, but does not require that any particular input to 2 leads to a particular action, owing to contingency related to other causal pathways.

We can conceive of all sorts of partial versions to suit protozoa or brain damaged individuals who can indicate they are collating information through fMRI scan results etc. etc. So 'consciousness' is not one parameter. Nevertheless, it can be studied as a cluster of issues, in the way that digestion or locomotion can.

The mathematics of 1 are tough but are gradually being broken down. We start with Hubel and Wiesel and move through to Quian Quiroga at the macro level and Hausser at the micro level and Buzacki at an intermediate level perhaps. The way differentials in space and time are achieved are now being worked out in terms of cell populations and the dynamics of post synaptic integration.

The mechanisms in 3 are even better worked out, although there is more to do in understanding e.g. cerebellar control. The connection between 2 and 3 will follow similar rules but at the moment we are not sure where 2 is. As indicated above we have the irony that people like Dehaene have got very close to pinning down where 2 is but do not ask the question in terms of 2.

We then have the apparently thorny question of why input at 2 is 'overt' and 'phenomenal' rather than any other input. The simple answer to this, which Leibniz gives us, is that all inputs are overt and phenomenal, or at least we have no evidence whatever for a dichotomy between overt and non-overt. What will differ is the extent to which the input correlates with any aspect of the distal world in such a way that it is 'about' that aspect in any useful sense. What will differ is whether or not the input is in a form that could function as a 'clear perception' of the distal world. But that will be what the analysis of 1 defines, so we have covered that.

Many people will complain that it seems that only one input seems to be overt in their 'mind'. However, by the anthropic principle, when any group of people is discussing and writing net posts about such overt experience, the only inputs being referred to will by definition be those that activate the type 3 pathways involved in internet discussion - via language centres etc. Any other overt inputs just don't get a look in. So the 'specialness' of 'conscious input' is a self-fulfilling tautology.

Finally, we need a mathematical model of the input relation that we do discuss - that of this distilled content about the distal world (sometimes more about memory or self). We want to know what determines its richness. How many degrees of freedom does it have? We also want to know the dynamic significance of the relations between input elements. These ought in some way to match up with the way 2 usefully influences 3 but it may be that this matching takes a very indirect form. We need to factor in the likelihood that there are massive numbers of parallel inputs of the 2 type (all with the same 'content' about the same aspect of distal world) involved in a form of computation a bit like a connectionist net, despite the fact that we are under the illusion that there is only one input of the 2 type.

The biophysics of a 2 input more or less have to be the sort of biophysics Michael Hausser, Idan Segev, Nelson Spruston and others have done so much brilliant work on. The difficulties involved are huge but there seems to have been a major breakthrough recently in understanding time dependent non-linear relations.

So., in summary, I would say that your 500,000 years is too long. I think it will be 15 years until we can say with reasonable confidence that we know what sorts of models we need all the way along the line and have some first level mathematical rules that will withstand empirical testing.

Dear Jonathan,

I think that boxes with inputs and outputs would not lead to definition nor to modeling of consciousness. If you show todays toy robots (that listen and speak) to a peasants that lived 150 years ago or to Arhimedus I'm sure they would believe it is a conscious being. But only because we know more today we know it is just an electronics-mechanical toy with no brains, much less feelings or consciousness. As we will learn more we will discard more and more models of the type that you propose now.

In quantum mechanics we already know that mathematics (logic) is very limited in understanding reality. We know of many systems simple or complex that cannot be mathematically described in detail, but only some of their characteristics can. For example if you have an atom in excited state there is no way you can calculate when and to what state it will decay. The only thing yo are allowed to calculate are probabilities of what will happen in a specified period of time. If such systems cannot be calculated why hope that one could model nothing less than consciousness?

I think it is plain to understand that love or other feelings, much less consciusness, are almost by definition out of reach of logic, that is (by equivalence of logic to mathematics) to mathematics.

Note also that nothing in science happens nearly as fast as we naively hope. Remember the years mentioned in sci-fi films like "Space 1999" or Orwell's 1984 or promise of fusion, or promise of cure for cancer? Did you notice that fusion, or cancer pill are always 10-15 years ahead, for 40-50 years now ? It now seems that there will be at least 400 years before anything of that happens, but in reality a paradigm shift in thinking would require much longer time. Did you notice that nothing happened in science from AD 0 to 1500 ? There was some knowledge advance in 5-7 years before that and in 500 years after that. But before that people existed for about 1 million year without significant advance of any kind. To solve really big things like beating the speed of light for Space travels or understanding Brain we need on the order om ~1M years (with possibly a top-predator spieces change) at least. That is just a tiny blink of time in what is ahead of the Earth. There is absolutely nothing except more confusion that can be generated in next 100 years.

That seems a remarkably unacademic and unfounded set of statements Mario. But it is good to have a devil's advocate around, to tear their arguments to shreds. Nothing can be more fun than debate.

The first thing you got wrong was the cancer cure. My colleagues have been curing cancers for decades. Colon cancer has been curable for over a century - my wife was cured of it 40 years ago. I have recently been cured of prostate cancer. Those are cases of surgery but Hodgkin's disease started to be cured with drugs in the 1970s and now at least 70% is cured. Chorioncarcinoma was cured even earlier, breast cancers are now cured. Leukaemias are cured. Most cancers are cured now in fact. You are a bit behind the times!

The things that have not happened' like beating the speed of light and cold fusion, have not happened for good reasons, as you know. Your arguments about rate of progress are knocked down with a feather. I started out 30 years ago trying to understand a disease and discovered a very effective treatment without even thinking that was possible. If you want to be a great scientist - which you should do - then I suggest you wipe the pessimism from your eyes and try something bold - it often works.

Consciousness is not such a big problem, certainly not the 'hard problem'. It was solved 300 years ago in principle and we just need to believe that it is entirely consistent with our physics. That does mean thinking hard about what our physics is about though.

Understanding love is tough, and I think tougher than consciousness, but maybe no tougher than understanding 'red'. But remember that before Watson and Crick (remember them, making a wee bit of progress?) everybody thought the genetic code was completely insoluble and then it turned out to be sort of ABC. Love will take 30 years, but I was talking of consciousness.

Then you complain that mathematics cannot tell us when an atom will decay. Maybe that is because there is nothing to know? Maybe the atom doesn't know? Why shouldn't reality be statistical and open to doubt. Leibniz gives good reasons why it has to be. The Newtonian idea that all predictions had probability 1 was always a non-starter. Quantum theory seems to confirm that. I think that is a dud, or at least unproven, argument.

