I want to discuss a hypothetical understanding of the functioning of a simple brain. This is not based on a detailed understanding of biology. I work as a programmer, with an interest in Mathematics and Logic, and an amateur knowledge of biology. This started with a philosophical, perhaps science-fiction concept regarding "mirroring" the universe, it had nothing to do with reality, until I made, or more correctly realized, an extremely simple observation. An observation that takes more time to explain than I would expect when I sat down to write, but is easy enough to understand once understood.

At a fundamental level, the set of cells in a creature that respond to their surroundings form a model of the creature's surroundings. This certainly includes the nerve cells, and I will mention them below, but other parts of the creature are also part of this model and may play a part, rather like anchors or buffers, constraining the overall behaviour of the nerve cells.

First I must build up an understanding of this observation. To start this analysis I must assume that the creature of my example will not move in relation to the world around it. At this initial stage of my analysis I believe this observation is not an invention of my mind, but instead an understanding of a basic reality, rather like Newton's falling apple. Then I will examine the issues involved when the creature moves. At that point of the analysis I must debate in my mind whether I am observing or inventing, but naturally I hope it more an observation of an essential detail than a phantasy of the desirable features. After building an understanding then I will start inventing details - hopefully to show a realistic possibility of how this model may form the basis of important capabilities of the brain.

Now to begin. Consider what happens when the light strikes a sensory nerve cell in an eye. Not the details, but at a simple conceptual level. The light strikes the nerve, the nerve responds by transmitting a signal to some other nerve. That's one way to look at it. But let's view it another way, as follows. Something exists in the environment. There is light emitted from a small area of that "thing". The nerve responds to that light in some manner that is detectable to other cells. Now consider, the light can be used to detect details about a small part of the "thing", but just as well, the state of the nerve cell as detected by its response provides the same information. In other words, you can view the nerve as transmitting a signal to be used elsewhere, OR you can view the cell as being a model of one particular small piece of the environment. That's not entirely true of course, my example nerve does not really have a one-to-one correspondence with the light from the "thing". However, it is true that the nerve does correspond consistently based on the light it receives over time. If I wanted, I could determine a mathematical function that maps the light being received over time and the nerve would be a model of THAT (the results of that function). The key item to realize is that even though the function describing the behaviour might lose information about the environment, and in a sense the cell is working at a "lower resolution" that its surroundings, the cell is never the less taking on a one-to-one correspondence to some "aspect" of its environment. In other words the cell is implicitly, inherently, and automatically a small model of its environment.

As you will see I don't care what the details are of that correspondence, I will simply say that the nerve is a model of some "aspect" of the environment.

Presumably some "aspects" would be more important than others, but conceptually I don't care about that, only that the model is an accurate representation of whatever details are being modelled.

Now consider a second nerve cell, for example, very simplistically and purely for the sake of illustration of the concepts, assume a nerve just at the edge of a leg of a bug. The leg changes position, the nerve cell measuring the leg responds. As with the eye's nerve cell above, to know the position of the leg you could examine the leg itself, or just as well you could examine the state of the nerve cell. And again this is not quite true, but again just as described above it is true that this cell is a model of some "aspect" about the position of the leg.

As I admitted in the introduction, this is an extremely simplistic view of the way nerve cells work. However, the essential point is that none of the complexities of reality make any difference to this fundamental understanding. Any cell that responds consistently to its surroundings is inherently a model of some aspect of the creature's environment.

Now imagine, admittedly also just as simplistically, that a third nerve is connected to both the eye nerve and the leg nerve just described. This nerve will also respond to its environment. Its environment is the output of the first two nerves. There must be some way that the third cell combines the two inputs from the first two cells, but I don't care what this is, neither physically how it happens in the cell nor logically what rule is used when interpreted mathematically. All I care is that the output is consistent based on the input.

Is consistent output based on the input a fair assumption to make? Not necessarily. The internal state of the cell could alter how the cell handles the input. However, I am going to assume that the effect of the inputs would be consistent if I could ignore the internal state of the cell (how could nerves usefully function at all if that were not true, and anyway I believe that this is basically known to be true).

What effect could the internal state of the cell have on the how the cell responds to its inputs? Well there are two broad situations, either the internal state affects it, or it does not affect it.

Consider the situation where the internal state does not affect the response of the cell to the inputs. This is of course the simplest to deal with. In this case the cell will obviously respond consistently if the basic assumption of consistent response is correct at all. In this case the cell will be modelling some relationship between its two inputs.

At this point someone might wonder what logic the cell is applying - is this working like a NAND gate, an XOR gate, or etc, as in a computer circuit, or a person might wish to try to determine the exact mathematic function that describes the cells response. We might also wonder whether the relationship between the two inputs has any importance at all - is there an actual relationship between the two inputs at all? We might wonder wether some methods of combining inputs could provide more information, and some combinations of inputs be more useful than others.

However, I am not going to do that analysis because it is irrelevant to the key concept I am trying to describe. My only concern is that the responses of the cell always correspond to the situations that occur in the cells environment. The essential feature is that the cell never takes on a state that does not correspond to its environment.

Now let's consider the situation where the internal state does affect the response of the cell to the inputs.

There are again several broad situations to consider. The internal state of the cell, and therefore the effect it has on how it combines the inputs, could depend upon the previous inputs and environment of the cell. Another situation is that the effect from the internal state is purely random. Finally, the effect from the internal state is not random but is also not based on what has happened to the cell at all.

Let's deal with that first situation first, where the response of the cell to its inputs is modified by the internal state of the cell, but where that internal state is based in some consistent manner upon the previous inputs and environment of the cell. But in fact this simply means that the cell is combining its inputs, just as described above except that the details might be harder for us to understand. This is still ultimately the same situation as where the internal state of the cell does not affect the response. The responses of the cell still always correspond to the environment of the cell, it's just that the "environment" now includes details from the past, not just the details at this moment. It could be that this is a component of memory, but that is not what I am suggesting. I will refer to this as a "residual" effect within the cell that is (as before) modelling some aspect of its environment.

