# About Fractals – a revisit and reflection

I have been thinking about fractals for the last few years, and found some renewed interests here in its application in social media.

I believe that there might be some ground breaking ideas behind fractals especially in describing how it could be represented as a pattern in
(a) our brain
(b) our origins of life
(c) our way of communication and networking, especially in a complex open networked environment
(d) our future of education.

Here are my meanderings:

The basis of fractals is routed from (you could watch the video series 1-6 and it was mentioned in one of them on the formula of fractals basis https://suifaijohnmak.wordpress.com/2010/03/30/the-map-is-the-treasure/

f(Z)= Z x Z +C  where Z is a complex number (a+bi) – where a and b are real numbers and i is the square root of -1, an imaginary number.  I include this as a brief background only, and I must admit that I am too new to it. 🙂

This is similar in concept to the Newton’s iteration equation in solving numerical problem, which is also fundamental in computation using iteration.

Relating again on the video https://suifaijohnmak.wordpress.com/2010/03/30/the-map-is-the-treasure/development of fractals based on just the growth of two lines (could be both equal in length, or unequal, with same or different directions) is fascinating, as this may provide some cues in lots of areas:

(a) Our brain.  First, I suspect that the development of dendrites in the nerve cells and the connections are formed could be simulated using the fractals development pattern.  I don’t know if there are any simulation based on that, but surely the full brain scan provides a pattern that could be studied in greater details, to see how such “fractals” are formed and developed.  I realise patterns of fractals appear when I wash my hairs with hot water, and such images of fractals could be “visualised” naturally.  Have you got similar experience?

(b) Origins of life.  I have written an article (never published) back on 22 November 1997 at 11:36 pm.  Here is part of it (though some other parts have been added/revised now):

A basic mathematical theory on the multiplication of cell.
(details not shown)

As life begins in the multiplication of cells:
Imagine a round cell is now sub-divided into two identical cells of the same size as the original one.

The surface area of the multiplied cells could be equal to the surface of another cell of radius r2

By equating 4x pi x r2xr2 = 2 x 4 x pi x r1 x r1

r2 = square root 2 x r1

This suggest that the cells increase by square root 2 the original size of the radius but two-folds in area for any division of cells.

The formula f(Z) = ZxZ +C could be a general formula for explaining this division of cells (I don’t think I have learnt anything about fractals in 1997, and I just made up that formula to prove my point in the division of cells).  So, when I watch the video now and realise that the same formula was used in fractal formation, I was so amazed.  I am just not sure where I got that idea from.  Remember in 1997, the Internet wasn’t popular as yet, and I don’t think I knew the formula as mentioned in the M-SET.

But I really did a lot of original work without referencing to any literature.

Let  Z be a complex number denoted by a+bi, you could derive that

C=square root 2 x a (working not shown here)

If we apply this principle to the multiplication of basic cell, it means that one cell will be divided into two, and the two cells will be divided into four and so onwards.

It seems that the square root of 2 is the mysterious figure that should be investigated.  And I suggest that this is fundamental “number” that could unfold the origins of life – i.e. square root 2.  That is, if we keep squaring root the 2 objects, then it would become 1.

This is similar to the concepts of uniting the sperm and ovary in human birth, where the ovary will begin to subdivide once the sperm unite with ovary.  So the sperm is C and ovary is Z, where the ovary multiplies when the sperm entered into the equation, and the life begins.  Does it make sense?
(c) way of communication and networking, especially in a complex open networked environment.  I have written a post on this – the map is the treasure https://suifaijohnmak.wordpress.com/2010/03/30/the-map-is-the-treasure/
(d) our future of education.  Given the current trend, could we predict the future using fractals as pattern?  May be.  I am still pondering on this, but I would postulate Z (future education) = Z (present education + imaginary or predicted condition of education) x Z (present education + imaginary or predicted condition of education) + C (paradigm shift: based on networking, social media and technology affordance, and promotion and support from government, institutions, communities, local and global networks, social medias etc.)