Why are you young guys so pessimistic?I realise that at your age I was less sanguine about solving a big problem but I didn't go around saying there's no point trying!

But to get back to consciousness, we are not talking about inputs to boxes, like toy robots. I am talking about inputs to individual dynamic events - because you cannot add together causal relations; each is a relation of itself in its own locality. And that is important to the toy robot argument. You say we know that toy robots have no feelings but you have zero evidence for that - precisely because the only evidence you could have would be based on inference from a theory, which you deny is going to be available for a millenium, since you cannot get empirical evidence. So you are making that up. But you are likely to be right because within a robot there is no individual dynamic event, or causal relation, the input to which would be an encoding of an idea with enough degrees of freedom to be a feeling of the range we feel we have.

So we have already mathematically modelled consciousness. We have an idea of how many degrees of freedom the input to a dynamic event must have to have a chance of experiencing and feeling like us (at least 100 and very likely 1000)

And to come back to boxes, the mistake that everyone is making that is the main reason why we do not have the necessary paradigm shift is that it is a person or a frog or a robot or a fly that hosts an experience, and in that meaning 'is conscious'. We know this is nonsense. Experiences are hosted by much much smaller domains within us and frogs and flies. It is very difficult to generate a model that involves more than 1000 neurons because it would just have far too many degrees of freedom. It is just as easy to build a model with less than 1000 and since it is even easier to do it with 1 then I think that is the way to go.

Consciousness is not spooky like time travel and cold fusion. It is a basic biological function here and now. I think I can dismiss all your arguments as prejudice and rhetoric. But I may be wrong, and welcome your defence. What puzzles me is why nobody young wants to play the game of solving this puzzle with some serious logical argument. Why is the younger generation not even prepared to get their hiking boots on when the mountains are calling? Life is short.

Dear All,

Regarding my engineering background I am not an expert of brain science however this topic has stimulated my receptors very much...

Excellent previous comments give answers to the question in some sense but Narasim's interest about this topic is not unique at all, and thus, there are plenty of unanswered questions around.

A recently appeared scientific topic, the Cognitive Infocommunications (http://www.coginfocom.hu/) and one of its branch the Cognitive Control (http://dx.doi.org/10.1109/CogInfoCom.2012.6422046) exploits the synergies of engineering and cognitive sciences in a practice-oriented way using mathematical abstractions of concepts related to consciousness and other complex biological systems.

Studying of Cognitive Infocommuncations might give some fresh input to the thinking about these serious questions.

http://www.coginfocom.hu

http://dx.doi.org/10.1109/CogInfoCom.2012.6422046

http://coginfocom.hu/documents/dissertation_Csapo.pdf

Thanks Jonathan for sharing your experience and thoughts .It is

Indeed inspiring and invigorating. With all the excellent comments

received so far I think it is possible to begin with a tentative  definition as suggested

 by one commenter.  It could be along the axioms of probability viz  define

Entity,World, nonlinear memory network, random combination,internal mapping

by Thanks once again.

Cheers

I am unable to edit/ correct my previous post .. it is incomplete.. my apologies

Cheers.

.. cont definition...AWARENESS,sensor inputs/outputs..

IMHO ...planes and rockets haave been developed inspired by birds flyiing . but flapping wings

was dropped early on.. same with wheels swift surface travel works on wheels ...so

Consciousness model need not mimic the brain exactly. I expect robots developed

using such a model would be more humanlike and intuitive...

Cheers

Dear all:

I propose my viewpoint about the mathematic model of consciousness.

Consciousness is physical states in brain or machanism.

The artificial consciousness might be more involed in digital ( discrete ) information , while, the natural (human and animals) consciousness is  less discrete information processing.

So human can definitly make or describe consciouosness with more digital information processing.The essence of consciousness iis isomorphism between elements like brain or softeware and objects beyond it.

See my isomorphic model of consciousness， the paper is attached here.It is published in

Proceedings - 2nd Asia International Conference on Modelling and Simulation, AMS 2008 , Pages:  574-578 , Article number:  4530539 , ISBN-13:  9780769531366

Thanks Yinsheng Zhang    I did use your idea of isomorhism in the

proposed definition above,,also awareness would imply that action due to

consciousness need not only result in pure  output only but could also be

like a feedback loop connected to input..The World can be defined as

a limited universe(as I think implied in your paper) like the sample space S in probability theory .An entity could be a mathematical object equipped with AWARENESS and nonlinear memory  network etc

Cheers

The crucial missing ingredient in the opening question of this topic is the definition of "consciousness".   Yinsheng, I have read your very interesting paper that defines, if I understand well, "conscious being" as something that can find a function that establishes a homomorphic mapping between two sets. However, I think this is too simple while I do not deny a certain charnm to the idea, but I think it should be pushed further. In the example of table and cup of tea it seems appealing but note that when it comes to groups elements are not important. They could be just numbers and a moderately intelligent computetr program might be able to do what you define as conscious action. 

For example, Google search can understand questions, syntax and many more things, is it conscious?

Then there is a question whether it takes a conscuousness to write a computer program (algorithm) that can mimic (simulate, model) consciousness ?

What bothers me with mathematical modeling of consciousness is that mathematical   logical Turing realizable by only 2-input AND and NOT gates. Would we accept that a large and complex enough network of logic AND and NOT gates posesses consciousness?

Or to formulate it witha question that concludes a song of Black Eyed Peas: "Is it all there is?"  

Dear all,

I am an engineer doing very practical developments in AI (expert systems), nothing near research about consciousness.

Of course I am very interested in this subject for even a small progress in this field may help me make better systems.

I was thinking about the difficulty an arthropod (say a centipede, a predator like us), after their first 130 million years of evolution (we, as primates, have no more than 13 million years of evolution, depending how you count them), would have to understand the level of consciousness and the cognitive powers a human, a species that would exist some 300 million years in their future would have. I am supposing we, primates and arthropods, are two points in an evolutionary tree and that we have much in common, like a nervous system ;) .

Maybe many people are not bothered at all when someone says it would be possible to model the consciousness of a centipede by a Turing machine. But then why would one be bothered if someone says it would be possible to model human consciousness alike.