Before continuing with the last two situations, I want to sum up what it means for this cell to respond consistently to its inputs. In the same manner as previously described for the first two cells, this cell is also just model of its environment. But since its environment (the two inputs) are from cells that are already small models of two aspects of the world outside the creature, so this third cell is ultimately also just a model of some aspect of the world outside the creature. This time the "aspect" involves some sort of detail about what light was being seen by the eye at the time the leg was in a particular position. (And again this is far too simplistic except to point out the key points to be pointed out - which is that the third cell is modelling something about the creature's environment, and that it is a model that shows something about how two things in the environment are related.)

In this manner, the entire brain of the animal, and in fact all the cells that tie into the brain, form a model of the world in which the creature lives. This model may lose many details, but for the details that it retains it is an accurate model in the sense that it corresponds correctly to those details that it is modelling. You can view this rather like a mathematical homomorphism, though a simpler intuitive description of this accuracy would be to think about what happens to an image on a computer screen as the resolution changes. If you display a picture at a lower resolution then many details can be lost, but this does not mean the picture that remains is not accurate to whatever degree is inherently possible for a picture at that resolution.

What of the situation in which the internal state randomly affects the response to the inputs? I would expect this to have a similar affect to the white noise that occurs in recorded music. It interferes, but as long as it's not too great then the main wave forms remain and the music can still be heard. Or consider the model formed by a collection of numerous cells, then we might expect random variations on average to cancel each other out, so the model over all would still have a "shape" close to the correct shape, and therefore still retain some level of accuracy. Also, in any situation during the evolution of cells with the ability to respond, one would expect a random interference from within the cell to decrease the effectiveness of having the cell respond at all, therefore I would expect the cells with random interference to be weeded out during evolution before we see them joining together into a more complex network. For all these reasons, I am simply going to assume that any such randomness is not too large and choose to ignore this issue.

As for the situation in which the internal state could non-randomly affect the response but not in any way related to the cells history - how would such a capability evolve? Obviously I can't say that this would not happen, and this must be the one situation that I simply skip so I can continue this discussion.

In the above I have assumed a nerve has only one output, which is directly or indirectly detected by the other cells at the synapse. This assumption is not essential to this description. Consider if there are many outputs from a single cell, perhaps for example the signal detected at the synapse plus a hormone released by the cell over a larger area of its surface (and likely dispersing over a larger time frame). If the hormone was released over the entire surface of the cell then it would be detected by different cells than those which detect the signal at the synapse. You might initially think this means that the cells has multiple outputs and can't be viewed as a single "thing" in the model I have described, but that would be wrong. In terms of the logical understanding I am presenting, the outputs can simply be considered as a single output that is the combination of them all, a single output but with more possible states. To again refer to the computer screen analogy, instead of imagining each cell as a single pixel being turned off and on, imagine each cell as being a multiple valued pixel - e.g. a pixel that displays multiple colours. As for the fact that different portions of that output would be used as the inputs for the different sets of cells, this also makes no difference. Each set of cells would be receiving a subset of the available data, the input it receives is just a reduced version of whatever the sending cell is modelling. Let's again imagine a computer monitor but this time one of the colours is not working, the picture displayed will of course be missing that colour, but the image is still correct overall, you still see the picture being displayed. This is exactly the situation with a person who is colour blind. Except for the colour(s) they can't see a colour blind person still sees the same details of the world around them. In likewise in this same manner, a cell that receives only a portion of the first cell's output is receiving a reduced, but never the less still accurate, rendition of some aspect of the environment being modelled by the first cell.

To sum up the above discussion, and not forgetting the assumption that the creature is not moving, the cells in a creature that respond to their surroundings inherently, and automatically form a model of the creature's surroundings. That model may lose information but it is not inaccurate. To use more dramatic words, every creature contains a homomorphism reflection of the universe.

If the creature is allowed to move then the situation is more complicated. Various questions come to mind. What additional features must the cells have to be able to say that their network still forms a model of the environment, and what would prevent the brain from automatically being such a model? Which portions of the network form such a model? How does our own experience guide us to understand, in very general terms, what would be the features of such a model?

Consider the following simple schematic diagram that shows details about the world being mapped to cells within an extremely simple (and hypothetical) creature. "W" points are things in the world around the creature. "E" points are the cells at the edge of the creature that respond to what they detect. "I" points are cells that are internal, and are responding indirectly to the senses.

In this first set of schematics we assume that the cells contain no historical information about their inputs, they are just responding to their current inputs.

        Diagram 1

                W4  W5  W6  W7  W8  W9
                |       |        |
                |       |        |
W1 --- E1       E3      E4       E5
          \      \      / \      / 
           \      \    /   \    /  
W2          Ia      Ib       Ic    
           /  \     / \     /
          /    \  /    \  /  
W3 --- E2       Id      Ie
                 \     /
                   \  /  
                    If

Each edge point will be modelling some aspect of one W point, in the above we see E1 for W1, E2 for W3, etc. Each interior point is modelling some aspect its inputs, which ultimately comes from some number of W points. E.g. Ia is modelling some aspect of W1 and W3. Similarly, Ib is modelling some aspect of W4 and W6. Following all the connections, we see that point If is modelling some aspect of the entire world around the creature. (That "aspect" includes the loss of details about the W points that are not being sensed by the E points, but retains some detail about the rest).

Now let's assume the creature moves, some of the edge points will be sensing different W points.

        Diagram 2

                W4  W5  W6  W7  W8  W9
                    |       |        | 
                    |       |        | 
W1 ----- E1         E3      E4       E5
            \        \      / \      /
             \        \    /   \    / 
W2            Ia        Ib       Ic   
             /  \       / \     /     
            /     \   /    \  /       
W3 ----- E2         Id      Ie        
                     \     /          
                       \  /           
                        If            

Each edge point will still be modelling some aspect of one W point, we still have E1 for W1, but now E3 is sensing W5, and etc. In the interior points we see that Ia is still modelling some aspect of W1 and W3, but Ib is now modelling some aspect of W5 and W7. Following all the connections, we see that point If is still modelling some aspect of the entire world around the creature, though the points for which information is lost or retained is different.