The following is just my intuitive thoughts only.
Finally, assume that a is our present life, b is our future life (imaginary) in the Z=a+bi then if our present life is “equated” to our future life, then we will have eternal life (as a Catholic, that is a teaching by Jesus Christ).  The eternal life could also be a reality by applying the principle of multiplication of cells.  Also our faith will multiply as a multiple of two just as the cell division.  This is also how religious beliefs gain its life in its spread of good news, IMHO.

Hope you don’t mind me sharing these really “strange thoughts” with you, but I could assure that you would never find it in any literature, as I made all these up myself.

I am posting it here onto my blog, though such are just half-baked ideas, not yet ready for “cooking”.

Let me know what you think.

Photo: From wikipedia on Fractals

I enjoyed watching this video about chaos and order

Postscript:

I love watching these videos on fractals too.  This is Part 6 of 6.  I have shared it in my previous blog post.

## 24 thoughts on “About Fractals – a revisit and reflection”

1. A couple of principles out of that BBC video:

Morphogenesis and self-organization. I wonder if these principles apply to networked learning, and if the seeming affinity for us to form groups for group learning is an observable phenomena of these principles in action?

Non-predictive theory (e.g. Chaos): Kinda interesting that the ‘Newtonian scientific certainty’ is now considered dissolved, an illusion, an act of faith that is unfounded. This reminds me of the post-modernist view I have been arguing within, although in different language.

Feedback: produces both chaos and order patterns (fractals). “Pattern is everywhere, just waiting to happen” (38:25) I wonder if the power law is an example of this phenomenon, an example of a fractal?

Self-similarity (fractals) – this seems to be similar to cascade learning. Evolution seems to be the ‘guiding hand’ of the world, kinda like Adam Smiths ‘guiding hand’ in Economics.

2. Hi Ken,
Thank for your comments. Plenty food for thoughts. I could see that we are all learning subconsciously with and through nature (morphogenesis and self-organization) – and I resonate with your comment: I wonder if these principles apply to networked learning, and if the seeming affinity for us to form groups for group learning is an observable phenomena of these principles in action?

I am also wondering if the group-network cycle as a natural phenomena based on a self-organizing principle. There are groups formed, then dissociated due to various reasons of natural or artificial development (or decay), and reform into bigger or smaller groups (like the fractals). Some of these may interact with other groups or networks, forming other sorts of groups or networks, and so on. This pattern is everywhere, just waiting to happen. So true.

May I use an example to illustrate: We study in school, forming groups, then once we leave school, we join an organization (group), and we belong to a group, which is part of a bigger group. We also form groups with colleagues, and networks with those within and outside organisation, and these may then be self-organizing with both “genetic” makeup and artificial “manipulation”.

I like your guiding hand concept, especially relating to cascade learning. I think virus spreading and infection is a good example illustrating how such learning could lead to network breakdown, and that is a risk that we need to look into. Cascade learning is also apparent in case of forest fires, where a few sparks of fire could cascade throughout the network of trees. The financial crisis could also be viewed as a product of chaos and order patterns (fractals) – where the crisis of a network affected their neighborhood nodes and networks, leading to a series of breakdown. The earthquake could be another example of fractals “formation”, and the consequences are a product of chaos and fractals.

In social media, there is already a phenomena that we have coined as meme, and also teme in case of having technology as a mediator. Is it a product due to a combination of chaos and order patterns (fractals)?

Even the demand and supply could be interpreted as an extension of the fractal development, where market penetration (supply) could be self-organizing (with its agents), and the consumers also self-organizing. Would these achieve a balance between chaos and order?

How will power laws be “correlated” to this chaos and order patterns (fractals)? Does it follow the 20-80% or 10-90% rule etc.? These “guiding hands” or Powers are interesting for us to research.

3. Hi John. I wander along the same lines as you have stated:

>I am also wondering if the group-network cycle as a natural phenomena based on a self-organizing principle.

