As per my understanding, brain is objective in nature whereas mind is subjective. Although we can model an objective quantity (as it is quantifiable) in terms of numbers. So use of real numbers to model brain seems to be justified. But as mind is subjective in nature, I am unable to understand it to be quantified and represented in terms of numbers anyhow. If I am hell-bound to model it in terms of numbers, I'd model it in terms of complex numbers. So smaller or greater mind type phenomenon wouldn't exist.

Regards, Manish

Not sure how subjective and objective imply use of real or complex numbers. Remember the words 'real' and 'imaginary' when applied to numbers do not have the same meaning as they do in English. Similarly, -4 is not worse than +4, and pi doesn't act in any less rational a way than 42. 

Very interesting philosophical question ! Maybe my answer is very strange? But "the number" is a human invention. Perhaps there are ways to describe the processes in nature without our "numbers".

I believe that the modeling of the brain and mind with the use of numbers has the problem mainly in the definitions of modeled structures and processes. Many phenomena once considered impossible to understand and modeling, later had became somehow understandable and then modeled more and more accurately (e.g. such as lightning, tornado, earthquake, etc.)

It seems to me that the main problem is not the mathematical apparatus. For the simulation of those examples - lightning etc there were no need to invent a new kind of numbers. But a new hypothesis was absolutely necessary. The main problem in all these cases was the development of a working hypothesis, the numbering of which became the creation of quantitative model of the phenomenon. We must develop new hypothesis that explain the functioning of the phenomenon under study: patterns of development and change, spontaneous action, response to external stimuli etc. That hypothesis may be seen as qualitative model, the necessary stage for preparing quantitative model. That way successfully worked on all natural phenomena. Why not on brain and mind?

In other words, building a hypothesis (qualitative modeling with notions) is a necessary step for the transition to a more accurate quantitative modeling (with numbers). Both notions and numbers are invented by man to describe events, so I do not think that the manipulation with numbers is radically different from the same with notions. Rather, these are different levels of accuracy of one description, and without sufficiently complete and consistent description of phenomena in the "rough" notions, we can not move to a more accurate description in numbers.

Dear Sergey, in principle you are right, however we have external quantitative data about tornado (output). We can model decision making process using expert knowledge and discrete mathematics. I am not sure that  we can build mathematical model which will connect between input and output of our brain. It is similar to  a man who is trying to pull itself out of the water by the hair. May be my answer is wrong according to the epistemology. Joseph

Yes, Joseph, I agree, the system can not know itself and can not know a more complex system.

But we can know the principles of the elements and its functions in a complex system, and to know more simple system that works on the same principles. I believe that we can simulate a very simple "mini-mind», which has the same functional structure of elements as our mind. To do that we have to develop some theory of basic structural and functional elements of the mind and to prepare in the model some set of such elements. Then we may see if laws of the life (interactions, development etc) of that model are similar to laws of the real mind (psychological laws)? When we see similarity, we may believe that we on the right way. Is this approach correct from your point of view?

One of the main functional principles of the mind, from my point of view, is self-organization (of the mind itself and of its new structures). When we agree with this, then we have an additional criterion of proximity to reality and our task is simplified :-). It is enough to create some functional elements and look at their self-organization. The more elements, the self-organization is becoming more spontaneous, unpredictable and interesting...

Dear Sergey thank you for this interesting answer!

The most important issue is the self-organization of our mind and especially of the memory. A very simple e.g. : someone forgot the phone number and suddenly he remembered. How does he know that this is the exact number ? 

Maybe we have "super memory"? .We can restore our memory? 

I do not deny the presence of external memory though I'm an atheist.

Nice question. I would say yes to both. If you can measure it you can use numbers. Now the question is: what do you want to measure? In the case of the brain it is possible to quantify volume, number of cells of any structure, synapses… For the mind, I understand that we’re talking about cognitive processes depending on the brain function. There you can choose if you want to measure memory, attention, perception… As far as you can measure it you can use numbers. However, if you’re talking about subjective experiences, that can’t be measured and it can’t be treated scientifically (how could I know that my experience of “red color” is similar to yours?).