In both diagrams, the points shown form a model of the world around the creature. The model as described is limited to the current situation because we have assumed that each cell retains no history of the past.

At this stage one item in particular is note worthy - the models as shown in the two diagrams above are not of the same set of world points - diagram two is not a model of the same "thing" as diagram one. If the creature moves, and if we wish the model continually being build to be modelling the same "thing" from one moment to the next, then the edge points need to respond to points in the world that "fill in the gaps" between each other, or the points sensed must be similar enough to the points around them so that they are representative of each other so any one of those points can be the input without impacting the "shape" of the model.

Hence our first assumption. We shall assume that the sensory inputs provide enough coverage of the possible world points that we need only consider a set of world points equivalent to the number of sensory inputs - other possible points will be ignored. That is not necessarily a big assumption. If, for example, a creature can sense the temperature around it then very frequently that temperature will be similar all around the creature. Detecting the temperature at one point will be equivalent to detecting it at any other point in the same general vicinity. Consider an extremely primitive eye, in fact the first phase in its evolution will consist of cells that detect light with very little regard to direction, in other words the information the creature gleans about the light around it will not depend on the position or direction of the creature. It seems reasonable to then assume that as the eye evolves and its directional capabilities become greater, that each sensor in the eye will still sense an area large enough that there are no "gaps" between each sensor that are large enough to contain (lost) information significant to the creature. Or for example consider a single cell organism that can detect the direction of the earth's magnetic field. The cell could be considered as its own singular edge point with the schematic diagram: [ W1 -- E1 ]. (It has no I points at all). The part of this creature's internal chemistry that is modified by the magnetic field is a model of the direction of the magnetic field relative to the cell - it seems safe to assume that the direction anywhere near the cell can be accurately represented by a single world point in such a diagram of that creature's place in its environment.

We will now repeat the above, but with two changes. We will lose the world points that are not detected (as per the assumption described just above), and we will add historical information. Historical information means any residual effects current occurring within a cell that were caused by earlier input. Historical information is not memory, though in a more evolved brain a memory function in a cell would be causing residual effects that would be included in this historical information.

In reality those effects will take place within the individual cells, but that is harder to show in a simple schematic diagram, so I will use a bit of a trick to help track the history within the cells. The diagrams will now include Historical world points (H points). Each H point is a World point as it was in the recent past. These H points will then be treated as if they were inputs, which allows us to easily track the position of historical data within the cells. These diagrams will never become complex enough to worry about distinguishing H points from different times.

The first of these new diagrams is similar to Diagram 1, but the extra W points are removed and renumbered and some more points added that will come into play later. H points are shown but for this diagram they are not inputs to any edge points.

        Diagram 3, before movement, history not "seen" yet.

            W3 H3   W4 H4   W5 H5   W6 H6   W7 H7   W8
                    |       |        |
                    |       |        |
    W1 --- E1       E3      E4       E5
    H1        \      \      / \      / 
               \      \    /   \    /  
                Ia      Ib       Ic    
               /  \     / \     /
              /    \  /    \  /  
    W2 --- E2       Id      Ie
    H2               \     /
                       \  /  
                        If

Now we move the creature, much as in diagram 2 above, but this time we add the Historical world points to show the locations of the residual effects of the previous inputs. To help in our analysis, two possible movements are shown.

        Diagram 4.1, after movement, history now "seen".

            W3 H3   W4 H4   W5 H5   W6 H6   W7 H7    W8
                        \   |   \   |    \   | 
                          \ |     \ |      \ | 
    W1 ----------- E1       E3      E4       E5
    H1 ___________/   \      \      / \      / 
                       \      \    /   \    /  
                        Ia      Ib       Ic    
                       /  \     / \     /      
                      /    \  /    \  /        
    W2 ----------- E2       Id      Ie         
    H2 ___________/          \     /           
                               \  /            
                                If             

        Diagram 4.2, after alternate movement

            W3   H4 W4   H5 W5   H6 W6   W7   
            |   /   |   /    |  / 
            |  /    | /      | /
    W1 -E1  E3      E4       E5
    H1_/|    \      / \      / 
        |     \    /   \    /  
        Ia      Ib       Ic    
        | \     / \     /      
        |  \  /    \  /        
    W2 -E2  Id      Ie         
    H2_/     \     /           
               \  /            
                If             

Each edge point is still modelling some aspect of one W point, but the H points allow us to track the locations of the residual effects from the W point they were previously modelling. E1 is always modelling W1, but after the move the internal points Ia, Id, and If may be modelling some aspect of W1 that includes both its current state and its previous state. E3 was modelling W4. After the movement shown in 4.1 it's modelling W5, and in 4.2 it's modelling W3. In both cases, by following H4 we can see that the internal points Ib, Id, Ie, and If may include residual effects from W4.

Can the cells shown in either Diagram 4 be considered a model of the creatures environment?

The problem (that I try to hint at with the two diagrams) is that during whatever time period we consider the creature can move any distance in any direction (within some physical limitations of course). Take Ib for example. What aspect of the creatures surroundings is it modelling? It would have to be modelling something involving H4, W5, H5 and W6, or something involving W3, H4, W4 and H5 - but which? There is no way to know based on the states of the cells - Ib contains no information that would differentiate the two possibilities. We can no longer make the consistent one to one correspondence between "aspects" of the environment and the state of each nerve cell that would allow us to claim that the cells are forming a model of the creatures surroundings.

There are (at least) two ways around this, two general arrangements of the interconnections between the cells that would preserve the correspondence between cells and the creatures surroundings even as the creature moves.

I would like to prove the following graph theoretically, but have not done so yet. For now I must assume I am correct. You will have to form your own opinion of the validity of the claims.

First, recall that the issue with the above is that the information contained within each cell includes changes due to movement, but there is no information about the movement itself and so no way to correlate the changes in the state to the movement. One "solution" is to simply combine all the data that moves together. The prototypical example will be an eye. If all the inputs within the eye are combined into a single value then all parts of the brain that are "downstream" from that point will not need to have information about movement of the eye relative to the rest of the creature. Let's assume the top row of points in diagram 3 (E3..5) is the eye and the left points (E1,2) is a part of the creature that moves relative to the position of the eye. Then let's remove one I point so that all the eye responses are channeled through a single point.