In fact, I do have doubts if humans like the ones of the present will ever be able to have a complete understanding of what we call physics (dark matter and energy and what cames after). Maybe another species, superior to humans in this aspect, will be able to understand a little more. And then again…

If biology becomes ccomputer science then consciousness will be the field of  psychology. It is also possible that mathematics becomes philosophy. Consciousness is everything together.

@Mario Stipčević:

When I wrote that paper, I believed all the things of consciousness can be described by Turing computation, as Turing thought before. Now, as you mentioned , we should consider : is it true?  I noted a field in consciousness which cannot be described by Turing computation. That is somethings in consciousness like continuious processing, mainly involved in feeling.

In conclusion, homomorphism might be high layer's characteristics of consciousness. That is ,Turing or discrete models for consciousness might be a griddle， which bears holes, in which  consciousness exists truely. So Turing model might loss something in the holes. Just like that the number of points in a line is un-denumbered (not enumberred) by Turing computation.

If we take neurons as denumberred, then, we can think that counsciousness is denumbered so it is a Turing computed and descrete. Then my homomorphic model of consciousness is proper, which covers the discriptions of all phenomenon of consciousness for descrete neurons.

Quantum mechanics does not in any way provide an answer to the question "how does consciousness work". We do not know this answer yet. Can consciousness be mathematically modeled - sure it can, mathematics can model just about anything, depending on your perspective. I think the real question is, how can consciousness be implemented? It seems extremely likely that complex systems that does functionally do mathematics, is required to implement consciousness (if you mean consciousness as 'the ability to experience qualia'). We do not even have a theoretical understanding of HOW qualia is possible in principle, so it seems that asking questions about specifics of how and in what mediums it can be implemented is premature. 

 Marius thank you for a different perspective.It is indeed very interesting

to bring in qualia . For other possible commentators  I refer

to :

1.http://en.wikipedia.org/wiki/Qualia

2.http://plato.stanford.edu/entries/qualia/

from where I gather qualia refers to

quote"Philosophers often use the term ‘qualia’ (singular ‘quale’) to refer to the introspectively accessible, phenomenal aspects of our mental lives. In this broad sense of the term, it is difficult to deny that there are qualia. Disagreement typically centers on which mental states have qualia, whether qualia are intrinsic qualities of their bearers, and how qualia relate to the physical world both inside and outside the head. The status of qualia is hotly debated in philosophy largely because it is central to a proper understanding of the nature of consciousness. Qualia are at the very heart of the mind-body problem. "unquote.

 you are right ..the intention of the question is to practically implement

 consciousness in an engineering sense...and it is also true we

 model some phenomena with perhaps an incomplete

knowledge of the complete phenomena  by using an input/output model

IMHO.e.g

1. fuzzy logic

2. genetic algorithm

falls into such examples..

but as you state.. it would be great if qualia could also be modeled..

but first baby steps is I think to define a limited "world"

with known objects ..and entities..but capable of additions..

I think the model of Yinsheng Zhang  is a good beginning ....although it does not include  qualia...

Cheers

Hi,

I agree, we need to walk before we can run. And we need baby steps before we can even walk fully. For that reason, I absolutely agree that, in terms of the field of artificial intelligence, we need to define a limited "world", and work with that and see how much actual intelligence we can endow such limited systems with. And by that argument, well, consciousness itself, qualia, is running on an Olympic level :). It is not something we can do yet. We must thing about it yes, we must think about it all the time to find an explanation for this phenomenon. But yes, questions about modeling it, which is what the question is about, seems premature, if we do not even have an understanding of consciousness 'in principle'. Using the walking / running analogy, that seems to be like asking about building a robot that can run marathons, before we have even a slight comprehension of gravity, mass, and joints.

But yes - if the question is can we model intelligence in a computational device (a computer), the answer of course is, at least I am sure of this, is yes, of course we can (at least in principle. Perhaps we need technological advancements to do it in practice, today - but that is not the question (or maybe it is?)).

I have a question: what is the simplest system that, if you see it, you would attribute to it the property of 'intelligence'? I am very interested in this because of my personal research. I am looking into this to see if I can implement a system that most people would describe as possessing real intelligence.

Could you (and other readers) describe an example (probably behavioural?) minimal intelligent system?

Thank you for the reference to Yinsheng Zhang, I will have a look at his work, it sounds interesting.

Cheers!

As long as we get restrictions to ‘qualia’ all models loose there value.

The future will be about  creativity and feelings. What it is can never be said, the whole art is about expression of consciousness. The problem is who speaks the truth. The numbers can’t tell it anymore.

Rita , it is not suggested to restrict qualia.. but usual approaches

to engineering applications is to idealize .. and ignore.

imponderables initi ally.. but as to the future I am in complete

agreement .. the future .. will only be about creativity and

and feelings (emotions?)  if as predicted human beings

lose the race on "intelligence" to robots...

so.. maybe    extrapolating. your comment.. there is a yet to be discovered discipline...that combines art +mathematics...

Cheers

Marius Myburg,

You have posed a most interesting question ..viz intelligence..= useful system devoid of creativity  and feelings (emotions?)  (ref:Rita De Vuyst 

above)

..I hope there will be further contributions  on this from all..

..meanwhile I need to ponder..

Cheers

Please refer to URL

   http://www.churchmall.ca/item/kevin-t-favero/the-science-of-the-soul-scientific-evidence-of-human/110946.htm

as I would be interested in your views of Favero's  'theories' as expressed in his book.

Thank You

Bernard,

your link is dead:

THE PAGE YOU ARE LOOKING FOR DOES NOT EXIST OR HAS MOVED

Thanks , sorry about that, just Google     Kevin T Favero The Science of the Soul      and it will probably bring up Amazon US, but at least you can then read the reviews for what they are worth.

Thanks and good reading

Bernard McGarry

Dear All,

I note a certain dreariness and exhaustion in the various arguments promoting or not the possibility to mathematically model consciousness. I am not sure that we can find a simple yes or no answer to this query. In fact, as many of you have noticed, there have been several threads on RG that belabour similar questions, e.g. Is mathematics a human contrivance or is it innate to nature? or What are the advantages and what are the problems of the hypothesis about “retinoid system”? It is interesting to note that in most related discussions Gödel’s inconsistency theorem has been heavily debated in regard to its significance in both quantitative as well as qualitative research – including its specific threads that have been entirely devoted to the Gödel paradox!