I wonder if there is a self-organization cycling in the nature of a network, from star to mesh and back and with some in-between steps and maybe even some forms beyond star/mesh. Kinda like the changing colours observed in the fractal depictions. Yes, cascade effects could have undesired consequences if viral, but I don’t think a forest fire or a viral spreading would qualify as learning. Definitely a cascade of energy and disease, though, with destructive effects. I wonder if equilibrium (balance) is really an achievable state? It suggests statis, stability, lack of change. It is a state that Stephen Downes argues for, believing as he does that it can be obtained through a mesh network structure. But your videos on fractals, chaos etc. suggest a more dynamic structure, with ordered patterns and chaotic through unpredictability. Stephen Downes argues for a predictability that seems to be a throw-back to the ‘Newtonian scientific certainty’ era, an era that seems to be an illusion, given our current knowledge, as I understand it, and with the help of the information transmitted in the videos on your blog.

On another note, have you considered collecting your various writing together and producing a book or paper? You are a prolific writer and researcher, and I’m convinced you have the ability to construct a writing of great value, whether it be in the form of a conference paper or an online creative commons paper/book etc. Certainly it could contain a chapter on fractal learning, among other topics. Maybe you could solicit articles from other writers, and compile an edited book.

Ken

4. Oh, if you do compile a book, can I contribute a chapter? Not sure the topic yet, but I’m thinking of a sci-fi piece, maybe with a title something like: “Fractal riding in the life of Plutonimous Rex” where the plot is around a fictional P. Rex who rides a fractal from initiation to miniaturization passing through the planet Zeros where time stands still as the fractal moves through without him. Without spoiling the ending, P. Rex meets up with the last surviving member of the human race on Zeros and they produce a new generation of beings, one of whom is named Magnanimous Rex, who rides a fractal from his initiation to miniaturization passing through the planet Aeros, where time stands still, and so on, and so on……….

5. Hi Ken,
I like your ideas about “self-organization cycling in the nature of a network, from star to mesh and back and with some in-between steps and maybe even some forms beyond star/mesh.” Based on my limited observations, such cycling are ubiquitous, only that they are so fragmented and distributed that it’s hard to harvest and aggregate. It could take another “mining” and analytics to understand the dynamics behind such cycling.

I would suggest to solicit views of Stephen on the mesh network structure. I think there are merits in the mesh and distributed networked learning (social and digital in particular) as compared to the star and hub (distributive) network of learning, though I think there are always inclusivity rather than exclusivity of the different sorts of networks in the “mother nature”.

Does it mean that there would be convergence or divergence as these networks develop? What do those settlement of the network mean? If we conceptualise such learning on social movement (the recent social unrests in many countries), then would those networks merging and re-configuration be a mirror image of what could happen with the star to hub to distributed networks, as those are the signs of democratisation of networked “learning” and power re-distribution.

So, taking connectivism from a different macro learning perspective, I do see substantive values in looking at it as a Macro learning model for re-conceptualising learning amongst communities. I don’t think there are boundaries in such learning, though I reckon there are certain political elements involved in these learning. Would that provide another direction apart from the micro-personal learning perspective? Would that be the semiology of networks at a sociological level?

Like to learn Stephen’s views on this.

Relating to the collection of writings and compilation of a book, I thank you for your wonderful suggestion and would think about it. I have still got many outstanding tasks to complete, like the research on MOOC and PLENK, but surely if I were to write a book, you would be invited to include such a chapter.
I have a dream of writing books and research papers for more than a decade, and so I hope one day this dream would come true.
I also prefer to be a free lance writer, though have never thought that “writing” has become a part of my life.
I like to write a lot, with many writings never published. So, it could be interesting to see how such fractals would develop.
How about you? Are you writing any papers or books?
Thanks again for your insights and visit.
John

6. Hi John. Yes, I’ve asked for Stephen Downes’ explanation regarding mesh networks, hopefully he will provide an answer. Maybe he doesn’t yet know why he prefers the mesh, maybe it is just his favourite pattern?