        Diagram 5, modified from diagram 4, note that Id is gone.

        W3 H3   W4 H4   W5 H5   W6 H6   W7 H7    W8
                |       |        |
                |       |        |
W1 --- E1     ( E3      E4       E5 ) <==the "eye"
H1        \      \      / \      / 
           \      \    /   \    /  
            \       Ib       Ic    
             \        \     /
              \        \  /  
W2 --- E2 -----Ia       Ie   (note Id is gone).
H2               \     /
                   \  /  
                    If

Now we move the eye relative to the creature, much as in diagram 4 above.

        Diagram 6, after movement, history now "seen", "brain" marked.

        W3 H3   W4 H4   W5 H5   W6 H6   W7 H7    W8
                    \   |   \   |    \   | 
                      \ |     \ |      \ | 
        W1 --- E1       E3      E4       E5
        H1 ___/   \      \      / \      / 
                   \      \    /   \    /  
                    \       Ib       Ic    
                     \        \     /      
                     =\========\==/=       
        W2 --- E2 ------Ia      Ie =        
        H2 ___/      =   \     /   = <== the "brain" 
                     =     \  /    =        
                     =      If     =        
                     ===============

Ie now contains all the possible information about all the inputs to the eye. All the details from the eye that correspond to position have been "lost". Let's define a "brain", but from the eye we will only include Ie and all points downstream from it. The "brain" now contains three points which could still be considered to form a valid model of the creatures surroundings, Ia, Ie, and If. Ia represents some single aspect about W1, H1, W2, and H2. Ie also represents some single aspect, in this case a single detail of information about the "light" around the creature. And finally the point If represents some aspect about the total environment of the creature. Notice that as the eye moves, the points in the brain will still have the same correspondence to the creatures surroundings as before, and that this correspondence still holds precisely because the brain has the simplest possible representation of the eye. Basically the creature "knows" only whether there is light or not, and that "knowledge" does not change randomly simply because the eye has moved.

Let's examine two examples about this issue. These examples are different but do not contradict each other, and are simply to help think about the above.

Example one. Ie detects changes of light in the environment, day vs. night, covered vs. exposed, etc. One would assume that that single detail would be useful to know to help modify other movements within the creature, even though the creature has no concept of direction or motion.

Example two, Ie detects changes in light caused by movements of the eye. Most creatures have light sensors at the front. One might expect that the direction of the eye would correspond to the direction in which the creature would move simply due to the physical arrangements of the creature. Assume for the sake of argument that it is beneficial for the creature to move towards the light. Random movements of the eye will change the single detail about the light modelled by point Ie, and if that controls other movements then the creature can move towards the light - even though it has no concept of direction.

In either of the above, the loss of detail from the eye (by combining all details into a single point) may actually benefit the creature because it makes it possible for a set of cells to use the eye information in some centralized way that makes sense for the creature even though the brain is too simple to use the full details available from the eye.

I said that there are (at least) two ways around the issues that arise when the creature moves. Above I mention how losing details is one way around the issues of movement, now let's discuss a second.

These two schematics show a hypothetical eye and two other sets of points. A nerve or set of nerves (E4 and E5) which respond based upon the direction of the eye, and a matrix of cells (I1 through I6) connected to both the eye and the new position responding cells (E4,5).

        Diagram 7, eye and detection of position

                W1 H1
                |           W2 H2
                |          /
                |         /            W3 H3
                |        /           /
(eye is E1,2,3) E1      /         /
                |     E2       /   W4 H4  <=== this W/H point is on the
                |     |     E3       \          creature, its position
                |     |     |         \         changes as the eye moves.
                |     |     |          \
               / \   / \   / \         / \
              I1--\-I2--\-I3--\----<==E4  \    E4 connects to I1 I2 & I3
                   \ \   \     \           \
                   I4-|--I5----I6-----<==  E5  E5 connects to I4 I5 & I6
                    | |               
                    \ /               
                     I7

This schematic does not show all the connections, just the ones necessary to show how the movement of the eye relative to the body can be accommodated so that an inner portion of the network will retain its correspondence to the world points.

E1 is connected to both I1 and I4, E2 is connected to both I2 and I3. E4 is connected to all of I1, I2, and I3, and E5 is connected to all of I4, I5, and I6.

I1 through I6 will respond if they have two inputs, and I7 will respond if it has any input. E4 responds when the eye is in the position shown above. The result is that I2 will respond to W2, and since it is connected to I7, I7 is modelling W2.

        Diagram 8, eye moved, detection of position

                W1 H1
                   .        W2 H2
                   .       /   .        W3 H3
                   .      /   .        /    
                    .    /   .       /    W5
                     .  /   .     /      /  
(eye moves) =>        E1    .  /      /                                
                     /      E2     / W4 H4 <== position change detected
                   /      /     E3    \                                  
                 /     /      /        \
               / \   / \   / \         / \
              I1--\-I2--\-I3--\----<==E4  \    E4 connects to I1 I2 & I3
                   \ \   \     \           \
                   I4-|--I5----I6-----<==  E5  E5 connects to I4 I5 & I6
                    | |               
                    \ /               
                     I7

Diagram 7 represents the eye changing its angle slightly relative to the body. World point W2 was originally detected by edge point E2, E1 was originally detecting W1. After this movement W2 is now being detected by E1. The H points will be mentioned later.

Due to the change in angle, E4 is no longer responding, instead E5 is responding. The result is that I1,2,3 can no longer receive two inputs (one of the two has to come from E4), and so they won't respond to any input from E1,2,3. On the other hand, I4,5,6 are receiving input from E5, and therefore they can be activated in response to E1,2,3. In particular, I4 will be activated in response to E1, but due to the movement, E1 is now detecting light from W2 (recall it was responding to W1 above). But since I4 is connected to I7, I7 is still modelling W2, just as it was in diagram 7 above.