Before giving my view, I am very thankful to you for the many excellent postings made here. I have learnt a lot. Nevertheless I have found some components in this discussion missing, in particular the science of biology based on Darwin’s paradigm, needs “more backing” from physics and chemistry. The conceptual development of biology, cf. the writings of the great Ernst Mayr, needs a physical law that accounts for e.g. the genetic code, or generally the teleonomical aspects of evolution. Finding such a law would go along way towards the goal of a positive answer to this present question. Yet I do not think we can do the modelling completely because of Gödel’s theorem.

In short my own suggestion to the formulation of a teleonomic dynamical  physical law gives insights as regards the genetic code and phenotypic information and furthermore on the communication aspects between molecular aggregates, cells, microtubules,  neurons, retinoid systems etc., see e.g. my RG page for more details. Lifting communication to the level of a physical law imparts codes of immaterial properties (qualia) but nevertheless the mathematical modelling of the latter including consciousness will stumble on the Gödel paradox, cf. Penrose book “Shadows …”

These and associated aspects have been discussed in particular in the thread Is mathematics a human contrivance or is it innate to nature?, see more below. Since I did put forward a consistent remark, based on the paradigm evolution, I did feel it appropriate to make a short appraisal of the discussion. Here it comes:

Summary from: Is mathematics a human contrivance or is it innate to nature?

 This thread with well over 4000 answers has been both dramatic and fascinating. I felt a certain responsibility to finish my interventions by some final remarks, since I have been one of the most articulate representative of an opinion in stark contrast to Derek Abbott’s view that “Mathematics is a human invention for describing patterns and regularities” excellently expressed in his POINT OF VIEW article “The Reasonable Ineffectiveness of Mathematics”, Proceedings of the IEEE 01/2013; 101(10): 2147 - 2153.

 It may sound perhaps a bit presumptuous of me to take on this job, but another alternative is of course be to write a new POINT OF VIEW article (an updated article is nevertheless under way) regarding the paradigm of evolution and the subsequent stance that support math’s innateness of nature without its Platonic characteristics.

RG threads (or other similar arenas) are like a specific life form by itself, a complex life form that consists of a collection of connected brains tied up via highly interacting Internet platforms like the RG social networking site. The material system comprises the member-brains, with senses “prolonged” by an enormous software development bringing fast and accurate tools to consumers providing indispensable and vital infrastructure for extended communication.

In analogy with the “selfish gene” that many scientists believe to drive evolution via the information inherent in the genetic code and translated into proteins by living cells, the thread is driven by the “selfish brain” translated to the social networking site via the English language. As evolution develops towards more diverse phenotypic assemblies, the “simple” genetic code evolves into higher order codes, where e.g. language is a member of this hierarchy. In one of its most original and trivial form simple mathematical structures serve as basic semiotic communicata for messages and their decoding instructions.

While the interactive instrumentation segment has increased exponentially due to vast technological advances, our physical theories do not say anything about the contents of the “living” thread. Here one meets the border that concerns Arnold (Arnold Trehub the “father” of the Retinoid theory) in particular as he promotes the retinoid system as a fundamental link between an anatomical sub-entity of the human brain and its subjective functions, where the present laws of physics are inadequate.

As macroscopic concepts as causality, subjectivity, objectivity etc., loose their meaning in the microscopic ranks a supplementary understanding is called for in order to incorporate a satisfactory fundamental description and associated worldview.  

Let me remind you of two basic lines in this thread. Is mathematics platonic in the sense that math structures like Pythagoras' theorem has a meaning when the physical universe has ceased to exist. If so the view is that math is innate. There is also the possibility that math as an immaterial part of universe is innate although it will not be platonic. It is no secret that the paradigm of evolution supports a non-platonic view of intrinsic mathematical innateness. 

As explained earlier, the living system requires a fundamental formulation of open dissipative systems. From the inner subjective level to the outer, Gödel’s selfreferential characteristics mandate a direct connection with the cosmological arena.

Combining the present paradigm of evolution with operator arrays in a non-Hermitian setting yields a very simple space-time independent formulation in concert with Einstein’s laws. The environment to our Universe is bequeathed by black hole like objects from which the material and immaterial world is created. Since all we know of the “black hole” is its rotational energy (given by the Kerr metric) its undefined angular momentum direction imparts a given orientation (the conjugate entity). If you prefer a multiverse scenario these “black holes” serve as “selfish germs” for “phenotypic” universes, whose information content is only known to its communicating life forms.

 Hence the discussions regarding the relevance, accuracy, precision, patterns, isomorphisms ….., that we can use in our communication with our invironment using math, language, music, art, poetry is not the central point, however, interesting in itself. It is also beside the point whether math took its present form after the humans entered the scene. Rather it is the fact that “Communication” does exist as a physical law as I have written in my earlier comments on this thread. The immaterial is conjugate to the material world hence there is a certain ontology that goes beyond a conventional epistemic interpretations. The clue here is the self-referential property that guides evolution as a teleodynamic process.

With these analogies it follows, cf. Max Tegmark’s mathematical universe that math is an innate structure of the immaterial (and material) world, but in contrast to the former it is not a Platonic Eternal Universe!

There are so many brilliant thoughts in this thread  and indeed great food for the mind..

and particularly fascinating is the new insight that each input brings.... and my thanks to everyone..Erkki J. Brändas (thanks) detailed comments was heavy going ..but with due

apologies .my paraphrasing of it in the present context is .. mathematics is the

 bridge between Platonic idea of inner world ( maybe qualia ) with Stoicism

which deals with influence of external  reality .. Applying then this idea

to the model of  Yinsheng Zhang  it seems the proposal of implementing

 a" limited inner  world " (defined by us as creator?) and  isomorphing

 this to an external world using the idea  of Awareness  could move the

discussion to a usable mathematical theory.. because of the "teleodynamic process"

 stated above.

.would welcome corrections and modifications of the same

Cheers..

Dear Narasim,

I would add to your comment that I promote monism in that the material and immaterial worlds are entangled. This implies that the Platonic characteristic of eternality does not hold, since “our” universe is created and will end (materially-immaterially) without one or the other being split with “infinite” existence.

I agree with Jonathan Edwards and others about the critique of Hoffman’s (MUI) Multimodal User Interface theory. The latter is indeed very interesting, since it does not claim that perception should resemble the “objective world” (which is hence not definable) and that conscious experiences are fundamental. Hence he introduces the concept of user interface and launches a mathematically precise theory of conscious experiences in terms of conscious agents and their dynamics thereby making empirically testable predictions. In this ontology evolution concern conscious agents with all their intrinsic complexities thereby avoiding interpreting natural selection from a physicalist perspective including the existence of an observer independent physical world, while still being consistent with quantum theory.