I think the community of practice analysis of some parts of the networks formed in these courses could be informative. Right now, my writing centres around course papers and conference papers, with the goal of bringing that work together into a dissertation at some point. Some dissertations lead to books, but that is off in the distance, if I ever get that far. Watching the video by Arthur C. Clarke reminded me of the value of sci-fi literature in expanding thought. I’ve had an interest in sci-fi (Asimov) and satire (Vonnegut) and would like to self-develop that style of writing a little more. We’ll see what happens, the future is ‘unpredictable’ in the chaos of my life! 🙂

7. Hi Ken,
“I think the community of practice analysis of some parts of the networks formed in these courses could be informative.” Yes, I think it would illuminate lights too. Based on our previous experience with CCK, CritLit, FutureEd and PLENK etc. I speculate the “cohort” of “new” or novice participants to MOOC could make a big difference, even though there has been significant changes to the course design, and the introduction of the practice: “Aggregation, Remixing, Repurposing, and Feeding Forward” as recommended as a best practice.

I could see that COP forms normally with a “cohesive structure” once a “group” of practitioners found common interest, then there might be the stages of group formation – forming, storming, norming and performing, followed by adjourning all appearing in the COP. In reflection, I had witnessed a small group of the participants undergoing all 4 stages, whilst the majority going through the first two or three stages for a while as lurkers, and others learning as self-directed learners likely independently after the first two stages, (or the third to fourth stages). So, what I am interested in knowing is: Is COP’s formation dependent on the type of “participants” the group has in the first place? Or will such COP formation be dependent on the type of networks that are developed (i.e. star, hub, or meshed/distributed networks)?

My experience with charity COP is that once the mission is accomplished, then it is likely to re-configure as a network, and then the members may stay or leave the networks dependent on their needs and aspirations. Most charity COPs have a limited life, and the life span may also be dependent on the sponsorship provided by the charity institutions or government.

So, COP in education is still a challenging one, as I have witnessed the rapid growth of those COPs followed by a multiplication of decentralized networks, mainly because all these COPs were quite “fragmented”. Also it seems that the scale and size of COP would have an impact on the members, where a typical 1-10% active members to 80-90% non active members are still prevalent. I haven’t seen any virtual COPs with more than 80-90% active members. Is power law (or power issue) an issue with COPs?

Have we witnessed some of the above via our CCK (Connectivism Education Learning) group on Ning and FB? I am optimistic on the development of CCK11, but as we have seen, it is a combination of chaos and order (fractals) that could emerge out of CCK11, and who knows the future?

Finally, I didn’t participate much in any discussion platforms like FB CCK11 or the course wiki, not because of my lack of interest in the theory and principles. I think I am in a “retreat” and reflection mode, looking back into the formation of networks and COPs as a way to go. I am more interested in research and the practical activities (like collaborative projects, or cooperative events – like the CCK09 Elluminate Session that Frances, Roy and you organised) etc. As Stephen has mentioned, action and experience is the basis of learning under Connectivism, and it is through action learning that we could actually see how it works.

Is PLE and COP compatible? That is a critical question!

So much for my ranting.

John

8. Hi John. I’m taking a linguistics theory/methods course now, and the COP perspective of the professor is that what distinguishes the study of COPs from the study of speech communities is that in COPs “identities emerge in practice through the effects of structure and entities”. So, for example, in CCK courses identities would emerge, which might include the jester (mine previously), the conciliator, the teacher, the protagonist etc. To quote the prof: “Local identities and the linguistic practices that produced them beome visible to our analyses as purposeful choices of individuals operating inside and outside the constraints of the social structure”.
So CCK courses could be studied under this lens of COP to see what type of identities emerge.

9. Oh, I forgot my main point for raising the COP identity issue: A PLE could very well be an emergent identity, and it certainly is a way in which an individual can interact with the CCK structure or other learning structures, and would be an important part of an analysis from the COP perspective.