But what of any residual effects (tracked with the H points)? Diagram 8 helps us to see that the I4 point connected to I7 could still be impacted by the previous inputs from W1, so in fact I7 maybe corresponding to some aspect of both H1 and W2, not just W2 (contradicting the claim I just made above where I said that I7 is simply a model of W2). Though I have not shown it, it is easy to see that if the movement were the reverse (from the position shown in diagram 8 to that shown in diagram 7) then I2 could contain residual effects from H3, so in that case I7 could be modelling some aspect of both H3 and W2. So which is it that I7 is modelling - H1 and W2, or H3 and W2?

You can see that the above network does not totally solve the issue of how the model can be a consistent accurate model of some constant aspect of the creature's environment. This is because the matrix connections shown in diagrams 7 and 8 do not have any way to relate residual effects with the current inputs and therefore the impact of the history is effectively random within I7. However this is exactly the situation I listed much further above (before I discussed the issue of movement) when I said "Another situation is that the effect from the internal state is purely random." We can see that the cells "upstream" from I7 need to isolate it from any residual effects.

As long as the upstream cells have a minimal residual response then diagrams 7 and 8 show a second technique that enables an inner portion of the nerve cells to correctly model the creatures surroundings even as the creature moves.

The two techniques could of cause be combined. The motion detection shown in diagrams 7 and 8 does not require the matrix (I1 .. I6) to be as complex as the eye or the motion, just so long as the sensory details from parts of the creature that move together are combined _before_ they enter the matrix.

We have now seen how the nerve cells (and possibly other cells) would automatically and inherently form a model of the world around a creature if the creature did not move. Then I have shown how an "inner" portion of the network of nerve cells can still form such a model as long as the "outer" cells have certain arrangements, one of which is so simple that I can easily imagine it occurring during an early period of evolution.

At this stage I would like to introduce some definitions.

The "brain".

The inner portion just mentioned above is what I would wish to call the brain. It is the portion that forms a model of the creatures surroundings.

An "observation".

An "observation" is the state of the brain at some point in time. At that point in time the brain is a model that "reflects" or "mirrors" the state of the world as it is at this moment and in the recent past.

In reality you could never identify a single observation. The state of the brain as a whole is continuously changing as each cell responds to the changes it perceives, trying to reach its own new equilibrium. Also, the state of many nerve cells cannot really be considered at a single point in time because it is the frequency of its responses that indicate its state - so the state at a point in time must really be the states seen over some suitable period. Regardless, I will continue.

This ongoing process is what I will refer to as "observing".

The "consciousness".

I am not going to discuss consciousness except as a useful tool to help understand the model I am describing.

You could ask, what exactly is it that the consciousness is conscious of?

My answer would start with the observation that the consciousness "lives" inside the model. Physically (i.e. the molecular interactions that somehow provide the consciousness functionality) the consciousness is presumably part of the brain, and therefore is itself part of the model's structure. Either the portions of the brain that make up the consciousness are responding to (and therefore modelling) its environment (the rest of the brain, and ultimately "aspects" of the creatures surroundings) or it's embedded in the model and yet somehow not responding to its environment, but in either case it is certainly interconnected with the parts of the brain that are modelling the creatures environment.

(On this note you could view the consciousness in two manners. Either it is modelling the environment, which begs philosophical questions about how our sense of consciousness may actually be reflecting a feature of the universe as a whole, or the consciousness involves some "rigid" framework in the brain (since it is not changing to reflect its inputs) and the consciousness itself could then somehow be the "tension" between this rigid framework and the changing model in which it is embedded. However this is diverging fundamentally from what I wish to discuss here.)

To get back to the question, "what exactly is it that the consciousness is conscious of"? My answer is that everything that the consciousness is aware of consists of the things in the model. To give a specific example, if you "see" a mountain in the distance then it is not the mountain that you see at all. Your nerves do not _transmit_ details of the mountain to your consciousness. Instead, the brain automatically forms a model of the mountain (as part of its overall model of its surroundings) and then quite literally the mountain becomes a part of your consciousness.

In other words, what it means to be consciousness of something is for a model of that thing to exist in the brain.

(Actually my philosophical observation that the consciousness could consist of a "tension" between the model and a fixed framework somewhat contradicts the above paragraph. In this case you might wish to interpret the brain as "transmitting" an image to the consciousness, but I don't think this difference makes much difference to the descriptions I will give below - so I will ignore it and move on.)

One penultimate introductory comment to ensure there is no misunderstanding. If you were to examine the brain to see the states of the cells when a person was seeing (for example) a mountain, the "shape" of the model of the mountain would not in any way be physically similar to the shape of the mountain. The logical "shape" of the mountain in the model consists of all the individual details and all the details that are the correlations between the other details. The physical shape of that within the brain will be the pathways that include all the cells that represent those details.

The last introductory comment. Whatever it is about the way a cell works, the details can never have a purpose. Each cell is only ever attempting to reach an equilibrium with its surroundings. Even the word "attempting" is wrong as it might imply the cell is _trying_ to reach that equilibrium - it is not "trying" to do anything. At each stage where the cells are expected to do anything, that action must always be part of the process of reaching an equilibrium.

The above (all of it, not just the last paragraph) may or may not be correct, though obviously I believe it is a fair way to view this situation, but correct or not, nothing has been invented by me. I have simply described one way that a person might choose to look at a situation. I have observed (correctly or not) that with some very simple assumptions about cell arrangements, including one that could trivially evolve, the brain is a model. Then I introduced some other minor observations and definitions.

HYPOTHETICAL FUNCTIONING OF A SIMPLE BRAIN

I am now about to invent various details to show how this understanding - that the brain is a model - could be the basis of how the brain functions. The description will follow the course I think easiest to understand as I build the concepts. However it is important to realize that my description does not follow the way the brain would evolve. I will actually start near the end, and my progression will arrive at the beginning. In fact this is one reason why the idea struck me as I originally considered the ramifications of the "brain as a model" concept. The understanding arrives at the point which one might consider the most complicated - the ability to make a decision - but in fact that ability may be the simplest. It is of course also the most important because it is useful. Therefore it provides a starting point to evolve all the other capabilities which are easier to describe and hence introduced earlier in my progression below.

