Playing with Chaos

Rereading Gleick’s “Chaos” and decided to have a look myself at what it looks like.

Redoing this post – and adding 3 more images, with updated program code.

Here is a series of pictures I produced from the simple equation:
xp[next] = r.xp.(1 – xp)

To produce these images I simply ran the equation for each point on the x axis for a set of ranges of values of r (initially between 1 and 4). Starting the population at .1, I ran it for 600 cycles to reach stability if possible, then continued to run it, recording adding one to each y axis pixel corresponding to a result, recording until one pixel reached 3,200 hits. Then I ran a process over it to change those numbers into a visual rainbow – with red being the lowest numbers to violet being the highest (roy g biv). This makes it easy to see the curves of probability distribution of results in the chaotic zone between 3.6 and 4.

A link to the code I wrote is included below the images.

The first image shows the big picture,  as r increases from 1 to 4 the population increases until r get to 3, when suddenly instead of settling to a single value, it starts to alternate between two values,   then at around 3.4 it changes behaviour again, now alternating between 4 values, then at about 3.55 it starts alternating between 8 values, and by around 3.66, it becomes completely chaotic, not settling into any particular repeating pattern, but over many cycles displaying interesting probability distributions.

big picture - r values 1 - 4

big picture – r values 1 – 4

The next image (Key) just shows what I have done with the two images that follow it.

Key showing areas expanded in following images

Key showing areas expanded in following images

The image following is the box A stretched to the left, to show more detail.

Box A - r value 3.5 - 4 expanded

Box A – r value 3.5 – 4 expanded

The final image is the tiny area shown in Box B – r values between 3.565 and 3.585  and y values between 0.8775 and 0.895.   This massively enlarged section shows the same fractal pattern almost (but not quite) repeating, at ever finer scales.

Box B -  r values between 3.565 and 3.585  and y values between 0.8775 and 0.895

Box B – r values between 3.565 and 3.585 and y values between 0.8775 and 0.895

Python 2.7 code is on my fishnet site -


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Best & worst of place – and more on collarbone

27 June 2014 ~Question of the Day~ Best/Worst Your Location

What are the 3 best and 3 worst aspects of where you live?

Similar to Eric & FOS


Nature – High mountain, forests, rivers, ocean, weather

People – small community where most are known and friendly

Isolation – an hour’s drive in any direction to reach the next town.


The extremes of nature – mountains come with the threat of very large earthquake, the extremes of weather here can get scary (I have been blown over while walking and cars and trucks are regularly blown off the roads), floods, droughts

Small town people tend to have fairly small horizons – not too many think outside of the ways of the past or beyond the desires of today.

Isolation – It is over two hour’s drive to reach the nearest city, so making personal contact with people outside this community is expensive. Example – 5 hours driving to see a specialist about my broken collarbone 2 days ago.

[followed by]



Complications are only that the break is exceptionally complex and unusual.

The bone actually shattered into 4 pieces on 3 different planes.

The 4 pieces have not aligned very well – so my collarbone will be very bumpy.

The specialist offered me the option of surgery and warned of the dangers of complications of such surgery.

I decided to just leave it heal as is.

When technology develops to the point that we can print new material from our own cells then I will get a new shoulder printed up and installed, and that could be few decades away (though some people are doing some very interesting work printing up simple organs – getting all the nerves, blood vessels and lymph systems is still a ways off).

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26 Jun ’14 Question of the Day ~TRUST

What is trust,
and what role does it play in relationships?

What is trust?