10. Rod Sims says:

Ken – I’m intrigued by this discussion on fractals having just found it through links from CCK. I’ve written in isolation about emergent learning and am hoping to embark on further articles for a journal. I’d just like to get back into this loop and the main discussions that have been going on as I have, as you said, been ‘out of the connectivist/emergence loop’.

11. Hi John,

Thank you for writing such interesting posts on fractals. In relation to market equilibrium, I remember when doing an economics blog, Lee Smolin attempted to evaluate about Time and Symmetry in Financial Markets the equations of which you might understand, they are beyond me right now.

Also in relation to equilibrium and the efficient market hypothesis from Eugene Fama e.g. decision making under uncertainty, and Benoit Mandelbrot himself in Misbehaviour of Markets including stress testing
“Letting a computer simulate everything that could possibly go wrong and seeing if any of the possible outcomes are so unbearable that you want to rethink the whole strategy. The Monte Carlo Simulation. You tell a computer how you think prices should vary – what random number generator it should use..you feed it all the initial data…then you press the start button..under the rules of randomness you gave it the computer starts generating hypothetical prices for each stock, then it does it again and again, thousands of times…at the end it totes up all the scores and tells you which simulated outcomes happened most often…finally you use your own intelligence to decide whether you like the scenario the computer paints…You can now simulate the performance of an options contract in under a minute on a standard pc” 1 and he refers the DNA strand code as fractal code.

Your connecting ideas sounds like the early stages of trying to compute telepathy but we are reliant on those who are able to take advantage of the computing power and capacity needed to perform those equations. And as long as those big companies have strategic advantages in terms of market dominance, it will take more than a butterfly to produce chaos for which they are not already calculating their way out of. However your posts and writing give hope for all of us.

Thank you for sharing these

12. @Ken and Rod, there seems to be limited research on this Chaos Theory and Fractals. It is an emergent field, when applied in COPs.

@Nicola, Thanks for your wonderful references. There are a few researches done in the area, with one highlighting the importance of strange attractor:
“A strange attractor is a kind of fractal that has a powerful influence over the processes and structures that emerge in a system undergoing transformation. Fractals are similar to what Dawkins called “memes,” which are ideas or cultural beliefs that are “the social counterpoints to genes in the physical organism” and have the power to organize a system in a specific way (Caine & Caine, 1997, p. 33).”

The ideas about the origins of life and future education were based on my intuitive thoughts, and so I don’t think you will find it documented elsewhere (not in the internet, as I am aware of). Also, I haven’t published any of these concepts so far, as they are still half-baked ideas only. Further research is needed to explore Chaos Theory and Fractals in those areas.
John

13. Hi Rod. That would be great if you write/publish regarding emergent learning. If I can help in any way, let me know.

14. Hi John, thanks for the reference about strange attractors which I don’t think I have come across before. I found a strange attractors of meaning article which I think is what you are trying to say – in that the meaning emerges from those who are best places (fittest as in survival) to undergo a creative crisis and (guessing now) resonance between those fittest and their thinking, helps new memes and meanings emerge?

In other words, the financial institutions which are have higher levels of self-efficacy are mostly like to be creative in a crisis – and to them chaos does not look like chaos, they have already visualised different trajectories to move along whilst everyone else is losing their heads / investments.

I have read Caine and Caine’s work before, but found an interview with Renate Caine and also on the brain connection

“Caine and Caine conclude that “Optimizing the use of the human brain means using the brain’s infinite capacity to make connections–and understanding what conditions maximize this process.” They identify three interactive and mutually supportive elements that should be present in order for complex learning to occur: “relaxed alertness,” “orchestrated immersion,” and “active processing.”

1. An optimal state of mind that we call relaxed alertness, consisting of low threat and high challenge.
2. The orchestrated immersion of the learner in multiple, complex, authentic experience.
3. The regular, active processing of experience as the basis for making meaning.”