MEMORY

Let us assume that each cell has some way to record its own state at a point in time.

This is already known to be possible for short periods in which a single previous state is saved and compared to the current state. Some bacteria apparently use this to control their motion. This also happens when the nerve cells acclimatise themselves to their input. This can be viewed as a form of memory in which a number of states are recorded and the effect of those states adds up until they are large enough to prevent the "normal" response of the cell.

I want to describe an imagined possibility. It is hypothetical and simplistic, and not based on observation, just "thinking out loud" to help understand some general details that might be involved in such as process so as to help understand if it is at all feasible from a logical and physical point of view to assume that a cell could somehow record its own states over time.

My schematic cell will have four molecules that measure its state, named A, B, C and D. The concentrations of these molecules are the state of the cell.

        Diagram 9, nerve cell state

                              +--------+
    -- input from synapse --> | A    C | -- output via synapse -->
                              |        |
                              |  cell  |
                              |        |
    -- input from hormone --> | B    D | -- output via hormone -->
                              +--------+

Assume the concentrations of A and C will increase to indicate input. The concentrations of C and D are controlled by the cell, and drive the outputs. The "logic" of the cell will use A and B to drive C and D.

Let's create a short memory. In particular let's assume that some DNA drives the creation of a strand of RNA that I will call M (for memory).

    Diagram 10, creation of M

    DNA
    ||
    ||          RNA "M"
    ||
    || --> =fA=fA=fB=fC=fD=fA=end=
    ||
    ||
    ||

M will contain a series of sequences that I will call "factors" of A, B, C and D. Each factor is associated with its namesake molecule. The associations are what I describe next.

Invent another factor "x", which can move along M. x has the property that its actions are effected by A, B, C and D.

    Diagram 11, x moves along M

    =fA=fA=fB=fC=fD=fA=end=
     x -->

"x" will attach itself at the start of M and then attempt to move along it. However we will assume that it can't move unless the balance of A, B, C and D are "close enough" to the factors in M to keep it in motion. E.g. if x wants to progress past fA then it needs to encounter A. At that stage, encounters with B, C or D will slowly break its connection to M, until eventually it detaches from M and nothing will happen. On the other hand, if it does encounter A then it moves, and the process continues. If the changes of A, B, C and D over time are a close enough match to the series of factors in M then x can arrive at the end of M, and then some other action can occur.

Diagram 10 shows a "hard coded" sequence of factors. These would be built into the DNA. Now I invent another molecule called F that will allow us to built a series of factors that record the state of the cell.

    Diagram 12, creation of N by F

    DNA
    ||
    ||          RNA "N"
    ||
    || -+-> =fA=fA=fB=fC=fD=fA=end=
    ||  F
    ||   \
    ||    \
           +---< A, B, C, D

N and M might be functionaly identical, the important difference is only in how they are created. Assume that F is corrupting the RNA as it is being made. F is impacted by A, B, C and D in a manner similar to how x is impacted. As N is being created, F will replace the RNA sequence that would be created with the factors of A, B, C or D depending on their concentrations. If A is twice as concentrated as B then F will encounter A twice as often, and fA will be written into N twice as often.

Since the only important difference between N and M is how they are created, I will often refer only to M below.

"x" was assumed to cause an action when it arrived at the end of M. Let's suppose another molecule, "y", that is similar to x but causes an action while it moves. The action will be to create A, B, C, or D based on the factors of A, B, C and D. As with x, it is also affected by the concentrations of A, B, C and D. If the concentrations are too different from what it is trying to create then it detaches from M. The effect will be to reproduce the previous changing concentration levels of A, B, C and D over some time period, just so long as these concentrations are compatible with how other processes are impacting the state of the cell.

    Diagram 13, y moves along M creating A, B, C or D.

    =fA=fA=fB=fC=fD=fA=end=
     y -->
     |
     |    
     A is created

Finally, let's assume another strand of RNA called "L" (for life line). Somehow, the strands of M and N will receive some kind of "tag". Since M comes from the DNA, then its tag would also come from the DNA. The tag would then provide a mechanism to access and reproduce M from the DNA. How the N strands would be tagged and reproduced I can't say. Anyway, as x arrives at the end of and M or N, the action would be to write the tag onto the end of the L strand.

    Diagram 14, x writes the tag into L

        RNA M or N
    =fA=fA=fB=fC=fD=fA=tag1=
                   --> x 
                       |
                      \ /   RNA "L"
                       tag1=tag2=tag3=tag4=...

The tags would of course not be numbered, but instead be random sequences with a useful chance of being unique from each other if they came from different M's and N's.

The upshot would be that a final process, similar to x and y, could read L, and invoke the N's and M's, which would in turn attempt to recreate the original balances of A, B, C and D. As with x and y, this final process would not be able to continue if the results (the concentration levels) diverged too greatly from the concentration levels being forced on the cell from any other processes.

One could imagine that there is an ongoing process reading L, continually reproducing the original balance at that point in time in its immediate vicinity within the cell. "Normally" that balance will not impact the cell much if at all, but if some other process amplifies this then the recorded balance might be reproduced to a large enough degree that the cell will respond externally in the same way it responded previously. Presumably this will not cause anything in the memory to be modified, but will instead just drive the balances in the cell to be the same as before.

So, using the mechanism described above, the cell can "return" to the state it was in at some earlier point in time and replay the states of the cell. The effect is that the cell will be replaying the states it passed thru before, starting at the time to which it returned.

For the sake of argument let's assume that somehow all the cells can be affected in the same way so they all return to the same point in time and then all replay their original states starting at the same point in time.

Now ask yourself "what would the consciousness see"?

The answer is that the brain as a whole would progress through the same series of observations as earlier. If the consciousness was earlier perceiving a mountain then it would now again be perceiving that mountain because the mountain is again existing in the consciousness exactly as it did before. In other words, the creature would be "having a memory".