From the Oxford:

As a noun:
“Confidence in or reliance on some quality or attribute of a person or thing, or the truth of a statement.”
“take on or upon trust, to accept or give credit to without investigation or evidence.”
“That in which one’s confidence is put; an object of trust.”
“Confident expectation of something; hope.”
“The condition of having confidence reposed in one, or of being entrusted with something”
“The obligation or responsibility imposed on one in whom confidence is placed or authority is vested, or who has given an undertaking of fidelity.”

as an adjective:
“Confident, safe, secure, sure.”
“Faithful, trusty; reliable, sound.”

as a verb:
“To have faith or confidence; to place reliance; to confide.”
“To have faith or confidence that something desired is, or will be, the case;”
“To give credence to, believe (a statement); to rely upon the veracity or evidence of (a person, etc.).”
“To commit the safety of (something) with confidence to a place, etc., to or with a person; to entrust; to place or allow (a person or thing) to be in a place or condition, or to do some action, with expectation of safety, or without fear of the consequences.”
“To invest with a charge; to confide or entrust something to the care or disposal of.”

It seems to me that society must be fundamentally cooperative. Without cooperation, we can achieve very little.

Modern capitalism seems to sanction cooperation only within corporations and for the benefit of capitalists, and to have a lot of incentives against it in other situations – pushing hard on the competitive model in all other situations.

It seems clear to me that we are primed as a species for cooperative behaviour, and we also come with a strong sense of justice which can destroy cooperation when we feel wronged.

So it seems to me that learning to cultivate trust and forgiveness is fundamental to us creating the sort of abundance and security that is possible. And we need to have discernment in that trust, as there are some who would abuse it at any opportunity.

It seems clear to me that trust is fundamental to building strong secure and meaningful relationships.

[followed by]

Agree totally Kathy, that trust is an active choice required in order to build strong relationships at any level.

Agree too Jeff that trust comes more easily from a state where love is present, and that extending that love and trust beyond the proven creates an invitation for another to step up a level, and most respond positively to such invitations (only a small minority taking advantage of them).

Agree too Lulu that reciprocal trust allows a blossoming of relationship that is not possible otherwise.

And as both you and Kathy have noted, self trust is foundational.

I love the Zalman story, of the dangers inherent in competitive zero sum games. Cooperative games give so much more potential for positive sum (whole is greater than than the sum of the parts) outcomes.

I love Bridge’s analogy of trust as the catalyst to the flow of relationship – appeals to my biochemist’s understanding of the physicality of processes – and I find it is always easiest to have a physical process on which to model something more abstract.

Kathy – your traffic experience is a great practical example of how much more powerful cooperative strategies are than simple competitive strategies are, on a choked free-way competition leads to gridlock. Only cooperation allows optimal traffic flow.

OM – a discussion of the definition of capital and capitalism could be very long indeed. There are several fundamental asymmetries and not a few myths underlying capitalism. One myth/asymmetry is that it is somehow a fair transaction when one side (the capitalist) by denying employment can deny survival, while the labourer has no such power over the capitalist. Another myth is that it is somehow sensible that money should have the power of growth (interest) simply by existence – the asymmetries of information and power guarantee that capitalists will take the vast bulk of any growth – which is proven by statistics that demonstrate that real wages have stagnated in Western economies for the last 30 years, while real household wealth has declined, while the growth of the wealth has for the most part gone to a very small fraction of 1% of the population. Add into the mix that under the modern conception of capitalism it is ok to buy anything – including political control (lobbiests and party donations), and dominant social “beliefs” (advertising and news media). From my experience of the last 40 years involvement in the NZ legal system (by all international measures one of the most free and least corrupt) my best guess is that over 80% of the legislation on our books is there primarily to deliver value to some subset of the interests of capital (however it may have been portrayed in the news media or debates within the house).

And as I have said many times, I fully acknowledge the beneficial role that both money and capital have played in bringing us (humanity) to this point. Both have had a nett positive role in social evolution, and that balance may remain positive for a few years yet, but the time is rapidly approaching when the concepts of money and capital pose far more of an existential risk than they deliver in benefit. If we fail to start planning and transitioning to a post capitalist world of universal abundance then the results are highly unlikely to be pretty for any group – most particularly those currently atop the capital heap.

And to be absolutely clear, I am not proposing a world of equal distribution, I am proposing a world where the minimum is about where the top 1% are now, and there is infinite extensibility above that – not driven by exploitation of the needs of survival, but driven by the cooperation of groups for commonly held visions.