If I link that back to martial arts, just for a change 😉 then this relaxed alertness is related back to the conflicts and I guess some kind of equilibrium between the parasympathetic nervous system calming down the sympathetic nervous system which is ready for fight or flight. And they say that is the optimal state of mind. Taking that further, the two nervous systems are under the autonomic system of involuntary control with no conscious co-ordination of physiological activity taking place.

I am not sure that I completely agree in that high threat and high challenge, there may be a lot of subconscious learning, possibly optimum learning going on, but due to the speed, there is something lost in translation between the conscious and subconscious during those moments that makes it difficult to then process consciously (maybe in long term memory).

For example once in a fight where I was getting kicked a lot, I managed to get in an attacking kick back that I am not particularly good at in training, and it wasn’t until after the kick that I appeared to be processing the thought, this is what you need to do and I don’t know if I could reproduce it again in another fight – hope to find out soon 🙂

So whilst the relaxed alert seems logical and maybe you could calculate different variances of what it might be – I think that for better learning to occur, we need to understand more about what the subconscious does and this will be difficult to reproduce without examples from people in high threat, high challenge situations.

Maybe if you were in a position of advantage (not you personally!) you might want others to face these situations including in a financial crisis if you lose your house, maybe family or whatever – so that you can use them as data to analyse what to do in the future – a casualty of chaos, or something like that. In which case, high threat and high challenge analysis may produce interesting data but would it be worth the human consequences of the damage it might cause.

Nicola

PS So fascinated by how you managed to develop and perform the calculations in a totally different part of the world, experiencing different education, different cultures, different lifestyles and yet you have similar formulas.

PPS re fractals emerging from earthquakes, there is a financial index of market shocks based on richter scales (<a href="http://www.bertrand-maillet.net/research.html&quot;.http://www.bertrand-maillet.net/research.html and http://bit.ly/fks3YC ) I don’t know whether they have looked and visualized fractals through the results of their research or not.

15. Thanks Nicola for your sharing.
Your extension of the application on martial arts and financial crisis – based on the three identified interactive and mutually supportive elements that are present in order for complex learning to occur: “relaxed alertness,” “orchestrated immersion,” and “active processing.” is wonderful. There are yet numerous emergent complex learning that evolved in COPs to be explored. Doesn’t it sound like a Pandora’s box (a meme or thing that once activated will generate many unmanageable problems, but sounds quite to be like stream of thoughts that take up its meaning all over different domains when reflected upon) with learning in a positive sense?
In this Dr Vladimir Dimitrov homepage http://www.zulenet.com/VladimirDimitrov/pages/home.html there are some interesting resources.

I could identify the stranger attractors emerging out of this conversation giving rise to more attractors (fractals), and that seem to explain why it’s worthwhile to explore more: So fascinated by how you managed to develop and perform the calculations in a totally different part of the world, experiencing different education, different cultures, different lifestyles and yet you have similar formulas.

There are still more empirical researches needed to substantiate the explanation of the unknowns, and unpredictable, as I am finding it more and more difficult to explain why those cause and effects, but that such patterns (of fractals) are so familiar to us. The earthquakes, economic and financial crisis, the flood, the SARS, the pandemics and even terrorist attacks all seems to provide heaps of learning based on Chaos and fractals…

May be one of the difficulties with such researches lies with the complexity involved, and the complicated mathematical concepts and a diverse fields of “knowledge” required to understand how all these make sense (meaning behind the aftermath) to our learning.

John

16. @Nicola,
This paper http://www.zulenet.com/VladimirDimitrov/pages/complexthink.html provides an useful account on complexity and chaos.

“In society, the ‘improvements’ of chaotic behaviour, based on system thinking, gravitate to establishment of hierarchical models of order. When put into operation, such models of order serve to assert power and control. So, almost in an invisible way, the application of system thinking to social reality contributes in strengthening the power-oriented aspirations and ambitions in society. The sphere of economics and politics is saturated with such kind of aspirations and ambitions; L. Victor [2] refers to them as a “Global Free Market Capitalist Religion” , which he calls a “metastasizing cancer on humankind”.