How could all the cells return to the same recorded point in time? If the cell has a life cycle that enables differing portions of its DNA over a long period of time then something in the exposed DNA could act as a "meta-tag" within the L strand(s?). That meta-tag would be written into L, and be the starting point corresponding to a specific moment in time. Since all the cells have the same DNA, then all the cells would have L strands that are in sync with each other. I can't give any good suggestion as to how this would be used to coordinate the cells' memories. Perhaps each nerve cell is affected by a hormone that causes the replay process to start. How would this restart them at the particular point in time? That is much harder to say.

As for this happening over a large portion of the brain all at the same time, perhaps a network of cells release this hormone, and those cells are spread out throughout the brain. Those cells respond to each other quickly, effectively at the same time. Their actions are not driven by their internal memory process, but is simply the normal nerve response to an input. The effect is that this network of cells would all release the hormone at effectively the same time, and then all the other cells are affected the same way at the same time, and thus each replays their individual states, with the overall effect to the consciousness of causing the memory.

Anyways, to keep track of where we are, the nerve cells will rebuild the earlier observations of the world by recreating their own little piece of the model.

We know cells work via chemical equilibriums. One can imagine in my hypothetical process the cells will be trying to output what they were outputting before, but their ability to do this will be continually affected by their immediate environment. The inputs they are receiving will be trying to drive processes that will either help or hinder the processes driven by the internal memory process. And not just the inputs, but, for example, if they attempt to output a neuro transmitter but the receiving cell is in a state where the molecules are being absorbed more slowly than normal, then that may provide a kind of "push back" to the ability of the first cell to output the transmitter, which will in turn cause some kind of "push back" for the internal processes of the cell.

If the various external effects on the cell correspond to causing approximately the same output as the internal memory process at that moment, then this could tend to keep the cell running the same process (and be reproducing the same outputs as earlier), whereas if the external effects "contradict" the balance of the chemistry of the internal memory process then they might be able to "over power it" and push the internal memory process into some other state, perhaps stopping it entirely, or forcing it to restart based on the state from some other point in time.

This continual "rebalancing" might assist the cells to stay "in sync" as they replay, by forcing them to maintain states that are in some way "compatible" with the cells around them.

INSTINCT, or inherited memory.

Let's side track for a moment.

As hinted at above I will treat instinct as "inherited" memory. A very simple creature would have only M strands, x molecules to read the strands, and perhaps an initial short L strand.

These M strands are therefore "pre-recorded memories", which are of course not memories at all but instead are random sequences built up over time by evolution because the behaviour they invoke is useful. As the brain grows and cells differentiate you could arrive at a point where all the cells within a region would have the same "instinct" memory enabled. In the memory model I described above, each cell records the one "aspect" to which it corresponds, and all the cells record slightly different sequences. Now consider the instinct memory. All the cells in a region would contain the same "pre-recorded" sequences. Assume the cells were then to "replay" these sequences in the same manner as a regular memory. From the point of view of the consciousness this would not be any different than a normal memory, except that the model thus built in the brain would be made of a much smaller number of pieces, which I liken to a memory with a lower resolution. Using the same analogy as before, imagine if the brain were a computer monitor. A regular memory would be like a high resolution monitor showing a detailed picture. The instinct memory would be like switching the monitor into very low resolution, thereby showing a very undetailed picture, so undetailed that the consciousness would not perceive any concrete image of the world, just a vague impression. But since each aspect of the instinct memory is stored in a large number of cells, one could imagine that such a memory would be very strong. I.e. all the cells in a region would be helping to keep each other in sync, and any other input that might normally impact the memory replay process would have to be large enough to impact an entire region before the replay of an instinct memory could be disrupted.

As a note, I theorized by example above that a network of cells would control the replay of memory by having each cell of the network release hormones that would affect the other cells within the same region as that cell. One could then also imagine that the regions of inherited memory described above would be the same regions controlled by such a network. Each region as it initially develops would include one or more cells that will control that region, and those cells would be connected to each other in their own network.

THINKING, or imagination.

Let's imagine that a number of cells were all to go back to previous points in their recorded time but not the same recorded time. Now let's imagine they each try to replay the sequence of events they have recorded. Note that each cell is modelling something that has actually happened and is therefore possible. As each cell steps forwards it will try to produce an output. As mentioned earlier, the cell is never entirely free to do anything, it is continually impacted by the environment around itself. In this case the cell may attempt to replay its stored memory events and thereby output the same responses as earlier, but if those external responses somehow "clash" too greatly with the state of the cells immediate environment, which in this case would include the outputs of the other cells that are trying to replay their histories, then the cell may not be able to complete this process and therefore not be able to replay its previous states.

What would happen? The following is only one example how a cell might attempt to replay its state while remaining somehow "compatible" with its inputs and immediate environment. Perhaps the cell would skip forwards or backwards through its memory sequences. Each time the process attempts to restart the replay at the new location the same issue would arise as to whether the result was "compatible" enough with its neighbours to be able to continue. By random chance, after "re syncing" in this manner some number of times, then the cells near each other would likely find sequences that are compatible enough that they rarely need to resync. At this stage the model as a whole would be progressing through sequences of "fake" observations. At what would the consciousness perceive? The consciousness would perceive a world changing around it just as if it were observing reality, or just as if it were having a memory, except that the "reality" it is perceiving is not one that has ever actually existed.

There is something very important to notice about this process, a most essential feature: Notice that the individual cells are all replaying things that have occurred - which means the individual pieces of the model are all "describing" things that CAN occur. Then consider, because each cell is forced to be "compatible" with its neighbours, and this "compatibility" must occur when the individual states are "close" to the ones that occurred previously in reality, therefore the overall state of all the cells must also approximate the groupings of states that CAN exist.

In other words, with a few assumptions about the individual cell behaviours, we find that the model can play events that have never happened but which are similar to events that could happen.

Briefly, this describes a mechanism that allows even a simple brain to perform logical correct "thinking".

One essential point is the concept of "compatibility", and an issue skipped above which the astute may have noticed: how would the brain start a thought? How would the cells be able to begin at different recorded times but in states that correspond to something real so as to be able to progress through a period of "thinking" in a manner that would have any chance of being able to form an approximation of a possible reality?