To my mind, I was and am using the terms precisely and accurately, and obviously the terms mean something very different to each of us.

Agree Deb that there is a huge difference between trust as an expression of possibility and trust as a demand of expectations; the former being powerful as an invitation to possibility and the latter being destructive in limiting possibility through judgement.

And having been in relationship with Ailsa for 22 years, and married for 20, the only thing truly predictable about her is her unpredictability – so I’m not sure that I do agree that predictability increases over time. It seems to me that if both parties are growing in relationship there is infinite room for expansion of unpredictability into new realms.

And I agree OM that outcomes are far less reliable than intentions; and there is far more power to be gained by trusting intentions and accepting whatever outcomes show up, and repeating.

@ Eric – Your first dimension of trust is one I tend to characterise as acceptance rather than as trust, and there is certainly a sense in which trust is commonly used that way. And I agree with you that there is great honour both in bestowing and receiving the trust of a life – it is the most profound trust possible – treated far too lightly in too many cultures.

And I totally align with you that there is no power in forgetting and huge power in forgiving.

I agree totally Mendy that both emotions and intuitions can be complex beyond our abilities to rationally understand. One must bring a degree of simple acceptance to that aspect of being.

Agree also that contracts can be extremely tricky, and are best avoided if one wants to develop depth of relationship. In my experience alignment of intention is far more powerful than any definition of contract. Most contracts seem to me to be more about exploitation than about creativity – in my 30 years in the world of software development I have rarely signed a contract with a client, and none of those who insisted on contracts have remained clients. Most of the clients I have have been with me for over 20 years, by free choice and alignment on both sides.

Agree OM, that for the vast majority of the population, genuine trust will be reciprocated, and there is a small percentage of the population who are consistently pathological in this respect, and a larger portion who will break trust if they think the reward is worth the risk.

Thank you all for this exploration, and the nuances you have each contributed.

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25 June ’14 Question of the Day ~INVENTIONS

Which invention in the last 10 years do you use or appreciate the most?

My laptop is certainly the thing I use and appreciate the most. This particular model of Toshiba Portege R830 is certainly new to the last 10 years – I’ve actually only had it two years. I spend about half my life typing or reading on this machine.

And I really appreciate some older inventions – flush toilets, soft toilet paper, running water, electricity.

My smartphone (Galaxy S4) with Teamviewer installed is amazing – I can be on duty and available to clients anywhere I am in cell phone range – able to take control of client machines and sort out issues from the golf course, or from a mountain bike trail (though I’m doing neither at present).

I have really appreciated my seat these last 3 weeks, have spent over 20 hours a day in it – it is a Zero Gravity recliner.

[followed by]


This is the version of Zero Gravity chair I have – though mine has a darker stain on the wood, and black leather.

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Hitch your wagon

Hitch Your Wagon

What have you hitched your wagon to?

Hi Laurie

My wagon aint hitched, its still rolling.
No hitching post where I’m headed – no-one’s been there before.

Universal abundance, universal liberty, universal security.

As to my base of operations – Kaikoura seems as good a place as any, and better than most.

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24 June ’14 Question of the Day ~PERCEPTIONS~

How do you know your perceptions are real?

This question is as old as philosophy itself.

As children we all start with the simplistic assumption that things are either true or false, real or unreal.
Many ancient philosophers started with the assumption that it is possible to know reality.

Modern science teaches us differently.
Our modern understanding has uncertainty built into it at many different levels.
All acts of measurement have built in uncertainties at several different levels.
All understandings are less than reality due to our need to chunk down the complexity of reality into units we are capable of dealing with in a reasonable time period.

Just look at the complexity in each of us. Each one of us has about 10,000 times as many cells in our bodies as there are people on the planet. Each of those cells has about as many molecules in it as there are cells in our bodies.
There is no possible way that our brains can deal with the actual reality that is any one of us, we have to make simplifying assumptions, and most of the time many of them are useful approximations.