Yes, we can not measure my and your subjective feeling of red color as one and the same phenomenon.

But we can measure the subjective feeling of the same objective events (e.g., the presence or absence of the red circle). If one and the same object we both identified as specified for the search red circle, it is comparable and countable events. Further, we can detect and measure quantitative indicators of subjective events - the time of origin (from stimulus presentation), frequency of identification, error rate, etc. Thus, for subjective events related to objective world, we can use completely objective measurement units.

Moreover, in the subjective world we may use corresponding subjective countable units. They may be some "standard unit" that are subjective but "standardized" in human notions. For example, those may be images of abstract sets (1, 2, 3 …) and geometric shapes (as units of subjective number and volume), the images of logical operations (as units of movement and transformation of the subjective world), images of sequences of perceptual, logical, emotional and other subjective events (as subjective time units) etc. We may detect and measure these events in a binary format (on/off or 0/1), and therefore, in any other numerical format.

These measurements can be performed both on the person and on the model. The difficulty of measuring subjective phenomena in the model is that the model can not "tell" of their subjective world with the human language. But this is not a problem, many studied phenomena can not tell us anything. And we often use the knowledge and new theories to define something that we can not observe (for example, the internal structure of the Sun). The main problem is the presence of any theory that will allow us to draw conclusions about subjective events that corresponds to any state of the model. If the model is based on the theory that determines not "stimulus” and “reaction", but the subjective (informational) processes in the model, the same theory will allow us to draw conclusions about the subjective world of the model in every it’s condition. Compared with the study of the human the model has a great advantage: we can stop the model and measure the detailed "snapshot" of the state of its physical structure and the subjective world. Many psychologists probably dream about such a possibility in experimental psychology :-) And even if that subjective world will consists of several simple images in simple model system, it may be interesting and perspective.

The starting place of course is the conceptual definition of what you understand the brain and mind to be and thus what they can and cannot enact, and then what you believe are the actual dynamics in and through which the resulting 'objective' or 'subjective' behaviour is triggered - before attending to any attempt to then model the dimensions and contents of an emergent gestalt.

Starting with concepts that suggest the brain is objective whilst the mind is subjective seems to muddle up the categories you might wish to portray with your modelling. What about the proposition (albeit a very dangerous and disruptive idea!) that the brain is the organ in and through which fired emissions emerge, and that the human perspective of mind is much like an instrument in and through which a perception comes forth. Thus, it is the experienced form of the contents which can then be modelled or mapped, both in its internal dimensions and a possible rate of formed shift - which would thus represent the actual shift in the person's living system or psyche as that gestalt had been fired.

This generative approach then opens the question to study through modelling with two different aspects:

(I) What sets up the generative dynamic behind an emergent emission (this could be modelled in terms of a diagram that represents the actions): and

(ii) What kind of 'constructors' or principles would dictate the emergent shape and the flow of a realised perception - and could these be modelled in forms that have certain geometric dimensions or laws to which the domain of numbers apply.

Deutsch has been exploring this question of 'constructors' or principles (see recent communication at: http://edge.org/conversation/constructor-theory). I'm working on a means of explaining these two questions above that could also explain how the actual geometric dimensions of all spatial arrangements and phased shifting in physics could have come into existence originally, however the doctoral thesis is drafted but not yet examined - so 'watch this space' as they say with an enquiring perspective of mind

The discussion really has multiple levels and it is important to distinguish between them. For example, there are mental representations, which can be modeled using well-defined systems incorporating either rule-based principles or probabilistic information (i.e. NNets, SOMs, etc.). The modeling of decision processes can also be accomplished this way. Those seem to be somewhat static entities compared to the qualia associated with the hard problem of consciousness. Though I don't take Penrose's grim view of the inability to describe consciousness with a Universal Turing Machine, I do believe that the ability to describe the whole of consciousness lies with a fundamental shift in the understanding of