For those who think systemically, chaos has been always considered as a synonym of disorder, and disorder means collapse of any optimally adjusted regime of a system’s functioning. That is why, chaos is anathema for the system interventionists obsessed with the idea of “improvement” of systems’ behaviour, where “to improve” means simply “to impose a pre-designed model of order” or “to make system follow a prescribed set of rules”.

For complexity thinking, chaos involves all the spectrum of potential dynamic orders that might emerge; therefore, it is opposite to disorder. Chaotic dynamics of life’s manifestation are impregnated with creativity. To ‘improve’ or ‘fix’ chaos, with an absurd intent to turn it into order, means to eradicate its creative potential and thus to kill the life.”

Aren’t these fascinating?

I have yet to balance my time in working through this and my current research on MOOC 🙂 So, many strange attractors taking on my pathways in learning!
John

17. @Nicola,
I noted that the use of Jungian subconscious concepts and subliminal learning, and an interpretation of the subliminal effects of “learning” in online education. I have once written the 8 hats – with the 7th and 8th hats relating to he exploration of those concepts of knowledge and inner thoughts. This also relates to our individual tacit knowledge which could only be manifested individually through meditation or collectively or connectively through collective inquiry, and these would result in emergent learning.

These are the metaphorical interpretation of knowledge and learning, and I think more empirical research is needed to substantiate the claims. Besides, these are based on observations, with a behavioural approach towards learning, which could sometimes be “subjective” when interpreted even with experiments.

I think the use of a Neuroscience approach – using fMRI to study what it means for meditation, or deep reflection, may be interesting in exploring this subliminal effects of learning, as that could provide more evidences of how such learning would differ from shallow learning (like rote learning).

Also, back to the fractals and strange attractors concept, we may need to differentiate the difference between individual learning and that of collective and connective learning, and see if such learning online is a product of the interaction amongst nodes, or the cognition of individuals, though it may be both.

John

18. Hi Nicola. In my training we referred to this as muscle memory:

>Taking that further, the two nervous systems are under the autonomic system of involuntary control with no conscious co-ordination of physiological activity taking place.

19. Hi Ken, sorry in advance, this is a bit babbly – I wonder how muscles remember – maybe somewhere between the muscles learning about position, alignment with ligaments, tendons, bones via sensory nerve cells generating electrical signals going up and down from the brain – which then next time you want to move, the connections and signals are already ready for firing – or is there more inside the cells inside the muscle tissue that has some kind of additional brain connection – properties or something – that makes it easier or harder to connect with the appropriate nerve cells in the brain associated with memory.

I don’t know but was there something in the design/DNA or proteins which have begun to emerge in those cells – based on other physiological processes not related to making that muscle move in a particular way – already there that made them more brain friendly to reproducing specific movements or did they learn through those connections ? E.g such as eating particular stuff on a day then the nutrients passed into those cells in the muscle tissue and said yeah we’re ready now for action. And how was the whole process related – deciding to change to eat more healthy stuff which increased flexibility in the muscle tissue, was that the strange attractor and where did it emerge from and why?

Hi John, it does sounds like a Pandora’s box and the familiarity with the different fractals regardless of where anyone lives, age etc is totally fascinating. I remember your post on the hats too.

Noting your points about empirical research. Re the subliminal tacit knowledge below the threshold of conscious thought. I felt this does not explain how a brain can project hallucinations in an augmented way onto the physical world – for example seeing images, phrases and sentences which appear to be there and then not later. At that point subconscious and conscious are communicating in a completely different way – different kind of wavelike interference (?), but am assuming as humans that physiologically this is not something that they can maintain for long periods of time. Maybe being so intuitively/instinctively sure of something that then doesn’t appear to be the case – the strange attractors again – how to identify those patterns though !

Thanks for the links to the papers, will go and read more of the website, it looks really interesting.

Nicola

PS I left out a ‘not’ again – meant to say have not read Caine and Caine (wonder where the ‘nots’ go whilst I start typing, they are definitely there consciously at the start of trying to type !)