Hoffman then establishes precise connections with modern concepts of theoretical physics by e.g. portraying well-known equations of physics with new interpretations from conscious realism.

This approach is of course not better nor worse than the hypothesis of faithful depiction. It only transfers the problem from one corner to another in the hope of gaining more insights and understanding of the underlying Mind-Body Problem. However both approaches will run into inconsistencies of the Gödel conundrum, since it does not incorporate the necessary self-referential trait, cf. Penrose’s “Shadows …”  

I cannot see that Tonino’s integrated information theory (see also Maguire et al.) will do the job either. The integrated information concept will be too imprecise to catch the qualia of a particular experience since it will not be “immune” against inconsistencies emerging from self-references, the Gödel paradox.

Perhaps Arnold Trehub’s Retinoid Theory might provide an interesting avenue, but it needs to be accompanied by a self-referential property that provides qualitative elucidations of the mechanism of consciousness.

As I got a down vote for my remark that the ‘quality’ never can be put in a mathematical model I must say that I am not agree with the sentence of Narasim Ramesh.

‘Mathematics as the bridge between the platonic idea of inner world with the stoicism which deals with influence of external reality…applying this to the model of Zang of implementing a limited inner world….’

The world of Plato is not so easy understood and neither is the stoicism. Both teachings were secret and still are. The definition of archetypes does not exist let stand the working out.

(The archetypes are connected with synchronicity as nonlocality). If that mechanism is better understood which, indeed I have found in art and creativity, we can turn towards consciousness.

Also the platonic ideas and the stoicism are too often be seen as opposites, in the ground they are meeting on the deepest level.

So all this can never be connected to a ‘limited inner world’, they are just the whole.

As Erkki Brändas quoted: it is no secret that the paradigm of evolution supports a non-platonic view of intrinsic mathematical innateness.

I just came across the words of Whitehead: that the European philosophy could best be described as a footnote by the oeuvre of Plato.

What I like from Erkki is that: mathematics can serve as basic semiotic communicator for messages and their decoding instructions.

The language of mathematics is very rich and can suggest very special things. It is indeed valuable to search for some connections.

What triggers my interest about the world of Pythagoras is how the colours of musical notes and mathematics are  related? This is an issue I really want to know.

In consciousness we never can lose track of Plato, and instead of Darwin’s evolution, driven by chance I should like to see the evolution driven by premonitions.

.Rita De Vuyst...Thank you .I consider all inputs highly valuable..... art is not an easy subject to comprehend....(at least for me)

 nevertheless fascinating ..the "limited world" referred to is not in the philosophical sense

 but more as small scale model of reality . for actual simulation....  IMHO (open to correction) 

1. the intent is to" search for valuable connections" as mentioned between awareness and response to be incorporated in a non biological entity..perhaps if we

compare to other fields...there was "heart transplant" replaced by pumps..,

electrical pacers replacing innate generators, exoskeleton robots..etc one may

thus extrapolate  to either a robot (endowed with consciousness ) or enhancement

of human consciousness by  other than chemical (cannabis) methods....

2.Actually your view point raises even further questions.viz Is consciouness

an external universal phenomena or is it individual? do animals experience

consciousness..(depends I suppose on the definition) .. I did find the

there are computer  programs which show how a scene appears to

a dog compared to a human being .. but can we be sure it is so?

3. Finally .. pursuing your idea further.. maybe the robot should

   have an organic (or quantum computer?) to actually simulate consciousness..

 because after all "thought" does not require all the addendum of

limbs, digestion etc  but only the "brain"( a collection of highly complex interconnected neurons with external sensor inputs as well as innate

trigger sources...which  brings us back to a possibility of a model..

Thank you once again for valuable inputs and enlarging the discussion ..

 Cheers

neurons

Rita De Vuyst...Further your comment "What triggers my interest about the world of Pythagoras is how the colours of musical notes and mathematics are related?" is indeed very intriguing and very interesting. . would you care to open a thread with some explanation

 Cheers

Dear Narasim,

Rita correctly spotted the “mistake” in your remark regarding mathematics. It can certainly be a bridge, but not between metaphysical ideas, but between life forms as they evolve teleonomically. The quintessence of these various practises of communication and their psychological processes are certainly not driven by chance, but my vocabulary is a bit different from Rita.

Narasim, you seem to have some problems with the editing of your postings. Perhaps the RG helpdesk can help you.

Best

erkki

Dear Erkki J. Brändas 

Thank you for your remarks and observations. I have a question( cf Rita De Vuyst) as quote "Also the platonic ideas and the stoicism are too often be seen as opposites, in the ground they are meeting on the deepest level.". How can  they meet unless there are laws that can be interpreted mathematically? . I am assuming that mathematics

is a mechanism to identify patterns and their connections .As an example, if we

 look at a painting, it is in digital form , a matrix of pixel values (Linear algebra)).Now

this painting is a result of the operations inside an artist's mind. The painting itself is

a manifestation of ideas from the inner world of the artist to others in the external world . Is mathematics then not connecting ideas?

Hopefully my future comments would be more presentable and neat. .

Cheers

narsim

My apologies for some reason the sentences break up after adding my comments..

 Cheers

narsim..

Why not write and edit your comment as e.g a wordfile etc. and then paste the result on RG!

Narasim,

You are correct that mathematics can be used to connect ideas if the interpretation is a manifestation of communication between life forms. Note, however, that "ideas" here refers to a non-Platonic concept commensurate with evolution.

Best

erkki

Erkki

 Thank you very much. I used to copy and paste but sometimes on Tablets

 it was not easy and even after pasting (I use Open Office  ) the pasted output is not   neat, but your suggestion is well taken.

Thanks once again

 Cheers

narsim

Just found this discussion. Reading through ..particularly  Jonathon Edwards' posts.

I originally though that consciousness would defy mathematical modelling. But perhaps not. In signal processing problems where feedback is often used to form  recurrent relations for filters and given that it is a real-time input dominated (sensor orientated ) system then perhaps we can describe the expected form of the modelling. 