So modern science teaches us that if we are dealing with anything other than commonly accepted situations, our perceptions are very likely to contain significant errors.
Our brains’ tendency to categorise those perceptions introduces more sets of potential for errors.
Reality seems to be that it is highly likely that our perceptions contain many errors, and in ordinary situations they are sufficiently useful approximations that we don’t notice the difference.

[followed by]

I’ll try from another angle, as to me they are both views of the same thing.

It seems that reality is whatever it is, but that we have no direct access to reality.

It seems that all each of us (as conscious entities) has access to is our model of reality that our brain constructs for us. This model of reality is made up from a mixture of perceptions and recollections of past experiences and learned patterns (in the first instance most of us adopt the default model supplied by the cultures of our birth). It seems that the model is predictive in nature most of the time, in that it projects what we expect to see much of the time by about a third of a second – and usually it is remarkably accurate.
It seems that our only access to reality is via this model.
Historically many people have mistaken the model of reality for reality itself, giving rise to the false notion that we create our own reality.
It seems that we certainly have a lot of influence of the model of reality that we get to experience, and that model is only ever a poor imitation of the complexity of reality itself.

Given that we only experience our model, and not reality itself, then it is possible for us to live in models that are quite divergent from reality in many aspects, as long as none of those divergent aspects lead to lethal outcomes to our bodies in reality. Its fine to have a model of reality where buses are made of sugar candy, just so long as you don’t step out in front of those sugar candy buses – because in the real reality, the tons of metal frame of the bus will likely have a lethal impact on your body, the model contained within it and the software entity experiencing the model (the conscious you).

Modern science has given us many tools to help us understand the reality of the world in which we exist, and those tools all seem to be giving the sort of answer that while the reality in which we exist is real, it is not possible for us to be certain about anything in it at the finest scale, so thus it will always have elements of unpredictability and novelty about it.

There are several sources of uncertainty.

There are the simple sorts of uncertainties, the simple errors of measurement, not quite being accurate enough.

There are more fundamental sorts of uncertainty, like Heisenberg uncertainty, where even with the best possible tools, it is possible to know the position or the momentum of something, but not both. The only way to measure one is by disturbing the other. But only scientists run into that sort of uncertainty, because the smallest things our eyes can resolve still contain trillions of molecules, and Heisenberg uncertainty only really becomes significant at the level of individual particles.

Then there are the levels of uncertainty delivered by non-linear systems. Non linear systems are systems where the output of one state forms part of the input to the next state. Such systems are fundamental unknowable and intractable. Their behaviour, while lawful, is not predictable. The only way to see how such systems behave is to try them and see.

Then there are category errors, our brains mistaking input as belonging to one category when in fact it belongs to another which is similar in some aspects, and very different in others. This is a really complex set of topics – a good introduction being the Stanford course on Human Behaviour that I think OM posted a link to recently.

So even if one starts out with a belief that certainty is possible, and our senses can deliver truth, one is forced by the experience of scientific tests into accepting that all such notions are false, and that uncertainty is a fundamental aspect of everything in reality.

[followed by]

Hi Bhatta

It seems to me that the Vivekananda has taken the inverse interpretation that Goedel or I have.

To me, our models of reality (from which we take our conscious experience) are always less than reality itself (that is the nature of a model).

To me, that does not mean that reality is dependent on our perceptions, but rather that our models are dependent on the constructs we have to create them. It seems that we can have no direct perceptions of reality. It seems that all of what we see (or otherwise experience) as reality is actually the model created within our brains by our brains. It is easy to see how the Vivekananda could take this reality and interpret it as they did (not having computers and software to offer an alternative model of interpretation).

It seems that the reality in which we live is strange in many ways, including the relativistic ways described by Einstein and the various quantum mechanical aspects of reality (QED, QCD, QM etc).

Goedel’s insight was at a different level.

What Goedel demonstrated in logic was that all descriptions of any system are fundamentally incomplete, as there are always statements that are true of systems that are not provable even if a complete description of the system constraints and starting conditions are given.

For me, Goedel’s insight stands in relation to logic in an analogous manner to which Heisenberg’s insight stands in relation to particle measurement.