I am not going to try to guess how that would occur, but certainly this ability would have to have evolved from some earlier simpler process. And that brings us to something that might initially appear to be the most complex processing of the brain but in fact may be the simplest, and also be the driving force necessary to start the evolution of the other processes.

DECISIONS

For a thought to work correctly the cells involved would presumably all need to start at points in their recorded memories where the cells are in reasonably compatible states.

How can that happen? I don't want to assume some process exists to make this happen. I want the decision making process to require fewer assumptions, not more, because I wish to assume it was available at the start of the evolutionary phases that lead to the modern brain. I want the decision making process to exist as a useful facility which could then lead to the more complicated processes I described above.

But in fact there is always one point at which the cells must all be in sync, in compatible states, and therefore able to start the thinking process with some hope of deriving a correct thought (one which mimics a possible reality). This collective state is one that _must_ occur, it require no assumptions as to _if_ or _how_. It is also a state from which it would presumably be extremely useful to be able to make a decision. That state is the _current observation_! I.e. the observation which is the "shape" of the model in the brain at the current moment due to the current situation of the creature.

As explained at the very beginning, the current observation requires no assumptions except that the cells respond in a consistent manner.

But how would a decision occur? My first question would be "how does the brain do the actual decision itself"?. Not the overall process that enables or leads up to the decision, but the final conclusion to either DO SOMETHING or to DONT DO SOMETHING?

I think that the core detail of the actual decision is not too hard to imagine. We use words such as "pain" and "pleasure". Individual cells don't "feel" pain or pleasure, but they have evolved appropriate responses to situations that are good or bad for their survival. If a very small group of cells is working together, if one cell has a problem - perhaps it encounters something stressful to itself - it will (presumably) release some hormone indicating this fact. The other cells will detect that hormone and change their behaviour. The evolved behaviour of the other cells will more frequently than not result in the decrease of the level of the hormone, which will happen because the result of their behaviour will be that the first cell will end up being under less stress, with the eventual outcome that the group of cells survive. Likewise, if something particularly beneficial is happening a similar set of events will occur, but with the effect of behaviours that maximize the interaction instead of minimizing it.

Let's follow that process through to see the implication of what it means within the model that forms in the nerve cells.

Assume a (non nerve) cell releases a hormone indicating stress. For simplicity let's call that a "feeling of pain". Some cells will respond directly to the pain. The way that some nerve cells respond directly will be to transmit a signal of "pain" to other cells, and those cells will then respond to the transmitted "feeling of pain".

The evolved response in either case will be behaviour that results in minimizing the pain, and coincidently but consequently resulting in the survival of the creature.

So what happens if the model were to take on the same shape it had when it was earlier transmitting the feelings of pain? The result will be that the nerve cells are retransmitting the earlier feelings of pain, and the result of that will be that the cells connected to the nerve cells and which receive the signal of pain will behave in whatever manner they normally behave that attempts to minimize the pain.

Please consider another small detail. When a standalone cell, or a cell within a very small relatively uncoordinated group of cells of an extremely primitive creature, performs an action such as moving then that movement is not based on any degree of decision-like logic. The action consists of random motions based only on the overall situation in which the cell finds itself. One must wonder, how much difference would it make for the survival of the cell or creature, whether the cell responds immediately but in a random manner, versus responding with a slight delay, but in a non-random way that is calculated to be "good" by some measurement?

So how does this all lead to the ability to make a decision? Well for the sake of example, let's assume a small creature. In evolution this would be much simpler than anything like an insect, but since an insect is easy to picture in one's mind, let's assume an insect.

We know that the brain of an insect has the tendency to suppress the uncoordinated motions of individual appendages. We know that the individual parts of the creature are continually acting in a random manner. Let's suppose that perhaps that is a basic mechanism for the way a creature makes a decision.

So how exactly does our insect decide what to do next? Let us suppose that a leg tries to jump. That may or may not be a good idea. Let's suppose that the first reaction of the nerve cells is to suppress the motion, but nevertheless the nerve outputs the same state as if it was responding to measuring the leg jumping. The impact on the brain of the creature will be to start to build a model of the creature as if it were jumping.

Now from this point let's suppose that the rest of the brain were to shift into the thinking process. The result will be that the brain builds a series of models that closely mimic what could happen to the creature if the leg had actually jumped. In other words the insect "imagines", or "thinks about" the jump. And the decision? What if some portion of the brain starts to model a pain situation? The cells that receive the pain signals don't know or care whether the pain is real or not, in either case the result will be that they suppress the current actions in the creature. On the other hand, if some portion of the brain starts to model a pleasure situation then the result will be for the cells to allow the current action, which in this case was the leg trying to jump.

The consequence is that the insect jumps, or not, based on whether the model detected it would lead to a good or bad situation.

In other words the result is a logical decision - one that tends to avoid problems while allowing beneficial actions.

To do this we assumed that portions of the creature attempt to move in random manners. We assumed that the nerve cells initially inhibit this. We assumed that the internal states of the nerve cells could eventually reach a balance that would either allow, or continue to inhibit the original motion (and though not stated earlier, that balance may have to occur during the time that the cell(s) are trying to make the motion).

The internal states of the nerve cells includes some process that impacts the nerve responses based in some manner on progressing through a sequence of states. For instinctive behaviour that progression is hard coded and will be identical within the cells in a region of the brain, for learned behaviour the available progressions are recordings of the states through which the cell has previously passed.

As the cells progress through their sequences the overall balance will force individual cells to lose their place in the progression and resync themselves when their state diverges too greatly from some "allowable" balance range.

The resulting state of the brain will be a series of "observations" similar to what would be made if the creature had in fact allowed the action. The state will include the same signals that correspond to "pain" and "pleasure". The result of those signals will be the same as if the brain was not performing any such process - the action will be inhibited or encouraged - but due to the modelling process this result will occur before the creature commits to the action.

In this manner a creature with even a very simple brain having very limited degrees of the above described processes could have a statistical advantage over a creature that does not have these processes. And that statistical advantage would be the basis for the evolution of the more complicated memory processes described earlier.