1) It would be a bulk effect style of modelling (eg statistical, state based)

2) ... represented in recursive forms such as recurrent relations ( feedback modelling),

3) ...It would require a kind of linear basis approach to map on to regions of control

4) ... output could be functional so that it would map onto emitted responses

5) ... the models would tend to be heuristic (local optimisation rather than definitive (logical))

Thus we use:

  Responset1  => Contextt0 + Inputt0 + Responset0    (subscripts are successive time intervals)

or

Responset1 + Contextt1 => Contextt0 + Inputt0 + Responset0

=> implies (associative/states + transitions)

Where the terms are basis sets defining states

The Context defines a collection of states occurring at a given moment and includes the observer which implies consciousness (self referential feedback)

If we can define the form of the model then we might progress ... ?

Thanks John David Sanders

Your suggestion would seem to concur with the model of Yinsheng Zhang · '

Would urge you to see a brilliant lecture by Donald Hoffman

at https://www.youtube.com/watch?v=dqDP34a-epI 

pointed out by by [Vahid Bastani]

Cheers

narsim

Here is an interesting news item

at

http://www.eetimes.com/document.asp?doc_id=1323441&_mc=RSS_EET_EDT&elq=7f4e3752465b4bb79055b4c56198838f&elqCampaignId=18479

quote"

The most brain-like computer chip to date has been produced by IBM for the Defense Advanced Research Project Agency's (DARPA's) Systems of Neuromorphic Adaptive Plastic Scalable Electronics (SyNAPSE) program, in collaboration with Cornell Tech and iniLabs, Ltd.

"When the SyNAPSE project was launched six years ago, many people thought it was impossible," Dharmendra Modha, an IBM fellow and chief scientist of brain-inspired Computing at IBM Research, told EE Times. "But today we have proven that it is possible, and we are working toward making it a commercial reality in the future."

The IBM SyNAPSE chip has 1 million artificial neurons (brain-like cells) and 256 million synapses (storage cells), all powered by 4,096 neurosynaptic cores integrating memory, computation, communication, and operating in an asynchronous event-driven, parallel, and fault-tolerant manner." unquote

Dear John,

The parameters you suggest for modelling seem rather too abstract to me. I would prefer to start with known neurophysiological processes, since these are likely to be quite unlike anything in a computer. For instance, I doubt that the idea of 'states' is much use for brains since there are no fixed time frames. Shifting salience in feedforward signalling may, for instance, depend on transgression of temporarily established cycle locking for a local set of pathways, with time frames in other parts of brain proceeding independently. I am not sure what 'bulk effects' would be in terms of post synaptic integration in individual dendritic trees. The interesting part of the mathematics that at present is missing is that of PSP integration in real time on a background of a refractory cycle. The equations you give would have an applicability to individual neurons but I am not sure what they would mean for a whole brain. And I am not clear why consciousness would entail self referential feedback although reporting of it would require feedback in terms of retrieving previous input patterns. For me consciousness has little or nothing to do with intelligence. It doesn't really require any output at all since you can have it while lying paralysed in an anaesthetic room or just browsing RG questions of lesser interest. But I realise that other people use the word differently.

Dear Narasim,

This machine sounds impressive, but given, as indicated above, that consciousness does not necessarily imply anything about output I wonder if this machine tells us anything about the mathematics of consciousness. If it is based in silicon then the maximum complexity of any input to any juncture is two bits. To my mind that bears no relation to a brain where there are junctures that have 40,000 input channels - presumably the source of the great richness and variety of our experiences. I personally see little or no prospect of understanding our own consciousness through playing with machines that we know have fundamentally different microdynamics.

Thanks Narasim for the info regarding the SyNAPSE project. It is certainly interesting and will be very useful in modelling complex system performances.

However, and this concerns also John, Yinsheng and others, proposing new strategies, increased performances and other schemes for carrying out the “hypothesis of faithful depiction”, the modelling needs conscious agents (to use the vocabulary of Don Hoffman). Hence the “difficulty” is just transferred to another “corner”.

As I have advocated before, we lack a physical principle that extends standard physical laws (so-called teleomatic ones in the words of Ernst Mayr) to teleonomic ones, i.e. those processes that evolves governed by a program, cf. the genetic code.

Even if such a physical law would exist (there are some work done here) the mapping between the inner and the outer reality becomes subject to Gödel’s paradox, cf. Penrose etc.

Nevertheless building a “communication level” between the “subjective-” and the “objective reality” would go a long way towards unravelling the understanding of life forms in general and consciousness in particular. However, we will not be able to completely model consciousness mathematically from top to bottom even if we could disentangle the communication aspects of biological systems.

Thanks and indebted to Jonathan Edwards and Erkki J. Brändas for

their valued views .I have a question . Is it valid to think of an individual

biological  cell as possessing consciousness :? It is known (open to correction) that

even trees/plants respond to stimuli.There are two other questions  which

seem to surface..viz Is consciousness a function of numerical complexity ?

Is it transmission of information at infinite speeds that causes consciousness 

(I have in mind quantum computers which are supposed to be the ultimate

 cryptographically  secure systems).

Cheers

Dear Narasim,

You have several questions it seems ! I will answer them for you.

Is it valid to think of a cell as conscious? Note that consciousness has nothing to do with responding - that is just our usual way of telling if something is conscious. As a physician I have often had to judge consciousness in those who cannot respond in the usual ways. Consciousness is about input, not output.

Consciousness is a -ness property like hardness or happiness. It is not a substance but a dispositional aspect of an entity. It is nothing in addition to that entity.

Consciousness as commonly conceived has to be broken down into two aspects. The first is the 'having of experience' that was 'cogito' for Descartes. The second is that the only experiences we talk about are of a very special type that benefit from a vastly complex collating, focusing and integrating sensory machine that presents whatever has experience (some part of the brain) with a 'narrative' of the world pre-constructed in terms of complex concepts like objects and movements and expectations of contingency and continuation. Thus, these two aspects of consciousness imply two quite different sorts of entity or aggregate 'system' - the experiencing unit and a feeder sensory system. Nothing can be a property of both, so 'consciousness' as we usually talk about it is a confused idea. The experiencing unit is conscious in the sense of having the sort of experience we talk about but we are used to applying the term 'conscious' to the whole aggregate of not just the sensory system but the active body that goes with it.