[followed by]

Hi Bhatta

For me, I can accept the quote:

“….says the Vedantist, for he has proved beyond all doubt that the mind is limited, that it cannot go beyond certain limits — beyond time, space, and causation. As no man can jump out of his own self, so no man can go beyond the limits that have been put upon him by the laws of time and space.”

in a physical sense.

Certainly, our bodies are limited by space and time, and in so far as our sentient existence requires the matrix of brain to house both our model of reality and our awareness of that model, then our awareness is constrained in this physical sense.

Yet for me, just as I can say my laptop is constrained by the rules of nature, there is no constraint on the software which can run on that laptop – it could model worlds without such constraints.

So too for me with our models of reality and our awareness.

In accepting that the unaided man cannot fly, we can create 747s, and travel in chairs bolted to carpets at 40,000 ft going as far every minute as a man can walk in a day.

Our ability to envisage possibilities not yet existent, and work towards bringing those possibilities into existence, does not seem to be constrained in any meaningful sense. Sure there are rules, and I have always loved the ancient wisdom “nature to be commanded must first be obeyed”.

And it seems to me that there are potentially infinitely extensible levels available, and not yet utilised, by nature within which we can explore and play.

So I accept, in the almost trivial (and at the same time most deeply profound) sense – that all things are constrained in some sense in their current instantiation. All things must be so limited, for without such limitations there could be no distinction, no differentiation, only an amorphous undistinguished, undifferentiated infinity. Distinction, instantiation, requires boundaries – and the boundaries need not be hard, they can be permeable.

So in this sense I accept all that is, yet I do not accept that it places any sort of ultimate limitation on what may become. I see no such requirement in Goedel or anyone else.

All I see Goedel & Heisenberg telling us is that no matter where and what we are, there will likely be surprises in store for us in our becoming.

I accept that I have the limits that I have today, yet I see no reason to suspect that I will be forever constrained by them, for in some tomorrow I may create a way past them.

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22 June ’14 Question of the Day ~COMMUNITIES DEFINED~

What do you think it is that defines communities?

Enjoyed all the responses thus far.
It is a question I have been pondering for a while.
In one sense it seems possible to define a community by the commonality of that which is included.
In another sense it seems that communities are defined by the boundaries that surround them. And many sorts of boundaries are more like gradients than any sort of distinct wall – which can lead to very fuzzy definitions.

The Oxford gives a variety of definitions of community:
“Common character; quality in common; commonness, agreement, identity.”
“Social intercourse; fellowship, communion.”
“Life in association with others; society, the social state.”
“A body of individuals.”
“Often applied to those members of a civil community, who have certain circumstances of nativity, religion, or pursuit, common to them, but not shared by those among whom they live;”
“A body of nations acknowledging unity of purpose or common interests”

Here at ANG it is easy to define community simply by presence in this electronic “place”.

It seems that our presence in most communities has a random aspect to it.
I was doing a Landmark course in Christchurch about 9 years ago when another participant (Doreen) suggested I check out an online course, run by Michael Skye.
Michael was based in Austin Tx, and met Brian at an evening networkers meeting two years later – and suggested to me that I check out this new Zaadz thing.
Without Doreen I would probably never heard of Michael, and without Michael I would have been unlikely to find Brian and Zaadz.
It’s over 20 years since a cousin of mine suggested to me that I check out Landmark Education.

The path from Zaadz to Ang has been one of community of interest.

It is something that is profoundly intriguing to me at present, the balance in life between the intentional, the habitual, and the chaotic (which perhaps includes the random and perhaps not – rereading James Gleick’s Chaos at present).
Then there is the role they play in the definition of life, which in part is defined by the communities with which we engage.
So many balances.

When one looks within, at the communities within us. All our cells contain the same genetic material, but it gets to express differently in different communities of cells. One community becomes a heart, another a liver, another a bone, another a biceps, another a pattern recognition system within the brain. Communities within communities within communities, ….

Ideas get together in communities, to define contexts and modes of thought and being.

‘Tis an amazing thing this thing called life.

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