So in common parlance a person is conscious, but it is not a person that has the sort of experience we talk of when we say we are conscious and Descartes talked of. Descartes rightly realised that what has the experience must be some small inner entity or soul that is fed by sensory pathways and memory. Modern neurology confirms this amply but ironically it is fashionable to deny that there is any inner receiving entity. This must be complete nonsense because if signals in the brain are not received by anything they are not even worth calling signals. 

In my view, and that of Steven Sevush in Miami, Decartes mistake was not to propose an inner experiencing unit but to suggest that there is only one. We now know that there is no one unit in a brain that receives sensory signals - there are millions. And they are neurons. Nothing else other than individual neurons receives signals in brains so it must be the neurons that experience. This might seem too simple but I don't think it is. It is a conclusion that people like Leibniz, Herbart, Lotze, and William James have come to repeatedly over the centuries and it is, as James says, the only view that is not self-contradictory. It is just very hard for people to believe that there is no single 'me' in a body. The objection to the right model is not a scientific one. It is purely an emotional one.

This is just a very brief explanation of why it is valid to say that a cell is 'conscious' at least in Descartes's sense - and that 'persons' are not conscious in this sense. The detail is given on my UCL website and in various publications that are linked to my RG site.

The answer to your second question, Narasim, must, I think, be that the richness of a conscious experience necessitates some richness of causal dynamics (or physics) of the input. Without knowing exactly what physics we are dealing with it is hard to say much more, but I think one can require that the input must have enough degrees of freedom to be able to specify all the different experiences we seem to have. So if we have inputs that are 'on or off' or binary then for 1024 experiences we need 10 independent binary input channels. Neurons have up to 40,000 more or less binary input channels so the potential for richness looks pretty good. As Masataka Watanabe pointed out on another thread, a lot of synaptic activity is noisy so we might need redundancy. This introduces the additional idea that the 'grain' of experience may not just be the number of degrees of freedom of input but a function of the way those degrees of freedom couple to the dynamics of integration - which might for instance operate on bunches of 10 inputs. The model I am personally interested in involves electromechanical coupling between electrostatic potentials and an acoustic waveform and that might depend on the wavelength of the acoustic mode. So this is where I see mathematics modelling consciousness in some considerable detail.

The idea that one can produce a mathematical estimate of the richness of consciousness has of course also been raised by Tononi. However, his numerical measure, or Phi, of consciousness does not seem to relate to anything actually experiencing anything and I am doubtful it can predict anything empirically testable. In IIT 3.0 he uses models of the sort seen in computer based automata but at the end of his account he admits that this cannot be applied to brains.

The answer to the third question, I would suspect, is that conscious experience is based on the standard fundamental interactions that go on in condensed matter. Few people are aware that the ordinary dynamic events in everyday materials are hugely complex and can readily provide the sort of richness we find in experience without any need to call for entanglement or Bose Einstein condensation or other abstruse occurrences at absolute zero.

The basic puzzle is explored by Leibniz - how does a single entity consist of a 'point of view' that can experience simultaneously perhaps 1000 independent features of its environment? Leibniz suggests that the answer must be something like a point with rays of light passing through it at many different angles. However, Leibniz simply used this as an analogy because he knew it was wrong. He knew that fundamental entities are not physical points - he knew that they have internal complexity. Fortunately, modern physics solves his riddle because we now know that fundamental entities are indeed internally complex and that they are modes of excitation based on complex oscillatory patterns in a domain of spacetime coupled to an environment of potentials. What recent condensed matter physics has shown is that many familiar everyday events are in fact based directly on fundamental modes. The formation of a symmetrical ice crystal depends on modes that occupy the whole crystal. Conduction of electricity in a wire depends on electron modes that occupy the whole wire. Reflection by a mirror involves modes that specify the 'flatness' of the surface. Sound waves are indivisible modes. 

So we have a way to resolve Leibniz's puzzle. We can expect experience to be the interaction of a mode distributed over a domain of space with the potentials it encounters in that space. This is described on my website in 'Mohammed must go to the Mountain'. A cell membrane can support modes that can interact with electrical potentials distributed over it. There is no 'non-local' Einstein Podolsky Rosen type weirdness about this. In fact it can all be described in nineteenth century physics without any reference to the oddities of the quantum level - bar one. The one feature of the quantum level that it requires is that of dynamic indivisibility. It is no good if there are two modes, each interacting with half of the potentials. But the principle of indivisibility is not actually so threatening since even in classical mechanics and statistical thermodynamics the indivisibility of modes of oscillation is implicit.

In the end the modern approach leaves us with something reassuringly like everyday objects. Even tables and chairs have modes that make them 'objects' in the familiar sense. 

So, for the reasons given, I do not think that models built out of silicon chips in which the informational interactions are not rich in this way but have deliberately been broken up into events with only two degrees of freedom, can tell us anything at all about consciousness.

Dear Jonathan

I am extremely grateful for  a patient and highly valuable insight

on so many aspects. It requires considerable effort and pondering , at least for me.

but it is exciting and mind expanding.and without doubt highly rewarding.I am at the biblical age limit so these ideas are even more fascinating. .Thank you very much indeed..

 Cheers

Narsim

Dear Narasim,

Again I like your questions very much! I also appreciate the amount of efforts that Professor Jonathan Edwards has provided to explain and sort out the various levels of understanding from his vast experience at the UCL’s Department of Medicine.

As my background is quite different (theoretical chemical physics), I can at best try to add some angles from my own arena (see e.g.my “The Statement of Goals of the International Society for Theoretical Chemical Physics” on my RG page).

1. Is it valid to think of an individual biological cell as possessing consciousness :?

Let me start at a less ambitious level and ask whether cells communicate. This is easier to answer since (i) communication is a fundamental concept that covers as well as demands a deeper and philosophical understanding at all levels of physical, chemical and biological (even social) processes (ii) communication appears between various parts of a microscopic biological system, e.g. to interpret single-molecule-information transfer or in understanding molecular, enzymatic and protein catalytic properties of biological systems. Hence communication and pattern recognition play a decisive role in the specific evolution of the cell. Concepts such as microtubules, spindles, molecular propellers etc., are contained in biological information systems governing the conversion of chemical energy to mechanical energy.

Although consciousness emerges as a dynamic property of communication, I am not in favour of defining consciousness as a stationary state. Biological evolution generally appears to be a dynamic teleonomic process that continues until the life form is dead.

2. Is consciousness a function of numerical complexity ?

Obviously a complex enough system must be able to communicate at such a high level, being perhaps intelligent enough, to pick out, to discern, distinguish, differentiate and recognize and understand something in order to evolve successfully. This calls for “numerical complexity” in terms of encoding and decoding purposes. Metaphorically the cell can be imagined as a tuning fork coupled to a resonance box, i.e. the cell confinement containing the cell nucleus. Like a Q factor of a resonant systems relative band width, a cells Q-value would depend on the actual position of the cell in the hierarchy of the organism and the corresponding assignment for the business of building material structures of a particular kind. As an example one might consider nerve cells or neurons, which regulates the flow of information from sensory input to motor output, via the production of appropriate neurotransmitters.

3. Is it transmission of information at infinite speeds that causes consciousness ?

I understand that your reference to infinite speed implies a hidden question whether quantum mechanics may play a fundamental role in understanding consciousness.

Let me first talk about transmission of information. As I understand it a central question in cognitive neuroscience is the way the collection of neurons combines external signals with internal memories.

One strategy would be to study quantum aspects of chaotic neuron dynamics, see e.g. Arecchi, F. T., (2003): Chaotic Neuron Dynamics, Synchronization, and Feature Binding: Quantum Aspects. Mind and Matter 1, 15-43, where he puts forward a novel conjecture in terms of homoclinic chaotic systems and studied the Feature Binding Problem, finding that mutual synchronizations of spike trains may contribute to well-defined perceptions. This conjecture is of great interest but it is wanting in the verification of an explicit code.

A stumbling problem when applying quantum mechanics to molecular evolution in e.g. the brain is the wet and warm environment that inevitably seem to prohibit quantum phenomena due to the phenomenon of decoherence. Traditional quantum mechanics for isolated systems are therefore useless and modern non-hermitean quantum theories for dissipative (open) systems are mandatory! I have advanced some explicit suggestions in this regard on my RG page.

One might consider, as already suggested, that consciousness emerges as dynamic property of “microscopic communication”.

Dear Erkki.

 Thank you very much .It is with much pleasure I read your prized insights.You were right about the intention "hidden question whether quantum mechanics may play a fundamental role in understanding consciousness."..it still fascinates and intrigues me especially when it is said observation changes the state of an inanimate(?)entity , so we can never know what existed prior to observation I suppose..

Especially I am attracted to your description "consciousness emerges as a dynamic property of communication" which brings me to another question viz does consciousness end with biological life termination? I am conscious(?) that this treads on other areas besides science , but my question posed is intended in a purely objective(?) scientific sense..

 I am grateful for your patience and time.

(I did the opposite by copying and pasting in 'word ' to clean up and edit and then

pasting here ). Hope  this is more presentable.

Cheers

Dear Narasim,

Thanks for your insistence and clarification regarding your question.

My simple vision, of course brought about by investigating chemical and physical problems based fundamentally on quantum mechanics, but also with a focus on the border territory where the classical and the quantum meet, imparts a communication level that bridges the inner subjective core with the outer “objective reality”.

While it might now and then appear a hopeless endeavour it nevertheless brings about surprises that gives novel insights and practises that might at the end become beneficial to mankind, cf. Prof. Edwards treatment of patients suffering from rheumatoid arthritis.

I bring this example up since there are those who does not believe medicine to be scientific, see e.g. Clifford Miller

https://www.researchgate.net/public...Knowledge-based_Medicine?ev=prf_pub

 Medicine is not science: Guessing the Future, Predicting the past. Introducing Knowledge-based Medicine.

Best regards

erkki

Dear Erkki

 Thank you very much .I am grateful  for all your answers and your patience.

Cheers

narsim

In 1970 Jacques Monod wrote: “In the course of three centuries, science founded upon the postulate of objectivity, has won its place in society – in men’s practice, but not in their hearts.

Armed with all the powers, enjoying all the riches they awe to science, our societies are still trying to live by and to teach systems of values already blasted at the root by science itself.

For the first time in history, a civilisation is trying to shape itself while clinging desperately to the animist tradition in an effort to justify its values, and at the same time abandoning it as the source of knowledge of truth.

The divorce science-society, is so great, the lie so fragrant, that it can only obsess and lacerate (torture) anyone who has some culture or intelligence,, or is moved by that moral questioning which is the source of all creativity.”

 Thinking about consciousness; it is the same where we start, we end up in the universe as a whole. I always want to widen the circle except for concentration, the focusing which is important for vectoring the attention.

Everything fuses into consciousness so also the unconscious, the implicate levels, mathematics, art and mystic. The more elements we absorb, the higher the semantic value, the richer the output in creativity of science, art and daily life.

Indeed consciousness has no limits in time and space, it is nonlocal, so it transcends life and dead.

As Plato is still at the core of the problem it means that his consciousness is lingering on as he invented the ‘ideas’ which are eternal.

It is not that the cell has a certain consciousness on its own, also the particles, elements and proteins must be governed by an information wave. If the nature of that wave could be found, we would have a better insight into the psychology of Jung, the I Ching, intuition and premonition.

 My personal idea is that consciousness can in special situations synchronise events, the same as the cell is synchronising the production of proteins and her reproduction.

That leads to the idea if the cell could not be better equipped as human beings to regulate her mission. This idea supports the depressive idea of Monod considering society.

 If I copy right Erkki Brändas:

"The immaterial is conjugate to the material world, hence there is a certain ontology that goes beyond a conventional epistemic interpretation. The clue here is the self-referential property that guides evolution as a teleodynamic process.

The paradigm of evolution that supports a non-platonic view of intrinsic mathematical innateness."

 I think that mathematics were platonic in the time of Pythagoras and Plato; in that time numbers had a quality, they were divine. Now scientists are searching to integrate all these qualities consciousness has conserved in art and mystics.

In this process the philosophy of science stumbles over the ‘goal’ and the ‘end’.

Teleological processes can be discussed till the infinite.  There are external teleological and internal teleological explanations, again Plato and Aristotle are opposite poles.

Teleonomic stands for goal seeking, teleomatic for not goal seeking, there is an adopted system for survival and a cosmic teleology.

The content of our personal goals covers a big part of consciousness.

So for  modelling  consciousness the main question will be which values we put into the system and which rhythm; without the good, the honest, the wisdom, and the Eros of Plato the goal will not be reached.

What Pythagoras is concerned, I didn’t unravelled yet. I wait until a mathematician will find the connection between colours, the rhythm of numbers and musical notes. The fact is that some musicians are seeing the colour of music.